Estimation of gas composition and char conversion in a fluidized bed biomass gasifier

Fuel 107 (2013) 419–431

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Fuel
journal homepage: www.elsevier.com/locate/fuel

Estimation of gas composition and char conversion in a fluidized bed
biomass gasifier
A. Gómez-Barea a,⇑, B. Leckner b
a
b

Bioenergy Group, Chemical and Environmental Engineering Department, Escuela Superior de Ingenieros, University of Seville, Camino de los Descubrimientos s/n, 41092 Seville, Spain
Department of Energy and Environment, Chalmers University of Technology, S-412 96 Göteborg, Sweden

h i g h l i g h t s
" The model predicts gas composition and carbon conversion in biomass FB gasifiers.
" Correction of equilibrium is applied to improve the estimation of the gas composition.
" Kinetics models are applied to predict char, tar and methane conversion.
" Fluid-dynamics, entrainment and attrition are accounted for the calculation of char conversion.
" The model has predictive capability in contrast to available pseudo-equilibrium models.

a r t i c l e

i n f o

Article history:
Received 14 August 2012
Received in revised form 17 September 2012
Accepted 27 September 2012

Available online 22 October 2012
Keywords:
Gasification
Fluidized-bed
Biomass
Model
Char

a b s t r a c t
A method is presented to predict the conversion of biomass in a fluidized bed gasifier. The model calculates the yields of CO, H2, CO2, N2, H2O, CH4, tar (represented by one single lump), and char, from fuel
properties, reactor geometry and some kinetic data. The equilibrium approach is taken as a frame for
the gas-phase calculation, corrected by kinetic models to estimate the deviation of the conversion processes from equilibrium. The yields of char, methane, and other gas species are estimated using devolatilization data from literature. The secondary conversion of methane and tar, as well as the approach to
equilibrium of the water–gas-shift reaction, are taken into account by simple kinetic models. Char conversion is calculated accounting for chemical reaction, attrition and elutriation. The model is compared
with measurements from a 100 kWth bubbling fluidized bed gasifier, operating with different gasification
agents. A sensitivity analysis is conducted to establish the applicability of the model and to underline its
advantages compared to existing quasi-equilibrium models.
Ó 2012 Elsevier Ltd. All rights reserved.

1. Introduction
Modeling and simulation of fluidized bed biomass gasifier (FBG)
is a complex task. Advanced models have been developed for bubbling [1–8] and circulating [9–11] FBG. These models usually require physical and kinetic input, which is difficult to estimate
and it is sometimes not available to industrial practitioners. Simple
and reliable tools to predict reactor performance with reasonable
input are needed to support design and optimization. Besides
purely empirical models only valid for specific units, more universal approaches presented up to date have been based on gas phase
equilibrium [12].
Equilibrium models (EM) have been widely used because they
are simple to apply and independent of gasifier design [13–15].
However, under practical operating conditions in biomass gasifica⇑ Corresponding author. Tel.: +34 95 4487223; fax: +34 95 4461775.
E-mail address: (A. Gómez-Barea).

0016-2361/$ - see front matter Ó 2012 Elsevier Ltd. All rights reserved.
/>
tion, they overestimate the yields of H2 and CO, underestimate the
yield of CO2, and predict a gas nearly free from CH4, tar, and char.
Despite these limitations, EM are widely used for preliminary estimation of gas composition in a process flowsheet. However, EM are
not accurate enough as tools for design, optimization, and scale-up
of FBG units.
Quasi-equilibrium models (QEM) [16–22] improve the accuracy
of the prediction of the gas composition. The foundation of the QE
approach was given by Gumz [16], who introduced the ‘‘quasiequilibrium temperature’’, an approach where the equilibrium of
the reactions is evaluated at a lower temperature than that of
the actual process. The concept was applied for the simulation of
a circulating FBG unit in the range of 740–910 °C [17] and for various pilot and commercial coal gasifiers [18]. The approach is still
applied, although the method is far from predictive.
Another type of QEM has been developed [14,20–22] for the
simulation of biomass and coal gasifiers. The essential idea of
this approach was to reduce the input amounts of carbon and


420

A. Gómez-Barea, B. Leckner / Fuel 107 (2013) 419–431

Nomenclature
A
a
cp
c
CkHlOm
dch

fWGSR
E
Fgp
Ff,daf
h, hf
k
K
Katt
Lb, Lfb
m
madd,b
mc,p
mc,b
mch,b
mch,b,crit
mT,b
M
k, l, m
n1, n2,m
p
Ql
R
Rg
rc,ch
rCþH2 O
rCþCO2
T
Th
t
u0

xi,j
Xtar
X CH4
Xch
xadd
xash,da
xch,d
xch,2
xch,3
xc,da
xtar,d
xCH4 ;d
xH2 O;f
xi,ga
wi,f
wc,b

pre-exponential factor, 1/s
decay coefficient, –
specific heat, J KÀ1 kgÀ1
gas concentration, mol mÀ3
tar component
average char particle diameter in the reactor, m
coefficient of approach to WSGR equilibrium, –
activation energy, kJ/mol
gas yield, molgp/kgfuel(daf)
flowrate of fuel, dry and ash-free (daf), kg/s
specific enthalpy and enthalpy of formation, J/kg,
kinetic coefficient, various units
equilibrium constant, –

attrition constant, –
bed and freeboard heights, m
mass, kg
mass of additive/inert in the reactor, kg
mass of carbon in a char particle, kg
mass of carbon in the reactor, kg
mass of char (carbon and fuel ash) in the reactor, kg
critical value of mass of char in the reactor, kg
mass of total inventory (additive and char) in the reactor, kg
molecular mass, kg kmolÀ1
atoms in equivalent tar, C, H and O, –
fragmentation coefficients in Eq. (29)
pressure, Pa
specific rate of heat loss, W/kgfuel(daf)
reaction rate, kmol mÀ3 sÀ1
universal constant of gases, J K molÀ1
overall reactivity of the char, sÀ1
intrinsic reactivity of carbon in char with H2O, sÀ1
intrinsic reactivity of carbon in char with CO2, sÀ1
temperature, K
Throughput, kg/(m2 h)
time, s
superficial gas velocity, m sÀ1
mass of compound i in stream j per kgfuel(daf), kg/kg
conversion of tar
conversion of methane
conversion of carbon in the char through the reactor
mass of additive fed to the reactor per kgfuel(daf), kg/kg
ash (non-carbon) in discharged ash (fly + bottom) per
kgfuel(daf), kg/kg

mass of char per kgfuel(daf) produced during fuel devolatilization, kg/kg
mass of char in the bottom ash discharge (stream 2) per
kgfuel(daf), kg/kg
mass of char in the bottom fly ash (stream 3) per
kgfuel(daf), kg/kg
mass of carbon in discharged ash (fly + bottom) per
kgfuel(daf), kg/kg
mass tar per kgfuel(daf) produced during fuel devolatilization, kg/kg
mass of methane per kgfuel(daf) produced during fuel
devolatilization, kg/kg
moisture (in fuel) per kgfuel(daf), kg/kg
mass of i (i=O2, H2O, N2) in the gasification agent per
kgfuel(daf), kg/kg
mass fraction of the i-component (i = C, H, O, N, ash,
m(iosture)) in the fuel, kg/kg
mass fraction of carbon in the reactor, kg/kg

hydrogen, fed to the control volume where the equilibrium is calculated. The underlying reason for the reduction of the C–H–O in-

wc,ch,b
wc,ch,d
wc,ch,2
wc,ch,3
wch,b,crit
yi

mass fraction of carbon in the char of the reactor, kg/kg
mass fraction of carbon in the char after devolatilization, kg/kg
mass fraction of carbon in the char of bottom ash discharge (stream 2), kg/kg
mass fraction of carbon in the char of fly ash (stream 3),

kg/kg
critical value of the char mass fraction in the reactor, kg/
kg
molar fractions of i in the produced gas, kmol/kmolgp

Greek symbols
r
coefficient in Eq. (29), –
s
residence time, s
s2
rate constant of bottom ash discharged, s
s3
rate constant of fly ash, s
sR
time constant of reaction (the inverse of reactivity of
char sR = 1/rc,char), s
u
coefficient in Eq. (29), –
Subscripts
0
standard conditions superficial (velocity)
2, 3
bottom discharge, fly ash
ash
ash
att
attrition
b
bed, reactor

