Renewable Energy 66 (2014) 288e298 Contents lists available at ScienceDirect 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 May 2012 Accepted 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 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: kamel.halouani@ipeis.rnu.tn, kamel_ipeis@yahoo.fr (K Halouani) 0960-1481/$ e see front matter Ó 2013 Elsevier Ltd All rights reserved http://dx.doi.org/10.1016/j.renene.2013.12.016 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 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 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 Physical model of the gasification zone 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 : 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 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 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 PH ¼ x5 X : xi x2 i ¼ (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 Considered chemical reactions occurring in the gasification zone [7,10,12] Reaction Equation Frequency factor (sÀ1) Activation energy (kJ/mol) Enthalpy (kJ/mol) 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 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 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 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  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 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 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 þ εrW ¼ À À ε Wþ W vr vz vz K dp ε !   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 At the exit of the reduction zone, we assume a fully developed condition for all variables: X 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 X À Á DHi Ri À hSa Tg À Ts À Qfew (14)     X À Á 1v vTs v vTs DHi Ri þhSa Tg ÀTs ¼0 ð1ÀεÞr ls ð1ÀεÞls þ þ r vr vz vr vz (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 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 þ εrW ¼ À À ε Uþ U vr vr vr K dp ε3 !   v vðrU Þ v2 U þ þm vr r vr vz (18) vTg vW vU vCi vTs ¼ ¼ ¼ ¼ ¼ 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 e e þ wall þ air lwall S lair S hint :S   þ 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 (23) And for the species concentrations and solid and gas temperatures, a Neumann type boundary condition is used: Table 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 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 vTg vCi vTs ¼ ¼ ¼ 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 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* À dR Fig 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 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) 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 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 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 shows the gaseous fractions obtained at the exit of the gasifier numerically and Fig 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 Predicted axial temperature profile along the gasification zone compared with the experimental and numerical data of Jayah et al [8] Fig 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 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 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 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 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 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 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 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 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 [1] Banapurmath NR, Tewari PG Comparative performance studies of a 4-stroke CI engine operated on dual fuel mode with producer gas and Honge oil and its methyl ester (HOME) with and without carburetor Renew Energy 2009;34: 1009e15 [2] Aloui T, Halouani K Analytical modeling of polarizations in a solid oxide fuel cell using biomass syngas product as fuel Appl Thermal Eng 2007;27:731e7 [3] Kantarelis E, Zabaniotou A Valorization of cotton stalks by fast pyrolysis and fixed bed air gasification for syngas production as precursor of second generation biofuels and 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superficial velocity on the gasification process in a downdraft fixed bed gasifier An experimental and modeling study Fuel Process Technol 2008;89:1076e89 [24] Sharma AK Modeling fluid and heat transport in the reactive, porous bed of downdraft (biomass) gasifier Int J Heat Fluid Flow 2007;28:1518e30 [25] Yang YB, Phan AN, Changkook R, Sharifi V, Swithenbank J Mathematical modelling of slow pyrolysis of segregated solid wastes in a packed-bed pyrolyser Fuel 2007;86:169e80 [26] Todd B, Young JB Thermodynamic and transport properties of gases for use in solid oxide fuel cell modeling J Power Sources 2002;110:186e200 [27] Paviet F, Bals O, Antonini G The effects of diffusional resistance on wood char gasification Proc Safety Environ Prot 2008;86:131e40 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