- Email: [email protected]
A comprehensive two dimensional Computational Fluid Dynamics model for an updraft biomass gasifier
Renewable Energy 99 (2016) 698e710
Contents lists available at ScienceDirect
Renewable Energy journal homepage: www.elsevier.com/locate/renene
A comprehensive two dimensional Computational Fluid Dynamics model for an updraft biomass gasifier Niranjan Fernando*, Mahinsasa Narayana Department of Chemical and Process Engineering, University of Moratuwa, Sri Lanka
a r t i c l e i n f o
a b s t r a c t
Article history: Received 27 June 2015 Received in revised form 19 July 2016 Accepted 21 July 2016
This study focuses on developing a dynamic two dimensional Computational Fluid Dynamics (CFD) model of a moving bed updraft biomass gasifier. The model uses inlet air at room temperature as the gasifying medium and a fixed batch of biomass. The biomass batch is initially ignited by a heat source which is removed after a certain amount of time. This model operates by the heat emitted by combustion reactions, until the fuel is finished. Since the operation is batch wise, model is transient and takes into consideration the effect of bed movement as a result of shrinkage. The CFD model is capable of simulating the movement of interface between solid packed bed and gas free board and this motion is also presented. The model is validated by comparing the simulation results with experimental data obtained from a laboratory scale updraft gasifier operated in batch mode with Gliricidia. The developed model is used to find the optimum air flow rate that maximizes the cumulative CO production. It is found that from the simulation study for the particular experimental gasifier, a flow rate of 7 m3/h maximizes the CO production. The maximum cumulative CO production was 6.4 m3 for a 28 kg batch of Gliricidia. © 2016 Elsevier Ltd. All rights reserved.
Keywords: Gasification Mathematical model Computational Fluid Dynamics Moving bed
1. Introduction With the depletion of fossil fuels, alternative, renewable energy sources are promoted as possible ways of providing the world's energy demand. In this respect, biomass is a promising energy source to produce green energy. It is expected that biomass will provide half of the present world's main energy consumption in future [1] [2]. However, the direct combustion of biomass has several drawbacks to produce thermal energy. These drawbacks include; low heating value of biomass, unsuitability as a fuel for high temperature applications, cannot be used directly as a fuel for internal combustion engines and low versatility. Therefore, corresponding to industrial requirements, biomass is usually converted into a more versatile secondary fuel by thermo-chemical, bio echemical or extraction processes [3] [4]. Gasification is a major thermo-chemical process, which is being used worldwide to convert biomass into a versatile, energy efficient fuel gas called Syngas. This gas is a mixture of carbon monoxide, carbon dioxide, hydrogen, methane, small amount of light hydrocarbons and nitrogen [5]. The gas produced is more versatile than original raw
* Corresponding author. E-mail addresses: [email protected] (N. Fernando), mahinsasa@ uom.lk (M. Narayana). http://dx.doi.org/10.1016/j.renene.2016.07.057 0960-1481/© 2016 Elsevier Ltd. All rights reserved.
biomass fuel and can be used for a variety of applications. Examples are electricity generation, heat generation and hydrogen production [5]. It can also be used as a raw material to produce liquid biofuels [6]. Gasification of biomass is carried out in a special reactor called a gasifier. Number of other factors related to gasifier design and fuel properties significantly affect the produced gas quality. These include; gasifying medium, properties of biomass, moisture content, particle size, temperature of the gasification zone, operating pressure and equivalence ratio [5] [7]. The optimization of gasifiers based on these design factors can be done in two main ways; through experimental approach and through computer aided simulations. Experimental approach follows a series of experiments, usually on scaled down laboratory scale gasifiers. Parameters such as the optimum equivalence ratio can be determined by measuring the gas quality under various equivalence ratios until the best results are obtained. However, experimental approach leads in to a series of difficulties and drawbacks. It is very difficult to perform experimental analysis on pilot scales systems, especially when considering geometry optimization, therefore scaled down models have to be used for experimental analysis. The results obtained on scaled down systems may not fully work on the pilot scale system. The scale down systems cannot be used to determine the effects of biomass particle
N. Fernando, M. Narayana / Renewable Energy 99 (2016) 698e710
Nomenclature A Ac Ad Ag Aj Ar a ap Cg Cs Di;g d Ei fi G h k kg ks km;j Mi mi Nu n Pr p pin Qrad Qi Qsg qr Re Rg;pyro
Specific surface area of packed bed (m1) Specific surface area of char (m1) Specific surface area for gas diffusion (m1) Cross sectional area of gasifier (m2) pre-exponential factor for heterogeneous reactions (m s1 T1) Specific surface area available for radiation (m1) Absorption coefficient of gas phase (m1) Absorption coefficient of solid phase (m1) Heat capacity of gas phase (J kg1K1) Heat capacity of solid phase (J kg1K1) Diffusion coefficient of gas species i (m2 s1) Particle size of biomass (m) Activation energy of reaction i (J mol1) Pre-exponential factor of reaction i (s1) Radiation intensity (W m2) Heat transfer coefficient (W m2 K1) Turbulent kinetic energy (m2 s2) Thermal conductivity of gas phase (W m1 K1) Thermal conductivity of solid phase (W m1 K1) Mass transfer coefficient of species j (m s1) Molecular weight of species i (kg mol1) Specific mass of species i in a computational cell (kg m3) Nusselt number Refractive index of gas phase Prandtl number Pressure (Pa) Inlet pressure (Pa) Radiation heat source (W m3) Initial heat source (W m3) Convective heat transfer rate (W m3) Radiation heat flux (W m2) Reynolds number Rate of release of pyrolytic volatiles (Kg m3 s1)
sizes, as particle size relies on the diameter of the real system. Scaling down the particle size will not produce equivalent results because the packing factors will differ between the two systems. Also, taking measurements inside packed beds is a difficult task considering the higher temperatures present in an operational gasifier. Because of these reasons, the experimental approach is usually difficult, time consuming, costly and the accuracy of the results are also low. Therefore many researchers use the computer based approach to analyze packed bed processes. A large number of research works are available in literature where numerical models are used to optimize packed bed processes [2] [8] [9] [10]. Mathematical models offer certain advantages over the conventional experimental procedure. Mathematical models can produce a large number of data points as compared to fewer experimental data, for example, when measuring temperature, experimental analysis can provide temperatures at only a finite number of locations along the packed bed, while numerical models can provide the complete variation of the temperature profile over the region of interest. With the development of the computer hardware technology, Computational Fluid Dynamics (CFD) is widely applied as a numerical modeling tool [11] [12] [13] [14]. CFD models can be made to match the exact geometry of the real scale gasifier, as a result no
ri ri;hetero ri;homo rm;i rk;i rt;i Shj S∅ Ss;∅ Sg;∅ sij Tg Tg;in Ts Ug Ug;in Us vi Yi;g Yi;air Yi;s
s sp
ε ∅ εg εs
rg rs rj m si;air Ui;air ε
DHi 5
699
Rate of reaction i (Kg m3 s1) Rate of heterogeneous reaction i (Kg m3 s1) Rate of homogenous reaction i (Kg m3 s1) Mass transfer limited reaction rate (Kg m3 s1) Kinetic reaction rate (Kg m3 s1) Turbulent mixing limited reaction rate (kg m3 s1) Sherwood number for species j Source term for property ∅ Source term for property ∅ due to solid phase Source term for property ∅ due to gas phase Reynolds stress tensor (Pa) Gas phase temperature (K) Inlet gas temperature (K) Solid phase temperature (K) Gas phase velocity (m s1) Inlet gas velocity (m s1) Shrinkage velocity (m s1) Stoichiometric coefficient of species i Mole fraction of gas species i Mole fraction of i in air Mole fraction of solid species i Stefan constant (W m2 K4) Scattering coefficient of solid particles (m1) Emissivity of solid particles A general transport property Volume fraction of gas phase Volume fraction of solid phase Density of gas phase (Kg m3) Density of solid phase (Kg m3) Cell density of species j (Kg m3) Dynamic viscosity (Pa s) Average collision diameter (A) Diffusion collision integral Turbulent dissipation rate (m2 s3) Enthalpy of reaction i (J kg1) Vector outer product
scaling down problems arise, in CFD simulations, any number of input parameters can be easily changed at will, including equivalence ratio, particle size, moisture content, feed properties, superficial velocity etc. and system performance can be obtained accordingly. CFD simulations are best suited to perform geometry optimization. A large number of geometrical parameters can be optimized by simply changing the computational mesh. Because of these advantages CFD models are now widely used by researchers around the world as a tool to study and optimize gasification process. In the present work a two dimensional dynamic two fluids CFD model has been developed for an updraft biomass moving bed gasifier. This model uses inlet air at room temperature as the gasification medium and a fixed batch of biomass. The biomass batch is initially ignited by a heat source, which is removed after a certain amount of time. The mathematical model developed in this study is capable of maintaining the operation by the own heat emitted by combustion reactions, until the fuel is finished, as in the real world scenario. Since the operation is batch wise, model is transient and takes into consideration the effect of bed movement as a result of shrinkage. This model is capable to detect the movement of interface between solid packed bed and gas free board in time domain. The two phase model is developed by using
700
N. Fernando, M. Narayana / Renewable Energy 99 (2016) 698e710
the Euler-Euler approach. The overall model consists of several sub models; including reaction models, which govern the reaction rates and compositions of the products, turbulence model for packed bed gas phase and free board, a radiation model for solid phase, a bed shrinkage model, and interphase heat transfer model. In this study, the ultimate mathematical model for the gasifier is converted into a numerical model by using open source CFD tool OpenFOAM. CFD code was developed using Cþþ language and available tools in OpenFOAM package to include all the relevant differential equations and procedures in the mathematical model. The code is developed for two dimensional generic analyses, which is capable to perform two dimensional geometrical optimizations, such as inclusion of tapered sections in gasifier body. To validate the CFD model, simulation results are compared against experimental data from an operational laboratory gasifier. It is found that the model is in good agreement with experimental data.
considered in the present work. A schematic diagram of the presented mathematical model is shown in Fig. 1.
2.1. Governing equations Conservation equations for momentum, energy and species are solved in the gas phase.
v rg εg U g þ V$ rg εg U g 5U g V$mεg VU g vt T 2 rg kI þ S ¼ εg Vp þ V$εg VU g þ VU g 3 With I the second order identity tensor. Gasesolid momentum exchange rate [17];
1 εg S ¼ 150 d2 ε2g
2. Mathematical model A two dimensional, transient, two-phase, Euler-Euler model was developed in the present study. The two phases consist of gas and solid phases. In the Euler-Euler approach, both solid and gas phases are treated as continuums, as a result, motion of individual particles in solid phase are not calculated based on forces acting on them. The motion of solid continuum is resolved using continuity equation. Heat and mass transfer between two phases due to chemical reactions are modelled through source terms of governing equations. Radiation heat transfer is modelled in the solid phase. It is assumed that the optical thickness of gas phase is small and gas does not absorb radiation energy [15]. Gas phase turbulence is modelled using standard k ε model [16]including the effects of porosity. Motion of the biomass bed and solid-freeboard interface is
(1)
2 Ug þ 1:75
rg 1 εg Ug dεg
Ug
vrg εg Cv;g Tg þ V$rg εg Cv;g Tg U g V$ εg kg VTg vt X ¼ hA Ts Tg þ DHi ri;homo þ Rg;pyro Cv;g Ts Tg
(2)
(3)
i
v rg εg Yi;g þ V$ rg εg Yi;g U V$ εg Di;g VYi;g vt X X ¼ ri;homo þ ri;hetero i
(4)
i
Energy conservation and species conservation equations are solved in the solid phase,
Fig. 1. Schematic diagram of the mathematical model.
N. Fernando, M. Narayana / Renewable Energy 99 (2016) 698e710
vrs εs Cs Ts þ V$rs εs Cs Ts U s V$ðεs ks VTs Þ vt X ¼ hA Ts Tg þ DHi ri;hetero þ Qrad þ Qi
(5)
i
X v r εs Y þ V$ rs εs Yi;s U s V$ εs Di;s VYi;s ¼ ri;hetero vt s i;s i
(6)
2.2. Evaluation of source terms Terms appearing on the right hand side of each governing equation represent generation terms of transport property described by the equation. These consist of convective heat transfer between phases, radiation heat transfer terms, heat generation due to chemical reactions and species generation due to chemical reactions. These source terms are evaluated by considering correlations of parameters and kinetic models of chemical reactions. 2.2.1. Inter-phase heat transfer Two main processes are responsible for interphase heat transfer. These are; 1. Convective transfer of heat between two phases as a result of temperature difference between gas and solid phases. 2. During pyrolysis stage, hot volatile gases generated within the porous structure of biomass release into gas phase. These hot volatile gases introduce an energy flow to the gas phase.
