Numerical investigation of combustion characteristics in an oxygen transport reactor

Numerical investigation of combustion characteristicsin an oxygen transport reactorA. E. Farooqui, H. M. Badr*,†, M. A. Habib and R. Ben-Mansour

Mechanical Engineering Department, King Fahd University of Petroleum and Minerals, Dhahran 31261, Saudi Arabia

SUMMARY

The paper presents a numerical investigation of thermal characteristics of oxyfuel combustion in an oxygen transport reactor(OTR). The reactor is made of a combustion chamber of tubular shape and surrounded by an annular air flow compartment.The walls of the combustion chamber are made of dense, nonporous, mixed-conducting ceramic membranes that only allowoxygen permeation from the annular air compartment into the combustion chamber. A mixture of CO2 and CH4 (sweep gas)enters the reactor from one side and mixes with the oxygen permeating through the ion transport membrane. The resultingcombustion products (composed of H2O and CO2) are discharged from the other side of the reactor. The modeling ofthe flow process is based on a numerical solution of the conservation equations of mass, momentum, energy and speciesin the axi-symmetric flow domain. The membrane is modeled as a selective layer in which the oxygen permeation dependson the prevailing temperatures as well as the oxygen partial pressure at both sides of the membrane. The comparison betweenreactive and separation-only OTR units showed that combining reaction and separation increases significantly O2 perme-ation rate to about 2.5 times under the assumptions given herein. Uniform axial temperature of about 1250 K is achievedin most of the reactor length with high CH4 conversion of 75% to 35% for CH4/CO2 mass ratio ranging from 0.5/0.5 to1.0/0. Since the thermal resistance of these membranes is low, the heat of reaction is mostly transferred to the air side witha portion used to heat the O2 permeating flux. Copyright © 2013 John Wiley & Sons, Ltd.

KEY WORDS

oxyfuel combustion; oxygen transport reactor; carbon capture; ion transport membrane

Correspondence

*H. M. Badr, Mechanical Engineering Department, King Fahd University of Petroleum and Minerals, KFUPM Box # 322, Dhahran31261, Saudi Arabia.†E-mail: [email protected]

Received 22 April 2012; Revised 4 March 2013; Accepted 18 May 2013

1. INTRODUCTION

Currently, most of energy produced is from fossil fuelsbecause of its abundance in nature. These fossils fuelsproduce CO2 which is considered as a main contributorof global warming. At present, oxyfuel combustion is oneof the most promising carbon capture technologies [1]. Inthis technology, fuel is burned with oxygen in a combus-tion chamber in the absence of N2, and the combustionproducts include only CO2 and H2O. H2O can be separatedeasily by condensation process leaving only CO2 thatcan be either recycled or stored through sequestrationprocesses. The pure oxygen required for combustion isobtained from air via cryogenic distillation [2]. This pro-cess of separation of O2 is very costly, and typical powerrequirement ranges from 160 KWh to 260 KWh/ton ofO2 with purity in the range 85–99% [3,4]. Typically, theefficiency loss using these cryogenic units is 13% com-pared to a typical natural gas combined cycle without

carbon capture [5]. The thermodynamic and economicpenalties incurred by the use of cryogenic air separationunit could easily offset any advantages gained by oxyfuelcombustion prompting many researchers to investigatethe use of alternative air separation systems. One of thealternative systems is the use of ion transport membranes(ITMs) which are expected to reduce the penalty of airseparation units in oxycombustion [6,7]. Kvamsdal et al.[8] conducted efficiency analysis for all the carbon capturetechnologies and showed that the efficiency penalty withthe membrane separation is about 7% with 100% CO2

capture.ITMs are dense nonporous, mixed electronic and ionic

conducting in nature. These ITMs have the capability ofseparating oxygen from air at elevated temperatures(typically above 700�C). Oxygen permeation through thesemembranes depends on partial pressures of oxygen acrossthe membranes, membrane thickness and temperature atwhich these membranes are operating. Figure 1 shows

INTERNATIONAL JOURNAL OF ENERGY RESEARCHInt. J. Energy Res. (2013)

Published online in Wiley Online Library (wileyonlinelibrary.com). DOI: 10.1002/er.3070

Copyright © 2013 John Wiley & Sons, Ltd.

the mechanism of O2 transport through ITM in whichoxygen from bulk air stream is being adsorbed at the\surface of the membrane. Then, dissociation of oxygenalong with electron–hole transfer occurs. The next step isthe incorporation of vacancy and ion transfer through thebulk of the membrane. The above phenomenon also occurson the other side (sweep side) of the membrane leaving O2

molecules at the sweep side by the following equations(1 and 2).

O2 gð Þ þ 4e! 2O2�

O2 sð Þ ! O! O2�

)air side (1)

2O2� sð Þ ! O2 gð Þ þ 4e

O2 gð Þ O O2�

)sweep side (2)

Based on the thickness of the membrane, the oxygentransport mechanism is classified as surface reaction limitedand bulk diffusion limited. For the very thin membrane, thesurface reaction limited mechanism is dominated. Manyresearchers [9–14] conducted experiments based on differ-ent ITM materials and found that Ba0.5Sr0.5Co0.8Fe0.2O3-d

(BSCF) membrane can only give high oxygen permeationflux. Kim et al. [15] developed a semi-empirical correlationfor oxygen permeation flux for BSCF membrane forsurface reaction limited mechanism, and it is given as:

