Effect of Char Combustion Product Distribution Coefficient on the CFD

Article pubs.acs.org/IECR

Effect of Char Combustion Product Distribution Coefficient on the CFD Modeling of Biomass Gasification in a Circulating Fluidized Bed Hui Liu,† Ali Elkamel,*,† Ali Lohi,‡ and Mazda Biglari† †

Department of Chemical Engineering, University of Waterloo, Waterloo, Ontario, Canada N2L3G1 Department of Chemical Engineering, Ryerson University, Toronto, Ontario, Canada M5B2K3

‡

ABSTRACT: A three-dimensional unsteady-state CFD (computational fluid dynamics) model is built to simulate biomass gasification in a circulating fluidized bed. The RNG (renormalization group) k-epsilon turbulence model is coupled with the enhanced wall treatment to describe the hydrodynamic regime of the gas-particle system. The conservation of momentum, mass, and energy equations are integrated with reaction kinetics to simulate chemical reactions in the gasifier. The impact of product distribution coefficient, θ, for char combustion on the CFD biomass gasification model is examined in nine cases. According to the simulation results, the coefficient of θ has a minor effect on the predictions of outlet gas compositions. However, it is found that the value of θ can influence the profile of gasifier temperature, and the peak temperature regions from the cases assigning 0.50 to the coefficient appear faster than those from the models using higher values of θ.

1. INTRODUCTION Char combustion is an important reaction in the gasification process, and the primary reaction product would be supposedly CO2. However, a mechanism in which both CO and CO2 are considered as primary products has been widely accepted.1−7 A product distribution coefficient of char combustion, θ, is applied to determine the split of reaction products (CO and CO2) as follows: C + θ O2 → 2(1 − θ)CO + (2θ − 1)CO2

char combustion in a CFD model of an air-blown updraft coal gasifier. The same value of θ was also applied in a 3D (threedimensional) CFD model of gasification in a cross-type twostage reactor.15 Despite different values of θ being used, all of the results from the above models were reportedly in good agreement with their experimental data, but it was unclear how the value of θ influences the predictions of the gasification model. Yan et al.16 developed a 1D isothermal model of BFB coal gasification. On the basis of this isothermal model, Yan and Zhang9 conducted an investigation and concluded that θ with a value between 0.75 and 0.85 had negligible impact on the predictions of reactor temperature, gas production rate, and gas product composition. However, due to the complex flow pattern in the gasifier, the isothermal hypothesis may not be realistic for a fluidized-bed gasifier. Additionally, the model was built for a bubbling fluidized-bed gasifier, and the conclusion might not be suitable for another type of fluidized-bed gasifier such as circulating fluidized-bed (CFB) gasifier which has a different flow pattern and can present more efficient mass and energy transfer for gasification.17 The detailed and accurate distributions of gas composition and gasifier temperature predicted from 3-D CFD models are valuable for the design and scale-up of fluidized gasifiers. The predicted temperature profile can be used to select the refractory linings or bricks of the gasifier, and the predicted gas composition distribution may help to determine the size and shape of the gasifier. However, since the value of θ may affect these predictions, it is necessary to investigate the effect of this coefficient on the modeling of CFB biomass gasification. A clear understanding of the role of θ in the modeling can improve the accuracy of the model and further present more accurate insights for the design and scale-up of gasifiers.

(R1)

