2D Modeling of thermokinetics coupled with heat and mass transfer in the reduction zone of a fixed bed downdraft biomass gasifier

Renewable Energy 66 (2014) 288e298

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Renewable Energy
journal homepage: www.elsevier.com/locate/renene

2-D Modeling of thermo-kinetics coupled with heat and mass transfer
in the reduction zone of a fixed bed downdraft biomass gasifier
Mohamed Ali Masmoudi a, Melik Sahraoui b, Najla Grioui a, Kamel Halouani a, *
a
b

UR: Micro Electro Thermal Systems-ENIS, IPEIS, University of Sfax, B.P: 1172-3018 Sfax, Tunisia
LASMAP, Polytechnic Engineering School of Tunis, University of Carthage, La Marsa, Tunis, Tunisia

a r t i c l e i n f o

a b s t r a c t

Article history:
Received 3 May 2012
Accepted 9 December 2013
Available online

A two dimensional modeling is developed in the reduction zone of a fixed bed downdraft biomass
gasifier based on mass, energy and momentum conservation equations written for the solid and fluid
phases and coupled with chemical kinetics. Kinetics parameters are derived from previous works and an
effectiveness factor was used in the reaction rate correlation to quantify the mass transfer resistance in
the bed. The obtained numerical results are compared with experimental and numerical data from
literature and a reasonable agreement is observed. Fields of temperature, gaseous concentrations are

investigated for the two-dimensional domain. Results show that the solid and fluid inlet temperatures to
the reduction zone and the reactivity of the bio-char including the effectiveness factor are the main
variables affecting the conversion of char to syngas in the gasification zone of the fixed bed reactor.
Ó 2013 Elsevier Ltd. All rights reserved.

Keywords:
Biomass
Gasification
Fixed bed downdraft gasifier
Modeling
Kinetics
Heat and mass transfer

1. Introduction
Biomass, including forestry and agricultural residues, industrial, human and animal wastes, is one of the most important
renewable energy sources in the world. Upgrading available
biomass feeds into efficient and clean way has several environmental and economical benefits. Indeed, it could substitute for the
traditional fossil fuels in several energy applications, help in the
green house gases mitigation and participate in Clean Development Mechanism (CDM), while it could avoid problems related to
wastes disposal.
Energy recovery from biomass can be achieved through several
ways including biological and thermochemical conversion technologies. The use of either one technology is usually imposed by
some conditions (mainly by feed properties and the desired
application). Thermochemical conversions enable the transformation of biomass into several energy vectors such as electricity, liquid (bio-oil) and gaseous fuels. Particularly, gasification
permits the conversion of solid biomass into a mixture of
combustible gases (essentially CO and H2) called producer gas or
syngas, which is easier and more versatile to use than the original
biomass. In fact, it can be burned to produce heat or used as a fuel
* Corresponding author. Tel.: þ216 98 954 415; fax: þ216 74 246 347.
E-mail

addresses:
,

(K. Halouani).
0960-1481/$ e see front matter Ó 2013 Elsevier Ltd. All rights reserved.
/>
for gas engines and gas turbines [1]. Otherwise, it can be used as
fuel in Solid Oxide Fuel Cells (SOFC) where it was shown more
efficient than conventional fuels [2].
The low or medium heat value of syngas can also satisfy the
growing demand of fuels for the transport sector. Indeed, it could
serve as an alternative fuel for the internal combustion engines.
Firstly, it can substitute a considerable amount of diesel oil in engines operating on dual fuel mode [1]. Secondly, it can be used for
the production of the 2nd generation bio-fuels using the Fischer
Tropsch synthesis [3]. Consequently, gasification could be considered as a process that adds value to low- or negative-value feedstock by converting it into marketable fuels and products [4]. These
applications, among others, indicate that its potential would be
enhanced in the next future.
Many researchers studied the gasification process experimentally. Different reactors were developed and tested to achieve the
conversion. Basically, gasifiers can be classified according to reactor
design, gasification agent, heat source or gasifier pressure [4].
Several designs were implemented which resulted in the development of two main categories: fixed bed and fluidized bed gasifier.
Fluidized bed reactors operate with a fluidized mixture of biomass
and a bed material (inert sand or catalyst); they are usually used for
large scale power generation: Integrated Gasification Combined
Cycle (IGCC). Fixed bed reactors are gaining growing attention as
they are simple and suitable for small scale use [5e7]. Particularly,
the fixed bed downdraft gasifier (Fig. 1) received great interest due


M.A. Masmoudi et al. / Renewable Energy 66 (2014) 288e298

Biomass input

Pyro-oxidation
zone
Air input

Reduction zone
Syngas outlet
Fig. 1. Schematic diagram of an air blown downdraft gasifier.