701
2.2.2. Radiation heat transfer Radiation heat transfer plays a major role in transporting heat generated in combustion zone from combustion reactions, to top wood layers of the packed bed. This heat provides the energy for thermal cracking of biomass and other endothermic solid phase reactions that take place in top layers. In the present work, P1 radiation model is applied to model radiation in the packed bed with following assumptions [19] [20]. Biomass bed can be treated as an absorbing, emitting, scattering medium of dispersed solid particles. Combustion zone can be approximated by a hot emissive plate located at the bottom of the gasifier. The gas phase is optically thin and does not interact with radiation. A schematic diagram of the radiation model is shown in Fig. 2. The governing transport equation of P1 model for incident intensity, G, with a dispersed solid phase is given by equation (12) [20];
V$ðGVGÞ þ 4 an2 sTg4 þ Ep a þ ap G ¼ 0
(12)
whereG is given by,
1 3 a þ ap þ sp
G¼
(13)
The equivalent emission of particles, Ep , is calculated by;
Ep ¼ εAr Ts4
(14)
Convective heat transfer is modelled by using an overall heat transfer coefficient. The heat transfer rate is evaluated by;
With the simplifying assumptions of an optically thin gas phase (a ¼ 0 and n ¼ 0), Eq. (12) can be reduced to;
Qsg ¼ hA Ts Tg
V$ðGVGÞ þ 4Ep ap G ¼ 0
(7)
The specific surface area A of biomass is calculated by the correlation of the following equation [18].
A¼
6εs d
(8)
The heat transfer coefficient h is evaluated using definition of the Nusselt number [14].
kg εg Nu h¼ d
(9)
The Nusselt number is evaluated using the following relationship [14].
where,
1 3 ap þ sp
G¼
(16)
The radiation heat flux in P1 model is given by Eq. (17) [19].
qr ¼ GVG
(17)
The radiation source term in energy equation is given by Vqr , which is obtained by applying gradient operator to Eq. (17) and simplifying with the use of Eq. (15).
Vqr ¼ ap G 4Ep
Nu ¼ 7 10εg þ 5ε2g 1 þ 0:7Re0:2 Pr 0:33 þ 1:33 2:4εg þ 1:2ε2g Re0:7 Pr 0:33
(18)
This term is substituted in the solid phase energy equation as the source term for thermal radiation.
(10) During the process of pyrolysis, the solid biomass decomposes into gas products, which is released into the gas phase. It is assumed that these gas products are of the temperature of the solid phase. The release of these higher temperature gases into the gas phase results in an additional energy transfer term in gas phase energy equation given by;
Hpyro ¼ Rg;pyro Cv;g Ts Tg ;
(15)
(11)
where, Hpyro is the heat generation rate due to biomass pyrolysis.
Fig. 2. Schematic of Radiation model.
702
N. Fernando, M. Narayana / Renewable Energy 99 (2016) 698e710
2.2.3. Reaction sub models 2.2.3.1. Heterogeneous reactions. Four main heterogeneous reactions are considered in the present work. These are drying, pyrolysis, reduction and combustion. In mathematical modelling of a gasifier, these processes are included in the mathematical model as rate terms in governing equations. Because of this, in modelling view point, the most important parameter of these processes is the rate of the process. A number of different models are available for describing the rate of each of these processes. The reaction sub models used in the present study are described in following sections. 2.2.3.1.1. Drying. Drying is the process through which moisture in the biomass transfers into the gas phase. In the present work drying process is represented by a one-step global reaction in which moisture in the solid phase transfers to gas phase [21].
ðC2:85 H3:69 O:H2 OÞs /ðC2:85 H3:69 OÞdry;s þ ðH2 OÞ g
(R1)
Here ðC2:85 H3:69 O$H2 OÞs represents the initial moist Gliricidia biomass species and ðC2:85 H3:69 OÞdry;s represents dry Gliricidia biomass species. The drying rate is calculated by an Arrhenius rate equation [22] [18] [23].
rd ¼ fd exp
Ed εs rs YH2 O;s RTs
(19)
The values of pre exponential factor, fd , and activation energy, Ed , for the drying rate are obtained from Ref. [22]and are listed in Table 2. 2.2.3.1.2. Pyrolysis. Pyrolysis is the thermal decomposition of biomass into volatile gases and char. Pyrolysis is an important step in gasification process because products of pyrolysis process are the reactants of all the other chemical processes that take place in the system. The decomposition, which is a result of pyrolysis, is a complex series of reactions in different pathways. These pathways may depend on heating conditions and biomass species [24]. Various researchers have developed different reaction schemes of varying complexity [25]. These models can be classified into three classes, they are; one step global models, single stage multi reaction models and multi stage semi global models [24]. The applicability of these models depends on the species of wood and heating conditions. In the present work, a one-step global reaction scheme is used to model the pyrolysis processes [24], [26]. The scheme is presented in following equation [27].
C2:85 H3:69 O/aC þ bCO þ cCO2 þ dH2 þ eCH4 þ fAsh
(R2)
It is assumed that the stoichiometric coefficients are dependent on the species of wood. This gives the overall mathematical model the ability to analyze different wood species. The coefficients are determined using experimental data obtained by proximate analysis and an assumed distribution of volatiles gases based on previous literature. The coefficients for carbon and ash are directly determined by the fraction of free carbon and ash content given by proximate analysis. For gas species, each coefficient is determined by following equation.
ai ¼ bi VF
(20)
Where, ai represents a, b, c etc. for different values of i. The factor
b describes the distribution of gases in the volatile fraction and VF is
the volatile fraction of wood species under interest. For present study values for b is estimated by using data given in previous literatures [15]. The pyrolysis rate is calculated by,
Ep εs rs YC2:85 H3:69 O rp ¼ fp exp RTs
(21)
2.2.3.1.3. Char combustion and gasification reactions. Three main heterogeneous reactions of char are considered in the present study. These are combustion, carbon dioxide gasification and water gasification as follows;
C þ aO2 /2ð1 aÞCO þ ð2a 1ÞCO2
(R3)
C þ CO2 /2CO
(R4)
C þ H2 O /CO þ H2
(R5)
The parameter a is dependent on the fuel temperature and is given by Eq. (22) [14] [18].
2 þ 2512exp 6420 Ts
: a¼ 2 1 þ 2512exp 6420 Ts
(22)
The actual reaction rates of these reactions depend on two factors. The kinetic rate and mass transfer rate of the reactant gas into the surface of the porous char. Usually the reaction rate is limited by the mass transfer process, because mass transfer rates are much slower than the kinetic rates at higher temperatures. The kinetic rates of above reactions can be generally expressed as follows [28];
E Mc rk;i ¼ Ac Ai Ts exp i r RTs vi Mi i
(23)
As the solid phase is a collection of three components; unreacted biomass, char and ash, only a fraction of the solid phase contains char. Because of this fact, the entire specific surface area of solid phase, which is given by Eq. (8), is different to the specific surface area of char. The specific surface area of char, Ac ,is evaluated based on the ratio of char formation to the maximum amount of possible char generation due to total pyrolysis process. This is expressed in equation (24).
Ac ¼
mchar A a:mðC2:85 H3:69 OÞinitial
(24)
In Eq. (24), mchar is the mass of char per unit volume in a given position, a is the stoichiometric coefficient of char in pyrolysis reaction (Eq. R2) and mðC2:85 H3:69 OÞinitial is the initial mass of wood per unit volume at the same position. A is the total specific surface area of solid phase given by Eq. (8). Mass transfer rate of a reactant gas to the surface of the char particle was calculated by the following equation [29].
rm;i ¼ km;i Ad ri ri;s
(25)
Two simplifying assumptions are used to derive Eq. (25). First, it is noted that diffusion is anisotropic in the vicinity of biomass particle. This effect is due to the air flow around the biomass particle. Diffusion is stronger in parallel to the air flow and minimum in the direction of perpendicular to the air flow. In order to account for this anisotropy with an isotropic mass transfer coefficient, it is assumed that mass diffusion occurs only parallel to the flow, and based on a cubic biomass particle. This assumption reduces the specific diffusive surface area to 1/6th of total specific surface area, as given in Eq. (26).
N. Fernando, M. Narayana / Renewable Energy 99 (2016) 698e710
1 Ad ¼ A 6
(26)
Second assumption is used to evaluate ri;s , the density of the gasifying agent at the surface of the biomass particle. After the gasifying agent reaches the surface of char particle, diffusion process is completed and reaction between gasifying agent and char progresses at the kinetic rate given by Eq. (23). At the temperatures prevailing in combustion processes, this rate is higher compared with diffusion rate. Hence it is assumed that once the gasifying agent reaches the particle surface, it undergoes immediate conversion and as a result ri;s ¼ 0 can be used in evaluating the diffusion rate using Eq. (25). The mass transfer coefficient of ith gas, km;i , is evaluated using following correlation [18]. 1
Shi ¼ 2 þ 0:1Sc 3 Re0:6
(27)
The overall reaction rates of heterogeneous reactions are obtained by evaluating the equivalent parallel resistance of the kinetic and mass transfer rates, this is given by Eq. (28) [18];
rk;i rm;i ri ¼ : rk;i þ rm;i
703
Table 2 Kinetic data for evaluation of reaction rates. Reaction
Pre-exponential factor
Activation energy
Source
R1 R2 R3 R4 R5 R6 R7 R8 R9
5.56 106 s1 1 108 s1 0.652 m s1 K1 3.42 m s1 K1 3.42 m s1 K1 2.32 1012 (kmol/m3)0.75s1 1.08 1013 (kmol/m3)1s1 5.16 1013 (kmol/m3)1s1 K 12.6 (kmol/m3)1s1
87.9 kJ mol1 125.4 kJ mol1 90 kJ mol1 129.7 kJ mol1 129.7 kJ mol1 167 kJ mol1 125 kJ mol1 130 kJ mol1 2.78 kJ mol1
[22] [24] [28] [28] [28] [19] [19] [19] [19]
to the minimum value of kinetic rate and turbulent mixing rate [14].There are certain areas of flow, especially near walls where turbulence is low, in such areas reactants are not well mixed together for reactions to proceed at kinetic rates. Limiting assumption in Eq. (30) is used to account for this effect. Kinetic rates play a major role in free board area and away from the walls, where turbulence is well developed.
ri ¼ min rk;i ; rt;i
(30)
(28)
2.3. Modelling of bed shrinkage 2.2.3.2. Homogenous reactions. Following homogenous reactions taking place between gas phase components are considered in this study.
CO þ 0:5O2 /CO2
(R6)
H2 þ 0:5O2 /H2 O
(R7)
CH4 þ 2O2 /CO2 þ 2H2 O
(R8)
CO þ H2 O#H2 þ CO2
(R9)
Expressions for kinetic reaction raterk , of these reactions are obtained from literature [19] and are listed in Table 1. Kinetic data used for evaluation of reaction rates are summarized in Table 2. The kinetic reaction rate is limited by the turbulent mixing rate of the gas species. The turbulent mixing rate is calculated according to the eddy dissipation model, which is given by Eq. (29) [14];
rt;i
Yj ε Y ¼ 4rg min ; k k vj Mj vk Mk
! (29)
where; j and k represents the reactants of reaction i. The reaction rate for each gas phase reaction is taken to be equal
Table 1 Rate expressions for homogenous reactions. Reaction R6 R7 R8 R9
Rate expression
0:25 ½H2 O0:5 2:32 1012 exp 167 RTg ½CO½O2
1:08 1013 exp 125 RTg ½H2 ½O2
5:16 1013 Tg1 exp 130 RTg ½CH4 ½O2 1 0
½CO2 ½H2 2:78 A @ CO H2 O 12:6exp RTg 0:0265exp
3968 Tg
As heterogeneous reactions of char progresses, the volume of char particles reduces. As a result, top layers of the biomass bed moves downwards. This motion is important to keep the combustion zone stable. When fuel is consumed in combustion zone, new char particles from pyrolysis zone enters to the combustion zone as a result of this bed motion. If particle movement is not there, the combustion zone tends to propagate along the height of the gasifier, reducing the quality of the producer gas. So it is important that the model should be capable of predicting the bed motion. The effect of bed motion is included into solid species equations as a convective flow term. It is assumed that the bed motion can be represented by a continuous velocity field of the solid phase and this velocity, called shrinkage velocity is applied to all solid species as in Eq. (31). Shrinkage velocity is calculated by equating the downward volumetric flow rate of solid phase to total reduction rate of volume caused as a result of heterogeneous reactions of char. Shrinkage velocity in Eqs. (5) and (6) is evaluated using following equation.
