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CFD modeling of gasiﬁcation process in tapered ﬂuidized bed gasiﬁer Hossein Askaripour Department of Chemical and Petroleum Engineering, Sharif University of Technology, Tehran, Iran

a r t i c l e i n f o

a b s t r a c t

Article history: Received 26 August 2019 Received in revised form 23 October 2019 Accepted 7 November 2019 Available online xxx

This article presents a two-dimensional simulation of the coal gasiﬁcation in tapered ﬂuidized bed gasiﬁer. The effects of tapered angle, gasiﬁer temperature, velocity of gasifying agent, and steam-to-air ratio on the gas compositions, lower heating value (LHV), and higher heating value (HHV) were examined. In order to ﬁnd the appropriate operating conditions of coal gasiﬁcation, carbon conversion efﬁciency (CCE) and cold gas efﬁciency (CGE) were also explored. It was found that with an increase of the gasiﬁer temperature, CCE and CGE of the tapered gasiﬁer diminishes. Increasing tapered angle results in a decrease of the LHV and HHV of the gas products, whereas the CCE of gasiﬁcation process increases. The CGE of the gasiﬁer increases as the tapered angle goes up from 3 to 5 , but it slightly varies with a further increase of the tapered angle from 5 to 11. The results indicate that as the velocity of gasifying agent increases, LHV and HHV of the product gas drop while CCE of the gasiﬁer enhances. It was also found that the concentrations of H2, CO, and CO2 decrease with an increase in the steam-to-air ratio. © 2019 Elsevier Ltd. All rights reserved.

Keywords: Tapered ﬂuidized bed gasiﬁer Tapered angle Gasiﬁer temperature Steam-to-air ratio Eulerian modeling

1. Introduction Gasiﬁcation is a thermochemical process converting the solid fuels (e.g., coal, biomass, etc.) into a gaseous mixture that contains mainly methane, carbon dioxide, carbon monoxide, hydrogen, and nitrogen. In addition to the product gases, some byproducts like ash, tar, char particles, and heavier hydrocarbons are also produced from the gasiﬁcation reactions [1]. The application of the ﬂuidized bed gasiﬁers for gasifying solid fuels has attracted much attention because of high rate of heat and mass transfer and good mixing properties. The complicated behavior of hydrodynamics and chemical reactions in gasiﬁers necessitates performing experimental and theoretical works to obtain enough valuable information about the ﬂuidized bed gasiﬁers in different sizes [2,3]. To describe the gasiﬁcation process in a ﬂuidized bed gasiﬁer, two modeling approaches have been proposed in the literature, i.e., equilibrium modeling and kinetic modeling [1]. Because the equilibrium modeling does not involve the hydrodynamics of gas and solid phases, this approach is independent of the gasiﬁer type. Based on the calculation process of the product gas compositions, the ﬁrst approach is classiﬁed into stoichiometric and nonstoichiometric models. However, the kinetic modeling considers the ﬂuidized bed hydrodynamics along with the reaction kinetics [1]. In this regard, the second approach is classiﬁed into Eulerian-

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Lagrangian [4e6] and Eulerian-Eulerian [7e9] models. With an increase in the computational capability of computers, researchers become more interested in the CFD modeling of gasiﬁcation process using Eulerian-Lagrangian and Eulerian-Eulerian approaches. Lv et al. [10] conducted an experimental work to explore the effects of biomass particle size, equivalence ratio, and reactor temperature on the gas compositions, lower heating value (LHV), and carbon conversion efﬁciency (CCE). It was found that with an increase in the reactor temperature, hydrogen production increased and with an increase in the equivalence ratio, LHV of the fuel gas decreased. Gerber et al. [11] applied a Eulerian model to simulate the wood gasiﬁcation in a ﬂuidized bed gasiﬁer. They examined the effects of different parameters including the reactor throughput, static bed height, feeding rate, and the kinetics of primary pyrolysis. The results showed that operating parameters slightly affected the outlet gas compositions while amount of the tar produced in the gasiﬁer was strongly dependent on the operating and model parameters. The experimental study of biomass gasiﬁcation was carried out in interconnected ﬂuidized beds [12]. The effects of steam to biomass (S/B) ratio and reactor temperature on the tar content, carbon gasiﬁcation, and composition of H2-rich gas were investigated. It was found that S/B ratio slightly affected the gas compositions and with an increase in the reactor temperature, H2 content decreased and CO content increased. A twodimensional CFD study was carried out by Couto et al. [13] to investigate the effect of oxygen-enriched air on the gasiﬁcation temperature and gas compositions. The results showed that as the