JO2 ¼2pr1r2LCikio

ffiffiffiffiP1P0

q-

ffiffiffiffiP2P0

q� �S r1þr2ð Þ (3)

where r1 and r2 are the outer and inner radii of the mem-brane tube, respectively, L is the effective length of thetube, S = 2pr1L is the effective area of the membrane, Ci

is the density of oxygen ions, kio is the surface exchangecoefficient, P1 is the global partial pressure of O2 at the feedside, P2 is the global partial pressure of O2 at the permeate

side and P0 is 1 atm. From equation (3), it can be clearlyseen that JO2 is mainly dependent on the O2 partial pressuredifferential across the membrane. Since P1 is almostconstant, the only way to maximize JO2 is to lower P2,and that can be achieved by purging the permeated O2 usingan inert gas (such as He) or having O2 consumed by fuel(such as CH4). Balanchandran et al. [16] conductedexperiments using CH4 as sweeping gas instead of He andfound no significant change in oxygen permeation throughITM. Therefore, the use of CH4 as fuel is viable withoutaffecting the performance of the ITM. The performance ofITM reactors was studied in different configurations suchgas single-tube, hollow-fiber membrane module, capillariesand monolithic multi-channels. Of all the configurations,the hollow-fiber module has highest surface area and issuggested for use in oxyfuel combustion applications [17].

It is deduced from previous studies that combustion inhollow fiber leads to low temperatures due to higher heattransfer coefficients. Based on geometry, compositionsand flow rate, flames are quenched in confined spaces.There are two mechanisms by which quenching occurs,namely thermal and radial quenching [18]. Thermalquenching occurs when most of the heat lost through thewalls and combustion cannot be self-sustained. Radicalquenching occurs by adsorption of radicals on the wallsand subsequent recombination, which results in lack ofhomogenous chemistry. These small scales are prone toboth quenching mechanisms because of high surface tovolume ratios, i.e., enhanced heat transfer from the flameto wall and increased radial mass transfer. In addition toabove said processes, blowout can occur when the exitvelocity exceeds the flame burning velocity [19]. In thismechanism, the reaction shifts downstream until it exitsthe reactor. In the present reactor, O2 is permeated fromconcentric wall (ITM) for (non-premixed) combustion ofmethane taking place in almost the entire reactor.

Very few researchers [20–23] tried to simulate theseparation of species from a mixture of gases. A 1-D modeldeveloped by Zhang et al. [24] for O2 permeation through

Figure 1. A mechanism of oxygen transport through ITMs.

Oxyfuel combustion in OTRAzharuddin et al.

Int. J. Energy Res. (2013) © 2013 John Wiley & Sons, Ltd.DOI: 10.1002/er

ITM perovskite membrane [(LaCa)(CoFe)O3-d] for non-reacting and reacting flow conditions resulted in adeviation of about 15% with the experimental data.Azharuddin et al. [25] developed a 2-D mathematicalmodel for predicting oxygen separation and mixing in acylindrical oxygen transport reactor (OTR). Mancini andMitsos [26] developed a black box 1-D model for ITMreactor based on an empirical equation for O2 permeationfrom the experimental data of Xu and Thomson [27]. Themodel gives the axial profiles with and without reaction,but there is no validation of their model. In the presentwork, a CFD model is developed for oxygen permeationthrough ITM and chemical reaction with the fuel. TheCFD calculations were carried out using FLUENT 12.1,while the mass transfer of oxygen through the membraneis modeled using a set of user-defined functions (UDF).

2. PROBLEM STATEMENT

In this work, the combustion process taking place in an OTRis numerically modeled. The reactor has a tubular shape andis surrounded by an annular air feed compartment as shownin Figure 2. A mixture of CH4 and CO2 is fed from one sideof the reactor and mixes with the oxygen permeating throughthe reactor walls that are made of ITM. Fresh air (77%N2+23%O2 by wt.) is fed in shell side, and a mixture ofCH4 and CO2 is fed into the core side of the reactor. Theeffect of reaction of CH4 with the permeated O2 on theoxygen permeation rate through the ITM membrane isstudied. The membrane considered in this work is BSCFwith an effective surface area of 12.56 cm2. The reactiveITM has the advantage of combining the separation ofoxygen from air and oxidation of methane in order to reducethe overall size of the reactor and number of equipments inthe power cycle. The effect of different operating parameterson the temperature distribution along the membrane surfaceis investigated with the objective of achieving isothermalOTR and also optimizing the consumption of CH4 withmaximum O2 permeation.

3. GOVERNING EQUATIONS

A CFD model that is based on finite-volume discretizationmethod is developed. In this model, velocity and pressurefields of gas mixture are obtained by solving continuity,

momentum and energy equations. The species distributionand the fluxes at the feed and permeate sides are obtainedby the convection-diffusion equation. The species transportacross the membrane is carried out using a source term.The steady-state equations for conservation of mass, mo-mentum, energy and species can be written as:

r: rUð Þ ¼ Si (4)

r: rUUð Þ ¼ -rpþ mr2U (5)

rCp

� �U�rT ¼ r� lrTð Þ (6)

r� rUYið Þ-r� rDi;mrYiÞ ¼ Si�

(7)

This source/sink term (Si) accounts for the mass flow ofspecies across the membrane. At the membrane boundarycells, the species are allowed to disappear from one side ofthe membrane through the sink term and to come out onthe other side through the source term. The source/sink termcan be formulated based on the membrane characteristicssuch as permeability of membrane, surface exchange coeffi-cient and partial pressure of O2 on either side of the mem-brane and the membrane thickness. Equation (8) representsthe source/sink terms based on the partial pressure of O2.