C, H, O, N carbon, hydrogen, oxygen, nitrogen
c
carbon
daf
dry and ash-free
ch
char
coar
coarse particle fraction
crit
critical value
d
devolatilization
da
discharged ash
df
dry fuel
f
fuel,
fin
fine particle fraction
ga
gasification agent
gp
gas produced
i, j
indices
mf
minimum fluidization
k, l, m

atoms in equivalent (heavy) lumped tar
p
particle
R
reaction
T
total
tar
tar
Abbreviations
av
average
daf
based on dry and ash-free substance
CSTR
continuous stirred tank reactor
EM
equilibrium model
ER
fuel equivalence ratio, –
FBG
fluidized biomass gasification (gasifier)
LHV
lower heating value (lower), J kgÀ1
na
not available
QEM
quasi equilibrium model
RZ
reduction zone

SBR
steam to biomass ratio
SRMR
steam reforming of methane reaction
WGSR
water–gas-shift reaction

put is that, under practical operation conditions in a gasifier, the
conversion of tar, light hydrocarbons, especially methane, and char


421

A. Gómez-Barea, B. Leckner / Fuel 107 (2013) 419–431

are kinetically limited, and so they are controlled by non-equilibrium factors. The interaction between the main four species in
the bulk gas is determined by the rate of the water–gas-shift reaction (WGSR). This reaction can also be far from equilibrium,
although the existing QEM have assumed it to be in equilibrium.
In the following, the main aspects of these conversion processes
are discussed for biomass FBG:
 The methane generated during devolatilization and primary
conversion of gas and tar is very stable, and it is hardly affected
by secondary conversion without Ni-based (or similar) catalysts
at sufficiently high temperatures [22,23]. Then, in intermediatetemperature gasification systems, i.e. the typical situation in
FBG of biomass, the amount of methane in the exit stream of
the gasifier is roughly that formed by devolatilization of the fuel
[22,24].
 The attainment of equilibrium of WGSR has been analyzed in
various gasification systems [15,22,23,25–29]. The use of a synthetic catalyst allows the attainment of equilibrium above
750 °C [30]. However, such catalysts are rarely used as bed

material. Mineral catalysts (dolomite, calcite, magnetite, olivine, etc.) are conventional bed materials, but their catalytic
activity on WGSR (and also on tar reforming) is lower, and equilibrium is not generally attained at the usual temperature in
biomass FBG, i.e. below 900 °C, with sand or similar (bauxite,
alumina, ofite). The residence time of the gas also plays a substantial role, and this can differ between the units. Moreover,
the real contact time with a catalyst in a FBG is usually lower
than the residence time calculated using the superficial velocity
of the gas. The reason is that fluid-dynamic factors affect the
performance of FBG, such as poor contact of gas and solid
caused by the bypass of gas through the bubbles or the plumes
generated during devolatilization. These factors also affect other
reactions in the bed, for instance, hydrocarbon reforming.
 The conversion of char is the most decisive factor in FBG,
because the main loss of efficiency is due to unconverted carbon
in the ashes. The time for char conversion in an FBG is limited
by entrainment and extraction of solids (if applied). Then the
rate of char gasification has to be fast enough for the char to
be converted during practical operation, mainly by reactions
with H2O and CO2. The small amount of O2 added to the gasifier
combines more rapidly with volatiles than with char. It is concluded that to determine the extent of char conversion in an
FBG, all these processes have to be taken into account.
Due to the complications discussed, the QEM are usually applied together with experimental correlations obtained for the specific system under analysis [14,20,21]. Applied in this way, QEM
refine the estimation of the gas phase composition compared to
pure EM, but the prediction capability is limited. It was attempted
to overcome this inconvenience by developing a general method
for the estimation of the gas composition, based on three parameters: carbon conversion, methane yield during devolatilization, and
conversion of methane by steam reforming [22]. Gross recommendations were given [22] for the values of the three parameters
based on practical considerations: temperature, type of catalyst,
and gasification agent. The recommendations are useful for the
evaluation, for a given fuel, of the gas composition resulting from
various gasification methods (air vs. steam-oxygen, catalyzed vs.

non-catalyzed). However, the method is not generally useful to
analyze the performance of a given FBG under different operating
conditions, like the change of flowrates of biomass and gasification
agent, topology of the gasifier, etc. The reason is that the three
parameters are sensitive to the reactivity of fuel, gas velocity,
and temperature in the gasifier. Moreover, the distribution of the
main species in the gas, CO, H2, CO2, and H2O, is governed by the

rate of WGSR, a reaction which rarely attains equilibrium in biomass FBG.
The objective of the present work is to develop a model, taking
advantage of the simple framework of QEM, but expanding their
predictive capability. There are three requisites: (i) to allow estimation of gas composition and solid fuel (char) conversion; (ii)
to capture the effect of changes in operating conditions on the
FBG performance, including velocity of the gas and the main geometry of the reactor, and therefore, to be useful for design, optimization and scale-up; and (iii) to be simple enough for
implementation in flowsheet simulations, needing limited input,
obtained by reasonable effort. Below, the validity of such a model
compared to existing QEM is discussed, underlining the advantages
of the present development.

2. Model development
2.1. Model approach
The process is simplified by decoupling primary (devolatilization) and secondary conversion, considering the different rates of
these processes [31]. Volatiles and char are assumed to be well
mixed in the isothermal reactor. Although sharp gradients in
species concentration are observed in most FBGs [3], this occurs
locally where the oxygen and fuel are injected (feed ports and
gas distributor). As a result, most of the reactor remains with quasi-constant concentration, making the simplification of constant
temperature and concentration reasonable. The residence time of
volatiles depends on the flows of the biomass and gasification
agent and the geometry of the reactor, whereas the residence time

of char particles also depends on the rate of removal by entrainment (mainly governed by gas velocity) and bed extraction applied
to maintain smooth operation.
Fig. 1 presents the model concept. The gas species and char are
released where the fuel is devolatilized. The yield of species from
devolatilization depends on fuel, temperature, and heating rate
and can be estimated empirically [28,32]. The main yields concerned in the present model are methane, tar and char, xCH4 ;d , xtar,d
and xch,d, (see Fig. 1). Other species (CO, H2O, H2 and CO2) are also
considered for the estimation of WGSR conversion, but only a

Discharged ashes

Produced gas

OVERALL MASS AND HEAT BALANCE,
PSEUDO-EQUILIBRIUM IN THE GAS PHASE

xCH 4 ,gp
WGSR
FACTOR

( f WGSR )

xchar ,gp

xtar ,gp

METHANE
CONVERSION

CHAR

GASIFICATION

TAR
CONVERSION

( X CH 4 )

( X char )

( X tar )

xCH 4 ,d

xchar ,d

DEVOLATILIZATION

GASIFICATION AGENT

FUEL

Fig. 1. Scheme of the model.

xtar ,d


422

A. Gómez-Barea, B. Leckner / Fuel 107 (2013) 419–431

rough estimate is sufficient for the present development, as explained below. The devolatilization yield is the source for the subsequent conversion in the reduction zone (RZ), represented by the
dashed line in Fig. 1, where there is no oxygen left. In fact, the devolatilization box in Fig.1 also includes the reactions of volatiles
(mainly H2 and CO) with oxygen. Therefore this zone is sometimes
called flaming pyrolysis zone [31]. In the RZ H2O and CO2 react
with the char, the methane is converted by steam reforming, and
the tar by reforming/cracking. The main compounds in the gas
phase react through the WGSR. The conversions of the tar, methane, and char in RZ are Xtar, X CH4 , and Xch. The factor fWGSR is the
ratio of the actual coefficient K exp ¼ yCO2 yH2 =ðyCO yH2 O ) and that of
equilibrium KWGSR, y being molar fraction in the gas. The kinetics
of WGSR are taken into account to calculate Kexp.
Once the four parameters Xtar, X CH4 , Xch, and fWGSR are estimated,
the gas composition is evaluated by a pseudo-equilibrium model
(thick solid line in Fig. 1). The composition of the final (outlet)
gas is obtained by the overall atomic mass and heat balance over
the entire gasifier.
2.2. Model formulation

wN2 ;f þ xN2 ;ga ¼ yN2 M N2 F gp

wC;f þ wH;f þ wO;f þ wN;f þ wash;f þ wH2 O;f þ xO2 ;ga þ xH2 O;ga þ xN2 ;ga þ xadd
|{z}
|fflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflffl{zfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflffl} |fflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflffl{zfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflffl}
Gasification agentðO2 ;H2 O and N2 Þ

Additive



! MCO yCO þ MH2 yH2 þ MH2 O yH2 O þ MCO2 yCO2 þ M CH4 yCH4 þ MN2 yN2 þ MCk Hl Om yCk Hl Om F gp þxash;da þ xc;da
|fflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflffl{zfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflffl} |fflfflfflfflfflfflfflfflffl{zfflfflfflfflfflfflfflfflffl}

