two phase biomass air-steam gasification model for fluidized bed reactors_ part i—model...

Biomass and Bioenergy 22 (2002) 439–462

Two phase biomass air-steam gasi�cation model for !uidizedbed reactors: Part I—model development

Samy S. Sadakaa ; ∗, A.E. Ghalyb, M.A. Sabbahc

aAgricultural and Biosystems Engineering Department, Iowa State University, NSRIC, Ames, IA, 50011, USAbBiological Engineering Department, Dalhousie University, Halifax, NS, Canada, B3J.2X4

cDesert Development Center, American University - Cairo, Cairo, Egypt

Received 29 April 1999; received in revised form 26 November 2001; accepted 16 January 2002

Abstract

A two-phase model capable of predicting the performance of !uidized bed biomass air-steam gasi�cation reactor duringdynamic and steady state operations was developed based on the two phase theory of !uidization. Material and energybalances were taken into consideration and the minimization of free energy technique was used to calculate the gas molefractions. The !uidized bed was divided into three zones (jetting, bubbling and slugging) and the mass and heat transfercoe8cients were calculated for each zone in both bubble and emulsion phases. The model includes the hydrodynamics,transport and thermodynamic properties of !uidized bed. The �nite element method was used to solve the partial di9erentialequations. The input variables of the computer program included !uidization velocity, steam !ow rate and biomass to steamratio. The model is capable of predicting the bed temperature, gas mole fractions, higher heating value and productionrate. ? 2002 Elsevier Science Ltd. All rights reserved.

Keywords: Fluidization velocity; Air-steam; Gasi�cation; Higher heating value; Model; Straw

1. Introduction

During the period 1991–1996, the world crop yields of sorghum, corn, rye, rice and wheat increased by20.1%, 19.5%, 30.1%, 8.7% and 4.6%, respectively. Crop production will continue to increase to feed theever-increasing population of the world. The current world production of cereals is about 2:0 × 109 metrictones [1]. This means that about 2:34 × 109 ton of straw are produced annually for which the market isbecoming rather limited [2]. Ghaly et al. [3] reported that wheat crop alone yields over 750 million ton ofstraw of which 60–80% can be utilized for energy through energy conversion processes such as pyrolysis,combustion and gasi�cation. Gasi�cation is the process by which organic matter is converted to gas, tar andchar through thermal decomposition in a low oxygen environment, followed by secondary reactions of theresulting volatiles [4]. The produced combustible char and tar can be burned with air to provide the necessaryenergy for processing [5].

∗ Corresponding author. Tel.: +00-1-515-294-4330; fax: +00-1-515-294-4250.E-mail address: [email protected] (S.S. Sadaka).

0961-9534/02/$ - see front matter ? 2002 Elsevier Science Ltd. All rights reserved.PII: S 0961 -9534(02)00023 -5

440 S.S. Sadaka et al. / Biomass and Bioenergy 22 (2002) 439–462

Nomenclature� is a weighting coe8cient lying between 0 and 1, Z = iZ; t = kt� is the volume fraction of the emulsion phase (dimensionless) is the void fraction in the bed at minimum !uidization (dimensionless) is the weight of straw in the reactor (kg)�b is the binary mixture density (kg m−3)�b is the volume fraction of the bubble phase (dimensionless)�c is the sand density (kg m−3)�cr is the char density (kg m−3)�e is the volume fraction of the emulsion phase (dimensionless)Kf0i is the heat of formation of species i at 25◦C (kJ kmol−1)�g is the density of the gas (kg m−3)KGfi0 is the free energy of formation of compound i at temperature T (kJ kg−1)KH is the enthalpy of gas (kJ kmol−1)KH is the sensible heat of gaseous components in the bubbles (kJ kmol−1)KHie is the sensible heat of gaseous components in the emulsion (kJ kmol−1)KH 0

rj is the heat of reaction j at 25◦C (kJ kmole−1)KHrl is the heat of reaction (1) at reference temperature (298:15 K) (kJ kmol−1)�ib is the gas density in the bubble phase (kg m−3)�j is the jet gas density (kg m−3)�k is the reaction latent energy (kJ kg−1)(kje)j is the volume interchange coe8cient (m3 m−3(jet) s−1)mf is the bed voidage at minimum !uidization conditions (dimensionless)�s is the density of sand particles (kg m−3)KZ is the increment in axial direction (m)� is the viscosity of the gas (kg m−1 s−1)�i is the viscosity (N s m−2)A is the bed cross sectional area (m2)a1-f1 are constants (dimensionless)aik is the number of atoms of kth element present in each molecule of chemical species

(dimensionless)Ar is Archimedes number (dimensionless)Cbiomass is the weight of carbon in the straw (kg)Cib is the concentration of ith species in the bubble phase (kmol m−3)Cie is the concentration of ith species in the emulsion phase kmol m−3)Cij is the concentration of ith species in the jet region (kmol m−3)Ci0 is the initial and inlet concentration of species i (kmol m−3)Cis is the concentration of ith species in the slugging region (kmol m−3)Cpb is the speci�c heat of the gas mixture in bubble phase (kJ kmol K−1)Cpe is the speci�c heat of the gas mixture in emulsion phase (kJ kmol K−1)Cpg is the mean heat capacity of the gas mixture (kJ kmol−1K−1)Cpg; j is the heat capacity of the jet (kJ kmol−1 K−1)Cpj; i is the heat capacity of gas i (kJ kmol−1 K−1)