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oxygen content of the inlet air increased, H2 and N2 mole fractions decreased while CO2 mole fraction increased. The biomass gasiﬁcation in a ﬂuidized bed reactor was simulated by Ku et al. [14] using CFD-DEM model, and the effects of operating parameters such as S/B ratio, injection position of biomass, and temperature were studied. The results showed that with an increase of the S/B ratio, mole fractions of CO2 and H2 increased while that of CO decreased. The gasiﬁcation of coffee husks was simulated using Eulerian-Eulerian approach [15] and the effects of moisture content and equivalence ratio on the reactor temperature, higher heating value (HHV), and cold gas efﬁciency (CGE) were studied. It was found that the moisture content had negative effect on the CGE and HHV and with an increase in the equivalence ratio, mole fractions of CH4, H2, and CO decreased and those of CO2 and N2 increased. Xia et al. [16] used Eulerian approach to simulate the process of coal gasiﬁcation in a ﬂuidized bed with a pair of embedded high-speed jets. The results showed that the embedded jets could split large gas bubbles and enhance the contacts between gas and solid phases. In addition, conversion of steam and carbon for the embedded jets gasiﬁer was higher than that for the conventional gasiﬁer. The biomass gasiﬁcation was studied using a two-dimensional Eulerian model in a bubbling ﬂuidized bed gasiﬁer [17]. The effects of steam temperature, S/B ratio, and equivalence ratio on the gas compositions were examined. It was found that with an increase in S/B ratio from 0.5 to 1.5, H2 concentration enhanced 87% and with an increase in equivalence ratio from 0.15 to 0.4, H2 concentration lowered 72%. To examine the effect of biomass properties, ten types of lez-Va zquez et al. [18] and biomass fuels were considered by Gonza the gasiﬁcation performance and gas compositions were studied. The correlations obtained for the biomass gasiﬁcation showed that carbon and volatile matter contents, and HHV of biomass have positive effects on the CO and caloriﬁc value of product gas. An experimental work in a two-stage ﬂuidized bed gasiﬁer was conducted using the rice straw as biomass fuel [19]. The results indicated that the gasiﬁer performance improved as the temperature increased and HHV of the product gas decreased with an increase in equivalence ratio. The steam gasiﬁcation of biomass in a ﬂuidized bed reactor was simulated using coarse grain model [20]. The effects of S/B ratio and operating temperature on the gas compositions were studied and it was found that increasing the S/B ratio led to an increase in H2 mole fraction while the mole fraction of CO decreased. It was also found that coarse grain model could reliably predict the gasiﬁcation process with shorter computational time than the discrete element method. Meng et al. [21] studied the effect of different types of gasifying agents (oxygen-steam, air, oxygen-enriched air, and air-steam) on the gasiﬁcation process of a novel pilot scale ﬂuidized bed. The results indicated that type of the gasifying agent signiﬁcantly affected the product gas compositions. The respective LHV and H2 content for oxygen-enriched air and airsteam gasifying agents were higher than that the air was only used. Tapered ﬂuidized beds have received lots of attention because of their capability for ﬂuidization of solids with different properties [22] and better mixing of solid and ﬂuid phases [23]. Gradual decrease of the gas velocity, due to change in the cross-sectional area of the column, promotes the use of tapered ﬂuidized beds in chemical processes, like solid fuel combustion or gasiﬁcation, which encounter continuous decreasing size of particles. Despite the numerous investigations performed about the gasiﬁcation process, no simulation or experimental study for tapered ﬂuidized bed gasiﬁers have been reported to date. Accordingly, the present author was convinced to conduct a study regarding this type of gasiﬁers. To validate the simulation results, predictions for the product gas compositions were compared with the experimental data of a cylindrical gasiﬁer [24]. In addition, the effects of tapered

angle, gasiﬁer temperature, steam-to-air ratio, and velocity of gasifying agent on the gas compositions, lower and higher heating values, cold gas efﬁciency, and carbon conversion efﬁciency were comprehensively explored. 2. Mathematical model In the present study, an unsteady-state Eulerian multiphase model with the kinetic theory of granular ﬂow (KTGF) was employed to simulate the coal gasiﬁcation in tapered ﬂuidized bed gasiﬁer. The balance equations of mass, momentum, turbulence, energy, and species transport for gas and solid phases along with the equation of granular temperature for the solid phase were solved together. The constitutive relations required for the solid phase equations were also obtained based on the KTGF to model the stresses of solid particles. Here the governing equations for gas and solid phases are explained in detail, then pyrolysis, homogeneous gas phase reactions, and heterogeneous gasiﬁcation reactions are presented. 2.1. Hydrodynamic equations To model the hydrodynamics of gas and solid phases in gasiﬁcation process using Eulerian approach, conservation equations of mass and momentum for each phase closed with appropriate constitutive relations should be solved. The interactions between gas and solid phases are taken into account by introducing additional terms in conservation equations. The continuity equations for gas and solid phases can be represented by Ref. [1].

v ag rg þ V: ag rg ! v g ¼ Sgs vt

(1)

v ðas rs Þ þ V:ðas rs ! v s Þ ¼ Ssg vt

(2)

where a is the volume fraction, r is the density, ! v is the velocity, and subscripts g and s denote the gas and solid phases, respectively. The source terms, Sgs and Ssg , are the mass transfer between gas and solid phases owing to the heterogeneous chemical reactions and can be evaluated from:

Sgs ¼ Ssg ¼ wi

X

gi Rhet;i

(3)

where wi , gi , and Rhet;i are the molecular weight, stoichiometric coefﬁcient, and reaction rate of species i, respectively. To consider the effect of momentum and energy carried along with the exchanged mass between gas and solid phases, the source terms are added to the momentum and energy equations. The momentum equations for gas and solid phases can be expressed as follows [1]:

v ! ag rg ! v g þ V: ag rg ! v g! v g ¼ ag Vp þ V:tg þ ag rg g vt v g þ Sgs ! vg v s ! þ Kgs !

(4)

v ! ðas rs ! v s Þ þ V:ðas rs ! v s! v s Þ ¼ as Vp Vps þ V:ts þ as rs g vt ! v s þ Ssg ! vs þ Kgs v g ! (5) ! where p is the pressure, t is the stress tensor, g is the gravitational acceleration, and Kgs is the interphase momentum exchange coefﬁcient. The stress-strain tensors of gas and solid phases can be represented by

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2 3

v g þ! tg ¼ ag rg V! v g ag mg V:! vg I T

2 3

T

(6)

viscosity, can be deﬁned as a function of granular temperature. The algebraic form of the granular temperature was employed in this study [16]:

(7)

ð ps I þ ts Þ : V! v s gQs ¼ 0

v s þ! v sI ts ¼ as rs V! v s þ as ls ms V:!

where m and l are the shear and bulk viscosities, respectively. The expression proposed by Lun et al. [25] was applied for evaluating the bulk viscosity of solid phase:

4 3

ls ¼ as rs ds g0;ss ð1 þ ess Þ

Q 1 s

2

The shear viscosity of particles, that is a combination of kinetic, collisional, and frictional terms, can be given by Ref. [3].