Gas produced

discharged ash

All quantities in Eq. (1) are in kg/kgfuel(daf). wi,f represents the mass
fraction of the ith component in the dry ash-free fuel (daf), whereas
xi,j is the mass of i flowing in or out in stream j of the system per kg
fuel (daf). The gasification agent (‘ga’) is in general composed of
oxygen, xO2 ;ga , steam, xH2 O;ga , and nitrogen, xN2 ;ga . yi and Mi are the
molar fraction of the species i in the produced gas (molei/molegp)
and its molecular mass. The gas yield (molegp/kgfuel(daf)) is Fgp. The
additive, xadd, can be a catalyst, sand or any material fed to the system for the improvement of the gasification performance. The char
is assumed to comprise the inorganic material from the fuel and
unconverted carbon; small contents of hydrogen and oxygen in
the char are neglected. Then, discharged ash (‘da’) contains unconverted carbon in the char xc,da and ash xash,da, this latter consists of
the ash from the fuel and bed material removed from the bed. The
discharged ash in Eq. (1) includes both fly and bottom ash. The tar
component is given by the species CkHlOm, which can be estimated
[33,34]. The entire quantity of the nitrogen supplied (from the fluidisation agent and the biomass) is assumed to be released as N2.
The oxygen demand will be characterized by the oxygen equivalence ratio, ER, defined as the amount of oxygen supplied to the
gasifier over the oxygen required for stoichiometric combustion.

xO2 ;ga
À
Á
32 1 þ wH;f =ð4wC;f Þ À wO;f =ð32wC;f Þ

ð2Þ

The atomic CHON balances applied to Eq. (1) are:

wC;f ¼ ðyCO þ yCO2 þ yCH4 þ kytar ÞM C F gp þ xc;da
wH2 ;f þ

ð6Þ

whereas the ash balance is:

wash;f þ xadd ¼ xash;da

ð7Þ

2.2.2. Equilibrium of the modified gas-phase (QEM)
The composition of a gas in pseudo-equilibrium is calculated
according to Jand et al. [22]. Three quantities (Fig. 1) are subtracted
from the product gas to attain the equilibrium: methane, tar, and
carbon (xCH4 ;gp , xtar,gp, and xc,da) calculated as

Methane removed ¼ unconverted methane ¼ xCH4 ;gp
¼ xCH4 ;d ð1 À X CH4 Þ

¼ xtar;d ð1 À X tar Þ

ð8Þ

ð3Þ



Á

M H2 À
‘
wH2 O;f þ xH2 O;ga ¼ yH2 O þ yH2 þ 2yCH4 þ ytar M H2 F gp
2
M H2 O
ð4Þ

ð9Þ

Carbon in char removed ¼ unconverted carbon in char
¼ xc;da ¼ xc;ch;d ð1 À X ch Þ

ð10Þ

where X CH4 , Xtar, and Xch are the methane, tar, and char conversions
in the RZ and xCH4 ;d , xtar,d, and xc,ch,d the corresponding yields of these
compounds after devolatilization of the fuel. Then, the CHON balances for the pseudo-equilibrium calculation of the gas phase, corresponding to Eqs. (3)–(6), are:

wC;f À xc;da À xtar;gp k

ð1Þ

ER ¼

ð5Þ

Tar removed ¼ unconverted carbon in tar ¼ xtar;gp

2.2.1. Overall atomic balances
The models for the estimation of the parameters (Xtar, X CH4 , Xch

and fWGSR), as well as the yields xCH4 ;d xch,d, and xtar,d and other species from fuel devolatilization are presented in the following.
The fuel conversion in the gasifier related to 1 kg of dry, ash-free
fuel (daf) (1 kgdaf = wC,f + wH,f + wO,f + wN,f) can be written as
(fuel + gasification agent + additive = gas produced + discharged
ash):
1 kg fuel daf

Á
1 M O2 À
wH2 O;f þ xH2 O;ga þ xO2 ;ga
2 M H2 O


1
1
k
yCO þ yCO2 þ yH2 O þ ytar M O2 F gp
¼
2
2
2

wO2 ;f þ

MC
MC
À xCH4 ;gp
M tar
MCH4

¼ ðyCO þ yCO2 þ yCH4 ÞM C F gp

ð11Þ

Á
M H2 À
‘ M H2
M H2
wH2 O;f þ xH2 O;ga À xtar;gp
À xCH4 ;gp 2
2 M tar
M H2 O
M CH4


¼ yH2 O þ yH2 þ 2yCH4 M H2 F gp

ð12Þ

wH2 ;f þ

Á
1 M O2 À
m M O2
wH2 O;f þ xH2 O;ga þ xO2 ;ga À xtar;gp
2 M H2 O
2 M tar


1

1
¼
y þ yCO2 þ yH2 O MO2 F gp
2 CO
2

wO2 ;f þ

wN2 ;f þ xN2 ;ga ¼ yN2 MN2 F gp

ð13Þ
ð14Þ

The equilibrium equations for the WGSR and SRMR (steam reforming of methane) are:




yH2 yCO2
4094
¼ fWGSR Á 0:029 exp
T
yH2 O yCO
y3H2 yCO
yCH4 yH2 O




28116

¼ 6:14 Â 1013 exp À
T

ð15Þ

ð16Þ

where the terms within brackets on the right-hand side of Eqs. (15)
and (16) are the equilibrium constants of WGSR and SRMR [31].
fWGSR is the factor that measures the approach to equilibrium of
the WGSR, obtained by taking into account the kinetics as explained
below. To replace the contribution of methane and tar removed
from the gas (Eqs. (8) and (9)) in the pseudo-equilibrium calculations, a fictitious inert gaseous compound is considered [22], given
by xCH4 ;d ð1 À X CH4 Þ=M CH4 þ xtar;d ð1 À X tar Þ=Mtar (kmol inert/kgfuel(daf)).


423

A. Gómez-Barea, B. Leckner / Fuel 107 (2013) 419–431

Eqs. (11)–(16) are solved for a given temperature and parameters (Xtar, X CH4 , Xch, xCH4 ;d , xtar,d, and xc,ch,d and fWGSR) yielding the
composition of the pseudo-gas (yi): yCO, yH2 ; yCO2 ; yN2 ; yH2 O and
yCH4 . Then, the composition of the final outlet gas is obtained by
restoring the amount of methane (xCH4 ;gp calculated from Eq. (8)),
and tar (xtar,gp calculated from Eq. (9)) previously subtracted.
2.2.3. Overall heat balance
Once the gas composition of the outlet gas and the amount of
unconverted fuel (xc,da and xash,da) have been calculated by the kinetic model described below, an energy balance over the gasifier
yields for 1 kg fuel:

hf ;df þ

Z

T f ;in

T0

cp;df dT þ wH2 O;f hf ;H2 OðlÞ þ xH2 O;ga hf ;H2 OðgÞ þ xN2 ;ga hf ;N2

þ xO2 ;ga hf ;O2 ¼ F gp

Z
7
X
yi hf ;gp;i þ xc;da hf ;c þ xash;da

Tb

cp;ash;da dT þ Q l ð17Þ

T0

i¼1

The enthalpy of formation of the dry fuel hf,df, char hf,c, and tar
hf,gp,tar, are calculated from their heating values. The heating value
of the fuel is the input from an analysis, while the heating value
of char and tar are estimated from Ref. [34].
2.2.4. Kinetic models for secondary conversion of gas

Methane and tar conversions are calculated assuming perfect
mixing of the gas in the bed and freeboard (CSTR) and first order
kinetics

Xi ¼

ki si
i ¼ CH4 ; tar
1 þ ki si

ð18Þ

The kinetics of the methane and tar reactions have been discussed
in [31]. The selected kinetic parameters for the two reactions are
presented in Table 1. The kinetics for the methane is that for homogeneous conversion and it has been considered pseudo-first order
reaction by lumping a typical steam concentration into the kinetics
coefficient. The methane conversion below 1000 °C is very low so
this simplification is quite insignificant. If a catalyst is added to
the bed, the rate should be modified to account for its influence.
The conversion of tar compounds is a complex process, still to
be addressed in its details. The objective of modeling tar decomposition in the present work is to give rough estimates of tar concentration in the gas, with the purpose of capturing the effects in the
change of operation conditions of FBG. The tar concentration in the
outlet gas of an FBG is small compared to other components CO,
and CH4, etc. Although tar in the gas is a decisive issue for the

utilization of the gas, its effect on the mass balance is not significant. The effect of tar concentration on the heat balance could have
some significance due to its high energy density. Here the kinetics
of Baumlin et al. [35] are taken to represent the overall tar decomposition of an lumped tar in a CSTR. If an active catalyst is present
this kinetics should be changed to account for the impact of the
bed material on tar decomposition.