S.S. Sadaka et al. / Biomass and Bioenergy 22 (2002) 439–462 441

Cps is the particle’s speci�c heat (kJ kg−1 K−1)Cs is the concentration of the char (kg char kg inter solids−1)d� is the nozzle diameter (m)db is the diameter of the binary mixture (m)dbm is the maximum bubble diameter (m)db0 is the initial bubble diameter (m)dc is the diameter of alumina sand (m)dcr is the diameter of char (m)Dg is the gas di9usivity (m2 s−1)Dib is the dispersion coe8cient of the ith species in the bubble phase (m2 s−1)Die is the dispersion coe8cient of the ith species in the emulsion phase (m2 s−1)Dij is the dispersion coe8cient of the ith species in the jet (m2 s−1)Dis is the dispersion coe8cient of the ith species in the slugging phase (m2 s−1)dp is the bubble diameter (m)dp is the mean particle diameter (m)dpi is the mean diameter of particles related to the ith sieve in a sieve analysis (m)dt is the bed diameter (m)F is the global force vectorg is the acceleration of gravity, 9:807 (m s−2)H is the bed height (m)Hbe is the heat interchange coe8cient between bubbles and emulsion (kJ m−3 s−1 K−1)HHV is the higher heating value of the gas (kJ m−3)hi is the internal heat transfer coe8cient (kJ m−2 s−1 K−1)hj is the heat transfer coe8cient between jet and emulsion phase (kJ m−2 s−1 K−1)h0 is the external heat transfer coe8cient (kJ m−2 s−1 K−1)hp is the heat transfer coe8cient (kJ m−2 s−1 K−1)(Hbc)b is the heat interchange coe8cient between bubble and cloud (kJ m−3 s−1 K−1)(Hbc)s is the heat interchange coe8cient between slug and cloud (kJ m−3 s−1 K−1)(Hbe)b is the heat interchange coe8cient between bubble and emulsion (kJ m−3 s−1 K−1)(Hbe)s is the heat interchange coe8cient between slug and emulsion (kJ m−3 s−1 K−1)(Hce)b is the heat interchange coe8cient between cloud and emulsion (kJ m−3 s−1 K−1)(Hce)s is the heat interchange coe8cient between cloud and emulsion (kJ m−3 s−1 K−1)(Hje)j is the heat interchange coe8cient (kJ m−3(jet) s−1 K−1)K is the global sti8ness matrixKbe is the volume interchange coe8cient between bubble and emulsion (m3 m−3(bubble) s−1)kg is the thermal conductivity of the gas mixture (kJ m−1 s−1 K−1)Kgi is the gas thermal conductivity (MW m−1 K−1)kj is the mass transfer coe8cient between jet and emulsion phase (kg m−2 s−1)Kje is the gas interchange coe8cient between jet and emulsion phases (s−1)Kse is the gas interchange coe8cient between the slugs and emulsion phase (s−1)Lj is the jet penetration depth (m)Lsb is the height at which transition from bubbling to slugging occurs (m)lsb is the height at which transition from bubbling to slugging occurs (m)m is the bed material mass (kg)


Mg; j is the average molecular weight of the jet (kg kmol−1)n is the sieve number (dimensionless)nC is the number of moles of carbon in straw (dimensionless)nCH4 is the number of moles of methane (dimensionless)nCO is the number of moles of CO (dimensionless)nCO2 is the number of moles of CO2 (dimensionless)nd is the number of nozzles (dimensionless)nH is the number of moles of hydrogen in straw (dimensionless)nH2 is the number of moles of hydrogen (dimensionless)nH2O is the number of moles of H2O (dimensionless)nN2 is the number of moles of N2 (dimensionless)nO is the number of moles of O2 in straw (dimensionless)nO2 is the number of moles of O2 (dimensionless)ntot is the total number of moles (dimensionless)Nu is Nusselt’s number (dimensionless)P is the component partial pressure (kPa)Pr is Prandetl’s number (dimensionless)R is the universal gas constant (8:314 kJ kmol−1 K−1)Re is Reynold’s number (dimensionless)ri is the internal radius of the bed (m)Rib is the rate of generation of ith species in the bubble phase (kmol m−3)Rie is the rate of generation of ith species in the emulsion phase (kmol s−1 m−3)Rij is the rate of generation of ith species in the jet (kmol m−3)ris is the rate of generation of ith species in the bubble phase (kg m−3 s−1)Ris is the rate of generation of ith species in the slugging region (kmol s−1 m−3)Rl is the rate of reaction (kmol s−1 m−1)r0 is the external radius of the bed (m)RR is the vector of residual equationsRs is the rate of generation of ith species in the bubble phase (kg s−1)Rs is the fraction of carbon in the biomass converted into char (dimensionless)t is the time (s)T is the temperature (K)TARy is the tar yield weight (%)Tb is the bubble temperature (K)Tgi is the inlet gas temperature (K)Ti0 is the initial and inlet temperature of species i (kmol m−3)Tr is the reference temperature (298:15 K)Ts is the initial bed temperature (K)Ts is the solid’s temperature (K)U is the inlet gas velocity (m s−1)U� is the jet nozzle velocity (m s−1)Ub is the rising velocity (m s−1)Uj is the jet rising velocity (m s−1)Umf is the minimum !uidization velocity of straw (m s−1)Us is the slugging rising velocity at (m s−1)


Vij is the stoichiometric coe8cient of species i in reaction j, positive for productW ′ is the particle’ s weight per control volume (kg m−3)Win is the rate of char inlet to the reactor (kg s−1)Wout is the rate of char exiting from reactor (kg s−1)xi is the weight fraction of particles retained on the ith sieve (dimensionless)yi is the mole fraction of component (number of moles of i=total number of moles)yi is the mole fraction of the gases (dimensionless)Z is the axial distance from the distributor (m)

Fluidized bed gasi�ers have been used for converting agricultural wastes into energy. The advantages of!uidized bed reactors include: good gas solids contact, excellent heat transfer characteristics, better temper-ature control, large heat storage capacity, good degree of turbulence and high volumetric capacity. Severalresearchers studied the e9ects of operating and design parameters on the performance of !uidized bed gasi-�ers theoretically [6–12]. The existing !uidized bed gasi�cation models can be classi�ed as thermodynamicmodels, !ow regime models and transient models. However, most of these gasi�cation models were reportedfor coal gasi�cation and those dealing with biomass gasi�cation did not include the hydrodynamic parameterswhich a9ect both the mass and heat interchange coe8cients between the bubble and emulsion phases [13].Howard et al. [14] applied gasi�cation modeling by focusing on the liquid production. In their model, theydid not include the hydrodynamics of the !uidized bed. Five kinetic parameters (water gas reaction, carbonoxidation reaction, methane formation reaction, water gas shift reaction and methanation reaction) involvingin developing the model were evaluated by �tting the model to the experimental data obtained. The modelpredicted the oil and did not predict the gas composition. Furthermore, the variations of the assumptions ofgasi�cation models are numerous and even contradicting. This makes the evaluation of these models very di8-cult with limited experimental data. Very few attempts were found in the literature to simulate a self-sustainedgasi�cation process and that includes the hydrodynamic, transport and thermodynamic properties.

2. Objectives

The aim of this study was to develop a comprehensive two-phase dynamic �nite element model capable ofdescribing the !uidized bed biomass gasi�cation phenomenon. The model must be capable of predicting thetemperature distribution in the vertical direction of the bed, the concentration and distribution of each speciesin the vertical direction of the bed in both the bubble and emulsion phases, the composition of the producedgas, the heating value of the produced gas and the produced gas production rate.