pﬃﬃﬃﬃﬃﬃﬃﬃﬃ

2 10rs ds Qs p 4 1 þ as g0;ss ð1 þ ess Þ 5 96ð1 þ ess Þas g0;ss Q 1 p sin f 4 2 s 2 s þ as rs ds g0;ss ð1 þ ess Þ þ pﬃﬃﬃﬃﬃﬃﬃ 5 p 2 I2D

ms ¼

(9)

where ds is the particle diameter, rs is the particle density, g0;ss is the radial distribution function, ess is the coefﬁcient of restitution, Qs is the granular temperature, ps is the solid pressure, f is the angle of internal friction, and I2D is the second invariant of deviatory stress tensor. The solid phase pressure and radial distribution function can be evaluated by Ref. [3]:

ps ¼ as rs Qs þ 2rs ð1 þ ess Þa2s g0;ss Qs

(10)

as 1=3 1 g0;ss ¼ 1

(11)

ag 0:8

s

CD ¼

> :

0:687 i 24 h 1 þ 0:15 ag Res ag Res

(16)

Various turbulence models have been proposed in the literature to compute the ﬂuctuations in a turbulent ﬂow. In this work, the standard k-ε turbulence model consisted of two separate transport equations for turbulent kinetic energy and dissipation rate was employed. Because of reasonable accuracy and robustness in simulation of the industrial mass and heat transfer phenomena, this semi-empirical model becomes popular. The turbulent kinetic energy, k, and its dissipation rate, ε, can be obtained from the following transport equations [29]:

mt;m vðrm kÞ þ V:ðrm ! v m kÞ ¼ V: Vk þ Gk;m rm ε vt sk

(17)

mt;m vðrm εÞ ε þ V:ðrm ! v m εÞ ¼ V: Vε þ C1ε Gk;m C2ε rm ε vt k sε

T v m þ V! vm Gk;m ¼ mt;m V! v m : V!

ag > 0:8

(19)

where sk and sε are the inverse turbulent Prandtl number for k and ε, respectively, and C1ε and C2ε are the model constants. In addition, rm is the mixture density, ! v m is the mixture velocity, and mt;m is the turbulent viscosity that can be computed, respectively, from Ref. [29]:

rm ¼

X

ai ri

P ar! v ! v m ¼ Pi i i

ai ri

(20)

(21)

Res 1000 Res > 1000

0:44

3 12 1 e2ss g0;ss pﬃﬃﬃ rs a2s Q2s ds p

2.2. k-ε Turbulence equations

(12)

In which

8 > <

gQs ¼

where

The interphase momentum exchange coefﬁcient is used to determine the drag force between gas and solid phases. The drag model of Gidaspow [26] that is a combination of Wen-Yu equation [27] for the dilute phases (as < 0:2) and Ergun equation [28] for the dense phases (as > 0:2) was applied.

! > ! > > > : 3C as rg v s v g a1:65 g ds 4 D

where

(18)

as;max

Kgs ¼

(15)

(8)

p

! 8 vs! a2s mg v g > > þ 1:75rg as 150 > > < ds ag d2

3

mt;m ¼ rm Cm

k2 ε

(22)

(13)

vg ! rg ds ! v s Res ¼ mg

(14)

where CD and Res are the drag coefﬁcient and solid Reynolds number, respectively. Analogous with the gas temperature in thermodynamics, the kinetic energy associated with the ﬂuctuations of solid particles can be represented by a pseudo-thermal temperature. The equation of granular temperature is derived on the basis of kinetic theory of granular ﬂow and the properties of particles, such as pressure and

2.3. Conservation equations of species transport and energy To model the coal gasiﬁcation in tapered ﬂuidized bed gasiﬁer, the equations of energy and species transport for gas and solid phases should be coupled with hydrodynamic equations of the gasiﬁer. The gas phase is considered to be a multicomponent mixture of O2, N2, H2O, CO, CO2, H2, and CH4 while the solid phase consists of raw coal, inert sand and char. The conservation equation of species transport for ith species can be given by Ref. [1].

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! v ag rg Yg;i þ V: ag rg ! v g Yg;i ¼ V: ag J g;i þ ag Rg;i þ Rhet;i vt (23) ! where Yg;i , J g;i , Rg;i , and Rhet;i are the mass fraction, diffusion ﬂux, and the homogeneous and heterogeneous reaction rate for species i, respectively. The modiﬁed Fick’s law was employed to calculate the diffusion ﬂux of species i in the turbulent ﬂow [1]:

! m J g;i ¼ rg Di;m þ t VYg;i Sct

(24)

In which

(R2)

In which the reaction rate can be given by Ref. [31]:

12581 Cc rc ¼ 2 105 exp T

(30)

(25)

Di;j

2.5. Homogeneous gas phase reactions

where Sct , Di;m , Xi , and Di;j are the turbulent Schmidt number, mass diffusion coefﬁcient of species i in the mixture, mole fraction of species i, and binary diffusion coefﬁcient of species i and j, respectively. Accounting the mechanisms of heat transfer in each phase and the heat exchange between phases, the energy conservation equations for gas and solid phases are obtained as follows [16]:

vpg v þ tg ag rg hg þ V: ag rg ! v g hg ¼ ag vt vt : V! v g þ V: ag kg VTg þ hgs Tg Ts þ Sgs hg þ DHg

(26)

v vps ðas rs hs Þ þ V:ðas rs ! þ ts v s hs Þ ¼ as vt vt ! : V v s þ V:ðas ks VTs Þ þ hgs Ts Tg þ Ssg hs

(27)

where h is the speciﬁc enthalpy, k is the thermal conductivity, T is the temperature, hgs is the heat transfer coefﬁcient between gas and solid phases, and DHg is the heat of homogeneous gas phase reactions. The heat transfer coefﬁcient between phases is a function of solid phase Nusselt number, Nus , and can be computed from Ref. [3].

hgs ¼

k

Coal !ð1 hÞchar þ h volatile

where Cc is the concentration of unreacted coal particles and h is the pyrolysis coefﬁcient. The value of h was set to 0.3 [31].