The kinetics of WGSR have been measured [36] both for the
homogeneous case and for various bed materials used in FBG.
The kinetics obtained were similar to those usually applied in modeling gasifiers [37], but they differ from others [38]. The kinetic
expressions and related parameters are presented in Table 1.
Note that for the estimation of methane and tar conversion (Eq.
(18)), the initial yields of methane and tar from devolatilization do
not need to be known as a consequence of the 1st order reactions.
For WGSR, however, the amounts of CO, H2O, H2 and CO2 entering
RZ are needed, since the kinetics correspond to a reversible reaction (Table 1).
The gas residence time is that of the total flow of gas in the bed
and freeboard of the specific geometry considered (diameter and
height).
2.2.5. Char conversion model
Fig. 2 outlines the main input and output streams in the reactor
(using quantities x, which are mass flowrate per kilogram of daf).
The control volume is represented by the dashed line. The fuel
decomposes into char and volatiles during devolatilization, and
these are the inputs to the control volume together with added
material xadd. The volatiles, fluidization agent, and produced gas
interact with the solids, resulting in a temperature, a gas composition, and a gas velocity in the reactor. The normalized flowrates of
solids x are those of the additives (add) and char (ch). The solids enter the control volume (d) and leave as bottom ash (2) and fly ash
(3). wc,ch,d and wc,ch,b are the carbon (c) contents in the entering char
(ch) stream and in the char found in the bed (b). The solids are assumed to be perfectly mixed in the reactor so wc,ch,2 = wc,ch,3 = wc,ch,b
as indicated in Fig. 2. The normalized mass flowrate of char leaving
the reactor is then xch,2 + xch,3 = xch,da = xc,da + xash,da, and the corresponding normalized flowrate of carbon is xc,da=(xch,2 + xch,3)wc,ch,b
(carbon is exiting the system in the solids of streams 2 and 3, where
the char particles have the same composition as the bed, wc,ch,b).
Similarly, the ash balance is xash,da=(xch,2 + xch,3)(1 À wc,ch,b) + xadd.
Under steady state conditions a constant mass of char inventory
mch,b (fuel ash and carbon) and carbon mc,b = mch,bwc,ch,b remain in

the bed, constituting the char and carbon load. Note the difference

Table 1
Kinetics of gas (methane reforming, tar thermal decomposition and WGSR) and char reactions (with H2O and CO2).
Reaction

Stoichiometry

Kinetic expression

Methane reforming

CH4 þ H2 O ! CO þ 3H2

RCH4 ¼ kcCH4 cH2 O (kmol mÀ3 sÀ1)

ÀE=Rg T

k ¼ Ae
A = 3.00 Â 108 m3 kmolÀ1 sÀ1
E = 125 kJ molÀ1

[39]

Thermal decomposition

Tar ? lighter gas

Rtar ¼ k ctar (kmol mÀ3 sÀ1)

k ¼ AeÀE=RT
A = 1.93 Â 103 sÀ1
E = 59 kJ molÀ1

[35]

RCO ¼ ki ðcCO2 cH2 À K e cCO cH2 O Þ (kmol mÀ3 sÀ1)

ki ¼ AeÀE=Rg T

[36]

WGSR

kd

CO þ H2 O ¢ CO2 H2

Kinetics parameters

Ref.

ki

A = 1.41 Â 105 m3 kmolÀ1 sÀ1
E = 54.2 kJ molÀ1
K e ¼ 0:029 expð4094=TÞ
Gasification

C þ CO2 ! 2CO

À1
r C—CO2 ¼ k p0:38
CO2 (s )

k ¼ AeÀE=Rg T
A = 3.1 Â 106 sÀ1 barÀ0.38
E = 215 kJ molÀ1

[40]

Gasification

C þ H2 O ! CO þ H2

À1
r C—H2 O ¼ k p0:57
H2 O (s )

k ¼ AeÀE=Rg T
A = 2.6 Â 108 sÀ1 barÀ0.57
E = 237 kJ molÀ1

[41]


424

A. Gómez-Barea, B. Leckner / Fuel 107 (2013) 419–431

reactor dch, is estimated from the fuel size, taking into account
shrinkage, fragmentation and reaction as detailed below.
Eqs. (21) and (22) allow the determination of s and wc,ch,b for given s2, s3 and sR. The overall carbon (char) conversion in the reactor is obtained by applying a balance of carbon, i.e. (carbon in –
carbon out)/carbon in) to give:

X ch ¼ 1 À

(a)

(b)

Fig. 2. (a) Control volume for the char conversion model with the main gas and
solids streams. (b) Solids balance in the control volume: Inlet solids stream (index
d) comprises char generated after devolatilization and additive; Outlet solids
streams are: extraction or bottom ash (index 2) and elutriation or fly ash (index 3).

between the mass fraction of carbon in the char remaining in the
bed, wc,ch,b, and that in the whole bed, which includes also the inert
additives, wc,b = mc,b/mT,b = wch,bwc,ch,b. The total mass of bed material
(inert/additive and char) in the reactor is mT,b = mch,b + madd,b. The
char load at steady state depends on the char reactivity and the
residence time of the char particles in the bed. The main operation
variables in the reactor are indicated in the figure: temperature T,
superficial velocity u0, and the partial pressures pCO2 and pH2 O of
CO2 and H2O.
A balance of char and carbon in the control volume of Fig. 2b
gives (in = out + reacted):

xch;d ¼ xch;2 þ xch;3 þ xR

ð19Þ

xch;d wc;ch;d ¼ ðxch;2 þ xch;3 Þwc;ch;b þ xR

ð20Þ

where xR=(rc,chmc,b)/Ff,daf is the normalized rate of reaction of the
carbon in the char (kg carbon reacted in the char/kgfuel,daf). By defining the residence time of char in the reactor as s = mch,b/(xch,dFf,daf)
and s2 and s3 as the time constants of removal of solids material
from the reactor by extraction s2 = mT,b/(x2Ff,daf) and elutriation,
s3 = mT,b/(x3Ff,daf) (1/s2 and 1/s3 are the constant rates of solids removal), Eqs. (19) and (20) can be solved for the two unknowns s
and wc,ch,b:

s¼



1
wc;ch;d =sR
1À
ð1=s2 þ 1=s3 Þ
ð1=s2 þ 1=s3 þ 1=sR Þ

wc;ch;b ¼

ð1=s2 þ 1=s3 Þwc;ch;d
ð1=s2 þ 1=s3 þ ð1 À wc;ch;d Þ=sR Þ

ð21Þ

ð22Þ

where the char conversion time sR is the inverse of the reactivity of
the char sR = 1/rc,ch, the latter defined as rc,ch=(1/mc,p)dmc,p/dt where
mc,p is the mass of carbon in a char particle in the bed. The intrinsic
reactivities of biomass char with CO2 and H2O, used for the simulation presented in Section 3, are given in Table 1. For other chars
(from other fuels) the intrinsic reactivity has to be changed consistently. The reactivity of a single particle, taking into account diffusion, is obtained by a simple model [31] where two effectiveness
factors are calculated for a char particle of size dch in a gas at a temperature T and pressures pCO2 and pH2 O (with two coupled equations). The effective diffusivity and mass transfer coefficient,
necessary for the char-particle model, are estimated by a correlation sensitive to the operating conditions (velocity, temperature,
size of char, etc.) [31]. The size of the average char particle in the

wc;ch;b
wc;ch;d



s s
þ
s2 s3


ð23Þ

wc,ch,d is given as input (or estimated as explained below), and the
reactivity of the char (and so sR) is calculated as a function of the
conditions in the reactor (T, pCO2 and pH2 O ) with the expressions given in Table 1. s3 is calculated by the elutriation model presented
below.
Various operation modes can be applied to remove bed material
by bed extraction: (i) the extraction of material is adjusted to a given rate (an overflow or bottom pipe continuously removes material from the bed, or it is adjusted by a given sequence). Then s2 is
known, and Eqs. (21)–(23) can be directly applied to obtain the

solution. (ii) the char content in the bed mch,b is maintained to
some prescribed value mch,b,crit in relation to the total inventory
of the bed, mT,b, for instance to avoid accumulation of ash in the
bed; Then s2 has to be calculated to control the bed at wch,b,crit =
mch,b,crit/mT,b. In such a case s is known (s = scrit = mch,b,crit/(xch,dFf,daf))
and Eqs. (21)–(23) can be solved for wc,ch,b and s2 to give:

