Fuel 89 (2010) 3650–3661

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A comprehensive mathematical model for biomass gasification in a bubblingfluidized bed reactor

Priyanka Kaushal, Jalal Abedi *, Nader MahinpeyDepartment of Chemical and Petroleum Engineering, University of Calgary, 2500 University Dr. NW, Calgary, Alberta, Canada T2N 1N4

a r t i c l e i n f o a b s t r a c t

Article history:Received 29 January 2010Received in revised form 20 July 2010Accepted 21 July 2010Available online 4 August 2010

Keywords:Chemical processGasificationFluidizationKineticsMathematical model

0016-2361/$ - see front matter � 2010 Elsevier Ltd. Adoi:10.1016/j.fuel.2010.07.036

* Corresponding author. Tel.: +1 403 2205594; fax:E-mail address: jabedi@ucalgary.ca (J. Abedi).

A mathematical model of biomass gasification in bubbling fluidized gasifier has been developed. It is aone-dimensional, two-phase (bubble and emulsion), two-zone (bottom dense bed and upper freeboard),steady state model. The model is based on global reaction kinetic, mass and energy balances and is capa-ble of predicting temperature, solid hold ups and gas concentration along the reactor’s major axis. Theoverall model has sub-models to deal with biomass pyrolysis, gasification, bed hydrodynamics, materialclassification and property calculation. A sub-model for tar generation and cracking is included in thisstudy. The model is capable of dealing with wide variety of biomasses and fluidizing agents, i.e. air, oxy-gen, steam or a mix of these gases. Results show that during devolatilization step, gases release and mix-ing are sensitive and critical parameters. They have a strong influence on the overall performance of agasifier. A comparison with experimental data from numerous literature works was done, which showedfairly good agreement. The model can be used to study and optimize the operation of bubbling fluidizedbed gasifier. However, further validation with diverse data will help to fine-tune the model.

� 2010 Elsevier Ltd. All rights reserved.

1. Introduction

Bioenergy is expected to become one of the major energy re-sources in the future because biomass is renewable and free fromnet CO2 emissions. It is also the only sustainable source of organiccarbon [1]. Using biomass as a fuel offers certain advantages, interms of energy, environment, society and economy. Gasificationis one of the most important areas in the research, developmentand demonstration (RD&D) of the biomass-to-energy framework.

Gasification is a promising green route for conversion of bio-mass materials to useful Product gas that can be utilized in poly-generartion or in production of value added chemicals (VACs).Gasification of biomass in fluidized bed has certain benefits: it iseasy to scale up, it gives near isothermal condition inside bedand it gives easy controllability of the process. However, fluidizedbeds are not economical for small scale application. Mathematicalmodels are helpful for designing, for predicting gasifier behaviorand studying effect of operating parameter on gasifier perfor-mance, startup, shutdown etc. Literature focusing on coal particleand coal gasification is in plenty [2–8]. However modeling workbased on biomass fired fluidized bed are limited. Though coal gas-ification information is often exploited to model biomass gasifica-tion, there are some basic differences between coal and biomass.Biomass is more reactive: it pyrolyzes fast, has more volatile and

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+1 403 2824852.

moisture, has less energy density, has little ash and sulfur content.These differences call for a robust and detailed model for biomassgasification; however, detailed and advanced models for bubblingfluidized bed gasification are scarce [9–12].

The objective of this study was the development of a compre-hensive one-dimensional steady state model for a bubbling fluid-ized bed biomass gasification-unit. Biomass gasification below1000 �C always produces important amounts of tar whose pres-ence in the product gas has to be estimated with a good model.It is a common assumption to consider devolatilization to beinstantaneous because they are much faster than the gasificationprocess. However there are few gasification models where devola-tilization step is modeled with a rate limiting step [13–14]. In thisstudy, a simplified semi-kinetic approach was used to model thedevolatilization step. The devolatilization sub-model not only pre-dicts the volatile yield but also its composition. The model is capa-ble of predicting the concentration and distribution of gas speciesand tar along the height of the gasifier, the overall composition,heating value, production rate of the product gas, and the averagetemperature in the bed.

2. Biomass gasification process

There exist a number of methods for utilizing biomass potential.A promising alternative to extract energy out of solid fuel is gasifi-cation, as gases have fundamental advantages over solid fuels[15–17]. Gasification is a high-temperature partial oxidation

Abbreviations

A area (cross-sectional area) [m2]Ar Archimedes number [-]a decay constant [m�1]C concentration [mol/m3]Cp heat capacity [J/molK]CW coefficient [–]D diameter of Column [m]D molecular diffusivity [m2/s]Dia diameter [m]d diameter [m]E Activation energy [j/mol]f volume fraction of char [m3/m3]DG standard state Gibbs Free energy [j/mol]g gravity [m/s2]H height [m]Hj enthalpy of the species ‘j’ [j/mol]

DH0f ;298 enthalpy of formation at 298.15 K [j/mol]

hm mass transfer coefficient [kg/barm2s]k mass transfer coefficient [m/s]K equilibrium constant [–]k cell number [–]k reaction rate constant [dependent]k0 frequency factor [dependent]M molecular weight [kg/mol]m mass [kg]_m mass flow rate [kg/s]

N number [–]n amount of substance [mol]P pressure [Pa]p partial pressure [Pa]Q volumetric flow rate [m3/s]_Q heat flow [j/s]q rate based on external surface [kg/m2s]R universal gas constant [j/molK]Re Reynolds number [–]r rate of reaction [mol/m3s]S surface area [m2]