to its numerous advantages. In fact, it is comparatively a cheap and
practical facility for biomass gasification [6], and it is also known for
the production of syngas with low tar content. Banapurmath and
Tewari [1] quoted that downdraft gasifier coupled with an IC engine
is a good choice for moderate quantities of available biomass, up to
500 kW of electric power. Puig-Arnavat et al. [4] reported that 75%
of the manufactured gasifiers in the world are of downdraft gasifier
type.
Modeling of gasification process within fixed bed gasifiers has
been also studied extensively in the literature [6e18]. Two main
approaches were used: the equilibrium and kinetic modeling. The
equilibrium models are based on thermodynamic parameters and
the chemical equilibrium of the process. The gas composition
resulting from the equilibrium computations is often not equal to
the real chemical composition at the exit of the gasifier [6]. Kinetic
models are based on the chemical kinetics of the heterogeneous
char-gas reactions and are more accurate and representative of the
real phenomena. They are used to describe the thermochemical
processes using kinetic rate correlations obtained from experiments and permit better simulation of the conversion. However,

kinetic models must include detailed transport phenomena since
char gasification is a process controlled by both chemical reactions
and internal and external mass and heat transfer processes. Indeed,
interaction between the chemical and transport mechanisms during gasification is of fundamental importance in the description of
the process. Moreover, the developed kinetic models in literature
assume one dimensional variation of the fields along the reduction
zone [6e8,11,12,14e18]. Di Blasi [11] developed an unsteady numerical model to simulate biomass gasification process in a stratified downdraft gasifier. The flaming pyrolysis step was formulated
using finite rate kinetics of primary and secondary pyrolysis, and
combustion of carbon monoxide, hydrogen, tars and methane. The
kinetics of char combustion and gasification were also implemented into the mathematical model and all of them were coupled
with the mass and energy equations, allowing the investigation of
the important operational parameters on the dynamic behavior of

289

the reactor, particularly the structure of the reaction front and
quality of the producer gas. Giltrap et al. [6] developed a one
dimensional model for the reduction zone of a downdraft biomass
gasifier to predict the composition of the syngas under steady state
operations. Assuming a constant value of the char reactivity factor
and cracking of pyrolysis products into equivalent amount of CO,
CH4 and H2O limited the accuracy of this model, and resulted in an
over prediction of the methane fraction at the outlet of the
reduction zone. Babu and Sheth [7] modified Giltrap’s model by
incorporating a variation of the char reactivity factor. The finite
difference method was used to predict the temperature and gas
composition profiles along the reduction zone of the downdraft
gasifier. It was found that an exponential varying of the char
reactivity factor gives the better result for both the temperature
field and the gas composition when compared to the experimental

data of Jayah et al. [8]. Recently, Roy et al. [12,15] investigated the
gasification of different biomass feedstocks (blend of cow dung and
wood, three woody biomasses and different agricultural wastes) in
a downdraft gasifier to assess the feasibility of animal wastes
gasification and the suitability of the producer gas for the running
of an IC engine. They developed a one dimensional numerical
model for the reduction zone and adopted a variable char reactivity
factor that combines a constant term, linear and exponential
functions to achieve a better prediction of the experimental temperature profile [15]. The model was used to evaluate the performance of the gasifier in term of the heating value of the producer
gas, the gas production rate, and conversion efficiency. The obtained results showed that the use of cow dung as a feedstock for
biomass gasifiers is not technologically viable unless it is used as a
supplement fuel to the woody biomass in the gasifier. Moreover,
the producer gas heating value was particularly changing with
respect to the biomass feed which imply an adjustment of the
rating of the engine coupled to the gasifier. Gordillo and Belghit [16]
developed a one dimensional numerical model to simulate the
gasification of a biochar packed bed in dynamic and steady states.
The model is based on mass and energy balances and the chemical
kinetics with an exponential char reactivity function. Heat was
provided externally to the downdraft gasifier using concentrated
solar energy on an emitter at the top of the bed, which improved
the process efficiency. Simone et al. [17] experimented a pilot scale
air blown throated downdraft gasifier. They also implemented a
one dimensional model with distinct temperatures for the solid and
fluid phases to simulate the behavior of the reactor at different
operating conditions. The model allows the investigation of the
effect of operating parameters on the loading and the performance
of the process. An experimental and modeling work was conducted
by Janajreh and Al Shrah [18] on a small scale batch type downdraft
gasifier. A near steady state was observed to appear after approximately 15 min of operating time and heat losses through the

reactor walls were found to be important. The 2D model established using commercial CFD software allowed the simulation of
the gas distribution within the gasifier. An extensive and detailed
review of these models and others was previously presented by
Puig-Arnavat et al. [4].
The objective of the present work is to study numerically the
thermo-kinetics mechanisms coupled with transport phenomena
during bio-char particles gasification in a conical shaped reduction
zone of a downdraft gasifier (Fig. 2). Bio-char gasification, being the
slower and the rate limiting step, usually controls the overall conversion process, and a better understanding of this step is essential
to the design and operation of a biomass gasifier. A two dimensional model for the reduction zone is therefore implemented using
chemical kinetics and fluid flow dynamics equations. Producer gas
composition and temperature fields are then computed and predicted in the conical shaped reduction zone.


290

M.A. Masmoudi et al. / Renewable Energy 66 (2014) 288e298

- All the sub processes (pyrolysis, oxidation, tar cracking and
reforming) have been achieved before the reduction zone
[6,7,9].
- The gas flowing in the reduction zone consists of six species: N2,
CO, H2, CO2, H2O, and CH4 which lumps traces of light hydrocarbons [6,7,9].
- Temperature difference between gas and solid phases is of about
400 K at the inlet of the reduction zone [8,14,23].
- Bio-char consists of pure carbon and is constantly renewed
[6,7].
- Particle size at the inlet of the gasification zone is estimated to
the half of the initial size at the reactor inlet (shrinking caused
by the flaming-pyrolysis step) [13].