wc;ch;b ¼ ð1 þ sR =scrit Þ=2 þ ð1=4ð1 þ sR =scrit Þ2
À wc;ch;d s3 =scrit Þ1=2

s2 ¼

ð24Þ

1
ð1=scrit À 1=s3 À wc;ch;b =sR Þ

ð25Þ

In some cases the system can operate safely at s < scrit because s3 is
high enough to entrain the ash at sufficient rate to maintain the required condition. In such a case 1/s2 = 0, and Eqs. (24) and (25) are
used. Alternatively, Eqs. (21)–(23) can be used directly with
1/s2 = 0. Finally, the flowrate of the inert solids, necessary to maintain the inventory during operation, can be calculated by an overall
mass balance, Eq. (7):

xadd ¼

mT;b
F f ;daf





wc;b 1
1
1
þ þ
wc;ch;b
À

sR

s

s2

s3

ð26Þ

In operation with low-ash fuel, such as wood, there is no bed
extraction (1/s2 = 0) during a long time, so the material in the reactor is not strictly maintained steady (there is only a single value of
s3 that makes xadd in Eq. (26) zero for given input), but the accumulation (or loss) is slow and the system is operated in a quasi-steady
manner.
To calculate s3 (i.e., x3) an elutriation model is applied [42]. Two
types of char particle are elutriated: coarse particles (xch,coar,3) generated after devolatilization and fragmentation, and fines (xch,fin,3)
produced by abrasion of char in the bed. Particles are carried away
in the fly-ash stream x3 = xch,3 + xadd,3 with xch,3 = xch,coar,3 + xch,fin,3. xadd,3
is calculated similar to char but applying the density, size and

attrition constant of the additive. In the following, the case of char
is explained, since the impact of inert material in x3 is negligible in
steady state operation of bubbling FBG provided that the size of
additive particles are large enough, i.e. xadd,3 ( xch,3.
Fines are assumed to be produced by attrition at a rate [43,44],

xch;fin;3 ¼

K att mch;b ðu0 À umf Þ
F f ;daf dch

ð27Þ

Katt is the dimensionless attrition constant, determined experimentally for a variety of chars and solids, ranging from 1 Â 10À7 and
1 Â 10À8 for various biomasses [43]. dch is the average particle size
of the coarse char in the reactor, calculated below, and umf is the


A. Gómez-Barea, B. Leckner / Fuel 107 (2013) 419–431

minimum fluidization velocity corresponding to that average size.
The fines are assumed to be elutriated immediately as they are produced, and their conversion along the reactor is small; it takes just a
few seconds for the gas to carry them away. The coarse particles can
be converted or elutriated depending on their size, dch, and operating conditions (mainly velocity).
To calculate Fch,coar,3 a fluid-dynamic model of the FBG is solved
to give

xch;coar;3 ¼ xch;1 þ ðxch;b À xch;1 Þ expðÀaðLfb À Lb ÞÞ

ð28Þ

Lb and Lfb are the height of the dense bed and the freeboard, xch,b is
the entrainment flux of coarse char particles at the surface of the
dense bed [45], xch,1 is the particle flux of coarse char in an imaginary long column, whose height is higher than the transport disengaging height, calculated by applying the correlation in [46] and a is
the decay coefficient [47].
In general, population balances on the particle sizes in the bed
are necessary for precise evaluation of the processes. In this work,
however, an approximate method estimates dch as a function of
fuel particle size df [42,48],

dch % df rðu=ðn1 n2;m ÞÞ1=3

ð29Þ

n1, n2m, u being parameters related with shrinkage and fragmentation of the fuel in a fluidized bed [48].
In summary, x3 in s3 is calculated by x3 = xch,3 + xadd,3 where
xch,3 = xch,coar,3 + xch,fin,3. xch,coar,3 is calculated by Eq. (28) and xch,fin,3
by Eq. (27). Similar equations are used for the additive. Most of
the fluid-dynamics correlations used for the solution of Eqs. (27)
and (28) are valid for both bubbling and circulating FB and the
two types only need to be distinguished in some details [31].

425

empirical models [32,34], or by rough estimation like the one given
in the following. Here we have demonstrated that the exact evaluation of these yields does not significantly improve the estimation
of the gas phase composition, so the following typical values can be
assigned for the yields (kg/kgdaf): 0.15 for CO, 0.20 for CO2, 0.02 for
H2 and 0.10 for H2O.
2.3. Solution procedure

The main steps to solve the model are summarized in the
following:
1. Introduction of inputs:
– Geometry: internal diameter and height of bed and freeboard. Total bed inventory in the reactor, or pressure
drop.
– Fuel: Composition (elemental and ultimate analyses) and
calorific value.
– Flow rates of biomass and gasification agent. Alternatively, the model can be specified with gas velocity and
temperature, from which the flowrate of the gasification
agent is obtained once the iteration is finished.
– In Step 3 (see below) some dedicated inputs are required.
2. The reactor temperature, flowrate and gas composition of
the produced gas, gas velocity in the bed and freeboard,
are assumed as guess for the first iteration (Steps 3–7, below).
3. The conversions of methane, tar, and char are calculated, as
well as the factor of approaching the equilibrium of WGSR
by applying the kinetic models indicated in Sections 2.2.4
(tar, methane, and WGSR) and Section 2.2.5 (char).
For the kinetic models various additional inputs are required:

2.2.6. Estimation of devolatilization yields
The yield of devolatilization (xch,d, xCH4 ;d , xtar,d, xCO,d,
xCO2 ;d ; xH2 ;d ; xH2 O;d ) is ideally estimated for fluidized bed conditions
(fuel and temperature) similar to that to be modeled. Such data
have been obtained for different fuels, providing correlations as a
function of temperature [28]. When the yield cannot be determined experimentally, data from compilations can be taken,
searching for similar fuel and operating conditions [32]. The following can be generally applied: The char yield xch,d can be taken
from the proximate analysis of the fuel with reasonable accuracy,
since its variation with temperature and heating rate is small
[28]. The yield of methane xCH4 ;d depends on fuel but is in the range

of 50–80 g/kgdaf for most biomass species devolatilized in FB even
under quite different conditions [22]. The yield of tar xtar,d can be
assumed to be between 0.15 and 0.20 kgtar/kgdaf a range which is
consistent with the model of tar conversion presented above. This
treatment is enough for the present model because the solution is
not much sensitive to the actual tar concentration in the gas due to
its low concentration in the produced gas of FBG, but the value
chosen may be sensitive to different operating conditions.
For the calculation of WGSR, the yields of CO, CO2, H2 and H2O
(xCO,d, xCO2 ;d ; xH2 ;d ; xH2 O;d ) have to be estimated (see the kinetic
expression in Table 1). The yield of devolatilization, followed by
partial combustion of the fuel gas with the O2 fed to the gasifier,
is considered, following the treatment of Wang [49]. This is made,
knowing that O2 will be consumed rapidly, mainly by H2 and CO
yielding CO2 and H2O [49] and very little char and methane are
burned owing to the low combustion rates in the gasifier. Instead
of calculating the competition between H2 and CO for the O2, it is
assumed that H2 is consumed first, because of its higher combustion rate compared to CO [31], yielding H2O, and the remaining
O2 combines with CO to give CO2. The yields of CO, CO2, O2 and
H2O from devolatilization of a given fuel can be estimated from
correlations as a function of temperature [28], by simple pseudo-

– The devolatilization yields (xch,d, xCH4 ;d , xtar,d, xCO,d,
xCO2 ;d ; xH2 ;d ; xH2O;d ): these are taken as input in the form
of correlations (for instance as a function of temperature)
or by estimations from literature for the same fuel and
operating conditions, or by the gross recommendation
made in Section 2.2.6.
– Size and density of fuel and additive.
– The kinetics of steam reforming, tar conversion, WGSR,

and reactivity of char (Table 1). The former may depend
on the additive used in the bed and the reactivity has to
be selected for the fuel/char to be modeled.
– Input to the char conversion model (attrition constant,
Katt, fragmentation parameters, n1 and n2m). Other
parameters for the fluid-dynamic model, such as decay
factor in the freeboard a, umf,. . . are taken from the specified correlations for the properties of bed material and
calculated char diameter in the bed, dch.
4. Calculation of CHO to be subtracted from QEM (Eqs. (8)–
(10))
5. Solution of QEM (Eqs. (11)–(16)) for the calculation of the
pseudo-gas phase (yi).
6. Calculation of char xch,d(1 À Xch) and the bed material
removed from the bed (entrainment or extraction). Then
xc,da and xash,da are calculated. Determination of the
amount of methane (xCH4 ;gp in Eq. (8)) and tar (xtar,gp in
Eq. (9)) to be restored to the gas phase.
7. With the gas and solids compositions in the outlet
streams, the atomic balances (Eqs. (3)–(6)) and the
energy balance over the gasifier (Eq. (17)) are solved to
yield the actual gas phase composition (yi) and its temperature (the thermal losses are given as input, although
this value can be determined easily). From this, the flowrate of gas produced and gas velocities in the bed and