1X Di;m ¼ P X i j jsi

The composition of raw coal was determined based on the proximate and ultimate analyses shown in Table 1. Because of small percent of nitrogen and sulfur, the chemical reactions of these species were ignored and the following single-equation model was considered for the coal pyrolysis [31]:

6kg ag as Nus

(28)

d2s

Nus ¼ 7 10ag þ 5a2g 1 0

The following homogeneous gas phase reactions were considered in this study:

H2 þ 0:5O2 /H2 O

(R3)

CH4 þ 2O2 /CO2 þ 2H2 O

(R4)

CO þ 0:5O2 /CO2

(R5)

CO þ H2 O4H2 þ CO2

(R6)

The ﬁrst three reactions are the exothermic oxidation of H2, CH4, and CO and the fourth one is the water-gas shift reaction. The kinetic rate of these reactions are given below [32].

3430 1:5 r3 ¼ 5:159 1015 exp T g CO2 C 1:5 H2 Tg

(31)

15700 1 T g CCH4 CO2 r4 ¼ 3:552 1014 exp Tg

(32)

16000 CCO C 0:5 r5 ¼ 1:0 1015 exp O2 Tg

(33)

CCO2 CH2 1510

CCO CH2 O r6 ¼ 2780 exp Tg 0:0265 exp 3968 Tg (34)

1 1 3A 3 þ 1:33 2:4ag þ 1:2a2g Re0:7 @1 þ 0:7Re0:2 s Pr s Pr =

=

2.6. Heterogeneous gasiﬁcation reactions

(29) The solid char particles produced via the pyrolysis reaction are gasiﬁed in heterogeneous reactions. The gasiﬁcation reactions depend on the gaseous species surrounding atmosphere of char particles. The four heterogeneous reactions considered here are as follows:

where Pr is the Prandtl number.

2.4. Reaction kinetics of coal pyrolysis The thermochemical decomposition of solid coal in the absence of air or oxygen is termed pyrolysis and is a very complex process resulting a mixture of gaseous species and carbonaceous particles known as char. Various models for pyrolysis reactions have been proposed in the literature [30]. In this work, the reaction of coal pyrolysis and its products were considered as follows: Coal / Char þ H2O þ Ash þ Volatile (CO, CH4, CO2, H2)

(R1)

C þ H2 O/CO þ H2

(R7)

C þ CO2 /2CO

(R8)

C þ O2 /CO2

(R9)

C þ 2H2 /CH4

(R10)

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The reaction kinetic and diffusion rate were both considered in the heterogeneous reactions of char. The rate of above reactions can be expressed as [11]:

kdiff ¼

r7 ¼ k7;het CH2 O

(35)

Sh ¼ 2 þ 0:6Re1=2 Sc1=3

r8 ¼ k8;het CCO2

(36)

r9 ¼ k9;het CO2

(37)

where kdiff and kkin are the diffusion and the kinetic rate constants, and Sh, Dg , R, and Sc are the Sherwood number, gas phase diffusion coefﬁcient, universal gas constant, and the Schmidt number, respectively.

r10 ¼ k10;het CH2

(38)

The heterogeneous rate constant, khet , is given by Ref. [33]:

khet ¼

1 kdiff

1 þ kkin

!1 (39)

Dg Sh RTs ds

(44)

(45)

2.7. Performance evaluation of gasiﬁcation process To assess the performance of gasiﬁcation process in tapered ﬂuidized bed gasiﬁer, lower heating value (LHV), higher heating value (HHV), carbon conversion efﬁciency (CCE), and cold gas efﬁciency (CGE) are deﬁned as follows [10,18]:

. LHVg MJ Nm3 ¼ 11:76 ð%COÞ þ 11:882 ð%H2 Þ þ 37:024 ð%CH4 Þ

(46)

In which [11].

11200 k7;kin ¼ 1:04 103 Ts exp Ts

(40)

. . HHVg MJ Nm3 ¼ LHVg MJ Nm3 þ 1:83 ð%H2 OÞ CCEð%Þ ¼

15600 k8;kin ¼ 3:42Ts exp Ts

(41) CGEð%Þ ¼

15600 k9;kin ¼ 3:42Ts exp Ts

(42)

15600 k10;kin ¼ 3:42 103 Ts exp Ts

(43)

and [33].

(47)

Vg 1000 ð%CH4 þ %CO þ %CO2 Þ 12=22:4 100 W %C (48) m_ g HHVg 100 m_ c HHVc

(49)

where %CO, %H2 , %CH4 , and %CO2 are the gas species concentration, Vg is the volumetric ﬂow rate of product gas, W is the coal feeding rate, and %C is the carbon content in the ultimate analysis of coal. In addition, m_ g and m_ c are the mass ﬂow rates, and HHVg and HHVc are the higher heating values for the product gas and coal, respectively. 2.8. Initial and boundary conditions

Table 1 Properties of raw coal and operating conditions [24]. Proximate analysis (wt.%) Moisture Volatile matter Fixed carbon Ash Ultimate analysis (wt.%) Carbon Hydrogen Nitrogen Oxygen Sulfur Ash Bed materials Particle density (kg/m3) Particle size (mm) Higher heating value (kJ/kg) Operating conditions Air supply, Fa (kg/h) Steam supply, Fs (kg/h) Coal feed, Fc (kg/h) Inlet temperature of air and steam, Tin ( C)

2.6 41.8 54.1 1.5 75.3 5.4 1.8 15.6 0.4 1.5 1250 0.62 29695 Case #1 19.4 4.6 8.0 422