Si ¼þJO2 �Acell�MWO2

Vcellat low partial pressure of O2

-JO2 �Acell�MWO2

Vcellat high partial pressure of O2

8>><>>:

(8)

The source/sink Si term ismodelled in such a way that it iszero unless i =O2 and the computational cell is adjacent tothe membrane surface. The diffusion coefficient is deter-mined by specifying, the binary mass diffusion coefficientof the component i in the component j. The correspondingdiffusion coefficient in the mixture is computed by equation(9) [28].

Di;m ¼ 1-XiXj;j6¼i

Xi

Di;j

� � (9)

4. DOMAIN DISCRETIZATION

The dimensions of the computational domain for validationwere identical with that of experimental membrane cell

Feed side

Permeate side

1.0

mm

2.0 mm

100mm

Membrane

CH4+CO2

Air inletAir outlet

Combustion products

Figure 2. Schematic of the oxygen transport reactor.

Oxyfuel combustion in OTR Azharuddin et al.


(Figure 3) ofWang et al. [9]. In order to reduce the numericalerrors, structured meshing was performed to divide the flowdomain into subdomains (feed side and permeate side) with12,500 quadrilateral cells. The computational geometryconsisted of two mass flow inlets, boundaries for introducingthe feed and sweep gas mixture and two pressure outlets forfeed and permeate flows. The membrane in the domain wasdefined as selective layer. The computational grid consistedof 40 ‘Mass-Flow-Inlet’ edge cells for air inlet with 50‘Pressure-Outlet’ edge cells and 250 cells along the axis ofthe OTR. Grid refinement was performed to achieve the gridindependence by analyzing the mass fractions within thegeometrical domain.

5. SOLUTION PROCEDURE

The numerical simulations were performed using CFDsoftware FLUENT 12.1. In the present simulations, the gasmixture properties were defined before executing thesimulation loop. For model validation, operating parameterssuch as mass flow rate and species concentrations wereobtained from the data of Wang et al. [9]. The simulationswere performed using steady flow conditions as given inTable I. The discretization of the governing equations wasperformed using a segregated compressible flow solver inwhich each governing equation is solved separately. TheseITM membranes activate the process of permeating oxygenmolecules at very high temperatures of the order of 700�C.These high temperatures are achieved by high inlet feed andpermeate temperature, and once the combustion is initiatedthen the high membrane temperature is maintained by the

combustion process. Moreover, the inlet air is heated usingthe high-temperature exhaust gases and part of the exhaustCO2 is recycled in the sweep gas.

To obtain a stable solution, under-relaxation factors of0.3 and 0.7 were used for pressures and velocities at allnodal points in the solution domain. The pressure–velocitycoupling is done using Semi-Implicit Method for Pressure-Linked Equations algorithm [29]. To ensure a completeconverged solution, the continuity and momentum residualvalues were set to 10�6, and those for species and energyequations were set to 10�9. The gas density is calculatedusing the ideal gas law, and the gas viscosity, specific heatand thermal conductivity are calculated as a mass fraction-weighted average of all species. The specific heat of eachspecies is calculated using a piecewise polynomial fit oftemperature. Pressure was set to pressure staggered scheme(PRESTO), and momentum, species and energy were set tosecond-order upwind discretization scheme for moreaccurate results [28].

Transport of O2 across the membrane was achievedusing series of UDF that are written in VC++ and compiledand hooked to the FLUENT software. The three differentmacros used in UDF are ‘define initialize’, ‘define source’and ‘define adjust’ as defined in FLUENT software. Thesemacros link the cell index across the membrane, whichallows the addition and subtraction of the source term incontinuity and species transport equation. Additionally,the UDF updates the solver data with the new parameterat the membrane wall in every iteration. The issue ofhydraulic jump across the membrane was resolved bypatching the cells from the upper and lower zones withtwo different values of initial partial pressures of species.In the computational simulation, the membrane isconsidered as a wall of zero thickness with source/sinksterms that account for the mass transfer across the mem-brane wall. However, in the heat transfer calculations, themembrane thickness is considered for the determinationof the heat loss from the permeate side to air side. At thebeginning, there is no oxygen at the permeate side whilethe O2 partial pressure at the feed side is 0.23 atm. This cre-ated numerical instability and the solution diverges. Hence,in order to attain a stable solution without divergence,initial partial pressures (non zero values) for the species atthe feed and permeate side are assumed. Equation (3) isbased on the global partial pressures at air and permeateside. The source and sink terms in the UDF were calculatedusing semi-empirical equation (10 and 11) developed fromthe experimental results of Wang et al. [9] which accountfor the local O2 partial pressure. The partial pressure givenin the oxygen flux equation (10) is calculated as concentra-tion Yi (% wt.). The mass fraction, Yi, is converted intomole fraction and then applied in calculating the sourceterm. Figure 4 shows the flow chart representing theiterative calculations during the simulations.

JO2 ¼ K1K21 Tð Þ

ffiffiffiffiffiffiffiP’1P0

r-

ffiffiffiffiffiffiffiffiP’’2P0

r� �0:623

(10)

Feed side

Permeate side

14.5

mm

2.28 mm

17.68 mm

Membrane

Figure 3. Dimensions of the OTR used in the experimentalwork done by Wang et al. [9].

Table I. List of model parameter values.