1 Us ¼ rs Ag
Z
R3;R4;R5 X
! ri dV
(31)
i
Use of this velocity in convective terms of solid species equations cause the solid species fields of the gasifier to move downwards at the shrinking rate. This causes the solid phase to move downwards and extend the free board region. But mathematical equations used in free board region and solid phase region are different. Therefore when shrinkage modelling is used there has to be a procedure to track the interface and change the mathematical equations above and below the interface to obtain an accurate solution. The changes of the equations are presented in graphical form in Fig. 3. Gas phase equations differ in two regions with respect to the gas phase porosity, which is defined as the volume fraction of gas phase in each computational cell. The porosity field is initialized in the beginning of the simulation through initial conditions. Gas phase porosity is equal to one in free board region and a variable (<1) in packed bed. The source terms that arise as interactions with solid
704
N. Fernando, M. Narayana / Renewable Energy 99 (2016) 698e710
Fig. 3. Changes of governing equations as a result of bed shrinkage.
equation [18].
kg ¼ 4:8 104 Tg0:717 :
(35)
The thermal conductivity of solid phase is evaluated using a correlation developed for thermal conductivity of a quiescent bed, with a correction for the effect of gas flow, as proposed in the literature [18]. This correlation is presented by Eq. (36).
ks ¼ 0:8kg þ 0:5Re:Pr:kg Fig. 4. Motion of unit step variable c in the direction of bed shrinkage.
phase are not present in free board region. Solid phase equations are different entirely in two regions. In free board, a solid phase does not exist and values of solid phase quantities should be zero. The CFD solver should consider these changes as shrinkage progresses. This is achieved by multiplying certain terms of the general transport equation by a new field variablec, which is a unit step function moving along with shrinkage velocity, as illustrated in Fig. 4. The value of c is evaluated based on gas phase porosity; it is assumed that a certain point (i.e a computational cell) in the solution domain belongs to free board when gas phase porosity exceeds 95%. Classification of computational cells based on porosity is discussed in literature [15]. Hence c can be written as,
c¼
1 ; if εg < 0:95 0 ; if εg > 0:95
(32)
This produces a moving c field along with the packed bed as expected. The transport equations for gas and solid phases indicated in Fig. 3 can be then generalized as,
vðεs rs ∅Þ þ cV$ðεs rs ∅U s Þ ¼ cV$ðGV∅Þ þ cS∅ þ cSg;∅ vt v εg rg ∅ vt
þ V$ εg rg ∅U g ¼ V$ðGV∅Þ þ S∅ þ cSs;∅
(33)
(34)
Depending on the value of c the solver will selectively apply equations in packed bed and free board region as shrinkage progresses. 2.4. Physical properties Gas phase thermal conductivity is evaluated by following
(36)
Biomass particle diameter is used as the characteristic length in evaluating the Reynolds number. Two approaches are used to calculate the evolution of particle diameter in literature. These are shrinking core model and volumetric shrinking density model [28]. In shrinking core model, particle diameter gradually reduces with conversion. In volumetric shrinking density model particle size is held fixed while density reduces [28]. In the present case, shrinking density model is used and particle diameter is held constant while density of solid phase is reduced according to Eq. (37). This assumption is used, as the developed model is a two fluid model, which considers the solid phase as a continuum rather than an assembly of solid particles and the motion of the solid phase is affected by its density rather than the particle size.
rs;t ¼ rs;tΔt YðC2:85 H3:69 OÞ;tΔt þ rs;tΔt Ychar;tΔt þ rs;tΔt Yash;tΔt (37) ðC2:85 H3:69 OÞ Density value is updated explicitly using Eq. (37) during each temporal iteration. Heat capacities of solid and gas phases are assumed to vary according to the relations given in Eqs. (38) and (39). The correlation for gas phase heat capacity is taken from the literature [18]. Solid phase heat capacity is modelled by using Eq. (38) [22].
Cs ¼ 420 þ 2:09Ts þ 6:85 104 Ts2
(38)
Cg ¼ 990 þ 0:122Tg 5680 103 Tg2
(39)
Volume fractions of solid and gas phases are calculated using Eqs. (40) and (41).
εs ¼
mC2:85 H3:69 O
rC2:85 H3:69 O
εg ¼ 1 εs
þ
mchar
rchar
þ
mash
rash
(40)
(41)
The binary diffusion coefficients based on diffusion of a specific component in air, are calculated using Eq. (42) [30].
N. Fernando, M. Narayana / Renewable Energy 99 (2016) 698e710
Di;air
sffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi
1 1 1 ¼ 0:0018583 T 3g þ Mi Mair ps2i;air Ui;air
705
Table 3 Discretization schemes.
(42)
Term
Discretization scheme
V$ðrg εg U g 5U g Þ
Upwind
V$rg εg Cv;g Tg U g
Upwind
V$rs εs Cs Ts U s V$ðrg εg Yi U g Þ
3. Numerical solution
V$ðrs εs Yi U s Þ
Upwind Upwind MUSCL
The open source CFD software OpenFOAM was used to develop a numerical solution to mathematical model presented in the previous section. The equations are numerically solved using finite volume method. Required code was developed by using Cþþ language in OpenFOAM package, including all the relevant differential equations and procedures in the CFD model using built in tools of OpenFOAM. The solution domain is assumed to be two dimensional and consists of radial (x e direction) and axial (y edirection) dimensions only. The computational domain of CFD model is presented in Fig. 5. Discretization schemes used to discretize convective and divergence terms are listed in Table 3. A schematic of solution algorithm is presented in Fig. 6. Grid size is determined based on the value of non-dimensional turbulent wall distance (yþ). A value of y þ approximately equal to one is used. This results in Dx ¼ 0:0094 m for near wall cell layer. Dy ¼ 0:0188 m is used based on a cell aspect ratio of 1:2. All cells in the domain were set uniform in size ðDx ¼ 0:0094 m; Dy ¼ 0:0188 mÞ to get a better numerical resolution. Simulations were performed using a 32 core High Performance Computer with 2.2 GHz processor speed and 64 Gb RAM. To simulate a single batch wise run, approximately 2 h were needed in parallel mode using 32 processors for above mesh resolution. Mesh independence is investigated by increasing the cell number by 50% and 75% from initial value. Solid phase temperature at the same location in mesh at same time was compared under refined meshes. It is found that deviation is less than 1%. As a result, initial mesh is used for subsequent simulations and results are validated through experiment. 3.1. Initial and boundary conditions It is assumed that the gasification process is carried out in a cylindrical reactor using air at room temperature as the gasifying medium. This air stream is supplied at constant flow rate from bottom of the reactor. To model the initial ignition process, a distributed heat source similar to magnitude of heat generated by a
Producer gas outlet (Outlet boundary condiƟons applied)
Free board
Insulated Wall (Wall boundary condiƟons applied)
Insulated Wall (Wall boundary condiƟons applied) Porous biomass packed bed
Air inlet (Inlet boundary condiƟons applied) Fig. 5. Computational domain of the CFD solution.
Fig. 6. Solution algorithm.
combustion reaction is applied over a bed region of 0.2 m above the grate and removed after model is capable of continuing operation by own heat emitted by its combustion reactions. The initial heat source is responsible for pyrolysing a small region of packed to generate char necessary to initiate combustion reactions. This start up method was chosen as it closely resembles the real world operation of a gasifier. The required time for initial ignition was found by trial and error by simulating the system. Initially 5 min time was applied and it was increased gradually until simulation was successfully progressed. The initial velocity field within the reactor is taken as zero. Pressure is set to atmospheric pressure. The initial temperatures of gas and solid phases are taken as 300 K. Initial compositions of product gases are taken as zero and the inlet gas composition is taken to be equal to that of air at room temperature and atmospheric pressure. Boundary conditions for velocity, pressure, temperature and species mole fractions are indicated in following equations. Inlet boundary conditions
706
N. Fernando, M. Narayana / Renewable Energy 99 (2016) 698e710
U ¼ ð0; Uin ; 0Þ
(43)
P ¼ Pin
(44)
Tg ¼ Tg;in
(45)
vTs ¼0 vz
(46)
Yi ¼ Yi;air
(47)
Wall boundary conditions
U¼
vP vTg vTs vYi ¼ ¼ ¼ ¼0 vr vr vr vr
(48)
Outlet boundary conditions;
vU vP vTg vTs vYi ¼ ¼ ¼ ¼ ¼0 vz vz vz vz vz
(49)
Table 4 Physical and chemical properties of fuel. Species
Gliricidia
Particle size Particle shape Batch weight Free carbon (dry basis) Volatiles (dry basis) Ash (dry basis) Initial moisture content (dry basis)
20 mm Cubic 28 kg 17.8% 82.16% 0.04% 20%
phase. There readings comply with gas phase temperatures at the points, as evident from the figure. The results indicate that temperature in the combustion zone rises to a value about 1300 K, with a peak value resulting in few centimetres above the grate. A similar behaviour of temperature variation can be observed in experimental work of Wei Chen at el [31] for updraft gasification of mesquite and juniper wood. Their results indicate a combustion zone temperature of nearly 1300 K.
1200
4. Model validation
Ts-Simulation Tg-Simulation Experimental gas temperature
800
600
400
200 0
0.2
0.4
0.6 Height from grate (m)
Cyclone separator Thermocouples
800 600 400 200 0
0.2
0.4
0.6 Height from grate (m)
0.8
1
1.2
1400 Ts-Simulation Tg-Simulation Exerimental gas temperature
Temperature (K)
1000 800 600 400 200 0
Air blower
1.2
1000
1200
Gas outlet
1
Ts-Simulation Tg-Simulation Experimental gas temperature
1200
Top lid Outlet pipe
0.8
1400
Temperature (K)
Model is validated by comparing the simulation results with data obtained from a laboratory scale updraft gasifier. The gasifier consists of a vertical cylinder with a grate at the bottom. Biomass is fed from the top of the gasifier through a lid, which is closed after loading one batch of biomass. The loaded batch is ignited at the bottom of the gasifier. Air at room temperature is supplied through the grate by using an air blower. In this experimental facility, four thermocouples, which record the temperature along the centre line, were installed along the height of the gasifier. A schematic diagram of the experimental facility is shown in Fig. 7. Simulation results were compared against experimental data for gasification of Gliricidia under an airflow rate of 6 m3/hr. The physical and chemical properties of fuel are listed in Table 4. The comparison of temperature profiles obtained from simulations with experimentally measured temperature values using four thermocouples are presented in Fig. 8. Exit gas temperatures predicted by simulation and experimental exit gas temperatures are displayed in Fig. 9. Theoretical and experimental outlet gas compositions are presented in Fig. 10. It can be observed from these figures that the model is in good agreement with experimental data. In Fig. 8(c), which presents the temperature profiles after 2.5 h of initial ignition, the biomass bed has reduced as a result of fuel consumption due to heterogeneous reactions. The thermocouples located at 60 cm and 90 cm positions do not encounter any solid
Temperature (K)
1000
0.2
0.4
0.6 Height from grate (m)
0.8
1
1.2
Grate Ash collecƟng chamber
Fig. 7. Schematic diagram of experimental laboratory scale gasification system.
Fig. 8. Theoretical and experimental temperature profiles; (a) 45 min after ignition (b) 75 min after ignition (c) 150 min after ignition.
Temperature (K)
N. Fernando, M. Narayana / Renewable Energy 99 (2016) 698e710
900 800 700 600 500 400 300 200 100 0
707
SimulaƟon Experimental data
45 75 120 150 180 minutes minutes minutes minutes minutes Fig. 9. Theoretical and Experimental exit gas temperatures.
20 15 SimulaƟon 10
Fig. 11. Development of reaction zones in the solution domain.
Experimental data
5 0 CO2
CO
H2
CH4
Fig. 10. Theoretical and Experimental gas compositions after 30 min of ignition.