If θ is equal to 0.5 or 1.0, the sole gas product is CO or CO2, respectively. When θ is in the range of 0.5−1.0, both CO and CO2 are the primary reaction products. The value of θ is determined by many factors such as particle diameter, temperature, carbonaceous material and ash contents, and oxygen partial pressure.8,9 Some correlations were developed to determine the ratio of the products. As indicated by Arthu,1 the value of CO/CO2 was independent of burning time, and air velocity did not affect the ratio until reaction temperature reached 900 °C. Meanwhile, the ratio was found to be exclusively related to reaction temperature, and increased exponentially with temperature. Rajan and Wen10 proposed that the ratio was determined by both temperature and particle diameter. Du et al.11 reported that, in addition to reaction temperature, the value of CO/CO2 was also affected by partial pressure of O2, and it decreased as oxygen partial pressure increased. Ashman and Mullinger8 pointed out that CO/CO2 might vary significantly for different chars or carbons, and the recommended ratio values from the literature might be specific for the chars tested in the literature. For the sake of simplicity, θ is generally treated as a constant rather than a variable for the modeling of biomass or coal gasification. Yan et al.12 built a one-dimensional (1D) steadystate model of coal gasification in a bubbling fluidized bed (BFB), using a prescribed value of 0.8 for θ. In a two-dimensional (2D) CFD model of coal gasification by Yu et al.,13 the value of θ was set as 2/3. A constant value of 0.5 was used by Murgia et al.14 for © 2014 American Chemical Society

Received: Revised: Accepted: Published: 5554

December 15, 2013 March 7, 2014 March 12, 2014 March 12, 2014 dx.doi.org/10.1021/ie404239u | Ind. Eng. Chem. Res. 2014, 53, 5554−5563

Industrial & Engineering Chemistry Research

Article

∂ (αgρg kg) + ∇·(αg ρg vgkg) ∂t

In this paper, a 3D unsteady-state model using the Eulerian− Eulerian approach is built for the simulation of biomass gasification in a CFB reactor. The RNG (re-normalization group) k-epsilon turbulence model is integrated with the continuity, momentum, and energy equations to simulate biomass gasification. The predicted distributions of gas compositions are validated by experimental data,18 and various values of θ will be applied to investigate the impact of θ on the predictions of gas composition, temperature, and reaction rates in the gasifier. The effect of θ will be further examined by increasing air supply to the gasifier.

= ∇·(αg αkμeff,g ∇kg) + αgG k,g + G b,g − αgρg εg ∂ (αgρg εg) + ∇·(αgρg vgεg) ∂t εg = ∇·(αgαεμeff,g ∇εg) + [C1εαgG k,g − C2εαgρg εg kg + C3εG b,g ] − αgR ε

∂t

∂αsρs

+ ∇·(αgρg vg) = Sgs

(1)

+ ∇·(αsρs vs) = −Sgs

∂t

α − 1.3929 α0 − 1.3929

(2)

∂t

∂αgρg Hg

+ ∇·(αgρg vgvg)

= −αg

0.3679

=

μ μeff

∂αsρs Hs ∂t

+ ∇·(αsρs vsvs)

∂pg ∂t

+ τg : ∇vg + ∇·(αgkeff,g∇Tg ) + Sg + Q gs

+ ∇·(αsρs vsHs)

= −αs t

∂ps ∂t

+ τs: ∇vs + ∇·(αskeff,s∇Ts) + Ss + Q sg

= −αs∇p − ∇ps + ∇·τs + ∇·τs + αsρs g + msg vs + β(vg − vs)

(11)

where H is the specific enthalpy of the phase, keff is the effective thermal conductivity, S is the source enthalpy owing to chemical reactions and thermal radiation, and Q is the intensity of heat transfer between the gas and solid phases. keff, the effective thermal conductivity, is defined as follows:

(4)

where p is the pressure, μ is the molecular viscosity, ξ is the bulk viscosity, τ is the viscous stress tensor, and τt is the Reynolds stress tensor for turbulent flows. β is the momentum exchange coefficient between the gas and solid phases and is calculated by the Gidaspow model.19,20 The molecular viscosity and bulk viscosity of solid phase, μs and ξs, are estimated by the fluctuating energy equation developed from the kinetic theory of granular flow.19−22 The reader is referred to the Appendix for more details of the fluctuating energy equation and Gidaspow drag model. 2.2. RNG (Re-Normalization Group) k-epsilon turbulence model. The Reynolds stress tensor for the gas and solid phases, τt, is defined as:20 τ t = αμt (∇v + ∇v T) − μt = ρCμ

k2 ε

2 (αρk + αμt ∇·v)I 3

(9)