- Conversion of bio-char particles in the reduction zone is achieved following the shrinking unreacted core model (external
surface based reaction) [14].
- Ideal gas law is applicable to all gas species.

pyrolysis and oxidation
products

r

z

2.3. Chemical model of the pyrolysiseoxidation zone

product gas
Fig. 2. Physical model of the gasification zone.

2. Model development
2.1. Model description
The present model deals with the reduction zone (Dimensions
given in Table 1) of a downdraft gasifier (tested experimentally by
Jayah et al. [8]). It consists of a fixed bed of bio-char particles
crossed by a reactive gas flow (Fig. 2). As the reactive gas coming
from the upper zones (pyrolysis and oxidation) flows across the
bio-char bed, the conversion of char to producer gas is achieved
involving several chemical and transport phenomena: the heterogeneous gasification reactions of steam, carbon dioxide and
hydrogen with the bio-char; the homogeneous reactions between
gaseous species; fluid flow in the void spaces and pressure drop
across the packed bed caused by surface and form drag forces; heat
transfer by conduction, radiation and convection between the solid
and gas phases and heat losses through the reactor walls;

convective and diffusive transport of species in the void spaces. The
increase of hydrogen and carbon monoxide concentrations at the
exit of the gasifier is directly governed by the interaction between
these phenomena.
2.2. Model assumptions
The elaborated model is based on the following simplifying
assumptions:
- The model is two-dimensional and axisymmetric.
- The gasifier is assumed to load in steady state conditions:
the analysis is performed after the transient initial period
[6,7,14].

In the downdraft gasifier, biomass feed undergoes pyrolysis and
oxidation steps before it gets reduced in the gasification zone. Pyrolysis and oxidation are characterized by intensive chemical
phenomena. In addition, their fronts occur simultaneously in the
same region and they may overlap. They are therefore described in
some papers by a single process called flaming-pyrolysis or pyrooxidation process [8,9,12].
In the present work, this pyro-oxidation step in the gasifier is
modeled using a single global reaction scheme [12]. The products of
this reaction are the bio-char and six gaseous species: N2, CO, CO2,
H2O, CH4 and H2. The whole process of drying, pyrolysis and
oxidation in presence of restricted air is represented by the
following reaction:

CHy Oz þ w H2 O þ t O2 þ 3:76 t N2 /x Char þ x1 CO þ x2 CO2
þ x3 H2 O þ x4 H2 þ x5 CH4 þ x6 N2
(1)
Six equations are required to calculate the values of the unknowns x, x1, x2, x3, x4 and x5. Three of these equations are given by
the mass balances of carbon, hydrogen and oxygen (equations (2)e
(4)). The other remaining equations are derived from the equilibrium of the water gas-shift reaction (5) and the methanation reaction (6), while the char yield is obtained as the ratio of the fixed

carbon and the carbon content (from the elemental analysis of
rubber wood) and is considered to be divided into solid carbon and
methane (7) [12].
Mass balances:

Carbon balance : 1 ¼ x þ x1 þ x2 þ x5

(2)

Hydrogen balance : y þ 2w ¼ 2x3 þ 2x4 þ 4x5

(3)

Oxygen balance : z þ w þ 2t ¼ x1 þ 2x2 þ x3

(4)

The equilibrium of the water gas-shift reaction is given by:
K1

Table 1
Geometrical characteristics of the gasification zone [8].
Characteristic dimension

(mm)

Bed height
Throat diameter
Grate diameter

220
100
170

CO þ H2 O 4CO2 þ H2

(5)

With

K1 ¼

PH2 :PCO2
x :x
¼ 4 2
PH2 O :PCO
x3 :x1

The equilibrium of the methanation reaction is given by:

(5.1)


M.A. Masmoudi et al. / Renewable Energy 66 (2014) 288e298
K2

C þ 2H2 4CH4

(6)

With

K2 ¼

PCH4
2
PH
2

¼

6
x5 X
:
xi
2
x2 i ¼ 1

(6.1)

The equilibrium constants K1 and K2 are functions of temperature. Their expressions are derived using data reported in Sharma
[9]. The char fraction is derived as [12]:

x þ x5 ¼

FC
C

reactants

xi Hi ðT0 Þ À

Table 2
Considered chemical reactions occurring in the gasification zone [7,10,12].
Reaction

Equation

Frequency
factor (sÀ1)

Activation
energy
(kJ/mol)

Enthalpy
(kJ/mol)

1.
2.
3.
4.

C þ H2O4CO þ H2
C þ CO242CO
C þ 2H24CH4
CH4 þ H2O4CO þ 3H2

15,170
36.16

0.004189
0.07301

121.62
77.39
19.21
36.15

135.8
169.8
À91
226.6

CO þ H2O4CO2 þ H2

0.02824

32.84

5.