Case #2 21.9 4.6 8.0 420

A schematic representation of the tapered ﬂuidized bed gasiﬁer is shown in Fig. 1. The gasiﬁer is composed of a tapered section at the bottom connected to a cylindrical section at the top. As shown in this ﬁgure, inlet and outlet diameters of the gasiﬁer are 10 and 22 cm, respectively, and the entire height of the gasiﬁer is 2 m. The velocity-inlet boundary condition was set for the gasifying agent (a mixture of air and steam) and coal particles at the inlet, whereas the pressure-outlet boundary condition was set at the outlet of gasiﬁer. Temperature and mass fractions of the gas species were also set at the gasiﬁer inlet. No-slip wall boundary condition was set at the gasiﬁer walls, and the heat ﬂux and diffusion ﬂux of gas species into the walls were considered to be zero. Initially, a given height of tapered gasiﬁer was ﬁlled with inert sand with a volume fraction of 0.48, and the velocities of gas and solid phases were considered to be zero. 2.9. Solution procedure Governing

equations

of

continuity,

momentum,

energy,

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appropriate mesh size, the gasiﬁer was simulated with the grid numbers of 16 360, 22 400, and 27 440 and molar fractions of CH4, CO, CO2, H2, and N2 in the product gas as well as temperature distribution along the gasiﬁer were compared. The results indicated that increasing the grid number more than 22 400 (Dx ¼ 10 mm and Dy ¼ 5 mm) insigniﬁcantly inﬂuences the simulation results. Therefore, this mesh size was used in the rest of these simulations. In the following subsections, a comparison of the species molar fractions in the product gas between simulation results and experimental data [24] is initially presented, then the effects of different parameters including the tapered angle, gasiﬁer temperature, steam-to-air ratio, and the velocity of gasifying agent on the product gas compositions, lower and higher heating values, cold gas efﬁciency, and the carbon conversion efﬁciency are explored. The simulation parameters and operating conditions of the tapered gasiﬁer are summarized in Table 2. 3.1. Validation

Fig. 1. A schematic representation of tapered ﬂuidized bed gasiﬁer.

turbulence, and species transport for gas and solid phases were solved using ﬁnite volume method (FVM) to simulate coal gasiﬁcation in tapered gasiﬁer. The phase-coupled SIMPLE algorithm was employed to couple the pressure and velocity equations, and the ﬁrst order upwind scheme was applied for the spatial discretization of volume fraction, momentum, energy, species, and turbulence. In addition, ﬁrst order implicit scheme was applied for the time discretization, and a time step of 3 104 s with a maximum number of 25 iterations for each time step were used in the simulations. The simulation runs were performed for 25 s, the initial 10 s was considered as the start-up period and the variables of interest (velocities, temperatures, and gas phase concentrations) were averaged for the rest 15 s duration. 3. Results and discussions Despite increasing the number of grid points, i.e., decreasing the mesh size, can usually provide better simulation results, it affects the complexity of computations. In order to determine the

To verify the validity of the present modeling, validation with experimental data is essential. In this study, experimental data reported in Ref. [24] for dry compositions of the product gas in a cylindrical gasiﬁer were compared with the simulation results. Ocampo et al. [24] considered a cylindrical reactor with a height of 2 m and a diameter of 22 cm and a mixture of coal and limestone was introduced into the gasiﬁer. They experimentally measured the gas concentrations at various operating conditions such as inlet temperature, and ﬂow rates of gas and solid. The characteristics of coal used in their experiments were the same as reported in Table 1. Fig. 2(a) and (b) illustrates gas compositions at the gasiﬁer outlet for the two operating conditions expressed in Table 1. It can be seen that the predictions obtained from simulation are in good agreement with the experimental data and the mean absolute error for molar fractions of the gaseous species are 1.4% and 3.2% for Fig. 2(a) and (b), respectively; therefore, the validity of the present modeling can be conﬁrmed. However, the results of these ﬁgures indicate that there is a small underestimation for H2 and CO2 molar fractions as well as small overestimation for CO, CH4, and N2 molar fractions. The ﬁrst reason for the discrepancies between simulations and experiments can be attributed to simpliﬁcation of gasiﬁer geometry from 3D to 2D conﬁguration. The second reason may be owing to the uncertainty of kinetic parameters applied to heterogeneous reactions, because different kinetic parameters were proposed in the literature for heterogeneous reactions. As stated above, Ocampo et al. [24] used a mixture of coal and limestone as inlet feed in their experiments, whereas the coal was only considered in these simulations. Ignoring the effects of chemical reactions relating to

Table 2 Values of simulation parameters and operating conditions used in the CFD simulation. Parameter

Value

Specularity coefﬁcient Particle-wall restitution coefﬁcient Particle-particle restitution coefﬁcient Angle of internal friction ( ) Maximum packing limit (as,max) Gasiﬁer height (m) Inlet diameter of gasiﬁer (m) Outlet diameter of gasiﬁer (m) Tapered angle ( ) u/umf of gasifying agent Gasiﬁer temperature Inlet molar fraction of steam Molar fraction of O2 in air stream Flow rate of coal (kg/h)

0.5 0.9 0.9 30 0.64 2.0 0.1 0.22 3, 5, 7, 9, 11 1.6 695 K 0.275 0.21 8.0

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Fig. 2. Comparison of outlet molar fractions between experimental data and simulation results for the operating condition given in Table 1: (a) Case I; (b) Case II.

limestone on the gasiﬁcation process may be the third reason for these under- or overestimations.