Parameter Value

_minlet;pemeate 1.625� 10�7 kg/s_minlet;feed 5.85� 10�6 kg/sTinlet,pemeate 1073 KTinlet,feed 1073 KYCH4 ;YCH2ð Þpermeate variedYO2 ;YN2ð Þair 0.23; 0.77rmembrane 3000 kg/m3

lmembrane 20 W/m/K [25]



K1 ¼ 2pr1r2LS r1þr2ð Þ (11)

whereP ’ 1 and P ’ ’ 2are the local partial pressure of O2 atmembrane surface on feed and permeate side, respectively,K1 is a geometric constant and K2 is a constant that dependson temperature.

The main focus of the present study is to understand thethermal and combustion characteristics within the ITMreactor. The O2 permeation and heat transfer along the ITMstrongly affects the flame stability and flame position whichmakes the ITM reactor very different from the conventionalcontinuous stirred-tank reactor and plug flow reactor. Forsmall reactor, thermal effects are well captured with fewsteps of chemistry [30]. Specifically, the one-step irreversiblereaction mechanism for methane determined by Westbrookand Dryer [31] is applied at permeate side as shown below.

CH4þ2O2!k2H2Oþ CO2

RCH4 ¼ -k CH4½ �nCH4 O2½ �nO2

k ¼ ATbexp-Ea

RT

� �

nCH4 ¼ 0:2; nO2 ¼ 1:3;

where the concentrations are in units of kg-mol/m3,RCH4is thereaction rate, A= 2.110� 1011, Ea = 2.07� 108 J/kg-mol,b=0 and k is the Arrhenius reaction rate. This one-stepapproximation is a useful tool for describing the thermalcharacteristics and flame dynamics [32].

6. MODEL VALIDATION

In order to verify the computational scheme developed forthe membrane permeation model, the simulation wasperformed for the reactor shown in Figure 3 that was usedin the experimental setup of Wang et al. [9]. The operatingconditions are taken exactly the same as those used byWang et al. [9]. A comparison is made between the modelprediction and the measured values of O2 permation flux(Figure 5) shows a good accuracy especially at highoxygen partial pressure in the feed side. The largestdeviation was about 15% occurring at 900�C and 0.19atm. This deviation may be attributed to experimentaluncertainties at high temperatures.

7. RESULTS AND DISCUSSION

The performance of the OTR is investigated consideringoxygen separation, mixing and reaction with the sweepgas. Air (containing 77% N2 and 23% O2) enters at inletof the feed side, and a sweep gas mixture (CH4 and CO2)enters at inlet of the permeate side of an OTR havingBSCF tubular membrane (Figure 2). The wall of the

Figure 4. Flowchart for solving for source/sink term.

0 0.2 0.4 0.6 0.8 10

0.5

1

1.5

2

2.5

3

3.5

Oxygen partial pressure in the shell side (atm)

O2

perm

eatio

n flu

x (m

l/cm

2 -m

in)

800oC

900oC

700oC

Figure 5. Variation of O2 permeation flux with O2 partial pres-sure in the shell side; (■□▼) experimental data by Wang et al.

[9], (—— ) present numerical results.



reactor is assumed to be adiabatic [9,33] to ensuresimilarity with the experimental model for permeationdone by Wang et al. [9]. The bouyancy and radiationeffects are neglected because of the small diameter ofITM reactor that leads to high convective heat transfercoefficients, implying that the difference of membranetemperature and free stream is small. The flow is steadyand laminar because of the low velocities and smalldiameter of the reactor. In this work, we have neglectedthe surface chemistry of the reacting species and also theeffect of change of ITM temperature along the length ofthe reactor. This is mainly because the effect of O2 partialpressure outweighs the effect of change of membranetemperature in the considered reactor.

The consumption of oxygen in the chemical reactionat the permeate side results in a significant reduction ofO2 partial pressure in that side. This creates high partialpressure difference along the membrane tending toincreases the oxygen permeation flux. To study theOTR combustion characteristics, numerical simulationsare carried out for the conditions shown in Table I.The hermal conductivity of perovskite membranes (suchas LSCF, BaCeO3, BaZrO3) ranges from 5 to 12 W/m.K for operating temperatures in the range 500–1000�C[34–36]. The thermal conductivity is still unknown forBSCF, and the analysis done by Kaisare and Vlachos[37] suggested that for ceramic membranes the thermalconductivity varies from 3 to 100 W/m.K. In the presentstudy, the thermal conductivity of BSCF is assumed 20W/m.K.

In order to investigate the influence of combustion onoxygen permeation, the results of the two cases of O2

separation only and separation with reaction werecompared. Figure 6a shows the O2 permeation flux (JO2)for the same case considering separation-only and reactivemodes. It is evident from the figure that the local O2

permeation flux for the case of reactive mode is very highcompared to the separation-only mode over a large portionof the ITM surface. This is attributed to the high partialpressure difference of O2 created across the membranedue to the oxygen consumption in the permeate side. Thefavorable increase of the rate of O2 permeation enables toburn more fuel for the same reactor length. Figure 6bshows the total oxygen permeation rate in mol/s from themembrane for cold combustion (separation only) andreactive cases for different compositions of the fuelmixture. The amount of oxygen permeated through themembrane for cold combustion (mixing) is 3.29� 10�6

mol/s to 3.97� 10�6 mol/s while reaching in thecombustion case 4.11� 10�6 mol/s to 9.33� 10�6 mol/sfor 10% to 100% of CH4 at inlet of fuel mixture. Theoxygen permeation rate through the membrane increasesfor 10% to 33% CH4 at inlet and becomes almost constantfor the high CH4 percentages. This is attributed to thecomplete combustion of CH4 up to 33% at inlet. Oxygenpermeation rate through ITM for combustion is very muchhigher compare with sweep mixture of cold mixing andequals 25% to 135% higher for 10% to 100% CH4.