3. Model development

3.1. Discretization of the Fluidized bed gasi8er

The proposed gasi�cation dynamic model represents two stages: instantaneous devolatilization of straw andcombustion of the char at the bottom of the gasi�er and the gasi�cation in the !uidized bed. Thus, a two-phaserepresentation of the !uidized bed incorporates the phenomena of jetting, bubbling, slugging and dynamicmass and energy balances. Fig. 1 shows the !uidized bed domain divided into three regions: jet, bubbles andslugs. The following assumptions were made regarding to the gas !ow divisions and the !ow patterns of gas


Fig. 1. The !uidized bed gasi�er zones.

and solids:(a) the !uidized bed consists of a dilute phase (jets, bubbles and=or slugs) and an emulsion phase,(b) the emulsion phase is divided into an interstitial gas phase and a solid phase [15,16],(c) mass and heat exchange take place between the dilute phase and interstitial gas and between the interstitial

gas and the solids,(d) the !uidizing gas enters the bed through nozzles in a jet form. The jets degenerate into bubbles, which

rise through the bed and grow by coalescence with other bubbles to form slugs,(e) slugging occurs if the bubble diameter becomes larger than one third of the reactor diameter, (Slugging

occurs in improper !uidization [17])(f) the dilute gas and the interstitial gas are in plug !ow and the dilute gas is free of solids,(g) the gas behaves ideally, and(h) the produced gas consist of CO, CO2, H2, H2O, CH4 and N2.

3.2. Mass balance

A control volume (KV = AKZ) is �xed in space in the !uidized bed gasi�er as shown in Fig. 2.A mixture of i and other gases is !owing within the element (KV ). The species i may be producedby a chemical reaction at a rate R. A mass balance can, therefore, be written in the following


Fig. 2. A control volume in the !uidized bed.

equation:

rate of mass

accumulationof species i

=

net rateof massof species iby gas !ow

+

net rateof massof species iby dispersion

+

net rate of massexchange of speciesi between bubbleand emulsion

+

rate of massgenerationof species iby reaction

:

(1)

The rate of mass accumulation of species i (change of concentration) can be calculated in the controlvolume in the bubble phase as follows:

@�ib@t

AKZ: (2)

The input of species i by the gas !ow across the face at the axial distance Z can be described as follows:

A(�ibUb)Z |Z : (3)

The output of species i by the gas !ow across the face at the axial distance Z + KZ can be described asfollows:

A(�ibUb)Z |Z+KZ : (4)


The input of species i by dispersion across the face at the axial distance Z can be described as follows:(DibA

@�ib@Z

)∣∣∣∣Z: (5)

The output of species i by dispersion across the face at the axial distance Z + KZ can be described asfollows:(

DibA@�ib@Z

)∣∣∣∣Z+KZ

: (6)

The rate of gas interchange between bubble and emulsion phases can be described as follows:

Kbe(�ib − �ie)AKZ: (7)

The rate of production of species i by chemical reaction can be described as follows:

ribAKZ: (8)

By substituting each term (2)–(8) into Eq. (1), dividing by A. KZ and the number of moles=kg and thentaking the limits at Z → 0, the following equation can be obtained:

@Cib

@t= Dib

@2Cib

@Z2 − @@Z

(CibUb) + Kbe(Cib − Cie) + Rib: (9)

Fitzgerald [18] reported on his two-phase model of !uidization processes that a !uidized bed consists of acontinuous phase (emulsion phase) where particles are uniformly distributed in a supporting gas stream anda discontinuous phase (dilute phase) consisting of gases only (no particles) in the form of bubbles, channelsand slugs. Flow and density within the emulsion phase are independently of super�cial gas velocity.

Eq. (9) is valid for the three zones and can be rewritten for the jet region as follows:

@Cij

@t= Dij

@2Cij

@Z2 − @@Z

(CijUj) + Kje(Cij − Cie) + Rij: (10)

Similarly, the mass balance equation for the slugging region can be written as follows:

@Cis

@t= Dis

@2Cis

@Z2 − @@Z

(CisUs) + Kse(Cis − Cie) + Ris: (11)

The bubble and emulsion phases assumed to be separated according to the two-phase theory of !uidization.Therefore, the mass balance for the gas in the emulsion phase can be written as follows [8]:

@Cie

@t= Die

@2Cie

@Z2 − Ue

�e

@Cie

@Z+

�bKbe

�e(CibUb) + Kbe(Cib − Cie) + Rie: (12)

Eq. (12) has the same form in the jet, bubble and slugging regions. However, the only factor that changesin these three regions is the gas interchange coe8cient value Kje, Kbe and Kse in the jet, bubbling and sluggingregions, respectively.

By using the same technique, the mass balance equation for the char can be written as follows:

@Cs

@t=Win −Wout + Rs: (13)


3.2.1. The initial conditionsThe initial conditions are as follows:

Cij = Ci0

Cib = Ci0

Cis = Ci0

Cie = Ci0

Cs = 0

at t = 0 and 06Z6H: (14)

3.2.2. The boundary conditionsThe boundary conditions are as follows:

Cib − Dib@Cib

@Z= Ci0

Cie − Dib@Cie

@Z= Ci0

at Z = 0 and t¿ 0; (15)

Cib = Cij at Z = Lj and t � 0; (16)

Cis = Cib at Z = Lsb and t � 0; (17)

@Cib

@Z= 0

@Cie

@Z= 0

at Z = H and t � 0: (18)

The �ve species (CO2, CO, H2O, H2 and CH4) as well as the char were considered.

3.3. Energy balance

Energy balance was performed in the bubbling, emulsion and particle phases for each individual elementon the basis of material balance of the gas and solids.

3.3.1. The bubble phaseBy taking the same control volume (Fig. 2) with the, the energy balance equation in the bubble phase can

be written as follows [10]:

rate of heataccumulationin the bubblephase

=

heat input bygas !owin the bubblephase

−

heat outputby gas !owin the bubblephase

+

net heat exchangebetween thebubble and theemulsion

±

heat generatedby reactionsin the bubblephase

:(19)

The heat accumulation in bubble phase in the control volume can be described as follows.