3.2. Effects of tapered angle To assess the effects of tapered angle on the performance of tapered gasiﬁer, ﬁve tapered angles of 3, 5, 7, 9, and 11 were considered and the species concentrations, LHV, HHV, CGE, and CCE of the product gas were examined. For all tapered angles, pressure drop of tapered ﬂuidized bed gasiﬁer was obtained as a function of superﬁcial gas velocity via the hydrodynamic simulation and the gas velocity at maximum bed pressure drop was considered as minimum ﬂuidization velocity. To similarly simulate the coal gasiﬁcation for different tapered angles, inlet velocity of the gasifying agent was set as 1.6 times the minimum ﬂuidization velocity. The effects of tapered angle on the molar fractions of CH4, CO, CO2, H2, and H2O are shown in Fig. 3(a). It can be seen that with an increase in tapered angle, the concentration of CH4 in the product gas decreases while the concentrations of CO2 and H2 show an opposite trend. It can be deduced that increasing tapered angle strengthens the reaction (R4) and favors the reaction (R6) in the forward direction, so the molar fraction of CH4 decreases and that of CO2 and H2 increases. It can be also observed that as the tapered angle increases, CO concentration increases up to the tapered angle of 7, and then decreases. The results obtained from the simulations indicate that the amount of unreacted carbon in the outlet of tapered gasiﬁer lowers as the tapered angle goes up. The char consumption rate occurs mainly through the reactions (R7) to (R9); hence, it can be inferred that increasing tapered angle strengthens the heterogeneous chemical reactions. As a result, with an increase in tapered angle, the CO production rate via the reactions (R7) and (R8) and the CO consumption rate via the reaction (R6) increase. The opposite effects of these chemical reactions on CO concentration are the reason of the trend observed in Fig. 3(a). Fig. 3(b) shows heating values of the product gas for different tapered angles. It can be observed that increasing tapered angle results in a decrease of the LHV. It can be seen from Equation (46) that lower heating value is calculated based on the concentrations of CH4, CO, and H2 in product gas. In addition, CH4 concentration plays more important role in determining the LHV because the combustion heat of CH4 is higher than that of CO and H2. From

Fig. 3(a), it can be also seen that the reduction slope of CH4 molar fraction is higher than the increase slope of H2 molar fraction. Hence, lower heating value of the product gas decreases with an increase of the tapered angle. Moreover, this ﬁgure shows that HHV of the product gas decreases with an increase in tapered angle. To obtain the higher heating value, latent vaporization heat of water is taken into account in addition to the combustion heat of the product gas. From Fig. 3(a), it can be seen that the steam concentration in the product gas decreases as the tapered angle increases; therefore, HHV of the product gas diminishes. The simulation results for CGE and CCE efﬁciencies of the product gas versus tapered angle are shown in Fig. 3(c). It can be observed that CGE increases as the tapered angle goes up from 3 to 5 while it insigniﬁcantly changes with a further increase of the tapered angle from 5 to 11. As mentioned before, the inlet velocityto-minimum ﬂuidization velocity ratio was considered the same for all tapered angles to provide similar ﬂuidization conditions. The hydrodynamic results indicate that with an increase of the tapered angle, minimum ﬂuidization velocity increases; as a result, the ﬂow rate of the product gas increases. Despite the HHV shown in Fig. 3(b) decreases with an increase of the tapered angle from 3 to 5 , total higher heating value in terms of MJ for the product gas increases. A fairly high increase in the outlet ﬂow rate for the tapered angle of 5 in comparison with 3 can justify the increase observed for the total HHV as well as CGE of gasiﬁcation process. However, the results obtained for the outlet gas ﬂow rate for tapered angles of 5e11 indicate that increasing tapered angle causes a small increase in the ﬂow rate of the product gas. Hence, the total HHV as well as CGE of the gasiﬁcation slightly change as the tapered angle goes up from 5 to 11.

3.3. Effects of gasiﬁer temperature Gasiﬁer temperature is a crucial variable affecting the gasiﬁer performance, so temperature was varied from 700 to 900 K in 50 C increment and the species concentrations, LHV, HHV, CGE, and CCE of the product gas were explored. The molar fractions of CH4, CO, CO2, H2, and H2O as a function of gasiﬁer temperature are illustrated in Fig. 4(a) and (b) for the tapered angles of 5 and 9 , respectively. It can be seen that with an increase in gasiﬁer temperature, molar fraction of CH4 slightly increases for the tapered

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Fig. 3. Effects of tapered angle on (a) product gas compositions; (b) heating values; and (c) efﬁciencies.

angle of 5 while that slightly decreases for the tapered angle of 9 . It shows that, for CH4 species, the CH4 consumption rate in reaction (R4) and CH4 production rate in reaction (R10) were almost the same as the gasiﬁer temperature increases, so CH4 concentration slightly changes. Fig. 4 indicates that H2 molar fraction varies little when the temperature increases. As the temperature increases, the H2 consumption in reaction (R6) increases because higher temperatures favor the reactants in exothermic reactions. It can be inferred that the reaction (R7) is strengthened with an increase in temperature, so the net variations in H2 concentration is small. It can be also seen that, for both tapered angles, increasing temperature from 700 to 800 K insigniﬁcantly affects molar fractions of CO and CO2, whereas

molar fraction of CO decreases and that of CO2 increases as the temperature goes up from 800 to 900 K. Therefore, it can be deduced that the reaction (R5) is strengthened with an increase of the gasiﬁer temperature from 800 to 900 K, which results in a decrease of the CO concentration and increase of the CO2 concentration. Of course, the change occurred in reaction (R4) with an increase of the temperature has also positive effect on CO2 production. The heating values of the product gas as a function of gasiﬁer temperature are illustrated in Fig. 5(a) and (b) for the tapered angles of 5 and 9 , respectively. This ﬁgure indicates that both LHV and HHV of the outlet gas decrease with an increase in temperature. As shown in Fig. 4, variations in CH4, CO, and H2

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Fig. 4. Effects of gasiﬁer temperature on the product gas compositions for (a) q ¼ 5 and (b) q ¼ 9 .