The axial temperature profiles within the reactor fordifferent sweep gas mixture composition are shown inFigure 7. The temperature rises quickly to 1250 K at 1/5th

of the reactor length from inlet and then decreases in thedownstream direction. This decrease is mainly due to thecooling of the flue gases by the permeating O2 through themembrane. When the mixture mass ratio (mR=mass ratioof CH4/CO2 in the sweep gas) increases beyond 0.4/0.6,the exit temperature of the reactor becomes almost constantat about 1222 K. In order to explain the temperature profiles,the axial variations of the rate of chemical reaction arepresented in Figure 8. The figure shows that the rate ofreaction reaches to nearly 0.0062 kg-mol/m3-s and decreasesalong the length of the reactor. For values of mR rangingfrom 10% to 30%, the fuel (CH4) is totally consumed withinthe reactor and for mR=33%, the rate of reaction drops tozero at exit of the reactor. It is noted that temperatures andrate of reaction profiles for values of mR ranging from 50%to 100% differ only slightly, and the combustion in thesecases is incomplete leaving some unburned fuel dischargingat high temperatures. One of the main concerns in the reactor

0 0.02 0.04 0.06 0.08 0.1

x 10-6

0.0

1.0

2.0

3.0

4.0

5.0

6.0

7.0

Distance along the length (m)

J O2(

mo

l/m2 -

s)

Reaction

Separation only

0 20 40 60 80 100

x

2.0

4.0

6.0

8.0

10-6

1.0x101

CH4% in inlet

Oxy

gen

per

mea

tio

n r

ate

(mo

l/s)

With Reaction

Separation only

minlet = 1.625·10-7 (Kg/s)

a

b

Figure 6. Oxygen permeation flux for the reactive and separa-tion only case. b. Comparison between oxygen permeation rate

from the ITM with and without combustion.



design is the uniformity of the temperature distribution alongthe membrane surface. It is clear from Figure 7 that thetemperature distribution is nearly uniform over a largedistance of the reactor length for sweep gas mixtures havingmR ranging from 50% to 100%. However, the incompletecombustion in the reactor may be rectified by splitting thereactor into a series of units where the exhaust of the first unitis fed in the second and so on till the fuel is totally consumed.From the above discussion, it can be concluded that with lessdiluent CO2 at inlet high maximum temperatures can beachieved for increasing mass flow rate. This is accompaniedby a reduction in conversion percentage of CH4. With splitITM reactor design, the problem of fuel conversion can beovercome with nearly uniform temperature along the reactor.

For the optimal design of ITM reactor which combinesO2 separation and fuel oxidation, the amount of CH4

conversion is an important parameter that is affected bythe diluent CO2 concentration and O2 permeation flux.Figure 9 shows the CH4 mass fraction profiles fordifferent sweep gas compositions when the sweep gas flowrate is 1.625� 10�7 kg/s. It is evident that the conversion ofCH4 to combustion products decreases with the increase ofCH4 percentage at the inlet. The maximum temperature

within the reactor is almost the same for all sweep gascompositions (Figure 7), while the temperature at exitdepends on the CH4 mass ratio. In order to increase theO2 permeation flux from the ITM, there must be sufficientmethane input so that the chemical reaction doesn’t stopat the first part of the reactor. Two related factors havesignificant effect on the O2 permeation flux. The first isthe membrane temperature that should be kept as high aspossible along the length of the reactor, and the second isthe O2 partial pressure in the permeate side that should bekept as low as possible. Both favorable effects can beachieved when the CH4 mass ratio is high. For example,when mR is in the range 10% to 30%, all the CH4 isconsumed, and the permeating O2 downstream cools theflue gases resulting in a decrease in the membranetemperature. For the case of mR = 33%, the reaction endsnear the exit of the reactor. However, for cases of mR

33%, the CH4 conversion gets less with the increase ofmR until reaching a conversion rate of 36.8% when mR

reaches 100% as can be seen in Figure 10. The figure alsoshows the total O2 permeation rate for at differentpercentages of CH4 at the inlet. It is evident from the figurethat up to mR = 33%, the CH4 conversion is 100% for a

0 0.02 0.04 0.06 0.081050

1100

1150

1200

1250

1300


Tem

per

atu

re (

K) CH4 / CO2 : 0.1 / 0.9

CH4 / CO2 : 0.3 / 0.7CH4 / CO2 : 0.33 / 0.67

CH4 / CO2 : 0.35 / 0.65CH4 / CO2 : 0.4 / 0.6

CH4 / CO2 : 0.5 / 0.5CH4 / CO2 : 0.7 / 0.3

CH4 / CO2 : 1.0 / 0

CH4 / CO2 : 0.2 / 0.8

Figure 7. Temperature profiles for the different sweep gases.

0 0.02 0.04 0.06 0.08 0.10

0.001

0.002

0.003

0.004

0.005

0.006

0.007


Kin

etic

rat

e o

f re

acti

on

(K

g-m

ol/m

3 -s)

CH4 / CO2 : 0.10 / 0.90

CH4 / CO2 : 0.30 / 0.70CH4 / CO2 : 0.33 / 0.67CH4 / CO2 : 0.35 / 0.65CH4 / CO2 : 0.40 / 0.60CH4 / CO2 : 0.50 / 0.50CH4 / CO2 : 0.70 / 0.30CH4 / CO2 : 1.0 / 0

CH4 / CO2 : 0.20 / 0.80

Figure 8. Kinetic rate of reaction profiles for different sweep gas mixtures for three different mass flow rates.



mass flow rate of 1.625� 10�07 kg/s. On the other hand,the O2 permeation rate increases with the increase of mR

up to mR = 40% and then becomes constant (9.33� 10�06

mol/s) until reaching mR = 100%. It is worth mentioning

that similar profiles for O2 permeation rate and conversionof CH4 and O2 are obtained by Tan et al. [38] for LSCF-ITM membrane.