426

A. Gómez-Barea, B. Leckner / Fuel 107 (2013) 419–431

freeboard are calculated. The assumed values in Step 2
are corrected, and the iterative process is repeated until

convergence.
3. Results and discussion
3.1. Comparison of model with measurements
The model developed has been compared with experiments
conducted in a bubbling FBG with different gasification agents:
air, air–steam, and oxygen-enriched air–steam. The gasification
agent was preheated to enter the reactor at 400 °C. The fuel was
wood pellets with the empirical formula CH1.4O0.64, (dry and free
of ash). The moisture and ash contents were 6.3% and 0.5% (mass
basis), and the lower heating value of the fuel (as received) was
17.1 MJ/kg. The pellets were cylindrical with a mean diameter of
6 mm and a height between 5 and 10 mm. The apparent density
of a pellet was 1300 kg/m3, whereas the bulk density was
600 kg/m3. The bed material used in the FBG was ofite with density
of 2650 kg/m3 and an average size of 290 lm. Ultimate and elemental analyses as well as particle size distribution of the ofite
are reported in [50]. The main geometrical parameters of the FBG
unit are: bed and freeboard diameters 150 and 250 mm; bed and
freeboard heights 1500 and 3500 m. The initial bed inventory in
all tests was 12 kg, which was kept roughly constant by controlling
the pressure drop across the bed. The rig, test procedure, and analysis of results have been reported in detail in Refs [29,51].
Other inputs needed for the simulations are the following: attrition and fragmentation parameters obtained from measurements
in a lab-scale FB with wood pellets [28] and literature data for various biomasses [43]. The inputs chosen for the simulations are:
Katt = 1 Â 10À7, n1 = 2, n2m = 3, and r = 0.8. The calculated shrinkage
factor is u = 1.22, and the resulting average char particle size in
the bed is dch = 2 mm. The tar component is given by the species

CkHlOm with k = 6; l = 6.2; m = 0.2, estimated from [33,34]. The
estimated heating values of char and tar are 33 and 37 MJ/kg.
The char reactivity and other kinetics are given in Table 1.
Table 2 presents the gas composition and other measured

parameters together with those calculated by the model. The model was run at the same temperatures as those measured in the
experiments by adjusting the heat loss, which varied between 2%
and 14% of the heating value of the fuel. In all the tests, except in
the first one, there was no mechanical extraction of material from
the bed. The factor fWGSR was evaluated by setting the temperature
in the freeboard about 100 °C lower than that of the bed to represent the temperature drop measured in the experiments.
The gas composition was generally well predicted. Especially,
the model confirmed that the methane in the outlet gas is nearly
that produced during devolatilization and calculated methane conversion was below 0.01% in all the tests. This fact underlines the
importance for the model of a good estimation of the methane
yield from devolatilization. The carbon in the gas phase is reasonably well predicted, although the distribution between CO and CO2
calculated by the model varies to some extent. More importantly,
the main changes during variations in the operating conditions
were captured by the model. The char conversion does not seem
to agree too well with the two tests where it was measured.
Nevertheless, the measured values of char conversion reported in
[29] have to be taken as rough estimates, since they were the average
values calculated from the material collected in the cyclones after
two or three tests conducted under different operating conditions.
The simulations show that the WGSR is far from equilibrium, with
fWGSR ranging from 0.40 to 0.65. In all simulations, the rate of entrainment of coarse char was much smaller than that of attrition, i.e.
xch,coar,3 ( xch,fin,3 and x3 % xch,fin,3.
The model was capable of predicting the distribution of the four
main species (CO, CO2, and H2 and H2O) reasonably well, as assessed by inspection of CO, CO2, and H2 in the table (H2O was

Table 2
Comparison of model results with FB gasification tests from [29,51].
Test

1

Exp

2
Mod

Exp

3
Mod

Exp

4
Mod

Exp

5
Mod

Exp

6
Mod

Exp

Flowrates
Biomass (kg/h)
Air (Nm3/h)

Steam (kg/h)
Pure oxygen (Nm3/h)

20.5
17.0
0
0

15.0
17.0
0
0

15.0
17.0
3.2
0

12.4
11.9
3.7
1.5

11.8
8.3
6.2
1.8

12
6.8

6.4
2.1

Representative parameters
ER (kg O2fed/kg O2stoichiometric)
SBR (kg steam/kg biomass)
Throughput ðkg biomass=m2bed =hÞ

0.19
0
1160

0.27
0
848

0.27
0.23
850

0.36
0.32
701

0.34
0.56
667

0.33
0.57

679

Temperature and wall-heat loss
Bed temperature (average) (°C)
Freeboard temperature (average) (°C)
Wall-heat loss (%LHVfuel)

780
687
na

2.5

805
718
na

na

6.0
0.60

Gas phase outputs
CO (%v/v, dry gas)
H2 (%v/v, dry gas)
CO2 (%v/v, dry gas)
CH4 (%v/v, dry gas)
N2 (%v/v, dry gas)
H2O (%v/v, wet gas)
Tar (g/Nm3, dry gas)

LHV (MJ/Nm3, dry gas, no tar)

18.2
13.2
14.2
6.0
na
na
25.8
5.9

Solid conversion outputs
Carbon conversion (kg/kg)
Char conversion (kg/kg)

0.87
0.65

Rate of ash removal
Bottom discharged (kg/h)
Fly ash elutriated (kg/h))

Ã

779

807
4.7

786

708
na

na
na

0
0.43

20.1
13.2
12.6
6.4
47.0
12.4
26.1
6.2

17.6
12.6
14.9
5.2
na
na
23.8
5.4

0.81
0.52

0.88
0.65

787
5.2

808
715
na

0
na

0
0.58

21.6
12.2
10.8
5.0
50.0
8.8
16.0
5.8

15.0
14.0
16.2
4.7
na

na
na
5.1

0.95
0.87

0.90
na

809
14

795
725
na

na
na

0
0.20

16.6
14.0
14.1
4.9
49.7
16.8
18.8

5.3

18.9
16.4
17.6
5.5
na
na
na
6.1

0.93
0.82

0.94
na

794

Mod

11

806
727
na

805
10

na
na

0
0.22

na
na

0
0.18

15.2
14.7
20.1
5.2
44.3
21.2
15.0
5.4

17.5
21.8
18.0
6.1
na
na
na
6.7

15.1
19.7
23.2
5.9
35.6
29.3
16.3
6.1

19.3
25.7
17.0
6.7
na
na
na
7.6

16.4
22.2
24.6
6.1
30.4
30.0
11.0
6.7

0.98
0.94

0.95
na

0.97
0.93

0.96
na

0.98
0.95


427

A. Gómez-Barea, B. Leckner / Fuel 107 (2013) 419–431

not measured in the experiments). Test 1 was simulated with a bed
discharge of 6 kg/h. Although the reported test is said to be without
significant bed removal, the authors detected an accumulation of
material in the bed during the tests, noted by the increase of pressure in the bed, so steady state conditions were not reached. This is
reasonable, since the throughput of Test 1 was higher than in the
rest of tests and higher than that usually attained in bubbling
FBG (between 300 and 800 kg/(m2 h).
The comparison is a positive proof of the prediction ability of
the model. However, detailed conclusions should be taken with
caution because some key information from the measurements is
not clearly reported, such as: char accumulation during the startup period, the run time of each test after steady state (in fact, steady state of the char load has to be reached, and in some test this is
doubtful, as discussed above in relation to Test 1), the sequence of
opening the bottom ash pipe for ash removal sometimes applied,

the amount of fly ash collected, and its composition. An attempt
was made in [29,51] to minimize the heat loss during the tests in
order to simulate industrial autothermal units, where the heat loss
is small. However, the simulation showed that the heat loss was
significant and varied between the tests. The most likely explanation is that steady-state operation was not completely achieved in
some tests. In such a case, the additional heat requirement is not a
heat loss through external surfaces but additional heat required for
heating up the material. Due to the large size of the pilot gasifier
and the limited gasification runtime, this amount of heat could
be significant. This aspect is common to most pilot and laboratory
units. As we demonstrate below by means of a sensitivity analysis
of the model, this information is of concern for the simulation of
the real experimental operation point.
3.2. Sensitivity analysis and comparison with other QEM
The model is used to analyze the performance of an FBG under
different conditions. Simulations are made for the same fuel as in
the previous section. The flowrate of biomass per unit of cross section of bed, the throughput Th kg/(m2 h) characterizes the operation of the unit, allowing scale-up of results to geometrically
similar FBGs (freeboard height to bed diameter ratio and mass
inventory/bed diameter). The pilot FBG analyzed in the previous

