Generic Modeling Framework for Gas Separations Using Multibed Pressure Swing Adsorption Processes

1

A generic modeling framework for gas separations using

multibed Pressure Swing Adsorption processes

Dragan Nikolic1 Apostolos Giovanoglou

2 Michael C Georgiadis

3 Eustathios S Kikkinides

1

1 University of Western Macedonia Department of Engineering and Management of Energy Resources

Sialvera amp Bakola Str 50100 Kozani Greece

2 Process Systems Enterprise Ltd Thermi Business Incubator 9th Km Thessaloniki-Thermi 57001

Thessaloniki-Thermi Greece

3 Imperial College London Centre for Process Systems Engineering Department of Chemical

Engineering London SW7 2AZ UK

This is the accepted version of the following article

Nikolic D Giovanoglou A Georgiadis MC Kikkinides ES A generic modeling framework for gas separations

using multibed Pressure Swing Adsorption processes Ind Eng Chem Res 47 (9) 2008 3156ndash3169

The final publication is available at

httpdoiorg101021ie0712582

Abstract

This work presents a generic modeling framework for the separation of gas mixtures using multibed

Pressure Swing Adsorption (PSA) processes Salient features of the model include various mass heat

and momentum transport mechanisms gas valve models complex boundary conditions and realistic

operating procedures All models have been implemented in the gPROMS modeling environment and a

formal and user-friendly automatic procedure for generating multibed configurations of arbitrary

complexity has been developed The predictive power of the developed modeling framework for various

PSA multibed configurations has been validated against literature and experimental data The effect of

various operating conditions on the product purity and recovery is systematically analyzed Typical trade

offs between capital and operating costs are revealed

Keywords Pressure swing adsorption gas separations process modeling flowsheets

2

1 Introduction

Pressure swing adsorption (PSA) is a gas separation process which has attracted increasing interest

because of its low energy requirements as well as low capital investment costs in comparison to the

traditional separation processes12

The major industrial applications of PSA include small to

intermediate scale oxygen and nitrogen production from air small to large-scale gas drying hydrogen

recovery from different petrochemical processes (steam-methane reforming off gas or coke oven gas)

and trace impurity removal from contaminated gases

From an operational point of view PSA is an intrinsic dynamic process operating in a cyclic manner

with each bed undergoing the same sequence of steps The typical operating steps include pressurization

with feed or pure product high-pressure adsorption pressure equalization(s) blowdown and purge

Over the last three decades several PSA studies have appeared in the literature An overview of single-

bed PSA studies is presented in Table 1 Industrial practice indicates that difficult gas separations under

high product quality requirements (ie purity andor recovery) rely on complex PSA flowsheets with

several interconnected beds and complicated operating procedures The key literature contributions

involving two and multibed configurations under certain assumptions are summarized in Tables 2 and 3

One of the earliest attempts to realistically describe bed interactions is presented by Chou and Huang3

and is based on incorporating a gas valve equation into the PSA model to control flowrate The results

obtained are in good agreement with experimental data The proposed approach was followed to study

the dynamic behavior of two and four bed PSA processes in a subsequent work4

Warmuzinski and Tanczyk5 developed a generic multibed PSA model The main features of their

approach include support for multicomponent mixtures LDF approximation one or two adsorbent

layers and linear pressure changes The model was used to study the separation of coke oven gas in a

five-bed eight-step PSA process In a subsequent publication6 the same authors presented an

experimental verification of the model using a case study concerning hydrogen recovery from a

H2N2CH4CO mixture In both cases satisfactory agreement between theoretical predictions and

experimental data was achieved

Nilchan and Pantelides7 proposed a rigorous mathematical programming approach for the simulation

and optimization of PSA Their work is the first key contribution towards a formal framework for

optimizing a PSA process

Cho and co-workers8 developed a mathematical model for the separation of H2 from steam methane

reformer off gas They investigated the effects of carbon-to-zeolite ratio on adsorber dynamics In a

3

subsequent study9 they investigated the purification of hydrogen from cracked gas mixture

(H2CH4COCO2) using a double-layered four-bed eight-step PSA configuration

Secchi and co-workers10

studied the modeling and optimization of an industrial PSA unit for hydrogen

purification involving six beds and twelve steps The effects of step durations on process performance

were systematically analyzed

Sircar and Golden11 presented an overview of industrial PSA processes for the simultaneous

production of hydrogen and carbon dioxide and for the production of ammonia synthesis gas The

selection of adsorbents for hydrogen purification was also investigated Configurations of four nine

(two series of adsorbents six + three) and ten beds have been analyzed in detail The same authors12

carried out a parametric study of multibed PSA systems for the separation of hydrogen from a H2CH4

mixture Three different PSA configurations were employed and the effect of numerous process

variables on the separation quality was evaluated

Biegler and co-workers131415

developed a robust simulation and optimization framework for multibed

PSA processes They investigated the effect of different operating parameters on process performance

using a five-bed eleven-step PSA configuration for the separation of hydrogen from H2CH4N2COCO2

mixture Bed interactions have been described using gas valve equation To simulate the behavior of a

five-bed PSA configuration two different approaches were employed the ldquoUnibedrdquo and the ldquoMultibedrdquo

13 The ldquoUnibedrdquo approach assumes that all beds undergo identical steps so only one bed is needed to

simulate the multibed cycle Information about the effluent streams are stored in data buffers and linear

interpolation is used to obtain information between two time points The ldquoMultibedrdquo approach considers

a multibed process as a sequence of repetitive stages within the cycle

In most of the previous studies either complex mathematical models and simple bed arrangements or

simple mathematical models and complex bed arrangements have been presented Mass balance is

usually represented by the LDF approximation and heat balance by the typical bulk gas equation

Detailed mass and heat transfer mechanisms at the particle level are often neglected Transport

properties such as mass and heat transfer coefficients gas diffusivities (molecular Knudsen surface)

and mass and heat axial dispersion coefficients are often assigned to constant values Furthermore most

of the previous contributions focus on a relatively small number of units with simple bed interactions

(frozen solid model the linear pressure change or the information about streams are stored in data

buffers for later use) Moreover simulations of multibed PSA processes are usually carried out by

simulating only one bed with the exception of the works of Sircar and Golden11

and Jiang et al14

4

This work presents a generic modeling framework for multibed PSA flowsheets The framework is

general enough to support an arbitrary number of beds a customized complexity of the adsorbent bed

model one or more adsorbent layers automatic generation of operating procedures all feasible PSA

cycle step configurations and inter-bed connectivities The gPROMS16

modeling and optimization

environment has been served as the development platform

2 Mathematical modeling

The proposed framework consists of several mathematical models operating procedures and auxiliary

applications presented in Appendix A

21 Adsorbent bed models

The mathematical modeling of a PSA column has to take into account the simultaneous mass heat

and momentum balances at both bed and adsorbent particle level adsorption isotherm transport and

thermo-physical properties of the fluids and boundary conditions for each operating step The

architecture of the developed adsorbent bed model sets a foundation for the problem solution Internal

model organization defines the general equations for the mass heat and momentum balances adsorption

isotherm and transport and thermo-physical properties Phenomena that occur within the particles could

be described by using many different transport mechanisms However only the mass and heat transfer

rates through a particle surface in the bulk flow mass and heat balance equations have to be calculated

Hence the same adsorbent bed model could be used for implementing any transport mechanism as long

as it follows the defined interface that calculates transfers through the particle surface This way

different models describing mass and heat transfer within the particle can be plugged-in into the

adsorbent column model Systems where the mass transfer in the particles is fast enough can be

described by the local equilibrium model thus avoiding the generation of thousands of unnecessary

equations On the other hand more complex systems may demand mathematical models taking into

account detailed heat and mass transfer mechanisms at the adsorbent particle level They may even

employ equations for the phenomena occurring at the molecular level without any changes in the macro

level model This is also the case for other variables such as pressure drop transport and thermo-

physical properties of gases that can be calculated by using any available equation The result of such

architecture is the fully customizable adsorbent bed model that can be adapted for the underlying

application to the desired level of complexity

The following general assumptions have been adopted in this work (i) the flow pattern in the bed is

described by the axially dispersed plug flow (no variations in radial direction across the adsorber) (ii)

5

the adsorbent is represented by uniform micro-porous spheres and at the particle level only changes in

the radial direction occur

The following generic features have been implemented mass transfer in particles is described by four

different diffusion mechanisms (i) local equilibrium (LEQ) (ii) linear driving force (LDF) (iii) surface

diffusion (SD) (iv) pore diffusion (PD) three different thermal operating modes of the adsorber have

been implemented isothermal nonisothermal and adiabatic momentum balance is described by Blake-

Kozenyrsquos or Ergunrsquos equation multicomponent adsorption equilibrium is described by Henryrsquos law

extended Langmuir type isotherm or by using Ideal Adsorbed Solution theory thermo-physical

properties are calculated using the ideal gas equation or an equation of state transport properties are

assigned constant values or predicted using appropriate correlations In this work the Langmuir

isotherm has been applied as a pure component adsorption isotherm to calculate the spreading pressure

in the IAS theory However any isotherm equation having expression for spreading pressure which is

explicit in the pressure can be used Finally proper boundary conditions for the various operating steps

have been developed in accordance with previous studies on multibed configurations The overall

modeling framework is summarized in Appendix A

22 Gas valve model

The gas valve model describes a one-way valve The purpose of the one-way valve is to force the flow

only to desired directions and to avoid any unwanted flows Gas valve equations are also included in

Appendix A

23 The multibed PSA model

The single bed PSA model provides the basis for the automatic generation of the flowsheet via a

network-superstructure of single adsorbent beds The main building block of the multibed PSA model is

illustrated in Figure 1 The central part of the building block is the adsorbent bed model Feed purge

gas and strong adsorptive component streams are connected to the corresponding bed ends via gas

valves This is also the case for light and waste product sinks The bed is properly connected to all other

beds in the system at both ends via gas valves Such a configuration makes the flowsheet sufficiently

general to support all feasible bed interconnections This way all possible operating steps in every

known PSA process can be supported The main building block can be replicated accordingly through an

input parameter representing the number of beds in the flowsheet A typical four-bed PSA flowsheet is

shown in Figure 2

24 Operating procedures

6

Procedures for controlling the operation of multibed PSA processes are highly complex due to the

large number of interactions Hence an auxiliary program for automatic generation of operating

procedures has been developed This program generates operating procedures for the whole network of

beds according to the given number of beds and sequence of operating steps in one bed Operating

procedures govern the network by opening or closing the appropriate valves at the desired level and

changing the state of each bed This auxiliary development allows the automatic generation of a

gPROMS source code for a given number of beds and sequence of operating steps in one bed It also

generates gPROMS tasks ensuring feasible connectivities between the units according to the given

sequence A simplified algorithm illustrating the generation of operating procedures is presented in

Figure 3 The program is not limited only to PSA configurations where beds undergo the same sequence

of steps but it can also handle more complex configurations such as those concerning the production of

two valuable components11

3 Model validation

The single-bed pore diffusion model is validated against the results of Shin and Knaebel1718

The first

part of their work presents a pore diffusion model for a single column17 They developed a dimen-

sionless representation of the overall and component mass balance for the bulk gas and the particles and

applied Danckwertrsquos boundary conditions In this work the effective diffusivity axial dispersion

coefficient and mass transfer coefficient are taken by Shin and Knaebel Phase equilibrium is given as a

linear function of gas phase concentration (Henryrsquos law) The design characteristics of the adsorbent and

packed bed are also adopted from the work of Shin and Knaebel The axial domain is discretized using

orthogonal collocation on finite elements of third order with 20 elements The radial domain within the

particles is discretized using the same method of third order with five elements Shin and Knaebel used

six collocation points for discretization of the axial domain and eight collocation points for the radial

domain The bed is considered to be clean initially The target is to separate nitrogen from an air stream

using molecular sieve RS-10 Here oxygen is the preferably adsorbed component due to higher

diffusivity The PSA configuration consists of one bed and four operating steps (pressurization with

feed high-pressure adsorption counter-current blowdown and counter-current purge)

The effect of the following operational variables on the N2 purity and recovery is systematically ana-

lyzed duration of adsorption step for a constant feed velocity feed velocity (for a fixed duration of ad-

sorption step) duration of adsorption step for a fixed amount of feed duration of blowdown step purge

gas velocity for a fixed duration of purge step duration of purge step for a constant purge gas velocity

duration of purge step for a fixed amount of purge gas duration of pressurization step feedpurge step

pressure ratio and column geometry (lengthdiameter ratio)

7

The pore diffusion model presented in Section 2 and Appendix A has been used for comparison

purposes Gas valve constants and corresponding stem positions have been properly selected to produce

the same flow rates as in the work of Shin and Knaebel18

Since during the simulations several

parameters have been changed corresponding modifications in stem positions of the gas valves have

been made The stem positions of the gas valves for the base case are 015 for feed inlet 0002 for feed

outlet 07 for blowdown and 03 for purge All the other cases have been modified according to the

base case This was necessary since the flow rate through the gas valve depends linearly on the valve

pressure difference for a given stem position (eg in order to increase the flowrate through the gas valve

the stem position should be linearly increased)

Table 4 presents a comparison of experimental and simulation results of this work and the work of

Shin and Knaebel18

The modeling approach presented in this work predicts satisfactorily the behavior

of the process and the overall average absolute deviation from experimental data is limited to 197 in

purity and 223 in recovery while the deviations between Shin and Knaebelrsquos18

theoretical and

experimental results were 181 and 252 respectively These small differences can be attributed to

the use of a gas valve equation employed to calculate the flowrate and pressure at the end of the column

as opposed to linear pressure histories during pressure changing steps used in the original work of Shin

and Knaebel18 It should be emphasized that the gas valve equation results in exponential pressure

histories during the pressure changing steps Moreover different number of discretization points and

different package for thermo-physical property calculations have been used compared to the work of

Shin and Knaebel18

4 Case studies

The developed modeling framework has been applied in a PSA process concerning the separation of

hydrogen from steam-methane reforming off gas (SMR) using activated carbon as an adsorbent In this

case the nonisothermal linear driving force model has been used for simulation purposes The

geometrical data of a column adsorbent and adsorption isotherm parameters for activated carbon have

been adopted from the work of Park et al8 and are given in Tables 5 and 6 The effective diffusivity

axial dispersion coefficients and heat transfer coefficient are assumed constant in accordance with the

work of Park et al8 Two different cycle configurations have been used The sequence of the steps differs

only in the first step In the first configuration (configuration A) pressurization has been carried out by

using the feed stream whereas in the second (configuration B) by using the light product stream (pure

H2) Flowsheets of one four eight and twelve beds have been simulated These configurations differ

only in the number of pressure equalization steps introduced Thus the one-bed configuration contains

no pressure equalization steps the four-bed involves one the eight-bed configuration two and the

8

twelve-bed flowsheet involves three pressure equalization steps The following sequence of steps has

been used pressurization adsorption pressure equalization (depressurization to other beds) blowdown

purge and pressure equalization (repressurization from other beds) The sequence of steps for the one-

bed configuration is Ads Blow Purge CoCP and an overview of operating steps employed in the other

configurations is presented in Tables 7 to 9 where CoCP stands for co-current pressurization Ads for

adsorption EQD1 EQD2 and EQD3 are the pressure equalization steps (depressurization to the other

bed) Blow represents counter-current blowdown Purge is the counter-counter purge step and EQR3

EQR2 and EQR1 are the pressure equalization steps (repressurization from the other bed)

Configurations using pressurization by the light product (H2) are the same apart from the first step All

configurations have been generated using the auxiliary program described in section 2 The bed is

initially assumed clean

For simulation purposes the axial domain is discretized using orthogonal collocation on finite ele-

ments of third order with 20 elements In terms of numerical stability and accuracy other superior

discretization methods exist (eg adaptive multiresolution approach19

) which overcome problems of

non-physical oscillations or the divergence of the numerical method in the computed solution in the

presence of steep fast moving fronts These methods are capable of locally refining the grid in the

regions where the solution exhibits sharp features and this way allowing nearly constant discretization

error throughout the computational domain This approach has been successfully applied in the

simulation and optimization of cyclic adsorption processes2021 However in all case studies considered

in this work the contribution of diffusivedispersive terms is significant and all numerical simulations

did not reveal any non-physical oscillations Thus the orthogonal collocation on fixed elements was

considered as an adequate discretization scheme in terms of accuracy and stability

Three different sets of simulations have been carried out

Simulation Run I

In this case configuration A has been employed (pressurization with feed) The effect of number of

beds and cycle time (due to introduction of pressure equalization steps) on the separation quality has

been investigated The following operating conditions have been selected constant duration of ad-

sorption and purge steps and constant feed and purge gas flowrates The input parameters of the

simulation are given in Table 10 and the simulation results are summarized in Table 11 and Figure 4

The results clearly illustrate that as the number of beds increases an improved product purity (~3)

and product recovery (~38) are achieved The improved purity can be attributed to the fact that

flowsheets with lower number of beds process more feed per cycle (feed flowrate is constant but more

9

feed is needed to repressurize beds from the lower pressure) The noticeable increase in product

recovery is the direct result of the pressure equalization steps On the other hand power requirements

and adsorbent productivity decrease due to the lower amount of feed processed per unit time (the power

and productivity of the eight-bed configuration are lower than the power and productivity of the twelve-

bed configuration due to higher cycle time) The purity of the twelve-bed configuration is lower than the

purity of the four and eight-bed ones This interesting trend can be attributed to the fact that during the

third pressure equalization a small breakthrough takes place thus contaminating the pressurized bed

Simulation Run II

In simulation Run II configuration A has been employed (pressurization with feed) The effect of

number of beds for constant power requirements and constant adsorbent productivity on the separation

quality has been analyzed The following operating conditions have been selected constant adsorbent

productivity constant cycle time and constant amount of feed processed per cycle The input parameters

are given in Table 12 and the simulation results are summarized in Table 13 and Figure 5

The results show that increasing the number of beds a slight increase in the product purity (~1) and

a significant increase in product recovery (~52) are achieved In this run the amount of feed processed

per cycle is constant and improve in the purity cannot be attributed to the PSA design characteristics and

operating procedure Due to the same reasons described in Run I the purity of the twelve-bed

configuration is lower than the purity of the eight-bed one The power requirements and adsorbent

productivity remain constant due to the constant amount of feed processed per cycle

Simulation Run III

In this case configuration B (pressurization with light product) is used The effect of number of beds

for constant power requirements and constant adsorbent productivity on separation quality has been

investigated The following operating conditions have been selected constant adsorbent productivity

constant duration of adsorption and purge steps constant feed and purge gas flowrates constant cycle

time and constant amount of feed processed per cycle The input parameters are given in Table 14 and

the simulation results are presented in Figure 6 and Table 15

The results illustrate that the number of beds does not affect the product purity productivity and

power requirements (since the amount of feed per cycle is constant) However a huge improvement in

the product recovery (~64) is achieved due to three pressure equalization steps Similar to the results

in Run I and II the purity of the twelve-bed con-figuration is lower than the purity of the eight-bed one

10

The above analysis reveals typical trade-offs between capital and operating costs and separation

quality Thus by increasing the number of beds a higher product purityrecovery is achieved while

higher capital costs are required (due to a larger number of beds) On the other hand energy demands

are lower due to energy conservation imposed by the existence of pressure equalization steps

5 Conclusions

A generic modeling framework for the separation of gas mixtures using multibed PSA flowsheets is

presented in this work The core of the framework represents a detailed adsorbent bed model relying on

a coupled set of mixed algebraic and partial differential equations for mass heat and momentum balance

at both bulk gas and particle level equilibrium isotherm equations and boundary conditions according to

the operating steps The adsorbent bed model provides the basis for building a PSA flowsheet with all

feasible inter-bed connectivities PSA operating procedures are automatically generated thus facilitating

the development of complex PSA flowsheet for an arbitrary number of beds The modeling framework

provides a comprehensive qualitative and quantitative insight into the key phenomena taking place in

the process All models have been implemented in the gPROMS modeling environment and successfully

validated against experimental and simulation data available from the literature An application study

concerning the separation of hydrogen from the steam methane reformer off gas illustrates the predictive

power of the developed framework Simulation results illustrate the typical trade-offs between operating

and capital costs

Current work concentrates on the development of a mathematical programming framework for the

optimization of PSA flowsheets Recent advances in mixed-integer dynamic optimization techniques

will be employed for the solution of the underlying problems Future work will also consider the

detailed modeling and optimization of hybrid PSA-membrane processes

Acknowledgements

Financial support from PRISM EC-funded RTN (Contract number MRTN-CT-2004-512233) is

gratefully acknowledged The authors thank Professor Costas Pantelides from Process Systems

Enterprise Ltd for his valuable comments and suggestions

Nomenclature

a1 = Langmuir isotherm parameter molkg

a2 = Langmuir isotherm parameter K

b1 = Langmuir isotherm parameter 1Pa

11

b2 = Langmuir isotherm parameter K

b = Langmuir isotherm parameter m3mol

C = molar concentrations of gas phase in bulk gas molm3

Cp = molar concentrations of gas phase in particles molm

3

cp = heat capacity of bulk gas J(kgK)

cppg = heat capacity of gas within pellets J(kgK)

cpp = heat capacity of the particles J(kgK)

Cv = valve constant

Dz = axial dispersion coefficient m2s

Dm = molecular diffusion coefficient m2s

Ds = surface diffusion coefficient m2s

De = effective diffusivity coefficient m2s

εbed = porosity of the bed -

εp = porosity of the pellet -

F = molar flowrate mols

∆Hads = heat of adsorption Jmol

H = Henryrsquos parameter m3kg

kf = mass transfer coefficient m2s

kh = heat transfer coefficient J(m2Ks)

khwall = heat transfer coefficient for the column wall J(m2Ks)

L = bed length m

Q = adsorbed amount molkg

Q = adsorbed amount in equilibrium state with gas phase (in the mixture) molkg

12

Q

pure = adsorbed amount in equilibrium state with gas phase (pure component) molkg

Qtotal = total adsorbed amount molkg

Qm = Langmuir isotherm parameter molkg

Rbed = bed radius m

Rp = pellet radius m

T = temperature of bulk gas K

Tp = temperature of particles K

P = pressure Pa

P0 = pressure that gives the same spreading pressure in the multicomponent equilibrium Pa

u = interstitial velocity ms

X = molar fraction in gas phase -

X = molar fraction in adsorbed phase -

Z = compressibility factor -

ρ = density of bulk gas kgm3

micro = viscosity of bulk gas Pas

λ = thermal conductivity of bulk gas J(mK)

π = reduced spreading pressure -

ρpg = density of gas within pellets kgm3

ρp = density of the particles kgm

3

λp = thermal conductivity of the particles J(mK)

sp = stem position of a gas valve

spPressCoC = stem position of a gas valve during co-current pressurization -

spPressCC = stem position of a gas valve during counter-current pressurization -

13

spAdsIn = stem position of a gas valve during adsorption (inlet valve) -

spAdsOut = stem position of a gas valve during adsorption (outlet valve) -

spBlow = stem position of a gas valve during blowdown -

spPurgeIn = stem position of a gas valve during purge (inlet valve) -

spPurgeOut = stem position of a gas valve during purge (outlet valve) -

spPEQ1 = stem position of a gas valve during pressure equalization -



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14

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17

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Technol 2000 20 185

(53) Rajasree R Moharir AS Simulation based synthesis design and optimization of pressure swing

adsorption (PSA) processes Comput Chem Eng 2000 24 2493

(54) Mendes AMM Costa CAV Rodrigues AE PSA simulation using particle complex models

Sep Purif Technol 2001 24 1

(55) Botte GG Zhang RY Ritter JA On the use of different parabolic concentration profiles for

nonlinear adsorption and diffusion in a single particle Chem Eng Sci 1998 24 4135

(56) Ko D Siriwardane R Biegler L T Optimization of a pressure-swing adsorption process using

zeolite 13X for CO2 sequestration Ind Eng Chem Res 2003 42 339

(57) Cruz P Santos JC Magalhaes FD Mendes A Cyclic adsorption separation processes


(58) Jain S Moharir AS Li P Wozny G Heuristic design of pressure swing adsorption a

preliminary study Sep Purif Technol 2003 33 25

(59) Kim MB Jee JG Bae YS Lee CH Parametric study of pressure swing adsorption process

to purify oxygen using carbon molecular sieve AIChE J 2004

(60) Chang D Min J Moon K Park Y K Jeon JK Ihm SK Robust numerical simulation of

pressure swing adsorption process with strong adsorbate CO2 Chem Eng Sci 2004 59 2715

(61) Ko D Siriwardane R Biegler LT Optimization of pressure swing adsorption and fractionated

vacuum pressure swing adsorption processes for CO2 capture Ind Eng Chem Res 2005 44

8084

18

(62) Jee J Kim M Lee C Pressure Swing Adsorption Processes to Purify Oxygen Using a Carbon

Molecular Sieve Chem Eng Sci 2005 60 869

(63) Knaebel SP Ko D Biegler LT Simulation and optimization of a pressure swing adsorption

system Recovering hydrogen from methane Adsorption 2005 11 615


to purify oxygen using carbon molecular sieve Ind Eng Chem Res 2005 44 7208

(65) Grande CA Rodrigues AE Propanepropylene separation by pressure swing adsorption using

zeolite 4A Ind Eng Chem Res 2005 44 8815

(66) Reynolds SP Ebner AD Ritter JA Stripping PSA cycles for CO2 recovery from flue gas at

high temperature using a hydrotalcite-like adsorbent Ind Eng Chem Res 2006 45 4278

(67) Reynolds SP Ebner AD Ritter JA Enriching PSA cycle for the production of nitrogen from

air Ind Eng Chem Res 2006 45 3256

(68) OrsquoBrien JA Myers AL A comprehensive technique for equilibrium calculations in adsorbed

mixtures The generalized FastIAS method Ind Eng Chem Res 1988 27 2085

(69) Ahn H Brandani S A new numerical method for accurate simulation of fast cyclic adsorption

processes Adsorption 2005 11 113

19

Table1 Overview of single-bed PSA studies

Ref Mass

balance

Heat

balance

Momentum

balance

Isotherm

adsorbent

No of

steps

No of

layers Application

(3) LDF - - Linear CMS 4 1 Air separation

(8) LDF Bulk gas Ergun Langmuir AC+5A - 2 H2 CO2 CH4 CO

(26) PD - - Langmuir alumina 4 1 Air separation

(27) LEQ SD PD Bulk gas - IASLRC AC 5 1 H2 CO2 CH4

(29) BDPD Bulk gas - Langmuir 5A 5 1 H2 CH4

(17) PD - - Linear MS RS-10 4 1 Air separation theoretical

study

(18) PD - - Linear MS RS-10 4 1 Air separation

experimental study

(38) 4 different LDF Bulk gas Ergun Linear 13X - 1 Air separation

(43) LDF Bulk gas

solids -

Langmuir Freundlich 5A

5 1 H2 CO H2 CO2

(47) DG Bulk gas - Langmuir 5A - 1 Air separation


(54) DG LDF -DG

LDF-DGSD

LDF-DGSD

- - Langmuir 4A 5A

CMS 4 1 Air separation

(56) LDF Bulk gas Darcy Langmuir 13X 4 1 CO2 sequestr

(61) LDF Bulk gas - Langmuir AC 4 1 H2 CH4

(63) LDF Bulk gas Ergun Dual-site Langmuir

13X 4 1 CO2 capture

(65) Bi-LDF Bulk gas

solid Ergun Langmuir 4A 5 1 Propane propylene

LEQ ndash local equilibrium model LDF ndash linear driving force model SD ndash solid diffusion model PD ndash pore diffusion model

DG ndash dusty gas model

Table 2 Overview of two-bed PSA studies

Ref Mass

balance

Heat

balance

Momentum

balance

Isotherm

adsorbent

No of

beds

No of

steps

Bed

interactions

No of

layers Application

(3) LDF - - Langmuir

CMS5A 2 4 Valve eq 1 Air separation

(7) LDF PD - Darcy Linear-

Langmuir 5A 1 2 2 6 Valve eq 1 Air separation

(13) LDF Bulk gas Ergun

Dual-site

Langmuir

13X

1 2 3 6 Valve eq Inert +

ads Air separation

(28) LDF PD Bulk gas - LRC AC 2 4 - 1 H2 CH4

(31) LDF - - Linear CMS 2 6 Frozen solid 1 Air separation

(49) LDF Bulk gas Ergun Langmuir Freundlich

AC+5A

2 7 - 2 H2 CH4 CO

N2 CO2

(57) LDF DG Bulk gas Darcy Langmuir 2 4 - 1 Air separation

(64) LDF Bulk gas Ergun LRC AC+5A 2 6 - 1 Air separation

20

Table 3 Overview of multibed PSA studies

Ref Mass

balance Heat

balance

Momentum

balance

Isotherm adsorbent

No of beds

No of steps

Bed interactions

No of layers

Application

(4) LEQ - - Langmuir 5A 4 6 Valve eq 1 Air separation

(5) LDF Bulk gas - LRC AC+5A 5 8 Linear change 1 or 2 H2 CH4 CO

N2

(6) LDF Bulk gas - LRC AC5A 2 4 5 7 - 1 H2 CH4 N2

(9) LDF Bulk gas Ergun Langmuir

AC+5A 4 8

Only one bed is simulated

information

stored in data buffer

2 H2 CO2 CH4

CO

(10) LDF Bulk gas Darcy

Langmuir

Alumina+ AC+zeolite

6 12

Information


inert +

2 ads H2 CH4 CO

(11) - - - AC zeolite silica

gel 9 10

9 11 6+7

- -

Overview of

commercial PSA processes

(12) LDF Bulk gas Darcy Langmuir AC 4 5 7 9 12 - 1 H2 CH4


Dual-site

Langmuir APHP+5A

5 11 Valve eq 2 N2 CH4 CO2

CO H2

(51) LEQ Bulk gas - Ext Langmuir

13X 2 3 4 6 - 1

CO2 from flue

gases

(66) LDF Bulk gas - Langmuir 13X 4 5 4 5 5 Linear change 1 CO2 N2 H2O

21

Table 4 Comparison of the experimental and the simulation results

Recovery Purity

No Exp18

Model18

This

work Exp

18 Model

18

This

work

1 644 638 696 9975 10000 9931

2 816 864 850 9955 9989 9892

3 1065 1092 994 9900 9909 9855

4 1239 1215 1130 9835 9859 9815

5 707 825 852 9960 9988 9895

6 941 985 995 9885 9941 9854

7 1167 1172 1072 9830 9877 9833

8 1299 1213 1141 9780 9849 9811

9 2584 1702 2123 9080 9539 9447

10 2136 1609 2121 9070 9623 9475

11 2274 1550 2120 9140 9618 9478

12 2218 2274 2108 9120 9602 9477

13 939 835 845 9825 9970 9974

14 740 632 785 9890 9982 9991

15 510 500 738 9900 9988 9997

16 919 859 982 9845 9963 9960

17 707 762 856 9850 9976 9979

18 643 699 742 9870 9983 9989

19 541 613 612 9880 9993 9996

20 1151 1244 1128 9795 9871 9825

21 972 967 943 9850 9942 9940

22 674 659 726 9885 9979 9991

23 337 408 546 9900 9996 9999

24 1663 1433 1086 9585 9747 9869

25 1076 1155 962 9680 9872 9957

26 857 847 881 9730 9915 9984

27 826 721 844 9765 9910 9991

28 735 856 1135 9875 9987 9822

29 1195 1427 1117 9770 9792 9831

30 1330 1607 1120 9700 9657 9824

31 4156 3764 2638 8230 8227 8923

32 2246 1607 1511 9370 9497 9670

33 1254 800 899 9820 10000 9906

34 1383 1309 986 9380 9445 9606

35 2305 1673 1425 9370 9758 9775

42 2240 1646 2051 8900 9440 9496

43 2237 1615 2006 8230 8972 9012

22

Table 5 Geometrical and transport characteristics of PSA process

Parameter Value Units

Temperature of the feed 297 K

Temperature of the purge gas 297 K

Temperature of the wall 297 K

Feed pressure 263e5 Pa

Purge pressure 1e5 Pa

Gas valve constant 1e-5 -

Particle density 850 kgm3

Particle radius 3e-3 m

Bed void fraction 036 -

Bed inner diameter 01 m

Bed length 10 m

Molar fraction of H2 in feed 0755 -

Molar fraction of CO in feed 0040 -

Molar fraction of CH4 in feed 0035 -

Molar fraction of CO2 in feed 0170 -

Overall mass transfer

coefficient of H2 10 1s


coefficient of CO 03 1s


coefficient of CH4 04 1s


coefficient of CO2 01 1s

Heat capacity of the particles 87864 J(kgK)

Heat transfer coefficient

(wall) 13807 W(m

2K)

Heat axial dispersion

coefficient 1e-3 m

2s

Mass axial dispersion

coefficient 1e-3 m

2s

Table 6 Langmuir parameters and heat of adsorption for activated carbon

Comp a1 x10

3

(molg) a2

(K) b1 x10

9

(Pa-1

) b2

(K) -∆Hads (Jmol)

H2 432 000 5040 8505 786173

CO 092 052 5896 17309 1667742

CH4 -170 198 19952 14467 1875269

CO2 -1420 663 24775 14966 2557261

Table 7 A four-bed six-step PSA configuration (pressurization with feed one pressure equalization

step purge from tank) Bed 1 CoCP Ads Ads EQD1 Blow Purge Purge EQR1

Bed 2 Purge EQR1 CoCP Ads Ads EQD1 Blow Purge

Bed 3 Blow Purge Purge EQR1 CoCP Ads Ads EQD1

Bed 4 Ads EQD1 Blow Purge Purge EQR1 CoCP Ads

23

Table 8 A eight-bed eight-step PSA configuration (pressurization with feed two pressure equalization

steps purge from tank) Bed 1 CoCP Ads EQD1 EQD2 Blow Purge EQR2 EQR1

Bed 2 EQR1 CoCP Ads EQD1 EQD2 Blow Purge EQR2

Bed 3 EQR2 EQR1 CoCP Ads EQD1 EQD2 Blow Purge

Bed 4 Purge EQR2 EQR1 CoCP Ads EQD1 EQD2 Blow

Bed 5 Blow Purge EQR2 EQR1 CoCP Ads EQD1 EQD2

Bed 6 EQD2 Blow Purge EQR2 EQR1 CoCP Ads EQD1

Bed 7 EQD1 EQD2 Blow Purge EQR2 EQR1 CoCP Ads

Bed 8 Ads EQD1 EQD2 Blow Purge EQR2 EQR1 CoCP

Table 9 A twelve-bed ten-step PSA configuration (pressurization with feed three pressure equalization

steps purge from tank) Bed 1 CoCP Ads Ads EQD1 EQD2 EQD3 Blow Purge Purge EQR3 EQR2 EQR1

Bed 2 EQR1 CoCP Ads Ads EQD1 EQD2 EQD3 Blow Purge Purge EQR3 EQR2

Bed 3 EQR2 EQR1 CoCP Ads Ads EQD1 EQD2 EQD3 Blow Purge Purge EQR3

Bed 4 EQR3 EQR2 EQR1 CoCP Ads Ads EQD1 EQD2 EQD3 Blow Purge Purge

Bed 5 Purge EQR3 EQR2 EQR1 CoCP Ads Ads EQD1 EQD2 EQD3 Blow Purge

Bed 6 Purge Purge EQR3 EQR2 EQR1 CoCP Ads Ads EQD1 EQD2 EQD3 Blow

Bed 7 Blow Purge Purge EQR3 EQR2 EQR1 CoCP Ads Ads EQD1 EQD2 EQD3

Bed 8 EQD3 Blow Purge Purge EQR3 EQR2 EQR1 CoCP Ads Ads EQD1 EQD2

Bed 9 EQD2 EQD3 Blow Purge Purge EQR3 EQR2 EQR1 CoCP Ads Ads EQD1

Bed 10 EQD1 EQD2 EQD3 Blow Purge Purge EQR3 EQR2 EQR1 CoCP Ads Ads

Bed 11 Ads EQD1 EQD2 EQD3 Blow Purge Purge EQR3 EQR2 EQR1 CoCP Ads

Bed 12 Ads Ads EQD1 EQD2 EQD3 Blow Purge Purge EQR3 EQR2 EQR1 CoCP

24

Table 10 Input parameters of Run 1

Number of beds Parameter

1 4 8 12

spPressCoC 01000 0060 0030 00500

spAdsIn 03600 03600 03600 03600

spAdsOut 00035 00015 00015 00015

spBlow 08000 05000 02500 04000

spPurgeIn 02250 02250 02250 02250

spPurgeOut 00300 00300 0030 00300

spPEQ1 - 00040 00025 00030

spPEQ2 - - 00050 00040

spPEQ3 - - - 00080

Feed

flowrate m3s

360e-6 360e-6 360e-6 360e-6

Purge

flowrate m3s

225e-6 225e-6 225e-6 225e-6

τPress s 10 10 20 10

τAds s 20 20 20 20

τBlow s 10 10 20 10

τPurge s 20 20 20 20

τPEQ1 s - 10 20 10

τPEQ2 s - - 20 10

τPEQ3 s - - - 10

τcycle s 60 80 160 120

Table 11 Simulation results of Run I

No

beds

O2 purity

()

O2 recovery

()

Power

(W)

Productivity

(molkgs)

1 9687 3440 52902 918e-2

4 9950 5806 27949 485e-2

8 9958 6887 11987 208e-2

12 9936 7250 13936 242e-2

25

Table 12 Runtime parameters for Run II


1 4 8 12

spPressCoC 00300 00450 00500 00500

spAdsIn 01200 01300 03300 03600

spAdsOut 00004 000035 00014 00015

spBlow 02000 02200 03000 04000

spPurgeIn 05625 01500 03000 02250

spPurgeOut 00075 00200 00400 00300

spPEQ1 - 00025 00020 00300

spPEQ2 - - 00040 00040

spPEQ3 - - - 00080

Feed flowrate m

3s

120e-6 130e-6 330e-6 360e-6

Purge

flowrate m3s

075e-6 115e-6 300e-6 225e-6

τPress s 20 15 15 10

τAds s 40 30 15 20

τBlow s 20 15 15 10

τPurge s 40 30 15 20

τPEQ1 s - 15 15 10

τPEQ2 s - - 15 10

τPEQ3 s - - - 10

τcycle s 120 120 120 120

Table 13 Simulation results for Run II

No

beds

O2 purity

()

O2 recovery

()

Power

(W)

Productivity

(molkgs)

1 9811 2021 14420 250e-2

4 9929 3840 14069 244e-2

8 9979 6525 14092 245e-2

12 9936 7250 13936 242e-2

26

Table 14 Runtime parameters for Run III


1 4 8 12

spPressCC 00030 00030 00500 00040

spAdsIn 04000 03333 03450 05000

spAdsOut 000088 000085 00015 00014

spBlow 02500 04000 03000 04000

spPurgeIn 00900 01333 03000 02000

spPurgeOut 00140 00200 00400 00300

spPEQ1 - 00050 00020 00030

spPEQ2 - - 00040 00040

spPEQ3 - - - 00080

Feed flowrate m

3s

400e-6 333e-6 345e-6 500e-6

Purge

flowrate m3s

090e-6 133e-6 300e-6 200e-6

τPress s 20 15 15 10

τAds s 40 30 15 20

τBlow s 20 15 15 10

τPurge s 40 30 15 20

τPEQ1 s - 15 15 10

τPEQ2 s - - 15 10

τPEQ3 s - - - 10

τcycle s 120 120 120 120

Table 15 Simulation results for Run III

No beds

O2 purity ()

O2 recovery ()

Power (W)

Productivity (molkgs)

1 9987 141 18878 203e-2

4 9997 2847 11808 205e-2

8 9997 5058 11938 207e-2

12 9983 6516 11909 207e-2

27

APPENDIX A Table A1 Basic adsorbent bed model

Feature General equation

Bulk flow mass balance

( )( )

( )

1

0 1

i i ibed bed bed i bed z i

comp

uC C CN D

z t z z

z L i N

part part partpart ε + ε + minus ε = ε

part part part part

forall isin = hellip

(A1)

The generation term in bulk flow mass balance (transfer through a

particle surface)

( ) ( ) 0 1 i i compN f T P C Adsorbent type z L i N= forall isin = hellip (A2)

Bulk flow heat balance

( ) ( )( ) ( )

( )

31

0

bed pbed p h wallbed g wall

bed

bed z

c Tc uT kq T T

z t R

Tz L

z z

part ε ρpart ε ρ+ + minus ε + minus =

part part

part part = ε λ forall isin

part part

(A3)

The generation term in bulk flow

heat balance (transfer through a particle surface)

( ) ( ) 0 1 g i compq f T P C Adsorbent type z L i N= forall isin = hellip (A4)

Momentum balance ( ) ( ) 0 bed p

Pf u R z L

z

partminus = ε forall isin

part (A5)


coefficient ( )

0 1 f i p

compm i

k RSh f Sc Re z L i N

D= = forall isin = hellip (A6)

Overall heat transfer coefficient ( ) 0

h pk RNu f PrRe z L= = forall isin

λ (A7)

Mass axial dispersion coefficient

( )

0 1 z i bed

compm i

Df Sc Re z L i N

D

ε= forall isin = hellip (A8)

Heat axial dispersion coefficient

( ) 0 z f Pr Re z Lλ

= forall isin λ

(A9)

Equation of state ( ) 0 1 i Ncomp compP f T C C z L i N= forall isin = hellip (A10)

Thermo-physical properties ( ) [ ] 0 1 p i Ncomp compc f T P C C z L i Nρ λ micro = forall isin = hellip (A11)

( ) 0 or 1 in ii i z i comp

Cu C C D z z L i N

z

partminus = = = =

parthellip (A12)

0 or inT T z z L= = = (A13)

Boundary conditions for stream inlet into the bed

0 0 and u

z z Lz

part= = =

part (A14)

0 0 or 1 icomp

Cz z L i N

z

part= = = =

parthellip (A15) Boundary conditions for stream

outlet from the bed closed bed

end 0 0 or

Tz z L

z

part= = =

part (A16)

28

Table A2 Mass transport mechanisms

Model Equation

Mass transfer between a bulk gas and particles is assumed instantaneous and concentration of the gas

within the particles is equal to the concentration in the bulk flow

[ ] 0 0 1 p

i p compiC C r R z L i N = forall isin forall isin = hellip (A17)

The gas phase is in equilibrium with the solid phase

[ ] 0 0 1 i i p compQ Q r R z L i N = forall isin forall isin = hellip (A18) LEQ

The generation term is sum of accumulation in gas phase in particles and amount adsorbed

( )

0 1 p i ii p comp

Q CN z L i N

t t

part part= ρ + ε forall isin =

part parthellip

(A19)

Mass transfer between a bulk gas and particles is assumed instantaneous

[ ] 0 1 pi p compiC C r R z L i N= = forall isin = hellip

(A20)

Concentration profile within the particle is assumed parabolic

( ) [ ]

2

15 0 0 1

e iii i p comp

p

DQQ Q r R z L i N

t R

part = minus forall isin forall isin = part

hellip (A21) LDF


( ) 0 1 p i i

i p comp

Q CN z L i N

t t


part parthellip

(A22)

Gas phase within particles is neglected

) [ ]0 0 0 1 p

p compiC r R z L i N= forall isin forall isin = hellip (A23)

All adsorption happens at the particle surface Adsorbed phase is then transported towards particle

centre by surface diffusion (Fickrsquos first law of diffusion)

( ) [ ]22

1 0 0 1 i i

p s i p comp

p

Q QR D r R z L i N

t r rR

part partpart= forall isin forall isin =

part part part hellip

(A24)

Mass transfer between bulk gas and particles is carried out through the gas film around particles

( ) ( )3

0 1 p

f pi i r R compi

p

kN C C z L i N

R== minus forall isin = hellip

(A25)

Boundary conditions ( ) 1 p p

p if i i r R s i r R p compi

Qk C C D r R i N

r= =

partminus = = =

part (A26)