(10)

(3)

∂t

α + 2.3929 α0 + 2.3929

+ ∇·(αgρg vgHg)

∂t

= −αg∇p + ∇·τg + ∇·τgt + αgρg g + mgsvs + β(vs − vg) ∂(αsρs vs)

0.6321

where α0 = 1.0. 2.3. Conservation of Energy. The conservation of energy equations for the gas and solid phases are:20,25

where α is the volume fraction, ρ is the density, ν is the velocity, Sgs is the mass generation from the solid phase to the gas phase due to the heterogeneous reactions, and g and s represent the gas and solid phases, respectively. The momentum equations for the gas and solid phases are: ∂(αgρg vg)

(8)

where μeff is the effective viscosity,Gk is the generation of turbulence kinetic energy due to the mean velocity gradients, Gb stands for the generation of turbulence kinetic energy due to buoyancy, andRε is a new term, derived from the RNG theory.Cμ, C1ε, and C2ε are 0.0845, 1.42, and 1.68, respectively, based on the analytical solution of RNG theory. The same turbulence model is also applied to the solid phase. αk and αε are calculated by the following equation:

2. GOVERNING EQUATIONS The governing equations for the 3D unsteady-state model are described as follows: 2.1. Conservation of Mass and Momentum. The conservation of mass equations for the gas and solid phases are: ∂αgρg

(7)

keff = αeff,tCpμeff

(12)

αeff,t is calculated by eq 9 with α0 = (k)/(μCp), where k is the thermal conductivity, and Cp is the heat capacity. The enthalpy source from thermal radiation is computed by the P-1 model:20,26 ⎛ ⎞ 1 ∇·⎜ ∇G⎟ − aG + 4an2σT 4 = 0 ⎝ 3(a + σs) − Cσs ⎠ q=−

(5)

1 ∇G 3(a + σs) − Cσs

(13)

(14)

where a, σs, C, and n are the absorption coefficient, the scattering coefficient, the linear-anisotropic phase function coefficient, and the refractive index of the medium, respectively. q is the heat flux of thermal radiation, and −∇·qr is treated as an enthalpy source term for eqs 10 and 11.

(6)

The RNG k-epsilon turbulence model for the gas phase is shown as follows:20,23,24 5555

dx.doi.org/10.1021/ie404239u | Ind. Eng. Chem. Res. 2014, 53, 5554−5563


Article

Table 1. Kinetic Data of Chemical Reactions

reactions are computed by a diffusion and kinetic control model,13,28,29 and the rates of homogeneous gas-phase reactions are described by the global reaction schemes.30−34 2.6. Enhanced Wall Treatment. A so-called “enhanced wall treatment” is applied and coupled with the RNG k-epsilon turbulence model in this paper. As a method of near-wall treatment modeling, this approach includes the enhanced wall treatment of ε and momentum equations.20 The enhanced wall treatment of ε equation is applied to both the viscous affected regions and the fully turbulent region. In the viscous affected region (Rey < 200, where Rey ≡ (ρy√k)/μ), the equation of ε is not used, while the equations of momentum and k still remain as is. Meanwhile, in the fully turbulent region (Rey > 200), all of the momentum, k, and ε equations are retained. The turbulent viscosity in the near-wall region, μtenh, is defined by a smooth function as follows:20,36

The intensity of heat exchange between the phases is calculated by the model of Gunn:27 Q sg =

6kαgαsNus d p2

(Ts − Tg) (15)

Nus = (7 − 10αs + 5αs 2)(1 + 0.7Res 0.2Pr1/3) + (1.33 − 2.4αs + 1.2αs 2)Res 0.7Pr1/3