Figures 11 and 12 show the variations of O2 massfraction and O2 permeation flux along the reactor axisfor a constant mass flow rate of 1.625� 10�7 kg/s anddifferent values of CH4 concentration, respectively. Therelationship between the two figures can be understoodbased on the fact that the O2 permeation flux (JO2 inFigure 12) depends on the O2 partial pressure in the perme-ate side which in turn depends on the O2 mass fraction(Figure 10). Now, since the O2 partial pressure at the feedside is almost constant (=0.21 atm) as per equation (8), thevariation of JO2 is more governed by O2 partial pressure atpermeate side than temperature since the temperature risewithin the reactor is nearly of the order of 200 K. There-fore, the lesser the O2 partial pressure at the permeate side,the higher the O2 permeation flux. Figure 12 shows zeropartial pressure of O2 at inlet of the permeate side andhence maximum O2 permeation flux. The O2 mass fractionincreases downstream till O2 is sufficient to burn CH4

then decreases till the reaction rate reaches its maximum.

0 0.02 0.04 0.06 0.08 0.10

0.2

0.4

0.6

0.8

1


CH

4Mas

sFra

ctio

n CH4 / CO2 : 0.1 / 0.9

CH4 / CO2 : 0.3 / 0.7

CH4 / CO2 : 0.33 / 0.67CH4 / CO2 : 0.35 / 0.65

CH4 / CO2 : 0.4 / 0.6

CH4 / CO2 : 0.5 / 0.5

CH4 / CO2 : 0.7 / 0.3CH4 / CO2 : 1.0 / 0

CH4 / CO2 : 0.2 / 0.8

Figure 9. CH4 mass fraction profiles for different sweep gas compositions for a flow rate of 1.625� 10�7 kg/s.

0 10 20 30 40 50 60 70 80 90 100

x 10-6

0

20

40

60

80

100

2

4

6

8

10

12

CH4% at inlet

% c

onve

rsio

n

CH4 conversionO2 conversion

Rich composition

Lean composition

O2 permeation rate

O2

perm

eatio

n ra

te (

mol

/s)

Figure 10. Percentage of O2 and CH4 conversion and O2

permeation rate.

0 0.02 0.04 0.06 0.08 0.10

0.04

0.08

0.12

0.16

0.2


O2

Mas

s F

ract

ion

CH4 / CO2 : 0.3 / 0.7

CH4 / CO2 : 0.33 / 0.67

CH4 / CO2 : 0.35 / 0.65CH4 / CO2 : 0.4 / 0.6

CH4 / CO2 : 0.5 / 0.5CH4 / CO2 : 0.7 / 0.3

CH4 / CO2 : 1.0 / 0

CH4 / CO2 : 0.2 / 0.8

Figure 11. O2 mass fraction profiles for different sweep gas compositions.



For mR = 10%, the reaction rate reaches zero at X/L = 0.25as the total amount of CH4 is consumed, and this isfollowed by a continuous increase in the O2 mass fractioncausing a continuous decrease in the O2 permeation fluxtill reaching the exit section. For values of mR rangingfrom 20% to 33%, the trend of O2 mass fraction variation

is almost the same; however, for values of mR greater than33%, the O2 mass fraction is almost constant leading to al-most constant O2 permeation flux as shown in Figure 12.

Figure 13 shows the radial temperature profiles atdifferent sections along the reactor (X/L = 0.15, 0.25,0.5 and at 1.0). At X/L = 0.15, the reaction is just started,

0 0.02 0.04 0.06 0.08 0.1

x 10-6

0.0

1.0

2.0

3.0

4.0

5.0

6.0

7.0


JO2

(mo

l/m2 -

s)

CH4 / CO2 : 0.1 / 0.9

CH4 / CO2 : 0.3 / 0.7

CH4 / CO2 : 0.33 / 0.67CH4 / CO2 : 0.35 / 0.65

CH4 / CO2 : 0.4 / 0.6

CH4 / CO2 : 0.5 / 0.5CH4 / CO2 : 0.7 / 0.3CH4 / CO2 : 1.0 / 0

CH4 / CO2 : 0.2 / 0.8

Figure 12. O2 permeation flux for different sweep gas compositions.

0 0.002 0.004 0.006 0.008 0.011050

1090

1130

1170

1210

1250

Membrane

Air side

Fuel side At exit

0 0.002 0.004 0.006 0.008 0.011050

1090

1130

1170

1210

1250

Radial Distance (m) Radial Distance (m)


Tem

per

atu

re (

K)

Tem

per

atu

re (

K)

Tem

per

atu

re (

K)

Tem

per

atu

re (

K)

Air side

At X/L=0.15MembraneFuel Side

0 0.002 0.004 0.006 0.008 0.011050

1090

1130

1170

1210

1250

Air side

Membrane

Fuel Side

At X/L=0.25

0 0.002 0.004 0.006 0.008 0.011050

1090

1130

1170

1210

1250

At X/L=0.5

Air side

Membrane

Fuel side

CH4 / CO2 : 0.1 / 0.9

CH4 / CO2 : 0.33 / 0.67CH4 / CO2 : 0.4 / 0.6CH4 / CO2 : 0.5 / 0.5CH4 / CO2 : 1.0 / 0

CH4 / CO2 : 0.2 / 0.8

Figure 13. Radial temperature profiles at different sections.