The following figure compares the experimental and theoretical exit gas temperatures of the gasifier. It can be observed that at higher temperatures, the difference between experimental value and theoretical prediction is higher. The CFD model predicts a higher outlet gas temperature than the observed value. This is because the radiation losses from the gas phase through walls and the top lid of the gasifier are not accounted in the model. And the radiation losses become higher at higher temperatures. During the simulations, it is found that composition of produced gas varies with time, during initial period, lot of raw biomass is present in the bed and moisture levels are higher. This introduces moisture into gas phase. Pyrolysis in top layers is not complete and as a result low amount of char is available on the top layers to react with carbon dioxide produced in the combustion zone. The initial gas is therefore higher in carbon dioxide. Experimental data and simulation results for gas composition after 30 min of initial ignition are presented in Fig. 10. The values for gas compositions are also comparable with experimental observations of C.Mandlet et al. [22]. Their experimental data for a fixed bed updraft gasifier operated with softwood pellets indicate a final CO volume percentage of 22.6%, a CO2 percentage of 4.8%, H2 percentage of 4.3% and a CH4 percentage of 2.7%. Experimentally it is found that during the process of gasification, packed bed can be separated into four zones; drying, pyrolysis, reduction and combustion, depending on the main processes taking place in these zones. It is possible to identify the development of these zones in the present CFD model by observing the carbon dioxide mass fraction along the height of the gasifier. This is presented in Fig. 11. The two CO2 hot spots in Fig. 11 can be attributed to near wall flow stagnation. The dark blue and green interface just below the hot spots marks the pyrolysis reaction front. Pyrolysis reactions take place in region above this interface which generates CO2. The produced CO2 is transported to higher regions of the bed through
convection due to gas flow. In near wall region, flow velocity is very low. This reduces the convective transport and tends to accumulate CO2 in near wall cells, increasing its concentration in comparison with centre cells. During a batch process the quality of the produced gas varies with the time, mainly as a result of downward motion of the fuel bed. During experiments it is observed that a stable flame cannot be maintained approximately after 4 h of operation. Fig. 12 present the variation of outlet gas mass fractions and Fig. 13 present the bed movement. The packed bed location is identified by viewing the solid phase temperature profile. Velocity distributions within the gasifier at different times are presented in Figs. 14 and 15. An increase in flow velocity can be observed in free board region according to Fig. 14. This increase is due to the release of gases from packed bed to free board region, especially during pyrolysis. Volatiles are released to gas phase increasing its velocity and pyrolysis zone is located in top layers of the packed bed, which can be observed in Fig. 11. A span wise variation of velocity can be observed in free board region, which can be clearly noticed in Fig. 15. This variation is reduced in packed bed, mainly due to the effect of porosity. In a batch wise simulation as in the present case, free board region extends with time and span wise velocity variation becomes significant. Even within the packed bed, a reduction of flow velocity near walls can be noticed, this effect is reflected in CO2 hot spots in Fig. 11, where CO2 is accumulated due to low convective
0.35 CO2 H2 CH4 CO
0.3 0.25 Mass fraction
Volume percentage
25
0.2 0.15 0.1 0.05 0 0
2000
4000
6000
80 000 Time (s)
10000
12000
Fig. 12. Variation of gas phase component mass fractions with time.
14000
708
N. Fernando, M. Narayana / Renewable Energy 99 (2016) 698e710
Fig. 13. Bed reduction with time; (a) 1 h after ignition (b) 2 h after ignition (c) 3 h after ignition (d) 4 h after ignition. Location of interface between packed bed and free board is marked with the black arrow.
Fig. 14. Axial velocity distribution; (a) 2 h after ignition (b) 2.5 h after ignition (c) 3 h after ignition.
0.04 Packed bed Free boader
0.035
Axial velocity (m/s)
0.03 0.025 0.02 0.015 0.01 0.005 0
0
0.05
0.1
0.15 0.2 Spanwise distance (m)
0.25
0.3
0.35
Fig. 15. Span wise axial velocity distributions in free board and packed bed after 3 h from ignition.
transport. Fig. 16 presents the span wise variation of solid phase temperature at three different locations within the packed bed. A span wise variation of temperature can be observed in near wall area. It can be observed that temperature is lower in near wall regions and higher in central regions. This is due to the fact that lower heat transfer coefficient exists between solid and gas phases in near wall region, because of low value of flow velocity in vicinity of walls. Heat transfer coefficient between solid and gas phase is evaluated using Eq. (9). Dimensionless numbers are evaluated based on a characteristic particle length scale equal to initial particle size. Reynolds number for heat transfer varies in the range of 0e40. Prandlt number varies in the range 0.667e1.16 and Nusselt number varies between 2 and 9.98, with values closer to 2 in near wall region. Maximum temperature occurs near the central axis. This span wise variation reduces at regions closer to the grate, where heat is generated within bed through combustion reactions.
N. Fernando, M. Narayana / Renewable Energy 99 (2016) 698e710
1200
general experimental observations on packed bed gasification processes. The developed model evaluates optimal air flow rate to be 7 m3/h for maximum cumulative CO production for the studied gasifier. In future, the presented mathematical model can be used as a numerical tool to optimize batch wise moving bed gasification processes. The model consists of many runtime variable input parameters such as particle size, inlet air flow rate, inlet-gas compositions and physical & chemical properties of feed-stock. The model can be used to perform parameter studies to find the optimum values of these parameters for a particular process. The model can be further improved by implementing an advanced pyrolysis scheme, including primary and secondary pyrolysis reactions separately and tar formation reactions.
Temperature (K)
1000
800 0.3 m 0.4 m 0.5 m
600
400
200 0
0.05
0.1
0.15 Spamwise distance (m)
0.2
0.25
709
0.3
Acknowledgment Fig. 16. Span wise temperature distribution at different locations within packed bed after 1.5 h from ignition. Dashed line: 0.3 m from grate. Dash dot line 0.4 m from grate. Solid line: 0.5 m from grate.
Table 5 Simulation Results for different air flow rates.
The authors are thankful to senate versity of Moratuwa (SRC/CAP/14/06), port for the research project and experimental data from his research presented mathematical model.
research committee of Unifor providing financial supMr. M. Amin for sharing work for validation of the
Flow rate (m3/hr) Batch time (s) Peak CO composition Cumulative CO (m3) 4 5 6 7 8 9 10
21600 15800 14400 12800 11300 10800 9200
0.38 0.41 0.404 0.413 0.406 0.404 0.401
5.2 5.51 6.11 6.35 5.68 5.53 5.372
The temperature increase due to combustion reactions become dominant than convective heat transfer contribution. 5. Optimization of air flow rate to the gasifier based on CFD model The external air flow to the gasifier supply fuel needed to maintain combustion process. When air flow rate is higher, the extent of the combustion zone increases, causing the produced fuel gases to burn inside the reactor. This reduces the quality of the outlet gas. When flow rates are too small, combustion rates reduce and sufficient heat is not produced for complete cracking of biomass in top layers of the bed. The developed CFD model is used to evaluate optimal air flow rate for maximum cumulative carbon monoxide production. A series of simulations were performed for air flow rates ranging from 4 m3/hr to 10 m3/hr. The results are summarized in Table 5. Based on the cumulative CO production, it can be stated that, for the particular experimental gasifier, a flow rate of 7 m3/hr maximizes the CO yield from biomass batch. 6. Conclusion and future work A mathematical model for gasification of biomass in a batch wise updraft packed bed reactor was developed and simulated using open source CFD software OpenFOAM. The developed model in this study accounts for drying, pyrolysis, reduction and combustion reactions. All three modes of heat transfer; conduction, convection and radiation, was included in the packed bed model. It is found by the simulation study; radiation is the main mode of heat transfer through the biomass packed bed and critically important. Reduction of bed volume due to heterogeneous reactions are also considered and modelled in the simulations. The simulation results are in good agreement with experimental data and also with
References [1] P. McKendry, Energy production from biomass (part 1): overview of biomass, Bioresour. Technol. 83 (1) (May 2002) 37e46. [2] K. Umeki, T. Namioka, K. Yoshikawa, Analysis of an updraft biomass gasifier with high temperature steam using a numerical model, Appl. Energy 90 (1) (Feb. 2012) 38e45. [3] P. McKendry, Energy production from biomass (part 2): conversion technologies, Bioresour. Technol. 83 (1) (May 2002) 47e54. [4] K. Srirangan, L. Akawi, M. Moo-Young, C.P. Chou, Towards sustainable production of clean energy carriers from biomass resources, Appl. Energy 100 (Dec. 2012) 172e186. [5] E.G. Pereira, J.N. da Silva, J.L. de Oliveira, C.S. Machado, Sustainable energy: a review of gasification technologies, Renew. Sustain. Energy Rev. 16 (7) (Sep. 2012) 4753e4762. [6] P. McKendry, Energy production from biomass (part 3): gasification technologies, Bioresour. Technol. 83 (1) (May-2002) 55e63. [7] F. Guo, Y. Dong, L. Dong, C. Guo, Effect of design and operating parameters on the gasification process of biomass in a downdraft fixed bed: an experimental study, Int. J. Hydrogen Energy 39 (11) (Apr. 2014) 5625e5633. [8] M.A. Masmoudi, M. Sahraoui, N. Grioui, K. Halouani, 2-D Modeling of thermokinetics coupled with heat and mass transfer in the reduction zone of a fixed bed downdraft biomass gasifier, Renew. Energy 66 (Jun. 2014) 288e298. [9] A.H. Mahmoudi, F. Hoffmann, B. Peters, Application of XDEM as a novel approach to predict drying of a packed bed, Int. J. Therm. Sci. 75 (Jan. 2014) 65e75. [10] G. Cau, V. Tola, A. Pettinau, A steady state model for predicting performance of small-scale up-draft coal gasifiers, Fuel 152 (Jul. 2015) 3e12. [11] D.F. Fletcher, B.S. Haynes, F.C. Christo, S.D. Joseph, A CFD based combustion model of an entrained flow biomass gasifier, Appl. Math. Model. 24 (3) (Mar. 2000) 165e182. [12] K.D. Patel, N.K. Shah, R.N. Patel, CFD analysis of spatial distribution of various parameters in downdraft gasifier, Procedia Eng. 51 (2013) 764e769. [13] S. Murgia, M. Vascellari, G. Cau, Comprehensive CFD model of an air-blown coal-fired updraft gasifier, Fuel 101 (Nov. 2012) 129e138. [14] Y. Wu, Q. Zhang, W. Yang, W. Blasiak, Two-dimensional computational fluid dynamics simulation of biomass gasification in a downdraft fixed-bed gasifier with highly preheated air and steam, Energy Fuels 27 (6) (2013) 3274e3282. [15] K. Kwiatkowskia, P. Zukb, Biomass gasification solver based on OpenFOAM, Comput. Phys. Commun. (2013) 1e29. [16] H.K. Versteeg, W. Malalasekera, in: M. Harlow (Ed.), An Introduction to Computational Fluid Dynamics: the Finite Volume Method, 2 edition., Prentice Hall, England; New York, 2007. [17] Y.-Q. Zhuang, X. Gao, Y. Zhu, Z. Luo, CFD modeling of methanol to olefins process in a fixed-bed reactor, Powder Technol. 221 (May 2012) 419e430. [18] T. Jurena, Numerical Modelling of Grate Combustion, Brno University of Technology, Brno, 2012. [19] H. Liu, CFD Modeling of Biomass Gasification Using a Circulating Fluidized Bed Reactor, University of Waterloo, Ontario, Canada, 2014. [20] ANSYS Fluent, ANSYS FLUENT Theory Guide, 15317, ANSYS Inc, Canonsburg, PA, 2011, p. 2009. [21] A. Nikolopoulos, I. Malgarinos, N. Nikolopoulos, P. Grammelis, S. Karrelas, E. Kakaras, A decoupled approach for NOxeN2O 3-D CFD modeling in CFB plants, Fuel 115 (Jan. 2014) 401e415. [22] C. Mandl, I. Obernberger, F. Biedermann, Modelling of an updraft fixed-bed
710
N. Fernando, M. Narayana / Renewable Energy 99 (2016) 698e710
gasifier operated with softwood pellets, Fuel 89 (12) (Dec. 2010) 3795e3806. [23] Purnomo, Model for a Downdraft Solid Fuel Combustor, The University of Wisconsin, 1988. [24] S. Sinha, A. Jhalani, M.R. Ravi, A. Ray, Modelling of pyrolysis in wood: a review, SESI J. 10 (1) (2000) 41e62. [25] B.V. Babu, A.S. Chaurasia, Heat transfer and kinetics in the pyrolysis of shrinking biomass particle, Chem. Eng. Sci. 59 (10) (May 2004) 1999e2012. [26] N. Fernando, M. Amin, M. Narayana, T. Jayawickrama, S. Jayasena, A mathematical model for pyrolysis of biomass, in: Moratuwa Eng. Res. Conf. (MERCon), IEEE Conf. Publ, 2015, pp. 1e6. [27] M. Amin, Development of Updraft Gasifier and Performance Analysis for
Different Types of Biomass Materials, University of Moratuwa, Sri Lanka, 2015. [28] Y. Haseli, J.A. van Oijen, L.P.H. de Goey, A detailed one-dimensional model of combustion of a woody biomass particle, Bioresour. Technol. 102 (20) (Oct. 2011) 9772e9782. [29] R.E. Treybal, Mass-transfer Operations, third ed., McGraw-Hill Book Company, 1980. [30] R.B. Bird, W.E. Stewart, E.N. Lightfoot, Transport Phenomena, second ed., Wiley, New York, 2001. [31] W. Chen, K. Annamalai, R.J. Ansley, M. Mirik, Updraft fixed bed gasification of mesquite and juniper wood samples, Energy 41 (1) (May 2012) 454e461.