(16)

where Re is the Reynolds number, Nu is the Nusselt number, and Pr is the Prandtl number. 2.4. Conservation of Mass Species. The conservation of mass species equation for the gas phase is:20,25 ∂(ρg αgYi ,g) ∂t Ji ,g

+ ∇·(ρg αg vgYi ,g) = −∇·(αgJi ,g ) + αgR i ,g + R

∇T = −(αeff,mμ )∇Yi ,g − DT, i T

(17)

μt enh = λεμt + (1 − λε)μt 2layer

(19)

(18)

t μ2layer = ρCμlμ k

(20)

t

where Yi,g is the mass fraction of species i, Ji,g is the mass flux of species i, Ri,g is the mass source term due to homogeneous reaction, and R is the net production rate of heterogeneous reaction. αeff,m is calculated by eq 9 with α0 = 1/(Sc), where Sc is the molecular Schmidt number. 2.5. Heterogeneous and Homogeneous Reactions. As biomass particles are fed into the gasifier, volatiles and char are first generated from biomass pyrolysis. The volatiles are partially burned in the limited amount of O2, and the heat of combustion is provided to other chemical reactions. Char also reacts with O2, and when O2 is depleted, the residual char reacts with CO2, H2O (water vapor), and H2 respectively to generate CO, H2, and CH4. The gases in the gasifier can also react with each other to generate other gases. For the current study, the following chemical processes are included in the model: biomass pyrolysis, heterogeneous reactions of char, and homogeneous gas-phase reactions. As shown in Table 1, the rate of biomass pyrolysis is calculated by a one-step mechanism,13,14 the rates of char heterogeneous

λε =

A=

⎛ Rey − 200 ⎞⎤ 1⎡ ⎢1 + tanh⎜ ⎟⎥ 2⎣ A ⎝ ⎠⎦

(21)

|ΔRey| ar tanh(0.98)

(22)

where lμ is the length scale, y is the normal distance between the cell center and the wall, and ΔRey is a prescribed value. The enhanced wall treatment for the momentum equation is as follows:20,36 v+ = e Γv+ lam + e1/ Γv+ turb a(y+ )4 1 + by+

(24)

ρuτ y μ

(25)

Γ=−

y+ ≡ 5556

(23)



Article

where a = 0.01, b = 5, μτ is the friction velocity, and v+, v+lam, and v+turb are the normalized velocities for the near-wall, laminar, and turbulent regions, respectively. For further details, the reader is referred to the report by Kader.36

Table 3. Operating Conditions and Numerical Settings of CFD Model operating conditions air flow rate (Nm3/h) (Cases 1−3) biomass feed rate (kg/h) (Cases 1−3) Pressure (atm) CFD model settings

3. SETUP OF NUMERICAL EXPERIMENTS A 3D unsteady-state CFD model is built in ANSYS Fluent 14.0, and the simulation results will be compared and validated with ́ experimental data by Garcia-Ibañ ez, et al.18 Figure 1 shows the

109 60 1.0

number of computation cell 366,249 multiphase modeling approach Eulerian−Eulerian drag model Gidspow’s model turbulence model standard k-epsilon turbulence model near wall treatment enhanced wall treatment radiation model P-1 model transient formulation first order implicit time stepping method fixed time step size time step size (s) 0.001 boundary conditions air inlet condition inlet air flow rate (m/s) (Cases 1−3) air temperature at the inlet (K) solid inlet condition inlet solid mass flow rate (kg/s) (Cases 1−3) solid temperature at the inlet (K) gasifier outlet wall conditions for the gas and particle phases

velocity inlet 2.376 673.15 mass flow inlet 0.0167 300 pressure outlet no-slip

coefficient. As shown in Table 4, nine cases are then set up to conduct the investigation. The profiles of gas composition and Table 4. Setup of Case Studies for the coefficient, θ air flow rate (Nm3/h)

θ = 0.50

θ = 0.75

θ = 1.0

109 120 147

Case 1 Case 4 Case 7



Figure 1. Schematic diagram of gasifier.