Sh Sherwood Number [–]T temperature [K]t time [s]U velocity [m/s]Umf minimum fluidization velocity [m/s]V volume [m3]VM volatile matter [wt/wt]w weight fraction [wt/wt]x distance [m]Y correction factor [–]y mole fraction [–]z height [m]

Greekd fraction [–]e porosity [–]/ij viscosity coefficient [–]l viscosity [Pas]q density [kg/m3]m atomic diffusion volume [–]1 single isolated [–]1 above Transport Disengaging height [–]c stoichiometric coefficient [–]

IndicesB bubblebed bed Materialc carbonE emulsioneqlm equilibriumg gasj speciemax maximummf minimum fluidizationp particlet terminal

P. Kaushal et al. / Fuel 89 (2010) 3650–3661 3651

process of a carbonaceous feedstock using a gasifying agent, suchas steam, oxygen, air or a mixture of these gases. Gasification pro-duces a gas mixture (a mixture of hydrogen, carbon monoxide, car-bon dioxide, methane and small hydrocarbons) that is commonlyknown as product gas. Irrespective of the reactor configuration, itis believed that gasification occurs in the sequential steps of dry-ing, devolatilization and gasification. There are no sharp bound-aries between the steps, and these boundaries often overlap.Though both coal and biomass are carbonaceous feedstock, how-ever biomass (especially wood) has more volatile. Table 1 givesan overview of this process. It is clear from the table that devolatil-ization is the most important step during gasification, as it takesrelatively less time and releases almost 80–90% of the mass asgas [18,19]. Unlike pyrolysis, during gasification the emphasis isto maximizing the yield of gas. Therefore during gasification theprocess/operating parameters are optimized to favors the releaseof volatile present in the biomass. The progress in modeling bio-mass gasification and pyrolysis has recently been reviewed [20].

Table 1Overview of gasification steps.[59,87] *Depends on moisture present in feed (wood).

Gasification step Reaction time(seconds) Mass released

Drying 140–220 0.1–0.5*Devolatilization 250–660 0.78–0.9Gasification t>3000 0.1–0.2

3. Model development

The objective of this modeling was to couple the kinetics of dry-ing, devolatilization, gasification and the reactor hydrodynamic, inorder to study the performance of a fluidized bed gasifier. The

whole gasification process is divided into three sub-models: kinet-ics, hydrodynamics and streams (material classification and prop-erties). These sub-models are further divided into classes (shownin Fig. 1) in order to have a realistic approach toward the overallgasification process. Out of various regimes of fluidization, thisstudy focuses on bubbling regime. The Kinetic sub-model has sep-arate subroutines to take care of drying, devolatilization and gasi-fication. The streams that flow in and out of control volume aredescribed in material sub-model (as solid liquid or gas). The vari-ous thermodynamic properties of these streams are calculated inthis sub-model. It can be seen in the Fig. 1 that the informationcan flow both ways among the sub-models. The boundary of theinvestigated system is shown in Fig. 2. Bed geometry, temperature,pressure, composition and flow rate of the incoming streams arethe inputs of the model. It is assumed that the cyclone instanta-neously separates the gas from the solids and no reaction takesplace in the cyclone.

Biom

ass

Feed

Gasifying agent

blow down

Product gas

Addi

tiona

l stre

am(if

any

)

Dense bed

Free

boar

d

Fig. 2. Modeling boundary for the gasification process.

Main

Drying Devolatilization Gasification

Dense Freeboard

Solid, Liquid, Gas

Bubbling

Kinetic Sub-Model

Hyd

ro d

ynam

icSu

b-M

odel

Material Sub-Model

Results

Hid

den

laye

rs

Fig. 1. Simplified structure of model.

3652 P. Kaushal et al. / Fuel 89 (2010) 3650–3661

3.1. Hydrodynamic sub-model

As explained above, this model deals with the bubbling regimeof fluidization. The bubbling bed is divided into two-zones, i.e.dense and freeboard (Fig. 2). Each of these zones is divided intocells where the local variables (hydrodynamic, kinetic and thermo-dynamic) are evaluated. Cells are solved sequentially with the out-put of the Nth cell considered as the input for the (N + 1)th cell. Allhydrodynamic parameters are based on the properties of the bedmaterial. For simplification, an average particle diameter is used.

3.1.1. Dense zoneThe description of the expansion of a bubbling fluidized bed is

derived from the two-phase theory of fluidization by Tommeyand Johnstone [21]. However, in Original Two-Phase Theory(OTPT), the amount of gas flowing through the bed as bubbles isoverestimated. Modifications have been made to account for the

Table 2Flow assumed in various version of two-phase theory [24].

Theory VFB IFB

1 Two-phase ðU � Umf ÞA 02 Total deficit GB 03 Through flow GB Umf dBA4 n–type GB Umf ð1þ nÞdBA

VFB, visible flow in bubble phase; IFB, invisible flow in bubble phase (through flow); TF

overestimation [22–23]. According to the interpretation adoptedby different studies, it is clear that the fraction of the total flowin the dense phase can vary considerably (Table 2). The range ofthe emulsion phase flow is between 14% and 59% of the total gasflow. In this study, the bottom dense zone is modeled accordingto the modified two-phase theory [24]. The mathematical repre-sentation for the visible bubble flow rate is estimated as