AKZ7∑i=1

@(CibCpbTb)@t

: (20)


The heat input by gas !ow can be calculated as follows:

AUb

7∑i=1

Cib KH

∣∣∣∣∣Z

: (21)

The heat output by gas !ow can be calculated as follows:

AUb

7∑i=1

Cib KH

∣∣∣∣∣Z+KZ

: (22)

The heat exchange between bubbles and emulsion phases can be described as follows:

�AKZ(Hbe)(Te − Tb): (23)

The heat generated by chemical reaction can be characterized as follows:

�AKZ(Rl KHrl): (24)

The entire total energy balance in the bubble phase within the control volume can be written by substitutingeach term (20)–(24) in Eq. (19), dividing by AKZ and taking the limits at Z → 0 as follows:

@CibCpbTb

@t=

@@Z

7∑i=1

(UbCib KHib) + �Hbe(Te − Tb) + �Rl KHrl: (25)

3.3.2. The interstitial gas phaseThe same technique was used to describe the energy balance in the interstitial gas as follows: rate of heat

accumulationin emulsion phase

=

heat input

by gas !owin emulsion phase

−

heat output

by gas !owin emulsion phase

+

net heat exchangebetween bubble andemulsion incontrol volume

+

heat exchange

between solid and gasin emulsion phase

±

heat generated

by reactionsin emulsion phase

: (26)

The total energy balance in the control volume in the interstitial gas can be described by substituting eachterm in Eq. (26), dividing by AKZ and taking the limits at Z → 0 as follows:

@@t

(CieCpeTe) =@@Z

7∑i=1

(UeCie KHie) + (1 − �)(Hbe)(Tb − Te)

+ (1 − �)(1 − emf )as

(2kg

dp

)(Ts − Te) + (1 − �)

4∑i=1

Rl KH 0rl: (27)

3.3.3. The particle phaseThe temperature distribution of the solids in the !uidized bed was obtained by taking the energy balance

around the bed as follows: rate of heat

accumulationin particles

=

enthalpy

in bygases

−

enthalpy

out bygases

+

enthalpy in

by chemicalreaction

−

[heat lossto surroundings

]: (28)


Similarly, the energy balance of the particles can be written from Eq. (28) as follows:

@Ts

@t=

1W ′Cps

(@@Z

(Ub

7∑i=1

Cib KHib + Ue

7∑i=1

Cie KHie

)+ �Rl KH 0

rl

)

+(1 − �)4∑i=1

Rl KH 0rl −

(Ts − Te

1=20rihe + ln r0=ri=20r0l + 1=20r0h0

): (29)

3.3.4. The initial conditionsThe initial conditions are as follows:

Tj = Ti0

Tb = Ti0

Ts = Ti0

Tie = Ti0

at t = 0 and 06Z6H: (30)

3.3.5. Boundary conditionsThe boundary conditions are as follows:

Tj = Tgi

Te = Tgi

at Z = 0 and t¿ 0; (31)

Tb = Tj at Z = Lj and t � 0; (32)

Ts = Tb at Z = Lsb and t � 0; (33)

@Tb

@Z= 0

@Te

@Z= 0

at Z = H and t � 0: (34)

3.4. Tar formation

The chemical formula for tar is CHxOy. The parameters (x; y) are temperature and heating rate dependent.Instantaneous devolatilization of straw was visually observed by several researches in !uidized bed gasi�cation[12,19]. Ergudenler [20] found that extracting the tar increased the quality of the results in his model. Fromtar yield studies of wheat straw, Corella et al. [21] found that the best empirical equation for the tar yield isas follows:

TARy = 3598:0EXP−0:0029Ts : (35)

3.5. Fuel devolatilization

Devolatilization is a very complicated process and the distribution of products is particularly sensitive to therate of heating and the residence time in the reactor [22]. The products of pyrolysis are CO2, CO, H2O, H2 and


CH4. The simpli�cation of considering the reaction products to consist of only CO2, CO, H2O, H2 and CH4

has some experimental support from the pilot plant results [23,20,24]. The gases in their study did, however,contain some C2H2, C2H4, C2H6 and tar in addition to CH4, but considering these as CH4 did not changethe overall results. The simpli�ed product gas compositions can be used as a �rst approximation.

To estimate the composition of volatiles, 1 kg of straw releases (during devolatilization) atomic weights,nO, nH and nC of oxygen, hydrogen and carbon, respectively. Under the assumption that volatiles contain onlyCO2, CO, H2O, H2 and CH4, the elemental balances can be written as follows:

3.5.1. Oxygen balance

nCO + 2nCO2 + nH2O = nO: (36)

3.5.2. Carbon balance

nCO + 2nCO2 + nCH4 = nC: (37)

3.5.3. Hydrogen balance

2nH2O + 4nCH4 + 2nH2 = nH: (38)

The char is assumed to contain no hydrogen or oxygen, but only pure carbon. Thus, the following equationcan be written to describe the number of moles of carbon:

nC =Cbiomass(1 − Rs)

12: (39)

For simpli�cation, the following de�nition can be written for RCO and RCH:

RCO =nCO

nCO2

; (40)

RCH =nCH4

nH2

: (41)

Therefore, the number of moles resulting from the devolatilization of 1 kg straw could be determined.

3.6. Minimizing the free energy to calculate the gas compositions

The number of moles of CO2, CO, H2, H2O, CH4, O2 and char which enter into the system react togetherwhile the nitrogen was assumed to be an inert gas. The total number of moles, which enter the gasi�er fromthe straw volatiles and the gasifying agent, can be calculated as follows:

ntot = nCO2 + nCO + nH2O + nH2

+ nCH4 + nO2 + nN2 : (42)

Smith and Van ness [25] derived the following equation to minimize the free energy:

KG0� + RT ln (yiP) +

∑k

�kaik = 0: (43)


Eq. (43) represents a simultaneous set of N +W equations in which N represents the number of producedgas species while W represents the elemental balance equations. There are two reacting systems: the bubblephase (which is a single gas phase containing CO2, CO, H2O, CH4 and N2), the emulsion phase (whichallows the existence of solid carbon phase) and the gaseous phase with all six gas species present. Nitrogenis an inert gas and its reaction with O2 is neglected. The approach adapted by Bacon et al. [5] for solvingEq. (43) is �rst to linearize ln(yiP) by Taylor’s expansion followed by solving the linearized equations withsuccessive iteration. The solution can be written in the following linear form:

AX = B: (44)

