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

2-D Modeling of thermo-kinetics coupled with heat and mass transfera UR: Micro Electro Thermal Systems-ENIS, IPEIS, University of Sfax, B.P: 1172-3018 Sfax, Tunisia b LASMAP, Polytechnic

2-D Modeling of thermo-kinetics coupled with heat and mass transfer

a UR: Micro Electro Thermal Systems-ENIS, IPEIS, University of Sfax, B.P: 1172-3018 Sfax, Tunisia

b LASMAP, Polytechnic Engineering School of Tunis, University of Carthage, La Marsa, Tunis, Tunisia

a r t i c l e i n f o

Article history:

Received 3 May 2012

Accepted 9 December 2013

Available online

Keywords:

Biomass

Gasification

Fixed bed downdraft gasifier

Modeling

Kinetics

Heat and mass transfer

a b s t r a c t

A two dimensional modeling is developed in the reduction zone of afixed 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 andfluid 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

1 Introduction

Biomass, including forestry and agricultural residues,

indus-trial, 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

environ-mental 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

Develop-ment 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

tech-nologies The use of either one technology is usually imposed by

some conditions (mainly by feed properties and the desired

application) Thermochemical conversions enable the

trans-formation of biomass into several energy vectors such as

elec-tricity, 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

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 en-gines 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 consid-ered as a process that adds value to low- or negative-value feed-stock 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 experimen-tally 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 devel-opment of two main categories:fixed bed and fluidized bed gasifier Fluidized bed reactors operate with afluidized 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, thefixed bed downdraft gasifier (Fig 1) received great interest due

* Corresponding author Tel.: þ216 98 954 415; fax: þ216 74 246 347.

E-mail addresses: kamel.halouani@ipeis.rnu.tn , kamel_ipeis@yahoo.fr

(K Halouani).

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Renewable Energy 66 (2014) 288e298

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

experi-ments 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

dur-ing gasification is of fundamental importance in the description of

the process Moreover, the developed kinetic models in literature

assume one dimensional variation of thefields along the reduction

zone[6e8,11,12,14e18] Di Blasi[11]developed an unsteady

nu-merical model to simulate biomass gasification process in a

strati-fied downdraft gasifier The flaming pyrolysis step was formulated

usingfinite 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

imple-mented 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

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,

CH4and 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 tem-perature profile[15] The model was used to evaluate the perfor-mance of the gasifier in term of the heating value of the producer gas, the gas production rate, and conversion efficiency The ob-tained 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 approxi-mately 15 min of operating time and heat losses through the reactor walls were found to be important The 2D model estab-lished 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 con-version process, and a better understanding of this step is essential

to the design and operation of a biomass gasifier A two dimen-sional model for the reduction zone is therefore implemented using chemical kinetics andfluid flow dynamics equations Producer gas composition and temperaturefields are then computed and pre-dicted in the conical shaped reduction zone

Biomass input

Air input

Reduction zone

Pyro-oxidation zone

Syngas outlet

Fig 1 Schematic diagram of an air blown downdraft gasifier.

2 Model development

2.1 Model description

The present model deals with the reduction zone (Dimensions

given inTable 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 gasflow (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

hetero-geneous 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]

- All the sub processes (pyrolysis, oxidation, tar cracking and reforming) have been achieved before the reduction zone

[6,7,9]

- The gasflowing in the reduction zone consists of six species: N2,

CO, H2, CO2, H2O, and CH4which lumps traces of light hydro-carbons[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 theflaming-pyrolysis step)[13]

- Conversion of bio-char particles in the reduction zone is ach-ieved following the shrinking unreacted core model (external surface based reaction)[14]

- Ideal gas law is applicable to all gas species

2.3 Chemical model of the pyrolysiseoxidation zone

In the downdraft gasifier, biomass feed undergoes pyrolysis and oxidation steps before it gets reduced in the gasification zone Py-rolysis 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 calledflaming-pyrolysis or pyro-oxidation 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:

CHyOzþ w H2Oþ t O2þ 3:76 t N2/x Char þ x1COþ x2CO2

þ x3H2Oþ x4H2þ x5CH4þ x6N2

(1)

Six equations are required to calculate the values of the un-knowns x, x1, x2, x3, x4and 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 equilib-rium of the water gas-shift reaction(5)and the methanation re-action(6), while the char yield is obtained as the ratio of thefixed 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:

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

COþ H2O4K1

With

K1 ¼ PH 2:PCO 2

PH2O:PCO ¼ x4:x2

x3:x1

(5.1)

The equilibrium of the methanation reaction is given by:

Table 1

Geometrical characteristics of the gasification zone [8]

z

r

pyrolysis and oxidation products

product gas

Fig 2 Physical model of the gasification zone.