QB ¼ YðU0 � Umf ÞA ð1Þ

A correction factor ‘‘Y ” is introduced to cap the amount of gasflowing into bubble phase. Y is always below unity and usuallyin the range from 0.7 to 0.8. In case of OTPT, most of the gas passor slip through the reactor un-reacted as bubbles where as theemulsion phase, which is rich in solid (i.e. reactive biomass), hasgas deficiency. Hence the modified division of gas flow betweenphases is more favorable for gas–solid reactions. Bubbles and theirbehavior play a major role in gas–solid fluidization. Bubbles areresponsible for features that differentiate the fixed bed from thefluidized bed. They modify the gas flow in the system and causeparticle movement, which results in rapid and extensive particlemixing. One crucial factors that affect the velocity of the bubbleare the viscosity of the gas and the size and density of the solid par-ticles (both these parameters also affect the minimum fluidizationvelocity). The higher the minimum fluidization velocity, the lowerwill be the velocity of the rising bubble. Accordingly, the findingsof Davidson and Harrison [25] were adapted. The following equa-tion has been used to calculate the rising velocity of the bubbles:

UB ¼ UB;1 þ ðUo � Umf Þ ð2Þ

UB;1 is the rise velocity of a single isolated bubble of radius rB [26].Based on the two-phase theory, a significant part of the gas flows inthe bubble phase. Thus, the inter-phase mass transfer between thebubble and emulsion phases is essential for the gas–solid reactions(Fig. 3). A number of correlations can be found for inter-phase masstransfer [27–29]. However, in this model the interchange (masstransfer) coefficient kB,E (Eq. (3)), is based on the surface area

� 1VB

dNj;B

dt¼ �UB

dCj;B

dx¼ SB;E

VBkB;EðCj;B � Cj;EÞ ð3Þ

Table 3 lists the equations used for the hydrodynamic calcula-tion and are detailed elsewhere [30].

3.1.2. Freeboard zoneA plug flow model is assumed for the flow of gas through the

freeboard zone; and, although the freeboard zone is assumed tobe free of solids, the catalytic activities of the char and bed materialare considered for calculating the gas phase reaction kinetics [31].

3.2. Kinetic sub-model (process modeling)

Gasification involves the breakdown of large and heavy mole-cules of hydrocarbons into lighter ones. The process is a series ofsteps, as shown in Fig. 4. For this modeling study, drying, devolatil-ization and gasification are the three steps/processes considered. Itis assumed that these processes take place sequentially.

TFB FDP TF

ðU � Umf ÞA Umf A UAGB UA� GB UAGB þ Umf dBA AðU � Umf dBÞ � GB UAAðU � Umf ð1� dBÞÞ AðUmf ð1� dBÞÞ UA

B, total flow in bubble phase; FDP, flow in dense phase; TF, total flow.

Cracking, reforming

100-200oC

200-500oC

500-950oC

Steam

1

2 2

4 2

2

Fig. 4. Simplified representation of gasification steps.

EMU

LSIO

N

BUBB

LE

Mass Exchange

z

z+Δz

Δz

Gas in bubble phase

Gas in emulsion phase

Gas out bubble phase

Gas out emulsion phase

Fig. 3. Mass exchange between the bubble and emulsion phases.

P. Kaushal et al. / Fuel 89 (2010) 3650–3661 3653

3.2.1. DryingTypically, the moisture content of freshly cut wood ranges from

30% to 60%. However, most gasification systems use dry biomasswith moisture contents of 10–20%, in order to generate a highheating value product gas. In this study, a simplified approach isformulated to model drying. It is assumed that the loosely boundwater (moisture) present in the biomass irreversibly and instanta-neously changes its phase from liquid to gas at a temperatureabove 100 �C, as in Eq. (4)

wm _mBiojLiquid ¼ wm _mBiojGas ð4Þ

3.2.2. DevolatilizationDevolatilization is an extremely complex phenomenon due to

the large number of chemical and physical transformationoccurring rapidly and simultaneously. In general, when thedried fuel is heated in the range of 200–500 �C in absence ofoxygen (or any other oxidizing agent), it decomposes into solidchar and volatiles (condensable hydrocarbon or tar and gases).This process is called devolatilization. The relative yields ofgas and solid depend mostly on the heating-rate and the aver-age temperature. The devolatilization product then reacts withthe gasifying medium (air, oxygen or steam) to produce carbonmonoxide (CO), carbon dioxide (CO2), hydrogen (H2) and lighterhydrocarbons.

Table 3List of primary equations used in hydrodynamic model.

Name Expression

Correction factor for modified two-phase theory Y ¼ 0:26þ0:7 expð�0:0½0:15þðU�Umf Þ �

Bubble diameter dB ¼ 0:54ðU � Um

Maximum bubble diameter dB;max ¼ 2U2t

g

Velocity of single bubble UB;1 ¼ 0:71ffiffiffiffiffiffiffiffigdB

pBubble fraction dB ¼

YðU0�Umf ÞUB

Mass transfer coefficient KBE ¼Umf

4 þffiffiffiffiffiffiffiffiffi4emf D

pdB

qMinimum fluidization velocity Umf ¼

lg

qg dpðffiffiffiffiffiffiffiffiffi27:2

pPorosity at minimum fluidization emf ¼ 0:478Ar�0:01

Archimedes number Ar ¼ d3pqg ðqp�qg Þg

l2g

Terminal velocityUt ¼

ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi43 ð

qp�qg

qgÞ dp g

Cw

r

Diffusivity DA;B ¼ 1:43T

pffiffiffiffiffiffiffiMA;B

p Pvð

�Viscosity

lm ¼Pn

j¼1yjljPn

i¼1yi/

With respect to coal, thermal treatment of biomass is a recentdevelopment. Though biomass differs from coal, analogies fromcoal are often drawn for better understanding of biomass gasifica-tion process. The coal-devolatilization models available in litera-ture focus on the amount of volatile release (kg/s) and are basedon: kinetic approach with Arrhenius terms, particle size, massand heat transfer, etc. [32–37].