Contents lists available at ScienceDirect
Renewable Energy journal homepage: www.elsevier.com/locate/renene
A comprehensive two dimensional Computational Fluid Dynamics model for an updraft biomass gasifier Niranjan Fernando*, Mahinsasa Narayana Department of Chemical and Process Engineering, University of Moratuwa, Sri Lanka
a r t i c l e i n f o
a b s t r a c t
Article history: Received 27 June 2015 Received in revised form 19 July 2016 Accepted 21 July 2016
This study focuses on developing a dynamic two dimensional Computational Fluid Dynamics (CFD) model of a moving bed updraft biomass gasifier. The model uses inlet air at room temperature as the gasifying medium and a fixed batch of biomass. The biomass batch is initially ignited by a heat source which is removed after a certain amount of time. This model operates by the heat emitted by combustion reactions, until the fuel is finished. Since the operation is batch wise, model is transient and takes into consideration the effect of bed movement as a result of shrinkage. The CFD model is capable of simulating the movement of interface between solid packed bed and gas free board and this motion is also presented. The model is validated by comparing the simulation results with experimental data obtained from a laboratory scale updraft gasifier operated in batch mode with Gliricidia. The developed model is used to find the optimum air flow rate that maximizes the cumulative CO production. It is found that from the simulation study for the particular experimental gasifier, a flow rate of 7 m3/h maximizes the CO production. The maximum cumulative CO production was 6.4 m3 for a 28 kg batch of Gliricidia. © 2016 Elsevier Ltd. All rights reserved.
Keywords: Gasification Mathematical model Computational Fluid Dynamics Moving bed
1. Introduction With the depletion of fossil fuels, alternative, renewable energy sources are promoted as possible ways of providing the world's energy demand. In this respect, biomass is a promising energy source to produce green energy. It is expected that biomass will provide half of the present world's main energy consumption in future [1] [2]. However, the direct combustion of biomass has several drawbacks to produce thermal energy. These drawbacks include; low heating value of biomass, unsuitability as a fuel for high temperature applications, cannot be used directly as a fuel for internal combustion engines and low versatility. Therefore, corresponding to industrial requirements, biomass is usually converted into a more versatile secondary fuel by thermo-chemical, bio echemical or extraction processes [3] [4]. Gasification is a major thermo-chemical process, which is being used worldwide to convert biomass into a versatile, energy efficient fuel gas called Syngas. This gas is a mixture of carbon monoxide, carbon dioxide, hydrogen, methane, small amount of light hydrocarbons and nitrogen [5]. The gas produced is more versatile than original raw
* Corresponding author. E-mail addresses: [email protected] (N. Fernando), mahinsasa@ uom.lk (M. Narayana). http://dx.doi.org/10.1016/j.renene.2016.07.057 0960-1481/© 2016 Elsevier Ltd. All rights reserved.
biomass fuel and can be used for a variety of applications. Examples are electricity generation, heat generation and hydrogen production [5]. It can also be used as a raw material to produce liquid biofuels [6]. Gasification of biomass is carried out in a special reactor called a gasifier. Number of other factors related to gasifier design and fuel properties significantly affect the produced gas quality. These include; gasifying medium, properties of biomass, moisture content, particle size, temperature of the gasification zone, operating pressure and equivalence ratio [5] [7]. The optimization of gasifiers based on these design factors can be done in two main ways; through experimental approach and through computer aided simulations. Experimental approach follows a series of experiments, usually on scaled down laboratory scale gasifiers. Parameters such as the optimum equivalence ratio can be determined by measuring the gas quality under various equivalence ratios until the best results are obtained. However, experimental approach leads in to a series of difficulties and drawbacks. It is very difficult to perform experimental analysis on pilot scales systems, especially when considering geometry optimization, therefore scaled down models have to be used for experimental analysis. The results obtained on scaled down systems may not fully work on the pilot scale system. The scale down systems cannot be used to determine the effects of biomass particle
N. Fernando, M. Narayana / Renewable Energy 99 (2016) 698e710
Nomenclature A Ac Ad Ag Aj Ar a ap Cg Cs Di;g d Ei fi G h k kg ks km;j Mi mi Nu n Pr p pin Qrad Qi Qsg qr Re Rg;pyro
Specific surface area of packed bed (m1) Specific surface area of char (m1) Specific surface area for gas diffusion (m1) Cross sectional area of gasifier (m2) pre-exponential factor for heterogeneous reactions (m s1 T1) Specific surface area available for radiation (m1) Absorption coefficient of gas phase (m1) Absorption coefficient of solid phase (m1) Heat capacity of gas phase (J kg1K1) Heat capacity of solid phase (J kg1K1) Diffusion coefficient of gas species i (m2 s1) Particle size of biomass (m) Activation energy of reaction i (J mol1) Pre-exponential factor of reaction i (s1) Radiation intensity (W m2) Heat transfer coefficient (W m2 K1) Turbulent kinetic energy (m2 s2) Thermal conductivity of gas phase (W m1 K1) Thermal conductivity of solid phase (W m1 K1) Mass transfer coefficient of species j (m s1) Molecular weight of species i (kg mol1) Specific mass of species i in a computational cell (kg m3) Nusselt number Refractive index of gas phase Prandtl number Pressure (Pa) Inlet pressure (Pa) Radiation heat source (W m3) Initial heat source (W m3) Convective heat transfer rate (W m3) Radiation heat flux (W m2) Reynolds number Rate of release of pyrolytic volatiles (Kg m3 s1)
sizes, as particle size relies on the diameter of the real system. Scaling down the particle size will not produce equivalent results because the packing factors will differ between the two systems. Also, taking measurements inside packed beds is a difficult task considering the higher temperatures present in an operational gasifier. Because of these reasons, the experimental approach is usually difficult, time consuming, costly and the accuracy of the results are also low. Therefore many researchers use the computer based approach to analyze packed bed processes. A large number of research works are available in literature where numerical models are used to optimize packed bed processes [2] [8] [9] [10]. Mathematical models offer certain advantages over the conventional experimental procedure. Mathematical models can produce a large number of data points as compared to fewer experimental data, for example, when measuring temperature, experimental analysis can provide temperatures at only a finite number of locations along the packed bed, while numerical models can provide the complete variation of the temperature profile over the region of interest. With the development of the computer hardware technology, Computational Fluid Dynamics (CFD) is widely applied as a numerical modeling tool [11] [12] [13] [14]. CFD models can be made to match the exact geometry of the real scale gasifier, as a result no
ri ri;hetero ri;homo rm;i rk;i rt;i Shj S∅ Ss;∅ Sg;∅ sij Tg Tg;in Ts Ug Ug;in Us vi Yi;g Yi;air Yi;s
s sp
ε ∅ εg εs
rg rs rj m si;air Ui;air ε
DHi 5
699
Rate of reaction i (Kg m3 s1) Rate of heterogeneous reaction i (Kg m3 s1) Rate of homogenous reaction i (Kg m3 s1) Mass transfer limited reaction rate (Kg m3 s1) Kinetic reaction rate (Kg m3 s1) Turbulent mixing limited reaction rate (kg m3 s1) Sherwood number for species j Source term for property ∅ Source term for property ∅ due to solid phase Source term for property ∅ due to gas phase Reynolds stress tensor (Pa) Gas phase temperature (K) Inlet gas temperature (K) Solid phase temperature (K) Gas phase velocity (m s1) Inlet gas velocity (m s1) Shrinkage velocity (m s1) Stoichiometric coefficient of species i Mole fraction of gas species i Mole fraction of i in air Mole fraction of solid species i Stefan constant (W m2 K4) Scattering coefficient of solid particles (m1) Emissivity of solid particles A general transport property Volume fraction of gas phase Volume fraction of solid phase Density of gas phase (Kg m3) Density of solid phase (Kg m3) Cell density of species j (Kg m3) Dynamic viscosity (Pa s) Average collision diameter (A) Diffusion collision integral Turbulent dissipation rate (m2 s3) Enthalpy of reaction i (J kg1) Vector outer product
scaling down problems arise, in CFD simulations, any number of input parameters can be easily changed at will, including equivalence ratio, particle size, moisture content, feed properties, superficial velocity etc. and system performance can be obtained accordingly. CFD simulations are best suited to perform geometry optimization. A large number of geometrical parameters can be optimized by simply changing the computational mesh. Because of these advantages CFD models are now widely used by researchers around the world as a tool to study and optimize gasification process. In the present work a two dimensional dynamic two fluids CFD model has been developed for an updraft biomass moving bed gasifier. This model uses inlet air at room temperature as the gasification medium and a fixed batch of biomass. The biomass batch is initially ignited by a heat source, which is removed after a certain amount of time. The mathematical model developed in this study is capable of maintaining the operation by the own heat emitted by combustion reactions, until the fuel is finished, as in the real world scenario. Since the operation is batch wise, model is transient and takes into consideration the effect of bed movement as a result of shrinkage. This model is capable to detect the movement of interface between solid packed bed and gas free board in time domain. The two phase model is developed by using
700
N. Fernando, M. Narayana / Renewable Energy 99 (2016) 698e710
the Euler-Euler approach. The overall model consists of several sub models; including reaction models, which govern the reaction rates and compositions of the products, turbulence model for packed bed gas phase and free board, a radiation model for solid phase, a bed shrinkage model, and interphase heat transfer model. In this study, the ultimate mathematical model for the gasifier is converted into a numerical model by using open source CFD tool OpenFOAM. CFD code was developed using Cþþ language and available tools in OpenFOAM package to include all the relevant differential equations and procedures in the mathematical model. The code is developed for two dimensional generic analyses, which is capable to perform two dimensional geometrical optimizations, such as inclusion of tapered sections in gasifier body. To validate the CFD model, simulation results are compared against experimental data from an operational laboratory gasifier. It is found that the model is in good agreement with experimental data.
considered in the present work. A schematic diagram of the presented mathematical model is shown in Fig. 1.
2.1. Governing equations Conservation equations for momentum, energy and species are solved in the gas phase.
v rg εg U g þ V$ rg εg U g 5U g V$mεg VU g vt T 2 rg kI þ S ¼ εg Vp þ V$εg VU g þ VU g 3 With I the second order identity tensor. Gasesolid momentum exchange rate [17];
1 εg S ¼ 150 d2 ε2g
2. Mathematical model A two dimensional, transient, two-phase, Euler-Euler model was developed in the present study. The two phases consist of gas and solid phases. In the Euler-Euler approach, both solid and gas phases are treated as continuums, as a result, motion of individual particles in solid phase are not calculated based on forces acting on them. The motion of solid continuum is resolved using continuity equation. Heat and mass transfer between two phases due to chemical reactions are modelled through source terms of governing equations. Radiation heat transfer is modelled in the solid phase. It is assumed that the optical thickness of gas phase is small and gas does not absorb radiation energy [15]. Gas phase turbulence is modelled using standard k ε model [16]including the effects of porosity. Motion of the biomass bed and solid-freeboard interface is
(1)
2 Ug þ 1:75
rg 1 εg Ug dεg
Ug
vrg εg Cv;g Tg þ V$rg εg Cv;g Tg U g V$ εg kg VTg vt X ¼ hA Ts Tg þ DHi ri;homo þ Rg;pyro Cv;g Ts Tg
(2)
(3)
i
v rg εg Yi;g þ V$ rg εg Yi;g U V$ εg Di;g VYi;g vt X X ¼ ri;homo þ ri;hetero i
(4)
i
Energy conservation and species conservation equations are solved in the solid phase,
Fig. 1. Schematic diagram of the mathematical model.
N. Fernando, M. Narayana / Renewable Energy 99 (2016) 698e710
vrs εs Cs Ts þ V$rs εs Cs Ts U s V$ðεs ks VTs Þ vt X ¼ hA Ts Tg þ DHi ri;hetero þ Qrad þ Qi
(5)
i
X v r εs Y þ V$ rs εs Yi;s U s V$ εs Di;s VYi;s ¼ ri;hetero vt s i;s i
(6)
2.2. Evaluation of source terms Terms appearing on the right hand side of each governing equation represent generation terms of transport property described by the equation. These consist of convective heat transfer between phases, radiation heat transfer terms, heat generation due to chemical reactions and species generation due to chemical reactions. These source terms are evaluated by considering correlations of parameters and kinetic models of chemical reactions. 2.2.1. Inter-phase heat transfer Two main processes are responsible for interphase heat transfer. These are; 1. Convective transfer of heat between two phases as a result of temperature difference between gas and solid phases. 2. During pyrolysis stage, hot volatile gases generated within the porous structure of biomass release into gas phase. These hot volatile gases introduce an energy flow to the gas phase.