Water gas
Boudouard
Methanation
Steam
reforming
Water gas
Shift

À40

(7)

The exhaust temperature of this zone is evaluated by the energy
balance. The heat released by the partial combustion would raise
the temperature of the products. Considering a heat loss from the
sides of the gasifier Qsides (thermal convection and radiation), the
overall energy balance for this lumped zone in a steady state can be
written as:

X

291

X

xi Hi ðTÞ ¼

products

X

ZT
Cpi ðTÞdT þ Qsides

xi

products

T0

(8)
The resolution of the system composed by the above non-linear
equations (2)e(4), (5.1), (6.1) and (7) enables the evaluation of the
gases fractions, the char yield and the final temperature at the end
of the pyro-oxidation step. The calculation was performed using the
predefined function Newtonm on MATLAB. This function is a
generalization of the NewtoneRaphson method which is used to
solve single non linear equations. It was found that this function
gives more stable and accurate results than other available functions on MATLAB (fsolve for example). The convergence criterion
was set equal to 10À9 and the obtained data was stable and independent from the initial guess of the solution. The results of this
sub-model will be supplied to the 2D-model of the gasification
zone as input boundary conditions.

temperature (correlation are calculated using data taken from Ref.
[9]). CRF represents the bio-char reactivity factor [6,7].
The appropriate value for the bio-char reactivity factor (CRF)
was discussed by Babu and Sheth [7]. Indeed, the CRF is an intrinsic
property of each bio-char and its value depends on many factors
such as biomass type, pyrolysis conditions (heating rate and final
pyrolysis temperature [19]) and other physical factors (porosity,
inorganic compounds, etc.). It has therefore a great effect on the
loading of the reduction reactions and it is a key variable in the
simulation of the bio-char gasification [7]. Different values and
functions were tested to fit the experimental temperature profile
and to represent adequately the reactivity of the bio-char along the
gasification zone. It was shown that adopting a constant value of
CRF is far from describing the real reactivity because of the multiple
features that affect the char though the gaseous fractions were
comparable with the experimental data. In addition, the temperature field exhibited a different behavior when compared with the

experiment. It was then concluded that adopting a variable CRF
value using an exponentially or at least linearly correlation can
represent the real reactivity behavior of the bio-char [7]. A relatively good agreement between experimental and numerical data is
obtained with the corrected CRF, for both the gas composition and
temperature field along the gasification zone. Accordingly, an
exponential function for the bio-char reactivity factor is selected
here and is multiplied by the effectiveness factor (h).

2.4. Kinetic scheme of the reduction zone

CRF ¼ hÃAÃexpðBÃzÞ

The kinetic mechanism of bio-char gasification is of great
importance in the design and operation of biomass gasifiers. It is
also very crucial in the modeling of gasification process since the
conversion is governed by chemical kinetics and transfer phenomena. Based on existing literature [6,7,10,12], five chemical reactions are considered in the reduction zone to describe the whole
conversion of wood bio-char into producer gas. The set of the
considered reactions and their related kinetic parameters and enthalpies is given in Table 2. The WatereGas and the Boudouard
reactions are the main gasification reactions converting bio-char
into producer gas. The WatereGas shift reaction is an important
homogenous reaction though its extent is low in the condition of
fixed bed gasification.
The apparent reaction rate used for these reactions is considered
to have an Arrhenius law and to be proportional to a reactivity
factor and the difference between molar fractions of the reactant
and product to the equilibrium constant ratio [7,8,12]. It is given by:

It is well known that the gasification rate of large bio-char
particles in a packed bed is affected by intra-particle mass diffusion and the change of the particle size [20]. So the apparent (or
observed) gasification rate is lower than the intrinsic rate (the rate

of chemical reaction without heat and mass-transfer limitations).
The effectiveness factor (ranged between 0 and 1) is derived from
the catalyst theory and used to quantify how much the reaction rate
is lowered as a result of the resistance to internal mass diffusion
[21]. Several authors [20e22] evaluated this factor using experimental data on Thermo-Gravimetric Analyzers (TGA) in order to
assess the mass diffusion resistance that takes place during biochar gasification at various operating conditions (different particle diameters, temperatures, partial pressures of the gasifying
agent, etc.). In this work, the effectiveness factor is used to take
account of the diffusion limitations occurring in the packed biochar bed when calculating the gasification rates of large size particles. Its value is calculated using the following expression [20,21]:



ÀEi
Â
Ri ¼ Ct  CRF  Ai exp
RT

yproduct À

yreactant
Keq;i

!
(9)

where Ct is the sum of all species concentrations, Keq,i is the equilibrium constant of each reaction and is a function of local

h¼




Ri;app
1
1
1
À
¼
f tanhð3fÞ 3f
Ri;int

(10)

(11)

where F is the Thiele modulus which compares the reaction rate to
the diffusion rate and is given by Ref. [21]:


292

M.A. Masmoudi et al. / Renewable Energy 66 (2014) 288e298

 10:5
0
i
Ai exp ÀE
RT
A
f ¼ dp *@
Dj;eff

(12)

where dp is the particle diameter and Dj,eff is the effective diffusion
of the reactant in the void space of the char particle.

εrU



m
vW
vW
vP
1:75ð1 À εÞr 2
þ εrW
¼ À
À ε Wþ
W
vr
vz
vz
K
dp ε 3
!