However not much is said about the approaches to calculate thecomposition (yj) of the volatiles released [38–41]. Majority of theapproaches are based on the fuel analysis and assumption that vol-atile is made up of C, H, O, N, S and HC species and the final volatilehas CO, CO2, NO, SO2, H2, H2O and light or heavy HC (if any). Suchapproach is good for preliminary guess but is not recommended formodeling processes, especially when the model is predictive innature. Although a lot of effort has been made to model devolatil-ization step, majority of the gasification-models have their ownpitfalls. For e.g. a major drawback of these model was to assumethat devolatilization was instantaneous and producer gas was freeof tar [42–44]. Gómez-Barea and Leckner has recently reviewed theexisting models with their strength and weaknesses [45]. The tarfraction in the product-gas exiting a gasification-unit is lower thenthe product-gas exiting from a pyrolysis-unit. However, it is not toforget that, production of primary tar, Tar1 (Fig. 4) is measurable;however gasifiers are designed to promote tar cracking andreforming reactions. High temperature, high residence time, cata-lyst-bed, an oxidizing agent, etc. are to promote cracking andreforming reactions. Therefore tar fraction T2 (Fig. 4) is lower inthe final product gas.

033dpÞ0:33 ðzþ 4

ffiffiffiffiffiffiA

Nor

qÞ0:4

f Þ0:4ðzþ 4ffiffiffiffiffiffiA

Nor

qÞ0:8g�0:2

ffiffiffiffiffiUB

ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi2 þ 0:0408Ar � 27:2Þ8; 177 < Ar < 4030

ffiCw ¼

24RT ; Ret < 1 24

Re þ 4ffiffiffiffiffiffiRet

p þ 0:4; 1 < Ret < 30000:43; Ret > 3000n

;

1:75�10�7

Þ1=3

AþP

vð Þ1=3

B

�2

ji; /ji ¼

1þ lj=lið Þ1=2Mi=Mjð Þ1=4

� �2

8ð1þMj=MiÞ½ �1=2

kk+1

e

di

p

ght (

or c

ells

of d

ense

zon

e)

3654 P. Kaushal et al. / Fuel 89 (2010) 3650–3661

The devolatilization step of the biomass is a source of highuncertainty. Nevertheless unlike the popular ‘instantaneous devol-atilization’ assumption, in this study a simplified semi-kinetic ap-proach is used to model devolatilization process. This study dealswith bubbling fluidized bed gasification i.e. small particle size, hightemperature, near isothermal condition. At high temperature,small particle devolatilization is independent of heating-rate.Therefore Arrhenius type kinetic model is used to define devolatil-ized-gas composition.

Global decomposition of the wood is coupled to the ultimateand proximate analysis of the biomass feed to calculate the yieldand composition of the devolatilization product. The three compet-ing reactions that represent the devolatilization step are shown inFig. 5. The char produced post-devolatilization is a model parame-ter. However, by default, it takes the value of fixed carbon(proximate analysis). The sum of Tar1 and gases is equal to the vol-atile matter (proximate analysis). Additionally it is also assumed:that the entire hydrogen and oxygen content of the biomass is re-leased during the devolatilization process, and the volatile matterreleased, Eq. (5), is a mixture of CO, CO2, H2, water (H2O),methane(CH4) and primary tar (Tar1).

VM ¼ wCOCOþwCO2 CO2 þwH2 H2 þwH2OH2OþwCH4 CH4

þwTar1 Tar1 ð5Þ

The composition of devolatilized-gas is estimated from the rateequations as shown in Eqs. (7 and 8). The kinetic constant for therates are reported in Table 4 and are valid for temperature rangeof 200 �C < T < 950 �C.

wCO : wCO2 : wH2 : wH2O : wCH4 : wtar1 ¼ rCO : rCO2 : rH2 : rH2O

: rCH4 : rtar1 ð6Þ

rj

rjþ1¼ kjexp

�EjRT

� �

kjþ1exp�Ejþ1

RT

� � ð7Þ

While modeling gasification, another popular simplification isto assume devolatilization as instantaneous [45–51]. Consideringthe fact that devolatilization is much faster than gasification itseems correct from first principle. The gas released during devola-tilization has to mix with the other up-flowing gas stream (e.g. gas-ifying agent and the gas released from char gasification). However,if all the devolatilized-gas is mixed at one point it will affect theequilibrium and bed hydrodynamics and hence will influence thefinal gas composition. Gas mixing, is a sensitive parameter and is

wood

Gas

Tar1

Char

Volatile matter

Fixed carbon

Fig. 5. Simplified model for volatilization.

Table 4Kinetics of primary devolatilization [88,89].