701
2.2.2. Radiation heat transfer Radiation heat transfer plays a major role in transporting heat generated in combustion zone from combustion reactions, to top wood layers of the packed bed. This heat provides the energy for thermal cracking of biomass and other endothermic solid phase reactions that take place in top layers. In the present work, P1 radiation model is applied to model radiation in the packed bed with following assumptions [19] [20]. Biomass bed can be treated as an absorbing, emitting, scattering medium of dispersed solid particles. Combustion zone can be approximated by a hot emissive plate located at the bottom of the gasifier. The gas phase is optically thin and does not interact with radiation. A schematic diagram of the radiation model is shown in Fig. 2. The governing transport equation of P1 model for incident intensity, G, with a dispersed solid phase is given by equation (12) [20];
V$ðGVGÞ þ 4 an2 sTg4 þ Ep a þ ap G ¼ 0
(12)
whereG is given by,
1 3 a þ ap þ sp
G¼
(13)
The equivalent emission of particles, Ep , is calculated by;
Ep ¼ εAr Ts4
(14)
Convective heat transfer is modelled by using an overall heat transfer coefficient. The heat transfer rate is evaluated by;
With the simplifying assumptions of an optically thin gas phase (a ¼ 0 and n ¼ 0), Eq. (12) can be reduced to;
Qsg ¼ hA Ts Tg
V$ðGVGÞ þ 4Ep ap G ¼ 0
(7)
The specific surface area A of biomass is calculated by the correlation of the following equation [18].
A¼
6εs d
(8)
The heat transfer coefficient h is evaluated using definition of the Nusselt number [14].
kg εg Nu h¼ d
(9)
The Nusselt number is evaluated using the following relationship [14].
where,
1 3 ap þ sp
G¼
(16)
The radiation heat flux in P1 model is given by Eq. (17) [19].
qr ¼ GVG
(17)
The radiation source term in energy equation is given by Vqr , which is obtained by applying gradient operator to Eq. (17) and simplifying with the use of Eq. (15).
Vqr ¼ ap G 4Ep
Nu ¼ 7 10εg þ 5ε2g 1 þ 0:7Re0:2 Pr 0:33 þ 1:33 2:4εg þ 1:2ε2g Re0:7 Pr 0:33
(18)
This term is substituted in the solid phase energy equation as the source term for thermal radiation.
(10) During the process of pyrolysis, the solid biomass decomposes into gas products, which is released into the gas phase. It is assumed that these gas products are of the temperature of the solid phase. The release of these higher temperature gases into the gas phase results in an additional energy transfer term in gas phase energy equation given by;
Hpyro ¼ Rg;pyro Cv;g Ts Tg ;
(15)
(11)
where, Hpyro is the heat generation rate due to biomass pyrolysis.
Fig. 2. Schematic of Radiation model.
702
N. Fernando, M. Narayana / Renewable Energy 99 (2016) 698e710
2.2.3. Reaction sub models 2.2.3.1. Heterogeneous reactions. Four main heterogeneous reactions are considered in the present work. These are drying, pyrolysis, reduction and combustion. In mathematical modelling of a gasifier, these processes are included in the mathematical model as rate terms in governing equations. Because of this, in modelling view point, the most important parameter of these processes is the rate of the process. A number of different models are available for describing the rate of each of these processes. The reaction sub models used in the present study are described in following sections. 2.2.3.1.1. Drying. Drying is the process through which moisture in the biomass transfers into the gas phase. In the present work drying process is represented by a one-step global reaction in which moisture in the solid phase transfers to gas phase [21].
ðC2:85 H3:69 O:H2 OÞs /ðC2:85 H3:69 OÞdry;s þ ðH2 OÞ g
(R1)
Here ðC2:85 H3:69 O$H2 OÞs represents the initial moist Gliricidia biomass species and ðC2:85 H3:69 OÞdry;s represents dry Gliricidia biomass species. The drying rate is calculated by an Arrhenius rate equation [22] [18] [23].
rd ¼ fd exp
Ed εs rs YH2 O;s RTs
(19)
The values of pre exponential factor, fd , and activation energy, Ed , for the drying rate are obtained from Ref. [22]and are listed in Table 2. 2.2.3.1.2. Pyrolysis. Pyrolysis is the thermal decomposition of biomass into volatile gases and char. Pyrolysis is an important step in gasification process because products of pyrolysis process are the reactants of all the other chemical processes that take place in the system. The decomposition, which is a result of pyrolysis, is a complex series of reactions in different pathways. These pathways may depend on heating conditions and biomass species [24]. Various researchers have developed different reaction schemes of varying complexity [25]. These models can be classified into three classes, they are; one step global models, single stage multi reaction models and multi stage semi global models [24]. The applicability of these models depends on the species of wood and heating conditions. In the present work, a one-step global reaction scheme is used to model the pyrolysis processes [24], [26]. The scheme is presented in following equation [27].
C2:85 H3:69 O/aC þ bCO þ cCO2 þ dH2 þ eCH4 þ fAsh
(R2)
It is assumed that the stoichiometric coefficients are dependent on the species of wood. This gives the overall mathematical model the ability to analyze different wood species. The coefficients are determined using experimental data obtained by proximate analysis and an assumed distribution of volatiles gases based on previous literature. The coefficients for carbon and ash are directly determined by the fraction of free carbon and ash content given by proximate analysis. For gas species, each coefficient is determined by following equation.
ai ¼ bi VF
(20)
Where, ai represents a, b, c etc. for different values of i. The factor
b describes the distribution of gases in the volatile fraction and VF is
the volatile fraction of wood species under interest. For present study values for b is estimated by using data given in previous literatures [15]. The pyrolysis rate is calculated by,
Ep εs rs YC2:85 H3:69 O rp ¼ fp exp RTs
(21)
2.2.3.1.3. Char combustion and gasification reactions. Three main heterogeneous reactions of char are considered in the present study. These are combustion, carbon dioxide gasification and water gasification as follows;
C þ aO2 /2ð1 aÞCO þ ð2a 1ÞCO2
(R3)
C þ CO2 /2CO
(R4)
C þ H2 O /CO þ H2
(R5)
The parameter a is dependent on the fuel temperature and is given by Eq. (22) [14] [18].
2 þ 2512exp 6420 Ts
: a¼ 2 1 þ 2512exp 6420 Ts
(22)
The actual reaction rates of these reactions depend on two factors. The kinetic rate and mass transfer rate of the reactant gas into the surface of the porous char. Usually the reaction rate is limited by the mass transfer process, because mass transfer rates are much slower than the kinetic rates at higher temperatures. The kinetic rates of above reactions can be generally expressed as follows [28];
E Mc rk;i ¼ Ac Ai Ts exp i r RTs vi Mi i
(23)
As the solid phase is a collection of three components; unreacted biomass, char and ash, only a fraction of the solid phase contains char. Because of this fact, the entire specific surface area of solid phase, which is given by Eq. (8), is different to the specific surface area of char. The specific surface area of char, Ac ,is evaluated based on the ratio of char formation to the maximum amount of possible char generation due to total pyrolysis process. This is expressed in equation (24).
Ac ¼
mchar A a:mðC2:85 H3:69 OÞinitial
(24)
In Eq. (24), mchar is the mass of char per unit volume in a given position, a is the stoichiometric coefficient of char in pyrolysis reaction (Eq. R2) and mðC2:85 H3:69 OÞinitial is the initial mass of wood per unit volume at the same position. A is the total specific surface area of solid phase given by Eq. (8). Mass transfer rate of a reactant gas to the surface of the char particle was calculated by the following equation [29].
rm;i ¼ km;i Ad ri ri;s
(25)
Two simplifying assumptions are used to derive Eq. (25). First, it is noted that diffusion is anisotropic in the vicinity of biomass particle. This effect is due to the air flow around the biomass particle. Diffusion is stronger in parallel to the air flow and minimum in the direction of perpendicular to the air flow. In order to account for this anisotropy with an isotropic mass transfer coefficient, it is assumed that mass diffusion occurs only parallel to the flow, and based on a cubic biomass particle. This assumption reduces the specific diffusive surface area to 1/6th of total specific surface area, as given in Eq. (26).
N. Fernando, M. Narayana / Renewable Energy 99 (2016) 698e710
1 Ad ¼ A 6
(26)
Second assumption is used to evaluate ri;s , the density of the gasifying agent at the surface of the biomass particle. After the gasifying agent reaches the surface of char particle, diffusion process is completed and reaction between gasifying agent and char progresses at the kinetic rate given by Eq. (23). At the temperatures prevailing in combustion processes, this rate is higher compared with diffusion rate. Hence it is assumed that once the gasifying agent reaches the particle surface, it undergoes immediate conversion and as a result ri;s ¼ 0 can be used in evaluating the diffusion rate using Eq. (25). The mass transfer coefficient of ith gas, km;i , is evaluated using following correlation [18]. 1
Shi ¼ 2 þ 0:1Sc 3 Re0:6
(27)
The overall reaction rates of heterogeneous reactions are obtained by evaluating the equivalent parallel resistance of the kinetic and mass transfer rates, this is given by Eq. (28) [18];
rk;i rm;i ri ¼ : rk;i þ rm;i
703
Table 2 Kinetic data for evaluation of reaction rates. Reaction
Pre-exponential factor
Activation energy
Source
R1 R2 R3 R4 R5 R6 R7 R8 R9
5.56 106 s1 1 108 s1 0.652 m s1 K1 3.42 m s1 K1 3.42 m s1 K1 2.32 1012 (kmol/m3)0.75s1 1.08 1013 (kmol/m3)1s1 5.16 1013 (kmol/m3)1s1 K 12.6 (kmol/m3)1s1
87.9 kJ mol1 125.4 kJ mol1 90 kJ mol1 129.7 kJ mol1 129.7 kJ mol1 167 kJ mol1 125 kJ mol1 130 kJ mol1 2.78 kJ mol1
[22] [24] [28] [28] [28] [19] [19] [19] [19]
to the minimum value of kinetic rate and turbulent mixing rate [14].There are certain areas of flow, especially near walls where turbulence is low, in such areas reactants are not well mixed together for reactions to proceed at kinetic rates. Limiting assumption in Eq. (30) is used to account for this effect. Kinetic rates play a major role in free board area and away from the walls, where turbulence is well developed.
ri ¼ min rk;i ; rt;i
(30)
(28)
2.3. Modelling of bed shrinkage 2.2.3.2. Homogenous reactions. Following homogenous reactions taking place between gas phase components are considered in this study.
CO þ 0:5O2 /CO2
(R6)
H2 þ 0:5O2 /H2 O
(R7)
CH4 þ 2O2 /CO2 þ 2H2 O
(R8)
CO þ H2 O#H2 þ CO2
(R9)
Expressions for kinetic reaction raterk , of these reactions are obtained from literature [19] and are listed in Table 1. Kinetic data used for evaluation of reaction rates are summarized in Table 2. The kinetic reaction rate is limited by the turbulent mixing rate of the gas species. The turbulent mixing rate is calculated according to the eddy dissipation model, which is given by Eq. (29) [14];
rt;i
Yj ε Y ¼ 4rg min ; k k vj Mj vk Mk
! (29)
where; j and k represents the reactants of reaction i. The reaction rate for each gas phase reaction is taken to be equal
Table 1 Rate expressions for homogenous reactions. Reaction R6 R7 R8 R9
Rate expression
0:25 ½H2 O0:5 2:32 1012 exp 167 RTg ½CO½O2
1:08 1013 exp 125 RTg ½H2 ½O2
5:16 1013 Tg1 exp 130 RTg ½CH4 ½O2 1 0
½CO2 ½H2 2:78 A @ CO H2 O 12:6exp RTg 0:0265exp
3968 Tg
As heterogeneous reactions of char progresses, the volume of char particles reduces. As a result, top layers of the biomass bed moves downwards. This motion is important to keep the combustion zone stable. When fuel is consumed in combustion zone, new char particles from pyrolysis zone enters to the combustion zone as a result of this bed motion. If particle movement is not there, the combustion zone tends to propagate along the height of the gasifier, reducing the quality of the producer gas. So it is important that the model should be capable of predicting the bed motion. The effect of bed motion is included into solid species equations as a convective flow term. It is assumed that the bed motion can be represented by a continuous velocity field of the solid phase and this velocity, called shrinkage velocity is applied to all solid species as in Eq. (31). Shrinkage velocity is calculated by equating the downward volumetric flow rate of solid phase to total reduction rate of volume caused as a result of heterogeneous reactions of char. Shrinkage velocity in Eqs. (5) and (6) is evaluated using following equation.