concentrations in the temperature range of 700e800 K are small, which causes a small decrease in LHV and HHV of the product gas with an increase in temperature. Although variations in CH4 and H2 concentrations in the temperature range of 800e900 K are relatively small, the reduction slope of CO molar fraction is large; accordingly, a large decrease in LHV and HHV of the product gas can be seen in this temperature range. The efﬁciencies of CGE and CCE as a function of gasiﬁer temperature are shown in Fig. 6(a) and (b) for the tapered angles of 5 and 9 , respectively. From this ﬁgure, it can be observed that increasing temperature causes a decrease in CCE and CGE of the product gas. The results obtained from the simulations indicate that the ﬂow rate of the product gas diminishes with an increase of the gasiﬁer temperature; consequently, total HHV in terms of MJ as well as CGE of the gasiﬁcation process decrease. According to Equation (48), CCE of the gasiﬁcation process is calculated based on the molar ﬂow rates of CH4, CO, and CO2 species. The simulation

results show that the ﬂow rates of CH4, CO, and CO2 species vary similar to the trend observed for their molar fractions (Fig. 4) and with an increase in temperature, the sum of CH4 and CO ﬂow rates decrease with a larger intensity than that of which CO2 ﬂow rate increases, hence CCE of the product gas diminishes. 3.4. Effects of steam-to-air ratio In this section, the effects of steam-to-air ratio on the gas concentrations, heating values, and efﬁciencies of the gasiﬁcation process were studied. In this regard, the molar fraction of steam was varied in the range of 0e0.3 while the ﬂow rate of gasifying agent (air and steam) was kept constant and the results obtained for the molar fractions of CH4, CO, CO2, H2, and H2O are shown in Fig. 7(a) and (b) for the tapered angles of 5 and 9 , respectively. It can be observed that the molar fraction of CH4 slightly changes with an increase of steam molar fraction, hence it can be

Fig. 5. Effects of gasiﬁer temperature on LHV and HHV of the produced gas for (a) q ¼ 5 and (b) q ¼ 9 .

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Fig. 6. Effects of gasiﬁer temperature on CGE and CCE of the gasiﬁcation process for (a) q ¼ 5 and (b) q ¼ 9 .

deduced that increasing amount of the steam in gasiﬁcation process insigniﬁcantly affects the reactions (R4) and (R10). It can be also observed that as the steam molar fraction increases, H2 concentration is slightly affected for the tapered angle of 5 , whereas a small decrease is observed for the tapered angle of 9 . It seems that increasing amount of the steam in gasiﬁer strengthens the reaction (R3), which causes further consumption of H2 and production of H2O. In addition, as depicted in this ﬁgure, CO and CO2 concentrations diminish with an increase of the steam molar fraction. Examining simulation results indicates that the ﬂow rate of these two gas species have a decreasing trend; hence, increasing steam molar fraction has negative effect on the reactions relating to the production of CO and CO2. The LHV and HHV of the product gas versus steam molar fraction are depicted in Fig. 8(a) and (b) for the tapered angles of 5 and 9 , respectively. From this ﬁgure, a small decrease in LHV can be

seen as the molar fraction of steam increases, and the decrease intensity for the tapered angle of 5 is higher than that for the tapered angle of 9 . According to Equation (46), the decrease in lower heating value with an increase of the steam molar fraction can be justiﬁed with the decreasing trend of CO and H2 molar fractions observed in Fig. 7. In addition, it can be seen that HHV increases with an increase of the steam molar fraction, and the increase intensity for tapered angle of 9 is higher than that for tapered angle of 5 . The higher heating value is sum of the lower heating value and the vaporization heat of water, so the ascending trend of H2O molar fraction in the product gas (Fig. 7) is the reason for the increase observed for HHV. The CGE and CCE of tapered ﬂuidized bed gasiﬁer versus steam molar fraction are shown in Fig. 9(a) and (b) for the tapered angles of 5 and 9 , respectively. For both tapered angles, CGE of gasiﬁcation process is almost the same for the entire molar fractions of

Fig. 7. Effects of the ﬂow rate of steam-to-air ratio on the product gas compositions for (a) q ¼ 5 and (b) q ¼ 9 .

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3 Heating value (MJ/Nm )

3

11

(b)

LHV HHV

2

1

0

0

0.1 0.2 Mole fraction of inlet steam

0.3

Fig. 8. Effects of the ﬂow rate of steam-to-air ratio on LHV and HHV of the produced gas for (a) q ¼ 5 and (b) q ¼ 9 .

steam. Investigating ﬂow rate of the product gas shows a descending trend with an increase of the steam molar fraction while the trend of higher heating value is ascending (Fig. 8). Hence, the multiplication of the ﬂow rate and higher heating value, known as total HHV, slightly alters which in turn CGE of the gasiﬁer is almost the same for all steam molar fractions. Besides, as shown in this ﬁgure, CCE of the gasiﬁer drops with an increase in steam molar fraction. The reason is that, the ﬂow rates of CO and CO2 species drop and that of CH4 species slightly varies as the steam concentration increases and as a result, CCE of the gasiﬁer decreases. 3.5. Effects of velocity of gasifying agent To examine the effects of gas velocity on the performance of tapered gasiﬁer, inlet velocity-to-minimum ﬂuidization velocity

ratio was varied from 1.2 to 2.0 for the tapered angle of 5 and 1.4 to 2.2 for the tapered angle of 9 . The molar fractions of CH4, CO, CO2, H2, and H2O as a function of velocity are shown in Fig. 10(a) and (b). It can be seen that CH4 concentration slightly changes as the velocity rises, hence variations in the velocity of gasifying agent insigniﬁcantly affects the CH4 consumption rate in reaction (R4). In addition, it seems that velocity variations cannot push the reaction (R6) to the left/right hand, and consequently the molar fraction of H2 slightly changes. It can be also seen that with an increase of the velocity, CO and CO2 concentrations show a descending and ascending trend, respectively, and the variations intensity for tapered angle of 9 is more than that for tapered angle of 5 . The results obtained from simulations show that the carbon content in the gasiﬁer outlet slightly changes as the gas velocity increases, so it can be inferred

(b)

CGE CCE

Efficiency (%)

60

40

20

0

0

0.1 0.2 Mole fraction of inlet steam

0.3

Fig. 9. Effects of the ﬂow rate of steam-to-air ratio on CGE and CCE of the gasiﬁcation process for (a) q ¼ 5 and (b) q ¼ 9 .