1v
vW
v2 W
r

þ
þm
r vr
vr
vz2
(19)

2.5. Mathematical formulation

2.6. Boundary conditions

Based on the previous assumptions, the set of conservation
equations formulated in the 2-D cylindrical coordinates system (r,
z) is given by:
The continuity equation for the gas phase:

At the top of the reduction zone (Fig. 2), the input parameters
(gases fractions and gas temperature) are those computed using the
pyro-oxidation sub-model (Section 2.3). Given the relatively large
particle size used in the experiments of Jayah et al. [8], a temperature gradient between solid char particles and the pyro-oxidation
produced gases should be considered at the inlet of the gasification
zone as was concluded by Thunman and Leckner [5]. It was shown
by Tinaut et al. [23] that the temperature gradient occurs suddenly
in the partial oxidation front where the gas temperature rises up
instantaneously while solid temperature exhibits a continuous and
slow increase. Then, the temperature gradient between the two
phases decreases progressively when going down in the char bed.
Based on the multiple simulations and experiments performed by
Tinaut et al. [23] for different working conditions, a temperature
difference of 400 K is considered here at the inlet of the gasification

zone between the two phases.
Initial axial gas velocity was approximated using the air flow
entering to the gasifier [7] while the radial velocity component was
considered nil as the flow converges at the throat level and is
therefore considered unidirectional at the inlet of the reduction
zone. Boundary conditions are reported in Tables 3and 4.
At the exit of the reduction zone, we assume a fully developed
condition for all variables:

X
1 vðεr rUÞ vðεrWÞ
þ
¼
Mj Rj
r
vr
vz

(13)

j

Energy conservation for the gas and solid phases is respectively:

εrUCp






vTg
vTg
vTg
vTg
1v
v
rεlg
εlg
þ εrWCp
¼
þ
r vr
vz
vr
vz
vr
vz
þ

5
X

À

Á

DHi Ri À hSa Tg À Ts À Qfew

4

(14)




 X
3
À
Á
1v
vTs
v
vTs
DHi Ri þhSa Tg ÀTs ¼0
ð1ÀεÞr ls
ð1ÀεÞls
þ
þ
r vr
vz
vr
vz
1
(15)
where h is the interstitial convection coefficient between the solid
and gas phases.
The correlation used for the calculation of this coefficient is that
used by Yang et al. [25] given by:

hsÀg ¼ x

lg
dp

Nu ¼ xlg

À
Á
2 þ 1:1Re0:6 Pr 1=3
dp

(16)

where Nu, Re and Pr are respectively the Nusselt, Reynolds and
Prandtl numbers. z accounts for the effect of the heterogeneous
chemical reaction on the effectiveness of the heat transfer between
the solid particles and the gas mixture, and its value is taken equal
to 0.1 [11].
Species conservation written in terms of concentration is given
by:



εU

vCj
vCj
vCj
1v
εrDj

þ εW
¼
r vr
vr
vz
vr




þ

vCj
v
εDj
vz
vz


þ Rj

(17)

Momentum equations of the gas flow within the porous domain
in the radial and axial directions are respectively:

εrU




m
vU
vU
vP
1:75ð1 À εÞr 2
þ εrW
¼ À
À ε Uþ
U
vr
vr
vr
K
dp ε3
!


v 1 vðrU Þ
v2 U
þ 2
þm
vr r vr
vz

(18)

vTg
vW
vU
vCi

vTs
¼
¼
¼
¼
¼ 0
vz
vz
vz
vz
vz

(20)

At the reactor inclined wall (Fig. 2), heat losses by conduction,
convection and radiation are considered. An overall thermal resistance coefficient Rt is computed to assess the heat loss flux through
the radial boundary.

Rt ¼

1
e
e
þ 2 wall þ air
lwall S lair S
hint :S
1


þ

2
2
ðTwall þ Tamb Þ
hext S þ ε:s:S Twall þ Tamb

Qf Àw ¼

(21)

Tf À Tamb
Rt

(22)

And the no-slip boundary condition is used for the gas velocity:

U ¼ W ¼ 0

(23)

And for the species concentrations and solid and gas temperatures, a Neumann type boundary condition is used:

Table 3
Calculated gases fractions at the inlet of the gasification zone.
Gases fractions

yCO

yH2

yCH4

yH2 O

y N2

Input value
(wet basis %)
Input value
(dry basis %)

11.0830

9.8156

10.0448

0.0034

20.8919

48.1613

14.0100

12.4079

12.6976

0.0041

e

60.8804

yCO2


M.A. Masmoudi et al. / Renewable Energy 66 (2014) 288e298

293

Table 4
Parameters at the inlet of the gasification zone.
Parameter

Tg,in (K)

Ts,in (K)

P (atm)

Win (m sÀ1)

Uin (m sÀ1)

Initial value

1445

1045

1.01

1.175

0

vTg
vCi
vTs
¼
¼
¼ 0
vr
vr
vr

(24)

2.7. Calculation method
The model equations constitute a coupled nonlinear partial
differential equations system. Associated with the above boundary
conditions and the simplifying assumptions, they are solved using
the finite volume method (SIMPLE algorithm) with a staggered
non-uniform grid.
A FORTRAN code was then established to perform the calculations. The specific geometry was respected in the mesh setting. The
code computes fields only for control volumes inside the cone
shaped reduction zone (Fig. 3). The calculation flow chart used in
the code establishment is presented in Fig. 4. Grid sensitivity was

also verified by testing fine grid (21,000 control volumes) and
coarse grid (4000 control volumes) and the mass fraction and
temperature changed by less than 2%.