SD

0 0 0 1 icomp

Qr z L i N

r

part= = forall isin =

parthellip (A27)

Within the pores gas is transported by combined molecular and Knudsen diffusion

( ) ( ) [ ]

22

11 0 0 1

p ppi i i

p p p p e i p comp

p

C CQR D r R z L i N

t t r rR

part partpart part ε + minus ε ρ = ε forall isin forall isin =

part part part part hellip

(A28)

The gas phase in micro-pores is in equilibrium with the adsorbed phase

[ ] 0 0 1 i i p compQ Q r R z L i N = forall isin forall isin = hellip (A29)


( ) ( )3

0 1 p

f pi i r R compi

p

kN C C z L i N


(A30)


p if i i r R e i r R p compi

Qk C C D r R i N

r= =

partminus = = =

part (A31)

PD

0 0 0 1 p

icomp

Cr z L i N

r


parthellip (A32)

29

Table A3 Thermal operating modes

Mode Equation

( )0 0 T

z Lz

part= forall isin

part (A33)

Isothermal Temperature within the particles are constant and equal to the temperature of bulk flow

(no heat transfer between bulk flow and particles occurs)

0 0 ppT T r R z L = forall isin forall isin

(A34)


( ) ( )( ) ( )3

0 bed pbed p h wall

g wall bed zbed

c Tc uT k Tq T T z L

z t R z z

part ε ρpart ε ρ part part + + + minus = ε λ forall isin

part part part part

(A35)

Heat transfer between bulk gas and particles is assumed instantaneous and the

temperature of particles is equal to the temperature of the bulk flow


(A36)

LEQ

model The generation term qg is given by the sum of accumulations in gas and solid

phase within the particles and heat of adsorptiondesorption

( )( ) ( )

0 comp

p p Np p pg p pg

p ig ads i

i

c c TQ

q H z Lt t

part ρ + ε ρpart = + ρ ∆ forall isin

part partsum

(A37)




(A38)

LDF



( )( ) ( )

0 comp

p p Np p pg p pg

p ig ads i

i

c c TQ

q H z Lt t


part partsum

(A39)



0 0 p

pT T r R z L = forall isin forall isin

(A40)

SD

model The generation term qg is given by the sum of accumulation in solid phase within

the particles and heat of adsorptiondesorption

( )( ) ( ) 0

compp p N

p i Rppg ads i

i

c T Qq H z L

t t

part ρ part= + ρ ∆ forall isin

part partsum

(A41)

Heat transfer is carried out through the gas film around particles

( ) ( )3

0 p

phg R

p

kq T T z L

R= minus forall isin

(A42)

Particle heat balance

( )( ) ( )

2

2

1 0 0

p p ppp p pg p pg

p pg p p

p

c c TT

q R r R z Lt r rR

part ρ + ε ρ part part + = λ forall isin forall isin part part part

(A43)

The generation term qgp is given by the heat of adsorptiondesorption

( ) ( )

0 compN

p p ig ads i p

i

Qq H r R

t

part= ρ ∆ forall isin

partsum

(A44)

( ) p p

pp p

h r R r R p

Tk T T r R

r= =

partminus = λ =

part

(A45)

Nonisothermal

PD

model

Boundary conditions

0 0p

Tr

r

part= =

part (A46)

Adiabatic The same as in the Nonisothermal mode except the term

( )3 h wallwall

bed

kT T

Rminus

is neglected

30

Table A4 Momentum balance and equilibrium isotherms Feature Equation

Blake-Kozeny equation

( )

( )( )

2

2 3

180 1 0

2

bg bed

bedp

uPz L

z R

micro minus εpartminus = forall isin

part ε (A47)

Momentum balance Ergunrsquos equation

( )

( )( )

2

2 3

180 1 0

2

bg bed

bedp

uPz L

z R


part ε (A48)

Linear (Henry type)

( ) 0 1 pi i comp iiQ H C z L i N H f T P= forall isin = = hellip

(A49)

Extended Langmuir

2 2 1 1 exp 0 1

1

i ii ii m i m i i i i comp

j j

j

a bb PQ Q Q a b b z L i j N

b P T T

= = + = forall isin =

+ sumhellip (A50)

Ideal Adsorbed Solution theory (IAS)268

( )0

0

0

1 0 1 iP

pure i Langmuiri i m i i i compisotherm

QdP Q b P z L i N

Pπ = rarrπ = + forall isin = int hellip

(A51a)

1 0 1 1i i compz L i N+π = π forall isin = minus hellip

(A51b

)

2 2 1 1 exp 0 1

1

i ii ipure i m i m i i i i comp

i i

a bb PQ Q Q a b b z L i N

b P T T

= = + = forall isin = +

hellip (A51c)

0 0 1 i i i compX P X P z L i N= forall isin = hellip (A51d

)

1 0 1 i compX z L i N= forall isin = sum hellip (A51e)

1 0 1 i

comp

itotal pure i

Xz L i N

Q Q= forall isin = sum hellip (A51f)

Equilibrium isotherms

0 1 i i total compQ X Q z L i N= forall isin = hellip (A51g)

31

Table A5 Calculation of transport properties

Variable Equation

Overall mass transfer coefficient

Wakao correlation23

( ) 033 06 20 11 0 1

m if i comp

p

Dk Sc Re z L i N

R= + forall isin = hellip (A52)

Overall heat transfer

coefficient

Wakao correlation24

( )033 0620 11 Re 0 hp

k Pr z LR

λ= + forall isin

(A53)


coefficient

Wakao correlation23

( ) 20 05 0 1

m iz i comp

bed

DD ScRe z L i N= + forall isin =

εhellip

(A54)


coefficient

Wakao correlation24

( )7 05 0 z bg PrRe z Lλ = λ + forall isin (A55)

Chapman-Enskog equation2

3

3 2

12 12

1

18583 10 0 0 1 2im i p

TMW

D z L r R iP

minus = times forall isin forall isin = σ Ω

(A56)

Molecular diffusivity Fuller correlation

2

7 175 2

12

1

1013 10 0 0 1 2im i p

MWD T z L r R i

PX

minus = times forall isin forall isin = (A57)

Knudsen diffusivity

Kauzmann2 correlation

3 97 10 0 0 1 k i pore p comp

i

TD R z L r R i N

MW = times forall isin forall isin = hellip

(A58)

Effective diffusivity

0 0 1 p m i k i

e i p compp m i k i

D DD z L r R i N

D D

ε = forall isin forall isin = τ +

hellip (A59)

Table A6 Gas valve equation Variable Equation

If Pout gt Pcrit Pin

2

1

1

out

inv in comp

i i

P

PF C SP P i N

x MW T

minus = = hellip

sum (A60)

Molar flowrate

Otherwise ( )

21

1

critv in comp

i i

PF C SP P i N

x MW T

minus= = hellip

sum (A61)

Critical pressure 12

1critP

κ

minusκ =

+ κ (A62)

Power

1

11

feed feedfeed

low cycle

P NPower RT

P

κminus

κ κ

= minus κ minus τ

(A63)

32

Figure 1 Single bed PSA arrangement with all possible interconnections

33

Figure 2 Four-bed PSA flowsheet

34

Figure 3 A simplified algorithm of the operating procedure generator

Figure 4 Simulation results of Run I

35

Figure 5 Simulation results of Run II

Figure 6 Simulation results of Run III

2

1 Introduction

Pressure swing adsorption (PSA) is a gas separation process which has attracted increasing interest

because of its low energy requirements as well as low capital investment costs in comparison to the

traditional separation processes12

The major industrial applications of PSA include small to

intermediate scale oxygen and nitrogen production from air small to large-scale gas drying hydrogen

recovery from different petrochemical processes (steam-methane reforming off gas or coke oven gas)

and trace impurity removal from contaminated gases

From an operational point of view PSA is an intrinsic dynamic process operating in a cyclic manner

with each bed undergoing the same sequence of steps The typical operating steps include pressurization

with feed or pure product high-pressure adsorption pressure equalization(s) blowdown and purge

Over the last three decades several PSA studies have appeared in the literature An overview of single-

bed PSA studies is presented in Table 1 Industrial practice indicates that difficult gas separations under

high product quality requirements (ie purity andor recovery) rely on complex PSA flowsheets with

several interconnected beds and complicated operating procedures The key literature contributions

involving two and multibed configurations under certain assumptions are summarized in Tables 2 and 3

One of the earliest attempts to realistically describe bed interactions is presented by Chou and Huang3

and is based on incorporating a gas valve equation into the PSA model to control flowrate The results

obtained are in good agreement with experimental data The proposed approach was followed to study

the dynamic behavior of two and four bed PSA processes in a subsequent work4

Warmuzinski and Tanczyk5 developed a generic multibed PSA model The main features of their

approach include support for multicomponent mixtures LDF approximation one or two adsorbent

layers and linear pressure changes The model was used to study the separation of coke oven gas in a

five-bed eight-step PSA process In a subsequent publication6 the same authors presented an

experimental verification of the model using a case study concerning hydrogen recovery from a

H2N2CH4CO mixture In both cases satisfactory agreement between theoretical predictions and

experimental data was achieved

Nilchan and Pantelides7 proposed a rigorous mathematical programming approach for the simulation

and optimization of PSA Their work is the first key contribution towards a formal framework for

optimizing a PSA process

Cho and co-workers8 developed a mathematical model for the separation of H2 from steam methane

reformer off gas They investigated the effects of carbon-to-zeolite ratio on adsorber dynamics In a

3


































and Jiang et al14

4

































5
















22 Gas valve model



Appendix A











shown in Figure 2


6













3 Model validation


The first




















7












Shin and Knaebel18




theoretical and







Shin and Knaebel18

4 Case studies













8

























Simulation Run I









9








Simulation Run II












Simulation Run III











10





5 Conclusions













and capital costs





Acknowledgements




Nomenclature




11





3




Cv = valve constant













L = bed length m



12

Q




Rbed = bed radius m




P = pressure Pa












3





13









References












1998 4 113



14






2000 35 667


2000 6 179




















15





325










AIChE J 1987 33 1045



Eng 1987 65 512










16




141






1992 47 4305








York 1994










gas AIChE J 1998 44 1325

17






Technol 2000 39 51


Technol 2000 20 185



















8084

18

















19


Ref Mass

balance

Heat

balance

Momentum

balance

Isotherm

adsorbent

No of

steps

No of

layers Application







study


experimental study


(43) LDF Bulk gas

solids -


5 1 H2 CO H2 CO2



(54) DG LDF -DG

LDF-DGSD

LDF-DGSD

- - Langmuir 4A 5A





13X 4 1 CO2 capture






Ref Mass

balance

Heat

balance

Momentum

balance

Isotherm

adsorbent

No of

beds

No of

steps

Bed

interactions

No of

layers Application






Dual-site

Langmuir

13X


ads Air separation




AC+5A

2 7 - 2 H2 CH4 CO

N2 CO2



20


Ref Mass

balance Heat

balance

Momentum

balance

Isotherm adsorbent

No of beds

No of steps

Bed interactions

No of layers

Application



N2



AC+5A 4 8


information


2 H2 CO2 CH4

CO


Langmuir

Alumina+ AC+zeolite

6 12

Information


inert +

2 ads H2 CH4 CO


gel 9 10

9 11 6+7

- -

Overview of




Dual-site

Langmuir APHP+5A


CO H2


13X 2 3 4 6 - 1

CO2 from flue

gases


21


Recovery Purity

No Exp18

Model18

This

work Exp

18 Model

18

This

work

1 644 638 696 9975 10000 9931

2 816 864 850 9955 9989 9892

3 1065 1092 994 9900 9909 9855

4 1239 1215 1130 9835 9859 9815

5 707 825 852 9960 9988 9895

6 941 985 995 9885 9941 9854

7 1167 1172 1072 9830 9877 9833

8 1299 1213 1141 9780 9849 9811

9 2584 1702 2123 9080 9539 9447

10 2136 1609 2121 9070 9623 9475

11 2274 1550 2120 9140 9618 9478

12 2218 2274 2108 9120 9602 9477

13 939 835 845 9825 9970 9974

14 740 632 785 9890 9982 9991

15 510 500 738 9900 9988 9997

16 919 859 982 9845 9963 9960

17 707 762 856 9850 9976 9979

18 643 699 742 9870 9983 9989

19 541 613 612 9880 9993 9996

20 1151 1244 1128 9795 9871 9825

21 972 967 943 9850 9942 9940

22 674 659 726 9885 9979 9991

23 337 408 546 9900 9996 9999

24 1663 1433 1086 9585 9747 9869

25 1076 1155 962 9680 9872 9957

26 857 847 881 9730 9915 9984

27 826 721 844 9765 9910 9991

28 735 856 1135 9875 9987 9822

29 1195 1427 1117 9770 9792 9831

30 1330 1607 1120 9700 9657 9824

31 4156 3764 2638 8230 8227 8923

32 2246 1607 1511 9370 9497 9670

33 1254 800 899 9820 10000 9906

34 1383 1309 986 9380 9445 9606

35 2305 1673 1425 9370 9758 9775

42 2240 1646 2051 8900 9440 9496

43 2237 1615 2006 8230 8972 9012

22













Bed length 10 m















(wall) 13807 W(m

2K)


coefficient 1e-3 m

2s


coefficient 1e-3 m

2s


Comp a1 x10

3

(molg) a2

(K) b1 x10

9

(Pa-1

) b2

(K) -∆Hads (Jmol)

H2 432 000 5040 8505 786173

CO 092 052 5896 17309 1667742

CH4 -170 198 19952 14467 1875269

CO2 -1420 663 24775 14966 2557261






23























24



1 4 8 12

spPressCoC 01000 0060 0030 00500

spAdsIn 03600 03600 03600 03600

spAdsOut 00035 00015 00015 00015

spBlow 08000 05000 02500 04000

spPurgeIn 02250 02250 02250 02250

spPurgeOut 00300 00300 0030 00300

spPEQ1 - 00040 00025 00030

spPEQ2 - - 00050 00040

spPEQ3 - - - 00080

Feed

flowrate m3s

360e-6 360e-6 360e-6 360e-6

Purge

flowrate m3s

225e-6 225e-6 225e-6 225e-6

τPress s 10 10 20 10

τAds s 20 20 20 20

τBlow s 10 10 20 10

τPurge s 20 20 20 20

τPEQ1 s - 10 20 10

τPEQ2 s - - 20 10

τPEQ3 s - - - 10

τcycle s 60 80 160 120


No

beds

O2 purity

()

O2 recovery

()

Power

(W)

Productivity

(molkgs)

1 9687 3440 52902 918e-2

4 9950 5806 27949 485e-2

8 9958 6887 11987 208e-2

12 9936 7250 13936 242e-2

25



1 4 8 12

spPressCoC 00300 00450 00500 00500

spAdsIn 01200 01300 03300 03600

spAdsOut 00004 000035 00014 00015

spBlow 02000 02200 03000 04000

spPurgeIn 05625 01500 03000 02250

spPurgeOut 00075 00200 00400 00300

spPEQ1 - 00025 00020 00300

spPEQ2 - - 00040 00040

spPEQ3 - - - 00080

Feed flowrate m

3s

120e-6 130e-6 330e-6 360e-6

Purge

flowrate m3s

075e-6 115e-6 300e-6 225e-6

τPress s 20 15 15 10

τAds s 40 30 15 20

τBlow s 20 15 15 10

τPurge s 40 30 15 20

τPEQ1 s - 15 15 10

τPEQ2 s - - 15 10

τPEQ3 s - - - 10

τcycle s 120 120 120 120


No

beds

O2 purity

()

O2 recovery

()

Power

(W)

Productivity

(molkgs)

1 9811 2021 14420 250e-2

4 9929 3840 14069 244e-2

8 9979 6525 14092 245e-2

12 9936 7250 13936 242e-2

26



1 4 8 12

spPressCC 00030 00030 00500 00040

spAdsIn 04000 03333 03450 05000

spAdsOut 000088 000085 00015 00014

spBlow 02500 04000 03000 04000

spPurgeIn 00900 01333 03000 02000

spPurgeOut 00140 00200 00400 00300

spPEQ1 - 00050 00020 00030

spPEQ2 - - 00040 00040

spPEQ3 - - - 00080

Feed flowrate m

3s

400e-6 333e-6 345e-6 500e-6

Purge

flowrate m3s

090e-6 133e-6 300e-6 200e-6

τPress s 20 15 15 10

τAds s 40 30 15 20

τBlow s 20 15 15 10

τPurge s 40 30 15 20

τPEQ1 s - 15 15 10

τPEQ2 s - - 15 10

τPEQ3 s - - - 10

τcycle s 120 120 120 120


No beds

O2 purity ()

O2 recovery ()

Power (W)


1 9987 141 18878 203e-2

4 9997 2847 11808 205e-2

8 9997 5058 11938 207e-2

12 9983 6516 11909 207e-2

27




( )( )

( )

1

0 1


comp

uC C CN D

z t z z

z L i N


part part part part


(A1)


particle surface)



( ) ( )( ) ( )

( )

31

0


bed

bed z

c Tc uT kq T T

z t R

Tz L

z z


part part


part part

(A3)





Pf u R z L

z


part (A5)


coefficient ( )

0 1 f i p

compm i





λ (A7)


( )

0 1 z i bed

compm i

Df Sc Re z L i N

D




= forall isin λ

(A9)




Cu C C D z z L i N

z

partminus = = = =

parthellip (A12)

0 or inT T z z L= = = (A13)


0 0 and u

z z Lz

part= = =

part (A14)

0 0 or 1 icomp

Cz z L i N

z

part= = = =



end 0 0 or

Tz z L

z

part= = =

part (A16)

28


Model Equation



[ ] 0 0 1 p





( )

0 1 p i ii p comp

Q CN z L i N

t t


part parthellip

(A19)



(A20)


( ) [ ]

2

15 0 0 1

e iii i p comp

p

DQQ Q r R z L i N

t R


hellip (A21) LDF


( ) 0 1 p i i

i p comp

Q CN z L i N

t t


part parthellip

(A22)


) [ ]0 0 0 1 p




( ) [ ]22

1 0 0 1 i i

p s i p comp

p

Q QR D r R z L i N

t r rR



(A24)


( ) ( )3

0 1 p

f pi i r R compi

p

kN C C z L i N


(A25)



Qk C C D r R i N

r= =

partminus = = =

part (A26)

SD

0 0 0 1 icomp

Qr z L i N

r


parthellip (A27)


( ) ( ) [ ]

22

11 0 0 1

p ppi i i

p p p p e i p comp

p

C CQR D r R z L i N

t t r rR



(A28)




( ) ( )3

0 1 p

f pi i r R compi

p

kN C C z L i N


(A30)



Qk C C D r R i N

r= =

partminus = = =

part (A31)

PD

0 0 0 1 p

icomp

Cr z L i N

r


parthellip (A32)

29


Mode Equation

( )0 0 T

z Lz

part= forall isin

part (A33)




(A34)


( ) ( )( ) ( )3

0 bed pbed p h wall

g wall bed zbed


z t R z z


part part part part

(A35)




(A36)

LEQ



( )( ) ( )

0 comp

p p Np p pg p pg

p ig ads i

i

c c TQ

q H z Lt t


part partsum

(A37)




(A38)

LDF



( )( ) ( )

0 comp

p p Np p pg p pg

p ig ads i

i

c c TQ

q H z Lt t


part partsum

(A39)



0 0 p


(A40)

SD



( )( ) ( ) 0

compp p N

p i Rppg ads i

i

c T Qq H z L

t t


part partsum

(A41)


( ) ( )3

0 p

phg R

p

kq T T z L


(A42)


( )( ) ( )

2

2

1 0 0

p p ppp p pg p pg

p pg p p

p

c c TT

q R r R z Lt r rR


(A43)


( ) ( )

0 compN

p p ig ads i p

i

Qq H r R

t


partsum

(A44)

( ) p p

pp p

h r R r R p

Tk T T r R

r= =

partminus = λ =

part

(A45)

Nonisothermal

PD

model

Boundary conditions

0 0p

Tr

r

part= =

part (A46)


( )3 h wallwall

bed

kT T

Rminus

is neglected

30



( )

( )( )

2

2 3

180 1 0

2

bg bed

bedp

uPz L

z R


part ε (A47)


( )

( )( )

2

2 3

180 1 0

2

bg bed

bedp

uPz L

z R


part ε (A48)

Linear (Henry type)


(A49)

Extended Langmuir

2 2 1 1 exp 0 1

1


j j

j


b P T T


+ sumhellip (A50)


( )0

0

0

1 0 1 iP


QdP Q b P z L i N


(A51a)


(A51b

)

2 2 1 1 exp 0 1

1


i i


b P T T


hellip (A51c)


)


1 0 1 i

comp

itotal pure i

Xz L i N




31


Variable Equation


Wakao correlation23

( ) 033 06 20 11 0 1

m if i comp

p

Dk Sc Re z L i N



coefficient

Wakao correlation24

( )033 0620 11 Re 0 hp

k Pr z LR

λ= + forall isin

(A53)


coefficient

Wakao correlation23

( ) 20 05 0 1

m iz i comp

bed


εhellip

(A54)


coefficient

Wakao correlation24



3

3 2

12 12

1

18583 10 0 0 1 2im i p

TMW

D z L r R iP


(A56)


2

7 175 2

12

1

1013 10 0 0 1 2im i p

MWD T z L r R i

PX


Knudsen diffusivity


3 97 10 0 0 1 k i pore p comp

i

TD R z L r R i N


(A58)


0 0 1 p m i k i

e i p compp m i k i

D DD z L r R i N

D D


hellip (A59)



2

1

1

out

inv in comp

i i

P

PF C SP P i N

x MW T

minus = = hellip

sum (A60)

Molar flowrate

Otherwise ( )

21

1

critv in comp

i i

PF C SP P i N

x MW T

minus= = hellip

sum (A61)


1critP

κ

minusκ =

+ κ (A62)

Power

1

11

feed feedfeed

low cycle

P NPower RT

P

κminus

κ κ

= minus κ minus τ

(A63)

32


33


34



35



3


































and Jiang et al14

4

































5
















22 Gas valve model



Appendix A











shown in Figure 2


6













3 Model validation


The first




















7












Shin and Knaebel18




theoretical and







Shin and Knaebel18

4 Case studies













8

























Simulation Run I









9








Simulation Run II












Simulation Run III











10





5 Conclusions













and capital costs





Acknowledgements




Nomenclature




11





3




Cv = valve constant













L = bed length m



12

Q




Rbed = bed radius m




P = pressure Pa












3





13









References












1998 4 113



14






2000 35 667


2000 6 179




















15





325










AIChE J 1987 33 1045



Eng 1987 65 512










16




141






1992 47 4305








York 1994










gas AIChE J 1998 44 1325

17






Technol 2000 39 51


Technol 2000 20 185



















8084

18

















19


Ref Mass

balance

Heat

balance

Momentum

balance

Isotherm

adsorbent

No of

steps

No of

layers Application







study


experimental study


(43) LDF Bulk gas

solids -


5 1 H2 CO H2 CO2



(54) DG LDF -DG

LDF-DGSD

LDF-DGSD

- - Langmuir 4A 5A





13X 4 1 CO2 capture






Ref Mass

balance

Heat

balance

Momentum

balance

Isotherm

adsorbent

No of

beds

No of

steps

Bed

interactions

No of

layers Application






Dual-site

Langmuir

13X


ads Air separation




AC+5A

2 7 - 2 H2 CH4 CO

N2 CO2



20


Ref Mass

balance Heat

balance

Momentum

balance

Isotherm adsorbent

No of beds

No of steps

Bed interactions

No of layers

Application



N2



AC+5A 4 8


information


2 H2 CO2 CH4

CO


Langmuir

Alumina+ AC+zeolite

6 12

Information


inert +

2 ads H2 CH4 CO


gel 9 10

9 11 6+7

- -

Overview of




Dual-site

Langmuir APHP+5A


CO H2


13X 2 3 4 6 - 1

CO2 from flue

gases


21


Recovery Purity

No Exp18

Model18

This

work Exp

18 Model

18

This

work

1 644 638 696 9975 10000 9931

2 816 864 850 9955 9989 9892

3 1065 1092 994 9900 9909 9855

4 1239 1215 1130 9835 9859 9815

5 707 825 852 9960 9988 9895

6 941 985 995 9885 9941 9854

7 1167 1172 1072 9830 9877 9833

8 1299 1213 1141 9780 9849 9811

9 2584 1702 2123 9080 9539 9447

10 2136 1609 2121 9070 9623 9475

11 2274 1550 2120 9140 9618 9478

12 2218 2274 2108 9120 9602 9477

13 939 835 845 9825 9970 9974

14 740 632 785 9890 9982 9991

15 510 500 738 9900 9988 9997

16 919 859 982 9845 9963 9960

17 707 762 856 9850 9976 9979

18 643 699 742 9870 9983 9989

19 541 613 612 9880 9993 9996

20 1151 1244 1128 9795 9871 9825

21 972 967 943 9850 9942 9940

22 674 659 726 9885 9979 9991

23 337 408 546 9900 9996 9999

24 1663 1433 1086 9585 9747 9869

25 1076 1155 962 9680 9872 9957

26 857 847 881 9730 9915 9984

27 826 721 844 9765 9910 9991

28 735 856 1135 9875 9987 9822

29 1195 1427 1117 9770 9792 9831

30 1330 1607 1120 9700 9657 9824

31 4156 3764 2638 8230 8227 8923

32 2246 1607 1511 9370 9497 9670

33 1254 800 899 9820 10000 9906

34 1383 1309 986 9380 9445 9606

35 2305 1673 1425 9370 9758 9775

42 2240 1646 2051 8900 9440 9496

43 2237 1615 2006 8230 8972 9012

22













Bed length 10 m















(wall) 13807 W(m

2K)


coefficient 1e-3 m

2s


coefficient 1e-3 m

2s


Comp a1 x10

3

(molg) a2

(K) b1 x10

9

(Pa-1

) b2

(K) -∆Hads (Jmol)

H2 432 000 5040 8505 786173

CO 092 052 5896 17309 1667742

CH4 -170 198 19952 14467 1875269

CO2 -1420 663 24775 14966 2557261






23























24



1 4 8 12

spPressCoC 01000 0060 0030 00500

spAdsIn 03600 03600 03600 03600

spAdsOut 00035 00015 00015 00015

spBlow 08000 05000 02500 04000

spPurgeIn 02250 02250 02250 02250

spPurgeOut 00300 00300 0030 00300

spPEQ1 - 00040 00025 00030

spPEQ2 - - 00050 00040

spPEQ3 - - - 00080

Feed

flowrate m3s

360e-6 360e-6 360e-6 360e-6

Purge

flowrate m3s

225e-6 225e-6 225e-6 225e-6

τPress s 10 10 20 10

τAds s 20 20 20 20

τBlow s 10 10 20 10

τPurge s 20 20 20 20

τPEQ1 s - 10 20 10

τPEQ2 s - - 20 10

τPEQ3 s - - - 10

τcycle s 60 80 160 120


No

beds

O2 purity

()

O2 recovery

()

Power

(W)

Productivity

(molkgs)

1 9687 3440 52902 918e-2

4 9950 5806 27949 485e-2

8 9958 6887 11987 208e-2

12 9936 7250 13936 242e-2

25



1 4 8 12

spPressCoC 00300 00450 00500 00500

spAdsIn 01200 01300 03300 03600

spAdsOut 00004 000035 00014 00015

spBlow 02000 02200 03000 04000

spPurgeIn 05625 01500 03000 02250

spPurgeOut 00075 00200 00400 00300

spPEQ1 - 00025 00020 00300

spPEQ2 - - 00040 00040

spPEQ3 - - - 00080

Feed flowrate m

3s

120e-6 130e-6 330e-6 360e-6

Purge

flowrate m3s

075e-6 115e-6 300e-6 225e-6

τPress s 20 15 15 10

τAds s 40 30 15 20

τBlow s 20 15 15 10

τPurge s 40 30 15 20

τPEQ1 s - 15 15 10

τPEQ2 s - - 15 10

τPEQ3 s - - - 10

τcycle s 120 120 120 120


No

beds

O2 purity

()

O2 recovery

()

Power

(W)

Productivity

(molkgs)

1 9811 2021 14420 250e-2

4 9929 3840 14069 244e-2

8 9979 6525 14092 245e-2

12 9936 7250 13936 242e-2

26



1 4 8 12

spPressCC 00030 00030 00500 00040

spAdsIn 04000 03333 03450 05000

spAdsOut 000088 000085 00015 00014

spBlow 02500 04000 03000 04000

spPurgeIn 00900 01333 03000 02000

spPurgeOut 00140 00200 00400 00300

spPEQ1 - 00050 00020 00030

spPEQ2 - - 00040 00040

spPEQ3 - - - 00080

Feed flowrate m

3s

400e-6 333e-6 345e-6 500e-6

Purge

flowrate m3s

090e-6 133e-6 300e-6 200e-6

τPress s 20 15 15 10

τAds s 40 30 15 20

τBlow s 20 15 15 10

τPurge s 40 30 15 20

τPEQ1 s - 15 15 10

τPEQ2 s - - 15 10

τPEQ3 s - - - 10

τcycle s 120 120 120 120


No beds

O2 purity ()

O2 recovery ()

Power (W)


1 9987 141 18878 203e-2

4 9997 2847 11808 205e-2

8 9997 5058 11938 207e-2

12 9983 6516 11909 207e-2

27




( )( )

( )

1

0 1


comp

uC C CN D

z t z z

z L i N


part part part part


(A1)


particle surface)



( ) ( )( ) ( )

( )

31

0


bed

bed z

c Tc uT kq T T

z t R

Tz L

z z


part part


part part

(A3)





Pf u R z L

z


part (A5)


coefficient ( )

0 1 f i p

compm i





λ (A7)


( )

0 1 z i bed

compm i

Df Sc Re z L i N

D




= forall isin λ

(A9)




Cu C C D z z L i N

z

partminus = = = =

parthellip (A12)

0 or inT T z z L= = = (A13)


0 0 and u

z z Lz

part= = =

part (A14)

0 0 or 1 icomp

Cz z L i N

z

part= = = =



end 0 0 or

Tz z L

z

part= = =

part (A16)

28


Model Equation



[ ] 0 0 1 p





( )

0 1 p i ii p comp

Q CN z L i N

t t


part parthellip

(A19)



(A20)


( ) [ ]

2

15 0 0 1

e iii i p comp

p

DQQ Q r R z L i N

t R


hellip (A21) LDF


( ) 0 1 p i i

i p comp

Q CN z L i N

t t


part parthellip

(A22)


) [ ]0 0 0 1 p




( ) [ ]22

1 0 0 1 i i

p s i p comp

p

Q QR D r R z L i N

t r rR



(A24)


( ) ( )3

0 1 p

f pi i r R compi

p

kN C C z L i N


(A25)



Qk C C D r R i N

r= =

partminus = = =

part (A26)

SD

0 0 0 1 icomp

Qr z L i N

r


parthellip (A27)


( ) ( ) [ ]

22

11 0 0 1

p ppi i i

p p p p e i p comp

p

C CQR D r R z L i N

t t r rR



(A28)




( ) ( )3

0 1 p

f pi i r R compi

p

kN C C z L i N


(A30)



Qk C C D r R i N

r= =

partminus = = =

part (A31)

PD

0 0 0 1 p

icomp

Cr z L i N

r


parthellip (A32)

29


Mode Equation

( )0 0 T

z Lz

part= forall isin

part (A33)




(A34)


( ) ( )( ) ( )3

0 bed pbed p h wall

g wall bed zbed


z t R z z


part part part part

(A35)




(A36)

LEQ



( )( ) ( )

0 comp

p p Np p pg p pg

p ig ads i

i

c c TQ

q H z Lt t


part partsum

(A37)




(A38)

LDF



( )( ) ( )

0 comp

p p Np p pg p pg

p ig ads i

i

c c TQ

q H z Lt t


part partsum

(A39)



0 0 p


(A40)

SD



( )( ) ( ) 0

compp p N

p i Rppg ads i

i

c T Qq H z L

t t


part partsum

(A41)


( ) ( )3

0 p

phg R

p

kq T T z L


(A42)


( )( ) ( )

2

2

1 0 0

p p ppp p pg p pg

p pg p p

p

c c TT

q R r R z Lt r rR


(A43)


( ) ( )

0 compN

p p ig ads i p

i

Qq H r R

t


partsum

(A44)

( ) p p

pp p

h r R r R p

Tk T T r R

r= =

partminus = λ =

part

(A45)

Nonisothermal

PD

model

Boundary conditions

0 0p

Tr

r

part= =

part (A46)


( )3 h wallwall

bed

kT T

Rminus

is neglected

30



( )

( )( )

2

2 3

180 1 0

2

bg bed

bedp

uPz L

z R


part ε (A47)


( )

( )( )

2

2 3

180 1 0

2

bg bed

bedp

uPz L

z R


part ε (A48)

Linear (Henry type)


(A49)

Extended Langmuir

2 2 1 1 exp 0 1

1


j j

j


b P T T


+ sumhellip (A50)


( )0

0

0

1 0 1 iP


QdP Q b P z L i N


(A51a)


(A51b

)

2 2 1 1 exp 0 1

1


i i


b P T T


hellip (A51c)


)


1 0 1 i

comp

itotal pure i

Xz L i N




31


Variable Equation


Wakao correlation23

( ) 033 06 20 11 0 1

m if i comp

p

Dk Sc Re z L i N



coefficient

Wakao correlation24

( )033 0620 11 Re 0 hp

k Pr z LR

λ= + forall isin

(A53)


coefficient

Wakao correlation23

( ) 20 05 0 1

m iz i comp

bed


εhellip

(A54)


coefficient

Wakao correlation24



3

3 2

12 12

1

18583 10 0 0 1 2im i p

TMW

D z L r R iP


(A56)


2

7 175 2

12

1

1013 10 0 0 1 2im i p

MWD T z L r R i

PX


Knudsen diffusivity


3 97 10 0 0 1 k i pore p comp

i

TD R z L r R i N


(A58)


0 0 1 p m i k i

e i p compp m i k i

D DD z L r R i N

D D


hellip (A59)



2

1

1

out

inv in comp

i i

P

PF C SP P i N

x MW T

minus = = hellip

sum (A60)

Molar flowrate

Otherwise ( )

21

1

critv in comp

i i

PF C SP P i N

x MW T

minus= = hellip

sum (A61)


1critP

κ

minusκ =

+ κ (A62)

Power

1

11

feed feedfeed

low cycle

P NPower RT

P

κminus

κ κ

= minus κ minus τ

(A63)

32


33


34



35



4

































5
















22 Gas valve model



Appendix A











shown in Figure 2


6













3 Model validation


The first




















7












Shin and Knaebel18




theoretical and







Shin and Knaebel18

4 Case studies













8

























Simulation Run I









9








Simulation Run II












Simulation Run III











10





5 Conclusions













and capital costs





Acknowledgements




Nomenclature




11





3




Cv = valve constant













L = bed length m



12

Q




Rbed = bed radius m




P = pressure Pa












3





13









References












1998 4 113



14






2000 35 667


2000 6 179




















15





325










AIChE J 1987 33 1045



Eng 1987 65 512










16




141






1992 47 4305








York 1994










gas AIChE J 1998 44 1325

17






Technol 2000 39 51


Technol 2000 20 185



















8084

18

















19


Ref Mass

balance

Heat

balance

Momentum

balance

Isotherm

adsorbent

No of

steps

No of

layers Application







study


experimental study


(43) LDF Bulk gas

solids -


5 1 H2 CO H2 CO2



(54) DG LDF -DG

LDF-DGSD

LDF-DGSD

- - Langmuir 4A 5A





13X 4 1 CO2 capture






Ref Mass

balance

Heat

balance

Momentum

balance

Isotherm

adsorbent

No of

beds

No of

steps

Bed

interactions

No of

layers Application






Dual-site

Langmuir

13X


ads Air separation




AC+5A

2 7 - 2 H2 CH4 CO

N2 CO2



20


Ref Mass

balance Heat

balance

Momentum

balance

Isotherm adsorbent

No of beds

No of steps

Bed interactions

No of layers

Application



N2



AC+5A 4 8


information


2 H2 CO2 CH4

CO


Langmuir

Alumina+ AC+zeolite

6 12

Information


inert +

2 ads H2 CH4 CO


gel 9 10

9 11 6+7

- -

Overview of




Dual-site

Langmuir APHP+5A


CO H2


13X 2 3 4 6 - 1

CO2 from flue

gases


21


Recovery Purity

No Exp18

Model18

This

work Exp

18 Model

18

This

work

1 644 638 696 9975 10000 9931

2 816 864 850 9955 9989 9892

3 1065 1092 994 9900 9909 9855

4 1239 1215 1130 9835 9859 9815

5 707 825 852 9960 9988 9895

6 941 985 995 9885 9941 9854

7 1167 1172 1072 9830 9877 9833

8 1299 1213 1141 9780 9849 9811

9 2584 1702 2123 9080 9539 9447

10 2136 1609 2121 9070 9623 9475

11 2274 1550 2120 9140 9618 9478

12 2218 2274 2108 9120 9602 9477

13 939 835 845 9825 9970 9974

14 740 632 785 9890 9982 9991

15 510 500 738 9900 9988 9997

16 919 859 982 9845 9963 9960

17 707 762 856 9850 9976 9979

18 643 699 742 9870 9983 9989

19 541 613 612 9880 9993 9996

20 1151 1244 1128 9795 9871 9825

21 972 967 943 9850 9942 9940

22 674 659 726 9885 9979 9991

23 337 408 546 9900 9996 9999

24 1663 1433 1086 9585 9747 9869

25 1076 1155 962 9680 9872 9957

26 857 847 881 9730 9915 9984

27 826 721 844 9765 9910 9991

28 735 856 1135 9875 9987 9822

29 1195 1427 1117 9770 9792 9831

30 1330 1607 1120 9700 9657 9824

31 4156 3764 2638 8230 8227 8923

32 2246 1607 1511 9370 9497 9670

33 1254 800 899 9820 10000 9906

34 1383 1309 986 9380 9445 9606

35 2305 1673 1425 9370 9758 9775

42 2240 1646 2051 8900 9440 9496

43 2237 1615 2006 8230 8972 9012

22













Bed length 10 m















(wall) 13807 W(m

2K)


coefficient 1e-3 m

2s


coefficient 1e-3 m

2s


Comp a1 x10

3

(molg) a2

(K) b1 x10

9

(Pa-1

) b2

(K) -∆Hads (Jmol)

H2 432 000 5040 8505 786173

CO 092 052 5896 17309 1667742

CH4 -170 198 19952 14467 1875269

CO2 -1420 663 24775 14966 2557261






23























24



1 4 8 12

spPressCoC 01000 0060 0030 00500

spAdsIn 03600 03600 03600 03600

spAdsOut 00035 00015 00015 00015

spBlow 08000 05000 02500 04000

spPurgeIn 02250 02250 02250 02250

spPurgeOut 00300 00300 0030 00300

spPEQ1 - 00040 00025 00030

spPEQ2 - - 00050 00040

spPEQ3 - - - 00080

Feed

flowrate m3s

360e-6 360e-6 360e-6 360e-6

Purge

flowrate m3s

225e-6 225e-6 225e-6 225e-6

τPress s 10 10 20 10

τAds s 20 20 20 20

τBlow s 10 10 20 10

τPurge s 20 20 20 20

τPEQ1 s - 10 20 10

τPEQ2 s - - 20 10

τPEQ3 s - - - 10

τcycle s 60 80 160 120


No

beds

O2 purity

()

O2 recovery

()

Power

(W)

Productivity

(molkgs)

1 9687 3440 52902 918e-2

4 9950 5806 27949 485e-2

8 9958 6887 11987 208e-2

12 9936 7250 13936 242e-2

25



1 4 8 12

spPressCoC 00300 00450 00500 00500

spAdsIn 01200 01300 03300 03600

spAdsOut 00004 000035 00014 00015

spBlow 02000 02200 03000 04000

spPurgeIn 05625 01500 03000 02250

spPurgeOut 00075 00200 00400 00300

spPEQ1 - 00025 00020 00300

spPEQ2 - - 00040 00040

spPEQ3 - - - 00080

Feed flowrate m

3s

120e-6 130e-6 330e-6 360e-6

Purge

flowrate m3s

075e-6 115e-6 300e-6 225e-6

τPress s 20 15 15 10

τAds s 40 30 15 20

τBlow s 20 15 15 10

τPurge s 40 30 15 20

τPEQ1 s - 15 15 10

τPEQ2 s - - 15 10

τPEQ3 s - - - 10

τcycle s 120 120 120 120


No

beds

O2 purity

()

O2 recovery

()

Power

(W)

Productivity

(molkgs)

1 9811 2021 14420 250e-2

4 9929 3840 14069 244e-2

8 9979 6525 14092 245e-2

12 9936 7250 13936 242e-2

26



1 4 8 12

spPressCC 00030 00030 00500 00040

spAdsIn 04000 03333 03450 05000

spAdsOut 000088 000085 00015 00014

spBlow 02500 04000 03000 04000

spPurgeIn 00900 01333 03000 02000

spPurgeOut 00140 00200 00400 00300

spPEQ1 - 00050 00020 00030

spPEQ2 - - 00040 00040

spPEQ3 - - - 00080

Feed flowrate m

3s

400e-6 333e-6 345e-6 500e-6

Purge

flowrate m3s

090e-6 133e-6 300e-6 200e-6

τPress s 20 15 15 10

τAds s 40 30 15 20

τBlow s 20 15 15 10

τPurge s 40 30 15 20

τPEQ1 s - 15 15 10

τPEQ2 s - - 15 10

τPEQ3 s - - - 10

τcycle s 120 120 120 120


No beds

O2 purity ()

O2 recovery ()

Power (W)


1 9987 141 18878 203e-2

4 9997 2847 11808 205e-2

8 9997 5058 11938 207e-2

12 9983 6516 11909 207e-2

27




( )( )

( )

1

0 1


comp

uC C CN D

z t z z

z L i N


part part part part


(A1)


particle surface)



( ) ( )( ) ( )

( )

31

0


bed

bed z

c Tc uT kq T T

z t R

Tz L

z z


part part


part part

(A3)





Pf u R z L

z


part (A5)


coefficient ( )

0 1 f i p

compm i





λ (A7)


( )

0 1 z i bed

compm i

Df Sc Re z L i N

D




= forall isin λ

(A9)




Cu C C D z z L i N

z

partminus = = = =

parthellip (A12)

0 or inT T z z L= = = (A13)


0 0 and u

z z Lz

part= = =

part (A14)

0 0 or 1 icomp

Cz z L i N

z

part= = = =



end 0 0 or

Tz z L

z

part= = =

part (A16)

28


Model Equation



[ ] 0 0 1 p





( )

0 1 p i ii p comp

Q CN z L i N

t t


part parthellip

(A19)



(A20)


( ) [ ]

2

15 0 0 1

e iii i p comp

p

DQQ Q r R z L i N

t R


hellip (A21) LDF


( ) 0 1 p i i

i p comp

Q CN z L i N

t t


part parthellip

(A22)


) [ ]0 0 0 1 p




( ) [ ]22

1 0 0 1 i i

p s i p comp

p

Q QR D r R z L i N

t r rR



(A24)


( ) ( )3

0 1 p

f pi i r R compi

p

kN C C z L i N


(A25)



Qk C C D r R i N

r= =

partminus = = =

part (A26)

SD

0 0 0 1 icomp

Qr z L i N

r


parthellip (A27)


( ) ( ) [ ]

22

11 0 0 1

p ppi i i

p p p p e i p comp

p

C CQR D r R z L i N

t t r rR



(A28)




( ) ( )3

0 1 p

f pi i r R compi

p

kN C C z L i N


(A30)



Qk C C D r R i N

r= =

partminus = = =

part (A31)

PD

0 0 0 1 p

icomp

Cr z L i N

r


parthellip (A32)

29


Mode Equation

( )0 0 T

z Lz

part= forall isin

part (A33)




(A34)