Component kj (1/s) Ej (kj/mol)

CO 9.00 � 1009 111.0CO2 5.23 � 1009 105.0H2 4.73 � 1004 92.5H2O 3.68 � 1013 149.5CH4 1.09 � 1005 71.3Tar1 2.09 � 1010 112.7

a challenge for a 1 D model. Unlike coal, devolatilization of biomasshas a strong influence on the overall gasification process becausethe volatile fraction in biomass is approximately 6–7 times morethan coal. Therefore in this study the steam and gas released dur-ing drying and devolatilization are not added instantaneously tothe gas stream. They are added in a predefined pattern along theheight of the gasifier, as shown in Fig. 6. The profile gas distributionis to deal with the mixing problem of gas. By default equal distri-bution of gas along the height of the gasifier is assumed. Becauseof the high devolatilization rates, the gasifying agent can not reachthe particle surface, since gas diffusion to the particle is muchslower [52]. Therefore a progressive conversion model (PCM) isimplemented for the drying and devolatilization of the solid bio-mass. In PCM, it is assumed that the diameter of the particle staysconstant, whereas the density decreases, as in Eq. (8).

Dqbio ¼Dmbio

Vð8Þ

3.2.3. GasificationChar, is the product of the preliminary drying and devolatiliza-

tion step. Char is often modeled as carbon. However, hydrogen andoxygen fractions in char are reported [53]. This is because charcomposition is strongly dependent on the devolatilization step.Char gasification too is a complex process due to the combinationof different mechanisms like mass transfer, chemical reaction andheat transfer. The net carbon (char) after devolatilization is in-volved in a number of heterogeneous gasification reactions, aslisted in Table 5. Data reveals that with 10% addition of raw woodash in the gasifier, at temperature of 800 �C, the reactivity of woodhas increased nearly 6 times [54,55]. Hence the catalytic activity of

Qgas

Hei

Fig. 6. Gas mixing profile along the height. i: increasing; d: decreasing; e: equal; p:1st increases then decreases.

Table 5List of gasification reaction present in model.

Name Reaction Reaction rate

Heterogeneous:Steam C þ H2O! COþ H2 [90]Dry C þ CO2 ! 2CO [58]Hydro C þ 2H2 ! CH4 [91]Oxygen ð1þ bÞC þ ð1þ b=2ÞO2 ! bCOþ CO2 [92]HomogeneousShift COþ H2O$ CO2 þ H2 [31]General COþ 1=2O2 $ CO2 [93]General CH4 þ 3=2O2 $ COþ 2H2 [93]General 2H2 þ O2 $ 2H2O [93]Reforming CH4 þ H2O$ COþ 3H2 [94]

Table 6Relative yield of tar cracking product [63].

Species (j) cj Species (j) cj

CO 0.78 � 0.72222 CH4 0.78 � 0.11334CO2 0.78 � 0.14222 Tar1 �1.00000H2 0.78 � 0.02222 Tar2 0.22 x g

P. Kaushal et al. / Fuel 89 (2010) 3650–3661 3655

the ash which plays an important role in steam assisted char con-version is considered.

The Boudouard reaction or dry gasification has been studiedextensively, as the products do not enter into side reactions. How-ever, the activation energy for this reaction is strongly influencedby the type of carbon [56–57]. The methane formation by hydro-gasification is important, especially for air and oxygen gasification,because the energy content of the synthesis gas is increased due tothe presence of methane. The oxygen necessary for gasification isalso reduced because of the heat released in methane formation.The heterogeneous reaction kinetics parameters for different bio-mass feeds have been listed by Barrio and Hustard [58]. Chenand Gunkel studied the effect of char particle size and temperature,on gasification [59]. They found that, with fine particle at high tem-perature, the particle temperature (on surface and inside) is con-stant. So isothermal condition within the char particle is a fairassumption, however if the particle size is more than 10–40 mm,isothermal-particle is a false assumption. They also report thatfor bulk temperature up to 1000 K reaction kinetics control thereaction, but at higher bulk temperature gas diffusion can not beneglected. Based on their finding the char gasification is modeledin this study. It is assumed that, during gasification, the gasifyingagent from the bulk gas stream is transported to the char surface,where it reacts heterogeneously with the carbon in a thin layerwithout any ash formation. The gasification rate, in terms of masstransfer through the gas film, is described as:

q ¼ hmðpg � psÞ ð9Þ

hm ¼McShDg

dcharRTmð10Þ

where pg and ps are the partial pressure of gasifying agent in bulkgas and char surface respectively. hm is the mass transfer coeffi-cient. Dg is the molecular diffusivity of gasifying agent throughthe gas film. dp is the instantaneous diameter of the char particle.Tm is the average gas film temperature. The chemical reaction rateof char with gasifying agent per unit time per unit external surfacearea of the particle is:

q ¼ kchar;spns ð11Þ

Above equations, Eqs. (9 and 11) were solved under steady stateassumption i.e.

q ¼ kchar;spns ¼ hmðpg � psÞ ð12Þ

For the cases, where gasification reaction is first order, Eq. (12),was solved analytically

q ¼ 11

hmþ 1

kchar

pg ð13Þ

For other cases where n–1; Eq. (12), was solved numerically toestimate the value of ps. Also, the temperature dependency of therate constant was given by Arrhenius expression. Experimentaldata were fitted to the Arrhenius expression via minimization ofroot-of-mean-square-deviation method and the constants (k0 andE) were estimated [60]:

kchar;s ¼ k0 expð�EapRTpÞ ð14Þ

At any given time, char undergoes four heterogeneous gasifica-tion reactions simultaneously (Table 5). Therefore Eq. (15), is thesum of char gasified due to steam, carbon di oxide, hydrogen andoxygen as gasifying agents. Each of these four char gasificationreaction is modeled as per Eqs. (9–12).

qnet ¼ qst þ qdry þ qhydro þ qoxy ð15Þ

Char conversion is modeled as shrinking particle model where itis assumed that the diameter of the char particle decreases, whilethe density of the char remains constant. In this work the shrink-age is simply assumed to be mass-proportional [61]

r ¼ 34

mchar

pqchar

1=3

ð16Þ

The homogeneous reactions (gas or vapor phase reactions only)are modeled as non-elementary (global) reaction where the rateexpression follows a power law expression in the concentrations,Eq. (17)

dCj

dt¼ rj ¼ k½Cj�n ð17Þ

The pre-exponential factor and the activation energy for each ofthe reactions have to be supplied as inputs to the model. Forreversible reactions, the rate of the reverse reaction is calculatedusing thermodynamic data [62].