M.A Masmoudi et al / Renewable Energy 66 (2014) 288e298 290

Cþ 2H2 4K2

With

K2 ¼ PCH 4

P2

H 2

¼ x5

x2:X6

i¼ 1

The equilibrium constants K1and K2are functions of

tempera-ture Their expressions are derived using data reported in Sharma

[9] The char fraction is derived as[12]:

xþ x5 ¼ FC

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

reactants

xiHiðT0Þ  X

products

xiHiðTÞ ¼ X

products

xi

ZT

T 0

Cp iðTÞdT þ Qsides

(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 thefinal 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

func-tions on MATLAB (fsolve for example) The convergence criterion

was set equal to 109and the obtained data was stable and

inde-pendent 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

2.4 Kinetic scheme of the reduction zone

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

phe-nomena Based on existing literature[6,7,10,12],five chemical

re-actions 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

en-thalpies is given inTable 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:

Ri ¼ Ct CRF  Aiexp



Ei RT



 yproductyreactant

Keq;i

!

(9)

where Ctis the sum of all species concentrations, Keq,iis the

equi-librium constant of each reaction and is a function of local

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 andfinal 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 tofit 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 tempera-turefield 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 rela-tively 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)

It is well known that the gasification rate of large bio-char particles in a packed bed is affected by intra-particle mass diffu-sion 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 experi-mental data on Thermo-Gravimetric Analyzers (TGA) in order to assess the mass diffusion resistance that takes place during bio-char gasification at various operating conditions (different parti-cle 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 bio-char bed when calculating the gasification rates of large size par-ticles Its value is calculated using the following expression[20,21]:

h ¼ Ri;app

Ri;int ¼ 1f

 1 tanhð3fÞ

1

3f



(11)

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

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

factor (s1)

Activation energy (kJ/mol)

Enthalpy (kJ/mol)

1 Water gas C þ H 2 O4CO þ H 2 15,170 121.62 135.8

2 Boudouard C þ CO 2 42CO 36.16 77.39 169.8

3 Methanation C þ 2H 2 4CH 4 0.004189 19.21 91

4 Steam reforming

CH 4 þ H 2 O4CO þ 3H 2 0.07301 36.15 226.6

5 Water gas Shift

CO þ H 2 O4CO 2 þ H 2 0.02824 32.84 40

f ¼ dp*

0

@Aiexp



E i RT



Dj;eff

1 A

0:5

(12)

where dpis the particle diameter and Dj,effis the effective diffusion

of the reactant in the void space of the char particle

2.5 Mathematical formulation

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:

1

r

vðεrrUÞ

vðεrWÞ

X

j

Energy conservation for the gas and solid phases is respectively:

εrUCpvTg

vr þ εrWCpvTg

vz ¼

1 r

v vr



rεlgvTg

vr



þ v vz



εlgvTg

vz



þX5

4

DHiRi hSa



Tg Ts



 Qfew (14)

1

r

v

vr



ð1εÞrlsvTs

vr



þv vz

 ð1εÞlsvTs

vz



þX3

1

DHiRiþhSa



TgTs



¼0 (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:

hsg ¼ x lg

dpNu¼ xlg



2þ 1:1Re0:6Pr1=3

where Nu, Re and Pr are respectively the Nusselt, Reynolds and

Prandtl numbers.zaccounts 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:

εUvCvrjþ εWvCvzj ¼ 1rvrv

 εrDj

vCj

vr



þvzv



εDj

vCj

vz



Momentum equations of the gasflow within the porous domain

in the radial and axial directions are respectively:

εrUvU

vrþ εrWvU

vP

vr  εm

KUþ1:75 1  εð Þr

dpε3 U2

þm vrv1rv rUð Þvr þv2U

vz2

!

(18)

εrUvW

vr þ εrWvW

vP

m

KWþ1:75 1  εð Þr

dpε3 W2

þm 1rvrv rvW

vr

þv2W

vz2

!

(19)

2.6 Boundary conditions

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 (Section2.3) Given the relatively large particle size used in the experiments of Jayah et al.[8], a temper-ature 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 airflow 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 Tables3and4

At the exit of the reduction zone, we assume a fully developed condition for all variables:

vW

vU

vz ¼

vCi

vz ¼

vTg

vz ¼

vTs

At the reactor inclined wall (Fig 2), heat losses by conduction, convection and radiation are considered An overall thermal resis-tance coefficient Rtis computed to assess the heat lossflux through the radial boundary

Rt ¼ h1

int:Sþ 2

ewall

lwallSþ eair

lairS

hextSþ ε:s:ST2

wallþ T2 amb



Qfw ¼ Tf Tamb

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

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

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

Gases fractions y CO y CO 2 y H 2 y CH 4 y H 2 O y N 2

Input value (wet basis %)