( ) ( )( ) ( )3

0 bed pbed p h wall

g wall bed zbed


z t R z z


part part part part

(A35)




(A36)

LEQ



( )( ) ( )

0 comp

p p Np p pg p pg

p ig ads i

i

c c TQ

q H z Lt t


part partsum

(A37)




(A38)

LDF



( )( ) ( )

0 comp

p p Np p pg p pg

p ig ads i

i

c c TQ

q H z Lt t


part partsum

(A39)



0 0 p


(A40)

SD



( )( ) ( ) 0

compp p N

p i Rppg ads i

i

c T Qq H z L

t t


part partsum

(A41)


( ) ( )3

0 p

phg R

p

kq T T z L


(A42)


( )( ) ( )

2

2

1 0 0

p p ppp p pg p pg

p pg p p

p

c c TT

q R r R z Lt r rR


(A43)


( ) ( )

0 compN

p p ig ads i p

i

Qq H r R

t


partsum

(A44)

( ) p p

pp p

h r R r R p

Tk T T r R

r= =

partminus = λ =

part

(A45)

Nonisothermal

PD

model

Boundary conditions

0 0p

Tr

r

part= =

part (A46)


( )3 h wallwall

bed

kT T

Rminus

is neglected

30



( )

( )( )

2

2 3

180 1 0

2

bg bed

bedp

uPz L

z R


part ε (A47)


( )

( )( )

2

2 3

180 1 0

2

bg bed

bedp

uPz L

z R


part ε (A48)

Linear (Henry type)


(A49)

Extended Langmuir

2 2 1 1 exp 0 1

1


j j

j


b P T T


+ sumhellip (A50)


( )0

0

0

1 0 1 iP


QdP Q b P z L i N


(A51a)


(A51b

)

2 2 1 1 exp 0 1

1


i i


b P T T


hellip (A51c)


)


1 0 1 i

comp

itotal pure i

Xz L i N




31


Variable Equation


Wakao correlation23

( ) 033 06 20 11 0 1

m if i comp

p

Dk Sc Re z L i N



coefficient

Wakao correlation24

( )033 0620 11 Re 0 hp

k Pr z LR

λ= + forall isin

(A53)


coefficient

Wakao correlation23

( ) 20 05 0 1

m iz i comp

bed


εhellip

(A54)


coefficient

Wakao correlation24



3

3 2

12 12

1

18583 10 0 0 1 2im i p

TMW

D z L r R iP


(A56)


2

7 175 2

12

1

1013 10 0 0 1 2im i p

MWD T z L r R i

PX


Knudsen diffusivity


3 97 10 0 0 1 k i pore p comp

i

TD R z L r R i N


(A58)


0 0 1 p m i k i

e i p compp m i k i

D DD z L r R i N

D D


hellip (A59)



2

1

1

out

inv in comp

i i

P

PF C SP P i N

x MW T

minus = = hellip

sum (A60)

Molar flowrate

Otherwise ( )

21

1

critv in comp

i i

PF C SP P i N

x MW T

minus= = hellip

sum (A61)


1critP

κ

minusκ =

+ κ (A62)

Power

1

11

feed feedfeed

low cycle

P NPower RT

P

κminus

κ κ

= minus κ minus τ

(A63)

32


33


34



35



5
















22 Gas valve model



Appendix A











shown in Figure 2


6













3 Model validation


The first




















7












Shin and Knaebel18




theoretical and







Shin and Knaebel18

4 Case studies













8

























Simulation Run I









9








Simulation Run II












Simulation Run III











10





5 Conclusions













and capital costs





Acknowledgements




Nomenclature




11





3




Cv = valve constant













L = bed length m



12

Q




Rbed = bed radius m




P = pressure Pa












3





13









References












1998 4 113



14






2000 35 667


2000 6 179




















15





325










AIChE J 1987 33 1045



Eng 1987 65 512










16




141






1992 47 4305








York 1994










gas AIChE J 1998 44 1325

17






Technol 2000 39 51


Technol 2000 20 185



















8084

18

















19


Ref Mass

balance

Heat

balance

Momentum

balance

Isotherm

adsorbent

No of

steps

No of

layers Application







study


experimental study


(43) LDF Bulk gas

solids -


5 1 H2 CO H2 CO2



(54) DG LDF -DG

LDF-DGSD

LDF-DGSD

- - Langmuir 4A 5A





13X 4 1 CO2 capture






Ref Mass

balance

Heat

balance

Momentum

balance

Isotherm

adsorbent

No of

beds

No of

steps

Bed

interactions

No of

layers Application






Dual-site

Langmuir

13X


ads Air separation




AC+5A

2 7 - 2 H2 CH4 CO

N2 CO2



20


Ref Mass

balance Heat

balance

Momentum

balance

Isotherm adsorbent

No of beds

No of steps

Bed interactions

No of layers

Application



N2



AC+5A 4 8


information


2 H2 CO2 CH4

CO


Langmuir

Alumina+ AC+zeolite

6 12

Information


inert +

2 ads H2 CH4 CO


gel 9 10

9 11 6+7

- -

Overview of




Dual-site

Langmuir APHP+5A


CO H2


13X 2 3 4 6 - 1

CO2 from flue

gases


21


Recovery Purity

No Exp18

Model18

This

work Exp

18 Model

18

This

work

1 644 638 696 9975 10000 9931

2 816 864 850 9955 9989 9892

3 1065 1092 994 9900 9909 9855

4 1239 1215 1130 9835 9859 9815

5 707 825 852 9960 9988 9895

6 941 985 995 9885 9941 9854

7 1167 1172 1072 9830 9877 9833

8 1299 1213 1141 9780 9849 9811

9 2584 1702 2123 9080 9539 9447

10 2136 1609 2121 9070 9623 9475

11 2274 1550 2120 9140 9618 9478

12 2218 2274 2108 9120 9602 9477

13 939 835 845 9825 9970 9974

14 740 632 785 9890 9982 9991

15 510 500 738 9900 9988 9997

16 919 859 982 9845 9963 9960

17 707 762 856 9850 9976 9979

18 643 699 742 9870 9983 9989

19 541 613 612 9880 9993 9996

20 1151 1244 1128 9795 9871 9825

21 972 967 943 9850 9942 9940

22 674 659 726 9885 9979 9991

23 337 408 546 9900 9996 9999

24 1663 1433 1086 9585 9747 9869

25 1076 1155 962 9680 9872 9957

26 857 847 881 9730 9915 9984

27 826 721 844 9765 9910 9991

28 735 856 1135 9875 9987 9822

29 1195 1427 1117 9770 9792 9831

30 1330 1607 1120 9700 9657 9824

31 4156 3764 2638 8230 8227 8923

32 2246 1607 1511 9370 9497 9670

33 1254 800 899 9820 10000 9906

34 1383 1309 986 9380 9445 9606

35 2305 1673 1425 9370 9758 9775

42 2240 1646 2051 8900 9440 9496

43 2237 1615 2006 8230 8972 9012

22













Bed length 10 m















(wall) 13807 W(m

2K)


coefficient 1e-3 m

2s


coefficient 1e-3 m

2s


Comp a1 x10

3

(molg) a2

(K) b1 x10

9

(Pa-1

) b2

(K) -∆Hads (Jmol)

H2 432 000 5040 8505 786173

CO 092 052 5896 17309 1667742

CH4 -170 198 19952 14467 1875269

CO2 -1420 663 24775 14966 2557261






23























24



1 4 8 12

spPressCoC 01000 0060 0030 00500

spAdsIn 03600 03600 03600 03600

spAdsOut 00035 00015 00015 00015

spBlow 08000 05000 02500 04000

spPurgeIn 02250 02250 02250 02250

spPurgeOut 00300 00300 0030 00300

spPEQ1 - 00040 00025 00030

spPEQ2 - - 00050 00040

spPEQ3 - - - 00080

Feed

flowrate m3s

360e-6 360e-6 360e-6 360e-6

Purge

flowrate m3s

225e-6 225e-6 225e-6 225e-6

τPress s 10 10 20 10

τAds s 20 20 20 20

τBlow s 10 10 20 10

τPurge s 20 20 20 20

τPEQ1 s - 10 20 10

τPEQ2 s - - 20 10

τPEQ3 s - - - 10

τcycle s 60 80 160 120


No

beds

O2 purity

()

O2 recovery

()

Power

(W)

Productivity

(molkgs)

1 9687 3440 52902 918e-2

4 9950 5806 27949 485e-2

8 9958 6887 11987 208e-2

12 9936 7250 13936 242e-2

25



1 4 8 12

spPressCoC 00300 00450 00500 00500

spAdsIn 01200 01300 03300 03600

spAdsOut 00004 000035 00014 00015

spBlow 02000 02200 03000 04000

spPurgeIn 05625 01500 03000 02250

spPurgeOut 00075 00200 00400 00300

spPEQ1 - 00025 00020 00300

spPEQ2 - - 00040 00040

spPEQ3 - - - 00080

Feed flowrate m

3s

120e-6 130e-6 330e-6 360e-6

Purge

flowrate m3s

075e-6 115e-6 300e-6 225e-6

τPress s 20 15 15 10

τAds s 40 30 15 20

τBlow s 20 15 15 10

τPurge s 40 30 15 20

τPEQ1 s - 15 15 10

τPEQ2 s - - 15 10

τPEQ3 s - - - 10

τcycle s 120 120 120 120


No

beds

O2 purity

()

O2 recovery

()

Power

(W)

Productivity

(molkgs)

1 9811 2021 14420 250e-2

4 9929 3840 14069 244e-2

8 9979 6525 14092 245e-2

12 9936 7250 13936 242e-2

26



1 4 8 12

spPressCC 00030 00030 00500 00040

spAdsIn 04000 03333 03450 05000

spAdsOut 000088 000085 00015 00014

spBlow 02500 04000 03000 04000

spPurgeIn 00900 01333 03000 02000

spPurgeOut 00140 00200 00400 00300

spPEQ1 - 00050 00020 00030

spPEQ2 - - 00040 00040

spPEQ3 - - - 00080

Feed flowrate m

3s

400e-6 333e-6 345e-6 500e-6

Purge

flowrate m3s

090e-6 133e-6 300e-6 200e-6

τPress s 20 15 15 10

τAds s 40 30 15 20

τBlow s 20 15 15 10

τPurge s 40 30 15 20

τPEQ1 s - 15 15 10

τPEQ2 s - - 15 10

τPEQ3 s - - - 10

τcycle s 120 120 120 120


No beds

O2 purity ()

O2 recovery ()

Power (W)


1 9987 141 18878 203e-2

4 9997 2847 11808 205e-2

8 9997 5058 11938 207e-2

12 9983 6516 11909 207e-2

27




( )( )

( )

1

0 1


comp

uC C CN D

z t z z

z L i N


part part part part


(A1)


particle surface)



( ) ( )( ) ( )

( )

31

0


bed

bed z

c Tc uT kq T T

z t R

Tz L

z z


part part


part part

(A3)





Pf u R z L

z


part (A5)


coefficient ( )

0 1 f i p

compm i





λ (A7)


( )

0 1 z i bed

compm i

Df Sc Re z L i N

D




= forall isin λ

(A9)




Cu C C D z z L i N

z

partminus = = = =

parthellip (A12)

0 or inT T z z L= = = (A13)


0 0 and u

z z Lz

part= = =

part (A14)

0 0 or 1 icomp

Cz z L i N

z

part= = = =



end 0 0 or

Tz z L

z

part= = =

part (A16)

28


Model Equation



[ ] 0 0 1 p





( )

0 1 p i ii p comp

Q CN z L i N

t t


part parthellip

(A19)



(A20)


( ) [ ]

2

15 0 0 1

e iii i p comp

p

DQQ Q r R z L i N

t R


hellip (A21) LDF


( ) 0 1 p i i

i p comp

Q CN z L i N

t t


part parthellip

(A22)


) [ ]0 0 0 1 p




( ) [ ]22

1 0 0 1 i i

p s i p comp

p

Q QR D r R z L i N

t r rR



(A24)


( ) ( )3

0 1 p

f pi i r R compi

p

kN C C z L i N


(A25)



Qk C C D r R i N

r= =

partminus = = =

part (A26)

SD

0 0 0 1 icomp

Qr z L i N

r


parthellip (A27)


( ) ( ) [ ]

22

11 0 0 1

p ppi i i

p p p p e i p comp

p

C CQR D r R z L i N

t t r rR



(A28)




( ) ( )3

0 1 p

f pi i r R compi

p

kN C C z L i N


(A30)



Qk C C D r R i N

r= =

partminus = = =

part (A31)

PD

0 0 0 1 p

icomp

Cr z L i N

r


parthellip (A32)

29


Mode Equation

( )0 0 T

z Lz

part= forall isin

part (A33)




(A34)


( ) ( )( ) ( )3

0 bed pbed p h wall

g wall bed zbed


z t R z z


part part part part

(A35)




(A36)

LEQ



( )( ) ( )

0 comp

p p Np p pg p pg

p ig ads i

i

c c TQ

q H z Lt t


part partsum

(A37)




(A38)

LDF



( )( ) ( )

0 comp

p p Np p pg p pg

p ig ads i

i

c c TQ

q H z Lt t


part partsum

(A39)



0 0 p


(A40)

SD



( )( ) ( ) 0

compp p N

p i Rppg ads i

i

c T Qq H z L

t t


part partsum

(A41)


( ) ( )3

0 p

phg R

p

kq T T z L


(A42)


( )( ) ( )

2

2

1 0 0

p p ppp p pg p pg

p pg p p

p

c c TT

q R r R z Lt r rR


(A43)


( ) ( )

0 compN

p p ig ads i p

i

Qq H r R

t


partsum

(A44)

( ) p p

pp p

h r R r R p

Tk T T r R

r= =

partminus = λ =

part

(A45)

Nonisothermal

PD

model

Boundary conditions

0 0p

Tr

r

part= =

part (A46)


( )3 h wallwall

bed

kT T

Rminus

is neglected

30



( )

( )( )

2

2 3

180 1 0

2

bg bed

bedp

uPz L

z R


part ε (A47)


( )

( )( )

2

2 3

180 1 0

2

bg bed

bedp

uPz L

z R


part ε (A48)

Linear (Henry type)


(A49)

Extended Langmuir

2 2 1 1 exp 0 1

1


j j

j


b P T T


+ sumhellip (A50)


( )0

0

0

1 0 1 iP


QdP Q b P z L i N


(A51a)


(A51b

)

2 2 1 1 exp 0 1

1


i i


b P T T


hellip (A51c)


)


1 0 1 i

comp

itotal pure i

Xz L i N




31


Variable Equation


Wakao correlation23

( ) 033 06 20 11 0 1

m if i comp

p

Dk Sc Re z L i N



coefficient

Wakao correlation24

( )033 0620 11 Re 0 hp

k Pr z LR

λ= + forall isin

(A53)


coefficient

Wakao correlation23

( ) 20 05 0 1

m iz i comp

bed


εhellip

(A54)


coefficient

Wakao correlation24



3

3 2

12 12

1

18583 10 0 0 1 2im i p

TMW

D z L r R iP


(A56)


2

7 175 2

12

1

1013 10 0 0 1 2im i p

MWD T z L r R i

PX


Knudsen diffusivity


3 97 10 0 0 1 k i pore p comp

i

TD R z L r R i N


(A58)


0 0 1 p m i k i

e i p compp m i k i

D DD z L r R i N

D D


hellip (A59)



2

1

1

out

inv in comp

i i

P

PF C SP P i N

x MW T

minus = = hellip

sum (A60)

Molar flowrate

Otherwise ( )

21

1

critv in comp

i i

PF C SP P i N

x MW T

minus= = hellip

sum (A61)


1critP

κ

minusκ =

+ κ (A62)

Power

1

11

feed feedfeed

low cycle

P NPower RT

P

κminus

κ κ

= minus κ minus τ

(A63)

32


33


34



35



6













3 Model validation


The first




















7












Shin and Knaebel18




theoretical and







Shin and Knaebel18

4 Case studies













8

























Simulation Run I









9








Simulation Run II












Simulation Run III











10





5 Conclusions













and capital costs





Acknowledgements




Nomenclature




11





3




Cv = valve constant













L = bed length m



12

Q




Rbed = bed radius m




P = pressure Pa












3





13









References












1998 4 113



14






2000 35 667


2000 6 179




















15





325










AIChE J 1987 33 1045



Eng 1987 65 512










16




141






1992 47 4305








York 1994










gas AIChE J 1998 44 1325

17






Technol 2000 39 51


Technol 2000 20 185



















8084

18

















19


Ref Mass

balance

Heat

balance

Momentum

balance

Isotherm

adsorbent

No of

steps

No of

layers Application







study


experimental study


(43) LDF Bulk gas

solids -


5 1 H2 CO H2 CO2



(54) DG LDF -DG

LDF-DGSD

LDF-DGSD

- - Langmuir 4A 5A





13X 4 1 CO2 capture






Ref Mass

balance

Heat

balance

Momentum

balance

Isotherm

adsorbent

No of

beds

No of

steps

Bed

interactions

No of

layers Application






Dual-site

Langmuir

13X


ads Air separation




AC+5A

2 7 - 2 H2 CH4 CO

N2 CO2



20


Ref Mass

balance Heat

balance

Momentum

balance

Isotherm adsorbent

No of beds

No of steps

Bed interactions

No of layers

Application



N2



AC+5A 4 8


information


2 H2 CO2 CH4

CO


Langmuir

Alumina+ AC+zeolite

6 12

Information


inert +

2 ads H2 CH4 CO


gel 9 10

9 11 6+7

- -

Overview of




Dual-site

Langmuir APHP+5A


CO H2


13X 2 3 4 6 - 1

CO2 from flue

gases


21


Recovery Purity

No Exp18

Model18

This

work Exp

18 Model

18

This

work

1 644 638 696 9975 10000 9931

2 816 864 850 9955 9989 9892

3 1065 1092 994 9900 9909 9855

4 1239 1215 1130 9835 9859 9815

5 707 825 852 9960 9988 9895

6 941 985 995 9885 9941 9854

7 1167 1172 1072 9830 9877 9833

8 1299 1213 1141 9780 9849 9811

9 2584 1702 2123 9080 9539 9447

10 2136 1609 2121 9070 9623 9475

11 2274 1550 2120 9140 9618 9478

12 2218 2274 2108 9120 9602 9477

13 939 835 845 9825 9970 9974

14 740 632 785 9890 9982 9991

15 510 500 738 9900 9988 9997

16 919 859 982 9845 9963 9960

17 707 762 856 9850 9976 9979

18 643 699 742 9870 9983 9989

19 541 613 612 9880 9993 9996

20 1151 1244 1128 9795 9871 9825

21 972 967 943 9850 9942 9940

22 674 659 726 9885 9979 9991

23 337 408 546 9900 9996 9999

24 1663 1433 1086 9585 9747 9869

25 1076 1155 962 9680 9872 9957

26 857 847 881 9730 9915 9984

27 826 721 844 9765 9910 9991

28 735 856 1135 9875 9987 9822

29 1195 1427 1117 9770 9792 9831

30 1330 1607 1120 9700 9657 9824

31 4156 3764 2638 8230 8227 8923

32 2246 1607 1511 9370 9497 9670

33 1254 800 899 9820 10000 9906

34 1383 1309 986 9380 9445 9606

35 2305 1673 1425 9370 9758 9775

42 2240 1646 2051 8900 9440 9496

43 2237 1615 2006 8230 8972 9012

22













Bed length 10 m















(wall) 13807 W(m

2K)


coefficient 1e-3 m

2s


coefficient 1e-3 m

2s


Comp a1 x10

3

(molg) a2

(K) b1 x10

9

(Pa-1

) b2

(K) -∆Hads (Jmol)

H2 432 000 5040 8505 786173

CO 092 052 5896 17309 1667742

CH4 -170 198 19952 14467 1875269

CO2 -1420 663 24775 14966 2557261






23























24



1 4 8 12

spPressCoC 01000 0060 0030 00500

spAdsIn 03600 03600 03600 03600

spAdsOut 00035 00015 00015 00015

spBlow 08000 05000 02500 04000

spPurgeIn 02250 02250 02250 02250

spPurgeOut 00300 00300 0030 00300

spPEQ1 - 00040 00025 00030

spPEQ2 - - 00050 00040

spPEQ3 - - - 00080

Feed

flowrate m3s

360e-6 360e-6 360e-6 360e-6

Purge

flowrate m3s

225e-6 225e-6 225e-6 225e-6

τPress s 10 10 20 10

τAds s 20 20 20 20

τBlow s 10 10 20 10

τPurge s 20 20 20 20

τPEQ1 s - 10 20 10

τPEQ2 s - - 20 10

τPEQ3 s - - - 10

τcycle s 60 80 160 120


No

beds

O2 purity

()

O2 recovery

()

Power

(W)

Productivity

(molkgs)

1 9687 3440 52902 918e-2

4 9950 5806 27949 485e-2

8 9958 6887 11987 208e-2

12 9936 7250 13936 242e-2

25



1 4 8 12

spPressCoC 00300 00450 00500 00500

spAdsIn 01200 01300 03300 03600

spAdsOut 00004 000035 00014 00015

spBlow 02000 02200 03000 04000

spPurgeIn 05625 01500 03000 02250

spPurgeOut 00075 00200 00400 00300

spPEQ1 - 00025 00020 00300

spPEQ2 - - 00040 00040

spPEQ3 - - - 00080

Feed flowrate m

3s

120e-6 130e-6 330e-6 360e-6

Purge

flowrate m3s

075e-6 115e-6 300e-6 225e-6

τPress s 20 15 15 10

τAds s 40 30 15 20

τBlow s 20 15 15 10

τPurge s 40 30 15 20

τPEQ1 s - 15 15 10

τPEQ2 s - - 15 10

τPEQ3 s - - - 10

τcycle s 120 120 120 120


No

beds

O2 purity

()

O2 recovery

()

Power

(W)

Productivity

(molkgs)

1 9811 2021 14420 250e-2

4 9929 3840 14069 244e-2

8 9979 6525 14092 245e-2

12 9936 7250 13936 242e-2

26



1 4 8 12

spPressCC 00030 00030 00500 00040

spAdsIn 04000 03333 03450 05000

spAdsOut 000088 000085 00015 00014

spBlow 02500 04000 03000 04000

spPurgeIn 00900 01333 03000 02000

spPurgeOut 00140 00200 00400 00300

spPEQ1 - 00050 00020 00030

spPEQ2 - - 00040 00040

spPEQ3 - - - 00080

Feed flowrate m

3s

400e-6 333e-6 345e-6 500e-6

Purge

flowrate m3s

090e-6 133e-6 300e-6 200e-6

τPress s 20 15 15 10

τAds s 40 30 15 20

τBlow s 20 15 15 10

τPurge s 40 30 15 20

τPEQ1 s - 15 15 10

τPEQ2 s - - 15 10

τPEQ3 s - - - 10

τcycle s 120 120 120 120


No beds

O2 purity ()

O2 recovery ()

Power (W)


1 9987 141 18878 203e-2

4 9997 2847 11808 205e-2

8 9997 5058 11938 207e-2

12 9983 6516 11909 207e-2

27




( )( )

( )

1

0 1


comp

uC C CN D

z t z z

z L i N


part part part part


(A1)


particle surface)



( ) ( )( ) ( )

( )

31

0


bed

bed z

c Tc uT kq T T

z t R

Tz L

z z


part part


part part

(A3)





Pf u R z L

z


part (A5)


coefficient ( )

0 1 f i p

compm i





λ (A7)


( )

0 1 z i bed

compm i

Df Sc Re z L i N

D




= forall isin λ

(A9)




Cu C C D z z L i N

z

partminus = = = =

parthellip (A12)

0 or inT T z z L= = = (A13)


0 0 and u

z z Lz

part= = =

part (A14)

0 0 or 1 icomp

Cz z L i N

z

part= = = =



end 0 0 or

Tz z L

z

part= = =

part (A16)

28


Model Equation



[ ] 0 0 1 p





( )

0 1 p i ii p comp

Q CN z L i N

t t


part parthellip

(A19)



(A20)


( ) [ ]

2

15 0 0 1

e iii i p comp

p

DQQ Q r R z L i N

t R


hellip (A21) LDF


( ) 0 1 p i i

i p comp

Q CN z L i N

t t


part parthellip

(A22)


) [ ]0 0 0 1 p




( ) [ ]22

1 0 0 1 i i

p s i p comp

p

Q QR D r R z L i N

t r rR



(A24)


( ) ( )3

0 1 p

f pi i r R compi

p

kN C C z L i N


(A25)



Qk C C D r R i N

r= =

partminus = = =

part (A26)

SD

0 0 0 1 icomp

Qr z L i N

r


parthellip (A27)


( ) ( ) [ ]

22

11 0 0 1

p ppi i i

p p p p e i p comp

p

C CQR D r R z L i N

t t r rR



(A28)




( ) ( )3

0 1 p

f pi i r R compi

p

kN C C z L i N


(A30)



Qk C C D r R i N

r= =

partminus = = =

part (A31)

PD

0 0 0 1 p

icomp

Cr z L i N

r


parthellip (A32)

29


Mode Equation

( )0 0 T

z Lz

part= forall isin

part (A33)




(A34)


( ) ( )( ) ( )3

0 bed pbed p h wall

g wall bed zbed


z t R z z


part part part part

(A35)




(A36)

LEQ



( )( ) ( )

0 comp

p p Np p pg p pg

p ig ads i

i

c c TQ

q H z Lt t


part partsum

(A37)




(A38)

LDF



( )( ) ( )

0 comp

p p Np p pg p pg

p ig ads i

i

c c TQ

q H z Lt t


part partsum

(A39)



0 0 p


(A40)

SD



( )( ) ( ) 0

compp p N

p i Rppg ads i

i

c T Qq H z L

t t


part partsum

(A41)


( ) ( )3

0 p

phg R

p

kq T T z L


(A42)


( )( ) ( )

2

2

1 0 0

p p ppp p pg p pg

p pg p p

p

c c TT

q R r R z Lt r rR


(A43)


( ) ( )

0 compN

p p ig ads i p

i

Qq H r R

t


partsum

(A44)

( ) p p

pp p

h r R r R p

Tk T T r R

r= =

partminus = λ =

part

(A45)

Nonisothermal

PD

model

Boundary conditions

0 0p

Tr

r

part= =

part (A46)


( )3 h wallwall

bed

kT T

Rminus

is neglected

30



( )

( )( )

2

2 3

180 1 0

2

bg bed

bedp

uPz L

z R


part ε (A47)


( )

( )( )

2

2 3

180 1 0

2

bg bed

bedp

uPz L

z R


part ε (A48)

Linear (Henry type)


(A49)

Extended Langmuir

2 2 1 1 exp 0 1

1


j j

j


b P T T


+ sumhellip (A50)


( )0

0

0

1 0 1 iP


QdP Q b P z L i N


(A51a)


(A51b

)

2 2 1 1 exp 0 1

1


i i


b P T T


hellip (A51c)


)


1 0 1 i

comp

itotal pure i

Xz L i N




31


Variable Equation


Wakao correlation23

( ) 033 06 20 11 0 1

m if i comp

p

Dk Sc Re z L i N



coefficient

Wakao correlation24

( )033 0620 11 Re 0 hp

k Pr z LR

λ= + forall isin

(A53)


coefficient

Wakao correlation23

( ) 20 05 0 1

m iz i comp

bed


εhellip

(A54)


coefficient

Wakao correlation24



3

3 2

12 12

1

18583 10 0 0 1 2im i p

TMW

D z L r R iP


(A56)


2

7 175 2

12

1

1013 10 0 0 1 2im i p

MWD T z L r R i

PX


Knudsen diffusivity


3 97 10 0 0 1 k i pore p comp

i

TD R z L r R i N


(A58)


0 0 1 p m i k i

e i p compp m i k i

D DD z L r R i N

D D


hellip (A59)



2

1

1

out

inv in comp

i i

P

PF C SP P i N

x MW T

minus = = hellip

sum (A60)

Molar flowrate

Otherwise ( )

21

1

critv in comp

i i

PF C SP P i N

x MW T

minus= = hellip

sum (A61)


1critP

κ

minusκ =

+ κ (A62)

Power

1

11

feed feedfeed

low cycle

P NPower RT

P

κminus

κ κ

= minus κ minus τ

(A63)

32


33


34



35



7












Shin and Knaebel18




theoretical and







Shin and Knaebel18

4 Case studies













8

























Simulation Run I









9








Simulation Run II












Simulation Run III











10





5 Conclusions













and capital costs





Acknowledgements




Nomenclature




11





3




Cv = valve constant













L = bed length m



12

Q




Rbed = bed radius m




P = pressure Pa












3





13









References












1998 4 113



14






2000 35 667


2000 6 179




















15





325










AIChE J 1987 33 1045



Eng 1987 65 512










16




141






1992 47 4305








York 1994










gas AIChE J 1998 44 1325

17






Technol 2000 39 51


Technol 2000 20 185



















8084

18

















19


Ref Mass

balance

Heat

balance

Momentum

balance

Isotherm

adsorbent

No of

steps

No of

layers Application







study


experimental study


(43) LDF Bulk gas

solids -


5 1 H2 CO H2 CO2



(54) DG LDF -DG

LDF-DGSD

LDF-DGSD

- - Langmuir 4A 5A





13X 4 1 CO2 capture






Ref Mass

balance

Heat

balance

Momentum

balance

Isotherm

adsorbent

No of

beds

No of

steps

Bed

interactions

No of

layers Application






Dual-site

Langmuir

13X


ads Air separation




AC+5A

2 7 - 2 H2 CH4 CO

N2 CO2



20


Ref Mass

balance Heat

balance

Momentum

balance

Isotherm adsorbent

No of beds

No of steps

Bed interactions

No of layers

Application



N2



AC+5A 4 8


information


2 H2 CO2 CH4

CO


Langmuir

Alumina+ AC+zeolite

6 12

Information


inert +

2 ads H2 CH4 CO


gel 9 10

9 11 6+7

- -

Overview of




Dual-site

Langmuir APHP+5A


CO H2


13X 2 3 4 6 - 1

CO2 from flue

gases


21


Recovery Purity

No Exp18

Model18

This

work Exp

18 Model

18

This

work

1 644 638 696 9975 10000 9931

2 816 864 850 9955 9989 9892

3 1065 1092 994 9900 9909 9855

4 1239 1215 1130 9835 9859 9815

5 707 825 852 9960 9988 9895

6 941 985 995 9885 9941 9854

7 1167 1172 1072 9830 9877 9833

8 1299 1213 1141 9780 9849 9811

9 2584 1702 2123 9080 9539 9447

10 2136 1609 2121 9070 9623 9475

11 2274 1550 2120 9140 9618 9478

12 2218 2274 2108 9120 9602 9477

13 939 835 845 9825 9970 9974

14 740 632 785 9890 9982 9991

15 510 500 738 9900 9988 9997

16 919 859 982 9845 9963 9960

17 707 762 856 9850 9976 9979

18 643 699 742 9870 9983 9989

19 541 613 612 9880 9993 9996

20 1151 1244 1128 9795 9871 9825

21 972 967 943 9850 9942 9940

22 674 659 726 9885 9979 9991

23 337 408 546 9900 9996 9999

24 1663 1433 1086 9585 9747 9869

25 1076 1155 962 9680 9872 9957

26 857 847 881 9730 9915 9984

27 826 721 844 9765 9910 9991

28 735 856 1135 9875 9987 9822

29 1195 1427 1117 9770 9792 9831

30 1330 1607 1120 9700 9657 9824

31 4156 3764 2638 8230 8227 8923

32 2246 1607 1511 9370 9497 9670

33 1254 800 899 9820 10000 9906

34 1383 1309 986 9380 9445 9606

35 2305 1673 1425 9370 9758 9775

42 2240 1646 2051 8900 9440 9496

43 2237 1615 2006 8230 8972 9012

22













Bed length 10 m















(wall) 13807 W(m

2K)


coefficient 1e-3 m

2s


coefficient 1e-3 m

2s


Comp a1 x10

3

(molg) a2

(K) b1 x10

9

(Pa-1

) b2

(K) -∆Hads (Jmol)

H2 432 000 5040 8505 786173

CO 092 052 5896 17309 1667742

CH4 -170 198 19952 14467 1875269

CO2 -1420 663 24775 14966 2557261






23























24



1 4 8 12

spPressCoC 01000 0060 0030 00500

spAdsIn 03600 03600 03600 03600

spAdsOut 00035 00015 00015 00015

spBlow 08000 05000 02500 04000

spPurgeIn 02250 02250 02250 02250

spPurgeOut 00300 00300 0030 00300

spPEQ1 - 00040 00025 00030

spPEQ2 - - 00050 00040

spPEQ3 - - - 00080

Feed

flowrate m3s

360e-6 360e-6 360e-6 360e-6

Purge

flowrate m3s

225e-6 225e-6 225e-6 225e-6

τPress s 10 10 20 10

τAds s 20 20 20 20

τBlow s 10 10 20 10

τPurge s 20 20 20 20

τPEQ1 s - 10 20 10

τPEQ2 s - - 20 10

τPEQ3 s - - - 10

τcycle s 60 80 160 120


No

beds

O2 purity

()

O2 recovery

()

Power

(W)

Productivity

(molkgs)

1 9687 3440 52902 918e-2

4 9950 5806 27949 485e-2

8 9958 6887 11987 208e-2

12 9936 7250 13936 242e-2

25



1 4 8 12

spPressCoC 00300 00450 00500 00500

spAdsIn 01200 01300 03300 03600

spAdsOut 00004 000035 00014 00015

spBlow 02000 02200 03000 04000

spPurgeIn 05625 01500 03000 02250

spPurgeOut 00075 00200 00400 00300

spPEQ1 - 00025 00020 00300

spPEQ2 - - 00040 00040

spPEQ3 - - - 00080

Feed flowrate m

3s

120e-6 130e-6 330e-6 360e-6

Purge

flowrate m3s

075e-6 115e-6 300e-6 225e-6

τPress s 20 15 15 10

τAds s 40 30 15 20

τBlow s 20 15 15 10

τPurge s 40 30 15 20

τPEQ1 s - 15 15 10

τPEQ2 s - - 15 10

τPEQ3 s - - - 10

τcycle s 120 120 120 120


No

beds

O2 purity

()

O2 recovery

()

Power

(W)

Productivity

(molkgs)

1 9811 2021 14420 250e-2

4 9929 3840 14069 244e-2

8 9979 6525 14092 245e-2

12 9936 7250 13936 242e-2

26



1 4 8 12

spPressCC 00030 00030 00500 00040

spAdsIn 04000 03333 03450 05000

spAdsOut 000088 000085 00015 00014

spBlow 02500 04000 03000 04000

spPurgeIn 00900 01333 03000 02000

spPurgeOut 00140 00200 00400 00300

spPEQ1 - 00050 00020 00030

spPEQ2 - - 00040 00040

spPEQ3 - - - 00080

Feed flowrate m

3s

400e-6 333e-6 345e-6 500e-6

Purge

flowrate m3s

090e-6 133e-6 300e-6 200e-6

τPress s 20 15 15 10

τAds s 40 30 15 20

τBlow s 20 15 15 10

τPurge s 40 30 15 20

τPEQ1 s - 15 15 10

τPEQ2 s - - 15 10

τPEQ3 s - - - 10

τcycle s 120 120 120 120


No beds

O2 purity ()

O2 recovery ()

Power (W)


1 9987 141 18878 203e-2

4 9997 2847 11808 205e-2

8 9997 5058 11938 207e-2

12 9983 6516 11909 207e-2

27




( )( )

( )

1

0 1


comp

uC C CN D

z t z z

z L i N


part part part part


(A1)


particle surface)



( ) ( )( ) ( )

( )

31

0


bed

bed z

c Tc uT kq T T

z t R

Tz L

z z


part part


part part

(A3)





Pf u R z L

z


part (A5)


coefficient ( )

0 1 f i p

compm i





λ (A7)


( )

0 1 z i bed

compm i

Df Sc Re z L i N

D




= forall isin λ

(A9)




Cu C C D z z L i N

z

partminus = = = =

parthellip (A12)

0 or inT T z z L= = = (A13)


0 0 and u

z z Lz

part= = =

part (A14)

0 0 or 1 icomp

Cz z L i N

z

part= = = =



end 0 0 or

Tz z L

z

part= = =

part (A16)

28


Model Equation



[ ] 0 0 1 p





( )

0 1 p i ii p comp

Q CN z L i N

t t


part parthellip

(A19)



(A20)


( ) [ ]

2

15 0 0 1

e iii i p comp

p

DQQ Q r R z L i N

t R


hellip (A21) LDF


( ) 0 1 p i i

i p comp

Q CN z L i N

t t


part parthellip

(A22)


) [ ]0 0 0 1 p




( ) [ ]22

1 0 0 1 i i

p s i p comp

p

Q QR D r R z L i N

t r rR



(A24)


( ) ( )3

0 1 p

f pi i r R compi

p

kN C C z L i N


(A25)



Qk C C D r R i N

r= =

partminus = = =

part (A26)

SD

0 0 0 1 icomp

Qr z L i N

r


parthellip (A27)


( ) ( ) [ ]

22

11 0 0 1

p ppi i i

p p p p e i p comp

p

C CQR D r R z L i N

t t r rR



(A28)




( ) ( )3

0 1 p

f pi i r R compi

p

kN C C z L i N


(A30)



Qk C C D r R i N

r= =

partminus = = =

part (A31)

PD

0 0 0 1 p

icomp

Cr z L i N

r


parthellip (A32)

29


Mode Equation

( )0 0 T

z Lz

part= forall isin

part (A33)




(A34)


( ) ( )( ) ( )3

0 bed pbed p h wall

g wall bed zbed


z t R z z


part part part part

(A35)




(A36)

LEQ



( )( ) ( )

0 comp

p p Np p pg p pg

p ig ads i

i

c c TQ

q H z Lt t


part partsum

(A37)




(A38)

LDF



( )( ) ( )

0 comp

p p Np p pg p pg

p ig ads i

i

c c TQ

q H z Lt t


part partsum

(A39)



0 0 p


(A40)

SD



( )( ) ( ) 0

compp p N

p i Rppg ads i

i

c T Qq H z L

t t


part partsum

(A41)


( ) ( )3

0 p

phg R

p

kq T T z L


(A42)


( )( ) ( )

2

2

1 0 0

p p ppp p pg p pg

p pg p p

p

c c TT

q R r R z Lt r rR


(A43)


( ) ( )

0 compN

p p ig ads i p

i

Qq H r R

t


partsum

(A44)

( ) p p

pp p

h r R r R p

Tk T T r R

r= =

partminus = λ =

part

(A45)

Nonisothermal

PD

model

Boundary conditions

0 0p

Tr

r

part= =

part (A46)


( )3 h wallwall

bed

kT T

Rminus

is neglected

30



( )

( )( )

2

2 3

180 1 0

2

bg bed

bedp

uPz L

z R


part ε (A47)


( )

( )( )

2

2 3

180 1 0

2

bg bed

bedp

uPz L

z R


part ε (A48)

Linear (Henry type)


(A49)

Extended Langmuir

2 2 1 1 exp 0 1

1


j j

j


b P T T


+ sumhellip (A50)


( )0

0

0

1 0 1 iP


QdP Q b P z L i N


(A51a)


(A51b

)

2 2 1 1 exp 0 1

1


i i


b P T T


hellip (A51c)


)


1 0 1 i

comp

itotal pure i

Xz L i N




31


Variable Equation


Wakao correlation23

( ) 033 06 20 11 0 1

m if i comp

p

Dk Sc Re z L i N



coefficient

Wakao correlation24

( )033 0620 11 Re 0 hp

k Pr z LR

λ= + forall isin

(A53)


coefficient

Wakao correlation23

( ) 20 05 0 1

m iz i comp

bed


εhellip

(A54)


coefficient

Wakao correlation24



3

3 2

12 12

1

18583 10 0 0 1 2im i p

TMW

D z L r R iP


(A56)


2

7 175 2

12

1

1013 10 0 0 1 2im i p

MWD T z L r R i

PX


Knudsen diffusivity


3 97 10 0 0 1 k i pore p comp

i

TD R z L r R i N


(A58)


0 0 1 p m i k i

e i p compp m i k i

D DD z L r R i N

D D


hellip (A59)



2

1

1

out

inv in comp

i i

P

PF C SP P i N

x MW T

minus = = hellip

sum (A60)

Molar flowrate

Otherwise ( )

21

1

critv in comp

i i

PF C SP P i N

x MW T

minus= = hellip

sum (A61)


1critP

κ

minusκ =

+ κ (A62)

Power

1

11

feed feedfeed

low cycle

P NPower RT

P

κminus

κ κ

= minus κ minus τ

(A63)

32


33


34



35



8

























Simulation Run I









9








Simulation Run II












Simulation Run III











10





5 Conclusions













and capital costs





Acknowledgements




Nomenclature




11





3




Cv = valve constant













L = bed length m



12

Q




Rbed = bed radius m




P = pressure Pa












3





13









References












1998 4 113



14






2000 35 667


2000 6 179




















15





325










AIChE J 1987 33 1045



Eng 1987 65 512










16




141






1992 47 4305








York 1994










gas AIChE J 1998 44 1325

17






Technol 2000 39 51


Technol 2000 20 185



















8084

18

















19


Ref Mass

balance

Heat

balance

Momentum

balance

Isotherm

adsorbent

No of

steps

No of

layers Application







study


experimental study


(43) LDF Bulk gas

solids -


5 1 H2 CO H2 CO2



(54) DG LDF -DG

LDF-DGSD

LDF-DGSD

- - Langmuir 4A 5A





13X 4 1 CO2 capture






Ref Mass

balance

Heat

balance

Momentum

balance

Isotherm

adsorbent

No of

beds

No of

steps

Bed

interactions

No of

layers Application






Dual-site

Langmuir

13X


ads Air separation




AC+5A

2 7 - 2 H2 CH4 CO

N2 CO2



20


Ref Mass

balance Heat

balance

Momentum

balance

Isotherm adsorbent

No of beds

No of steps

Bed interactions

No of layers

Application



N2



AC+5A 4 8


information


2 H2 CO2 CH4

CO


Langmuir

Alumina+ AC+zeolite

6 12

Information


inert +

2 ads H2 CH4 CO


gel 9 10

9 11 6+7

- -

Overview of




Dual-site

Langmuir APHP+5A


CO H2


13X 2 3 4 6 - 1

CO2 from flue

gases


21


Recovery Purity

No Exp18

Model18

This

work Exp

18 Model

18

This

work

1 644 638 696 9975 10000 9931

2 816 864 850 9955 9989 9892

3 1065 1092 994 9900 9909 9855

4 1239 1215 1130 9835 9859 9815

5 707 825 852 9960 9988 9895

6 941 985 995 9885 9941 9854

7 1167 1172 1072 9830 9877 9833

8 1299 1213 1141 9780 9849 9811

9 2584 1702 2123 9080 9539 9447

10 2136 1609 2121 9070 9623 9475

11 2274 1550 2120 9140 9618 9478

12 2218 2274 2108 9120 9602 9477

13 939 835 845 9825 9970 9974

14 740 632 785 9890 9982 9991

15 510 500 738 9900 9988 9997

16 919 859 982 9845 9963 9960

17 707 762 856 9850 9976 9979

18 643 699 742 9870 9983 9989

19 541 613 612 9880 9993 9996

20 1151 1244 1128 9795 9871 9825

21 972 967 943 9850 9942 9940

22 674 659 726 9885 9979 9991

23 337 408 546 9900 9996 9999

24 1663 1433 1086 9585 9747 9869

25 1076 1155 962 9680 9872 9957

26 857 847 881 9730 9915 9984

27 826 721 844 9765 9910 9991

28 735 856 1135 9875 9987 9822

29 1195 1427 1117 9770 9792 9831

30 1330 1607 1120 9700 9657 9824

31 4156 3764 2638 8230 8227 8923

32 2246 1607 1511 9370 9497 9670

33 1254 800 899 9820 10000 9906

34 1383 1309 986 9380 9445 9606

35 2305 1673 1425 9370 9758 9775

42 2240 1646 2051 8900 9440 9496

43 2237 1615 2006 8230 8972 9012

22













Bed length 10 m















(wall) 13807 W(m

2K)


coefficient 1e-3 m

2s


coefficient 1e-3 m

2s


Comp a1 x10

3

(molg) a2

(K) b1 x10

9

(Pa-1

) b2

(K) -∆Hads (Jmol)