and the temperature starts rising, and at X/L = 0.25, thereaction rates attain their maximum for almost allcomposition mixtures. At X/L = 0.5, the temperature isdropped for low CH4 mixture composition due to thedepletion of CH4. The temperature drop at exit for casesof mR< 50% is mainly due to the drop of CH4 conversion

rate. Figure 14 shows the radial profiles of O2 mass frac-tion for three values of mR (mR = 10%, 50% and 100%)at four sections along the reactor (X/L = 0.15, 0.25,0.5, 1.0). At X/L = 0.15, the O2 mass fraction at the feedside drops from 0.225 at the outer wall of the shell to0.218 at the membrane surface. At the same section, the

0 0.0005 0.001 0.0015 0.0020.04

0.06

0.08

0.1

0.12

Radial Distance (m)

O2

Mas

s F

ract

ion

O2

Mas

s F

ract

ion

O2

Mas

s F

ract

ion

O2

Mas

s F

ract

ion

O2

Mas

s F

ract

ion

O2

Mas

s F

ract

ion

O2

Mas

s F

ract

ion

O2

Mas

s F

ract

ion

Permeate Side

X/L=0.15

0.002 0.004 0.006 0.008 0.01

0.22

0.222

0.224

0.226

Radial Distance (m)


Feed Side

X/L=0.15

0 0.0005 0.001 0.0015 0.002

0.036

0.042

0.048

0.054

0.06Permeate Side

X/L=0.25

0.002 0.004 0.006 0.008 0.010.214

0.216

0.218

0.22

0.222

X/L=0.25

Feed Side

0.002 0.004 0.006 0.008 0.010.202

0.204

0.206

0.208

0.21

0.212

0.214

0.216

Radial Distance (m)

Feed Side

X/L=0.5

0 0.0005 0.001 0.0015 0.0020.02

0.04

0.06

0.08

0.1

0.12

0.14

Radial Distance (m)

Permeate Side

X/L=0.5

0 0.0004 0.0008 0.0012 0.00160.04

0.06

0.08

0.1

0.12

0.14

0.16

0.18

0.2

Radial Distance (m)

Permeate Side

X/L=1.0

0.003 0.004 0.005 0.006 0.007 0.008 0.009 0.010.18

0.185

0.19

0.195

0.2

0.205

0.21

0.215

0.22

Radial Distance (m)

Feed Side

X/L=1.0

Figure 14. O2 mass fraction radial profiles; CH4/CO2 : 0.1/0.9; ; CH4/CO2 : 0.5/0.5; CH4/CO2 : 1.0/0.



O2 mass fraction at permeate side is very low in the caseof mR = 10% compared to the cases of mR = 50% and100% due to the early chemical reaction in the first case.At section X/L = 0.25, the reaction rate for the case ofmR = 50% is maximum compared to other cases, andhence the maximum temperature is achieved. From thetemperature distributions at sections X/L =0.5 and 1.0(Figure 13), it is clear that CH4 is totally consumed inthe case of mR = 10%, and there is no much variation ofO2 mass fraction radially (Figure 14). For values of mR =50% and 100%, there is no much difference in magnitudeof O2 mass fraction in the feed and permeate sides sincethe O2 permeation flux becomes constant for values of mR

33%. Figure 15 shows the temperature and compositionprofiles in radial direction for mR = 50% at differentstations (X/L = 0.15, 0.25, 0.5, 1.0). It can be seen thatthe maximum temperature and maximum ΔT along the

radial direction are achieved at X/L = 0.25, 0.5 andΔTmax is approximately 40 K.

Figure 16 shows the temperature and compositionprofiles for one value of mR (mR = 50%) and a massflow rate of 1.625� 10�7 kg/s. It can be seen fromthe figure that the difference in axial temperature andmembrane temperature is around 30 K. At this flowrate, the CH4 mass fraction reaches 0.05 at the reactorexit and exactly the same value for O2 mass fraction.Also, the temperature distribution is nearly uniformfollowing downstream of section X/L = 0.2. The smalldecrease of temperature downstream of X/L = 0.2 isattributed to the decrease in the reaction rate becauseof increasing the mass ratio of O2/CH4.

Figure 17 shows the temperature contours for differentsweep gas (CH4/CO2) mass ratios. It can be seen that thereaction starts at X/L� 0.15 for almost all values of mR

with O2 partial pressure at feed side P1 = 0.21 atm. Thefigure shows a maximum temperature of 1250 K in thecombustion zone. Oxy-fuel combustion normally resultsin high temperature; however, the use of CO2 in the sweepgas will provide the ballasting effect of the absent N2 andmoderate the furnace temperature. During combustion,the fall of oxygen concentration is equivalent to the riseof CO2 in the mixture, leading to increase of specific heatcapacity; thereby, the temperature rise rates decrease. Theincrease of membrane temperature due to combustionresults in an increase in the heat loss to the air domain byconduction. Under the relatively low temperatures of thereaction taking place, kinetics become important, and thismay lead to accumulation of oxygen downstream thereactor and hence will lead to a continuing reduction in

0 0.0005 0.001 0.0015 0.0020

0.1

0.2

0.3

0.4

0.5

1120

1140

1160

1180

Radial Distance (m)