Keqlm ¼kfor

kbackð18Þ

Keqlm ¼ expð�DG0

RTÞ ð19Þ

The primary tar (Tar1) that was produced during the devolatil-ization step undergoes cracking in the gasification step to producea mixture of non-condensable gases and light hydrocarbons. Eq.(20) represents the tar cracking step. The coefficients c for Eq.(20) are reported in Table 6.

tar ! cCOCOðgÞ þ cCO2CO2ðgÞ þ cCH4

CH4ðgÞ þ cH2H2ðgÞ

þ ctarinerttarinert ð20Þ

For the tar cracking rate (kg/kg/s), the kinetic model by Borosonand Howard [63] was used.

rjcrack¼ cjð10Þ4:98Expð�93:37 RT= ÞðwtarqgÞ ð21Þ

where wtarqg is the amount of tar in gas phase. From Table 6, it isevident that only 78% of the primary tar is cracked, and the rest(22%) remains unchanged. However, studies show that operatingparameters, such as fluidizing agent, temperature, residence time,certain bed materials, and additives have catalytic effect on tarcracking [64]. Tar yield as low as 6% has been reported [65]. Hence,to deal with this situation, a correction factor, g, is introduced, thevalue of which is 0:5 6 g 6 1: The remaining yield, in such a case, isloaded on H2 and CO2 [66].

3.3. Balances

A model is a mathematical representation of a process. The pri-mary purpose of modeling is to understand some existing processand to describe the concept mathematically. The elemental massbalances inside each cell are checked by the stoichiometry of thehomogeneous and heterogeneous reaction formulations. The glo-bal balance, Eq. (22) for char is applied across each zone.

_mcharin� ð _mcharout þ _mcharreact Þ ¼ 0 ð22Þ

750

800

850

par

atu

re (

C)

Measured Model (a)

3656 P. Kaushal et al. / Fuel 89 (2010) 3650–3661

_mCharreact ¼XN

i¼1

dmcharidt=

� �ð23Þ

where dmCharidt= is the amount of char reacted (or gasified) in the

control volume and is linked to the char fraction in the bed or zone.The char fraction in the zone is iterated until the global mass bal-ance, Eq. (24) is satisfied.

X_min ¼

X_mout ð24Þ

The energy conservation equation is solved across the entire zone,and it is assumed that, within a zone, the temperature is uniform.This assumption is based on efficient solid mixing and the domi-nance of the solid’s heat capacity within a fluidized bed. The overall

START

Read input file

Iterate height of dense bed

Provide height of

dense bed

Average temparature

Fraction of char in zone

Data transfer to next cell

Drying

Devolatilization

Gas mixing

Is ΔP over bed provided?

Yes

No

Thermo dynamic

Bedhydrodynamic

Reaction kinetics

Last cell ?

Mass balance ?

Energy balance ?

Yes

Yes

Yes

No

No

No

Write output file

STOP

Iterate char fraction

IterateTemperature

Local cell

calculation

Elemental balance

Last Zone ? No Data transfer to next zoneYes

Fig. 7. Model algorithm for the dense zone (bottom bed).

enthalpy balance across a zone delivers the average temperature ofthe zone. The simplified energy balance equation is:

_Qadd þXN

j¼1

njHjðTÞ��

In¼ _Q loss þ

XN

j¼1

njHjðTÞ��Out

ð25Þ

15

20

25

30

35

40

15 20 25 30 35 40

Experimental (Vol%)

Pre

dic

ted

(Vo

l%)

CO

T5

T2

T3

T4

T6T7

T8

T1

T9

(e)

15

20

25

30

35

40

15 20 25 30 35 40

Pre

dic

ted

(Vo

l%)

CO2 T5T2

T3

T4T6

T7

T8

T1

T9

(d)

15

20

25

30

35

40

15 20 25 30 35 40

Pre

dic

ted

(Vo

l%) H2

T5

T2

T3T4T6

T7T

T1

T9(c)

0

5

10

15

20

25

0 5 10 15 20 25

Pre

dic

ted

(Vo

l%)

CH4

(b)

650

700

700 Test Run

Tem

T1 T2 T3 T4 T5 T6 T7 T8 T9

Fig. 8. Comparison of model predictions with the measured data of Campoy et al.[73].

Table 7Model input, data extracted from tables in reference [73].