H2 432 000 5040 8505 786173

CO 092 052 5896 17309 1667742

CH4 -170 198 19952 14467 1875269

CO2 -1420 663 24775 14966 2557261






23























24



1 4 8 12

spPressCoC 01000 0060 0030 00500

spAdsIn 03600 03600 03600 03600

spAdsOut 00035 00015 00015 00015

spBlow 08000 05000 02500 04000

spPurgeIn 02250 02250 02250 02250

spPurgeOut 00300 00300 0030 00300

spPEQ1 - 00040 00025 00030

spPEQ2 - - 00050 00040

spPEQ3 - - - 00080

Feed

flowrate m3s

360e-6 360e-6 360e-6 360e-6

Purge

flowrate m3s

225e-6 225e-6 225e-6 225e-6

τPress s 10 10 20 10

τAds s 20 20 20 20

τBlow s 10 10 20 10

τPurge s 20 20 20 20

τPEQ1 s - 10 20 10

τPEQ2 s - - 20 10

τPEQ3 s - - - 10

τcycle s 60 80 160 120


No

beds

O2 purity

()

O2 recovery

()

Power

(W)

Productivity

(molkgs)

1 9687 3440 52902 918e-2

4 9950 5806 27949 485e-2

8 9958 6887 11987 208e-2

12 9936 7250 13936 242e-2

25



1 4 8 12

spPressCoC 00300 00450 00500 00500

spAdsIn 01200 01300 03300 03600

spAdsOut 00004 000035 00014 00015

spBlow 02000 02200 03000 04000

spPurgeIn 05625 01500 03000 02250

spPurgeOut 00075 00200 00400 00300

spPEQ1 - 00025 00020 00300

spPEQ2 - - 00040 00040

spPEQ3 - - - 00080

Feed flowrate m

3s

120e-6 130e-6 330e-6 360e-6

Purge

flowrate m3s

075e-6 115e-6 300e-6 225e-6

τPress s 20 15 15 10

τAds s 40 30 15 20

τBlow s 20 15 15 10

τPurge s 40 30 15 20

τPEQ1 s - 15 15 10

τPEQ2 s - - 15 10

τPEQ3 s - - - 10

τcycle s 120 120 120 120


No

beds

O2 purity

()

O2 recovery

()

Power

(W)

Productivity

(molkgs)

1 9811 2021 14420 250e-2

4 9929 3840 14069 244e-2

8 9979 6525 14092 245e-2

12 9936 7250 13936 242e-2

26



1 4 8 12

spPressCC 00030 00030 00500 00040

spAdsIn 04000 03333 03450 05000

spAdsOut 000088 000085 00015 00014

spBlow 02500 04000 03000 04000

spPurgeIn 00900 01333 03000 02000

spPurgeOut 00140 00200 00400 00300

spPEQ1 - 00050 00020 00030

spPEQ2 - - 00040 00040

spPEQ3 - - - 00080

Feed flowrate m

3s

400e-6 333e-6 345e-6 500e-6

Purge

flowrate m3s

090e-6 133e-6 300e-6 200e-6

τPress s 20 15 15 10

τAds s 40 30 15 20

τBlow s 20 15 15 10

τPurge s 40 30 15 20

τPEQ1 s - 15 15 10

τPEQ2 s - - 15 10

τPEQ3 s - - - 10

τcycle s 120 120 120 120


No beds

O2 purity ()

O2 recovery ()

Power (W)


1 9987 141 18878 203e-2

4 9997 2847 11808 205e-2

8 9997 5058 11938 207e-2

12 9983 6516 11909 207e-2

27




( )( )

( )

1

0 1


comp

uC C CN D

z t z z

z L i N


part part part part


(A1)


particle surface)



( ) ( )( ) ( )

( )

31

0


bed

bed z

c Tc uT kq T T

z t R

Tz L

z z


part part


part part

(A3)





Pf u R z L

z


part (A5)


coefficient ( )

0 1 f i p

compm i





λ (A7)


( )

0 1 z i bed

compm i

Df Sc Re z L i N

D




= forall isin λ

(A9)




Cu C C D z z L i N

z

partminus = = = =

parthellip (A12)

0 or inT T z z L= = = (A13)


0 0 and u

z z Lz

part= = =

part (A14)

0 0 or 1 icomp

Cz z L i N

z

part= = = =



end 0 0 or

Tz z L

z

part= = =

part (A16)

28


Model Equation



[ ] 0 0 1 p





( )

0 1 p i ii p comp

Q CN z L i N

t t


part parthellip

(A19)



(A20)


( ) [ ]

2

15 0 0 1

e iii i p comp

p

DQQ Q r R z L i N

t R


hellip (A21) LDF


( ) 0 1 p i i

i p comp

Q CN z L i N

t t


part parthellip

(A22)


) [ ]0 0 0 1 p




( ) [ ]22

1 0 0 1 i i

p s i p comp

p

Q QR D r R z L i N

t r rR



(A24)


( ) ( )3

0 1 p

f pi i r R compi

p

kN C C z L i N


(A25)



Qk C C D r R i N

r= =

partminus = = =

part (A26)

SD

0 0 0 1 icomp

Qr z L i N

r


parthellip (A27)


( ) ( ) [ ]

22

11 0 0 1

p ppi i i

p p p p e i p comp

p

C CQR D r R z L i N

t t r rR



(A28)




( ) ( )3

0 1 p

f pi i r R compi

p

kN C C z L i N


(A30)



Qk C C D r R i N

r= =

partminus = = =

part (A31)

PD

0 0 0 1 p

icomp

Cr z L i N

r


parthellip (A32)

29


Mode Equation

( )0 0 T

z Lz

part= forall isin

part (A33)




(A34)


( ) ( )( ) ( )3

0 bed pbed p h wall

g wall bed zbed


z t R z z


part part part part

(A35)




(A36)

LEQ



( )( ) ( )

0 comp

p p Np p pg p pg

p ig ads i

i

c c TQ

q H z Lt t


part partsum

(A37)




(A38)

LDF



( )( ) ( )

0 comp

p p Np p pg p pg

p ig ads i

i

c c TQ

q H z Lt t


part partsum

(A39)



0 0 p


(A40)

SD



( )( ) ( ) 0

compp p N

p i Rppg ads i

i

c T Qq H z L

t t


part partsum

(A41)


( ) ( )3

0 p

phg R

p

kq T T z L


(A42)


( )( ) ( )

2

2

1 0 0

p p ppp p pg p pg

p pg p p

p

c c TT

q R r R z Lt r rR


(A43)


( ) ( )

0 compN

p p ig ads i p

i

Qq H r R

t


partsum

(A44)

( ) p p

pp p

h r R r R p

Tk T T r R

r= =

partminus = λ =

part

(A45)

Nonisothermal

PD

model

Boundary conditions

0 0p

Tr

r

part= =

part (A46)


( )3 h wallwall

bed

kT T

Rminus

is neglected

30



( )

( )( )

2

2 3

180 1 0

2

bg bed

bedp

uPz L

z R


part ε (A47)


( )

( )( )

2

2 3

180 1 0

2

bg bed

bedp

uPz L

z R


part ε (A48)

Linear (Henry type)


(A49)

Extended Langmuir

2 2 1 1 exp 0 1

1


j j

j


b P T T


+ sumhellip (A50)


( )0

0

0

1 0 1 iP


QdP Q b P z L i N


(A51a)


(A51b

)

2 2 1 1 exp 0 1

1


i i


b P T T


hellip (A51c)


)


1 0 1 i

comp

itotal pure i

Xz L i N




31


Variable Equation


Wakao correlation23

( ) 033 06 20 11 0 1

m if i comp

p

Dk Sc Re z L i N



coefficient

Wakao correlation24

( )033 0620 11 Re 0 hp

k Pr z LR

λ= + forall isin

(A53)


coefficient

Wakao correlation23

( ) 20 05 0 1

m iz i comp

bed


εhellip

(A54)


coefficient

Wakao correlation24



3

3 2

12 12

1

18583 10 0 0 1 2im i p

TMW

D z L r R iP


(A56)


2

7 175 2

12

1

1013 10 0 0 1 2im i p

MWD T z L r R i

PX


Knudsen diffusivity


3 97 10 0 0 1 k i pore p comp

i

TD R z L r R i N


(A58)


0 0 1 p m i k i

e i p compp m i k i

D DD z L r R i N

D D


hellip (A59)



2

1

1

out

inv in comp

i i

P

PF C SP P i N

x MW T

minus = = hellip

sum (A60)

Molar flowrate

Otherwise ( )

21

1

critv in comp

i i

PF C SP P i N

x MW T

minus= = hellip

sum (A61)


1critP

κ

minusκ =

+ κ (A62)

Power

1

11

feed feedfeed

low cycle

P NPower RT

P

κminus

κ κ

= minus κ minus τ

(A63)

32


33


34



35



9








Simulation Run II












Simulation Run III











10





5 Conclusions













and capital costs





Acknowledgements




Nomenclature




11





3




Cv = valve constant













L = bed length m



12

Q




Rbed = bed radius m




P = pressure Pa












3





13









References












1998 4 113



14






2000 35 667


2000 6 179




















15





325










AIChE J 1987 33 1045



Eng 1987 65 512










16




141






1992 47 4305








York 1994










gas AIChE J 1998 44 1325

17






Technol 2000 39 51


Technol 2000 20 185



















8084

18

















19


Ref Mass

balance

Heat

balance

Momentum

balance

Isotherm

adsorbent

No of

steps

No of

layers Application







study


experimental study


(43) LDF Bulk gas

solids -


5 1 H2 CO H2 CO2



(54) DG LDF -DG

LDF-DGSD

LDF-DGSD

- - Langmuir 4A 5A





13X 4 1 CO2 capture






Ref Mass

balance

Heat

balance

Momentum

balance

Isotherm

adsorbent

No of

beds

No of

steps

Bed

interactions

No of

layers Application






Dual-site

Langmuir

13X


ads Air separation




AC+5A

2 7 - 2 H2 CH4 CO

N2 CO2



20


Ref Mass

balance Heat

balance

Momentum

balance

Isotherm adsorbent

No of beds

No of steps

Bed interactions

No of layers

Application



N2



AC+5A 4 8


information


2 H2 CO2 CH4

CO


Langmuir

Alumina+ AC+zeolite

6 12

Information


inert +

2 ads H2 CH4 CO


gel 9 10

9 11 6+7

- -

Overview of




Dual-site

Langmuir APHP+5A


CO H2


13X 2 3 4 6 - 1

CO2 from flue

gases


21


Recovery Purity

No Exp18

Model18

This

work Exp

18 Model

18

This

work

1 644 638 696 9975 10000 9931

2 816 864 850 9955 9989 9892

3 1065 1092 994 9900 9909 9855

4 1239 1215 1130 9835 9859 9815

5 707 825 852 9960 9988 9895

6 941 985 995 9885 9941 9854

7 1167 1172 1072 9830 9877 9833

8 1299 1213 1141 9780 9849 9811

9 2584 1702 2123 9080 9539 9447

10 2136 1609 2121 9070 9623 9475

11 2274 1550 2120 9140 9618 9478

12 2218 2274 2108 9120 9602 9477

13 939 835 845 9825 9970 9974

14 740 632 785 9890 9982 9991

15 510 500 738 9900 9988 9997

16 919 859 982 9845 9963 9960

17 707 762 856 9850 9976 9979

18 643 699 742 9870 9983 9989

19 541 613 612 9880 9993 9996

20 1151 1244 1128 9795 9871 9825

21 972 967 943 9850 9942 9940

22 674 659 726 9885 9979 9991

23 337 408 546 9900 9996 9999

24 1663 1433 1086 9585 9747 9869

25 1076 1155 962 9680 9872 9957

26 857 847 881 9730 9915 9984

27 826 721 844 9765 9910 9991

28 735 856 1135 9875 9987 9822

29 1195 1427 1117 9770 9792 9831

30 1330 1607 1120 9700 9657 9824

31 4156 3764 2638 8230 8227 8923

32 2246 1607 1511 9370 9497 9670

33 1254 800 899 9820 10000 9906

34 1383 1309 986 9380 9445 9606

35 2305 1673 1425 9370 9758 9775

42 2240 1646 2051 8900 9440 9496

43 2237 1615 2006 8230 8972 9012

22













Bed length 10 m















(wall) 13807 W(m

2K)


coefficient 1e-3 m

2s


coefficient 1e-3 m

2s


Comp a1 x10

3

(molg) a2

(K) b1 x10

9

(Pa-1

) b2

(K) -∆Hads (Jmol)

H2 432 000 5040 8505 786173

CO 092 052 5896 17309 1667742

CH4 -170 198 19952 14467 1875269

CO2 -1420 663 24775 14966 2557261






23























24



1 4 8 12

spPressCoC 01000 0060 0030 00500

spAdsIn 03600 03600 03600 03600

spAdsOut 00035 00015 00015 00015

spBlow 08000 05000 02500 04000

spPurgeIn 02250 02250 02250 02250

spPurgeOut 00300 00300 0030 00300

spPEQ1 - 00040 00025 00030

spPEQ2 - - 00050 00040

spPEQ3 - - - 00080

Feed

flowrate m3s

360e-6 360e-6 360e-6 360e-6

Purge

flowrate m3s

225e-6 225e-6 225e-6 225e-6

τPress s 10 10 20 10

τAds s 20 20 20 20

τBlow s 10 10 20 10

τPurge s 20 20 20 20

τPEQ1 s - 10 20 10

τPEQ2 s - - 20 10

τPEQ3 s - - - 10

τcycle s 60 80 160 120


No

beds

O2 purity

()

O2 recovery

()

Power

(W)

Productivity

(molkgs)

1 9687 3440 52902 918e-2

4 9950 5806 27949 485e-2

8 9958 6887 11987 208e-2

12 9936 7250 13936 242e-2

25



1 4 8 12

spPressCoC 00300 00450 00500 00500

spAdsIn 01200 01300 03300 03600

spAdsOut 00004 000035 00014 00015

spBlow 02000 02200 03000 04000

spPurgeIn 05625 01500 03000 02250

spPurgeOut 00075 00200 00400 00300

spPEQ1 - 00025 00020 00300

spPEQ2 - - 00040 00040

spPEQ3 - - - 00080

Feed flowrate m

3s

120e-6 130e-6 330e-6 360e-6

Purge

flowrate m3s

075e-6 115e-6 300e-6 225e-6

τPress s 20 15 15 10

τAds s 40 30 15 20

τBlow s 20 15 15 10

τPurge s 40 30 15 20

τPEQ1 s - 15 15 10

τPEQ2 s - - 15 10

τPEQ3 s - - - 10

τcycle s 120 120 120 120


No

beds

O2 purity

()

O2 recovery

()

Power

(W)

Productivity

(molkgs)

1 9811 2021 14420 250e-2

4 9929 3840 14069 244e-2

8 9979 6525 14092 245e-2

12 9936 7250 13936 242e-2

26



1 4 8 12

spPressCC 00030 00030 00500 00040

spAdsIn 04000 03333 03450 05000

spAdsOut 000088 000085 00015 00014

spBlow 02500 04000 03000 04000

spPurgeIn 00900 01333 03000 02000

spPurgeOut 00140 00200 00400 00300

spPEQ1 - 00050 00020 00030

spPEQ2 - - 00040 00040

spPEQ3 - - - 00080

Feed flowrate m

3s

400e-6 333e-6 345e-6 500e-6

Purge

flowrate m3s

090e-6 133e-6 300e-6 200e-6

τPress s 20 15 15 10

τAds s 40 30 15 20

τBlow s 20 15 15 10

τPurge s 40 30 15 20

τPEQ1 s - 15 15 10

τPEQ2 s - - 15 10

τPEQ3 s - - - 10

τcycle s 120 120 120 120


No beds

O2 purity ()

O2 recovery ()

Power (W)


1 9987 141 18878 203e-2

4 9997 2847 11808 205e-2

8 9997 5058 11938 207e-2

12 9983 6516 11909 207e-2

27




( )( )

( )

1

0 1


comp

uC C CN D

z t z z

z L i N


part part part part


(A1)


particle surface)



( ) ( )( ) ( )

( )

31

0


bed

bed z

c Tc uT kq T T

z t R

Tz L

z z


part part


part part

(A3)





Pf u R z L

z


part (A5)


coefficient ( )

0 1 f i p

compm i





λ (A7)


( )

0 1 z i bed

compm i

Df Sc Re z L i N

D




= forall isin λ

(A9)




Cu C C D z z L i N

z

partminus = = = =

parthellip (A12)

0 or inT T z z L= = = (A13)


0 0 and u

z z Lz

part= = =

part (A14)

0 0 or 1 icomp

Cz z L i N

z

part= = = =



end 0 0 or

Tz z L

z

part= = =

part (A16)

28


Model Equation



[ ] 0 0 1 p





( )

0 1 p i ii p comp

Q CN z L i N

t t


part parthellip

(A19)



(A20)


( ) [ ]

2

15 0 0 1

e iii i p comp

p

DQQ Q r R z L i N

t R


hellip (A21) LDF


( ) 0 1 p i i

i p comp

Q CN z L i N

t t


part parthellip

(A22)


) [ ]0 0 0 1 p




( ) [ ]22

1 0 0 1 i i

p s i p comp

p

Q QR D r R z L i N

t r rR



(A24)


( ) ( )3

0 1 p

f pi i r R compi

p

kN C C z L i N


(A25)



Qk C C D r R i N

r= =

partminus = = =

part (A26)

SD

0 0 0 1 icomp

Qr z L i N

r


parthellip (A27)


( ) ( ) [ ]

22

11 0 0 1

p ppi i i

p p p p e i p comp

p

C CQR D r R z L i N

t t r rR



(A28)




( ) ( )3

0 1 p

f pi i r R compi

p

kN C C z L i N


(A30)



Qk C C D r R i N

r= =

partminus = = =

part (A31)

PD

0 0 0 1 p

icomp

Cr z L i N

r


parthellip (A32)

29


Mode Equation

( )0 0 T

z Lz

part= forall isin

part (A33)




(A34)


( ) ( )( ) ( )3

0 bed pbed p h wall

g wall bed zbed


z t R z z


part part part part

(A35)




(A36)

LEQ



( )( ) ( )

0 comp

p p Np p pg p pg

p ig ads i

i

c c TQ

q H z Lt t


part partsum

(A37)




(A38)

LDF



( )( ) ( )

0 comp

p p Np p pg p pg

p ig ads i

i

c c TQ

q H z Lt t


part partsum

(A39)



0 0 p


(A40)

SD



( )( ) ( ) 0

compp p N

p i Rppg ads i

i

c T Qq H z L

t t


part partsum

(A41)


( ) ( )3

0 p

phg R

p

kq T T z L


(A42)


( )( ) ( )

2

2

1 0 0

p p ppp p pg p pg

p pg p p

p

c c TT

q R r R z Lt r rR


(A43)


( ) ( )

0 compN

p p ig ads i p

i

Qq H r R

t


partsum

(A44)

( ) p p

pp p

h r R r R p

Tk T T r R

r= =

partminus = λ =

part

(A45)

Nonisothermal

PD

model

Boundary conditions

0 0p

Tr

r

part= =

part (A46)


( )3 h wallwall

bed

kT T

Rminus

is neglected

30



( )

( )( )

2

2 3

180 1 0

2

bg bed

bedp

uPz L

z R


part ε (A47)


( )

( )( )

2

2 3

180 1 0

2

bg bed

bedp

uPz L

z R


part ε (A48)

Linear (Henry type)


(A49)

Extended Langmuir

2 2 1 1 exp 0 1

1


j j

j


b P T T


+ sumhellip (A50)


( )0

0

0

1 0 1 iP


QdP Q b P z L i N


(A51a)


(A51b

)

2 2 1 1 exp 0 1

1


i i


b P T T


hellip (A51c)


)


1 0 1 i

comp

itotal pure i

Xz L i N




31


Variable Equation


Wakao correlation23

( ) 033 06 20 11 0 1

m if i comp

p

Dk Sc Re z L i N



coefficient

Wakao correlation24

( )033 0620 11 Re 0 hp

k Pr z LR

λ= + forall isin

(A53)


coefficient

Wakao correlation23

( ) 20 05 0 1

m iz i comp

bed


εhellip

(A54)


coefficient

Wakao correlation24



3

3 2

12 12

1

18583 10 0 0 1 2im i p

TMW

D z L r R iP


(A56)


2

7 175 2

12

1

1013 10 0 0 1 2im i p

MWD T z L r R i

PX


Knudsen diffusivity


3 97 10 0 0 1 k i pore p comp

i

TD R z L r R i N


(A58)


0 0 1 p m i k i

e i p compp m i k i

D DD z L r R i N

D D


hellip (A59)



2

1

1

out

inv in comp

i i

P

PF C SP P i N

x MW T

minus = = hellip

sum (A60)

Molar flowrate

Otherwise ( )

21

1

critv in comp

i i

PF C SP P i N

x MW T

minus= = hellip

sum (A61)


1critP

κ

minusκ =

+ κ (A62)

Power

1

11

feed feedfeed

low cycle

P NPower RT

P

κminus

κ κ

= minus κ minus τ

(A63)

32


33


34



35



10





5 Conclusions













and capital costs





Acknowledgements




Nomenclature




11





3




Cv = valve constant













L = bed length m



12

Q




Rbed = bed radius m




P = pressure Pa












3





13









References












1998 4 113



14






2000 35 667


2000 6 179




















15





325










AIChE J 1987 33 1045



Eng 1987 65 512










16




141






1992 47 4305








York 1994










gas AIChE J 1998 44 1325

17






Technol 2000 39 51


Technol 2000 20 185



















8084

18

















19


Ref Mass

balance

Heat

balance

Momentum

balance

Isotherm

adsorbent

No of

steps

No of

layers Application







study


experimental study


(43) LDF Bulk gas

solids -


5 1 H2 CO H2 CO2



(54) DG LDF -DG

LDF-DGSD

LDF-DGSD

- - Langmuir 4A 5A





13X 4 1 CO2 capture






Ref Mass

balance

Heat

balance

Momentum

balance

Isotherm

adsorbent

No of

beds

No of

steps

Bed

interactions

No of

layers Application






Dual-site

Langmuir

13X


ads Air separation




AC+5A

2 7 - 2 H2 CH4 CO

N2 CO2



20


Ref Mass

balance Heat

balance

Momentum

balance

Isotherm adsorbent

No of beds

No of steps

Bed interactions

No of layers

Application



N2



AC+5A 4 8


information


2 H2 CO2 CH4

CO


Langmuir

Alumina+ AC+zeolite

6 12

Information


inert +

2 ads H2 CH4 CO


gel 9 10

9 11 6+7

- -

Overview of




Dual-site

Langmuir APHP+5A


CO H2


13X 2 3 4 6 - 1

CO2 from flue

gases


21


Recovery Purity

No Exp18

Model18

This

work Exp

18 Model

18

This

work

1 644 638 696 9975 10000 9931

2 816 864 850 9955 9989 9892

3 1065 1092 994 9900 9909 9855

4 1239 1215 1130 9835 9859 9815

5 707 825 852 9960 9988 9895

6 941 985 995 9885 9941 9854

7 1167 1172 1072 9830 9877 9833

8 1299 1213 1141 9780 9849 9811

9 2584 1702 2123 9080 9539 9447

10 2136 1609 2121 9070 9623 9475

11 2274 1550 2120 9140 9618 9478

12 2218 2274 2108 9120 9602 9477

13 939 835 845 9825 9970 9974

14 740 632 785 9890 9982 9991

15 510 500 738 9900 9988 9997

16 919 859 982 9845 9963 9960

17 707 762 856 9850 9976 9979

18 643 699 742 9870 9983 9989

19 541 613 612 9880 9993 9996

20 1151 1244 1128 9795 9871 9825

21 972 967 943 9850 9942 9940

22 674 659 726 9885 9979 9991

23 337 408 546 9900 9996 9999

24 1663 1433 1086 9585 9747 9869

25 1076 1155 962 9680 9872 9957

26 857 847 881 9730 9915 9984

27 826 721 844 9765 9910 9991

28 735 856 1135 9875 9987 9822

29 1195 1427 1117 9770 9792 9831

30 1330 1607 1120 9700 9657 9824

31 4156 3764 2638 8230 8227 8923

32 2246 1607 1511 9370 9497 9670

33 1254 800 899 9820 10000 9906

34 1383 1309 986 9380 9445 9606

35 2305 1673 1425 9370 9758 9775

42 2240 1646 2051 8900 9440 9496

43 2237 1615 2006 8230 8972 9012

22













Bed length 10 m















(wall) 13807 W(m

2K)


coefficient 1e-3 m

2s


coefficient 1e-3 m

2s


Comp a1 x10

3

(molg) a2

(K) b1 x10

9

(Pa-1

) b2

(K) -∆Hads (Jmol)

H2 432 000 5040 8505 786173

CO 092 052 5896 17309 1667742

CH4 -170 198 19952 14467 1875269

CO2 -1420 663 24775 14966 2557261






23























24



1 4 8 12

spPressCoC 01000 0060 0030 00500

spAdsIn 03600 03600 03600 03600

spAdsOut 00035 00015 00015 00015

spBlow 08000 05000 02500 04000

spPurgeIn 02250 02250 02250 02250

spPurgeOut 00300 00300 0030 00300

spPEQ1 - 00040 00025 00030

spPEQ2 - - 00050 00040

spPEQ3 - - - 00080

Feed

flowrate m3s

360e-6 360e-6 360e-6 360e-6

Purge

flowrate m3s

225e-6 225e-6 225e-6 225e-6

τPress s 10 10 20 10

τAds s 20 20 20 20

τBlow s 10 10 20 10

τPurge s 20 20 20 20

τPEQ1 s - 10 20 10

τPEQ2 s - - 20 10

τPEQ3 s - - - 10

τcycle s 60 80 160 120


No

beds

O2 purity

()

O2 recovery

()

Power

(W)

Productivity

(molkgs)

1 9687 3440 52902 918e-2

4 9950 5806 27949 485e-2

8 9958 6887 11987 208e-2

12 9936 7250 13936 242e-2

25



1 4 8 12

spPressCoC 00300 00450 00500 00500

spAdsIn 01200 01300 03300 03600

spAdsOut 00004 000035 00014 00015

spBlow 02000 02200 03000 04000

spPurgeIn 05625 01500 03000 02250

spPurgeOut 00075 00200 00400 00300

spPEQ1 - 00025 00020 00300

spPEQ2 - - 00040 00040

spPEQ3 - - - 00080

Feed flowrate m

3s

120e-6 130e-6 330e-6 360e-6

Purge

flowrate m3s

075e-6 115e-6 300e-6 225e-6

τPress s 20 15 15 10

τAds s 40 30 15 20

τBlow s 20 15 15 10

τPurge s 40 30 15 20

τPEQ1 s - 15 15 10

τPEQ2 s - - 15 10

τPEQ3 s - - - 10

τcycle s 120 120 120 120


No

beds

O2 purity

()

O2 recovery

()

Power

(W)

Productivity

(molkgs)

1 9811 2021 14420 250e-2

4 9929 3840 14069 244e-2

8 9979 6525 14092 245e-2

12 9936 7250 13936 242e-2

26



1 4 8 12

spPressCC 00030 00030 00500 00040

spAdsIn 04000 03333 03450 05000

spAdsOut 000088 000085 00015 00014

spBlow 02500 04000 03000 04000

spPurgeIn 00900 01333 03000 02000

spPurgeOut 00140 00200 00400 00300

spPEQ1 - 00050 00020 00030

spPEQ2 - - 00040 00040

spPEQ3 - - - 00080

Feed flowrate m

3s

400e-6 333e-6 345e-6 500e-6

Purge

flowrate m3s

090e-6 133e-6 300e-6 200e-6

τPress s 20 15 15 10

τAds s 40 30 15 20

τBlow s 20 15 15 10

τPurge s 40 30 15 20

τPEQ1 s - 15 15 10

τPEQ2 s - - 15 10

τPEQ3 s - - - 10

τcycle s 120 120 120 120


No beds

O2 purity ()

O2 recovery ()

Power (W)


1 9987 141 18878 203e-2

4 9997 2847 11808 205e-2

8 9997 5058 11938 207e-2

12 9983 6516 11909 207e-2

27




( )( )

( )

1

0 1


comp

uC C CN D

z t z z

z L i N


part part part part


(A1)


particle surface)



( ) ( )( ) ( )

( )

31

0


bed

bed z

c Tc uT kq T T

z t R

Tz L

z z


part part


part part

(A3)





Pf u R z L

z


part (A5)


coefficient ( )

0 1 f i p

compm i





λ (A7)


( )

0 1 z i bed

compm i

Df Sc Re z L i N

D




= forall isin λ

(A9)




Cu C C D z z L i N

z

partminus = = = =

parthellip (A12)

0 or inT T z z L= = = (A13)


0 0 and u

z z Lz

part= = =

part (A14)

0 0 or 1 icomp

Cz z L i N

z

part= = = =



end 0 0 or

Tz z L

z

part= = =

part (A16)

28


Model Equation



[ ] 0 0 1 p





( )

0 1 p i ii p comp

Q CN z L i N

t t


part parthellip

(A19)



(A20)


( ) [ ]

2

15 0 0 1

e iii i p comp

p

DQQ Q r R z L i N

t R


hellip (A21) LDF


( ) 0 1 p i i

i p comp

Q CN z L i N

t t


part parthellip

(A22)


) [ ]0 0 0 1 p




( ) [ ]22

1 0 0 1 i i

p s i p comp

p

Q QR D r R z L i N

t r rR



(A24)


( ) ( )3

0 1 p

f pi i r R compi

p

kN C C z L i N


(A25)



Qk C C D r R i N

r= =

partminus = = =

part (A26)

SD

0 0 0 1 icomp

Qr z L i N

r


parthellip (A27)


( ) ( ) [ ]

22

11 0 0 1

p ppi i i

p p p p e i p comp

p

C CQR D r R z L i N

t t r rR



(A28)




( ) ( )3

0 1 p

f pi i r R compi

p

kN C C z L i N


(A30)



Qk C C D r R i N

r= =

partminus = = =

part (A31)

PD

0 0 0 1 p

icomp

Cr z L i N

r


parthellip (A32)

29


Mode Equation

( )0 0 T

z Lz

part= forall isin

part (A33)




(A34)


( ) ( )( ) ( )3

0 bed pbed p h wall

g wall bed zbed


z t R z z


part part part part

(A35)




(A36)

LEQ



( )( ) ( )

0 comp

p p Np p pg p pg

p ig ads i

i

c c TQ

q H z Lt t


part partsum

(A37)




(A38)

LDF



( )( ) ( )

0 comp

p p Np p pg p pg

p ig ads i

i

c c TQ

q H z Lt t


part partsum

(A39)



0 0 p


(A40)

SD



( )( ) ( ) 0

compp p N

p i Rppg ads i

i

c T Qq H z L

t t


part partsum

(A41)


( ) ( )3

0 p

phg R

p

kq T T z L


(A42)


( )( ) ( )

2

2

1 0 0

p p ppp p pg p pg

p pg p p

p

c c TT

q R r R z Lt r rR


(A43)


( ) ( )

0 compN

p p ig ads i p

i

Qq H r R

t


partsum

(A44)

( ) p p

pp p

h r R r R p

Tk T T r R

r= =

partminus = λ =

part

(A45)

Nonisothermal

PD

model

Boundary conditions

0 0p

Tr

r

part= =

part (A46)


( )3 h wallwall

bed

kT T

Rminus

is neglected

30



( )

( )( )

2

2 3

180 1 0

2

bg bed

bedp

uPz L

z R


part ε (A47)


( )

( )( )

2

2 3

180 1 0

2

bg bed

bedp

uPz L

z R


part ε (A48)

Linear (Henry type)


(A49)

Extended Langmuir

2 2 1 1 exp 0 1

1


j j

j


b P T T


+ sumhellip (A50)


( )0

0

0

1 0 1 iP


QdP Q b P z L i N


(A51a)


(A51b

)

2 2 1 1 exp 0 1

1


i i


b P T T


hellip (A51c)


)


1 0 1 i

comp

itotal pure i

Xz L i N




31


Variable Equation


Wakao correlation23

( ) 033 06 20 11 0 1

m if i comp

p

Dk Sc Re z L i N



coefficient

Wakao correlation24

( )033 0620 11 Re 0 hp

k Pr z LR

λ= + forall isin

(A53)


coefficient

Wakao correlation23

( ) 20 05 0 1

m iz i comp

bed


εhellip

(A54)


coefficient

Wakao correlation24



3

3 2

12 12

1

18583 10 0 0 1 2im i p

TMW

D z L r R iP


(A56)


2

7 175 2

12

1

1013 10 0 0 1 2im i p

MWD T z L r R i

PX


Knudsen diffusivity


3 97 10 0 0 1 k i pore p comp

i

TD R z L r R i N


(A58)


0 0 1 p m i k i

e i p compp m i k i

D DD z L r R i N

D D


hellip (A59)



2

1

1

out

inv in comp

i i

P

PF C SP P i N

x MW T

minus = = hellip

sum (A60)

Molar flowrate

Otherwise ( )

21

1

critv in comp

i i

PF C SP P i N

x MW T

minus= = hellip

sum (A61)


1critP

κ

minusκ =

+ κ (A62)

Power

1

11

feed feedfeed

low cycle

P NPower RT

P

κminus

κ κ

= minus κ minus τ

(A63)

32


33


34



35



11





3




Cv = valve constant













L = bed length m



12

Q




Rbed = bed radius m




P = pressure Pa












3





13









References












1998 4 113



14






2000 35 667


2000 6 179




















15





325










AIChE J 1987 33 1045



Eng 1987 65 512










16




141






1992 47 4305








York 1994










gas AIChE J 1998 44 1325

17






Technol 2000 39 51


Technol 2000 20 185



















8084

18

















19


Ref Mass

balance

Heat

balance

Momentum

balance

Isotherm

adsorbent

No of

steps

No of

layers Application







study


experimental study


(43) LDF Bulk gas

solids -


5 1 H2 CO H2 CO2



(54) DG LDF -DG

LDF-DGSD

LDF-DGSD

- - Langmuir 4A 5A





13X 4 1 CO2 capture






Ref Mass

balance

Heat

balance

Momentum

balance

Isotherm

adsorbent

No of

beds

No of

steps

Bed

interactions

No of

layers Application






Dual-site

Langmuir

13X


ads Air separation




AC+5A

2 7 - 2 H2 CH4 CO

N2 CO2



20


Ref Mass

balance Heat

balance

Momentum

balance

Isotherm adsorbent

No of beds

No of steps

Bed interactions

No of layers

Application



N2



AC+5A 4 8


information


2 H2 CO2 CH4

CO


Langmuir

Alumina+ AC+zeolite

6 12

Information


inert +

2 ads H2 CH4 CO


gel 9 10

9 11 6+7

- -

Overview of




Dual-site

Langmuir APHP+5A


CO H2


13X 2 3 4 6 - 1

CO2 from flue

gases


21


Recovery Purity

No Exp18

Model18

This

work Exp

18 Model

18

This

work

1 644 638 696 9975 10000 9931

2 816 864 850 9955 9989 9892

3 1065 1092 994 9900 9909 9855

4 1239 1215 1130 9835 9859 9815

5 707 825 852 9960 9988 9895

6 941 985 995 9885 9941 9854

7 1167 1172 1072 9830 9877 9833

8 1299 1213 1141 9780 9849 9811

9 2584 1702 2123 9080 9539 9447

10 2136 1609 2121 9070 9623 9475

11 2274 1550 2120 9140 9618 9478

12 2218 2274 2108 9120 9602 9477

13 939 835 845 9825 9970 9974

14 740 632 785 9890 9982 9991

15 510 500 738 9900 9988 9997

16 919 859 982 9845 9963 9960

17 707 762 856 9850 9976 9979

18 643 699 742 9870 9983 9989

19 541 613 612 9880 9993 9996

20 1151 1244 1128 9795 9871 9825

21 972 967 943 9850 9942 9940

22 674 659 726 9885 9979 9991

23 337 408 546 9900 9996 9999

24 1663 1433 1086 9585 9747 9869

25 1076 1155 962 9680 9872 9957

26 857 847 881 9730 9915 9984

27 826 721 844 9765 9910 9991

28 735 856 1135 9875 9987 9822

29 1195 1427 1117 9770 9792 9831

30 1330 1607 1120 9700 9657 9824

31 4156 3764 2638 8230 8227 8923

32 2246 1607 1511 9370 9497 9670

33 1254 800 899 9820 10000 9906

34 1383 1309 986 9380 9445 9606

35 2305 1673 1425 9370 9758 9775

42 2240 1646 2051 8900 9440 9496

43 2237 1615 2006 8230 8972 9012

22













Bed length 10 m















(wall) 13807 W(m

2K)


coefficient 1e-3 m

2s


coefficient 1e-3 m

2s


Comp a1 x10

3

(molg) a2

(K) b1 x10

9

(Pa-1

) b2

(K) -∆Hads (Jmol)

H2 432 000 5040 8505 786173

CO 092 052 5896 17309 1667742

CH4 -170 198 19952 14467 1875269

CO2 -1420 663 24775 14966 2557261






23























24



1 4 8 12

spPressCoC 01000 0060 0030 00500

spAdsIn 03600 03600 03600 03600

spAdsOut 00035 00015 00015 00015

spBlow 08000 05000 02500 04000

spPurgeIn 02250 02250 02250 02250

spPurgeOut 00300 00300 0030 00300

spPEQ1 - 00040 00025 00030

spPEQ2 - - 00050 00040

spPEQ3 - - - 00080

Feed

flowrate m3s

360e-6 360e-6 360e-6 360e-6

Purge

flowrate m3s

225e-6 225e-6 225e-6 225e-6

τPress s 10 10 20 10

τAds s 20 20 20 20

τBlow s 10 10 20 10

τPurge s 20 20 20 20

τPEQ1 s - 10 20 10

τPEQ2 s - - 20 10

τPEQ3 s - - - 10

τcycle s 60 80 160 120


No

beds

O2 purity

()

O2 recovery

()

Power

(W)

Productivity

(molkgs)

1 9687 3440 52902 918e-2

4 9950 5806 27949 485e-2

8 9958 6887 11987 208e-2

12 9936 7250 13936 242e-2

25



1 4 8 12

spPressCoC 00300 00450 00500 00500

spAdsIn 01200 01300 03300 03600

spAdsOut 00004 000035 00014 00015

spBlow 02000 02200 03000 04000

spPurgeIn 05625 01500 03000 02250

spPurgeOut 00075 00200 00400 00300

spPEQ1 - 00025 00020 00300

spPEQ2 - - 00040 00040

spPEQ3 - - - 00080

Feed flowrate m

3s

120e-6 130e-6 330e-6 360e-6

Purge

flowrate m3s

075e-6 115e-6 300e-6 225e-6

τPress s 20 15 15 10

τAds s 40 30 15 20

τBlow s 20 15 15 10

τPurge s 40 30 15 20

τPEQ1 s - 15 15 10

τPEQ2 s - - 15 10

τPEQ3 s - - - 10

τcycle s 120 120 120 120


No

beds

O2 purity

()

O2 recovery

()

Power

(W)

Productivity

(molkgs)

1 9811 2021 14420 250e-2

4 9929 3840 14069 244e-2

8 9979 6525 14092 245e-2

12 9936 7250 13936 242e-2

26



1 4 8 12

spPressCC 00030 00030 00500 00040

spAdsIn 04000 03333 03450 05000

spAdsOut 000088 000085 00015 00014

spBlow 02500 04000 03000 04000

spPurgeIn 00900 01333 03000 02000

spPurgeOut 00140 00200 00400 00300

spPEQ1 - 00050 00020 00030

spPEQ2 - - 00040 00040

spPEQ3 - - - 00080

Feed flowrate m

3s

400e-6 333e-6 345e-6 500e-6

Purge

flowrate m3s

090e-6 133e-6 300e-6 200e-6

τPress s 20 15 15 10

τAds s 40 30 15 20

τBlow s 20 15 15 10

τPurge s 40 30 15 20

τPEQ1 s - 15 15 10

τPEQ2 s - - 15 10

τPEQ3 s - - - 10

τcycle s 120 120 120 120


No beds

O2 purity ()

O2 recovery ()

Power (W)


1 9987 141 18878 203e-2

4 9997 2847 11808 205e-2

8 9997 5058 11938 207e-2

12 9983 6516 11909 207e-2

27




( )( )

( )

1

0 1


comp

uC C CN D

z t z z

z L i N


part part part part


(A1)


particle surface)



( ) ( )( ) ( )

( )

31

0


bed

bed z

c Tc uT kq T T

z t R

Tz L

z z


part part


part part

(A3)





Pf u R z L

z


part (A5)


coefficient ( )

0 1 f i p

compm i





λ (A7)


( )

0 1 z i bed

compm i

Df Sc Re z L i N

D




= forall isin λ

(A9)




Cu C C D z z L i N

z

partminus = = = =

parthellip (A12)

0 or inT T z z L= = = (A13)


0 0 and u

z z Lz

part= = =

part (A14)

0 0 or 1 icomp

Cz z L i N

z

part= = = =



end 0 0 or

Tz z L

z

part= = =

part (A16)

28


Model Equation



[ ] 0 0 1 p





( )

0 1 p i ii p comp

Q CN z L i N

t t


part parthellip

(A19)



(A20)


( ) [ ]

2

15 0 0 1

e iii i p comp

p

DQQ Q r R z L i N

t R


hellip (A21) LDF


( ) 0 1 p i i

i p comp

Q CN z L i N

t t


part parthellip

(A22)


) [ ]0 0 0 1 p




( ) [ ]22

1 0 0 1 i i

p s i p comp

p

Q QR D r R z L i N

t r rR



(A24)


( ) ( )3

0 1 p

f pi i r R compi

p

kN C C z L i N


(A25)



Qk C C D r R i N

r= =

partminus = = =

part (A26)

SD

0 0 0 1 icomp

Qr z L i N

r


parthellip (A27)


( ) ( ) [ ]

22

11 0 0 1

p ppi i i

p p p p e i p comp

p

C CQR D r R z L i N

t t r rR



(A28)




( ) ( )3

0 1 p

f pi i r R compi

p

kN C C z L i N


(A30)



Qk C C D r R i N

r= =

partminus = = =

part (A31)

PD

0 0 0 1 p

icomp

Cr z L i N

r


parthellip (A32)

29


Mode Equation

( )0 0 T

z Lz

part= forall isin

part (A33)




(A34)


( ) ( )( ) ( )3

0 bed pbed p h wall

g wall bed zbed


z t R z z


part part part part

(A35)




(A36)

LEQ



( )( ) ( )

0 comp

p p Np p pg p pg

p ig ads i

i

c c TQ

q H z Lt t


part partsum

(A37)




(A38)

LDF



( )( ) ( )

0 comp

p p Np p pg p pg

p ig ads i

i

c c TQ

q H z Lt t


part partsum

(A39)



0 0 p


(A40)

SD



( )( ) ( ) 0

compp p N

p i Rppg ads i

i

c T Qq H z L

t t


part partsum

(A41)


( ) ( )3

0 p

phg R

p

kq T T z L


(A42)


( )( ) ( )

2

2

1 0 0

p p ppp p pg p pg

p pg p p

p

c c TT

q R r R z Lt r rR


(A43)


( ) ( )

0 compN

p p ig ads i p

i

Qq H r R

t


partsum

(A44)

( ) p p

pp p

h r R r R p

Tk T T r R

r= =

partminus = λ =

part

(A45)