Mas

s F

ract

ion

X/L=0.15

Tem

pera

ture

(K

)

0 0.0005 0.001 0.0015 0.0020

0.1

0.2

0.3

0.4

0.5

0.6

1200

1210

1220

1230

1240

1250

Radial Distance (m)

Mas

s F

ract

ion

X/L=0.25

Tem

pera

ture

(K

)

0 0.0005 0.001 0.0015 0.0020

0.1

0.2

0.3

0.4

0.5

0.6

1200

1210

1220

1230

1240

Radial Distance (m)

Mas

s F

ract

ion

Tem

pera

ture

(K

)

0 0.0004 0.0008 0.0012 0.00160

0.1

0.2

0.3

0.4

0.5

0.6

1155

1170

1185

1200

1215

Radial Distance (m)M

ass

Fra

ctio

n

Tem

pera

ture

(K

)X/L=0.50

X/L=1.0

Figure15. Radial temperature and composition profiles formRof 50%; CH4 O2 CO2 H2O Temp.

0 0.02 0.04 0.06 0.08 0.11073

1123

1173

1223

1273

1323

1373

0

0.1

0.2

0.3

0.4

0.5

0.6

0.7


Tem

pera

ture

(K

) Taxis

CH4O2CO2H20

Mas

s F

ract

ionTmem

Figure 16. Temperature and composition profiles for mR=50%.



the O2 permeation rate. It is also shown that the tempera-ture at the membrane surface is less than that at the coreof the reactor. This will reduce thermal stresses in themembrane material and accordingly reduce the possibilityof membrane fracture. The flame zone is in the middle ofthe reactor as shown in Figure 17. Most of the heat releasedis lost to air side through the membrane because thesemembranes have very low thermal resistance. Based onthe above, it is clear that ITM has a good potential forimplementation in an OTR where oxygen separation andcombustion are combined in one device.

8. CONCLUSION

A computational study that couples membrane permeationand chemical reaction in anOTRwas carried out. The reactoris made of a combustion chamber of tubular shape

surrounded by an annular air flow compartment. The wallsof the combustion chamber are made of ITM that only allowsoxygen permeation from the air compartment into thecombustion chamber. The study focused on the predictionof the thermal characteristics of the combustion process fordifferent sweep gas compositions (mass ratio of CH4 andCO2). The comparison between the reactive and O2

separation-only OTR units showed an increase in the O2

permeation rate by about 2.5 times by combining O2

permeation and combustion in one device but problemsassociated with sealing, soot formation and blow out needmore investigation. The effect of the sweep gas compositionon the uniformity of the temperature distribution along thereactor axis was also investigated. The results indicated thata CH4/CO2 mass ratio ranging from 50% to 100% givesalmost uniform axial temperature of about 1250 K over mostof the reactor length with CH4 conversion ranging from 75%to 35%, respectively. Because of the low thermal resistance

Figure 17. Temperature contours for different CH4/CO2 mixtures and a constant flow rate of 1.625� 10�07 kg/s.



of ITMmembranes, the heat of reaction is mostly transferredto the air side with a portion used to heat the O2 permeatingflux. From the study, it is concluded that CO2 addition insweep gas has a major impact because of its high heatcapacity and it plays a major role in keeping the reactor atlow temperature and slow reaction kinetics. The study isconducted by considering single step reaction chemistry fora single hollow fiber reactor and needs more investigationin designing a reactor with multiple hollow fibers to optimizeexisting conceptual ITM-based power cycles such as theAdvanced Zero Emission Power cycle [39] and also todevelop novel designs. The present results, herein, improveITM integration in power cycles conceptualization and canbe used to assist in design of pilot plants.

NOMENCLATURE

r1 = outer radius of the membrane tube[m]r2 = inner radius of the membrane tube[m]L = effective length of the tube [m]S = effective area of the membrane tube [m2]Ci = density of oxygen ions [mol/m3]kio = surface exchange coefficient [m/s]P1 = global partial pressure of oxygen at the

feed side [atm]P2 = global partial pressure of oxygen at the

permeate side [atm]P ’ 1 = local partial pressure of oxygen at the

feed side [atm]P ’ ’ 2 = local partial pressure of oxygen at the

permeate side [atm]P0 = 1 atm oxygen pressureJO2 = oxygen permeation flux [mol/m2-s]Yi = mass fraction of species i [�]r = density [kg/m3]Di,m = diffusion coefficient of mixture of

species i [m2/s]Si = source/sink term [kg/m3-s]U = velocity vector [m2/s]Cp = heat capacity [J/kg-K]T = temperature [K]m = viscosity [kg/m-s}p = pressure [Pa]Acell = area of the cell [m2]MWO2 = molecular weight of oxygen [kg/kmol]Vcell = volume of cell [m3]Xi = mole fraction of species i [�]K1

1= geometric constant [�]

K2 = constant depends on temperature [mol/m2-s]li = thermal conductivity of species i [W/m-K]

ACKNOWLEDGEMENTS

The financial support of KFUPM under the KFUPM-MITcollaboration program during the course of this work is

greatly appreciated. The support and collaboration ofMIT mechanical engineering department are also appreci-ated. The authors also wish to acknowledge the supportreceived from King Abdul-Aziz City for Science andTechnology through the Science and Technology Unitat King Fahd University of Petroleum and Minerals(KFUPM) for funding this work through Project No. 09-ENE755- 04 as part of National Science, Technologyand Innovation plan.

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Numerical investigation of combustion characteristics in an oxygen transport reactor

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