1 Us ¼ rs Ag
Z
R3;R4;R5 X
! ri dV
(31)
i
Use of this velocity in convective terms of solid species equations cause the solid species fields of the gasifier to move downwards at the shrinking rate. This causes the solid phase to move downwards and extend the free board region. But mathematical equations used in free board region and solid phase region are different. Therefore when shrinkage modelling is used there has to be a procedure to track the interface and change the mathematical equations above and below the interface to obtain an accurate solution. The changes of the equations are presented in graphical form in Fig. 3. Gas phase equations differ in two regions with respect to the gas phase porosity, which is defined as the volume fraction of gas phase in each computational cell. The porosity field is initialized in the beginning of the simulation through initial conditions. Gas phase porosity is equal to one in free board region and a variable (<1) in packed bed. The source terms that arise as interactions with solid
704
N. Fernando, M. Narayana / Renewable Energy 99 (2016) 698e710
Fig. 3. Changes of governing equations as a result of bed shrinkage.
equation [18].
kg ¼ 4:8 104 Tg0:717 :
(35)
The thermal conductivity of solid phase is evaluated using a correlation developed for thermal conductivity of a quiescent bed, with a correction for the effect of gas flow, as proposed in the literature [18]. This correlation is presented by Eq. (36).
ks ¼ 0:8kg þ 0:5Re:Pr:kg Fig. 4. Motion of unit step variable c in the direction of bed shrinkage.
phase are not present in free board region. Solid phase equations are different entirely in two regions. In free board, a solid phase does not exist and values of solid phase quantities should be zero. The CFD solver should consider these changes as shrinkage progresses. This is achieved by multiplying certain terms of the general transport equation by a new field variablec, which is a unit step function moving along with shrinkage velocity, as illustrated in Fig. 4. The value of c is evaluated based on gas phase porosity; it is assumed that a certain point (i.e a computational cell) in the solution domain belongs to free board when gas phase porosity exceeds 95%. Classification of computational cells based on porosity is discussed in literature [15]. Hence c can be written as,
c¼
1 ; if εg < 0:95 0 ; if εg > 0:95
(32)
This produces a moving c field along with the packed bed as expected. The transport equations for gas and solid phases indicated in Fig. 3 can be then generalized as,
vðεs rs ∅Þ þ cV$ðεs rs ∅U s Þ ¼ cV$ðGV∅Þ þ cS∅ þ cSg;∅ vt v εg rg ∅ vt
þ V$ εg rg ∅U g ¼ V$ðGV∅Þ þ S∅ þ cSs;∅
(33)
(34)
Depending on the value of c the solver will selectively apply equations in packed bed and free board region as shrinkage progresses. 2.4. Physical properties Gas phase thermal conductivity is evaluated by following
(36)
Biomass particle diameter is used as the characteristic length in evaluating the Reynolds number. Two approaches are used to calculate the evolution of particle diameter in literature. These are shrinking core model and volumetric shrinking density model [28]. In shrinking core model, particle diameter gradually reduces with conversion. In volumetric shrinking density model particle size is held fixed while density reduces [28]. In the present case, shrinking density model is used and particle diameter is held constant while density of solid phase is reduced according to Eq. (37). This assumption is used, as the developed model is a two fluid model, which considers the solid phase as a continuum rather than an assembly of solid particles and the motion of the solid phase is affected by its density rather than the particle size.
rs;t ¼ rs;tΔt YðC2:85 H3:69 OÞ;tΔt þ rs;tΔt Ychar;tΔt þ rs;tΔt Yash;tΔt (37) ðC2:85 H3:69 OÞ Density value is updated explicitly using Eq. (37) during each temporal iteration. Heat capacities of solid and gas phases are assumed to vary according to the relations given in Eqs. (38) and (39). The correlation for gas phase heat capacity is taken from the literature [18]. Solid phase heat capacity is modelled by using Eq. (38) [22].
Cs ¼ 420 þ 2:09Ts þ 6:85 104 Ts2
(38)
Cg ¼ 990 þ 0:122Tg 5680 103 Tg2
(39)
Volume fractions of solid and gas phases are calculated using Eqs. (40) and (41).
εs ¼
mC2:85 H3:69 O
rC2:85 H3:69 O
εg ¼ 1 εs
þ
mchar
rchar
þ
mash
rash
(40)
(41)
The binary diffusion coefficients based on diffusion of a specific component in air, are calculated using Eq. (42) [30].
N. Fernando, M. Narayana / Renewable Energy 99 (2016) 698e710
Di;air
sffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi
1 1 1 ¼ 0:0018583 T 3g þ Mi Mair ps2i;air Ui;air
705
Table 3 Discretization schemes.
(42)
Term
Discretization scheme
V$ðrg εg U g 5U g Þ
Upwind
V$rg εg Cv;g Tg U g
Upwind
V$rs εs Cs Ts U s V$ðrg εg Yi U g Þ
3. Numerical solution
V$ðrs εs Yi U s Þ
Upwind Upwind MUSCL
The open source CFD software OpenFOAM was used to develop a numerical solution to mathematical model presented in the previous section. The equations are numerically solved using finite volume method. Required code was developed by using Cþþ language in OpenFOAM package, including all the relevant differential equations and procedures in the CFD model using built in tools of OpenFOAM. The solution domain is assumed to be two dimensional and consists of radial (x e direction) and axial (y edirection) dimensions only. The computational domain of CFD model is presented in Fig. 5. Discretization schemes used to discretize convective and divergence terms are listed in Table 3. A schematic of solution algorithm is presented in Fig. 6. Grid size is determined based on the value of non-dimensional turbulent wall distance (yþ). A value of y þ approximately equal to one is used. This results in Dx ¼ 0:0094 m for near wall cell layer. Dy ¼ 0:0188 m is used based on a cell aspect ratio of 1:2. All cells in the domain were set uniform in size ðDx ¼ 0:0094 m; Dy ¼ 0:0188 mÞ to get a better numerical resolution. Simulations were performed using a 32 core High Performance Computer with 2.2 GHz processor speed and 64 Gb RAM. To simulate a single batch wise run, approximately 2 h were needed in parallel mode using 32 processors for above mesh resolution. Mesh independence is investigated by increasing the cell number by 50% and 75% from initial value. Solid phase temperature at the same location in mesh at same time was compared under refined meshes. It is found that deviation is less than 1%. As a result, initial mesh is used for subsequent simulations and results are validated through experiment. 3.1. Initial and boundary conditions It is assumed that the gasification process is carried out in a cylindrical reactor using air at room temperature as the gasifying medium. This air stream is supplied at constant flow rate from bottom of the reactor. To model the initial ignition process, a distributed heat source similar to magnitude of heat generated by a
Producer gas outlet (Outlet boundary condiƟons applied)
Free board
Insulated Wall (Wall boundary condiƟons applied)
Insulated Wall (Wall boundary condiƟons applied) Porous biomass packed bed
Air inlet (Inlet boundary condiƟons applied) Fig. 5. Computational domain of the CFD solution.
Fig. 6. Solution algorithm.
combustion reaction is applied over a bed region of 0.2 m above the grate and removed after model is capable of continuing operation by own heat emitted by its combustion reactions. The initial heat source is responsible for pyrolysing a small region of packed to generate char necessary to initiate combustion reactions. This start up method was chosen as it closely resembles the real world operation of a gasifier. The required time for initial ignition was found by trial and error by simulating the system. Initially 5 min time was applied and it was increased gradually until simulation was successfully progressed. The initial velocity field within the reactor is taken as zero. Pressure is set to atmospheric pressure. The initial temperatures of gas and solid phases are taken as 300 K. Initial compositions of product gases are taken as zero and the inlet gas composition is taken to be equal to that of air at room temperature and atmospheric pressure. Boundary conditions for velocity, pressure, temperature and species mole fractions are indicated in following equations. Inlet boundary conditions
706
N. Fernando, M. Narayana / Renewable Energy 99 (2016) 698e710
U ¼ ð0; Uin ; 0Þ
(43)
P ¼ Pin
(44)
Tg ¼ Tg;in
(45)
vTs ¼0 vz
(46)
Yi ¼ Yi;air
(47)
Wall boundary conditions
U¼
vP vTg vTs vYi ¼ ¼ ¼ ¼0 vr vr vr vr
(48)
Outlet boundary conditions;
vU vP vTg vTs vYi ¼ ¼ ¼ ¼ ¼0 vz vz vz vz vz
(49)
Table 4 Physical and chemical properties of fuel. Species
Gliricidia
Particle size Particle shape Batch weight Free carbon (dry basis) Volatiles (dry basis) Ash (dry basis) Initial moisture content (dry basis)
20 mm Cubic 28 kg 17.8% 82.16% 0.04% 20%
phase. There readings comply with gas phase temperatures at the points, as evident from the figure. The results indicate that temperature in the combustion zone rises to a value about 1300 K, with a peak value resulting in few centimetres above the grate. A similar behaviour of temperature variation can be observed in experimental work of Wei Chen at el [31] for updraft gasification of mesquite and juniper wood. Their results indicate a combustion zone temperature of nearly 1300 K.
1200
4. Model validation
Ts-Simulation Tg-Simulation Experimental gas temperature
800
600
400
200 0
0.2
0.4
0.6 Height from grate (m)
Cyclone separator Thermocouples
800 600 400 200 0
0.2
0.4
0.6 Height from grate (m)
0.8
1
1.2
1400 Ts-Simulation Tg-Simulation Exerimental gas temperature
Temperature (K)
1000 800 600 400 200 0
Air blower
1.2
1000
1200
Gas outlet
1
Ts-Simulation Tg-Simulation Experimental gas temperature
1200
Top lid Outlet pipe
0.8
1400
Temperature (K)
Model is validated by comparing the simulation results with data obtained from a laboratory scale updraft gasifier. The gasifier consists of a vertical cylinder with a grate at the bottom. Biomass is fed from the top of the gasifier through a lid, which is closed after loading one batch of biomass. The loaded batch is ignited at the bottom of the gasifier. Air at room temperature is supplied through the grate by using an air blower. In this experimental facility, four thermocouples, which record the temperature along the centre line, were installed along the height of the gasifier. A schematic diagram of the experimental facility is shown in Fig. 7. Simulation results were compared against experimental data for gasification of Gliricidia under an airflow rate of 6 m3/hr. The physical and chemical properties of fuel are listed in Table 4. The comparison of temperature profiles obtained from simulations with experimentally measured temperature values using four thermocouples are presented in Fig. 8. Exit gas temperatures predicted by simulation and experimental exit gas temperatures are displayed in Fig. 9. Theoretical and experimental outlet gas compositions are presented in Fig. 10. It can be observed from these figures that the model is in good agreement with experimental data. In Fig. 8(c), which presents the temperature profiles after 2.5 h of initial ignition, the biomass bed has reduced as a result of fuel consumption due to heterogeneous reactions. The thermocouples located at 60 cm and 90 cm positions do not encounter any solid
Temperature (K)
1000
0.2
0.4
0.6 Height from grate (m)
0.8
1
1.2
Grate Ash collecƟng chamber
Fig. 7. Schematic diagram of experimental laboratory scale gasification system.
Fig. 8. Theoretical and experimental temperature profiles; (a) 45 min after ignition (b) 75 min after ignition (c) 150 min after ignition.
Temperature (K)
N. Fernando, M. Narayana / Renewable Energy 99 (2016) 698e710
900 800 700 600 500 400 300 200 100 0
707
SimulaƟon Experimental data
45 75 120 150 180 minutes minutes minutes minutes minutes Fig. 9. Theoretical and Experimental exit gas temperatures.
20 15 SimulaƟon 10
Fig. 11. Development of reaction zones in the solution domain.
Experimental data
5 0 CO2
CO
H2
CH4
Fig. 10. Theoretical and Experimental gas compositions after 30 min of ignition.