Nonisothermal

PD

model

Boundary conditions

0 0p

Tr

r

part= =

part (A46)


( )3 h wallwall

bed

kT T

Rminus

is neglected

30



( )

( )( )

2

2 3

180 1 0

2

bg bed

bedp

uPz L

z R


part ε (A47)


( )

( )( )

2

2 3

180 1 0

2

bg bed

bedp

uPz L

z R


part ε (A48)

Linear (Henry type)


(A49)

Extended Langmuir

2 2 1 1 exp 0 1

1


j j

j


b P T T


+ sumhellip (A50)


( )0

0

0

1 0 1 iP


QdP Q b P z L i N


(A51a)


(A51b

)

2 2 1 1 exp 0 1

1


i i


b P T T


hellip (A51c)


)


1 0 1 i

comp

itotal pure i

Xz L i N




31


Variable Equation


Wakao correlation23

( ) 033 06 20 11 0 1

m if i comp

p

Dk Sc Re z L i N



coefficient

Wakao correlation24

( )033 0620 11 Re 0 hp

k Pr z LR

λ= + forall isin

(A53)


coefficient

Wakao correlation23

( ) 20 05 0 1

m iz i comp

bed


εhellip

(A54)


coefficient

Wakao correlation24



3

3 2

12 12

1

18583 10 0 0 1 2im i p

TMW

D z L r R iP


(A56)


2

7 175 2

12

1

1013 10 0 0 1 2im i p

MWD T z L r R i

PX


Knudsen diffusivity


3 97 10 0 0 1 k i pore p comp

i

TD R z L r R i N


(A58)


0 0 1 p m i k i

e i p compp m i k i

D DD z L r R i N

D D


hellip (A59)



2

1

1

out

inv in comp

i i

P

PF C SP P i N

x MW T

minus = = hellip

sum (A60)

Molar flowrate

Otherwise ( )

21

1

critv in comp

i i

PF C SP P i N

x MW T

minus= = hellip

sum (A61)


1critP

κ

minusκ =

+ κ (A62)

Power

1

11

feed feedfeed

low cycle

P NPower RT

P

κminus

κ κ

= minus κ minus τ

(A63)

32


33


34



35



12

Q




Rbed = bed radius m




P = pressure Pa












3





13









References












1998 4 113



14






2000 35 667


2000 6 179




















15





325










AIChE J 1987 33 1045



Eng 1987 65 512










16




141






1992 47 4305








York 1994










gas AIChE J 1998 44 1325

17






Technol 2000 39 51


Technol 2000 20 185



















8084

18

















19


Ref Mass

balance

Heat

balance

Momentum

balance

Isotherm

adsorbent

No of

steps

No of

layers Application







study


experimental study


(43) LDF Bulk gas

solids -


5 1 H2 CO H2 CO2



(54) DG LDF -DG

LDF-DGSD

LDF-DGSD

- - Langmuir 4A 5A





13X 4 1 CO2 capture






Ref Mass

balance

Heat

balance

Momentum

balance

Isotherm

adsorbent

No of

beds

No of

steps

Bed

interactions

No of

layers Application






Dual-site

Langmuir

13X


ads Air separation




AC+5A

2 7 - 2 H2 CH4 CO

N2 CO2



20


Ref Mass

balance Heat

balance

Momentum

balance

Isotherm adsorbent

No of beds

No of steps

Bed interactions

No of layers

Application



N2



AC+5A 4 8


information


2 H2 CO2 CH4

CO


Langmuir

Alumina+ AC+zeolite

6 12

Information


inert +

2 ads H2 CH4 CO


gel 9 10

9 11 6+7

- -

Overview of




Dual-site

Langmuir APHP+5A


CO H2


13X 2 3 4 6 - 1

CO2 from flue

gases


21


Recovery Purity

No Exp18

Model18

This

work Exp

18 Model

18

This

work

1 644 638 696 9975 10000 9931

2 816 864 850 9955 9989 9892

3 1065 1092 994 9900 9909 9855

4 1239 1215 1130 9835 9859 9815

5 707 825 852 9960 9988 9895

6 941 985 995 9885 9941 9854

7 1167 1172 1072 9830 9877 9833

8 1299 1213 1141 9780 9849 9811

9 2584 1702 2123 9080 9539 9447

10 2136 1609 2121 9070 9623 9475

11 2274 1550 2120 9140 9618 9478

12 2218 2274 2108 9120 9602 9477

13 939 835 845 9825 9970 9974

14 740 632 785 9890 9982 9991

15 510 500 738 9900 9988 9997

16 919 859 982 9845 9963 9960

17 707 762 856 9850 9976 9979

18 643 699 742 9870 9983 9989

19 541 613 612 9880 9993 9996

20 1151 1244 1128 9795 9871 9825

21 972 967 943 9850 9942 9940

22 674 659 726 9885 9979 9991

23 337 408 546 9900 9996 9999

24 1663 1433 1086 9585 9747 9869

25 1076 1155 962 9680 9872 9957

26 857 847 881 9730 9915 9984

27 826 721 844 9765 9910 9991

28 735 856 1135 9875 9987 9822

29 1195 1427 1117 9770 9792 9831

30 1330 1607 1120 9700 9657 9824

31 4156 3764 2638 8230 8227 8923

32 2246 1607 1511 9370 9497 9670

33 1254 800 899 9820 10000 9906

34 1383 1309 986 9380 9445 9606

35 2305 1673 1425 9370 9758 9775

42 2240 1646 2051 8900 9440 9496

43 2237 1615 2006 8230 8972 9012

22













Bed length 10 m















(wall) 13807 W(m

2K)


coefficient 1e-3 m

2s


coefficient 1e-3 m

2s


Comp a1 x10

3

(molg) a2

(K) b1 x10

9

(Pa-1

) b2

(K) -∆Hads (Jmol)

H2 432 000 5040 8505 786173

CO 092 052 5896 17309 1667742

CH4 -170 198 19952 14467 1875269

CO2 -1420 663 24775 14966 2557261






23























24



1 4 8 12

spPressCoC 01000 0060 0030 00500

spAdsIn 03600 03600 03600 03600

spAdsOut 00035 00015 00015 00015

spBlow 08000 05000 02500 04000

spPurgeIn 02250 02250 02250 02250

spPurgeOut 00300 00300 0030 00300

spPEQ1 - 00040 00025 00030

spPEQ2 - - 00050 00040

spPEQ3 - - - 00080

Feed

flowrate m3s

360e-6 360e-6 360e-6 360e-6

Purge

flowrate m3s

225e-6 225e-6 225e-6 225e-6

τPress s 10 10 20 10

τAds s 20 20 20 20

τBlow s 10 10 20 10

τPurge s 20 20 20 20

τPEQ1 s - 10 20 10

τPEQ2 s - - 20 10

τPEQ3 s - - - 10

τcycle s 60 80 160 120


No

beds

O2 purity

()

O2 recovery

()

Power

(W)

Productivity

(molkgs)

1 9687 3440 52902 918e-2

4 9950 5806 27949 485e-2

8 9958 6887 11987 208e-2

12 9936 7250 13936 242e-2

25



1 4 8 12

spPressCoC 00300 00450 00500 00500

spAdsIn 01200 01300 03300 03600

spAdsOut 00004 000035 00014 00015

spBlow 02000 02200 03000 04000

spPurgeIn 05625 01500 03000 02250

spPurgeOut 00075 00200 00400 00300

spPEQ1 - 00025 00020 00300

spPEQ2 - - 00040 00040

spPEQ3 - - - 00080

Feed flowrate m

3s

120e-6 130e-6 330e-6 360e-6

Purge

flowrate m3s

075e-6 115e-6 300e-6 225e-6

τPress s 20 15 15 10

τAds s 40 30 15 20

τBlow s 20 15 15 10

τPurge s 40 30 15 20

τPEQ1 s - 15 15 10

τPEQ2 s - - 15 10

τPEQ3 s - - - 10

τcycle s 120 120 120 120


No

beds

O2 purity

()

O2 recovery

()

Power

(W)

Productivity

(molkgs)

1 9811 2021 14420 250e-2

4 9929 3840 14069 244e-2

8 9979 6525 14092 245e-2

12 9936 7250 13936 242e-2

26



1 4 8 12

spPressCC 00030 00030 00500 00040

spAdsIn 04000 03333 03450 05000

spAdsOut 000088 000085 00015 00014

spBlow 02500 04000 03000 04000

spPurgeIn 00900 01333 03000 02000

spPurgeOut 00140 00200 00400 00300

spPEQ1 - 00050 00020 00030

spPEQ2 - - 00040 00040

spPEQ3 - - - 00080

Feed flowrate m

3s

400e-6 333e-6 345e-6 500e-6

Purge

flowrate m3s

090e-6 133e-6 300e-6 200e-6

τPress s 20 15 15 10

τAds s 40 30 15 20

τBlow s 20 15 15 10

τPurge s 40 30 15 20

τPEQ1 s - 15 15 10

τPEQ2 s - - 15 10

τPEQ3 s - - - 10

τcycle s 120 120 120 120


No beds

O2 purity ()

O2 recovery ()

Power (W)


1 9987 141 18878 203e-2

4 9997 2847 11808 205e-2

8 9997 5058 11938 207e-2

12 9983 6516 11909 207e-2

27




( )( )

( )

1

0 1


comp

uC C CN D

z t z z

z L i N


part part part part


(A1)


particle surface)



( ) ( )( ) ( )

( )

31

0


bed

bed z

c Tc uT kq T T

z t R

Tz L

z z


part part


part part

(A3)





Pf u R z L

z


part (A5)


coefficient ( )

0 1 f i p

compm i





λ (A7)


( )

0 1 z i bed

compm i

Df Sc Re z L i N

D




= forall isin λ

(A9)




Cu C C D z z L i N

z

partminus = = = =

parthellip (A12)

0 or inT T z z L= = = (A13)


0 0 and u

z z Lz

part= = =

part (A14)

0 0 or 1 icomp

Cz z L i N

z

part= = = =



end 0 0 or

Tz z L

z

part= = =

part (A16)

28


Model Equation



[ ] 0 0 1 p





( )

0 1 p i ii p comp

Q CN z L i N

t t


part parthellip

(A19)



(A20)


( ) [ ]

2

15 0 0 1

e iii i p comp

p

DQQ Q r R z L i N

t R


hellip (A21) LDF


( ) 0 1 p i i

i p comp

Q CN z L i N

t t


part parthellip

(A22)


) [ ]0 0 0 1 p




( ) [ ]22

1 0 0 1 i i

p s i p comp

p

Q QR D r R z L i N

t r rR



(A24)


( ) ( )3

0 1 p

f pi i r R compi

p

kN C C z L i N


(A25)



Qk C C D r R i N

r= =

partminus = = =

part (A26)

SD

0 0 0 1 icomp

Qr z L i N

r


parthellip (A27)


( ) ( ) [ ]

22

11 0 0 1

p ppi i i

p p p p e i p comp

p

C CQR D r R z L i N

t t r rR



(A28)




( ) ( )3

0 1 p

f pi i r R compi

p

kN C C z L i N


(A30)



Qk C C D r R i N

r= =

partminus = = =

part (A31)

PD

0 0 0 1 p

icomp

Cr z L i N

r


parthellip (A32)

29


Mode Equation

( )0 0 T

z Lz

part= forall isin

part (A33)




(A34)


( ) ( )( ) ( )3

0 bed pbed p h wall

g wall bed zbed


z t R z z


part part part part

(A35)




(A36)

LEQ



( )( ) ( )

0 comp

p p Np p pg p pg

p ig ads i

i

c c TQ

q H z Lt t


part partsum

(A37)




(A38)

LDF



( )( ) ( )

0 comp

p p Np p pg p pg

p ig ads i

i

c c TQ

q H z Lt t


part partsum

(A39)



0 0 p


(A40)

SD



( )( ) ( ) 0

compp p N

p i Rppg ads i

i

c T Qq H z L

t t


part partsum

(A41)


( ) ( )3

0 p

phg R

p

kq T T z L


(A42)


( )( ) ( )

2

2

1 0 0

p p ppp p pg p pg

p pg p p

p

c c TT

q R r R z Lt r rR


(A43)


( ) ( )

0 compN

p p ig ads i p

i

Qq H r R

t


partsum

(A44)

( ) p p

pp p

h r R r R p

Tk T T r R

r= =

partminus = λ =

part

(A45)

Nonisothermal

PD

model

Boundary conditions

0 0p

Tr

r

part= =

part (A46)


( )3 h wallwall

bed

kT T

Rminus

is neglected

30



( )

( )( )

2

2 3

180 1 0

2

bg bed

bedp

uPz L

z R


part ε (A47)


( )

( )( )

2

2 3

180 1 0

2

bg bed

bedp

uPz L

z R


part ε (A48)

Linear (Henry type)


(A49)

Extended Langmuir

2 2 1 1 exp 0 1

1


j j

j


b P T T


+ sumhellip (A50)


( )0

0

0

1 0 1 iP


QdP Q b P z L i N


(A51a)


(A51b

)

2 2 1 1 exp 0 1

1


i i


b P T T


hellip (A51c)


)


1 0 1 i

comp

itotal pure i

Xz L i N




31


Variable Equation


Wakao correlation23

( ) 033 06 20 11 0 1

m if i comp

p

Dk Sc Re z L i N



coefficient

Wakao correlation24

( )033 0620 11 Re 0 hp

k Pr z LR

λ= + forall isin

(A53)


coefficient

Wakao correlation23

( ) 20 05 0 1

m iz i comp

bed


εhellip

(A54)


coefficient

Wakao correlation24



3

3 2

12 12

1

18583 10 0 0 1 2im i p

TMW

D z L r R iP


(A56)


2

7 175 2

12

1

1013 10 0 0 1 2im i p

MWD T z L r R i

PX


Knudsen diffusivity


3 97 10 0 0 1 k i pore p comp

i

TD R z L r R i N


(A58)


0 0 1 p m i k i

e i p compp m i k i

D DD z L r R i N

D D


hellip (A59)



2

1

1

out

inv in comp

i i

P

PF C SP P i N

x MW T

minus = = hellip

sum (A60)

Molar flowrate

Otherwise ( )

21

1

critv in comp

i i

PF C SP P i N

x MW T

minus= = hellip

sum (A61)


1critP

κ

minusκ =

+ κ (A62)

Power

1

11

feed feedfeed

low cycle

P NPower RT

P

κminus

κ κ

= minus κ minus τ

(A63)

32


33


34



35



13









References












1998 4 113



14






2000 35 667


2000 6 179




















15





325










AIChE J 1987 33 1045



Eng 1987 65 512










16




141






1992 47 4305








York 1994










gas AIChE J 1998 44 1325

17






Technol 2000 39 51


Technol 2000 20 185



















8084

18

















19


Ref Mass

balance

Heat

balance

Momentum

balance

Isotherm

adsorbent

No of

steps

No of

layers Application







study


experimental study


(43) LDF Bulk gas

solids -


5 1 H2 CO H2 CO2



(54) DG LDF -DG

LDF-DGSD

LDF-DGSD

- - Langmuir 4A 5A





13X 4 1 CO2 capture






Ref Mass

balance

Heat

balance

Momentum

balance

Isotherm

adsorbent

No of

beds

No of

steps

Bed

interactions

No of

layers Application






Dual-site

Langmuir

13X


ads Air separation




AC+5A

2 7 - 2 H2 CH4 CO

N2 CO2



20


Ref Mass

balance Heat

balance

Momentum

balance

Isotherm adsorbent

No of beds

No of steps

Bed interactions

No of layers

Application



N2



AC+5A 4 8


information


2 H2 CO2 CH4

CO


Langmuir

Alumina+ AC+zeolite

6 12

Information


inert +

2 ads H2 CH4 CO


gel 9 10

9 11 6+7

- -

Overview of




Dual-site

Langmuir APHP+5A


CO H2


13X 2 3 4 6 - 1

CO2 from flue

gases


21


Recovery Purity

No Exp18

Model18

This

work Exp

18 Model

18

This

work

1 644 638 696 9975 10000 9931

2 816 864 850 9955 9989 9892

3 1065 1092 994 9900 9909 9855

4 1239 1215 1130 9835 9859 9815

5 707 825 852 9960 9988 9895

6 941 985 995 9885 9941 9854

7 1167 1172 1072 9830 9877 9833

8 1299 1213 1141 9780 9849 9811

9 2584 1702 2123 9080 9539 9447

10 2136 1609 2121 9070 9623 9475

11 2274 1550 2120 9140 9618 9478

12 2218 2274 2108 9120 9602 9477

13 939 835 845 9825 9970 9974

14 740 632 785 9890 9982 9991

15 510 500 738 9900 9988 9997

16 919 859 982 9845 9963 9960

17 707 762 856 9850 9976 9979

18 643 699 742 9870 9983 9989

19 541 613 612 9880 9993 9996

20 1151 1244 1128 9795 9871 9825

21 972 967 943 9850 9942 9940

22 674 659 726 9885 9979 9991

23 337 408 546 9900 9996 9999

24 1663 1433 1086 9585 9747 9869

25 1076 1155 962 9680 9872 9957

26 857 847 881 9730 9915 9984

27 826 721 844 9765 9910 9991

28 735 856 1135 9875 9987 9822

29 1195 1427 1117 9770 9792 9831

30 1330 1607 1120 9700 9657 9824

31 4156 3764 2638 8230 8227 8923

32 2246 1607 1511 9370 9497 9670

33 1254 800 899 9820 10000 9906

34 1383 1309 986 9380 9445 9606

35 2305 1673 1425 9370 9758 9775

42 2240 1646 2051 8900 9440 9496

43 2237 1615 2006 8230 8972 9012

22













Bed length 10 m















(wall) 13807 W(m

2K)


coefficient 1e-3 m

2s


coefficient 1e-3 m

2s


Comp a1 x10

3

(molg) a2

(K) b1 x10

9

(Pa-1

) b2

(K) -∆Hads (Jmol)

H2 432 000 5040 8505 786173

CO 092 052 5896 17309 1667742

CH4 -170 198 19952 14467 1875269

CO2 -1420 663 24775 14966 2557261






23























24



1 4 8 12

spPressCoC 01000 0060 0030 00500

spAdsIn 03600 03600 03600 03600

spAdsOut 00035 00015 00015 00015

spBlow 08000 05000 02500 04000

spPurgeIn 02250 02250 02250 02250

spPurgeOut 00300 00300 0030 00300

spPEQ1 - 00040 00025 00030

spPEQ2 - - 00050 00040

spPEQ3 - - - 00080

Feed

flowrate m3s

360e-6 360e-6 360e-6 360e-6

Purge

flowrate m3s

225e-6 225e-6 225e-6 225e-6

τPress s 10 10 20 10

τAds s 20 20 20 20

τBlow s 10 10 20 10

τPurge s 20 20 20 20

τPEQ1 s - 10 20 10

τPEQ2 s - - 20 10

τPEQ3 s - - - 10

τcycle s 60 80 160 120


No

beds

O2 purity

()

O2 recovery

()

Power

(W)

Productivity

(molkgs)

1 9687 3440 52902 918e-2

4 9950 5806 27949 485e-2

8 9958 6887 11987 208e-2

12 9936 7250 13936 242e-2

25



1 4 8 12

spPressCoC 00300 00450 00500 00500

spAdsIn 01200 01300 03300 03600

spAdsOut 00004 000035 00014 00015

spBlow 02000 02200 03000 04000

spPurgeIn 05625 01500 03000 02250

spPurgeOut 00075 00200 00400 00300

spPEQ1 - 00025 00020 00300

spPEQ2 - - 00040 00040

spPEQ3 - - - 00080

Feed flowrate m

3s

120e-6 130e-6 330e-6 360e-6

Purge

flowrate m3s

075e-6 115e-6 300e-6 225e-6

τPress s 20 15 15 10

τAds s 40 30 15 20

τBlow s 20 15 15 10

τPurge s 40 30 15 20

τPEQ1 s - 15 15 10

τPEQ2 s - - 15 10

τPEQ3 s - - - 10

τcycle s 120 120 120 120


No

beds

O2 purity

()

O2 recovery

()

Power

(W)

Productivity

(molkgs)

1 9811 2021 14420 250e-2

4 9929 3840 14069 244e-2

8 9979 6525 14092 245e-2

12 9936 7250 13936 242e-2

26



1 4 8 12

spPressCC 00030 00030 00500 00040

spAdsIn 04000 03333 03450 05000

spAdsOut 000088 000085 00015 00014

spBlow 02500 04000 03000 04000

spPurgeIn 00900 01333 03000 02000

spPurgeOut 00140 00200 00400 00300

spPEQ1 - 00050 00020 00030

spPEQ2 - - 00040 00040

spPEQ3 - - - 00080

Feed flowrate m

3s

400e-6 333e-6 345e-6 500e-6

Purge

flowrate m3s

090e-6 133e-6 300e-6 200e-6

τPress s 20 15 15 10

τAds s 40 30 15 20

τBlow s 20 15 15 10

τPurge s 40 30 15 20

τPEQ1 s - 15 15 10

τPEQ2 s - - 15 10

τPEQ3 s - - - 10

τcycle s 120 120 120 120


No beds

O2 purity ()

O2 recovery ()

Power (W)


1 9987 141 18878 203e-2

4 9997 2847 11808 205e-2

8 9997 5058 11938 207e-2

12 9983 6516 11909 207e-2

27




( )( )

( )

1

0 1


comp

uC C CN D

z t z z

z L i N


part part part part


(A1)


particle surface)



( ) ( )( ) ( )

( )

31

0


bed

bed z

c Tc uT kq T T

z t R

Tz L

z z


part part


part part

(A3)





Pf u R z L

z


part (A5)


coefficient ( )

0 1 f i p

compm i





λ (A7)


( )

0 1 z i bed

compm i

Df Sc Re z L i N

D




= forall isin λ

(A9)




Cu C C D z z L i N

z

partminus = = = =

parthellip (A12)

0 or inT T z z L= = = (A13)


0 0 and u

z z Lz

part= = =

part (A14)

0 0 or 1 icomp

Cz z L i N

z

part= = = =



end 0 0 or

Tz z L

z

part= = =

part (A16)

28


Model Equation



[ ] 0 0 1 p





( )

0 1 p i ii p comp

Q CN z L i N

t t


part parthellip

(A19)



(A20)


( ) [ ]

2

15 0 0 1

e iii i p comp

p

DQQ Q r R z L i N

t R


hellip (A21) LDF


( ) 0 1 p i i

i p comp

Q CN z L i N

t t


part parthellip

(A22)


) [ ]0 0 0 1 p




( ) [ ]22

1 0 0 1 i i

p s i p comp

p

Q QR D r R z L i N

t r rR



(A24)


( ) ( )3

0 1 p

f pi i r R compi

p

kN C C z L i N


(A25)



Qk C C D r R i N

r= =

partminus = = =

part (A26)

SD

0 0 0 1 icomp

Qr z L i N

r


parthellip (A27)


( ) ( ) [ ]

22

11 0 0 1

p ppi i i

p p p p e i p comp

p

C CQR D r R z L i N

t t r rR



(A28)




( ) ( )3

0 1 p

f pi i r R compi

p

kN C C z L i N


(A30)



Qk C C D r R i N

r= =

partminus = = =

part (A31)

PD

0 0 0 1 p

icomp

Cr z L i N

r


parthellip (A32)

29


Mode Equation

( )0 0 T

z Lz

part= forall isin

part (A33)




(A34)


( ) ( )( ) ( )3

0 bed pbed p h wall

g wall bed zbed


z t R z z


part part part part

(A35)




(A36)

LEQ



( )( ) ( )

0 comp

p p Np p pg p pg

p ig ads i

i

c c TQ

q H z Lt t


part partsum

(A37)




(A38)

LDF



( )( ) ( )

0 comp

p p Np p pg p pg

p ig ads i

i

c c TQ

q H z Lt t


part partsum

(A39)



0 0 p


(A40)

SD



( )( ) ( ) 0

compp p N

p i Rppg ads i

i

c T Qq H z L

t t


part partsum

(A41)


( ) ( )3

0 p

phg R

p

kq T T z L


(A42)


( )( ) ( )

2

2

1 0 0

p p ppp p pg p pg

p pg p p

p

c c TT

q R r R z Lt r rR


(A43)


( ) ( )

0 compN

p p ig ads i p

i

Qq H r R

t


partsum

(A44)

( ) p p

pp p

h r R r R p

Tk T T r R

r= =

partminus = λ =

part

(A45)

Nonisothermal

PD

model

Boundary conditions

0 0p

Tr

r

part= =

part (A46)


( )3 h wallwall

bed

kT T

Rminus

is neglected

30



( )

( )( )

2

2 3

180 1 0

2

bg bed

bedp

uPz L

z R


part ε (A47)


( )

( )( )

2

2 3

180 1 0

2

bg bed

bedp

uPz L

z R


part ε (A48)

Linear (Henry type)


(A49)

Extended Langmuir

2 2 1 1 exp 0 1

1


j j

j


b P T T


+ sumhellip (A50)


( )0

0

0

1 0 1 iP


QdP Q b P z L i N


(A51a)


(A51b

)

2 2 1 1 exp 0 1

1


i i


b P T T


hellip (A51c)


)


1 0 1 i

comp

itotal pure i

Xz L i N




31


Variable Equation


Wakao correlation23

( ) 033 06 20 11 0 1

m if i comp

p

Dk Sc Re z L i N



coefficient

Wakao correlation24

( )033 0620 11 Re 0 hp

k Pr z LR

λ= + forall isin

(A53)


coefficient

Wakao correlation23

( ) 20 05 0 1

m iz i comp

bed


εhellip

(A54)


coefficient

Wakao correlation24



3

3 2

12 12

1

18583 10 0 0 1 2im i p

TMW

D z L r R iP


(A56)


2

7 175 2

12

1

1013 10 0 0 1 2im i p

MWD T z L r R i

PX


Knudsen diffusivity


3 97 10 0 0 1 k i pore p comp

i

TD R z L r R i N


(A58)


0 0 1 p m i k i

e i p compp m i k i

D DD z L r R i N

D D


hellip (A59)



2

1

1

out

inv in comp

i i

P

PF C SP P i N

x MW T

minus = = hellip

sum (A60)

Molar flowrate

Otherwise ( )

21

1

critv in comp

i i

PF C SP P i N

x MW T

minus= = hellip

sum (A61)


1critP

κ

minusκ =

+ κ (A62)

Power

1

11

feed feedfeed

low cycle

P NPower RT

P

κminus

κ κ

= minus κ minus τ

(A63)

32


33


34



35



14






2000 35 667


2000 6 179




















15





325










AIChE J 1987 33 1045



Eng 1987 65 512










16




141






1992 47 4305








York 1994










gas AIChE J 1998 44 1325

17






Technol 2000 39 51


Technol 2000 20 185



















8084

18

















19


Ref Mass

balance

Heat

balance

Momentum

balance

Isotherm

adsorbent

No of

steps

No of

layers Application







study


experimental study


(43) LDF Bulk gas

solids -


5 1 H2 CO H2 CO2



(54) DG LDF -DG

LDF-DGSD

LDF-DGSD

- - Langmuir 4A 5A





13X 4 1 CO2 capture






Ref Mass

balance

Heat

balance

Momentum

balance

Isotherm

adsorbent

No of

beds

No of

steps

Bed

interactions

No of

layers Application






Dual-site

Langmuir

13X


ads Air separation




AC+5A

2 7 - 2 H2 CH4 CO

N2 CO2



20


Ref Mass

balance Heat

balance

Momentum

balance

Isotherm adsorbent

No of beds

No of steps

Bed interactions

No of layers

Application



N2



AC+5A 4 8


information


2 H2 CO2 CH4

CO


Langmuir

Alumina+ AC+zeolite

6 12

Information


inert +

2 ads H2 CH4 CO


gel 9 10

9 11 6+7

- -

Overview of




Dual-site

Langmuir APHP+5A


CO H2


13X 2 3 4 6 - 1

CO2 from flue

gases


21


Recovery Purity

No Exp18

Model18

This

work Exp

18 Model

18

This

work

1 644 638 696 9975 10000 9931

2 816 864 850 9955 9989 9892

3 1065 1092 994 9900 9909 9855

4 1239 1215 1130 9835 9859 9815

5 707 825 852 9960 9988 9895

6 941 985 995 9885 9941 9854

7 1167 1172 1072 9830 9877 9833

8 1299 1213 1141 9780 9849 9811

9 2584 1702 2123 9080 9539 9447

10 2136 1609 2121 9070 9623 9475

11 2274 1550 2120 9140 9618 9478

12 2218 2274 2108 9120 9602 9477

13 939 835 845 9825 9970 9974

14 740 632 785 9890 9982 9991

15 510 500 738 9900 9988 9997

16 919 859 982 9845 9963 9960

17 707 762 856 9850 9976 9979

18 643 699 742 9870 9983 9989

19 541 613 612 9880 9993 9996

20 1151 1244 1128 9795 9871 9825

21 972 967 943 9850 9942 9940

22 674 659 726 9885 9979 9991

23 337 408 546 9900 9996 9999

24 1663 1433 1086 9585 9747 9869

25 1076 1155 962 9680 9872 9957

26 857 847 881 9730 9915 9984

27 826 721 844 9765 9910 9991

28 735 856 1135 9875 9987 9822

29 1195 1427 1117 9770 9792 9831

30 1330 1607 1120 9700 9657 9824

31 4156 3764 2638 8230 8227 8923

32 2246 1607 1511 9370 9497 9670

33 1254 800 899 9820 10000 9906

34 1383 1309 986 9380 9445 9606

35 2305 1673 1425 9370 9758 9775

42 2240 1646 2051 8900 9440 9496

43 2237 1615 2006 8230 8972 9012

22













Bed length 10 m















(wall) 13807 W(m

2K)


coefficient 1e-3 m

2s


coefficient 1e-3 m

2s


Comp a1 x10

3

(molg) a2

(K) b1 x10

9

(Pa-1

) b2

(K) -∆Hads (Jmol)

H2 432 000 5040 8505 786173

CO 092 052 5896 17309 1667742

CH4 -170 198 19952 14467 1875269

CO2 -1420 663 24775 14966 2557261






23























24



1 4 8 12

spPressCoC 01000 0060 0030 00500

spAdsIn 03600 03600 03600 03600

spAdsOut 00035 00015 00015 00015

spBlow 08000 05000 02500 04000

spPurgeIn 02250 02250 02250 02250

spPurgeOut 00300 00300 0030 00300

spPEQ1 - 00040 00025 00030

spPEQ2 - - 00050 00040

spPEQ3 - - - 00080

Feed

flowrate m3s

360e-6 360e-6 360e-6 360e-6

Purge

flowrate m3s

225e-6 225e-6 225e-6 225e-6

τPress s 10 10 20 10

τAds s 20 20 20 20

τBlow s 10 10 20 10

τPurge s 20 20 20 20

τPEQ1 s - 10 20 10

τPEQ2 s - - 20 10

τPEQ3 s - - - 10

τcycle s 60 80 160 120


No

beds

O2 purity

()

O2 recovery

()

Power

(W)

Productivity

(molkgs)

1 9687 3440 52902 918e-2

4 9950 5806 27949 485e-2

8 9958 6887 11987 208e-2

12 9936 7250 13936 242e-2

25



1 4 8 12

spPressCoC 00300 00450 00500 00500

spAdsIn 01200 01300 03300 03600

spAdsOut 00004 000035 00014 00015

spBlow 02000 02200 03000 04000

spPurgeIn 05625 01500 03000 02250

spPurgeOut 00075 00200 00400 00300

spPEQ1 - 00025 00020 00300

spPEQ2 - - 00040 00040

spPEQ3 - - - 00080

Feed flowrate m

3s

120e-6 130e-6 330e-6 360e-6

Purge

flowrate m3s

075e-6 115e-6 300e-6 225e-6

τPress s 20 15 15 10

τAds s 40 30 15 20

τBlow s 20 15 15 10

τPurge s 40 30 15 20

τPEQ1 s - 15 15 10

τPEQ2 s - - 15 10

τPEQ3 s - - - 10

τcycle s 120 120 120 120


No

beds

O2 purity

()

O2 recovery

()

Power

(W)

Productivity

(molkgs)

1 9811 2021 14420 250e-2

4 9929 3840 14069 244e-2

8 9979 6525 14092 245e-2

12 9936 7250 13936 242e-2

26



1 4 8 12

spPressCC 00030 00030 00500 00040

spAdsIn 04000 03333 03450 05000

spAdsOut 000088 000085 00015 00014

spBlow 02500 04000 03000 04000

spPurgeIn 00900 01333 03000 02000

spPurgeOut 00140 00200 00400 00300

spPEQ1 - 00050 00020 00030

spPEQ2 - - 00040 00040

spPEQ3 - - - 00080

Feed flowrate m

3s

400e-6 333e-6 345e-6 500e-6

Purge

flowrate m3s

090e-6 133e-6 300e-6 200e-6

τPress s 20 15 15 10

τAds s 40 30 15 20

τBlow s 20 15 15 10

τPurge s 40 30 15 20

τPEQ1 s - 15 15 10

τPEQ2 s - - 15 10

τPEQ3 s - - - 10

τcycle s 120 120 120 120


No beds

O2 purity ()

O2 recovery ()

Power (W)


1 9987 141 18878 203e-2

4 9997 2847 11808 205e-2

8 9997 5058 11938 207e-2

12 9983 6516 11909 207e-2

27




( )( )

( )

1

0 1


comp

uC C CN D

z t z z

z L i N


part part part part


(A1)


particle surface)



( ) ( )( ) ( )

( )

31

0


bed

bed z

c Tc uT kq T T

z t R

Tz L

z z


part part


part part

(A3)





Pf u R z L

z


part (A5)


coefficient ( )

0 1 f i p

compm i





λ (A7)


( )

0 1 z i bed

compm i

Df Sc Re z L i N

D




= forall isin λ

(A9)




Cu C C D z z L i N

z

partminus = = = =

parthellip (A12)

0 or inT T z z L= = = (A13)


0 0 and u

z z Lz

part= = =

part (A14)

0 0 or 1 icomp

Cz z L i N

z

part= = = =



end 0 0 or

Tz z L

z

part= = =

part (A16)

28


Model Equation



[ ] 0 0 1 p





( )

0 1 p i ii p comp

Q CN z L i N

t t


part parthellip

(A19)



(A20)


( ) [ ]

2

15 0 0 1

e iii i p comp

p

DQQ Q r R z L i N

t R


hellip (A21) LDF


( ) 0 1 p i i

i p comp

Q CN z L i N

t t


part parthellip

(A22)


) [ ]0 0 0 1 p




( ) [ ]22

1 0 0 1 i i

p s i p comp

p

Q QR D r R z L i N

t r rR



(A24)


( ) ( )3

0 1 p

f pi i r R compi

p

kN C C z L i N


(A25)



Qk C C D r R i N

r= =

partminus = = =

part (A26)

SD

0 0 0 1 icomp

Qr z L i N

r


parthellip (A27)


( ) ( ) [ ]

22

11 0 0 1

p ppi i i

p p p p e i p comp

p

C CQR D r R z L i N

t t r rR



(A28)




( ) ( )3

0 1 p

f pi i r R compi

p

kN C C z L i N


(A30)



Qk C C D r R i N

r= =

partminus = = =

part (A31)

PD

0 0 0 1 p

icomp

Cr z L i N

r


parthellip (A32)

29


Mode Equation

( )0 0 T

z Lz

part= forall isin

part (A33)




(A34)


( ) ( )( ) ( )3

0 bed pbed p h wall

g wall bed zbed


z t R z z


part part part part

(A35)




(A36)

LEQ



( )( ) ( )

0 comp

p p Np p pg p pg

p ig ads i

i

c c TQ

q H z Lt t


part partsum

(A37)




(A38)

LDF



( )( ) ( )

0 comp

p p Np p pg p pg

p ig ads i

i

c c TQ

q H z Lt t


part partsum

(A39)



0 0 p


(A40)

SD



( )( ) ( ) 0

compp p N

p i Rppg ads i

i

c T Qq H z L

t t


part partsum

(A41)


( ) ( )3

0 p

phg R

p

kq T T z L


(A42)


( )( ) ( )

2

2

1 0 0

p p ppp p pg p pg

p pg p p

p

c c TT

q R r R z Lt r rR


(A43)


( ) ( )

0 compN

p p ig ads i p

i

Qq H r R

t


partsum

(A44)

( ) p p

pp p

h r R r R p

Tk T T r R

r= =

partminus = λ =

part

(A45)

Nonisothermal

PD

model

Boundary conditions

0 0p

Tr

r

part= =

part (A46)


( )3 h wallwall

bed

kT T

Rminus

is neglected

30



( )

( )( )

2

2 3

180 1 0

2

bg bed

bedp

uPz L

z R


part ε (A47)


( )

( )( )

2

2 3

180 1 0

2

bg bed

bedp

uPz L

z R


part ε (A48)

Linear (Henry type)


(A49)

Extended Langmuir

2 2 1 1 exp 0 1

1


j j

j


b P T T


+ sumhellip (A50)


( )0

0

0

1 0 1 iP


QdP Q b P z L i N


(A51a)


(A51b

)

2 2 1 1 exp 0 1

1


i i


b P T T


hellip (A51c)


)


1 0 1 i

comp

itotal pure i

Xz L i N




31


Variable Equation


Wakao correlation23

( ) 033 06 20 11 0 1

m if i comp

p

Dk Sc Re z L i N



coefficient

Wakao correlation24

( )033 0620 11 Re 0 hp

k Pr z LR

λ= + forall isin

(A53)


coefficient

Wakao correlation23

( ) 20 05 0 1

m iz i comp

bed


εhellip

(A54)


coefficient

Wakao correlation24



3

3 2

12 12

1

18583 10 0 0 1 2im i p

TMW

D z L r R iP


(A56)


2

7 175 2

12

1

1013 10 0 0 1 2im i p

MWD T z L r R i

PX


Knudsen diffusivity


3 97 10 0 0 1 k i pore p comp

i

TD R z L r R i N


(A58)


0 0 1 p m i k i

e i p compp m i k i

D DD z L r R i N

D D


hellip (A59)



2

1

1

out

inv in comp

i i

P

PF C SP P i N

x MW T

minus = = hellip

sum (A60)

Molar flowrate

Otherwise ( )

21

1

critv in comp

i i

PF C SP P i N

x MW T

minus= = hellip

sum (A61)


1critP

κ

minusκ =

+ κ (A62)

Power

1

11

feed feedfeed

low cycle

P NPower RT

P

κminus

κ κ

= minus κ minus τ

(A63)

32


33


34



35



15





325










AIChE J 1987 33 1045



Eng 1987 65 512










16




141






1992 47 4305








York 1994










gas AIChE J 1998 44 1325

17






Technol 2000 39 51


Technol 2000 20 185



















8084

18

















19


Ref Mass

balance

Heat

balance

Momentum

balance

Isotherm

adsorbent

No of

steps

No of

layers Application







study


experimental study


(43) LDF Bulk gas

solids -


5 1 H2 CO H2 CO2



(54) DG LDF -DG

LDF-DGSD

LDF-DGSD

- - Langmuir 4A 5A





13X 4 1 CO2 capture






Ref Mass

balance

Heat

balance

Momentum

balance

Isotherm

adsorbent

No of

beds

No of

steps

Bed

interactions

No of

layers Application






Dual-site

Langmuir

13X


ads Air separation




AC+5A

2 7 - 2 H2 CH4 CO

N2 CO2



20


Ref Mass

balance Heat

balance

Momentum

balance

Isotherm adsorbent

No of beds

No of steps

Bed interactions

No of layers

Application



N2



AC+5A 4 8


information


2 H2 CO2 CH4

CO


Langmuir

Alumina+ AC+zeolite

6 12

Information


inert +

2 ads H2 CH4 CO


gel 9 10

9 11 6+7

- -

Overview of




Dual-site

Langmuir APHP+5A


CO H2


13X 2 3 4 6 - 1

CO2 from flue

gases


21


Recovery Purity

No Exp18

Model18

This

work Exp

18 Model

18

This

work

1 644 638 696 9975 10000 9931

2 816 864 850 9955 9989 9892

3 1065 1092 994 9900 9909 9855

4 1239 1215 1130 9835 9859 9815

5 707 825 852 9960 9988 9895

6 941 985 995 9885 9941 9854

7 1167 1172 1072 9830 9877 9833

8 1299 1213 1141 9780 9849 9811

9 2584 1702 2123 9080 9539 9447

10 2136 1609 2121 9070 9623 9475

11 2274 1550 2120 9140 9618 9478

12 2218 2274 2108 9120 9602 9477

13 939 835 845 9825 9970 9974

14 740 632 785 9890 9982 9991

15 510 500 738 9900 9988 9997

16 919 859 982 9845 9963 9960

17 707 762 856 9850 9976 9979

18 643 699 742 9870 9983 9989

19 541 613 612 9880 9993 9996

20 1151 1244 1128 9795 9871 9825

21 972 967 943 9850 9942 9940

22 674 659 726 9885 9979 9991

23 337 408 546 9900 9996 9999

24 1663 1433 1086 9585 9747 9869

25 1076 1155 962 9680 9872 9957

26 857 847 881 9730 9915 9984

27 826 721 844 9765 9910 9991

28 735 856 1135 9875 9987 9822

29 1195 1427 1117 9770 9792 9831

30 1330 1607 1120 9700 9657 9824

31 4156 3764 2638 8230 8227 8923

32 2246 1607 1511 9370 9497 9670

33 1254 800 899 9820 10000 9906

34 1383 1309 986 9380 9445 9606

35 2305 1673 1425 9370 9758 9775

42 2240 1646 2051 8900 9440 9496

43 2237 1615 2006 8230 8972 9012

22













Bed length 10 m















(wall) 13807 W(m

2K)


coefficient 1e-3 m

2s


coefficient 1e-3 m

2s


Comp a1 x10

3

(molg) a2

(K) b1 x10

9

(Pa-1

) b2

(K) -∆Hads (Jmol)

H2 432 000 5040 8505 786173

CO 092 052 5896 17309 1667742

CH4 -170 198 19952 14467 1875269

CO2 -1420 663 24775 14966 2557261






23























24



1 4 8 12

spPressCoC 01000 0060 0030 00500

spAdsIn 03600 03600 03600 03600

spAdsOut 00035 00015 00015 00015

spBlow 08000 05000 02500 04000

spPurgeIn 02250 02250 02250 02250

spPurgeOut 00300 00300 0030 00300

spPEQ1 - 00040 00025 00030

spPEQ2 - - 00050 00040

spPEQ3 - - - 00080

Feed

flowrate m3s

360e-6 360e-6 360e-6 360e-6

Purge

flowrate m3s

225e-6 225e-6 225e-6 225e-6

τPress s 10 10 20 10

τAds s 20 20 20 20

τBlow s 10 10 20 10

τPurge s 20 20 20 20

τPEQ1 s - 10 20 10

τPEQ2 s - - 20 10

τPEQ3 s - - - 10

τcycle s 60 80 160 120


No

beds

O2 purity

()

O2 recovery

()

Power

(W)

Productivity

(molkgs)

1 9687 3440 52902 918e-2

4 9950 5806 27949 485e-2

8 9958 6887 11987 208e-2

12 9936 7250 13936 242e-2

25



1 4 8 12

spPressCoC 00300 00450 00500 00500

spAdsIn 01200 01300 03300 03600

spAdsOut 00004 000035 00014 00015

spBlow 02000 02200 03000 04000

spPurgeIn 05625 01500 03000 02250

spPurgeOut 00075 00200 00400 00300

spPEQ1 - 00025 00020 00300

spPEQ2 - - 00040 00040

spPEQ3 - - - 00080

Feed flowrate m

3s

120e-6 130e-6 330e-6 360e-6

Purge

flowrate m3s

075e-6 115e-6 300e-6 225e-6

τPress s 20 15 15 10

τAds s 40 30 15 20

τBlow s 20 15 15 10

τPurge s 40 30 15 20

τPEQ1 s - 15 15 10

τPEQ2 s - - 15 10

τPEQ3 s - - - 10

τcycle s 120 120 120 120


No

beds

O2 purity

()