Model input

Bed Diameter 0.15 m Fuel Wood PelletsFreeboard Diameter 0.25 m Fuel Flow Rate 10–21.6 kg/hFreeboard Height 2.15 m Gasification Agent Air + Oxygen + SteamBed Material Ofite [67] Operation Temperature 755–840 �C

Operational condition Test run

T1 T2 T3 T4 T5 T6 T7 T8 T9

Biomass feed (kg/hr) 11.5 12.2 12.2 15 15 12.4 10 16.2 12.0Air (Nm3/hr) 17 17 17 17 17 11.9 9.1 10.6 7.7Oxygen (Nm3/hr) 0 0 0 0 0 1.5 1.2 1.4 1.0Steam (Nm3/hr) 0 2.5 5.1 3.2 6 3.7 5.6 4.7 6.5

P. Kaushal et al. / Fuel 89 (2010) 3650–3661 3657

HjðTÞ ¼ DH0f ;298;j þ

Z T

298:15KCP;jðTÞ � dT ð26Þ

The enthalpy of the gas mixtures and the solid bed material are cal-culated using the 4th-order NASA polynomials [67] and data re-ported by Barin [68], respectively. Fig. 7 gives an overview of themodel algorithm for the bottom dense bed. For freeboard, whichis nothing but a plug flow reactor a global energy balance similarto Eq. (25) is applied to get an average temperature of the zone.

4. Results and discussion

There are some extensive models that exist today [9,69–72], butit is difficult to check their robustness. Most of them are very spe-cific and are formulated to study a particular case. It is hard to gen-eralize these models, because most of the key information or datarequired are not published. An effort has been made here to vali-date this model with as diverse data as possible. Fig. 8 is basedon the study of Campoy et al. [73]. They used wood pallets withempirical formula CH1.4O0.64 (dry, ash free basis). The moistureand ash content were 6.3% and 0.5% (wt basis). The test rig is de-tailed elsewhere [74]. The operating mode for all the tests in thepilot-scale FBG was auto-thermal and adiabatic. Also, the temper-ature of the gasification agent was fixed at 400 �C for all tests. Themode of operation they used for conducting the tests, for wood

15

20

25

30

35

40

45

Pre

dic

ted

(V

ol %

)

0

2

4

6

8

10

12

14

16

Pre

dic

ted

(V

ol %

)

Predicted Measured

CO CO2 H2 CH4

(sec

on

dar

y ax

is)

Fig. 9. Effect of different gas-mixing patterns on the gas composition for test run T1of Table 7.

pellets, consisted of four variables that could be independently var-ied: the flow rates of biomass, air, steam and oxygen. The flowrates of air and oxygen determined the oxygen content in the en-riched air. The experimental program comprised tests with air–oxygen–steam mixtures in different proportions i.e. to tests vary-ing stoichiometric ratio (SR), steam-to-biomass ratio (SBR), andthe oxygen percentage of the enriched air (OP). For their study,they varied SR, SBR and OP (between the indicated ranges: SR from0.24 to 0.38, SBR from 0 to 0.63 and OP from 21% to 40%) to explorethe effects of these variables on the quality and composition of theproduced gas. Table 7 lists the key operating parameters for Fig. 8.The details of the model inputs and operating parameters can befound elsewhere [75–76]. It can be seen in Fig. 8 that the modelpredictions are in good agreement with the measured values: allthe predictions are within ±5% of the measured value. During eachof the test runs, many of the operating parameters (stoichiometricratio, steam-to-biomass ratio, temperature, etc.) were changed.Therefore, it is not easy to find the exact cause for the observedchange in gas composition among the test runs. However, theauthors [73] have tried to give a detailed explanation.

In Fig. 8, both model predictions and measured data show thatthe percentage of hydrogen varied widely (19–35%), while themethane fraction in the produced gas was almost constant

0

10

20

30

40

50

60

70

700 750 800 850 900

Temperature (ºC)

Vo

lum

e %

Schuster et al. [77]

Model prediction

H2

CO

CO2

CH4

Low Temperature High Temperature

CO CO2

H2 CH4

Fig. 10. Comparison of model prediction for steam as the gasifying medium..

Table 8Model input parameters (*: 15% of total carbon present in biomass).

Column: Minimum Dia. 0.67 mTotal Height 6 mPressure drop (gasifier) 0.15 barBed material quartz sandChar Carbon*Fuel composition: (by weight)

C 48.26 Ultimate analysisH 05.82O 45.67Volatile 80 Proximate analysisMoisture 25

Temperature:Biomass 20 CSteam 400 C

Heat loss 5% (of input)Steam flow rate 500 kg/hrBiomass flow rate 2900 kg/hr

Table 9Model input parameters [79].

Internal Dia. 6 cmOperating temperature 800 �CBiomass throughput 260 kg/hr m2

Moisture in feed 2 5%Bed particle size 400 micronHeight of dense bed 20 cmBiomass feed rate 9 g/minBio feed (dry basis) Saw dust C4O2.7 H5.8 N0.02

Gas velocity 19 (�2Umf) cm/sGasifying agent AirBed material Silica sand

0

5

10

15

20

25

700 720 740 760

Tempe

Tar y

ield

(g/N

m3)

Experimental dat

Model

close fit of the experimental data

Fig. 11. Comparison of predicted

3658 P. Kaushal et al. / Fuel 89 (2010) 3650–3661

(9–11%). This suggests that hydrogen production was sensitive tothe fluidizing medium and its ratio to biomass fed while methaneis relatively insensitive to these parameters.

The reason to have small variation in methane percentage couldpossibly be: (a) the main source of methane in the product gas isvia devolatilization, which is primarily a function of temperature,and is practically independent of gasifying medium; (b) also as gas-ification is nothing put partial oxidation in under-stoichiometriccondition the reactive species, H2 and CO, react with the most ofthe gasifying agent. Another observation made during this studyis that the model was sensitive to the gas-mixing pattern. Fig. 9shows the predicted gas composition for the same operating con-ditions (T1 of Table 7), but with the different mixing patterns de-fined in Fig. 6. It can be seen that the difference between thepredicted and measured compositions was more than 10%. There-fore, proper selection of the mixing pattern is very important, in or-der to get close to practical experiences.