4. Derivation of the model parameters

4.1. Fluidized bed hydrodynamics

4.1.1. Particle diameter and densityTo minimize the complexities resulting from the non-uniform particle size distribution in the bed, the

average particle diameter is used to represent all particles in the reactor and can be calculated as follows:

dp =1∑n

i xi=dpi: (45)

All the hydrodynamic parameters are based on the binary particle mixture of char particles and refractorymaterial. The mean diameter (db) and density (�b) of the particle mixture can be calculated using Eqs. (46)and (47), respectively:

dp =dcdcr(mc + mcr)dcmcr + dcrmc

(46)

and

�b =dcdcr(mc + mcr)

dcmcr=�cr + dcrmc=�c: (47)

4.1.2. Bed voidage at minimum =uidization velocityMinimum !uidization voidage (mf ) is assumed for the ring, into which some particles are pushed as they

enter the transitional segment from below and others fall back from above the bed surface. To predict theminimum !uidization voidage, the following equation by Abrahamssen and Geldart [26] was used:

mf = 0:4025 + 603:7dp: (48)

4.1.3. Minimum =uidization velocityThe minimum !uidization velocity (Umf ) is the minimum velocity at which the bed moves from the �xed

state to the !uidizing state. The Umf is a function of particle shape, size, density and !uidizing gas transportproperties. Several correlation’s have been developed for the estimation of Umf . To estimate the minimum!uidization velocity of straw at minimum !uidization conditions, the equation developed by Botterill andBessant [27] was used:

Umf =(

��gdp

)[√

(1135:7 + 0:0408Ar) − 33:7]: (49)


The Archimedes number was calculated as follows:

Ar =d3

p�g(�s − �g)g

�2 : (50)

4.1.4. Bubble velocityThe bubble velocity (Ub) can be calculated using the equation developed by Davidson and Harison [28]:

Ub = U − Umf + 0:711√

(gdb): (51)

Bed hydrodynamics are related to the bubble diameter in the bubbling region. It was assumed that bubblesare uniform in size at any cross section of the bed but grow by coalescence with other bubbles while risingthroughout the bed. Mori and Wen [29] proposed a semi-empirical correlation for bubble growth as follows:

dp = dbm − (dbm − dbo) exp(

0:3Zdt

): (52)

The terms dbm and dbo were calculated as follows:

dbm = 1:64[A(U − Umf )]0:4; (53)

dbo = 0:872(A(U − Umf )

nd

)0:4

: (54)

4.1.5. Slugging velocityThe bubble velocity in the slugging region and the slugging velocity in a continuously !uidized bed reactor

were calculated using the equation developed by Mori and Wen [29]:

Us = U − Umf + 0:35√

(gdb): (55)

4.1.6. Emulsion velocityThe emulsion phase gas velocity (Ue) was calculated as follows [28]:

Ue =Umf

(1 − �): (56)

The volume fraction of the bubble phase (�) was calculated as follows:

�=(U − Umf )

Ub: (57)

4.2. Jetting region

The gas discharge from the ori�ces of a gas distributor takes the form of a jet.

4.2.1. Jet heightThe correlation developed by Merry [30] gives reasonable predictions of jet penetration depth at high

temperature conditions. This correlation was used to predict the depth of the jetting zone and was written asfollows:

Lj

d�= 5:2

(�gd��sdp

)0:3(

1:3

(U 2�

d�g

)− 1

): (58)


4.2.2. Mass transfer coe>cient in jet zoneBehie et al. [31] proposed the following simple model to describe the mass transfer between the jet and

the emulsion phase:

(kje)j =4kj

d��j: (59)

4.2.3. Heat transfer coe>cient in jet zoneBehie et al. [32] simpli�ed the following correlation to describe the heat transfer coe8cient between the

jet and the emulsion phase:

(Hje)j =4hj

d�: (60)

4.3. Bubbling region

The bubbling region begins after the jet height until the bubble diameter becomes one third the bed diameter.

4.3.1. Mass transfer coe>cient in bubble zoneThe following empirical correlation was used to approximate the gas interchange coe8cient between the

bubble and the emulsion gas [33]:

(Kbe)b =0:11db

: (61)

4.3.2. Heat transfer coe>cient in bubble zoneThe following equations were used to predict the heat interchange coe8cient between the bubble and the

emulsion phases [34]:Between bubble and cloud:

(Hbc)b = 4:5(UmfCCpg

dp

)+

10:4(kgCCpg)0:5

d1:25b

: (62)

Between cloud and emulsion:

(Hce)b = 6:78(emf kgCCpgUb

d3b

)0:5

: (63)

Between bubble and emulsion:

1(Hbe)b

=1

(Hbc)b+

1(Hce)b

: (64)

4.4. Slugging region

4.4.1. Slugging heightThe slugging region is the region, which starts after the bubbles become one-third of the bed diameter.


4.4.2. Mass interchange coe>cient in slugging zoneThe gas interchange between the slug and the cloud-wake consists of additive bulk !ow and di9usion

transfer terms. Homeland and Davidson [35] gave the following expression for the gas interchange coe8cient:

(Kbc)s =1dtm

(Umf +

16emf I1 + emf

(Dg

0

)0:5( gdt

)0:25): (65)

The term m and I are calculated as follows:

m=H − Lb − Lj

dt− 0:495

(H − Lb − Lj

dt

)0:5

+ 0:061; (66)

I = 0:379(H − Lb − Lj

dt

)0:8625

: (67)

Ragraman and Potter [36] derived the following expression for the gas interchange coe8cient between thecloud-wake and emulsion phases and between slug and emulsion phases, respectively:

(Kce)s =1 − �TDdt�

(0:35emf (gdt)0:5 − Umf ); (68)

1(Kbe)s

=1

(Kbc)s+

1(Kce)s

: (69)

4.4.3. Heat interchange coe>cient in slugging zoneThe heat interchange coe8cient between slugging and emulsion phases can be calculated as follows [36]:

(Hbc)s =1dtm

(UmfCCpg +

16emf I1 + emf

(kgCCpg

0

)0:5( gdt

)0:5); (70)

(Hce)s =1 − �TDdt�

(0:35emf (gdt)0:5 − Umf )CCpg; (71)

1(Hbe)s

=1

(Hbc)s+

1(Hce)s

: (72)

4.5. Heat transfer between interstitial gas and solids

The resistance for mass transfer between the interstitial gas and the solid surface is included in the rate lawsfor the heterogeneous reaction, which are expressed in terms of concentrations. The heat transfer coe8cientcan be obtained from a correlation proposed by Ranz and Marshall [37] as follows:

Nu = 2:0 + a(Pr)b(Re)c: (73)

Nusselt, Prandtl and Reynold’s numbers can be calculated as follows:

Nu =hpdp

kg; (74)


Pr =hpdp

kg; (75)

Re =�dpUb

�: (76)

The overall heat transfer between particles and interstitial gas is calculated, by considering each particle tobe a sphere bathed in a stagnant !uid, as follows:

hp =2:0kg

dp: (77)

4.6. Transport and thermodynamic properties

4.6.1. Viscosity of gasesViscosity of reactor gases is polynomials in temperature and can be described by the following equation

[38]:

� = a1 + b1T + c1T 2 + d1T 3 + e1T 4 + f1T 5: (78)

The equation recommended by Toulkian et al. [39] for steam was used:

�H2O = [80:4 + 0:407(T − 273:15) × 10−7] 273¿T ¿ 973(K): (79)

4.6.2. Viscosity of the gas mixtureThe viscosity of the gas mixture can be calculated from the following equation:

�ij =7∑i=1

yi�i: (80)

4.6.3. Thermal conductivity of the gasesToulkian et al. [40] correlated the thermal conductivity as follows:

Kgi = a2 + b2T + c2T 2 + d2T 3: (81)

4.6.4. Thermal conductivity of gas mixtureThe thermal conductivity of the gas mixture can be calculated as follows:

Kij =7∑i=1

yiKgi : (82)

4.6.5. Heat capacityHeat capacity data are used to correct the free energy (G0f), the heat of formation (H 0f) and the enthalpy

of the gas mixture to the temperature of interest. In all calculations, gases or gas mixtures are assumed to beideal (the heat of mixing and the pressure e9ect on enthalpy are neglected). The Reference state is taken asthe element at a pressure of 1 atm and a temperature of 298 K. Thus, the mean heat capacity was de�ned by


the following formula given by Reid et al. [41]:

Cpj; i = a3 + b3T + c3T 2 + d3T 3: (83)

4.6.6. Heat capacity of the gas mixtureThe heat capacity of the gas mixture can be calculated as follows [41]:

Cpg =7∑i=1

yiCpg; i : (84)

4.6.7. Heat of formationThe gaseous heat of formation at 25◦C were taken from Reid and Prausnits [41]. The heat of reaction at

25◦C was calculated from the heat of formation as follows:

KH 0rj =

N∑i=1

Vi Kf0i : (85)

4.6.8. The higher heating valueThe higher heating value of the produced gas can be calculated as follows [41]:

HHV =7∑i=1

KHCi: (86)

5. Finite element approximation

The �nite element method is a numerical procedure for obtaining solutions to many of the physical prob-lems governed by di9erential or partial di9erential equations, which are encountered in engineering analyses.It has two characteristics that distinguish it from other numerical procedures: (a) it utilizes an integral for-mulation to generate a system of algebraic equations and (b) it uses continuous piecewise smooth functionsfor approximating the unknown quantities [42]. By approximating the time derivative of Cj(t), the followingnumerical representation at any interior node can be obtained [43]:

16

(Ck+1i+1 − Ck

i+1

Kt+ 4

Ck+1i − Ck

i

Kt+

Ck+1i−1 − Ck

i−1

Kt

)+ �

(�Ck+1i+1 − Ck+1

i−1

2KZ+ (1 − �)

Cki+1 − Ck

i−1

2KZ

)

−Di

(�Ck+1i+1 − 2Ck+1

i + Ck+1i−1

(KZ)2 + (1 − �)Cki+1 − 2Ck

i + Cki−1

(KZ)2

)+ Kbe(Ck

ib − Ckei) − Rl = 0: (87)

The set of equations is written symbolically as follows:

[RR] = [K][Y ] − [F] = [0]: (88)

The numerical solution of the model equations was carried out as follows:

5.1. Carbon dioxide

The �nite element approximation for the carbon dioxide equations were written as follows:


5.1.1. In the bubble phase

16

(C1bk+1

i+1 − C1bki+1

Kt+ 4

C1bk+1i − C1bki

Kt+

C1bk+1i−1 − C1bki−1

Kt

)

+�

(�C1bk+1

i+1 − C1bk+1i−1

2KZ+ (1 − �)

C1bki+1 − C1bki−1

2KZ

)

−Di

(�C1bk+1

i+1 − 2C1bk+1i + C1bk+1

i−1

(KZ)2 + (1 − �)C1bki+1 − 2C1bki + C1bki−1

(KZ)2

)

+Kbe(C1bkib − C1eki ) − Rl = 0: (89)

5.1.2. In the emulsion phase

16

(C1ek+1

i+1 − C1eki+1

Kt+ 4

C1ek+1i − C1eki

Kt+

C1ek+1i−1 − C1eki−1

Kt

)

+�

(�C1ek+1

i+1 − C1ek+1i−1

2KZ+ (1 − �)

C1eki+1 − C1eki−1

2KZ

)

−Di

(�C1ek+1

i+1 − 2C1ek+1i + C1ek+1

i−1

(KZ)2 + (1 − �)C1eki+1 − 2C1eki + C1eki−1

(KZ)2

)

+Kbe(C1bkib − C1eki ) − Rl = 0: (90)

5.2. Temperature equations

Also, the �nite element approximation for the temperature equations were written as follows:

5.2.1. Bubble temperatureThe �nite element approximation of the bubble temperature can be calculated as follows:

CibCpb

6

(Tbk+1

i+1 − Tbki+1

Kt+ 4

Tbk+1i − Tbki

Kt+

Tbk+1i−1 − Tbki−1

Kt

)

UbCibCpb

(�Tbk+1

i+1 − Tbk+1i−1

2KZ+ (1 − �)

Tbki+1 − Tbki−1

2KZ

)+ �Hbe(Tbkib − Teki ) + �RlKHrl: (91)

5.2.2. Emulsion temperatureThe �nite element approximation of the emulsion temperature can be calculated as follows:

CieCpe

6

(Tek+1

i+1 − Teki+1

Kt+ 4

Tek+1i − Teki

Kt+

Tek+1i−1 − Teki−1

Kt

)


=UeCieCpe

(�Tek+1

i+1 − Tek+1i−1

2KZ+ (1 − �)

Teki+1 − Teki−1

2KZ

)

+(1 − �)Hbe(Tbkib − Teki ) + (1 − �)(1 − emf )as

(2kg

dp

)

×(Tksi − Tk

i ) + (1 − �)4∑i=1

RlKHrl: (92)

5.2.3. Solid temperatureThe same technique was used to solve the partial di9erential equation of the solids temperature [19].