The following figure compares the experimental and theoretical exit gas temperatures of the gasifier. It can be observed that at higher temperatures, the difference between experimental value and theoretical prediction is higher. The CFD model predicts a higher outlet gas temperature than the observed value. This is because the radiation losses from the gas phase through walls and the top lid of the gasifier are not accounted in the model. And the radiation losses become higher at higher temperatures. During the simulations, it is found that composition of produced gas varies with time, during initial period, lot of raw biomass is present in the bed and moisture levels are higher. This introduces moisture into gas phase. Pyrolysis in top layers is not complete and as a result low amount of char is available on the top layers to react with carbon dioxide produced in the combustion zone. The initial gas is therefore higher in carbon dioxide. Experimental data and simulation results for gas composition after 30 min of initial ignition are presented in Fig. 10. The values for gas compositions are also comparable with experimental observations of C.Mandlet et al. [22]. Their experimental data for a fixed bed updraft gasifier operated with softwood pellets indicate a final CO volume percentage of 22.6%, a CO2 percentage of 4.8%, H2 percentage of 4.3% and a CH4 percentage of 2.7%. Experimentally it is found that during the process of gasification, packed bed can be separated into four zones; drying, pyrolysis, reduction and combustion, depending on the main processes taking place in these zones. It is possible to identify the development of these zones in the present CFD model by observing the carbon dioxide mass fraction along the height of the gasifier. This is presented in Fig. 11. The two CO2 hot spots in Fig. 11 can be attributed to near wall flow stagnation. The dark blue and green interface just below the hot spots marks the pyrolysis reaction front. Pyrolysis reactions take place in region above this interface which generates CO2. The produced CO2 is transported to higher regions of the bed through
convection due to gas flow. In near wall region, flow velocity is very low. This reduces the convective transport and tends to accumulate CO2 in near wall cells, increasing its concentration in comparison with centre cells. During a batch process the quality of the produced gas varies with the time, mainly as a result of downward motion of the fuel bed. During experiments it is observed that a stable flame cannot be maintained approximately after 4 h of operation. Fig. 12 present the variation of outlet gas mass fractions and Fig. 13 present the bed movement. The packed bed location is identified by viewing the solid phase temperature profile. Velocity distributions within the gasifier at different times are presented in Figs. 14 and 15. An increase in flow velocity can be observed in free board region according to Fig. 14. This increase is due to the release of gases from packed bed to free board region, especially during pyrolysis. Volatiles are released to gas phase increasing its velocity and pyrolysis zone is located in top layers of the packed bed, which can be observed in Fig. 11. A span wise variation of velocity can be observed in free board region, which can be clearly noticed in Fig. 15. This variation is reduced in packed bed, mainly due to the effect of porosity. In a batch wise simulation as in the present case, free board region extends with time and span wise velocity variation becomes significant. Even within the packed bed, a reduction of flow velocity near walls can be noticed, this effect is reflected in CO2 hot spots in Fig. 11, where CO2 is accumulated due to low convective
0.35 CO2 H2 CH4 CO
0.3 0.25 Mass fraction
Volume percentage
25
0.2 0.15 0.1 0.05 0 0
2000
4000
6000
80 000 Time (s)
10000
12000
Fig. 12. Variation of gas phase component mass fractions with time.
14000
708
N. Fernando, M. Narayana / Renewable Energy 99 (2016) 698e710
Fig. 13. Bed reduction with time; (a) 1 h after ignition (b) 2 h after ignition (c) 3 h after ignition (d) 4 h after ignition. Location of interface between packed bed and free board is marked with the black arrow.
Fig. 14. Axial velocity distribution; (a) 2 h after ignition (b) 2.5 h after ignition (c) 3 h after ignition.
0.04 Packed bed Free boader
0.035
Axial velocity (m/s)
0.03 0.025 0.02 0.015 0.01 0.005 0
0
0.05
0.1
0.15 0.2 Spanwise distance (m)
0.25
0.3
0.35
Fig. 15. Span wise axial velocity distributions in free board and packed bed after 3 h from ignition.
transport. Fig. 16 presents the span wise variation of solid phase temperature at three different locations within the packed bed. A span wise variation of temperature can be observed in near wall area. It can be observed that temperature is lower in near wall regions and higher in central regions. This is due to the fact that lower heat transfer coefficient exists between solid and gas phases in near wall region, because of low value of flow velocity in vicinity of walls. Heat transfer coefficient between solid and gas phase is evaluated using Eq. (9). Dimensionless numbers are evaluated based on a characteristic particle length scale equal to initial particle size. Reynolds number for heat transfer varies in the range of 0e40. Prandlt number varies in the range 0.667e1.16 and Nusselt number varies between 2 and 9.98, with values closer to 2 in near wall region. Maximum temperature occurs near the central axis. This span wise variation reduces at regions closer to the grate, where heat is generated within bed through combustion reactions.
N. Fernando, M. Narayana / Renewable Energy 99 (2016) 698e710
1200
general experimental observations on packed bed gasification processes. The developed model evaluates optimal air flow rate to be 7 m3/h for maximum cumulative CO production for the studied gasifier. In future, the presented mathematical model can be used as a numerical tool to optimize batch wise moving bed gasification processes. The model consists of many runtime variable input parameters such as particle size, inlet air flow rate, inlet-gas compositions and physical & chemical properties of feed-stock. The model can be used to perform parameter studies to find the optimum values of these parameters for a particular process. The model can be further improved by implementing an advanced pyrolysis scheme, including primary and secondary pyrolysis reactions separately and tar formation reactions.
Temperature (K)
1000
800 0.3 m 0.4 m 0.5 m
600
400
200 0
0.05
0.1
0.15 Spamwise distance (m)
0.2
0.25
709
0.3
Acknowledgment Fig. 16. Span wise temperature distribution at different locations within packed bed after 1.5 h from ignition. Dashed line: 0.3 m from grate. Dash dot line 0.4 m from grate. Solid line: 0.5 m from grate.
Table 5 Simulation Results for different air flow rates.
The authors are thankful to senate versity of Moratuwa (SRC/CAP/14/06), port for the research project and experimental data from his research presented mathematical model.
research committee of Unifor providing financial supMr. M. Amin for sharing work for validation of the
Flow rate (m3/hr) Batch time (s) Peak CO composition Cumulative CO (m3) 4 5 6 7 8 9 10
21600 15800 14400 12800 11300 10800 9200
0.38 0.41 0.404 0.413 0.406 0.404 0.401
5.2 5.51 6.11 6.35 5.68 5.53 5.372
The temperature increase due to combustion reactions become dominant than convective heat transfer contribution. 5. Optimization of air flow rate to the gasifier based on CFD model The external air flow to the gasifier supply fuel needed to maintain combustion process. When air flow rate is higher, the extent of the combustion zone increases, causing the produced fuel gases to burn inside the reactor. This reduces the quality of the outlet gas. When flow rates are too small, combustion rates reduce and sufficient heat is not produced for complete cracking of biomass in top layers of the bed. The developed CFD model is used to evaluate optimal air flow rate for maximum cumulative carbon monoxide production. A series of simulations were performed for air flow rates ranging from 4 m3/hr to 10 m3/hr. The results are summarized in Table 5. Based on the cumulative CO production, it can be stated that, for the particular experimental gasifier, a flow rate of 7 m3/hr maximizes the CO yield from biomass batch. 6. Conclusion and future work A mathematical model for gasification of biomass in a batch wise updraft packed bed reactor was developed and simulated using open source CFD software OpenFOAM. The developed model in this study accounts for drying, pyrolysis, reduction and combustion reactions. All three modes of heat transfer; conduction, convection and radiation, was included in the packed bed model. It is found by the simulation study; radiation is the main mode of heat transfer through the biomass packed bed and critically important. Reduction of bed volume due to heterogeneous reactions are also considered and modelled in the simulations. The simulation results are in good agreement with experimental data and also with
References [1] P. McKendry, Energy production from biomass (part 1): overview of biomass, Bioresour. Technol. 83 (1) (May 2002) 37e46. [2] K. Umeki, T. Namioka, K. Yoshikawa, Analysis of an updraft biomass gasifier with high temperature steam using a numerical model, Appl. Energy 90 (1) (Feb. 2012) 38e45. [3] P. McKendry, Energy production from biomass (part 2): conversion technologies, Bioresour. Technol. 83 (1) (May 2002) 47e54. [4] K. Srirangan, L. Akawi, M. Moo-Young, C.P. Chou, Towards sustainable production of clean energy carriers from biomass resources, Appl. Energy 100 (Dec. 2012) 172e186. [5] E.G. Pereira, J.N. da Silva, J.L. de Oliveira, C.S. Machado, Sustainable energy: a review of gasification technologies, Renew. Sustain. Energy Rev. 16 (7) (Sep. 2012) 4753e4762. [6] P. McKendry, Energy production from biomass (part 3): gasification technologies, Bioresour. Technol. 83 (1) (May-2002) 55e63. [7] F. Guo, Y. Dong, L. Dong, C. Guo, Effect of design and operating parameters on the gasification process of biomass in a downdraft fixed bed: an experimental study, Int. J. Hydrogen Energy 39 (11) (Apr. 2014) 5625e5633. [8] M.A. Masmoudi, M. Sahraoui, N. Grioui, K. Halouani, 2-D Modeling of thermokinetics coupled with heat and mass transfer in the reduction zone of a fixed bed downdraft biomass gasifier, Renew. Energy 66 (Jun. 2014) 288e298. [9] A.H. Mahmoudi, F. Hoffmann, B. Peters, Application of XDEM as a novel approach to predict drying of a packed bed, Int. J. Therm. Sci. 75 (Jan. 2014) 65e75. [10] G. Cau, V. Tola, A. Pettinau, A steady state model for predicting performance of small-scale up-draft coal gasifiers, Fuel 152 (Jul. 2015) 3e12. [11] D.F. Fletcher, B.S. Haynes, F.C. Christo, S.D. Joseph, A CFD based combustion model of an entrained flow biomass gasifier, Appl. Math. Model. 24 (3) (Mar. 2000) 165e182. [12] K.D. Patel, N.K. Shah, R.N. Patel, CFD analysis of spatial distribution of various parameters in downdraft gasifier, Procedia Eng. 51 (2013) 764e769. [13] S. Murgia, M. Vascellari, G. Cau, Comprehensive CFD model of an air-blown coal-fired updraft gasifier, Fuel 101 (Nov. 2012) 129e138. [14] Y. Wu, Q. Zhang, W. Yang, W. Blasiak, Two-dimensional computational fluid dynamics simulation of biomass gasification in a downdraft fixed-bed gasifier with highly preheated air and steam, Energy Fuels 27 (6) (2013) 3274e3282. [15] K. Kwiatkowskia, P. Zukb, Biomass gasification solver based on OpenFOAM, Comput. Phys. Commun. (2013) 1e29. [16] H.K. Versteeg, W. Malalasekera, in: M. Harlow (Ed.), An Introduction to Computational Fluid Dynamics: the Finite Volume Method, 2 edition., Prentice Hall, England; New York, 2007. [17] Y.-Q. Zhuang, X. Gao, Y. Zhu, Z. Luo, CFD modeling of methanol to olefins process in a fixed-bed reactor, Powder Technol. 221 (May 2012) 419e430. [18] T. Jurena, Numerical Modelling of Grate Combustion, Brno University of Technology, Brno, 2012. [19] H. Liu, CFD Modeling of Biomass Gasification Using a Circulating Fluidized Bed Reactor, University of Waterloo, Ontario, Canada, 2014. [20] ANSYS Fluent, ANSYS FLUENT Theory Guide, 15317, ANSYS Inc, Canonsburg, PA, 2011, p. 2009. [21] A. Nikolopoulos, I. Malgarinos, N. Nikolopoulos, P. Grammelis, S. Karrelas, E. Kakaras, A decoupled approach for NOxeN2O 3-D CFD modeling in CFB plants, Fuel 115 (Jan. 2014) 401e415. [22] C. Mandl, I. Obernberger, F. Biedermann, Modelling of an updraft fixed-bed
710
N. Fernando, M. Narayana / Renewable Energy 99 (2016) 698e710
gasifier operated with softwood pellets, Fuel 89 (12) (Dec. 2010) 3795e3806. [23] Purnomo, Model for a Downdraft Solid Fuel Combustor, The University of Wisconsin, 1988. [24] S. Sinha, A. Jhalani, M.R. Ravi, A. Ray, Modelling of pyrolysis in wood: a review, SESI J. 10 (1) (2000) 41e62. [25] B.V. Babu, A.S. Chaurasia, Heat transfer and kinetics in the pyrolysis of shrinking biomass particle, Chem. Eng. Sci. 59 (10) (May 2004) 1999e2012. [26] N. Fernando, M. Amin, M. Narayana, T. Jayawickrama, S. Jayasena, A mathematical model for pyrolysis of biomass, in: Moratuwa Eng. Res. Conf. (MERCon), IEEE Conf. Publ, 2015, pp. 1e6. [27] M. Amin, Development of Updraft Gasifier and Performance Analysis for
Different Types of Biomass Materials, University of Moratuwa, Sri Lanka, 2015. [28] Y. Haseli, J.A. van Oijen, L.P.H. de Goey, A detailed one-dimensional model of combustion of a woody biomass particle, Bioresour. Technol. 102 (20) (Oct. 2011) 9772e9782. [29] R.E. Treybal, Mass-transfer Operations, third ed., McGraw-Hill Book Company, 1980. [30] R.B. Bird, W.E. Stewart, E.N. Lightfoot, Transport Phenomena, second ed., Wiley, New York, 2001. [31] W. Chen, K. Annamalai, R.J. Ansley, M. Mirik, Updraft fixed bed gasification of mesquite and juniper wood samples, Energy 41 (1) (May 2012) 454e461.