As we assumed that the conversion is achieved following the
shrinking unreacted core model, the density of the bio-char particle
is considered to have a constant value, while the particle diameter
decreases along the bed. The porosity of the char bed, which depends on the particles size distribution, is calculated using the
correlation reported by Sharma [24]:

εbed

where Dj is the bulk diffusion coefficient of the specie j in nitrogen,
and is function of the local gas temperature [26]:


DiÀN2 ¼ D0iÀN2

P0
P



T
T0

1:5
(31)

The bed porosity and tortuosity change inside the reduction

zone and the variation of their ratio is not predictable as reported in
literature [22,27]. The value of this ratio ranges between 0.15 and

2.8. Properties evaluation



dp
¼ 0:5 À 0:2* 1 À
dR

Fig. 3. Mesh setting in the gasification zone (cone shaped domain).

Variables declaration
Properties initialization

Start solution

(25)
Set up the cylindrical grid

where dR is the reactor diameter.
The thermal conductivity and dynamic viscosity of the gas
mixture are respectively given by Refs. [11,25]:

lgas ¼ 4:8:10À4 :T 0:6717
À7

m ¼ 4:847:10 :T

0:664

Calculate reaction rates, source terms…

(26)
(27)

The isobaric heat capacity of the gas mixture is taken from Ref.
[26] and expressed as:

Calculate physical properties and
diffusion coefficients

Call momentum solver
Call pressure correction solver

Cp;mix ¼

iX
¼6

yi
Cp;i
M
i¼0 i

(28)
Call temperatures solver

where the isobaric molar heat capacity of each gas is calculated

using a polynomial equation [26]:

Cp;i ¼

jX
¼6


aj

j¼0

T
1000

j
(29)

The effective diffusion coefficients for the gases species are
calculated considering the porosity and tortuosity of the packed
bed and neglecting the Knudsen diffusion [22]:

Dj;eff ¼

ε

s

Call species solver

Calculate the residues to check
the convergence

Yes

Print final results

Dj

(30)
Fig. 4. Iterative calculation algorithm.

No


294

M.A. Masmoudi et al. / Renewable Energy 66 (2014) 288e298

0.30 as stated in Ref. [27]. A constant value equal to 0.15 is then used
for this parameter [22].
Finally, the bio-char effective thermal conductivity is taken from
Di Blasi [11] and Sharma [24], and consists on a combination of a
conductive and radiative contribution. It is given by:

ls ¼ 0:0013 þ 0:05






2
Ts
Ts
16sTs3
þ 0:063
þ
1000
1000
3Uex

(32)

3. Model validation

experimentally under the conditions of 16% moisture content,
33 mm of particle diameter and 2.2 air/fuel ratio. The model results
are in a relatively good agreement with the experimental data. An
absolute average deviation of about 2.6% (except methane fraction)
is computed. A slight under prediction of the hydrogen fraction and
over prediction of the nitrogen fraction are observed, while the
carbon monoxide and the carbon dioxide fractions calculated are
practically close to the experimental values. These results confirm
the suitability of the CRF function adopted and the ability of the
developed model in predicting the thermo-chemistry of char
gasification and the heat and mass transfer phenomena within the
downdraft reactor.
4. Simulations

In this section, the results obtained from the developed numerical model are compared with the experimental data of Jayah

et al. [8]. As mentioned previously, Babu and Sheth [7] concluded
that an exponential variation for the CRF gives a better description
of the bio-char gasification process. The exponential function used
in their work was chosen to fit the experimental temperature curve
and to provide a minimum deviation from the experimental values
with a temperature of 1400 K at the entry of the gasification zone.
The same approach is applied here by computing the input temperature using the pyro-oxidation sub-model and adopting an
exponential function while adjusting its related constants to match
the experimental data.
Fig. 5 shows the temperature field produced by the elaborated
model using an exponential function for the CRF as:
CRF ¼ h:15expð0:0037:zÞ along with the experimental data and
the numerical results of Jayah et al. [8]. The shape of the curve is
similar to that obtained by Jayah et al. [8] and other previous papers
[7,8,14]. The temperature decreases along the gasification domain
due to the convection heat transfer that takes place between the
solid and fluid phases and the endothermicity of the overall process. The present model predicts the temperature field slightly
better than Jayah et al. model [8]. The observed deviation could be
explained by the uncertainties of the experimental measurements
in part, and the assumptions made in the model establishment
particularly the achievement of the sub-processes of pyrooxidation, cracking and reforming before the reduction zone.
The model results are further verified by comparing the
composition of the producer gas generated using the developed
model against the experimental data. Fig. 6 shows the gaseous
fractions obtained at the exit of the gasifier numerically and