X ch calculated with complete model

Temperature (T), ºC

1000

Xch=0.25
0.50

900

850

0.75

800

1.00

750
700
650
600
0.2

ooo X ch

0.22

0.24

0.26

0.28

0.3

Gas lower heating value (LHV), MJ/Nm

1050

950

3.2.1. Effect of oxygen equivalence ratio (ER) and comparison with
existing QEM
The main reason for the development of the present model was
the uncertainty caused by the assignment of an arbitrary value of
char conversion Xch in the existing QEM [22]. To study this aspect,
Fig. 3 presents the temperature and heating value of the product
gas as a function of equivalence ratio (ER) calculated with a QEM
at various pre-assigned (not calculated) values of Xch. Actually,
the model developed here becomes a QEM by setting char, methane and tar conversion, as well as the convergence factor fWGSR,
to prefixed values (not calculated as a function of process conditions). Under such conditions the model was used with X CH4 ¼ 0,
Xtar = 1, and fWGSR = 1 for various Xch, as shown in Fig. 3. The results
reveal that the value assigned for Xch has a major effect on the temperature and the gas heating value, and therefore on other parameters like gas composition and cold gas efficiency. The higher the
char conversion, the lower the temperature of the reactor and
the higher the heating value of the gas produced, because at higher
conversion more heat is consumed due to the endothermicity of
the char gasification reactions. In other words, sensible energy
from the gas is transformed into chemical energy in the gas
(mainly into H2 and CO).
The circle line in Fig. 3 shows the result from the present model
without pre-assignment of char conversion, but keeping the other
parameters at the same fixed values as used in the QEM: X CH4 ¼ 0,
Xtar = 1, and fWGSR = 1). It is demonstrated that the char conversion
varies significantly with the operating conditions (from about 0.5
at ER = 0.2 with a temperature around 730 °C, up to nearly 1 at
ER = 0.3, where the temperature is roughly 905 °C).
The dashed–dotted line in Fig. 3 shows the result of the complete model, i.e. with the calculation of all parameters Xch, X CH4 , Xtar
and fWGSR as a function of operating conditions. X CH4 , Xtar and fWGSR
calculated with the model for ER varying from 0.2 to 0.3, range

from 0.001 to 0.03, from 0.89 to 0.97, and from 0.7 to 0.8, respectively. By comparison of dashed-dotted and circle lines in Fig. 3 it is

3

1100

section is taken as reference geometry. The same fuel (wood pellets) and char reactivity and fragmentation parameters are chosen.
The gasification agent enters the reactor at 400 °C and the wall
heat loss is 3% of LHV of the input fuel in all simulations below.

calculated with simplified model

8
7.5
7
6.5
6
5.5
5
0.2

1.00
0.75
0.50
X ch=0.25

0.22

0.24

0.26

0.28

Equivalence ratio (ER)

Equivalence ratio (ER)

(a)

(b)

0.3

Fig. 3. Temperature and lower heating value of the gas produced as a function of equivalence ratio. Solid lines were calculated with a QEM with X CH4 ¼ 0; Xtar = 1 and
fWGSR = 1, for various values of Xch, 0.25, 0.5, 0.75 and 1 (each of the solid curves). The circle line curve was made with the present model calculating Xch as a function of process
conditions, but with pre-assigned values of X CH4 , Xtar, and fWGSR, equal to those used in the QEM to calculate the solid lines (X CH4 ¼ 0; Xtar = 1 and fWGSR = 1); the dashed–dotted
curve is calculated by the complete model, i.e. calculating all parameters Xch, X CH4 , Xtar and fWGSR as a function of process conditions.


428

A. Gómez-Barea, B. Leckner / Fuel 107 (2013) 419–431

concluded that the influence of X CH4 and Xtar is not so significant,
whereas the calculated fWGSR leads to visible differences in temperature (comparison between dashed line and circle line in Fig. 3a),
and, especially, in the heating value of the gas (Fig. 3b). In Fig. 4
the corresponding char conversion and gas composition are shown,
using the complete model. The char conversion rises from 0.6 at
ER = 0.2 (730 °C) to nearly 1 at ER = 0.3 (905 °C). The molar fraction

of CO in the gas presents a maximum at ER = 0.28 where the char is
almost converted (carbon boundary point), whereas hydrogen decreases monotonically with ER. While the available char decreases,
the additional oxygen tends to burn the fuel gas, increasing the
temperature and diminishing the heating value of the gas, as seen
in the circle and dashed–dotted lines in Fig. 3.
It is concluded that the most important parameter to be estimated is the char conversion. Tar concentration in the gas is small
and methane is not converted, so very little influence on the composition and thermal efficiency of the process is expected from the
variation of these parameters around the pre-assigned values, 1
and 0, respectively. The approach to WGSR equilibrium changes
the gas composition significantly, but its impact is less significant
than that of char conversion. Therefore QEM having a given char

conversion has no prediction ability. A char predictor inside the
QEM is needed to capture the change of performance with operating conditions.
3.2.2. Effect of throughput (Th)
For the calculation of Fig. 4 (and the dashed–dotted lines in
Fig. 3), the present model was run with a throughput of 500 kg/
m2 h (in QEM the throughput does not influence the results, since
QEM is not sensitive to the gas flow and other fluid-dynamic processes that affect the performance of the gasifier). The effect of the
throughput is studied with the present model in Figs. 5–7. The rise
in Th (a higher fuel flowrate in the given gasifier) increases the gas
velocity and so the rate of entrainment; the temperature and the
reactivity increase, resulting in lower char load in the bed. The
gas velocity (in fact, u0 À umf) is roughly proportional to Th, so
xch,3,fin increases through the term (u0 À umf) but decreases because
mch,b is lower (see Eq. (27)). Therefore, there are two competing effects. The char conversion as a function of Th is plotted in Fig. 5,
where a weak minimum is observed in Xch at around 900 kg/m2 h
at ER = 0.25. In contrast, the conversion decreases continuously
with Th for ER = 0.30, but in both cases the change in Xch with Th

0.25

Molar fraction in wet gas (%v/v)

Char conversion (Xch), kg/kg

1
0.95
0.9
0.85
0.8
0.75
0.7
0.65
0.6
0.2

0.22

0.24

0.26

0.28

CO
0.2

0.15

H2
CO2

0.1

H2O
0.05

CH 4
0
0.2

0.3

0.22

0.24

0.26

0.28

Equivalence ratio, ER

Equivalence ratio (ER)

(a)

(b)

0.3

Fig. 4. Char conversion (a) and gas composition (b) calculated with the complete model as a function of ER for Th = 500 kg/m2 h (the corresponding temperature and LHV as a
function of ER are those drawn as dashed-dotted lines of Fig. 3).

0.906

1

Char conversion (Xchar), kg/kg

Char conversion (X ch ), kg/kg

ER=0.30
0.98

0.96

0.94

0.92

ER=0.25

0.9

0.88
300

400

500

600

700

800
2

Throughput (Th), kg/(m h)

(a)

900

1000

0.904
0.902
0.9
0.898
0.896
0.894
0.892

ER=0.25

0.89
0.888

0.886

400

600

800

1000

1200

1400

2

Throughput (Th), kg/(m h)

(b)

Fig. 5. (a) Char conversion as a function of throughput for ER = 0.25 (—) and 0.30 (Á Á Á); (b) Detail of the case ER = 0.25 to visualize the minimum.


429

960
ER=0.30

Temperature (T), ºC

940
920
900
880
860
840
820

ER=0.25

800
780
760
300 400 500 600 700 800 900 1000

0.25

2.5

wch,b

0.2
ER=0.25

wc,b

0.15

wch,b

0.1
0.05

ER=0.30

wc,b
0
300 400 500 600 700 800 900 1000

Throughput (kg/(m2h))

Throughput (Th), kg/(m2 h))

(a)

(b)

Char residence time (τ), h

Mass fraction of char (wch,b ) and
carbon (wc,b ) in the reactor, kg/kg

A. Gómez-Barea, B. Leckner / Fuel 107 (2013) 419–431

2

ER=0.25

1.5
1

ER=0.30

0.5
0
300 400 500 600 700 800 900 1000
2
Throughput (Th), kg/(m h)

(c)

Fig. 6. Temperature (a), mass fraction of char and carbon in the bed (b), and residence time (c) as a function of throughput for ER = 0.25 (—) and 0.30 (Á Á Á).