O2 recovery

()

Power

(W)

Productivity

(molkgs)

1 9811 2021 14420 250e-2

4 9929 3840 14069 244e-2

8 9979 6525 14092 245e-2

12 9936 7250 13936 242e-2

26



1 4 8 12

spPressCC 00030 00030 00500 00040

spAdsIn 04000 03333 03450 05000

spAdsOut 000088 000085 00015 00014

spBlow 02500 04000 03000 04000

spPurgeIn 00900 01333 03000 02000

spPurgeOut 00140 00200 00400 00300

spPEQ1 - 00050 00020 00030

spPEQ2 - - 00040 00040

spPEQ3 - - - 00080

Feed flowrate m

3s

400e-6 333e-6 345e-6 500e-6

Purge

flowrate m3s

090e-6 133e-6 300e-6 200e-6

τPress s 20 15 15 10

τAds s 40 30 15 20

τBlow s 20 15 15 10

τPurge s 40 30 15 20

τPEQ1 s - 15 15 10

τPEQ2 s - - 15 10

τPEQ3 s - - - 10

τcycle s 120 120 120 120


No beds

O2 purity ()

O2 recovery ()

Power (W)


1 9987 141 18878 203e-2

4 9997 2847 11808 205e-2

8 9997 5058 11938 207e-2

12 9983 6516 11909 207e-2

27




( )( )

( )

1

0 1


comp

uC C CN D

z t z z

z L i N


part part part part


(A1)


particle surface)



( ) ( )( ) ( )

( )

31

0


bed

bed z

c Tc uT kq T T

z t R

Tz L

z z


part part


part part

(A3)





Pf u R z L

z


part (A5)


coefficient ( )

0 1 f i p

compm i





λ (A7)


( )

0 1 z i bed

compm i

Df Sc Re z L i N

D




= forall isin λ

(A9)




Cu C C D z z L i N

z

partminus = = = =

parthellip (A12)

0 or inT T z z L= = = (A13)


0 0 and u

z z Lz

part= = =

part (A14)

0 0 or 1 icomp

Cz z L i N

z

part= = = =



end 0 0 or

Tz z L

z

part= = =

part (A16)

28


Model Equation



[ ] 0 0 1 p





( )

0 1 p i ii p comp

Q CN z L i N

t t


part parthellip

(A19)



(A20)


( ) [ ]

2

15 0 0 1

e iii i p comp

p

DQQ Q r R z L i N

t R


hellip (A21) LDF


( ) 0 1 p i i

i p comp

Q CN z L i N

t t


part parthellip

(A22)


) [ ]0 0 0 1 p




( ) [ ]22

1 0 0 1 i i

p s i p comp

p

Q QR D r R z L i N

t r rR



(A24)


( ) ( )3

0 1 p

f pi i r R compi

p

kN C C z L i N


(A25)



Qk C C D r R i N

r= =

partminus = = =

part (A26)

SD

0 0 0 1 icomp

Qr z L i N

r


parthellip (A27)


( ) ( ) [ ]

22

11 0 0 1

p ppi i i

p p p p e i p comp

p

C CQR D r R z L i N

t t r rR



(A28)




( ) ( )3

0 1 p

f pi i r R compi

p

kN C C z L i N


(A30)



Qk C C D r R i N

r= =

partminus = = =

part (A31)

PD

0 0 0 1 p

icomp

Cr z L i N

r


parthellip (A32)

29


Mode Equation

( )0 0 T

z Lz

part= forall isin

part (A33)




(A34)


( ) ( )( ) ( )3

0 bed pbed p h wall

g wall bed zbed


z t R z z


part part part part

(A35)




(A36)

LEQ



( )( ) ( )

0 comp

p p Np p pg p pg

p ig ads i

i

c c TQ

q H z Lt t


part partsum

(A37)




(A38)

LDF



( )( ) ( )

0 comp

p p Np p pg p pg

p ig ads i

i

c c TQ

q H z Lt t


part partsum

(A39)



0 0 p


(A40)

SD



( )( ) ( ) 0

compp p N

p i Rppg ads i

i

c T Qq H z L

t t


part partsum

(A41)


( ) ( )3

0 p

phg R

p

kq T T z L


(A42)


( )( ) ( )

2

2

1 0 0

p p ppp p pg p pg

p pg p p

p

c c TT

q R r R z Lt r rR


(A43)


( ) ( )

0 compN

p p ig ads i p

i

Qq H r R

t


partsum

(A44)

( ) p p

pp p

h r R r R p

Tk T T r R

r= =

partminus = λ =

part

(A45)

Nonisothermal

PD

model

Boundary conditions

0 0p

Tr

r

part= =

part (A46)


( )3 h wallwall

bed

kT T

Rminus

is neglected

30



( )

( )( )

2

2 3

180 1 0

2

bg bed

bedp

uPz L

z R


part ε (A47)


( )

( )( )

2

2 3

180 1 0

2

bg bed

bedp

uPz L

z R


part ε (A48)

Linear (Henry type)


(A49)

Extended Langmuir

2 2 1 1 exp 0 1

1


j j

j


b P T T


+ sumhellip (A50)


( )0

0

0

1 0 1 iP


QdP Q b P z L i N


(A51a)


(A51b

)

2 2 1 1 exp 0 1

1


i i


b P T T


hellip (A51c)


)


1 0 1 i

comp

itotal pure i

Xz L i N




31


Variable Equation


Wakao correlation23

( ) 033 06 20 11 0 1

m if i comp

p

Dk Sc Re z L i N



coefficient

Wakao correlation24

( )033 0620 11 Re 0 hp

k Pr z LR

λ= + forall isin

(A53)


coefficient

Wakao correlation23

( ) 20 05 0 1

m iz i comp

bed


εhellip

(A54)


coefficient

Wakao correlation24



3

3 2

12 12

1

18583 10 0 0 1 2im i p

TMW

D z L r R iP


(A56)


2

7 175 2

12

1

1013 10 0 0 1 2im i p

MWD T z L r R i

PX


Knudsen diffusivity


3 97 10 0 0 1 k i pore p comp

i

TD R z L r R i N


(A58)


0 0 1 p m i k i

e i p compp m i k i

D DD z L r R i N

D D


hellip (A59)



2

1

1

out

inv in comp

i i

P

PF C SP P i N

x MW T

minus = = hellip

sum (A60)

Molar flowrate

Otherwise ( )

21

1

critv in comp

i i

PF C SP P i N

x MW T

minus= = hellip

sum (A61)


1critP

κ

minusκ =

+ κ (A62)

Power

1

11

feed feedfeed

low cycle

P NPower RT

P

κminus

κ κ

= minus κ minus τ

(A63)

32


33


34



35



16




141






1992 47 4305








York 1994










gas AIChE J 1998 44 1325

17






Technol 2000 39 51


Technol 2000 20 185



















8084

18

















19


Ref Mass

balance

Heat

balance

Momentum

balance

Isotherm

adsorbent

No of

steps

No of

layers Application







study


experimental study


(43) LDF Bulk gas

solids -


5 1 H2 CO H2 CO2



(54) DG LDF -DG

LDF-DGSD

LDF-DGSD

- - Langmuir 4A 5A





13X 4 1 CO2 capture






Ref Mass

balance

Heat

balance

Momentum

balance

Isotherm

adsorbent

No of

beds

No of

steps

Bed

interactions

No of

layers Application






Dual-site

Langmuir

13X


ads Air separation




AC+5A

2 7 - 2 H2 CH4 CO

N2 CO2



20


Ref Mass

balance Heat

balance

Momentum

balance

Isotherm adsorbent

No of beds

No of steps

Bed interactions

No of layers

Application



N2



AC+5A 4 8


information


2 H2 CO2 CH4

CO


Langmuir

Alumina+ AC+zeolite

6 12

Information


inert +

2 ads H2 CH4 CO


gel 9 10

9 11 6+7

- -

Overview of




Dual-site

Langmuir APHP+5A


CO H2


13X 2 3 4 6 - 1

CO2 from flue

gases


21


Recovery Purity

No Exp18

Model18

This

work Exp

18 Model

18

This

work

1 644 638 696 9975 10000 9931

2 816 864 850 9955 9989 9892

3 1065 1092 994 9900 9909 9855

4 1239 1215 1130 9835 9859 9815

5 707 825 852 9960 9988 9895

6 941 985 995 9885 9941 9854

7 1167 1172 1072 9830 9877 9833

8 1299 1213 1141 9780 9849 9811

9 2584 1702 2123 9080 9539 9447

10 2136 1609 2121 9070 9623 9475

11 2274 1550 2120 9140 9618 9478

12 2218 2274 2108 9120 9602 9477

13 939 835 845 9825 9970 9974

14 740 632 785 9890 9982 9991

15 510 500 738 9900 9988 9997

16 919 859 982 9845 9963 9960

17 707 762 856 9850 9976 9979

18 643 699 742 9870 9983 9989

19 541 613 612 9880 9993 9996

20 1151 1244 1128 9795 9871 9825

21 972 967 943 9850 9942 9940

22 674 659 726 9885 9979 9991

23 337 408 546 9900 9996 9999

24 1663 1433 1086 9585 9747 9869

25 1076 1155 962 9680 9872 9957

26 857 847 881 9730 9915 9984

27 826 721 844 9765 9910 9991

28 735 856 1135 9875 9987 9822

29 1195 1427 1117 9770 9792 9831

30 1330 1607 1120 9700 9657 9824

31 4156 3764 2638 8230 8227 8923

32 2246 1607 1511 9370 9497 9670

33 1254 800 899 9820 10000 9906

34 1383 1309 986 9380 9445 9606

35 2305 1673 1425 9370 9758 9775

42 2240 1646 2051 8900 9440 9496

43 2237 1615 2006 8230 8972 9012

22













Bed length 10 m















(wall) 13807 W(m

2K)


coefficient 1e-3 m

2s


coefficient 1e-3 m

2s


Comp a1 x10

3

(molg) a2

(K) b1 x10

9

(Pa-1

) b2

(K) -∆Hads (Jmol)

H2 432 000 5040 8505 786173

CO 092 052 5896 17309 1667742

CH4 -170 198 19952 14467 1875269

CO2 -1420 663 24775 14966 2557261






23























24



1 4 8 12

spPressCoC 01000 0060 0030 00500

spAdsIn 03600 03600 03600 03600

spAdsOut 00035 00015 00015 00015

spBlow 08000 05000 02500 04000

spPurgeIn 02250 02250 02250 02250

spPurgeOut 00300 00300 0030 00300

spPEQ1 - 00040 00025 00030

spPEQ2 - - 00050 00040

spPEQ3 - - - 00080

Feed

flowrate m3s

360e-6 360e-6 360e-6 360e-6

Purge

flowrate m3s

225e-6 225e-6 225e-6 225e-6

τPress s 10 10 20 10

τAds s 20 20 20 20

τBlow s 10 10 20 10

τPurge s 20 20 20 20

τPEQ1 s - 10 20 10

τPEQ2 s - - 20 10

τPEQ3 s - - - 10

τcycle s 60 80 160 120


No

beds

O2 purity

()

O2 recovery

()

Power

(W)

Productivity

(molkgs)

1 9687 3440 52902 918e-2

4 9950 5806 27949 485e-2

8 9958 6887 11987 208e-2

12 9936 7250 13936 242e-2

25



1 4 8 12

spPressCoC 00300 00450 00500 00500

spAdsIn 01200 01300 03300 03600

spAdsOut 00004 000035 00014 00015

spBlow 02000 02200 03000 04000

spPurgeIn 05625 01500 03000 02250

spPurgeOut 00075 00200 00400 00300

spPEQ1 - 00025 00020 00300

spPEQ2 - - 00040 00040

spPEQ3 - - - 00080

Feed flowrate m

3s

120e-6 130e-6 330e-6 360e-6

Purge

flowrate m3s

075e-6 115e-6 300e-6 225e-6

τPress s 20 15 15 10

τAds s 40 30 15 20

τBlow s 20 15 15 10

τPurge s 40 30 15 20

τPEQ1 s - 15 15 10

τPEQ2 s - - 15 10

τPEQ3 s - - - 10

τcycle s 120 120 120 120


No

beds

O2 purity

()

O2 recovery

()

Power

(W)

Productivity

(molkgs)

1 9811 2021 14420 250e-2

4 9929 3840 14069 244e-2

8 9979 6525 14092 245e-2

12 9936 7250 13936 242e-2

26



1 4 8 12

spPressCC 00030 00030 00500 00040

spAdsIn 04000 03333 03450 05000

spAdsOut 000088 000085 00015 00014

spBlow 02500 04000 03000 04000

spPurgeIn 00900 01333 03000 02000

spPurgeOut 00140 00200 00400 00300

spPEQ1 - 00050 00020 00030

spPEQ2 - - 00040 00040

spPEQ3 - - - 00080

Feed flowrate m

3s

400e-6 333e-6 345e-6 500e-6

Purge

flowrate m3s

090e-6 133e-6 300e-6 200e-6

τPress s 20 15 15 10

τAds s 40 30 15 20

τBlow s 20 15 15 10

τPurge s 40 30 15 20

τPEQ1 s - 15 15 10

τPEQ2 s - - 15 10

τPEQ3 s - - - 10

τcycle s 120 120 120 120


No beds

O2 purity ()

O2 recovery ()

Power (W)


1 9987 141 18878 203e-2

4 9997 2847 11808 205e-2

8 9997 5058 11938 207e-2

12 9983 6516 11909 207e-2

27




( )( )

( )

1

0 1


comp

uC C CN D

z t z z

z L i N


part part part part


(A1)


particle surface)



( ) ( )( ) ( )

( )

31

0


bed

bed z

c Tc uT kq T T

z t R

Tz L

z z


part part


part part

(A3)





Pf u R z L

z


part (A5)


coefficient ( )

0 1 f i p

compm i





λ (A7)


( )

0 1 z i bed

compm i

Df Sc Re z L i N

D




= forall isin λ

(A9)




Cu C C D z z L i N

z

partminus = = = =

parthellip (A12)

0 or inT T z z L= = = (A13)


0 0 and u

z z Lz

part= = =

part (A14)

0 0 or 1 icomp

Cz z L i N

z

part= = = =



end 0 0 or

Tz z L

z

part= = =

part (A16)

28


Model Equation



[ ] 0 0 1 p





( )

0 1 p i ii p comp

Q CN z L i N

t t


part parthellip

(A19)



(A20)


( ) [ ]

2

15 0 0 1

e iii i p comp

p

DQQ Q r R z L i N

t R


hellip (A21) LDF


( ) 0 1 p i i

i p comp

Q CN z L i N

t t


part parthellip

(A22)


) [ ]0 0 0 1 p




( ) [ ]22

1 0 0 1 i i

p s i p comp

p

Q QR D r R z L i N

t r rR



(A24)


( ) ( )3

0 1 p

f pi i r R compi

p

kN C C z L i N


(A25)



Qk C C D r R i N

r= =

partminus = = =

part (A26)

SD

0 0 0 1 icomp

Qr z L i N

r


parthellip (A27)


( ) ( ) [ ]

22

11 0 0 1

p ppi i i

p p p p e i p comp

p

C CQR D r R z L i N

t t r rR



(A28)




( ) ( )3

0 1 p

f pi i r R compi

p

kN C C z L i N


(A30)



Qk C C D r R i N

r= =

partminus = = =

part (A31)

PD

0 0 0 1 p

icomp

Cr z L i N

r


parthellip (A32)

29


Mode Equation

( )0 0 T

z Lz

part= forall isin

part (A33)




(A34)


( ) ( )( ) ( )3

0 bed pbed p h wall

g wall bed zbed


z t R z z


part part part part

(A35)




(A36)

LEQ



( )( ) ( )

0 comp

p p Np p pg p pg

p ig ads i

i

c c TQ

q H z Lt t


part partsum

(A37)




(A38)

LDF



( )( ) ( )

0 comp

p p Np p pg p pg

p ig ads i

i

c c TQ

q H z Lt t


part partsum

(A39)



0 0 p


(A40)

SD



( )( ) ( ) 0

compp p N

p i Rppg ads i

i

c T Qq H z L

t t


part partsum

(A41)


( ) ( )3

0 p

phg R

p

kq T T z L


(A42)


( )( ) ( )

2

2

1 0 0

p p ppp p pg p pg

p pg p p

p

c c TT

q R r R z Lt r rR


(A43)


( ) ( )

0 compN

p p ig ads i p

i

Qq H r R

t


partsum

(A44)

( ) p p

pp p

h r R r R p

Tk T T r R

r= =

partminus = λ =

part

(A45)

Nonisothermal

PD

model

Boundary conditions

0 0p

Tr

r

part= =

part (A46)


( )3 h wallwall

bed

kT T

Rminus

is neglected

30



( )

( )( )

2

2 3

180 1 0

2

bg bed

bedp

uPz L

z R


part ε (A47)


( )

( )( )

2

2 3

180 1 0

2

bg bed

bedp

uPz L

z R


part ε (A48)

Linear (Henry type)


(A49)

Extended Langmuir

2 2 1 1 exp 0 1

1


j j

j


b P T T


+ sumhellip (A50)


( )0

0

0

1 0 1 iP


QdP Q b P z L i N


(A51a)


(A51b

)

2 2 1 1 exp 0 1

1


i i


b P T T


hellip (A51c)


)


1 0 1 i

comp

itotal pure i

Xz L i N




31


Variable Equation


Wakao correlation23

( ) 033 06 20 11 0 1

m if i comp

p

Dk Sc Re z L i N



coefficient

Wakao correlation24

( )033 0620 11 Re 0 hp

k Pr z LR

λ= + forall isin

(A53)


coefficient

Wakao correlation23

( ) 20 05 0 1

m iz i comp

bed


εhellip

(A54)


coefficient

Wakao correlation24



3

3 2

12 12

1

18583 10 0 0 1 2im i p

TMW

D z L r R iP


(A56)


2

7 175 2

12

1

1013 10 0 0 1 2im i p

MWD T z L r R i

PX


Knudsen diffusivity


3 97 10 0 0 1 k i pore p comp

i

TD R z L r R i N


(A58)


0 0 1 p m i k i

e i p compp m i k i

D DD z L r R i N

D D


hellip (A59)



2

1

1

out

inv in comp

i i

P

PF C SP P i N

x MW T

minus = = hellip

sum (A60)

Molar flowrate

Otherwise ( )

21

1

critv in comp

i i

PF C SP P i N

x MW T

minus= = hellip

sum (A61)


1critP

κ

minusκ =

+ κ (A62)

Power

1

11

feed feedfeed

low cycle

P NPower RT

P

κminus

κ κ

= minus κ minus τ

(A63)

32


33


34



35



17






Technol 2000 39 51


Technol 2000 20 185



















8084

18

















19


Ref Mass

balance

Heat

balance

Momentum

balance

Isotherm

adsorbent

No of

steps

No of

layers Application







study


experimental study


(43) LDF Bulk gas

solids -


5 1 H2 CO H2 CO2



(54) DG LDF -DG

LDF-DGSD

LDF-DGSD

- - Langmuir 4A 5A





13X 4 1 CO2 capture






Ref Mass

balance

Heat

balance

Momentum

balance

Isotherm

adsorbent

No of

beds

No of

steps

Bed

interactions

No of

layers Application






Dual-site

Langmuir

13X


ads Air separation




AC+5A

2 7 - 2 H2 CH4 CO

N2 CO2



20


Ref Mass

balance Heat

balance

Momentum

balance

Isotherm adsorbent

No of beds

No of steps

Bed interactions

No of layers

Application



N2



AC+5A 4 8


information


2 H2 CO2 CH4

CO


Langmuir

Alumina+ AC+zeolite

6 12

Information


inert +

2 ads H2 CH4 CO


gel 9 10

9 11 6+7

- -

Overview of




Dual-site

Langmuir APHP+5A


CO H2


13X 2 3 4 6 - 1

CO2 from flue

gases


21


Recovery Purity

No Exp18

Model18

This

work Exp

18 Model

18

This

work

1 644 638 696 9975 10000 9931

2 816 864 850 9955 9989 9892

3 1065 1092 994 9900 9909 9855

4 1239 1215 1130 9835 9859 9815

5 707 825 852 9960 9988 9895

6 941 985 995 9885 9941 9854

7 1167 1172 1072 9830 9877 9833

8 1299 1213 1141 9780 9849 9811

9 2584 1702 2123 9080 9539 9447

10 2136 1609 2121 9070 9623 9475

11 2274 1550 2120 9140 9618 9478

12 2218 2274 2108 9120 9602 9477

13 939 835 845 9825 9970 9974

14 740 632 785 9890 9982 9991

15 510 500 738 9900 9988 9997

16 919 859 982 9845 9963 9960

17 707 762 856 9850 9976 9979

18 643 699 742 9870 9983 9989

19 541 613 612 9880 9993 9996

20 1151 1244 1128 9795 9871 9825

21 972 967 943 9850 9942 9940

22 674 659 726 9885 9979 9991

23 337 408 546 9900 9996 9999

24 1663 1433 1086 9585 9747 9869

25 1076 1155 962 9680 9872 9957

26 857 847 881 9730 9915 9984

27 826 721 844 9765 9910 9991

28 735 856 1135 9875 9987 9822

29 1195 1427 1117 9770 9792 9831

30 1330 1607 1120 9700 9657 9824

31 4156 3764 2638 8230 8227 8923

32 2246 1607 1511 9370 9497 9670

33 1254 800 899 9820 10000 9906

34 1383 1309 986 9380 9445 9606

35 2305 1673 1425 9370 9758 9775

42 2240 1646 2051 8900 9440 9496

43 2237 1615 2006 8230 8972 9012

22













Bed length 10 m















(wall) 13807 W(m

2K)


coefficient 1e-3 m

2s


coefficient 1e-3 m

2s


Comp a1 x10

3

(molg) a2

(K) b1 x10

9

(Pa-1

) b2

(K) -∆Hads (Jmol)

H2 432 000 5040 8505 786173

CO 092 052 5896 17309 1667742

CH4 -170 198 19952 14467 1875269

CO2 -1420 663 24775 14966 2557261






23























24



1 4 8 12

spPressCoC 01000 0060 0030 00500

spAdsIn 03600 03600 03600 03600

spAdsOut 00035 00015 00015 00015

spBlow 08000 05000 02500 04000

spPurgeIn 02250 02250 02250 02250

spPurgeOut 00300 00300 0030 00300

spPEQ1 - 00040 00025 00030

spPEQ2 - - 00050 00040

spPEQ3 - - - 00080

Feed

flowrate m3s

360e-6 360e-6 360e-6 360e-6

Purge

flowrate m3s

225e-6 225e-6 225e-6 225e-6

τPress s 10 10 20 10

τAds s 20 20 20 20

τBlow s 10 10 20 10

τPurge s 20 20 20 20

τPEQ1 s - 10 20 10

τPEQ2 s - - 20 10

τPEQ3 s - - - 10

τcycle s 60 80 160 120


No

beds

O2 purity

()

O2 recovery

()

Power

(W)

Productivity

(molkgs)

1 9687 3440 52902 918e-2

4 9950 5806 27949 485e-2

8 9958 6887 11987 208e-2

12 9936 7250 13936 242e-2

25



1 4 8 12

spPressCoC 00300 00450 00500 00500

spAdsIn 01200 01300 03300 03600

spAdsOut 00004 000035 00014 00015

spBlow 02000 02200 03000 04000

spPurgeIn 05625 01500 03000 02250

spPurgeOut 00075 00200 00400 00300

spPEQ1 - 00025 00020 00300

spPEQ2 - - 00040 00040

spPEQ3 - - - 00080

Feed flowrate m

3s

120e-6 130e-6 330e-6 360e-6

Purge

flowrate m3s

075e-6 115e-6 300e-6 225e-6

τPress s 20 15 15 10

τAds s 40 30 15 20

τBlow s 20 15 15 10

τPurge s 40 30 15 20

τPEQ1 s - 15 15 10

τPEQ2 s - - 15 10

τPEQ3 s - - - 10

τcycle s 120 120 120 120


No

beds

O2 purity

()

O2 recovery

()

Power

(W)

Productivity

(molkgs)

1 9811 2021 14420 250e-2

4 9929 3840 14069 244e-2

8 9979 6525 14092 245e-2

12 9936 7250 13936 242e-2

26



1 4 8 12

spPressCC 00030 00030 00500 00040

spAdsIn 04000 03333 03450 05000

spAdsOut 000088 000085 00015 00014

spBlow 02500 04000 03000 04000

spPurgeIn 00900 01333 03000 02000

spPurgeOut 00140 00200 00400 00300

spPEQ1 - 00050 00020 00030

spPEQ2 - - 00040 00040

spPEQ3 - - - 00080

Feed flowrate m

3s

400e-6 333e-6 345e-6 500e-6

Purge

flowrate m3s

090e-6 133e-6 300e-6 200e-6

τPress s 20 15 15 10

τAds s 40 30 15 20

τBlow s 20 15 15 10

τPurge s 40 30 15 20

τPEQ1 s - 15 15 10

τPEQ2 s - - 15 10

τPEQ3 s - - - 10

τcycle s 120 120 120 120


No beds

O2 purity ()

O2 recovery ()

Power (W)


1 9987 141 18878 203e-2

4 9997 2847 11808 205e-2

8 9997 5058 11938 207e-2

12 9983 6516 11909 207e-2

27




( )( )

( )

1

0 1


comp

uC C CN D

z t z z

z L i N


part part part part


(A1)


particle surface)



( ) ( )( ) ( )

( )

31

0


bed

bed z

c Tc uT kq T T

z t R

Tz L

z z


part part


part part

(A3)





Pf u R z L

z


part (A5)


coefficient ( )

0 1 f i p

compm i





λ (A7)


( )

0 1 z i bed

compm i

Df Sc Re z L i N

D




= forall isin λ

(A9)




Cu C C D z z L i N

z

partminus = = = =

parthellip (A12)

0 or inT T z z L= = = (A13)


0 0 and u

z z Lz

part= = =

part (A14)

0 0 or 1 icomp

Cz z L i N

z

part= = = =



end 0 0 or

Tz z L

z

part= = =

part (A16)

28


Model Equation



[ ] 0 0 1 p





( )

0 1 p i ii p comp

Q CN z L i N

t t


part parthellip

(A19)



(A20)


( ) [ ]

2

15 0 0 1

e iii i p comp

p

DQQ Q r R z L i N

t R


hellip (A21) LDF


( ) 0 1 p i i

i p comp

Q CN z L i N

t t


part parthellip

(A22)


) [ ]0 0 0 1 p




( ) [ ]22

1 0 0 1 i i

p s i p comp

p

Q QR D r R z L i N

t r rR



(A24)


( ) ( )3

0 1 p

f pi i r R compi

p

kN C C z L i N


(A25)



Qk C C D r R i N

r= =

partminus = = =

part (A26)

SD

0 0 0 1 icomp

Qr z L i N

r


parthellip (A27)


( ) ( ) [ ]

22

11 0 0 1

p ppi i i

p p p p e i p comp

p

C CQR D r R z L i N

t t r rR



(A28)




( ) ( )3

0 1 p

f pi i r R compi

p

kN C C z L i N


(A30)



Qk C C D r R i N

r= =

partminus = = =

part (A31)

PD

0 0 0 1 p

icomp

Cr z L i N

r


parthellip (A32)

29


Mode Equation

( )0 0 T

z Lz

part= forall isin

part (A33)




(A34)


( ) ( )( ) ( )3

0 bed pbed p h wall

g wall bed zbed


z t R z z


part part part part

(A35)




(A36)

LEQ



( )( ) ( )

0 comp

p p Np p pg p pg

p ig ads i

i

c c TQ

q H z Lt t


part partsum

(A37)




(A38)

LDF



( )( ) ( )

0 comp

p p Np p pg p pg

p ig ads i

i

c c TQ

q H z Lt t


part partsum

(A39)



0 0 p


(A40)

SD



( )( ) ( ) 0

compp p N

p i Rppg ads i

i

c T Qq H z L

t t


part partsum

(A41)


( ) ( )3

0 p

phg R

p

kq T T z L


(A42)


( )( ) ( )

2

2

1 0 0

p p ppp p pg p pg

p pg p p

p

c c TT

q R r R z Lt r rR


(A43)


( ) ( )

0 compN

p p ig ads i p

i

Qq H r R

t


partsum

(A44)

( ) p p

pp p

h r R r R p

Tk T T r R

r= =

partminus = λ =

part

(A45)

Nonisothermal

PD

model

Boundary conditions

0 0p

Tr

r

part= =

part (A46)


( )3 h wallwall

bed

kT T

Rminus

is neglected

30



( )

( )( )

2

2 3

180 1 0

2

bg bed

bedp

uPz L

z R


part ε (A47)


( )

( )( )

2

2 3

180 1 0

2

bg bed

bedp

uPz L

z R


part ε (A48)

Linear (Henry type)


(A49)

Extended Langmuir

2 2 1 1 exp 0 1

1


j j

j


b P T T


+ sumhellip (A50)


( )0

0

0

1 0 1 iP


QdP Q b P z L i N


(A51a)


(A51b

)

2 2 1 1 exp 0 1

1


i i


b P T T


hellip (A51c)


)


1 0 1 i

comp

itotal pure i

Xz L i N




31


Variable Equation


Wakao correlation23

( ) 033 06 20 11 0 1

m if i comp

p

Dk Sc Re z L i N



coefficient

Wakao correlation24

( )033 0620 11 Re 0 hp

k Pr z LR

λ= + forall isin

(A53)


coefficient

Wakao correlation23

( ) 20 05 0 1

m iz i comp

bed


εhellip

(A54)


coefficient

Wakao correlation24



3

3 2

12 12

1

18583 10 0 0 1 2im i p

TMW

D z L r R iP


(A56)


2

7 175 2

12

1

1013 10 0 0 1 2im i p

MWD T z L r R i

PX


Knudsen diffusivity


3 97 10 0 0 1 k i pore p comp

i

TD R z L r R i N


(A58)


0 0 1 p m i k i

e i p compp m i k i

D DD z L r R i N

D D


hellip (A59)



2

1

1

out

inv in comp

i i

P

PF C SP P i N

x MW T

minus = = hellip

sum (A60)

Molar flowrate

Otherwise ( )

21

1

critv in comp

i i

PF C SP P i N

x MW T

minus= = hellip

sum (A61)


1critP

κ

minusκ =

+ κ (A62)

Power

1

11

feed feedfeed

low cycle

P NPower RT

P

κminus

κ κ

= minus κ minus τ

(A63)

32


33


34



35



18

















19


Ref Mass

balance

Heat

balance

Momentum

balance

Isotherm

adsorbent

No of

steps

No of

layers Application







study


experimental study


(43) LDF Bulk gas

solids -


5 1 H2 CO H2 CO2



(54) DG LDF -DG

LDF-DGSD

LDF-DGSD

- - Langmuir 4A 5A





13X 4 1 CO2 capture






Ref Mass

balance

Heat

balance

Momentum

balance

Isotherm

adsorbent

No of

beds

No of

steps

Bed

interactions

No of

layers Application






Dual-site

Langmuir

13X


ads Air separation




AC+5A

2 7 - 2 H2 CH4 CO

N2 CO2



20


Ref Mass

balance Heat

balance

Momentum

balance

Isotherm adsorbent

No of beds

No of steps

Bed interactions

No of layers

Application



N2



AC+5A 4 8


information


2 H2 CO2 CH4

CO


Langmuir

Alumina+ AC+zeolite

6 12

Information


inert +

2 ads H2 CH4 CO


gel 9 10

9 11 6+7

- -

Overview of




Dual-site

Langmuir APHP+5A


CO H2


13X 2 3 4 6 - 1

CO2 from flue

gases


21


Recovery Purity

No Exp18

Model18

This

work Exp

18 Model

18

This

work

1 644 638 696 9975 10000 9931

2 816 864 850 9955 9989 9892

3 1065 1092 994 9900 9909 9855

4 1239 1215 1130 9835 9859 9815

5 707 825 852 9960 9988 9895

6 941 985 995 9885 9941 9854

7 1167 1172 1072 9830 9877 9833

8 1299 1213 1141 9780 9849 9811

9 2584 1702 2123 9080 9539 9447

10 2136 1609 2121 9070 9623 9475

11 2274 1550 2120 9140 9618 9478

12 2218 2274 2108 9120 9602 9477

13 939 835 845 9825 9970 9974

14 740 632 785 9890 9982 9991

15 510 500 738 9900 9988 9997

16 919 859 982 9845 9963 9960

17 707 762 856 9850 9976 9979

18 643 699 742 9870 9983 9989

19 541 613 612 9880 9993 9996

20 1151 1244 1128 9795 9871 9825

21 972 967 943 9850 9942 9940

22 674 659 726 9885 9979 9991

23 337 408 546 9900 9996 9999

24 1663 1433 1086 9585 9747 9869

25 1076 1155 962 9680 9872 9957

26 857 847 881 9730 9915 9984

27 826 721 844 9765 9910 9991

28 735 856 1135 9875 9987 9822

29 1195 1427 1117 9770 9792 9831

30 1330 1607 1120 9700 9657 9824

31 4156 3764 2638 8230 8227 8923

32 2246 1607 1511 9370 9497 9670

33 1254 800 899 9820 10000 9906

34 1383 1309 986 9380 9445 9606

35 2305 1673 1425 9370 9758 9775

42 2240 1646 2051 8900 9440 9496

43 2237 1615 2006 8230 8972 9012

22













Bed length 10 m















(wall) 13807 W(m

2K)


coefficient 1e-3 m

2s


coefficient 1e-3 m

2s


Comp a1 x10

3

(molg) a2

(K) b1 x10

9

(Pa-1

) b2

(K) -∆Hads (Jmol)

H2 432 000 5040 8505 786173

CO 092 052 5896 17309 1667742

CH4 -170 198 19952 14467 1875269

CO2 -1420 663 24775 14966 2557261






23























24



1 4 8 12

spPressCoC 01000 0060 0030 00500

spAdsIn 03600 03600 03600 03600

spAdsOut 00035 00015 00015 00015

spBlow 08000 05000 02500 04000

spPurgeIn 02250 02250 02250 02250

spPurgeOut 00300 00300 0030 00300

spPEQ1 - 00040 00025 00030

spPEQ2 - - 00050 00040

spPEQ3 - - - 00080

Feed

flowrate m3s

360e-6 360e-6 360e-6 360e-6

Purge

flowrate m3s

225e-6 225e-6 225e-6 225e-6

τPress s 10 10 20 10

τAds s 20 20 20 20

τBlow s 10 10 20 10

τPurge s 20 20 20 20

τPEQ1 s - 10 20 10

τPEQ2 s - - 20 10

τPEQ3 s - - - 10

τcycle s 60 80 160 120


No

beds

O2 purity

()

O2 recovery

()

Power

(W)

Productivity

(molkgs)

1 9687 3440 52902 918e-2

4 9950 5806 27949 485e-2

8 9958 6887 11987 208e-2

12 9936 7250 13936 242e-2

25



1 4 8 12

spPressCoC 00300 00450 00500 00500

spAdsIn 01200 01300 03300 03600

spAdsOut 00004 000035 00014 00015

spBlow 02000 02200 03000 04000

spPurgeIn 05625 01500 03000 02250

spPurgeOut 00075 00200 00400 00300

spPEQ1 - 00025 00020 00300

spPEQ2 - - 00040 00040

spPEQ3 - - - 00080

Feed flowrate m

3s

120e-6 130e-6 330e-6 360e-6

Purge

flowrate m3s

075e-6 115e-6 300e-6 225e-6

τPress s 20 15 15 10

τAds s 40 30 15 20

τBlow s 20 15 15 10

τPurge s 40 30 15 20

τPEQ1 s - 15 15 10

τPEQ2 s - - 15 10

τPEQ3 s - - - 10

τcycle s 120 120 120 120


No

beds

O2 purity

()

O2 recovery

()

Power

(W)

Productivity

(molkgs)

1 9811 2021 14420 250e-2

4 9929 3840 14069 244e-2

8 9979 6525 14092 245e-2

12 9936 7250 13936 242e-2

26



1 4 8 12

spPressCC 00030 00030 00500 00040

spAdsIn 04000 03333 03450 05000

spAdsOut 000088 000085 00015 00014

spBlow 02500 04000 03000 04000

spPurgeIn 00900 01333 03000 02000

spPurgeOut 00140 00200 00400 00300

spPEQ1 - 00050 00020 00030

spPEQ2 - - 00040 00040

spPEQ3 - - - 00080

Feed flowrate m

3s

400e-6 333e-6 345e-6 500e-6

Purge

flowrate m3s

090e-6 133e-6 300e-6 200e-6

τPress s 20 15 15 10

τAds s 40 30 15 20

τBlow s 20 15 15 10

τPurge s 40 30 15 20

τPEQ1 s - 15 15 10

τPEQ2 s - - 15 10

τPEQ3 s - - - 10

τcycle s 120 120 120 120


No beds

O2 purity ()

O2 recovery ()

Power (W)


1 9987 141 18878 203e-2

4 9997 2847 11808 205e-2

8 9997 5058 11938 207e-2

12 9983 6516 11909 207e-2

27




( )( )

( )

1

0 1


comp

uC C CN D

z t z z

z L i N


part part part part


(A1)


particle surface)



( ) ( )( ) ( )

( )

31

0


bed

bed z

c Tc uT kq T T

z t R

Tz L

z z


part part


part part

(A3)





Pf u R z L

z


part (A5)


coefficient ( )

0 1 f i p

compm i





λ (A7)


( )

0 1 z i bed

compm i

Df Sc Re z L i N

D




= forall isin λ

(A9)




Cu C C D z z L i N

z

partminus = = = =

parthellip (A12)

0 or inT T z z L= = = (A13)


0 0 and u

z z Lz

part= = =

part (A14)

0 0 or 1 icomp

Cz z L i N

z

part= = = =



end 0 0 or

Tz z L

z

part= = =

part (A16)

28


Model Equation



[ ] 0 0 1 p





( )

0 1 p i ii p comp

Q CN z L i N

t t


part parthellip

(A19)



(A20)


( ) [ ]

2

15 0 0 1

e iii i p comp

p

DQQ Q r R z L i N

t R


hellip (A21) LDF


( ) 0 1 p i i

i p comp

Q CN z L i N

t t


part parthellip

(A22)


) [ ]0 0 0 1 p




( ) [ ]22

1 0 0 1 i i

p s i p comp

p

Q QR D r R z L i N

t r rR



(A24)


( ) ( )3

0 1 p

f pi i r R compi

p

kN C C z L i N


(A25)



Qk C C D r R i N

r= =

partminus = = =

part (A26)

SD

0 0 0 1 icomp

Qr z L i N

r


parthellip (A27)


( ) ( ) [ ]

22

11 0 0 1

p ppi i i

p p p p e i p comp

p

C CQR D r R z L i N

t t r rR



(A28)




( ) ( )3

0 1 p

f pi i r R compi

p

kN C C z L i N


(A30)



Qk C C D r R i N

r= =

partminus = = =

part (A31)

PD

0 0 0 1 p

icomp

Cr z L i N

r


parthellip (A32)

29


Mode Equation

( )0 0 T

z Lz

part= forall isin

part (A33)




(A34)


( ) ( )( ) ( )3

0 bed pbed p h wall

g wall bed zbed


z t R z z


part part part part

(A35)




(A36)

LEQ



( )( ) ( )

0 comp

p p Np p pg p pg

p ig ads i

i

c c TQ

q H z Lt t


part partsum

(A37)




(A38)

LDF



( )( ) ( )

0 comp

p p Np p pg p pg

p ig ads i

i

c c TQ

q H z Lt t


part partsum

(A39)



0 0 p


(A40)

SD



( )( ) ( ) 0

compp p N

p i Rppg ads i

i

c T Qq H z L

t t


part partsum

(A41)


( ) ( )3

0 p

phg R

p

kq T T z L


(A42)


( )( ) ( )

2

2

1 0 0

p p ppp p pg p pg

p pg p p

p

c c TT

q R r R z Lt r rR


(A43)


( ) ( )

0 compN

p p ig ads i p

i

Qq H r R

t


partsum

(A44)

( ) p p

pp p

h r R r R p

Tk T T r R

r= =

partminus = λ =

part

(A45)

Nonisothermal

PD

model

Boundary conditions

0 0p

Tr

r

part= =

part (A46)


( )3 h wallwall

bed

kT T

Rminus

is neglected

30



( )

( )( )

2

2 3

180 1 0

2

bg bed

bedp

uPz L

z R


part ε (A47)


( )

( )( )

2

2 3

180 1 0

2

bg bed

bedp

uPz L

z R


part ε (A48)

Linear (Henry type)


(A49)

Extended Langmuir

2 2 1 1 exp 0 1

1


j j

j


b P T T


+ sumhellip (A50)


( )0

0

0

1 0 1 iP


QdP Q b P z L i N


(A51a)


(A51b

)

2 2 1 1 exp 0 1

1


i i


b P T T


hellip (A51c)


)


1 0 1 i

comp

itotal pure i

Xz L i N




31


Variable Equation


Wakao correlation23

( ) 033 06 20 11 0 1

m if i comp

p

Dk Sc Re z L i N



coefficient

Wakao correlation24

( )033 0620 11 Re 0 hp

k Pr z LR

λ= + forall isin

(A53)


coefficient

Wakao correlation23

( ) 20 05 0 1

m iz i comp

bed


εhellip

(A54)


coefficient

Wakao correlation24



3

3 2

12 12

1

18583 10 0 0 1 2im i p

TMW

D z L r R iP


(A56)


2

7 175 2

12

1

1013 10 0 0 1 2im i p

MWD T z L r R i

PX


Knudsen diffusivity


3 97 10 0 0 1 k i pore p comp

i

TD R z L r R i N


(A58)


0 0 1 p m i k i

e i p compp m i k i

D DD z L r R i N

D D


hellip (A59)



2

1

1

out

inv in comp

i i

P

PF C SP P i N

x MW T

minus = = hellip

sum (A60)

Molar flowrate

Otherwise ( )

21

1

critv in comp

i i

PF C SP P i N

x MW T

minus= = hellip

sum (A61)


1critP

κ

minusκ =

+ κ (A62)

Power

1

11

feed feedfeed

low cycle

P NPower RT

P

κminus

κ κ

= minus κ minus τ

(A63)

32


33


34



35



19


Ref Mass

balance

Heat

balance

Momentum

balance

Isotherm

adsorbent

No of

steps

No of

layers Application







study


experimental study


(43) LDF Bulk gas

solids -


5 1 H2 CO H2 CO2



(54) DG LDF -DG

LDF-DGSD

LDF-DGSD

- - Langmuir 4A 5A





13X 4 1 CO2 capture






Ref Mass

balance

Heat

balance

Momentum

balance

Isotherm

adsorbent

No of

beds

No of

steps

Bed

interactions

No of

layers Application






Dual-site

Langmuir

13X


ads Air separation




AC+5A

2 7 - 2 H2 CH4 CO

N2 CO2



20


Ref Mass

balance Heat

balance

Momentum

balance

Isotherm adsorbent

No of beds

No of steps

Bed interactions

No of layers

Application



N2



AC+5A 4 8


information


2 H2 CO2 CH4

CO


Langmuir

Alumina+ AC+zeolite

6 12

Information


inert +

2 ads H2 CH4 CO


gel 9 10

9 11 6+7

- -

Overview of




Dual-site

Langmuir APHP+5A


CO H2


13X 2 3 4 6 - 1

CO2 from flue

gases


21


Recovery Purity

No Exp18

Model18

This

work Exp

18 Model

18

This

work

1 644 638 696 9975 10000 9931

2 816 864 850 9955 9989 9892

3 1065 1092 994 9900 9909 9855

4 1239 1215 1130 9835 9859 9815

5 707 825 852 9960 9988 9895

6 941 985 995 9885 9941 9854

7 1167 1172 1072 9830 9877 9833

8 1299 1213 1141 9780 9849 9811

9 2584 1702 2123 9080 9539 9447

10 2136 1609 2121 9070 9623 9475

11 2274 1550 2120 9140 9618 9478

12 2218 2274 2108 9120 9602 9477

13 939 835 845 9825 9970 9974

14 740 632 785 9890 9982 9991

15 510 500 738 9900 9988 9997

16 919 859 982 9845 9963 9960

17 707 762 856 9850 9976 9979

18 643 699 742 9870 9983 9989

19 541 613 612 9880 9993 9996

20 1151 1244 1128 9795 9871 9825

21 972 967 943 9850 9942 9940

22 674 659 726 9885 9979 9991

23 337 408 546 9900 9996 9999

24 1663 1433 1086 9585 9747 9869

25 1076 1155 962 9680 9872 9957

26 857 847 881 9730 9915 9984

27 826 721 844 9765 9910 9991

28 735 856 1135 9875 9987 9822

29 1195 1427 1117 9770 9792 9831

30 1330 1607 1120 9700 9657 9824

31 4156 3764 2638 8230 8227 8923

32 2246 1607 1511 9370 9497 9670

33 1254 800 899 9820 10000 9906

34 1383 1309 986 9380 9445 9606

35 2305 1673 1425 9370 9758 9775

42 2240 1646 2051 8900 9440 9496

43 2237 1615 2006 8230 8972 9012

22













Bed length 10 m















(wall) 13807 W(m

2K)


coefficient 1e-3 m

2s


coefficient 1e-3 m

2s


Comp a1 x10

3

(molg) a2

(K) b1 x10

9

(Pa-1

) b2

(K) -∆Hads (Jmol)