5.3. Stability

To be able to formulate stability criteria for the dynamic �nite element model and for the related equations,the following correlation was used [44]:

0:5Ub(KZ − UbKt)6D6 0:5(

KZ2

Kt

)− 0:5U 2

b Kt: (93)

The left-hand side inequality of this equation state that D must be non-negative. This observation was usedto de�ne an optimal grid system (a grid system which uses a layer thickness as large as possible withoutbecoming unstable). The increments in the vertical direction and in the time domain can be described by thefollowing equations:

KZ =4DUb

; (94)

Kt =2DU 2

b: (95)

These equations were used in the selection of time step and layer thickness for the model.

5.4. The computational algorithm

A dynamic computer simulation program was developed to simulate the performance of the biomass !uidizedbed gasi�er. The computer program is called Finite Element Analysis of Fluidized Bed Biomass Gasi�cation(FEAFBBG). The model consists of the main program and thirty subroutines. Calculations begin at the bottomof the !uidized bed where the gas and the biomass enters. The computational algorithm is summarized in the!ow chart given in Fig. 3. Fig. 4 shows the main program and the supporting subroutines. The computerprogram is written in FORTRAN 77 for the HP UNIEX interactive computer. A detailed description of theprogram and its organization is presented in Sadaka [19]. The program can be adapted to speci�c needs ofpotential users.

6. Discussion and conclusions

The model developed in this study is a two-phase model based on the two-phase theory of !uidization. Themass and energy balances were taken into consideration and the minimization of the free energy technique


Fig. 3. The computer simulation !ow chart.

was used to calculate the gas mole fractions at the devolatilization stage. The !uidized bed hydrodynamiccharacteristics and the gas thermodynamic properties were also taken into consideration. The !uidized bedwas divided into three zones: jetting, bubbling and slugging. The mass and heat transfer coe8cients werecalculated for each zone in both bubble and emulsion phases. The �nite element method was used to solve


Fig. 4. The computer program organization.

the partial di9erential equations. The input variables of the computer program included: !uidization velocity,steam !ow rate and biomass to steam ratio.

The !uidized bed gasi�er was divided into three zones (jet, bubbles and slug). Each zone was assumed tocontain solid free gas and an emulsion phase (gas mixed with solids) [18,28]. Slugs occurred in improper!uidization. It was incorporated into the model to give wide range of predictions for all !uidization conditions.

Chang et al. [7] and Bacon et al. [5] used char gasi�cation reactions to predict the gas compositions at theexit of the gasi�er. Such reactions cannot represent the biomass gasi�cation process due to its high volatilecontent (70–90%). Ergudenler et al. [17] and Buekens and Schoeters [13] visually observed the releaseof volatile matter almost instantaneously, as soon as the biomass is introduced to the gasi�er. Neglectingthe hydrodynamic properties of the !uidization phenomenon would, therefore, decrease the model e8ciencybecause the jet, bubble and slug heat and mass transfer coe8cients play very important roles in the gasi�cationresults. Also, the transport and thermodynamic properties of the gas and its composition vary from place toanother. Therefore, the advantage of dealing with the hydrodynamic, transport and thermodynamic propertiesis that the gas compositions can be predicted at a fairly good accuracy without the assumption that they areconstant throughout the bed. Although most of the conversion takes place in the dense bed, it is known thatchar conversion continues in the freeboard region as well [19].

Desrosiers [45] reported that, no hydrocarbon other than CH4 is thermodynamically stable under gasi�cationconditions. Although C2H2, C2H4, C2H6 and other higher hydrocarbons (oil and tar) are produced in thegasi�er, they are accepted as nonequilibrium products. Therefore, in this model, all the hydrocarbons wereconsidered as CH4.


The model developed in this study is unique in considering all the variables taking place in the !uidizedbed gasi�cation. It is capable of predicting the bed temperature, gas mole fractions, gas higher heating valueand gas production rate. The model comprehends the biomass gasi�cation in a self-sustainable system andemphasizes the hydrodynamic, transport and thermodynamic properties of the gases in both the bubble andemulsion phases. It is capable of predicting the gasi�er performance during dynamic operation as well as steadystate operation. Applying the minimization of free energy technique and using the �nite element method tosolve the partial di9erential equations gave reasonable and stable solutions.

References

[1] FAO. Yearbook production 1992. Food and Agriculture Organization, vol. 46. FAO Basic Data Unit Statistics Dvison, Rome, Italy,1997.

[2] Langille WH, Ghaly AE. Environmental impact of alternative utilization of cereal straw. ASAE paper no. 91-6008, Michigan,St. Joseph, 1991.

[3] Ghaly AE, Al-Taweel AM, Hamdullaphur F, Ugwe I. Physical and chemical properties of cereal straws as related to thermochemicalconversion. In: Hogan EN, editor. Proceeding of the Seventh Bioenergy R&D Seminar. Ottawa, Ont., 1989. p. 655–61.

[4] Deglise X, Magne P. Pyrolysis and industrial of charcoal. In: Hall DO, Overend RP, editors. Biomass regenerable energy, 1987.p. 221–35.

[5] Bacon DW, Downie J, Hsu JC, Peters JA. Modelling of !uidized bed wood gasi�ers. In: Overend RP, Milne TA, Mudge KL,editors. Fundamentals of thermochemical biomass conversion. London, UK: Elsevier Applied Science Publishers, 1985. p. 717–32.

[6] Sundaresan S, Amundson N. Studies in char gasi�cation-II: The Davidson–Harrison two phase model of !uidization ChemicalEngineering Science 1979;34:355–8.

[7] Chang CC, Fan LT, Walawender WP. Dynamic modelling of biomass gasi�cation in a !uidized bed. American Institute of ChemicalEngineers Journal 1980;214:80–90.

[8] Raman KP, Walawender WP, Fan LT, Chang CC. Mathematical model for !uid bed gasi�cation of biomass material. Applicationto feedlot manures. Industrial Engineering Chemical Process Design and Development 1981;20:686–92.

[9] van den Aarsen FG, Beenackers AA, van Swaaij WP. Modelling of a !uidized bed wood gasi�er. In: Ostergaard VK, Sorensen A,editors. Fluidization. New York: Engineering Foundation, 1986. p. 521–30.