0.25

Molar fraction in wet gas (%v/v)

ER=0.25
0.2

ER=0.30

CO

0.15

0.1

H2

CO2

H 2O

0.05

CH 4
0
300

400

500

600

700

800

900

1000

Throughput (Th), kg/(m 2h)
Fig. 7. Gas composition as a function of throughput for ER = 0.25 (—) and 0.30 (Á Á Á).

Critical char mass fraction
in the reactor (w ch,b,crit ), kg/kg

0.4

ER=0.2
0.3

0.2

0.25
0.1

0.30
0.05
0

0

0.5

1

1.5

-1

1/τ , h
2

Fig. 8. Critical mass fraction of char in the bed, wch,b,crit , as a function of the
constant rate of bottom ash discharge (1/s2) for various ER(0.20 (—), 0.25 (—) and
0.30 (Á Á Á)). For each ER two throughputs are displayed (Th = 500 (black) and 1000
(red). The horizontal dot–dashed line is wch,b,crit = 0.05. (For interpretation of the

references to color in this figure legend, the reader is referred to the web version of
this article.)

is small. The analysis is better understood by inspecting Fig. 6,
where the temperature (Fig. 6a), mass fraction of char and carbon

in the bed, wch,b and wc,b (Fig. 6b), and residence time of the char, s
(Fig. 6c), are plotted as a function of throughput for the same conditions as in Fig. 5. Fig. 7 gives the corresponding main species in
the gas during variation of Th, showing that CO and H2 decrease,
whereas H2O and CO2 increase, leading to reduction of the efficiency of the processes at higher Th.
The small variation of char conversion with Th indicates that,
for a given ER, a QEM could have been used to predict the gas composition with a constant value of char conversion for the whole
range of Th. However, the actual value of Xch to be used has to be
calculated for each ER at least once with a model such as the one
developed here. The actual value depends much on the reactivity
and physical characteristics of the char, such as attrition, and average size of char particle in the bed. Therefore it is difficult to determine Xch without a char predictor, which is sensitive to operating
conditions. In addition, these conclusions are valid when 1/s2 is
zero (no mechanical removal is applied) and where the bed is operated with large enough char particles to make the entrainment
small compared to attrition. In other cases the results may change
drastically, as we will demonstrate below by allowing for variation
of the rate of bottom ash discharge. Once again, this conclusion
supports the opinion that a char predictor inside a QEM tool is
needed.
3.2.3. Effect of rate of bottom ash discharge
The above discussion was restricted to an FBG operating without extraction of bed material (1/s2 = 0). In this mode of operation
only the elutriation of char (carbon loss in fly ash) limits the char
conversion in the reactor. This is the usual case during operation
with low-ash fuel, such as wood. However, when processing fuel
with high ash content or when the ash contains impurities that
can lead to sintering, control of bed inventory affects the char content in the gasifier by the removal of bottom ash at a constant rate

given by 1/s2. This situation is analyzed in Figs. 8–10.
Fig. 8 shows the rate of solids removal 1/s2, which maintains
the mass fraction of char in the bed at a value of wch,b,crit at different
ER and Th. The analysis in the figure is made for wch,b,crit > 0.05, a
reasonable lower limit in practise. 1/s2 = 0 are the cases without
bed removal, which were analyzed in previous figures. It is observed that the mass fraction of char in the bed is higher at lower
ER (lower temperature) and that the influence of ash extraction is
higher for lower ER. At a given ER, the rate of ash removal to maintain the bed below a limit wch,b,crit, is higher as the throughput increases, except for very low rates of removal (1/s2 ? 0) where this
behavior is the opposite.
The corresponding char conversion, temperature and residence
time of the char, as a function of the bottom-ash removal constant


430

A. Gómez-Barea, B. Leckner / Fuel 107 (2013) 419–431

1000

3

Char residence time (τ), h

ER=0.30
950

0.8

Temperature (T), ºC

Char conversion (Xch), kg/kg

1

0.25

0.6
0.4

0.2

0.2
0

900

ER=0.30

850

0.25
800

0.2
750
700

0

0.5

1

1/ τ2, h

1.5

0

0.5

-1

1

1/ τ2, h

(a)

1.5

2.5
2

ER=0.20
1.5

0.25

1

0.5
0

0.30
0

-1

(b)

0.5

1

1/ τ2, h

1.5

-1

(c)

Fig. 9. Char conversion (a), temperature (b) and char residence time (c) as a function of the constant rate of bottom ash discharge (1/s2) for various ER (0.20 (—), 0.25 (—) and
0.30 (Á Á Á)). For each ER, two throughputs are displayed: Th = 500 (black) and 1000 (red). (For interpretation of the references to color in this figure legend, the reader is
referred to the web version of this article.)

conversion is not critical for the estimation of the main compounds
in the produced gas in conventional FBG. Though, a good estimate
of the yield of methane during devolatilization is a key factor for
the prediction of the methane in the produced gas. The yield of

methane varies with fuel type but not much with the operation
conditions. The conditions in the reactor, and thus the composition
of the gas and the efficiency of the process, are greatly influenced
when bottom ash is removed from the bed by bed extraction to
maintain the ash proportion in the reactor below some specified
limit. As demonstrated, the model developed here is able to predict
the changes in reactor performance with operating conditions.
Simple QEM with a given char conversion cannot be used for simulating FBG because they do not have the prediction ability to capture these effects.

Molar fraction in wet gas (%v/v)

0.25

0.2

CO
0.15

H2
CO2

0.1

H 2O
0.05

CH4
0

0

0.5

1

1.5

4. Summary and conclusions

-1

1/τ2, h

Fig. 10. Gas composition of main species in the gas as a function of the time
constant of bottom ash removal, s2 for various Th = 500 kg/m2 h and ER = 0.25.

rate 1/s2, are presented in Fig. 9. It is shown that the char conversion (Fig. 9a) decreases with 1/s2 (more carbon is lost by removing
more bed material). The temperature is seen to rise with 1/s2 up to
a certain value of 1/s2, and then it falls (Fig. 9b). The residence time
of the char decreases significantly as the rate of bottom-ash removal is increased (Fig. 9c), yielding lower char conversion, consistent with the conversion trend presented in Fig. 9a. The
composition of the gas as a function of 1/s2 for given ER and Th
is presented in Fig. 10, revealing the great influence of the rate of
bed extraction on the composition of the gas produced. The
amount of combustible gas is reduced a great deal with decrease
of 1/s2, lowering the heating value of the gas and the gasification
efficiency.
3.2.4. Concluding remarks
Overall, it is concluded that the most important parameter to
estimate in an FBG is the char conversion, because it determines
the temperature in the gasifier and the amount of carbon in the

gas-phase. The approach to WGSR equilibrium affects the gas composition markedly, but its impact is less significant than char conversion. Tar concentration in the gas is small and methane is
insignificantly converted, so precise prediction of tar and methane

A model has been developed to predict the performance of biomass fluidized bed gasifiers (FBG). The model uses an equilibrium
submodel to calculate the gas-phase composition, corrected with
kinetics sub-models to predict conversion processes that deviate
from equilibrium. A carbon predictor is implemented as a submodel, accounting for chemical conversion, attrition, elutriation and
mechanical removal of ash, allowing estimation of char conversion
in the gasifier under different operating conditions. The model improves the existing quasi-equilibrium models (QEM) in the sense
that essential information, such as the conversions of char and
water–gas-shift reaction are estimated as a part of the model in
contrast to other models, where these variables are input or are
based on correlations, useful only for specific systems. This aspect
makes the model developed here predictive, in contrast to existing
QEM. The model results were compared with measurements from
tests conducted in a pilot plant with various gasification agents.
Furthermore, a sensitivity analysis was made by simulating an
FBG under various operation modes (with and without removal
of bottom ash), revealing their great effect on gas composition
and char conversion in the gasifier. The great improvement with
respect to quasi-equilibrium models together with its simplicity
compared to more detailed models (the number of input data is
greatly reduced), makes the present model a compromise between
prediction and complexity, and therefore, an ideal tool for optimization and scale up free of complex codes.
The model can be applied to any stand-alone bubbling FB and
with minor modifications for circulating units. Besides the opera-


A. Gómez-Barea, B. Leckner / Fuel 107 (2013) 419–431

tional form (flowrate of biomass and gasification agent), the model
needs the following inputs: fuel properties, kinetics (the most relevant are those for the char and WGSR reactions), reactor geometry
(bed and freeboard diameter and length) and mass inventory in the
bed. The model can be applied to FBG of different scales and forms
of operation. The modular structure of the code permits the user to
modify the model at convenience, including the adjustment of kinetic data obtained in the lab when a given biomass is to be tested.
Acknowledgements
The authors acknowledge the European Commission and Commission of Science and Technology (CICYT) of Spain and Junta de
Andalucía for their financial support.
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