H2 432 000 5040 8505 786173

CO 092 052 5896 17309 1667742

CH4 -170 198 19952 14467 1875269

CO2 -1420 663 24775 14966 2557261






23























24



1 4 8 12

spPressCoC 01000 0060 0030 00500

spAdsIn 03600 03600 03600 03600

spAdsOut 00035 00015 00015 00015

spBlow 08000 05000 02500 04000

spPurgeIn 02250 02250 02250 02250

spPurgeOut 00300 00300 0030 00300

spPEQ1 - 00040 00025 00030

spPEQ2 - - 00050 00040

spPEQ3 - - - 00080

Feed

flowrate m3s

360e-6 360e-6 360e-6 360e-6

Purge

flowrate m3s

225e-6 225e-6 225e-6 225e-6

τPress s 10 10 20 10

τAds s 20 20 20 20

τBlow s 10 10 20 10

τPurge s 20 20 20 20

τPEQ1 s - 10 20 10

τPEQ2 s - - 20 10

τPEQ3 s - - - 10

τcycle s 60 80 160 120


No

beds

O2 purity

()

O2 recovery

()

Power

(W)

Productivity

(molkgs)

1 9687 3440 52902 918e-2

4 9950 5806 27949 485e-2

8 9958 6887 11987 208e-2

12 9936 7250 13936 242e-2

25



1 4 8 12

spPressCoC 00300 00450 00500 00500

spAdsIn 01200 01300 03300 03600

spAdsOut 00004 000035 00014 00015

spBlow 02000 02200 03000 04000

spPurgeIn 05625 01500 03000 02250

spPurgeOut 00075 00200 00400 00300

spPEQ1 - 00025 00020 00300

spPEQ2 - - 00040 00040

spPEQ3 - - - 00080

Feed flowrate m

3s

120e-6 130e-6 330e-6 360e-6

Purge

flowrate m3s

075e-6 115e-6 300e-6 225e-6

τPress s 20 15 15 10

τAds s 40 30 15 20

τBlow s 20 15 15 10

τPurge s 40 30 15 20

τPEQ1 s - 15 15 10

τPEQ2 s - - 15 10

τPEQ3 s - - - 10

τcycle s 120 120 120 120


No

beds

O2 purity

()

O2 recovery

()

Power

(W)

Productivity

(molkgs)

1 9811 2021 14420 250e-2

4 9929 3840 14069 244e-2

8 9979 6525 14092 245e-2

12 9936 7250 13936 242e-2

26



1 4 8 12

spPressCC 00030 00030 00500 00040

spAdsIn 04000 03333 03450 05000

spAdsOut 000088 000085 00015 00014

spBlow 02500 04000 03000 04000

spPurgeIn 00900 01333 03000 02000

spPurgeOut 00140 00200 00400 00300

spPEQ1 - 00050 00020 00030

spPEQ2 - - 00040 00040

spPEQ3 - - - 00080

Feed flowrate m

3s

400e-6 333e-6 345e-6 500e-6

Purge

flowrate m3s

090e-6 133e-6 300e-6 200e-6

τPress s 20 15 15 10

τAds s 40 30 15 20

τBlow s 20 15 15 10

τPurge s 40 30 15 20

τPEQ1 s - 15 15 10

τPEQ2 s - - 15 10

τPEQ3 s - - - 10

τcycle s 120 120 120 120


No beds

O2 purity ()

O2 recovery ()

Power (W)


1 9987 141 18878 203e-2

4 9997 2847 11808 205e-2

8 9997 5058 11938 207e-2

12 9983 6516 11909 207e-2

27




( )( )

( )

1

0 1


comp

uC C CN D

z t z z

z L i N


part part part part


(A1)


particle surface)



( ) ( )( ) ( )

( )

31

0


bed

bed z

c Tc uT kq T T

z t R

Tz L

z z


part part


part part

(A3)





Pf u R z L

z


part (A5)


coefficient ( )

0 1 f i p

compm i





λ (A7)


( )

0 1 z i bed

compm i

Df Sc Re z L i N

D




= forall isin λ

(A9)




Cu C C D z z L i N

z

partminus = = = =

parthellip (A12)

0 or inT T z z L= = = (A13)


0 0 and u

z z Lz

part= = =

part (A14)

0 0 or 1 icomp

Cz z L i N

z

part= = = =



end 0 0 or

Tz z L

z

part= = =

part (A16)

28


Model Equation



[ ] 0 0 1 p





( )

0 1 p i ii p comp

Q CN z L i N

t t


part parthellip

(A19)



(A20)


( ) [ ]

2

15 0 0 1

e iii i p comp

p

DQQ Q r R z L i N

t R


hellip (A21) LDF


( ) 0 1 p i i

i p comp

Q CN z L i N

t t


part parthellip

(A22)


) [ ]0 0 0 1 p




( ) [ ]22

1 0 0 1 i i

p s i p comp

p

Q QR D r R z L i N

t r rR



(A24)


( ) ( )3

0 1 p

f pi i r R compi

p

kN C C z L i N


(A25)



Qk C C D r R i N

r= =

partminus = = =

part (A26)

SD

0 0 0 1 icomp

Qr z L i N

r


parthellip (A27)


( ) ( ) [ ]

22

11 0 0 1

p ppi i i

p p p p e i p comp

p

C CQR D r R z L i N

t t r rR



(A28)




( ) ( )3

0 1 p

f pi i r R compi

p

kN C C z L i N


(A30)



Qk C C D r R i N

r= =

partminus = = =

part (A31)

PD

0 0 0 1 p

icomp

Cr z L i N

r


parthellip (A32)

29


Mode Equation

( )0 0 T

z Lz

part= forall isin

part (A33)




(A34)


( ) ( )( ) ( )3

0 bed pbed p h wall

g wall bed zbed


z t R z z


part part part part

(A35)




(A36)

LEQ



( )( ) ( )

0 comp

p p Np p pg p pg

p ig ads i

i

c c TQ

q H z Lt t


part partsum

(A37)




(A38)

LDF



( )( ) ( )

0 comp

p p Np p pg p pg

p ig ads i

i

c c TQ

q H z Lt t


part partsum

(A39)



0 0 p


(A40)

SD



( )( ) ( ) 0

compp p N

p i Rppg ads i

i

c T Qq H z L

t t


part partsum

(A41)


( ) ( )3

0 p

phg R

p

kq T T z L


(A42)


( )( ) ( )

2

2

1 0 0

p p ppp p pg p pg

p pg p p

p

c c TT

q R r R z Lt r rR


(A43)


( ) ( )

0 compN

p p ig ads i p

i

Qq H r R

t


partsum

(A44)

( ) p p

pp p

h r R r R p

Tk T T r R

r= =

partminus = λ =

part

(A45)

Nonisothermal

PD

model

Boundary conditions

0 0p

Tr

r

part= =

part (A46)


( )3 h wallwall

bed

kT T

Rminus

is neglected

30



( )

( )( )

2

2 3

180 1 0

2

bg bed

bedp

uPz L

z R


part ε (A47)


( )

( )( )

2

2 3

180 1 0

2

bg bed

bedp

uPz L

z R


part ε (A48)

Linear (Henry type)


(A49)

Extended Langmuir

2 2 1 1 exp 0 1

1


j j

j


b P T T


+ sumhellip (A50)


( )0

0

0

1 0 1 iP


QdP Q b P z L i N


(A51a)


(A51b

)

2 2 1 1 exp 0 1

1


i i


b P T T


hellip (A51c)


)


1 0 1 i

comp

itotal pure i

Xz L i N




31


Variable Equation


Wakao correlation23

( ) 033 06 20 11 0 1

m if i comp

p

Dk Sc Re z L i N



coefficient

Wakao correlation24

( )033 0620 11 Re 0 hp

k Pr z LR

λ= + forall isin

(A53)


coefficient

Wakao correlation23

( ) 20 05 0 1

m iz i comp

bed


εhellip

(A54)


coefficient

Wakao correlation24



3

3 2

12 12

1

18583 10 0 0 1 2im i p

TMW

D z L r R iP


(A56)


2

7 175 2

12

1

1013 10 0 0 1 2im i p

MWD T z L r R i

PX


Knudsen diffusivity


3 97 10 0 0 1 k i pore p comp

i

TD R z L r R i N


(A58)


0 0 1 p m i k i

e i p compp m i k i

D DD z L r R i N

D D


hellip (A59)



2

1

1

out

inv in comp

i i

P

PF C SP P i N

x MW T

minus = = hellip

sum (A60)

Molar flowrate

Otherwise ( )

21

1

critv in comp

i i

PF C SP P i N

x MW T

minus= = hellip

sum (A61)


1critP

κ

minusκ =

+ κ (A62)

Power

1

11

feed feedfeed

low cycle

P NPower RT

P

κminus

κ κ

= minus κ minus τ

(A63)

32


33


34



35



20


Ref Mass

balance Heat

balance

Momentum

balance

Isotherm adsorbent

No of beds

No of steps

Bed interactions

No of layers

Application



N2



AC+5A 4 8


information


2 H2 CO2 CH4

CO


Langmuir

Alumina+ AC+zeolite

6 12

Information


inert +

2 ads H2 CH4 CO


gel 9 10

9 11 6+7

- -

Overview of




Dual-site

Langmuir APHP+5A


CO H2


13X 2 3 4 6 - 1

CO2 from flue

gases


21


Recovery Purity

No Exp18

Model18

This

work Exp

18 Model

18

This

work

1 644 638 696 9975 10000 9931

2 816 864 850 9955 9989 9892

3 1065 1092 994 9900 9909 9855

4 1239 1215 1130 9835 9859 9815

5 707 825 852 9960 9988 9895

6 941 985 995 9885 9941 9854

7 1167 1172 1072 9830 9877 9833

8 1299 1213 1141 9780 9849 9811

9 2584 1702 2123 9080 9539 9447

10 2136 1609 2121 9070 9623 9475

11 2274 1550 2120 9140 9618 9478

12 2218 2274 2108 9120 9602 9477

13 939 835 845 9825 9970 9974

14 740 632 785 9890 9982 9991

15 510 500 738 9900 9988 9997

16 919 859 982 9845 9963 9960

17 707 762 856 9850 9976 9979

18 643 699 742 9870 9983 9989

19 541 613 612 9880 9993 9996

20 1151 1244 1128 9795 9871 9825

21 972 967 943 9850 9942 9940

22 674 659 726 9885 9979 9991

23 337 408 546 9900 9996 9999

24 1663 1433 1086 9585 9747 9869

25 1076 1155 962 9680 9872 9957

26 857 847 881 9730 9915 9984

27 826 721 844 9765 9910 9991

28 735 856 1135 9875 9987 9822

29 1195 1427 1117 9770 9792 9831

30 1330 1607 1120 9700 9657 9824

31 4156 3764 2638 8230 8227 8923

32 2246 1607 1511 9370 9497 9670

33 1254 800 899 9820 10000 9906

34 1383 1309 986 9380 9445 9606

35 2305 1673 1425 9370 9758 9775

42 2240 1646 2051 8900 9440 9496

43 2237 1615 2006 8230 8972 9012

22













Bed length 10 m















(wall) 13807 W(m

2K)


coefficient 1e-3 m

2s


coefficient 1e-3 m

2s


Comp a1 x10

3

(molg) a2

(K) b1 x10

9

(Pa-1

) b2

(K) -∆Hads (Jmol)

H2 432 000 5040 8505 786173

CO 092 052 5896 17309 1667742

CH4 -170 198 19952 14467 1875269

CO2 -1420 663 24775 14966 2557261






23























24



1 4 8 12

spPressCoC 01000 0060 0030 00500

spAdsIn 03600 03600 03600 03600

spAdsOut 00035 00015 00015 00015

spBlow 08000 05000 02500 04000

spPurgeIn 02250 02250 02250 02250

spPurgeOut 00300 00300 0030 00300

spPEQ1 - 00040 00025 00030

spPEQ2 - - 00050 00040

spPEQ3 - - - 00080

Feed

flowrate m3s

360e-6 360e-6 360e-6 360e-6

Purge

flowrate m3s

225e-6 225e-6 225e-6 225e-6

τPress s 10 10 20 10

τAds s 20 20 20 20

τBlow s 10 10 20 10

τPurge s 20 20 20 20

τPEQ1 s - 10 20 10

τPEQ2 s - - 20 10

τPEQ3 s - - - 10

τcycle s 60 80 160 120


No

beds

O2 purity

()

O2 recovery

()

Power

(W)

Productivity

(molkgs)

1 9687 3440 52902 918e-2

4 9950 5806 27949 485e-2

8 9958 6887 11987 208e-2

12 9936 7250 13936 242e-2

25



1 4 8 12

spPressCoC 00300 00450 00500 00500

spAdsIn 01200 01300 03300 03600

spAdsOut 00004 000035 00014 00015

spBlow 02000 02200 03000 04000

spPurgeIn 05625 01500 03000 02250

spPurgeOut 00075 00200 00400 00300

spPEQ1 - 00025 00020 00300

spPEQ2 - - 00040 00040

spPEQ3 - - - 00080

Feed flowrate m

3s

120e-6 130e-6 330e-6 360e-6

Purge

flowrate m3s

075e-6 115e-6 300e-6 225e-6

τPress s 20 15 15 10

τAds s 40 30 15 20

τBlow s 20 15 15 10

τPurge s 40 30 15 20

τPEQ1 s - 15 15 10

τPEQ2 s - - 15 10

τPEQ3 s - - - 10

τcycle s 120 120 120 120


No

beds

O2 purity

()

O2 recovery

()

Power

(W)

Productivity

(molkgs)

1 9811 2021 14420 250e-2

4 9929 3840 14069 244e-2

8 9979 6525 14092 245e-2

12 9936 7250 13936 242e-2

26



1 4 8 12

spPressCC 00030 00030 00500 00040

spAdsIn 04000 03333 03450 05000

spAdsOut 000088 000085 00015 00014

spBlow 02500 04000 03000 04000

spPurgeIn 00900 01333 03000 02000

spPurgeOut 00140 00200 00400 00300

spPEQ1 - 00050 00020 00030

spPEQ2 - - 00040 00040

spPEQ3 - - - 00080

Feed flowrate m

3s

400e-6 333e-6 345e-6 500e-6

Purge

flowrate m3s

090e-6 133e-6 300e-6 200e-6

τPress s 20 15 15 10

τAds s 40 30 15 20

τBlow s 20 15 15 10

τPurge s 40 30 15 20

τPEQ1 s - 15 15 10

τPEQ2 s - - 15 10

τPEQ3 s - - - 10

τcycle s 120 120 120 120


No beds

O2 purity ()

O2 recovery ()

Power (W)


1 9987 141 18878 203e-2

4 9997 2847 11808 205e-2

8 9997 5058 11938 207e-2

12 9983 6516 11909 207e-2

27




( )( )

( )

1

0 1


comp

uC C CN D

z t z z

z L i N


part part part part


(A1)


particle surface)



( ) ( )( ) ( )

( )

31

0


bed

bed z

c Tc uT kq T T

z t R

Tz L

z z


part part


part part

(A3)





Pf u R z L

z


part (A5)


coefficient ( )

0 1 f i p

compm i





λ (A7)


( )

0 1 z i bed

compm i

Df Sc Re z L i N

D




= forall isin λ

(A9)




Cu C C D z z L i N

z

partminus = = = =

parthellip (A12)

0 or inT T z z L= = = (A13)


0 0 and u

z z Lz

part= = =

part (A14)

0 0 or 1 icomp

Cz z L i N

z

part= = = =



end 0 0 or

Tz z L

z

part= = =

part (A16)

28


Model Equation



[ ] 0 0 1 p





( )

0 1 p i ii p comp

Q CN z L i N

t t


part parthellip

(A19)



(A20)


( ) [ ]

2

15 0 0 1

e iii i p comp

p

DQQ Q r R z L i N

t R


hellip (A21) LDF


( ) 0 1 p i i

i p comp

Q CN z L i N

t t


part parthellip

(A22)


) [ ]0 0 0 1 p




( ) [ ]22

1 0 0 1 i i

p s i p comp

p

Q QR D r R z L i N

t r rR



(A24)


( ) ( )3

0 1 p

f pi i r R compi

p

kN C C z L i N


(A25)



Qk C C D r R i N

r= =

partminus = = =

part (A26)

SD

0 0 0 1 icomp

Qr z L i N

r


parthellip (A27)


( ) ( ) [ ]

22

11 0 0 1

p ppi i i

p p p p e i p comp

p

C CQR D r R z L i N

t t r rR



(A28)




( ) ( )3

0 1 p

f pi i r R compi

p

kN C C z L i N


(A30)



Qk C C D r R i N

r= =

partminus = = =

part (A31)

PD

0 0 0 1 p

icomp

Cr z L i N

r


parthellip (A32)

29


Mode Equation

( )0 0 T

z Lz

part= forall isin

part (A33)




(A34)


( ) ( )( ) ( )3

0 bed pbed p h wall

g wall bed zbed


z t R z z


part part part part

(A35)




(A36)

LEQ



( )( ) ( )

0 comp

p p Np p pg p pg

p ig ads i

i

c c TQ

q H z Lt t


part partsum

(A37)




(A38)

LDF



( )( ) ( )

0 comp

p p Np p pg p pg

p ig ads i

i

c c TQ

q H z Lt t


part partsum

(A39)



0 0 p


(A40)

SD



( )( ) ( ) 0

compp p N

p i Rppg ads i

i

c T Qq H z L

t t


part partsum

(A41)


( ) ( )3

0 p

phg R

p

kq T T z L


(A42)


( )( ) ( )

2

2

1 0 0

p p ppp p pg p pg

p pg p p

p

c c TT

q R r R z Lt r rR


(A43)


( ) ( )

0 compN

p p ig ads i p

i

Qq H r R

t


partsum

(A44)

( ) p p

pp p

h r R r R p

Tk T T r R

r= =

partminus = λ =

part

(A45)

Nonisothermal

PD

model

Boundary conditions

0 0p

Tr

r

part= =

part (A46)


( )3 h wallwall

bed

kT T

Rminus

is neglected

30



( )

( )( )

2

2 3

180 1 0

2

bg bed

bedp

uPz L

z R


part ε (A47)


( )

( )( )

2

2 3

180 1 0

2

bg bed

bedp

uPz L

z R


part ε (A48)

Linear (Henry type)


(A49)

Extended Langmuir

2 2 1 1 exp 0 1

1


j j

j


b P T T


+ sumhellip (A50)


( )0

0

0

1 0 1 iP


QdP Q b P z L i N


(A51a)


(A51b

)

2 2 1 1 exp 0 1

1


i i


b P T T


hellip (A51c)


)


1 0 1 i

comp

itotal pure i

Xz L i N




31


Variable Equation


Wakao correlation23

( ) 033 06 20 11 0 1

m if i comp

p

Dk Sc Re z L i N



coefficient

Wakao correlation24

( )033 0620 11 Re 0 hp

k Pr z LR

λ= + forall isin

(A53)


coefficient

Wakao correlation23

( ) 20 05 0 1

m iz i comp

bed


εhellip

(A54)


coefficient

Wakao correlation24



3

3 2

12 12

1

18583 10 0 0 1 2im i p

TMW

D z L r R iP


(A56)


2

7 175 2

12

1

1013 10 0 0 1 2im i p

MWD T z L r R i

PX


Knudsen diffusivity


3 97 10 0 0 1 k i pore p comp

i

TD R z L r R i N


(A58)


0 0 1 p m i k i

e i p compp m i k i

D DD z L r R i N

D D


hellip (A59)



2

1

1

out

inv in comp

i i

P

PF C SP P i N

x MW T

minus = = hellip

sum (A60)

Molar flowrate

Otherwise ( )

21

1

critv in comp

i i

PF C SP P i N

x MW T

minus= = hellip

sum (A61)


1critP

κ

minusκ =

+ κ (A62)

Power

1

11

feed feedfeed

low cycle

P NPower RT

P

κminus

κ κ

= minus κ minus τ

(A63)

32


33


34



35



21


Recovery Purity

No Exp18

Model18

This

work Exp

18 Model

18

This

work

1 644 638 696 9975 10000 9931

2 816 864 850 9955 9989 9892

3 1065 1092 994 9900 9909 9855

4 1239 1215 1130 9835 9859 9815

5 707 825 852 9960 9988 9895

6 941 985 995 9885 9941 9854

7 1167 1172 1072 9830 9877 9833

8 1299 1213 1141 9780 9849 9811

9 2584 1702 2123 9080 9539 9447

10 2136 1609 2121 9070 9623 9475

11 2274 1550 2120 9140 9618 9478

12 2218 2274 2108 9120 9602 9477

13 939 835 845 9825 9970 9974

14 740 632 785 9890 9982 9991

15 510 500 738 9900 9988 9997

16 919 859 982 9845 9963 9960

17 707 762 856 9850 9976 9979

18 643 699 742 9870 9983 9989

19 541 613 612 9880 9993 9996

20 1151 1244 1128 9795 9871 9825

21 972 967 943 9850 9942 9940

22 674 659 726 9885 9979 9991

23 337 408 546 9900 9996 9999

24 1663 1433 1086 9585 9747 9869

25 1076 1155 962 9680 9872 9957

26 857 847 881 9730 9915 9984

27 826 721 844 9765 9910 9991

28 735 856 1135 9875 9987 9822

29 1195 1427 1117 9770 9792 9831

30 1330 1607 1120 9700 9657 9824

31 4156 3764 2638 8230 8227 8923

32 2246 1607 1511 9370 9497 9670

33 1254 800 899 9820 10000 9906

34 1383 1309 986 9380 9445 9606

35 2305 1673 1425 9370 9758 9775

42 2240 1646 2051 8900 9440 9496

43 2237 1615 2006 8230 8972 9012

22













Bed length 10 m















(wall) 13807 W(m

2K)


coefficient 1e-3 m

2s


coefficient 1e-3 m

2s


Comp a1 x10

3

(molg) a2

(K) b1 x10

9

(Pa-1

) b2

(K) -∆Hads (Jmol)

H2 432 000 5040 8505 786173

CO 092 052 5896 17309 1667742

CH4 -170 198 19952 14467 1875269

CO2 -1420 663 24775 14966 2557261






23























24



1 4 8 12

spPressCoC 01000 0060 0030 00500

spAdsIn 03600 03600 03600 03600

spAdsOut 00035 00015 00015 00015

spBlow 08000 05000 02500 04000

spPurgeIn 02250 02250 02250 02250

spPurgeOut 00300 00300 0030 00300

spPEQ1 - 00040 00025 00030

spPEQ2 - - 00050 00040

spPEQ3 - - - 00080

Feed

flowrate m3s

360e-6 360e-6 360e-6 360e-6

Purge

flowrate m3s

225e-6 225e-6 225e-6 225e-6

τPress s 10 10 20 10

τAds s 20 20 20 20

τBlow s 10 10 20 10

τPurge s 20 20 20 20

τPEQ1 s - 10 20 10

τPEQ2 s - - 20 10

τPEQ3 s - - - 10

τcycle s 60 80 160 120


No

beds

O2 purity

()

O2 recovery

()

Power

(W)

Productivity

(molkgs)

1 9687 3440 52902 918e-2

4 9950 5806 27949 485e-2

8 9958 6887 11987 208e-2

12 9936 7250 13936 242e-2

25



1 4 8 12

spPressCoC 00300 00450 00500 00500

spAdsIn 01200 01300 03300 03600

spAdsOut 00004 000035 00014 00015

spBlow 02000 02200 03000 04000

spPurgeIn 05625 01500 03000 02250

spPurgeOut 00075 00200 00400 00300

spPEQ1 - 00025 00020 00300

spPEQ2 - - 00040 00040

spPEQ3 - - - 00080

Feed flowrate m

3s

120e-6 130e-6 330e-6 360e-6

Purge

flowrate m3s

075e-6 115e-6 300e-6 225e-6

τPress s 20 15 15 10

τAds s 40 30 15 20

τBlow s 20 15 15 10

τPurge s 40 30 15 20

τPEQ1 s - 15 15 10

τPEQ2 s - - 15 10

τPEQ3 s - - - 10

τcycle s 120 120 120 120


No

beds

O2 purity

()

O2 recovery

()

Power

(W)

Productivity

(molkgs)

1 9811 2021 14420 250e-2

4 9929 3840 14069 244e-2

8 9979 6525 14092 245e-2

12 9936 7250 13936 242e-2

26



1 4 8 12

spPressCC 00030 00030 00500 00040

spAdsIn 04000 03333 03450 05000

spAdsOut 000088 000085 00015 00014

spBlow 02500 04000 03000 04000

spPurgeIn 00900 01333 03000 02000

spPurgeOut 00140 00200 00400 00300

spPEQ1 - 00050 00020 00030

spPEQ2 - - 00040 00040

spPEQ3 - - - 00080

Feed flowrate m

3s

400e-6 333e-6 345e-6 500e-6

Purge

flowrate m3s

090e-6 133e-6 300e-6 200e-6

τPress s 20 15 15 10

τAds s 40 30 15 20

τBlow s 20 15 15 10

τPurge s 40 30 15 20

τPEQ1 s - 15 15 10

τPEQ2 s - - 15 10

τPEQ3 s - - - 10

τcycle s 120 120 120 120


No beds

O2 purity ()

O2 recovery ()

Power (W)


1 9987 141 18878 203e-2

4 9997 2847 11808 205e-2

8 9997 5058 11938 207e-2

12 9983 6516 11909 207e-2

27




( )( )

( )

1

0 1


comp

uC C CN D

z t z z

z L i N


part part part part


(A1)


particle surface)



( ) ( )( ) ( )

( )

31

0


bed

bed z

c Tc uT kq T T

z t R

Tz L

z z


part part


part part

(A3)





Pf u R z L

z


part (A5)


coefficient ( )

0 1 f i p

compm i





λ (A7)


( )

0 1 z i bed

compm i

Df Sc Re z L i N

D




= forall isin λ

(A9)




Cu C C D z z L i N

z

partminus = = = =

parthellip (A12)

0 or inT T z z L= = = (A13)


0 0 and u

z z Lz

part= = =

part (A14)

0 0 or 1 icomp

Cz z L i N

z

part= = = =



end 0 0 or

Tz z L

z

part= = =

part (A16)

28


Model Equation



[ ] 0 0 1 p





( )

0 1 p i ii p comp

Q CN z L i N

t t


part parthellip

(A19)



(A20)


( ) [ ]

2

15 0 0 1

e iii i p comp

p

DQQ Q r R z L i N

t R


hellip (A21) LDF


( ) 0 1 p i i

i p comp

Q CN z L i N

t t


part parthellip

(A22)


) [ ]0 0 0 1 p




( ) [ ]22

1 0 0 1 i i

p s i p comp

p

Q QR D r R z L i N

t r rR



(A24)


( ) ( )3

0 1 p

f pi i r R compi

p

kN C C z L i N


(A25)



Qk C C D r R i N

r= =

partminus = = =

part (A26)

SD

0 0 0 1 icomp

Qr z L i N

r


parthellip (A27)


( ) ( ) [ ]

22

11 0 0 1

p ppi i i

p p p p e i p comp

p

C CQR D r R z L i N

t t r rR



(A28)




( ) ( )3

0 1 p

f pi i r R compi

p

kN C C z L i N


(A30)



Qk C C D r R i N

r= =

partminus = = =

part (A31)

PD

0 0 0 1 p

icomp

Cr z L i N

r


parthellip (A32)

29


Mode Equation

( )0 0 T

z Lz

part= forall isin

part (A33)




(A34)


( ) ( )( ) ( )3

0 bed pbed p h wall

g wall bed zbed


z t R z z


part part part part

(A35)




(A36)

LEQ



( )( ) ( )

0 comp

p p Np p pg p pg

p ig ads i

i

c c TQ

q H z Lt t


part partsum

(A37)




(A38)

LDF



( )( ) ( )

0 comp

p p Np p pg p pg

p ig ads i

i

c c TQ

q H z Lt t


part partsum

(A39)



0 0 p


(A40)

SD



( )( ) ( ) 0

compp p N

p i Rppg ads i

i

c T Qq H z L

t t


part partsum

(A41)


( ) ( )3

0 p

phg R

p

kq T T z L


(A42)


( )( ) ( )

2

2

1 0 0

p p ppp p pg p pg

p pg p p

p

c c TT

q R r R z Lt r rR


(A43)


( ) ( )

0 compN

p p ig ads i p

i

Qq H r R

t


partsum

(A44)

( ) p p

pp p

h r R r R p

Tk T T r R

r= =

partminus = λ =

part

(A45)

Nonisothermal

PD

model

Boundary conditions

0 0p

Tr

r

part= =

part (A46)


( )3 h wallwall

bed

kT T

Rminus

is neglected

30



( )

( )( )

2

2 3

180 1 0

2

bg bed

bedp

uPz L

z R


part ε (A47)


( )

( )( )

2

2 3

180 1 0

2

bg bed

bedp

uPz L

z R


part ε (A48)

Linear (Henry type)


(A49)

Extended Langmuir

2 2 1 1 exp 0 1

1


j j

j


b P T T


+ sumhellip (A50)


( )0

0

0

1 0 1 iP


QdP Q b P z L i N


(A51a)


(A51b

)

2 2 1 1 exp 0 1

1


i i


b P T T


hellip (A51c)


)


1 0 1 i

comp

itotal pure i

Xz L i N




31


Variable Equation


Wakao correlation23

( ) 033 06 20 11 0 1

m if i comp

p

Dk Sc Re z L i N



coefficient

Wakao correlation24

( )033 0620 11 Re 0 hp

k Pr z LR

λ= + forall isin

(A53)


coefficient

Wakao correlation23

( ) 20 05 0 1

m iz i comp

bed


εhellip

(A54)


coefficient

Wakao correlation24



3

3 2

12 12

1

18583 10 0 0 1 2im i p

TMW

D z L r R iP


(A56)


2

7 175 2

12

1

1013 10 0 0 1 2im i p

MWD T z L r R i

PX


Knudsen diffusivity


3 97 10 0 0 1 k i pore p comp

i

TD R z L r R i N


(A58)


0 0 1 p m i k i

e i p compp m i k i

D DD z L r R i N

D D


hellip (A59)



2

1

1

out

inv in comp

i i

P

PF C SP P i N

x MW T

minus = = hellip

sum (A60)

Molar flowrate

Otherwise ( )

21

1

critv in comp

i i

PF C SP P i N

x MW T

minus= = hellip

sum (A61)


1critP

κ

minusκ =

+ κ (A62)

Power

1

11

feed feedfeed

low cycle

P NPower RT

P

κminus

κ κ

= minus κ minus τ

(A63)

32


33


34



35



22













Bed length 10 m















(wall) 13807 W(m

2K)


coefficient 1e-3 m

2s


coefficient 1e-3 m

2s


Comp a1 x10

3

(molg) a2

(K) b1 x10

9

(Pa-1

) b2

(K) -∆Hads (Jmol)

H2 432 000 5040 8505 786173

CO 092 052 5896 17309 1667742

CH4 -170 198 19952 14467 1875269

CO2 -1420 663 24775 14966 2557261






23























24



1 4 8 12

spPressCoC 01000 0060 0030 00500

spAdsIn 03600 03600 03600 03600

spAdsOut 00035 00015 00015 00015

spBlow 08000 05000 02500 04000

spPurgeIn 02250 02250 02250 02250

spPurgeOut 00300 00300 0030 00300

spPEQ1 - 00040 00025 00030

spPEQ2 - - 00050 00040

spPEQ3 - - - 00080

Feed

flowrate m3s

360e-6 360e-6 360e-6 360e-6

Purge

flowrate m3s

225e-6 225e-6 225e-6 225e-6

τPress s 10 10 20 10

τAds s 20 20 20 20

τBlow s 10 10 20 10

τPurge s 20 20 20 20

τPEQ1 s - 10 20 10

τPEQ2 s - - 20 10

τPEQ3 s - - - 10

τcycle s 60 80 160 120


No

beds

O2 purity

()

O2 recovery

()

Power

(W)

Productivity

(molkgs)

1 9687 3440 52902 918e-2

4 9950 5806 27949 485e-2

8 9958 6887 11987 208e-2

12 9936 7250 13936 242e-2

25



1 4 8 12

spPressCoC 00300 00450 00500 00500

spAdsIn 01200 01300 03300 03600

spAdsOut 00004 000035 00014 00015

spBlow 02000 02200 03000 04000

spPurgeIn 05625 01500 03000 02250

spPurgeOut 00075 00200 00400 00300

spPEQ1 - 00025 00020 00300

spPEQ2 - - 00040 00040

spPEQ3 - - - 00080

Feed flowrate m

3s

120e-6 130e-6 330e-6 360e-6

Purge

flowrate m3s

075e-6 115e-6 300e-6 225e-6

τPress s 20 15 15 10

τAds s 40 30 15 20

τBlow s 20 15 15 10

τPurge s 40 30 15 20

τPEQ1 s - 15 15 10

τPEQ2 s - - 15 10

τPEQ3 s - - - 10

τcycle s 120 120 120 120


No

beds

O2 purity

()

O2 recovery

()

Power

(W)

Productivity

(molkgs)

1 9811 2021 14420 250e-2

4 9929 3840 14069 244e-2

8 9979 6525 14092 245e-2

12 9936 7250 13936 242e-2

26



1 4 8 12

spPressCC 00030 00030 00500 00040

spAdsIn 04000 03333 03450 05000

spAdsOut 000088 000085 00015 00014

spBlow 02500 04000 03000 04000

spPurgeIn 00900 01333 03000 02000

spPurgeOut 00140 00200 00400 00300

spPEQ1 - 00050 00020 00030

spPEQ2 - - 00040 00040

spPEQ3 - - - 00080

Feed flowrate m

3s

400e-6 333e-6 345e-6 500e-6

Purge

flowrate m3s

090e-6 133e-6 300e-6 200e-6

τPress s 20 15 15 10

τAds s 40 30 15 20

τBlow s 20 15 15 10

τPurge s 40 30 15 20

τPEQ1 s - 15 15 10

τPEQ2 s - - 15 10

τPEQ3 s - - - 10

τcycle s 120 120 120 120


No beds

O2 purity ()

O2 recovery ()

Power (W)


1 9987 141 18878 203e-2

4 9997 2847 11808 205e-2

8 9997 5058 11938 207e-2

12 9983 6516 11909 207e-2

27




( )( )

( )

1

0 1


comp

uC C CN D

z t z z

z L i N


part part part part


(A1)


particle surface)



( ) ( )( ) ( )

( )

31

0


bed

bed z

c Tc uT kq T T

z t R

Tz L

z z


part part


part part

(A3)





Pf u R z L

z


part (A5)


coefficient ( )

0 1 f i p

compm i





λ (A7)


( )

0 1 z i bed

compm i

Df Sc Re z L i N

D




= forall isin λ

(A9)




Cu C C D z z L i N

z

partminus = = = =

parthellip (A12)

0 or inT T z z L= = = (A13)


0 0 and u

z z Lz

part= = =

part (A14)

0 0 or 1 icomp

Cz z L i N

z

part= = = =



end 0 0 or

Tz z L

z

part= = =

part (A16)

28


Model Equation



[ ] 0 0 1 p





( )

0 1 p i ii p comp

Q CN z L i N

t t


part parthellip

(A19)



(A20)


( ) [ ]

2

15 0 0 1

e iii i p comp

p

DQQ Q r R z L i N

t R


hellip (A21) LDF


( ) 0 1 p i i

i p comp

Q CN z L i N

t t


part parthellip

(A22)


) [ ]0 0 0 1 p




( ) [ ]22

1 0 0 1 i i

p s i p comp

p

Q QR D r R z L i N

t r rR



(A24)


( ) ( )3

0 1 p

f pi i r R compi

p

kN C C z L i N


(A25)



Qk C C D r R i N

r= =

partminus = = =

part (A26)

SD

0 0 0 1 icomp

Qr z L i N

r


parthellip (A27)


( ) ( ) [ ]

22

11 0 0 1

p ppi i i

p p p p e i p comp

p

C CQR D r R z L i N

t t r rR



(A28)




( ) ( )3

0 1 p

f pi i r R compi

p

kN C C z L i N


(A30)



Qk C C D r R i N

r= =

partminus = = =

part (A31)

PD

0 0 0 1 p

icomp

Cr z L i N

r


parthellip (A32)

29


Mode Equation

( )0 0 T

z Lz

part= forall isin

part (A33)




(A34)


( ) ( )( ) ( )3

0 bed pbed p h wall

g wall bed zbed


z t R z z


part part part part

(A35)




(A36)

LEQ



( )( ) ( )

0 comp

p p Np p pg p pg

p ig ads i

i

c c TQ

q H z Lt t


part partsum

(A37)




(A38)

LDF



( )( ) ( )

0 comp

p p Np p pg p pg

p ig ads i

i

c c TQ

q H z Lt t


part partsum

(A39)



0 0 p


(A40)

SD



( )( ) ( ) 0

compp p N

p i Rppg ads i

i

c T Qq H z L

t t


part partsum

(A41)


( ) ( )3

0 p

phg R

p

kq T T z L


(A42)


( )( ) ( )

2

2

1 0 0

p p ppp p pg p pg

p pg p p

p

c c TT

q R r R z Lt r rR


(A43)


( ) ( )

0 compN

p p ig ads i p

i

Qq H r R

t


partsum

(A44)

( ) p p

pp p

h r R r R p

Tk T T r R

r= =

partminus = λ =

part

(A45)

Nonisothermal

PD

model

Boundary conditions

0 0p

Tr

r

part= =

part (A46)


( )3 h wallwall

bed

kT T

Rminus

is neglected

30



( )

( )( )

2

2 3

180 1 0

2

bg bed

bedp

uPz L

z R


part ε (A47)


( )

( )( )

2

2 3

180 1 0

2

bg bed

bedp

uPz L

z R


part ε (A48)

Linear (Henry type)


(A49)

Extended Langmuir

2 2 1 1 exp 0 1

1


j j

j


b P T T


+ sumhellip (A50)


( )0

0

0

1 0 1 iP


QdP Q b P z L i N


(A51a)


(A51b

)

2 2 1 1 exp 0 1

1


i i


b P T T


hellip (A51c)


)


1 0 1 i

comp

itotal pure i

Xz L i N




31


Variable Equation


Wakao correlation23

( ) 033 06 20 11 0 1

m if i comp

p

Dk Sc Re z L i N



coefficient

Wakao correlation24

( )033 0620 11 Re 0 hp

k Pr z LR

λ= + forall isin

(A53)


coefficient

Wakao correlation23

( ) 20 05 0 1

m iz i comp

bed


εhellip

(A54)


coefficient

Wakao correlation24



3

3 2

12 12

1

18583 10 0 0 1 2im i p

TMW

D z L r R iP


(A56)


2

7 175 2

12

1

1013 10 0 0 1 2im i p

MWD T z L r R i

PX


Knudsen diffusivity


3 97 10 0 0 1 k i pore p comp

i

TD R z L r R i N


(A58)


0 0 1 p m i k i

e i p compp m i k i

D DD z L r R i N

D D


hellip (A59)



2

1

1

out

inv in comp

i i

P

PF C SP P i N

x MW T

minus = = hellip

sum (A60)

Molar flowrate

Otherwise ( )

21

1

critv in comp

i i

PF C SP P i N

x MW T

minus= = hellip

sum (A61)


1critP

κ

minusκ =

+ κ (A62)

Power

1

11

feed feedfeed

low cycle

P NPower RT

P

κminus

κ κ

= minus κ minus τ

(A63)

32


33


34



35



23























24



1 4 8 12

spPressCoC 01000 0060 0030 00500

spAdsIn 03600 03600 03600 03600

spAdsOut 00035 00015 00015 00015

spBlow 08000 05000 02500 04000

spPurgeIn 02250 02250 02250 02250

spPurgeOut 00300 00300 0030 00300

spPEQ1 - 00040 00025 00030

spPEQ2 - - 00050 00040

spPEQ3 - - - 00080

Feed

flowrate m3s

360e-6 360e-6 360e-6 360e-6

Purge

flowrate m3s

225e-6 225e-6 225e-6 225e-6

τPress s 10 10 20 10

τAds s 20 20 20 20

τBlow s 10 10 20 10

τPurge s 20 20 20 20

τPEQ1 s - 10 20 10

τPEQ2 s - - 20 10

τPEQ3 s - - - 10

τcycle s 60 80 160 120


No

beds

O2 purity

()

O2 recovery

()

Power

(W)

Productivity

(molkgs)

1 9687 3440 52902 918e-2

4 9950 5806 27949 485e-2

8 9958 6887 11987 208e-2

12 9936 7250 13936 242e-2

25



1 4 8 12

spPressCoC 00300 00450 00500 00500

spAdsIn 01200 01300 03300 03600

spAdsOut 00004 000035 00014 00015

spBlow 02000 02200 03000 04000

spPurgeIn 05625 01500 03000 02250

spPurgeOut 00075 00200 00400 00300

spPEQ1 - 00025 00020 00300

spPEQ2 - - 00040 00040

spPEQ3 - - - 00080

Feed flowrate m

3s

120e-6 130e-6 330e-6 360e-6

Purge

flowrate m3s

075e-6 115e-6 300e-6 225e-6

τPress s 20 15 15 10

τAds s 40 30 15 20

τBlow s 20 15 15 10

τPurge s 40 30 15 20

τPEQ1 s - 15 15 10

τPEQ2 s - - 15 10

τPEQ3 s - - - 10

τcycle s 120 120 120 120


No

beds

O2 purity

()

O2 recovery

()

Power

(W)

Productivity

(molkgs)

1 9811 2021 14420 250e-2

4 9929 3840 14069 244e-2

8 9979 6525 14092 245e-2

12 9936 7250 13936 242e-2

26



1 4 8 12

spPressCC 00030 00030 00500 00040

spAdsIn 04000 03333 03450 05000

spAdsOut 000088 000085 00015 00014

spBlow 02500 04000 03000 04000

spPurgeIn 00900 01333 03000 02000

spPurgeOut 00140 00200 00400 00300

spPEQ1 - 00050 00020 00030

spPEQ2 - - 00040 00040

spPEQ3 - - - 00080

Feed flowrate m

3s

400e-6 333e-6 345e-6 500e-6

Purge

flowrate m3s

090e-6 133e-6 300e-6 200e-6

τPress s 20 15 15 10

τAds s 40 30 15 20

τBlow s 20 15 15 10

τPurge s 40 30 15 20

τPEQ1 s - 15 15 10

τPEQ2 s - - 15 10

τPEQ3 s - - - 10

τcycle s 120 120 120 120


No beds

O2 purity ()