[10] Ping-Chung R. Modelling a !uidized bed coal gasi�cation reactor. Unpublished Ph.D. thesis, North Carolina State University, NorthCarolina, 1987.

[11] Sett A, Bhattacharya SC. Mathematical modelling of a !uidized bed charcoal gasi�er. Applied Energy 1988;30:161–86.[12] Ergudenler A, Ghaly AE, Hamdullahpur F, Al-Taweel AM. Mathematical modeling of a !uidized bed gasi�er. Part I—model

development. Energy Source 1997;19:1065–84.[13] Buekens AG, Schoeters JG. Modelling of biomass gasi�cation. In: Overend RP, Milne TA, Mudge KL, editors. Fundamentals of

thermochemical biomass conversion. London, UK: Elsevier Applied Science Publishers, 1985. p. 619–89.[14] Howard JB, Stephens RH, Kosstrain H, Ahmed SM. Pilot scale conversion of mixed wastes to foul. Vol. I, project report To EPA,

W.W. Libertick, Project O8cer, 1979.[15] Grace JR, Clift R. On the two phase theory of !uidization. Chemical Engineering Science 1974;29:327–34.[16] Davidson JF, Harrison D, Darton RC, La Nauze RD. In: Lapidus L, Amundson NR, editors. Chemical reactor theory, a review.

New York: Prentice-Hall, 1979.[17] Rowe PN, MacGillivray HJ, Cheesman DJ. Gas discharge from an ori�ce into a gas !uidized bed. Transactions of the Institution

of Chemical Engineers 1979;57(3):194–9.[18] Fitzgerald TJ. Coarse particle systems. In: Davidson JF, Clift R, Harrison D, editors. Fluidization. New York: Academic Press, 1985.[19] Sadaka SS. Air steam gasi�cation of wheat straw in a !uidized bed reactor. Unpublished Thesis, Egypt, Alexandria University, 1994.[20] Ergudenler A. Gasi�cation of wheat straw in a dual-distributor type !uidized bed reactor. Unpublished Ph.D. thesis, Technical

University of Nova Scotia, NS, Canada, 1993.[21] Corella J, Herguido J, Gonzalez-Saiz J. Steam gasi�cation of Biomass in !uidized bed-e9ect of the type of feedstock. In: Ferrero GL,

Maniatis K, Buekens A, Bridgwater AV, editors. Pyrolysis and gasi�cations. London: Elsevier Applied Science, 1989. p. 618–23.[22] Milne T. Pyrolysis—The thermal behaviour of biomass below 600◦C. A survey of biomass gasi�cation, 1979; vol. II.

SERI=TR-33-239 [Chapter 5].[23] Black JW, Bircher KG, Chisholm KA. Fluidized bed gasi�cation of solid wastes and biomass—The C.I.L. program. Symposium on

Thermal Conversion of Solid Waste and Biomass. Washington, DC: American Chemical Society, 1979.[24] Mansary KG. Gasi�cation of rice husk in a !uidized bed reactor. Unpublished Ph.D. thesis, Dalhousie University, Nova Scotia,

Canada, 1998.[25] Smith JM, Van Ness HC. Introduction to chemical engineering thermodynamics. 3rd ed. New York: McGraw-Hill. 1976. p. 426.


[26] Abrahamsen AR, Geldart D. Behaviour of gas-!uidized beds of �ne powders part I. homogenous expansion. Powder Technology1980;26:35–42.

[27] Botterill JS, Bessant DJ. The !ow properties of !uidized solids. Powder Technology 1976;14:131–7.[28] Davidson JF, Harrison D. Fluidised particles. Cambridge: Cambridge University Press, 1963.[29] Mori S, Wen CY. Estimation of bubble diameter in gaseous !uidized beds. American Institute of Chemical Engineers Journal

1975;21(1):109–15.[30] Merry JM. Penetration of vertical jets into !uidized beds. American Institute of Chemical Engineers Journal 1975;21(3):507–10.[31] Behie LA, Bergougnou MA, Baker CG. Mass transfer from a grid jet in a large gas !uidized bed. In: Keairns DL, editor. Fluidization

technology, vol. I. Washington: Hemisphere Publishing Corporation, 1976. p. 261–78.[32] Behie LA, Bergougnou MA, Baker CG. Heat transfer from a grid jet in a large !uidized bed. Canadian Journal of Chemical

Engineers 1975;53(2):25–30.[33] Wen CY, Fan LT. Heterogeneous models. In: Albright LF, Maddox RN, McKetta JJ, editors. Models for !ow systems and chemicals

reactors. Chemical processing and engineering, vol. 3. New York: Marcel Dekker, Inc., 1975.[34] Kunii D, Levenspiel O. Fluidization Engineering. New York: Wiley, 1969.[35] Homeland S, Davidson JF. Chemical conversion in a slugging !uidized bed. Transactions of the Institution of Chemical Engineers,

46T 1968:190–203.[36] Ragraman J, Potter OE. Countercurrent backmixing model for slugging !uidized bed reactors. American Institute of Chemical

Engineers Journal 1978;24(4):698–704.[37] Ranz WE, Marshall WR. Evaporation from drops, Part II. Chemical Engineering Progress 1952;48(4):173–80.[38] Rohsnow MW, Hatenett JP. Handbook of heat transfer. New York: McGraw-Hill Book Company, 1973.[39] Toulkian YS, Saxena SC, Hestermans P. Thermophysical properties of matter, vol. II. Viscosity. New York: LFL=Plenum Press,

1970.[40] Toulkian YS, Liley YS, Saxena SC. Thermophysical properties of matter, vol. III. Thermal conductivity. New York: LFL=Plenum

Press, 1970.[41] Reid CR, Prausnits JM, Sherwood CK. The properties of gases and liquids. New York: McGraw-Hill, 1977.[42] Segeriland LJ. Applied �nite element analysis, 2nd ed. New York: Wiley, 1984.[43] Gray WG, Pinder GF. An analysis of the numerical solution of the transport equation. The American Geographical Union

1976;12(3):547–55.[44] Genuchten MT, Wierenga PJ. Simulation of one dimensional solute transfer in porous media. Agricultural Experiments Station.

Bulletin No. 628 1974; 1–40.[45] Desrosiers R. Thermodynamics of gas-char reactions. In: Reed TB, editor. Biomass gasi�cation—principles and technology. Park

Ridge, NJ: Noyes Data Corporation, 1981. p. 119–53.

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