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Fig. 10. Effects of the velocity of gasifying agent on the product gas compositions for (a) q ¼ 5 and (b) q ¼ 9 .

that the heterogeneous reactions (R7)-(R10) are affected a little with the variations in the gas velocity. Therefore, reaction (R5) is highly strengthened with an increase of the gas velocity that results in a decrease of the CO molar fraction and increase of the CO2 molar fraction. The results of Fig. 11(a) and (b) display the calculated heating values versus the velocity of gasifying agent for the tapered angles of 5 and 9 , respectively. LHV and HHV of the product gas drop as the velocity increases. The reason is that, CH4 and H2 concentrations are inﬂuenced a little with an increase of the velocity while CO concentration diminishes (Fig. 10) and thus the lower and higher heating values decrease. The sharper drop in the heating values for tapered angle of 9 in comparison with 5 is because of the trend of the variations in CO molar fraction. Fig. 12(a) and (b) displays the calculated gasiﬁcation efﬁciencies as a function of the gas velocity for the tapered angles of 5 and 9 , respectively. As shown in this ﬁgure, the variations trend of CGE for

tapered angle of 5 is different from that for tapered angle of 9 . For tapered angle of 5 , the CGE of gasiﬁer monotonically goes up with an increase of the gas velocity, whereas it increases up to u/ umf ¼ 1.8, and then decreases for the tapered angle of 9 . The results regarding the ﬂow rate of the product gas show an ascending trend as the velocity of gasifying agent goes up. Although the higher heating value diminishes with the velocity increase (Fig. 11), total HHV (MJ), which is a multiplication of the gas ﬂow rate and HHV, shows a different trend. As a result, the trend depicted in Fig. 12 is observed for carbon conversion efﬁciency of the gasiﬁer. Besides, it can be seen that higher velocities enhance CCE of the tapered gasiﬁer for both tapered angles. The CO and CO2 concentrations play important role in determining the CCE of the gasiﬁer owing to higher molar fractions (Fig. 10). The trend of the variations observed for the concentrations of CO and CO2 can justify the increase of the CCE as the velocity of gasifying agent goes up.

Fig. 11. Effects of the velocity of gasifying agent on LHV and HHV of the produced gas for (a) q ¼ 5 and (b) q ¼ 9 .

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Fig. 12. Effects of the velocity of gasifying agent on CGE and CCE of the gasiﬁcation process for (a) q ¼ 5 and (b) q ¼ 9 .

4. Conclusions A two-dimensional CFD model was develop and validated for coal gasiﬁcation in tapered ﬂuidized bed gasiﬁer to assess the effects of tapered angle, velocity of gasifying agent, gasiﬁer temperature, and steam-to-air ratio on the variations in lower and higher heating values, product gas compositions, carbon conversion efﬁciency, and cold gas efﬁciency. On the basis of the present simulations, the following conclusions can be drawn: a) With an increase in tapered angle, molar fraction of CH4 diminishes while that of H2 and CO2 increases. In addition, molar fraction of CO increases up to the tapered angle of 7, and then decreases. b) Increasing tapered angle results in a decrease of the LHV and HHV, whereas the CCE of gasiﬁer enhances. c) The gasiﬁer temperature slightly affects CH4 and H2 concentrations while the molar fractions of CO and CO2 sharply vary in the temperature range of 800e900 K. d) As the gasiﬁer temperature increases, the LHV, HHV, CGE, and CCE of gasiﬁcation process decrease. e) With an increase in steam molar fraction, the molar fractions of H2, CO, and CO2 drop. f) The LHV and HHV show a descending and ascending trend as the steam molar fraction increases. In addition, with an increase in steam molar fraction, the CGE value remains nearly constant while the CCE value decreases. g) Variations in the velocity of gasifying agent insigniﬁcantly affect the CH4 and H2 molar fractions, whereas the molar fraction of CO diminishes and that of CO2 increases. h) Increasing velocity of the gasifying agent results in a decrease of LHV and HHV of the product gas and the CCE of gasiﬁcation process enhances. Nomenclature A C C1ε ; C2ε CCE

pre-exponential factor, s1 concentration, kmol m3 constant parameters carbon conversion efﬁciency

CD CGE ds Di;j Di;m ess E ! g g0;ss h hgs HHV I I2D ! J g;i k Kgs LHV Nus p Pr R Rg Rhet Res S Sc Sh T ! v w W Xi Yg;i

drag coefﬁcient cold gas efﬁciency particle diameter, m binary diffusion coefﬁcient of species i and j mass diffusion coefﬁcient of species i in the mixture, m2 s1 coefﬁcient of restitution activation energy, J kmol1 gravitational acceleration, m s2 radial distribution function speciﬁc enthalpy, J kge1 heat transfer coefﬁcient between gas and solid phases, J me3 s‒1 K‒1 higher heating value, MJ Nm‒3 unit stress tensor second invariant of the deviatory stress tensor, se2 diffusion ﬂux of species i, kg me2 s‒1 turbulent kinetic energy, m2 se2 interphase momentum exchange coefﬁcient, kg m‒3 s‒ 1 lower heating value, MJ Nm‒3 solid phase Nusselt number pressure, Pa Prandtl number universal gas constant, J mol‒1 K‒1 homogeneous reaction rate, kmol m‒3 s‒1 heterogeneous reaction rate, kmol m‒3 s‒1 solid Reynolds number mass source term, kg m‒3 s‒1 Schmidt number Sherwood number temperature, K velocity, m se1 molecular weight, kg kmol‒1 coal feeding rate, kg h‒1 mole fraction of species i mass fraction of species i

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