Fig. 7 shows the evolution of the gas temperature profile inside
the gasification zone. The first plot 7.a represents the gas temperature field simulated with adiabatic reactor walls. This particular
situation is plotted to highlight the effect of the endothermic
gasification reactions solely on the heat transfer between the two

phases inside the conical shaped reduction zone without any
additional heat sink. It is observed that the temperature decreases
continuously along the reduction zone. Particularly, a high variation
occurs at the beginning of the char bed. The observed sharp
decrease is caused by the intensive convection heat transfer taking
place between the gas and solid phases. As the flow progresses
down through the bed, the temperature difference between the
two phases decreases and consequently the convection term diminishes. The gas temperature drop is then attenuated at the second half part of the bed. Indeed, the gas temperature in this region
is getting closer to the solid temperature until the thermal equilibrium is established. Moreover, the endothermic gasification reactions continue to proceed promoted by the increase of the
reactivity of the bio-char and the heat consumed from the solid
phase is subsequently recovered from the fluid phase.
The radial variation of the gas temperature is also shown in
Fig. 7a. The fluid temperature exhibits a quite uniform radial

Fig. 5. Predicted axial temperature profile along the gasification zone compared with
the experimental and numerical data of Jayah et al. [8].

Fig. 6. Comparison between computed gases fractions and experimental data [8].

In this section, the developed two-dimensional model is used to
study the evolution of heat and mass transfer mechanisms inside
the gasification zone in both radial and longitudinal directions.
4.1. Gas temperature field inside the reduction zone


M.A. Masmoudi et al. / Renewable Energy 66 (2014) 288e298

295

Fig. 7. Gas temperature field inside the gasification zone simulated with adiabatic reactor walls (a) and in real conditions (b) (half of the cone shaped domain).

distribution over the reduction zone except at the end of the char
bed where a slight thermal gradient is observed. The lowest temperature is located around the axis of the reactor. Although the
temperature difference is not very pronounced, it shows that the
endothermic gasification reactions have a slight higher activity at
the center of the domain.
Fig. 7b shows the gas temperature simulated in the real conditions. The axial distribution is similar to the previous simulation
with a high and moderate variation at respectively, the first and
second half parts of the bed. On the radial direction, it is shown that
the gas temperature drops when approaching the reactor wall. This
variation shows that the heat losses in that region caused by
thermal conduction, convection and radiation through the gasifier
walls (Equations (21) and (22)) are quite important (without wall
insulation [8]). Moreover, it is shown that the central region of the
reduction zone is insensitive to the heat losses through the radial
boundaries. This could be explained by the importance of the
convective term on the axial direction when compared with the
radial one. The radial thermal diffusion term is also expected to be
of lower importance which limits the radial temperature variation
in the center of the computational domain.
4.2. Solid temperature field
As bio-char particles present an important internal heat transfer
resistance especially when they have a relatively large size (high
Biot number), the assumption of thermal equilibrium state between the solid and fluid phases at the entry of the gasification
zone could be adopted only for small particles (order of a few mm).
Otherwise, the solid temperature would be lower than the gas
temperature, and it would rise progressively through the bed by the
convective gas flow. Thus, at the inlet of the reduction zone, the
fluid phase continues heating up the bio-char particles (already
started in the oxidation front) until reaching the thermal equilibrium. Fig. 8 exhibits this finding: it is shown that the solid temperature increases at the top of the gasification zone then it tends to

decrease in the remaining part of the bed. The higher char to fluid
heat capacities ratio makes the increase of the solid phase temperature largely lower when compared to the decrease of the gas
phase temperature and restricted to the top part of the char bed

(about 2 cm). Then, the solid temperature follows a decreasing
trend resulting from the endothermicity of the gasification
reactions.
The radial solid temperature evolution is also shown in Fig. 8.
The observed radial thermal gradient is caused by the convective
term and the enthalpies of the gasification reactions. At the top of
the bed, the temperature at the center is higher than that on the
boundaries which is similar to the gas temperature distribution.
This could be explained by the effect of the convective term on the
overall solid heat balance. However, at the bottom of the bed, the
opposite trend is observed. The lowest temperature is located at the
center of the domain which could be explained by the influence of
the gasification reactions since the temperatures of the solid and
the fluid phases are close and consequently the convective term is
minimized.
4.3. Analysis of gas concentration fields inside the reduction zone
Fig. 9 shows the evolution of hydrogen and carbon monoxide
concentrations inside the gasification zone. It is shown that the
hydrogen and carbon monoxide concentrations increase progressively and constantly along the reduction zone. At the inlet of the
bed, the kinetics are the driving terms in the reactions rates expressions due to the higher solid temperature, while at the bottom
of the bed, the reactivity of the char increases and becomes the
driving term in the reactions rates as the kinetics and reactants
concentrations are lowered. Indeed, the exponential increase of the
reactivity, which could be attributed to multiple causes but principally to the catalytic effect of the ash which promotes the gasification reactions in the remaining zone of the bed. In addition, the
char particles shrink along the reduction zone and the effectiveness
factor increases. In Fig. 9, one can also observe that the concentration fields have the same trend for both gases. The radial distribution shows that the concentrations are slightly higher at the

center of the bed than in the boundaries except at the bottom of the
computed domain. The increase of the concentrations on the bottom corners could be explained by hydrodynamics of the gas phase:
the gas velocity components are expected to be lower in these
zones causing a partial stagnation and a higher residence time of
the gas.


296

M.A. Masmoudi et al. / Renewable Energy 66 (2014) 288e298

Fig. 8. Solid temperature field inside the gasification zone (a) zoom drawing for detailed distribution (b) (half of the cone shaped domain).