11.0830 9.8156 10.0448 0.0034 20.8919 48.1613 Input value

(dry basis %)

14.0100 12.4079 12.6976 0.0041 e 60.8804 M.A Masmoudi et al / Renewable Energy 66 (2014) 288e298

292

vr ¼

vTg

vr ¼

vTs

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

thefinite volume method (SIMPLE algorithm) with a staggered

non-uniform grid

A FORTRAN code was then established to perform the

calcula-tions 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 calculationflow chart used in

the code establishment is presented inFig 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%

2.8 Properties evaluation

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

de-pends on the particles size distribution, is calculated using the

correlation reported by Sharma[24]:

εbed ¼ 0:5  0:2*



1dp

dR



(25)

where dRis the reactor diameter

The thermal conductivity and dynamic viscosity of the gas

mixture are respectively given by Refs.[11,25]:

The isobaric heat capacity of the gas mixture is taken from Ref

[26]and expressed as:

Cp;mix ¼ Xi¼ 6

i¼ 0

yi

where the isobaric molar heat capacity of each gas is calculated

using a polynomial equation[26]:

Cp;i ¼ X

j ¼ 6

j ¼ 0

aj



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]:

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

DiN2 ¼ D0

iN 2



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

Table 4

Parameters at the inlet of the gasification zone.

Parameter T g,in (K) T s,in (K) P (atm) W in (m s1) U in (m s1)

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

Variables declaration Properties initialization

Start solution

Yes

Calculate the residues to check the convergence

Print final results

No

Set up the cylindrical grid

Calculate reaction rates, source terms…

Calculate physical properties and diffusion coefficients

Call momentum solver Call pressure correction solver

Call temperatures solver Call species solver

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



Ts

1000



þ 0:063



Ts

1000

2

þ16sT3 s

3 Model validation

In this section, the results obtained from the developed

nu-merical 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 tofit 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

tem-perature using the pyro-oxidation sub-model and adopting an

exponential function while adjusting its related constants to match

the experimental data

Fig 5shows the temperaturefield produced by the elaborated

model using an exponential function for the CRF as:

CRF ¼h: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 andfluid phases and the endothermicity of the overall

pro-cess 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

pyro-oxidation, 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

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 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 temperaturefield inside the reduction zone

Fig 7shows the evolution of the gas temperature profile inside the gasification zone The first plot 7.a represents the gas temper-aturefield 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 di-minishes The gas temperature drop is then attenuated at the sec-ond half part of the bed Indeed, the gas temperature in this region

is getting closer to the solid temperature until the thermal equi-librium is established Moreover, the endothermic gasification re-actions 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 thefluid 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

M.A Masmoudi et al / Renewable Energy 66 (2014) 288e298 294

distribution over the reduction zone except at the end of the char

bed where a slight thermal gradient is observed The lowest

tem-perature 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

condi-tions The axial distribution is similar to the previous simulation

with a high and moderate variation at respectively, thefirst 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 temperaturefield

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

be-tween the solid andfluid 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 gasflow 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

equilib-rium.Fig 8exhibits thisfinding: it is shown that the solid

tem-perature increases at the top of the gasification zone then it tends to

decrease in the remaining part of the bed The higher char tofluid

heat capacities ratio makes the increase of the solid phase

tem-perature 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 inFig 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 thefluid phases are close and consequently the convective term is minimized

4.3 Analysis of gas concentrationfields inside the reduction zone

Fig 9shows the evolution of hydrogen and carbon monoxide concentrations inside the gasification zone It is shown that the hydrogen and carbon monoxide concentrations increase progres-sively and constantly along the reduction zone At the inlet of the bed, the kinetics are the driving terms in the reactions rates ex-pressions 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 prin-cipally to the catalytic effect of the ash which promotes the gasi-fication reactions in the remaining zone of the bed In addition, the char particles shrink along the reduction zone and the effectiveness factor increases InFig 9, one can also observe that the concen-trationfields have the same trend for both gases The radial dis-tribution 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 bot-tom 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

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).

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

gasification zone as: _min ¼ _moutþ converted char

The conversion rate is given by:

Fig 10shows the conversion rate of bio-char particles along the

reduction zone It is shown that the overall conversion and the

con-version 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 How-ever, 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 inFig 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).

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

M.A Masmoudi et al / Renewable Energy 66 (2014) 288e298 296

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 gasflow 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

non-homogenous distribution of the gasflow 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

satis-factory 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

tem-peraturefield and the reactivity of the char The simulated

distri-butions 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

devel-oped 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

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

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Glossary

Symbols

A i : frequency factor, s1

C j : concentration of specie j, mol m3

C p : heat capacity, J kg1K1 Fig 10 Conversion rate of bio-char along the gasification zone.