All the typical fluidizing/gasifying agents normally used for gas-ification were studied and are presented in Fig. 8.

Steam, as the only gasifying agent, is presented in Fig. 10.Schuster et al. [77] developed a Dual Fluidized Bed (DFB) modelfor the steam gasification of biomass. It is an allothermal unit. Un-like auto-thermal gasifier where a part of the biomass is com-busted inside the gasifier to generate heat in situ, in allothermalunit heat is transferred to the gasifier to sustain the endothermicgasification reactions. In DFB unit, heat is generated by combustingthe spent char, exiting the gasifier, in a separate fluidized bed com-bustor. Circulating bed material acts as a heat bridge between thetwo fluidized beds. The details of the DFB gasifier could be found inreference [78]. Separating the biomass gasification from char-com-bustion has an added advantage of generating clean and high

780 800 820 840

rature (ºC)

a [79]

tar yield to measured value..

P. Kaushal et al. / Fuel 89 (2010) 3650–3661 3659

heating value product gas. However modeling a circulating bed iscomplex. The gasifier is in bubbling regime, where as the combus-tor is in fast fluidization regime. Fast fluidized DFB combustionmodel is provided elsewhere [30]. The combustor and the gasifiermodels are linked to generate the result. Table 8 provides the mod-el parameter. The effect of average bed temperature on gas compo-sition is simulated in Fig. 10. Similar trends were observed in bothstudies. With the increase in the average temperature of the bed,the production of CO and H2 were increased, while CO2 and CH4

were decreased [79–81]. It can be seen in the Fig. 10 that thechange in concentration, in comparison to higher temperature, ismore prominent in the lower temperature range (700 �C <T < 800 �C). It brings to notice that at high temperature char-gasifi-cation rate is no longer controlled by surface reaction kinetics [59].Similar trends were observed in both studies. At an enhanced level,the differences at individual points are indispensable. The possiblereason may arise from the fact that tar formation was not consid-ered and equilibrium was assumed to be the dominant mode intheir model [77]. These could be the possible reasons for the min-imal production of methane in their study as well. However thereare no measured data to validate either of these simulation results.

While modeling a gasification process, it is common to neglecttar [82–83]; however, incorporating the formation of tar is anessential step towards commercialization of the process [84].Narvaez et al. carried out experiments in a small scale bubblingfluidized bed gasifier [79]. They used special tar and gas samplingdevice to measure tar and gas amount and composition. Their re-ported data were used to check the model’s tar handling feature.Input data are reported in Table 9. However additional details likeexperimental set ups and operating parameters could be found inthe literature [79]. In this study, tar was handled explicitly as aseparate subroutine (or object). In Fig. 11, the effect of temperatureon the tar yield is plotted. In accordance with popular observation,the tar yield decreased with the increase in the average tempera-ture of the gasifier [85–86]. This may arise from the facts that tarcracking is favored by high temperature and increased residencetime (due to the added height of the freeboard zone). Measureddata for this particular case are also shown in Fig. 11.

As seen in Fig. 11, for a temperature of approximately 800 �C,three values of tar yield were observed for the same operating con-ditions. This is because of the fact that the model predicts the aver-age value while the point from where the gas sample is collectedand analyzed is the local value. It also suggests that, in additionto the axial gradient, there is a strong radial gradient. This supportsthe above-mentioned claim that the gas mixing is a sensitiveparameter and has a strong influence on the overall performanceof the gasifier. Also, instantaneous gas release and mixing is nota fair assumption to model devolatilization step of gasification.

5. Conclusions

The presented gasification model is a one-dimensional, steadystate, two-phase model which allows mass transfer betweenphases. The model developed is robust and considers all thekey parameters for a bubbling fluidized bed gasifier. The bottomdense bed is modeled in accordance with the modified two-phase theory. The gasifier freeboard is assumed to be free of so-lid, however the catalytic activity of fine char particle on gasphase reactions were considered in freeboard. In the model, thechar-gasification rate was controlled by a mixed resistance ofreaction kinetics and bulk gas diffusion. Heterogeneous reactionswere assumed to take place on char surface and shrinking parti-cle model (SPM) was formulated to model the solid particles.During devolatilization around 80% of mass is released and is avery critical step. Unlike, common assumption devolatilization

step was not modeled as instantaneous and tar free. A partly ki-netic, partly mass balance scheme was adapted to model thestep. Tar, released during devolatilization, was represented by acombination of model compounds. The mass and energy balanceswere performed to get solid hold ups and average temperature,respectively.

Reactor geometry, mass flow rate, composition and tempera-ture of incoming streams were the model inputs. The model iscapable of predicting the bed temperature, tar yield, product gascomposition, heating value and production rate. To check therobustness of the model, an effort was made to validate this modelwith as diverse data as possible. The model had shown good qual-itative and quantitative agreement with other bubbling bed gasifi-cation models. A preliminary validation with some experimentaldata from the literature was conducted. Results show that themodel is capable of dealing with air, oxygen, steam or a mix ofthese gases as the gasifying medium.

The model performance could have been improved, if more de-tailed design and experimental data were available. Efforts are inprogress to generate data in-house for the purpose of additionalmodeling studies with parameter variation.

Acknowledgements

The financial support of the Alberta Agricultural Research Insti-tute (AARI), Institute for Sustainable Energy Environment andEconomy (ISEEE) and Natural Sciences and Engineering ResearchCouncil of Canada (NSERC) are acknowledged.

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