4.4. Bio-char conversion inside the reduction zone
The conversion of bio-char particles in the gasification zone is
not total and a residual mass fraction is retained at the bottom of
the gasifier as shown in the experimental work of Jayah et al. [8].
The residual mass includes the unreacted carbon and the ash
fraction in the bio-char particles which may fall from the grate after
each gasification cycle [8]. The conversion rate of the char particles
X can be calculated using a macroscopic mass balance applied to the
_ in ¼ m
_ out þ converted char.
gasification zone as: m
The conversion rate is given by:

_ in À m
_ out Þ=m
_ in
X ¼ ðm

(33)

Fig. 10 shows the conversion rate of bio-char particles along the
reduction zone. It is shown that the overall conversion and the conversion rate at the axis curves exhibit different shapes. The central
conversion increases rapidly at the beginning the bed and exceeds

60% then the increase is reduced at the remaining zone of the bed. In
fact, both the high temperature and the high reactant concentrations
at the inlet of the bed enhance the char conversion. In the remaining
zone of the bed, gasification reactions continue to proceed but with
lower rate due to the decrease of the reactant concentrations. However, for the overall conversion, the slope of the curve is initially lower
than unity and it increases when going down through the bed. This
variation could be explained by the effect of the geometrical shape of
the gasification zone: the number of bio-char particles increases as
the cross section of the domain increases which compensates the
decrease of the char conversion at the bottom of the bed.
4.5. Effect of particle size on the gas production
The effect of the particle diameter at the inlet of the gasification
zone is presented in Fig. 11. It is shown that the hydrogen and
carbon monoxide fractions decrease when the particle diameter

Fig. 9. Evolution of hydrogen (a) and carbon monoxide (b) concentrations inside the gasification zone (half of the cone shaped domain).


M.A. Masmoudi et al. / Renewable Energy 66 (2014) 288e298

297

composition and the effect of the inlet boundary conditions. The

used kinetic scheme will be ameliorated in a next future work by
taking into account of the thermal and catalytic cracking reactions
of the residual tar along the char bed.
References

Fig. 10. Conversion rate of bio-char along the gasification zone.

increases. In fact, the use of large size particles raises the porosity of
the bed while it decreases the reactive surface and increases
external and internal heat and mass diffusion resistances. Besides,
the effectiveness factor decreases as particle diameter increases
which indicates that diffusion limitations become more important.
Furthermore, preferential ways for the reactive gas flow may also
be created within the bed limiting considerably the extent of the
reduction reactions [27]. As a consequence, the production of the
syngas decreases. In addition, the use of small particles could cause
an important pressure drop inside the reactor and lead to nonhomogenous distribution of the gas flow within the bed. On the
other hand, when large size particles are used, pyrolysis step may
not be completed in its dedicated region in the gasifier.
5. Conclusion
A two dimensional steady state mathematical model for the
reduction zone of a downdraft gasifier was developed and
numerically solved in this paper. The model results show a satisfactory agreement with the experimental data using an exponential
variation for the bio-char reactivity factor and an effectiveness
factor. Simulations have been carried out and it was shown that the
loading of the gasification process is mainly affected by the temperature field and the reactivity of the char. The simulated distributions and fields highlighted the kinetic and the transport
phenomena occurring locally inside the gasification zone. The
particle size was found to have a considerable effect on the
hydrogen and carbon monoxide yield and distribution. The developed model could be considered as a useful simulation tool to study
bio-char gasification by predicting the different fields inside the

gasification zone and the gasifier performance in term of gas

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Glossary

Symbols

Fig. 11. Effect of particles size on the produced gas fractions.

Ai: frequency factor, sÀ1
Cj: concentration of specie j, mol mÀ3
Cp: heat capacity, J kgÀ1 KÀ1
CRF: char reactivity factor


298
Dj: diffusion coefficient, m2 sÀ1
d: diameter, m
Ei: activation energy, kJ molÀ1
h: convective coefficient, W mÀ2 KÀ1
K: bed permeability, m2
M: molar mass, kg molÀ1
_ char mass flow rate, kg sÀ1
m:
P: pressure, Pa
Q: heat sink, W mÀ3
r: radial coordinate, m
R: universal gas constant, J molÀ1 KÀ1
Ri: reaction rate, mol mÀ3 sÀ1
Rt: thermal resistance coefficient, K WÀ1

Sa: specific surface area, mÀ1
T: temperature, K
U: radial velocity, m sÀ1
W: axial velocity, m sÀ1
X: conversion rate
y: gas molar fraction
z: axial coordinate, m
Greek symbols

r: density, kg mÀ3
l: thermal conductivity, W mÀ1 KÀ1

M.A. Masmoudi et al. / Renewable Energy 66 (2014) 288e298
ε: bed porosity
s: bed tortuosity
s: StefaneBoltzmann constant, W mÀ2 KÀ4
U: extinction coefficient, mÀ1
m: gas dynamic viscosity, Pa s
DH: reaction enthalpy, kJ molÀ1
Subscript
amb: ambient
app: apparent
ext: external
f: fluid
few: fluid to wall
g: gas phase
i: reaction
in: inlet
int: intrinsic or internal
j: species

p: particle
R: reactor
s: solid phase
seg: solid to gas
t: total