O2 recovery ()

Power (W)


1 9987 141 18878 203e-2

4 9997 2847 11808 205e-2

8 9997 5058 11938 207e-2

12 9983 6516 11909 207e-2

27




( )( )

( )

1

0 1


comp

uC C CN D

z t z z

z L i N


part part part part


(A1)


particle surface)



( ) ( )( ) ( )

( )

31

0


bed

bed z

c Tc uT kq T T

z t R

Tz L

z z


part part


part part

(A3)





Pf u R z L

z


part (A5)


coefficient ( )

0 1 f i p

compm i





λ (A7)


( )

0 1 z i bed

compm i

Df Sc Re z L i N

D




= forall isin λ

(A9)




Cu C C D z z L i N

z

partminus = = = =

parthellip (A12)

0 or inT T z z L= = = (A13)


0 0 and u

z z Lz

part= = =

part (A14)

0 0 or 1 icomp

Cz z L i N

z

part= = = =



end 0 0 or

Tz z L

z

part= = =

part (A16)

28


Model Equation



[ ] 0 0 1 p





( )

0 1 p i ii p comp

Q CN z L i N

t t


part parthellip

(A19)



(A20)


( ) [ ]

2

15 0 0 1

e iii i p comp

p

DQQ Q r R z L i N

t R


hellip (A21) LDF


( ) 0 1 p i i

i p comp

Q CN z L i N

t t


part parthellip

(A22)


) [ ]0 0 0 1 p




( ) [ ]22

1 0 0 1 i i

p s i p comp

p

Q QR D r R z L i N

t r rR



(A24)


( ) ( )3

0 1 p

f pi i r R compi

p

kN C C z L i N


(A25)



Qk C C D r R i N

r= =

partminus = = =

part (A26)

SD

0 0 0 1 icomp

Qr z L i N

r


parthellip (A27)


( ) ( ) [ ]

22

11 0 0 1

p ppi i i

p p p p e i p comp

p

C CQR D r R z L i N

t t r rR



(A28)




( ) ( )3

0 1 p

f pi i r R compi

p

kN C C z L i N


(A30)



Qk C C D r R i N

r= =

partminus = = =

part (A31)

PD

0 0 0 1 p

icomp

Cr z L i N

r


parthellip (A32)

29


Mode Equation

( )0 0 T

z Lz

part= forall isin

part (A33)




(A34)


( ) ( )( ) ( )3

0 bed pbed p h wall

g wall bed zbed


z t R z z


part part part part

(A35)




(A36)

LEQ



( )( ) ( )

0 comp

p p Np p pg p pg

p ig ads i

i

c c TQ

q H z Lt t


part partsum

(A37)




(A38)

LDF



( )( ) ( )

0 comp

p p Np p pg p pg

p ig ads i

i

c c TQ

q H z Lt t


part partsum

(A39)



0 0 p


(A40)

SD



( )( ) ( ) 0

compp p N

p i Rppg ads i

i

c T Qq H z L

t t


part partsum

(A41)


( ) ( )3

0 p

phg R

p

kq T T z L


(A42)


( )( ) ( )

2

2

1 0 0

p p ppp p pg p pg

p pg p p

p

c c TT

q R r R z Lt r rR


(A43)


( ) ( )

0 compN

p p ig ads i p

i

Qq H r R

t


partsum

(A44)

( ) p p

pp p

h r R r R p

Tk T T r R

r= =

partminus = λ =

part

(A45)

Nonisothermal

PD

model

Boundary conditions

0 0p

Tr

r

part= =

part (A46)


( )3 h wallwall

bed

kT T

Rminus

is neglected

30



( )

( )( )

2

2 3

180 1 0

2

bg bed

bedp

uPz L

z R


part ε (A47)


( )

( )( )

2

2 3

180 1 0

2

bg bed

bedp

uPz L

z R


part ε (A48)

Linear (Henry type)


(A49)

Extended Langmuir

2 2 1 1 exp 0 1

1


j j

j


b P T T


+ sumhellip (A50)


( )0

0

0

1 0 1 iP


QdP Q b P z L i N


(A51a)


(A51b

)

2 2 1 1 exp 0 1

1


i i


b P T T


hellip (A51c)


)


1 0 1 i

comp

itotal pure i

Xz L i N




31


Variable Equation


Wakao correlation23

( ) 033 06 20 11 0 1

m if i comp

p

Dk Sc Re z L i N



coefficient

Wakao correlation24

( )033 0620 11 Re 0 hp

k Pr z LR

λ= + forall isin

(A53)


coefficient

Wakao correlation23

( ) 20 05 0 1

m iz i comp

bed


εhellip

(A54)


coefficient

Wakao correlation24



3

3 2

12 12

1

18583 10 0 0 1 2im i p

TMW

D z L r R iP


(A56)


2

7 175 2

12

1

1013 10 0 0 1 2im i p

MWD T z L r R i

PX


Knudsen diffusivity


3 97 10 0 0 1 k i pore p comp

i

TD R z L r R i N


(A58)


0 0 1 p m i k i

e i p compp m i k i

D DD z L r R i N

D D


hellip (A59)



2

1

1

out

inv in comp

i i

P

PF C SP P i N

x MW T

minus = = hellip

sum (A60)

Molar flowrate

Otherwise ( )

21

1

critv in comp

i i

PF C SP P i N

x MW T

minus= = hellip

sum (A61)


1critP

κ

minusκ =

+ κ (A62)

Power

1

11

feed feedfeed

low cycle

P NPower RT

P

κminus

κ κ

= minus κ minus τ

(A63)

32


33


34



35



24



1 4 8 12

spPressCoC 01000 0060 0030 00500

spAdsIn 03600 03600 03600 03600

spAdsOut 00035 00015 00015 00015

spBlow 08000 05000 02500 04000

spPurgeIn 02250 02250 02250 02250

spPurgeOut 00300 00300 0030 00300

spPEQ1 - 00040 00025 00030

spPEQ2 - - 00050 00040

spPEQ3 - - - 00080

Feed

flowrate m3s

360e-6 360e-6 360e-6 360e-6

Purge

flowrate m3s

225e-6 225e-6 225e-6 225e-6

τPress s 10 10 20 10

τAds s 20 20 20 20

τBlow s 10 10 20 10

τPurge s 20 20 20 20

τPEQ1 s - 10 20 10

τPEQ2 s - - 20 10

τPEQ3 s - - - 10

τcycle s 60 80 160 120


No

beds

O2 purity

()

O2 recovery

()

Power

(W)

Productivity

(molkgs)

1 9687 3440 52902 918e-2

4 9950 5806 27949 485e-2

8 9958 6887 11987 208e-2

12 9936 7250 13936 242e-2

25



1 4 8 12

spPressCoC 00300 00450 00500 00500

spAdsIn 01200 01300 03300 03600

spAdsOut 00004 000035 00014 00015

spBlow 02000 02200 03000 04000

spPurgeIn 05625 01500 03000 02250

spPurgeOut 00075 00200 00400 00300

spPEQ1 - 00025 00020 00300

spPEQ2 - - 00040 00040

spPEQ3 - - - 00080

Feed flowrate m

3s

120e-6 130e-6 330e-6 360e-6

Purge

flowrate m3s

075e-6 115e-6 300e-6 225e-6

τPress s 20 15 15 10

τAds s 40 30 15 20

τBlow s 20 15 15 10

τPurge s 40 30 15 20

τPEQ1 s - 15 15 10

τPEQ2 s - - 15 10

τPEQ3 s - - - 10

τcycle s 120 120 120 120


No

beds

O2 purity

()

O2 recovery

()

Power

(W)

Productivity

(molkgs)

1 9811 2021 14420 250e-2

4 9929 3840 14069 244e-2

8 9979 6525 14092 245e-2

12 9936 7250 13936 242e-2

26



1 4 8 12

spPressCC 00030 00030 00500 00040

spAdsIn 04000 03333 03450 05000

spAdsOut 000088 000085 00015 00014

spBlow 02500 04000 03000 04000

spPurgeIn 00900 01333 03000 02000

spPurgeOut 00140 00200 00400 00300

spPEQ1 - 00050 00020 00030

spPEQ2 - - 00040 00040

spPEQ3 - - - 00080

Feed flowrate m

3s

400e-6 333e-6 345e-6 500e-6

Purge

flowrate m3s

090e-6 133e-6 300e-6 200e-6

τPress s 20 15 15 10

τAds s 40 30 15 20

τBlow s 20 15 15 10

τPurge s 40 30 15 20

τPEQ1 s - 15 15 10

τPEQ2 s - - 15 10

τPEQ3 s - - - 10

τcycle s 120 120 120 120


No beds

O2 purity ()

O2 recovery ()

Power (W)


1 9987 141 18878 203e-2

4 9997 2847 11808 205e-2

8 9997 5058 11938 207e-2

12 9983 6516 11909 207e-2

27




( )( )

( )

1

0 1


comp

uC C CN D

z t z z

z L i N


part part part part


(A1)


particle surface)



( ) ( )( ) ( )

( )

31

0


bed

bed z

c Tc uT kq T T

z t R

Tz L

z z


part part


part part

(A3)





Pf u R z L

z


part (A5)


coefficient ( )

0 1 f i p

compm i





λ (A7)


( )

0 1 z i bed

compm i

Df Sc Re z L i N

D




= forall isin λ

(A9)




Cu C C D z z L i N

z

partminus = = = =

parthellip (A12)

0 or inT T z z L= = = (A13)


0 0 and u

z z Lz

part= = =

part (A14)

0 0 or 1 icomp

Cz z L i N

z

part= = = =



end 0 0 or

Tz z L

z

part= = =

part (A16)

28


Model Equation



[ ] 0 0 1 p





( )

0 1 p i ii p comp

Q CN z L i N

t t


part parthellip

(A19)



(A20)


( ) [ ]

2

15 0 0 1

e iii i p comp

p

DQQ Q r R z L i N

t R


hellip (A21) LDF


( ) 0 1 p i i

i p comp

Q CN z L i N

t t


part parthellip

(A22)


) [ ]0 0 0 1 p




( ) [ ]22

1 0 0 1 i i

p s i p comp

p

Q QR D r R z L i N

t r rR



(A24)


( ) ( )3

0 1 p

f pi i r R compi

p

kN C C z L i N


(A25)



Qk C C D r R i N

r= =

partminus = = =

part (A26)

SD

0 0 0 1 icomp

Qr z L i N

r


parthellip (A27)


( ) ( ) [ ]

22

11 0 0 1

p ppi i i

p p p p e i p comp

p

C CQR D r R z L i N

t t r rR



(A28)




( ) ( )3

0 1 p

f pi i r R compi

p

kN C C z L i N


(A30)



Qk C C D r R i N

r= =

partminus = = =

part (A31)

PD

0 0 0 1 p

icomp

Cr z L i N

r


parthellip (A32)

29


Mode Equation

( )0 0 T

z Lz

part= forall isin

part (A33)




(A34)


( ) ( )( ) ( )3

0 bed pbed p h wall

g wall bed zbed


z t R z z


part part part part

(A35)




(A36)

LEQ



( )( ) ( )

0 comp

p p Np p pg p pg

p ig ads i

i

c c TQ

q H z Lt t


part partsum

(A37)




(A38)

LDF



( )( ) ( )

0 comp

p p Np p pg p pg

p ig ads i

i

c c TQ

q H z Lt t


part partsum

(A39)



0 0 p


(A40)

SD



( )( ) ( ) 0

compp p N

p i Rppg ads i

i

c T Qq H z L

t t


part partsum

(A41)


( ) ( )3

0 p

phg R

p

kq T T z L


(A42)


( )( ) ( )

2

2

1 0 0

p p ppp p pg p pg

p pg p p

p

c c TT

q R r R z Lt r rR


(A43)


( ) ( )

0 compN

p p ig ads i p

i

Qq H r R

t


partsum

(A44)

( ) p p

pp p

h r R r R p

Tk T T r R

r= =

partminus = λ =

part

(A45)

Nonisothermal

PD

model

Boundary conditions

0 0p

Tr

r

part= =

part (A46)


( )3 h wallwall

bed

kT T

Rminus

is neglected

30



( )

( )( )

2

2 3

180 1 0

2

bg bed

bedp

uPz L

z R


part ε (A47)


( )

( )( )

2

2 3

180 1 0

2

bg bed

bedp

uPz L

z R


part ε (A48)

Linear (Henry type)


(A49)

Extended Langmuir

2 2 1 1 exp 0 1

1


j j

j


b P T T


+ sumhellip (A50)


( )0

0

0

1 0 1 iP


QdP Q b P z L i N


(A51a)


(A51b

)

2 2 1 1 exp 0 1

1


i i


b P T T


hellip (A51c)


)


1 0 1 i

comp

itotal pure i

Xz L i N




31


Variable Equation


Wakao correlation23

( ) 033 06 20 11 0 1

m if i comp

p

Dk Sc Re z L i N



coefficient

Wakao correlation24

( )033 0620 11 Re 0 hp

k Pr z LR

λ= + forall isin

(A53)


coefficient

Wakao correlation23

( ) 20 05 0 1

m iz i comp

bed


εhellip

(A54)


coefficient

Wakao correlation24



3

3 2

12 12

1

18583 10 0 0 1 2im i p

TMW

D z L r R iP


(A56)


2

7 175 2

12

1

1013 10 0 0 1 2im i p

MWD T z L r R i

PX


Knudsen diffusivity


3 97 10 0 0 1 k i pore p comp

i

TD R z L r R i N


(A58)


0 0 1 p m i k i

e i p compp m i k i

D DD z L r R i N

D D


hellip (A59)



2

1

1

out

inv in comp

i i

P

PF C SP P i N

x MW T

minus = = hellip

sum (A60)

Molar flowrate

Otherwise ( )

21

1

critv in comp

i i

PF C SP P i N

x MW T

minus= = hellip

sum (A61)


1critP

κ

minusκ =

+ κ (A62)

Power

1

11

feed feedfeed

low cycle

P NPower RT

P

κminus

κ κ

= minus κ minus τ

(A63)

32


33


34



35



25



1 4 8 12

spPressCoC 00300 00450 00500 00500

spAdsIn 01200 01300 03300 03600

spAdsOut 00004 000035 00014 00015

spBlow 02000 02200 03000 04000

spPurgeIn 05625 01500 03000 02250

spPurgeOut 00075 00200 00400 00300

spPEQ1 - 00025 00020 00300

spPEQ2 - - 00040 00040

spPEQ3 - - - 00080

Feed flowrate m

3s

120e-6 130e-6 330e-6 360e-6

Purge

flowrate m3s

075e-6 115e-6 300e-6 225e-6

τPress s 20 15 15 10

τAds s 40 30 15 20

τBlow s 20 15 15 10

τPurge s 40 30 15 20

τPEQ1 s - 15 15 10

τPEQ2 s - - 15 10

τPEQ3 s - - - 10

τcycle s 120 120 120 120


No

beds

O2 purity

()

O2 recovery

()

Power

(W)

Productivity

(molkgs)

1 9811 2021 14420 250e-2

4 9929 3840 14069 244e-2

8 9979 6525 14092 245e-2

12 9936 7250 13936 242e-2

26



1 4 8 12

spPressCC 00030 00030 00500 00040

spAdsIn 04000 03333 03450 05000

spAdsOut 000088 000085 00015 00014

spBlow 02500 04000 03000 04000

spPurgeIn 00900 01333 03000 02000

spPurgeOut 00140 00200 00400 00300

spPEQ1 - 00050 00020 00030

spPEQ2 - - 00040 00040

spPEQ3 - - - 00080

Feed flowrate m

3s

400e-6 333e-6 345e-6 500e-6

Purge

flowrate m3s

090e-6 133e-6 300e-6 200e-6

τPress s 20 15 15 10

τAds s 40 30 15 20

τBlow s 20 15 15 10

τPurge s 40 30 15 20

τPEQ1 s - 15 15 10

τPEQ2 s - - 15 10

τPEQ3 s - - - 10

τcycle s 120 120 120 120


No beds

O2 purity ()

O2 recovery ()

Power (W)


1 9987 141 18878 203e-2

4 9997 2847 11808 205e-2

8 9997 5058 11938 207e-2

12 9983 6516 11909 207e-2

27




( )( )

( )

1

0 1


comp

uC C CN D

z t z z

z L i N


part part part part


(A1)


particle surface)



( ) ( )( ) ( )

( )

31

0


bed

bed z

c Tc uT kq T T

z t R

Tz L

z z


part part


part part

(A3)





Pf u R z L

z


part (A5)


coefficient ( )

0 1 f i p

compm i





λ (A7)


( )

0 1 z i bed

compm i

Df Sc Re z L i N

D




= forall isin λ

(A9)




Cu C C D z z L i N

z

partminus = = = =

parthellip (A12)

0 or inT T z z L= = = (A13)


0 0 and u

z z Lz

part= = =

part (A14)

0 0 or 1 icomp

Cz z L i N

z

part= = = =



end 0 0 or

Tz z L

z

part= = =

part (A16)

28


Model Equation



[ ] 0 0 1 p





( )

0 1 p i ii p comp

Q CN z L i N

t t


part parthellip

(A19)



(A20)


( ) [ ]

2

15 0 0 1

e iii i p comp

p

DQQ Q r R z L i N

t R


hellip (A21) LDF


( ) 0 1 p i i

i p comp

Q CN z L i N

t t


part parthellip

(A22)


) [ ]0 0 0 1 p




( ) [ ]22

1 0 0 1 i i

p s i p comp

p

Q QR D r R z L i N

t r rR



(A24)


( ) ( )3

0 1 p

f pi i r R compi

p

kN C C z L i N


(A25)



Qk C C D r R i N

r= =

partminus = = =

part (A26)

SD

0 0 0 1 icomp

Qr z L i N

r


parthellip (A27)


( ) ( ) [ ]

22

11 0 0 1

p ppi i i

p p p p e i p comp

p

C CQR D r R z L i N

t t r rR



(A28)




( ) ( )3

0 1 p

f pi i r R compi

p

kN C C z L i N


(A30)



Qk C C D r R i N

r= =

partminus = = =

part (A31)

PD

0 0 0 1 p

icomp

Cr z L i N

r


parthellip (A32)

29


Mode Equation

( )0 0 T

z Lz

part= forall isin

part (A33)




(A34)


( ) ( )( ) ( )3

0 bed pbed p h wall

g wall bed zbed


z t R z z


part part part part

(A35)




(A36)

LEQ



( )( ) ( )

0 comp

p p Np p pg p pg

p ig ads i

i

c c TQ

q H z Lt t


part partsum

(A37)




(A38)

LDF



( )( ) ( )

0 comp

p p Np p pg p pg

p ig ads i

i

c c TQ

q H z Lt t


part partsum

(A39)



0 0 p


(A40)

SD



( )( ) ( ) 0

compp p N

p i Rppg ads i

i

c T Qq H z L

t t


part partsum

(A41)


( ) ( )3

0 p

phg R

p

kq T T z L


(A42)


( )( ) ( )

2

2

1 0 0

p p ppp p pg p pg

p pg p p

p

c c TT

q R r R z Lt r rR


(A43)


( ) ( )

0 compN

p p ig ads i p

i

Qq H r R

t


partsum

(A44)

( ) p p

pp p

h r R r R p

Tk T T r R

r= =

partminus = λ =

part

(A45)

Nonisothermal

PD

model

Boundary conditions

0 0p

Tr

r

part= =

part (A46)


( )3 h wallwall

bed

kT T

Rminus

is neglected

30



( )

( )( )

2

2 3

180 1 0

2

bg bed

bedp

uPz L

z R


part ε (A47)


( )

( )( )

2

2 3

180 1 0

2

bg bed

bedp

uPz L

z R


part ε (A48)

Linear (Henry type)


(A49)

Extended Langmuir

2 2 1 1 exp 0 1

1


j j

j


b P T T


+ sumhellip (A50)


( )0

0

0

1 0 1 iP


QdP Q b P z L i N


(A51a)


(A51b

)

2 2 1 1 exp 0 1

1


i i


b P T T


hellip (A51c)


)


1 0 1 i

comp

itotal pure i

Xz L i N




31


Variable Equation


Wakao correlation23

( ) 033 06 20 11 0 1

m if i comp

p

Dk Sc Re z L i N



coefficient

Wakao correlation24

( )033 0620 11 Re 0 hp

k Pr z LR

λ= + forall isin

(A53)


coefficient

Wakao correlation23

( ) 20 05 0 1

m iz i comp

bed


εhellip

(A54)


coefficient

Wakao correlation24



3

3 2

12 12

1

18583 10 0 0 1 2im i p

TMW

D z L r R iP


(A56)


2

7 175 2

12

1

1013 10 0 0 1 2im i p

MWD T z L r R i

PX


Knudsen diffusivity


3 97 10 0 0 1 k i pore p comp

i

TD R z L r R i N


(A58)


0 0 1 p m i k i

e i p compp m i k i

D DD z L r R i N

D D


hellip (A59)



2

1

1

out

inv in comp

i i

P

PF C SP P i N

x MW T

minus = = hellip

sum (A60)

Molar flowrate

Otherwise ( )

21

1

critv in comp

i i

PF C SP P i N

x MW T

minus= = hellip

sum (A61)


1critP

κ

minusκ =

+ κ (A62)

Power

1

11

feed feedfeed

low cycle

P NPower RT

P

κminus

κ κ

= minus κ minus τ

(A63)

32


33


34



35



26



1 4 8 12

spPressCC 00030 00030 00500 00040

spAdsIn 04000 03333 03450 05000

spAdsOut 000088 000085 00015 00014

spBlow 02500 04000 03000 04000

spPurgeIn 00900 01333 03000 02000

spPurgeOut 00140 00200 00400 00300

spPEQ1 - 00050 00020 00030

spPEQ2 - - 00040 00040

spPEQ3 - - - 00080

Feed flowrate m

3s

400e-6 333e-6 345e-6 500e-6

Purge

flowrate m3s

090e-6 133e-6 300e-6 200e-6

τPress s 20 15 15 10

τAds s 40 30 15 20

τBlow s 20 15 15 10

τPurge s 40 30 15 20

τPEQ1 s - 15 15 10

τPEQ2 s - - 15 10

τPEQ3 s - - - 10

τcycle s 120 120 120 120


No beds

O2 purity ()

O2 recovery ()

Power (W)


1 9987 141 18878 203e-2

4 9997 2847 11808 205e-2

8 9997 5058 11938 207e-2

12 9983 6516 11909 207e-2

27




( )( )

( )

1

0 1


comp

uC C CN D

z t z z

z L i N


part part part part


(A1)


particle surface)



( ) ( )( ) ( )

( )

31

0


bed

bed z

c Tc uT kq T T

z t R

Tz L

z z


part part


part part

(A3)





Pf u R z L

z


part (A5)


coefficient ( )

0 1 f i p

compm i





λ (A7)


( )

0 1 z i bed

compm i

Df Sc Re z L i N

D




= forall isin λ

(A9)




Cu C C D z z L i N

z

partminus = = = =

parthellip (A12)

0 or inT T z z L= = = (A13)


0 0 and u

z z Lz

part= = =

part (A14)

0 0 or 1 icomp

Cz z L i N

z

part= = = =



end 0 0 or

Tz z L

z

part= = =

part (A16)

28


Model Equation



[ ] 0 0 1 p





( )

0 1 p i ii p comp

Q CN z L i N

t t


part parthellip

(A19)



(A20)


( ) [ ]

2

15 0 0 1

e iii i p comp

p

DQQ Q r R z L i N

t R


hellip (A21) LDF


( ) 0 1 p i i

i p comp

Q CN z L i N

t t


part parthellip

(A22)


) [ ]0 0 0 1 p




( ) [ ]22

1 0 0 1 i i

p s i p comp

p

Q QR D r R z L i N

t r rR



(A24)


( ) ( )3

0 1 p

f pi i r R compi

p

kN C C z L i N


(A25)



Qk C C D r R i N

r= =

partminus = = =

part (A26)

SD

0 0 0 1 icomp

Qr z L i N

r


parthellip (A27)


( ) ( ) [ ]

22

11 0 0 1

p ppi i i

p p p p e i p comp

p

C CQR D r R z L i N

t t r rR



(A28)




( ) ( )3

0 1 p

f pi i r R compi

p

kN C C z L i N


(A30)



Qk C C D r R i N

r= =

partminus = = =

part (A31)

PD

0 0 0 1 p

icomp

Cr z L i N

r


parthellip (A32)

29


Mode Equation

( )0 0 T

z Lz

part= forall isin

part (A33)




(A34)


( ) ( )( ) ( )3

0 bed pbed p h wall

g wall bed zbed


z t R z z


part part part part

(A35)




(A36)

LEQ



( )( ) ( )

0 comp

p p Np p pg p pg

p ig ads i

i

c c TQ

q H z Lt t


part partsum

(A37)




(A38)

LDF



( )( ) ( )

0 comp

p p Np p pg p pg

p ig ads i

i

c c TQ

q H z Lt t


part partsum

(A39)



0 0 p


(A40)

SD



( )( ) ( ) 0

compp p N

p i Rppg ads i

i

c T Qq H z L

t t


part partsum

(A41)


( ) ( )3

0 p

phg R

p

kq T T z L


(A42)


( )( ) ( )

2

2

1 0 0

p p ppp p pg p pg

p pg p p

p

c c TT

q R r R z Lt r rR


(A43)


( ) ( )

0 compN

p p ig ads i p

i

Qq H r R

t


partsum

(A44)

( ) p p

pp p

h r R r R p

Tk T T r R

r= =

partminus = λ =

part

(A45)

Nonisothermal

PD

model

Boundary conditions

0 0p

Tr

r

part= =

part (A46)


( )3 h wallwall

bed

kT T

Rminus

is neglected

30



( )

( )( )

2

2 3

180 1 0

2

bg bed

bedp

uPz L

z R


part ε (A47)


( )

( )( )

2

2 3

180 1 0

2

bg bed

bedp

uPz L

z R


part ε (A48)

Linear (Henry type)


(A49)

Extended Langmuir

2 2 1 1 exp 0 1

1


j j

j


b P T T


+ sumhellip (A50)


( )0

0

0

1 0 1 iP


QdP Q b P z L i N


(A51a)


(A51b

)

2 2 1 1 exp 0 1

1


i i


b P T T


hellip (A51c)


)


1 0 1 i

comp

itotal pure i

Xz L i N




31


Variable Equation


Wakao correlation23

( ) 033 06 20 11 0 1

m if i comp

p

Dk Sc Re z L i N



coefficient

Wakao correlation24

( )033 0620 11 Re 0 hp

k Pr z LR

λ= + forall isin

(A53)


coefficient

Wakao correlation23

( ) 20 05 0 1

m iz i comp

bed


εhellip

(A54)


coefficient

Wakao correlation24



3

3 2

12 12

1

18583 10 0 0 1 2im i p

TMW

D z L r R iP


(A56)


2

7 175 2

12

1

1013 10 0 0 1 2im i p

MWD T z L r R i

PX


Knudsen diffusivity


3 97 10 0 0 1 k i pore p comp

i

TD R z L r R i N


(A58)


0 0 1 p m i k i

e i p compp m i k i

D DD z L r R i N

D D


hellip (A59)



2

1

1

out

inv in comp

i i

P

PF C SP P i N

x MW T

minus = = hellip

sum (A60)

Molar flowrate

Otherwise ( )

21

1

critv in comp

i i

PF C SP P i N

x MW T

minus= = hellip

sum (A61)


1critP

κ

minusκ =

+ κ (A62)

Power

1

11

feed feedfeed

low cycle

P NPower RT

P

κminus

κ κ

= minus κ minus τ

(A63)

32


33


34



35



27




( )( )

( )

1

0 1


comp

uC C CN D

z t z z

z L i N


part part part part


(A1)


particle surface)



( ) ( )( ) ( )

( )

31

0


bed

bed z

c Tc uT kq T T

z t R

Tz L

z z


part part


part part

(A3)





Pf u R z L

z


part (A5)


coefficient ( )

0 1 f i p

compm i





λ (A7)


( )

0 1 z i bed

compm i

Df Sc Re z L i N

D




= forall isin λ

(A9)




Cu C C D z z L i N

z

partminus = = = =

parthellip (A12)

0 or inT T z z L= = = (A13)


0 0 and u

z z Lz

part= = =

part (A14)

0 0 or 1 icomp

Cz z L i N

z

part= = = =



end 0 0 or

Tz z L

z

part= = =

part (A16)

28


Model Equation



[ ] 0 0 1 p





( )

0 1 p i ii p comp

Q CN z L i N

t t


part parthellip

(A19)



(A20)


( ) [ ]

2

15 0 0 1

e iii i p comp

p

DQQ Q r R z L i N

t R


hellip (A21) LDF


( ) 0 1 p i i

i p comp

Q CN z L i N

t t


part parthellip

(A22)


) [ ]0 0 0 1 p




( ) [ ]22

1 0 0 1 i i

p s i p comp

p

Q QR D r R z L i N

t r rR



(A24)


( ) ( )3

0 1 p

f pi i r R compi

p

kN C C z L i N


(A25)



Qk C C D r R i N

r= =

partminus = = =

part (A26)

SD

0 0 0 1 icomp

Qr z L i N

r


parthellip (A27)


( ) ( ) [ ]

22

11 0 0 1

p ppi i i

p p p p e i p comp

p

C CQR D r R z L i N

t t r rR



(A28)




( ) ( )3

0 1 p

f pi i r R compi

p

kN C C z L i N


(A30)



Qk C C D r R i N

r= =

partminus = = =

part (A31)

PD

0 0 0 1 p

icomp

Cr z L i N

r


parthellip (A32)

29


Mode Equation

( )0 0 T

z Lz

part= forall isin

part (A33)




(A34)


( ) ( )( ) ( )3

0 bed pbed p h wall

g wall bed zbed


z t R z z


part part part part

(A35)




(A36)

LEQ



( )( ) ( )

0 comp

p p Np p pg p pg

p ig ads i

i

c c TQ

q H z Lt t


part partsum

(A37)




(A38)

LDF



( )( ) ( )

0 comp

p p Np p pg p pg

p ig ads i

i

c c TQ

q H z Lt t


part partsum

(A39)



0 0 p


(A40)

SD



( )( ) ( ) 0

compp p N

p i Rppg ads i

i

c T Qq H z L

t t


part partsum

(A41)


( ) ( )3

0 p

phg R

p

kq T T z L


(A42)


( )( ) ( )

2

2

1 0 0

p p ppp p pg p pg

p pg p p

p

c c TT

q R r R z Lt r rR


(A43)


( ) ( )

0 compN

p p ig ads i p

i

Qq H r R

t


partsum

(A44)

( ) p p

pp p

h r R r R p

Tk T T r R

r= =

partminus = λ =

part

(A45)

Nonisothermal

PD

model

Boundary conditions

0 0p

Tr

r

part= =

part (A46)


( )3 h wallwall

bed

kT T

Rminus

is neglected

30



( )

( )( )

2

2 3

180 1 0

2

bg bed

bedp

uPz L

z R


part ε (A47)


( )

( )( )

2

2 3

180 1 0

2

bg bed

bedp

uPz L

z R


part ε (A48)

Linear (Henry type)


(A49)

Extended Langmuir

2 2 1 1 exp 0 1

1


j j

j


b P T T


+ sumhellip (A50)


( )0

0

0

1 0 1 iP


QdP Q b P z L i N


(A51a)


(A51b

)

2 2 1 1 exp 0 1

1


i i


b P T T


hellip (A51c)


)


1 0 1 i

comp

itotal pure i

Xz L i N




31


Variable Equation


Wakao correlation23

( ) 033 06 20 11 0 1

m if i comp

p

Dk Sc Re z L i N



coefficient

Wakao correlation24

( )033 0620 11 Re 0 hp

k Pr z LR

λ= + forall isin

(A53)


coefficient

Wakao correlation23

( ) 20 05 0 1

m iz i comp

bed


εhellip

(A54)


coefficient

Wakao correlation24



3

3 2

12 12

1

18583 10 0 0 1 2im i p

TMW

D z L r R iP


(A56)


2

7 175 2

12

1

1013 10 0 0 1 2im i p

MWD T z L r R i

PX


Knudsen diffusivity


3 97 10 0 0 1 k i pore p comp

i

TD R z L r R i N


(A58)


0 0 1 p m i k i

e i p compp m i k i

D DD z L r R i N

D D


hellip (A59)



2

1

1

out

inv in comp

i i

P

PF C SP P i N

x MW T

minus = = hellip

sum (A60)

Molar flowrate

Otherwise ( )

21

1

critv in comp

i i

PF C SP P i N

x MW T

minus= = hellip

sum (A61)


1critP

κ

minusκ =

+ κ (A62)

Power

1

11

feed feedfeed

low cycle

P NPower RT

P

κminus

κ κ

= minus κ minus τ

(A63)

32


33


34



35



28


Model Equation



[ ] 0 0 1 p





( )

0 1 p i ii p comp

Q CN z L i N

t t


part parthellip

(A19)



(A20)


( ) [ ]

2

15 0 0 1

e iii i p comp

p

DQQ Q r R z L i N

t R


hellip (A21) LDF


( ) 0 1 p i i

i p comp

Q CN z L i N

t t


part parthellip

(A22)


) [ ]0 0 0 1 p




( ) [ ]22

1 0 0 1 i i

p s i p comp

p

Q QR D r R z L i N

t r rR



(A24)


( ) ( )3

0 1 p

f pi i r R compi

p

kN C C z L i N


(A25)



Qk C C D r R i N

r= =

partminus = = =

part (A26)

SD

0 0 0 1 icomp

Qr z L i N

r


parthellip (A27)


( ) ( ) [ ]

22

11 0 0 1

p ppi i i

p p p p e i p comp

p

C CQR D r R z L i N

t t r rR



(A28)




( ) ( )3

0 1 p

f pi i r R compi

p

kN C C z L i N


(A30)



Qk C C D r R i N

r= =

partminus = = =

part (A31)

PD

0 0 0 1 p

icomp

Cr z L i N

r


parthellip (A32)

29


Mode Equation

( )0 0 T

z Lz

part= forall isin

part (A33)




(A34)


( ) ( )( ) ( )3

0 bed pbed p h wall

g wall bed zbed


z t R z z


part part part part

(A35)




(A36)

LEQ



( )( ) ( )

0 comp

p p Np p pg p pg

p ig ads i

i

c c TQ

q H z Lt t


part partsum

(A37)




(A38)

LDF



( )( ) ( )

0 comp

p p Np p pg p pg

p ig ads i

i

c c TQ

q H z Lt t


part partsum

(A39)



0 0 p


(A40)

SD



( )( ) ( ) 0

compp p N

p i Rppg ads i

i

c T Qq H z L

t t


part partsum

(A41)


( ) ( )3

0 p

phg R

p

kq T T z L


(A42)


( )( ) ( )

2

2

1 0 0

p p ppp p pg p pg

p pg p p

p

c c TT

q R r R z Lt r rR


(A43)


( ) ( )

0 compN

p p ig ads i p

i

Qq H r R

t


partsum

(A44)

( ) p p

pp p

h r R r R p

Tk T T r R

r= =

partminus = λ =

part

(A45)

Nonisothermal

PD

model

Boundary conditions

0 0p

Tr

r

part= =

part (A46)


( )3 h wallwall

bed

kT T

Rminus

is neglected

30



( )

( )( )

2

2 3

180 1 0

2

bg bed

bedp

uPz L

z R


part ε (A47)


( )

( )( )

2

2 3

180 1 0

2

bg bed

bedp

uPz L

z R


part ε (A48)

Linear (Henry type)


(A49)

Extended Langmuir

2 2 1 1 exp 0 1

1


j j

j


b P T T


+ sumhellip (A50)


( )0

0

0

1 0 1 iP


QdP Q b P z L i N


(A51a)


(A51b

)

2 2 1 1 exp 0 1

1


i i


b P T T


hellip (A51c)


)


1 0 1 i

comp

itotal pure i

Xz L i N




31


Variable Equation


Wakao correlation23

( ) 033 06 20 11 0 1

m if i comp

p

Dk Sc Re z L i N



coefficient

Wakao correlation24

( )033 0620 11 Re 0 hp

k Pr z LR

λ= + forall isin

(A53)


coefficient

Wakao correlation23

( ) 20 05 0 1

m iz i comp

bed


εhellip

(A54)


coefficient

Wakao correlation24



3

3 2

12 12

1

18583 10 0 0 1 2im i p

TMW

D z L r R iP


(A56)


2

7 175 2

12

1

1013 10 0 0 1 2im i p

MWD T z L r R i

PX


Knudsen diffusivity


3 97 10 0 0 1 k i pore p comp

i

TD R z L r R i N


(A58)


0 0 1 p m i k i

e i p compp m i k i

D DD z L r R i N

D D


hellip (A59)



2

1

1

out

inv in comp

i i

P

PF C SP P i N

x MW T

minus = = hellip

sum (A60)

Molar flowrate

Otherwise ( )

21

1

critv in comp

i i

PF C SP P i N

x MW T

minus= = hellip

sum (A61)


1critP

κ

minusκ =

+ κ (A62)

Power

1

11

feed feedfeed

low cycle

P NPower RT

P

κminus

κ κ

= minus κ minus τ

(A63)

32


33


34



35



29


Mode Equation

( )0 0 T

z Lz

part= forall isin

part (A33)




(A34)


( ) ( )( ) ( )3

0 bed pbed p h wall

g wall bed zbed


z t R z z


part part part part

(A35)




(A36)

LEQ



( )( ) ( )

0 comp

p p Np p pg p pg

p ig ads i

i

c c TQ

q H z Lt t


part partsum

(A37)




(A38)

LDF



( )( ) ( )

0 comp

p p Np p pg p pg

p ig ads i

i

c c TQ

q H z Lt t


part partsum

(A39)



0 0 p


(A40)

SD



( )( ) ( ) 0

compp p N

p i Rppg ads i

i

c T Qq H z L

t t


part partsum

(A41)


( ) ( )3

0 p

phg R

p

kq T T z L


(A42)


( )( ) ( )

2

2

1 0 0

p p ppp p pg p pg

p pg p p

p

c c TT

q R r R z Lt r rR


(A43)


( ) ( )

0 compN

p p ig ads i p

i

Qq H r R

t


partsum

(A44)

( ) p p

pp p

h r R r R p

Tk T T r R

r= =

partminus = λ =

part

(A45)

Nonisothermal

PD

model

Boundary conditions

0 0p

Tr

r

part= =

part (A46)


( )3 h wallwall

bed

kT T

Rminus

is neglected

30



( )

( )( )

2

2 3

180 1 0

2

bg bed

bedp

uPz L

z R


part ε (A47)


( )

( )( )

2

2 3

180 1 0

2

bg bed

bedp

uPz L

z R


part ε (A48)

Linear (Henry type)


(A49)

Extended Langmuir

2 2 1 1 exp 0 1

1


j j

j


b P T T


+ sumhellip (A50)


( )0

0

0

1 0 1 iP


QdP Q b P z L i N


(A51a)


(A51b

)

2 2 1 1 exp 0 1

1


i i


b P T T


hellip (A51c)


)


1 0 1 i

comp

itotal pure i

Xz L i N




31


Variable Equation


Wakao correlation23

( ) 033 06 20 11 0 1

m if i comp

p

Dk Sc Re z L i N



coefficient

Wakao correlation24

( )033 0620 11 Re 0 hp

k Pr z LR

λ= + forall isin

(A53)


coefficient

Wakao correlation23

( ) 20 05 0 1

m iz i comp

bed


εhellip

(A54)


coefficient

Wakao correlation24



3

3 2

12 12

1

18583 10 0 0 1 2im i p

TMW

D z L r R iP


(A56)


2

7 175 2

12

1

1013 10 0 0 1 2im i p

MWD T z L r R i

PX


Knudsen diffusivity


3 97 10 0 0 1 k i pore p comp

i

TD R z L r R i N


(A58)


0 0 1 p m i k i

e i p compp m i k i

D DD z L r R i N

D D


hellip (A59)



2

1

1

out

inv in comp

i i

P

PF C SP P i N

x MW T

minus = = hellip

sum (A60)

Molar flowrate

Otherwise ( )

21

1

critv in comp

i i

PF C SP P i N

x MW T

minus= = hellip

sum (A61)


1critP

κ

minusκ =

+ κ (A62)

Power

1

11

feed feedfeed

low cycle

P NPower RT

P

κminus

κ κ

= minus κ minus τ

(A63)

32


33


34



35



30



( )

( )( )

2

2 3

180 1 0

2

bg bed

bedp

uPz L

z R


part ε (A47)


( )

( )( )

2

2 3

180 1 0

2

bg bed

bedp

uPz L

z R


part ε (A48)

Linear (Henry type)


(A49)

Extended Langmuir

2 2 1 1 exp 0 1

1


j j

j


b P T T


+ sumhellip (A50)


( )0

0

0

1 0 1 iP


QdP Q b P z L i N


(A51a)


(A51b

)

2 2 1 1 exp 0 1

1


i i


b P T T


hellip (A51c)


)


1 0 1 i

comp

itotal pure i

Xz L i N




31


Variable Equation


Wakao correlation23

( ) 033 06 20 11 0 1

m if i comp

p

Dk Sc Re z L i N



coefficient

Wakao correlation24

( )033 0620 11 Re 0 hp

k Pr z LR

λ= + forall isin

(A53)


coefficient

Wakao correlation23

( ) 20 05 0 1

m iz i comp

bed


εhellip

(A54)


coefficient

Wakao correlation24



3

3 2

12 12

1

18583 10 0 0 1 2im i p

TMW

D z L r R iP


(A56)


2

7 175 2

12

1

1013 10 0 0 1 2im i p

MWD T z L r R i

PX


Knudsen diffusivity


3 97 10 0 0 1 k i pore p comp

i

TD R z L r R i N


(A58)


0 0 1 p m i k i

e i p compp m i k i

D DD z L r R i N

D D


hellip (A59)



2

1

1

out

inv in comp

i i

P

PF C SP P i N

x MW T

minus = = hellip

sum (A60)

Molar flowrate

Otherwise ( )

21

1

critv in comp

i i

PF C SP P i N

x MW T

minus= = hellip

sum (A61)


1critP

κ

minusκ =

+ κ (A62)

Power

1

11

feed feedfeed

low cycle

P NPower RT

P

κminus

κ κ

= minus κ minus τ

(A63)

32


33


34



35



31


Variable Equation


Wakao correlation23

( ) 033 06 20 11 0 1

m if i comp

p

Dk Sc Re z L i N



coefficient

Wakao correlation24

( )033 0620 11 Re 0 hp

k Pr z LR

λ= + forall isin

(A53)


coefficient

Wakao correlation23

( ) 20 05 0 1

m iz i comp

bed


εhellip

(A54)


coefficient

Wakao correlation24



3

3 2

12 12

1

18583 10 0 0 1 2im i p

TMW

D z L r R iP


(A56)


2

7 175 2

12

1

1013 10 0 0 1 2im i p

MWD T z L r R i

PX


Knudsen diffusivity


3 97 10 0 0 1 k i pore p comp

i

TD R z L r R i N


(A58)


0 0 1 p m i k i

e i p compp m i k i

D DD z L r R i N

D D


hellip (A59)



2

1

1

out

inv in comp

i i

P

PF C SP P i N

x MW T

minus = = hellip

sum (A60)

Molar flowrate

Otherwise ( )

21

1

critv in comp

i i

PF C SP P i N

x MW T

minus= = hellip

sum (A61)


1critP

κ

minusκ =

+ κ (A62)

Power

1

11

feed feedfeed

low cycle

P NPower RT

P

κminus

κ κ

= minus κ minus τ

(A63)

32


33


34



35



32


33


34



35



33


34



35



34



35



35



Generic Modeling Framework for Gas Separations Using Multibed Pressure Swing Adsorption Processes

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Transcript of Generic Modeling Framework for Gas Separations Using Multibed Pressure Swing Adsorption Processes