schematic diagram of the gasifier for the current studies, which sizes are the same as those of the gasifier used in the experiment.18 The properties of biomass sample in the experiment18 are also displayed in Table 2. The governing equations are solved using the finite control volume method, and the scheme of phase coupled SIMPLE is used for the coupling of pressure and velocity. The convergence criterions, absolute scaled residual, are set as 1.0 × 10−3 for the continuity equation and 1.0 × 10−4 for other equations; however, in the computation, all of the equations reach the converged solutions under 1.0 × 10−4. In order to reach a converged solution stably and quickly, a steady-state solution is first achieved with the same settings, and the unsteady-state solution is then developed from it in a period of 30-s real time. The time of computation for each test is about 8−9 days on a cluster of 12 CPU nodes at 2.9 GHz. The operation conditions and other settings of the CFD model are listed in Table 3. Different values, 0.50, 0.75, and 1.0, are assigned to the product distribution coefficient of char combustion, θ, meanwhile, the air flow rates are also varied to investigate the impact of this

gasifier temperature from the models using different values of θ and air flow rates are then compared with each other to examine the effect of θ.

4. RESULTS AND DISCUSSION 4.1. Grid Resolution Study (Case 3). In this study, Case 3 is set as a base case, built on a 366249-cell grid, as shown in Table 3. To ensure that the solution of Case 3 is independent of the grid resolution, a grid study is implemented, and the simulation results from a 366249-cell grid are compared with those from a finer grid with 484833 cells. As illustrated in Figure 2, the distributions of gas compositions predicted from two grids are similar to each other, and the differences between the predictions of two grids are insignificant. Due to less computation time needed by the model built on the 366k-cell grid, the 366k-cell grid is then chosen for the rest of the study.

Table 2. Biomass Sample Properties18 proximate analysis (dry basis)a

a

ultimate analysis (d.a.f basis)

moisture (wt %)

density (kg/m3)

particle diameter (mm)

VM

FC

ASH

C

H

O

others

8.9

659

1.89

74.4

17.1

8.5

52.7

7.2

38.1

2.0

VM: volatile matter; FC: fixed carbon; ASH: ash; d.a.f: dry ash free. 5557



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temperature profile with the experimental data may help to present more accurate predictions of gas compositions inside the gasifier. Since the simulation results from Case 3 are similar to our previous work,37 and for the simplification of this work, the reader is referred to our other work37 to find further details of model validation. 4.3. Gas Composition Distributions (Case 3). Figure 5 displays the distributions of gas compositions in the gasifier on XZ and XY planes. As shown in the figure, CO is first generated from pyrolysis in the bottom region of the gasifier, and then decreases slightly due to the existence of O2 and combustion reaction in the region. Thereafter, CO increases again due to the reaction of Char and H2O and keeps increasing in the rest of the gasifier. Meanwhile, H2 is mainly generated from the reaction of char and H2O right after biomass pyrolysis and continues to increase along the gasifier. The trends of CH4 and C2H4 are similar. Both of the two gases are mainly generated from pyrolysis in the bottom region, then decrease significantly due to gas combustion, and finally become constant in the middle and upper parts of the gasifier. On the other hand, as shown in the section views of the XZ plane, the gas concentrations are nonuniform in the lower part of the gasifier, but eventually in the upper part of the gasifier, these gas compositions tend to be uniform. The nonuniform patterns of gas compositions are mainly caused by the asymmetric structure of the gasifier where the air enters from the bottom and biomass particles are fed at the side. 4.4. Impact of θ on the Predictions of Gas Composition, Gas Combustion Rate, and Gasifier Temperature (Cases 1−3). 4.4.1. Impact of θ on the Predictions of Outlet Gas Compositions (Cases 1−3). Figure 6 demonstrates the outlet gas compositions predicted from Cases 1−3. As seen in this figure, the differences between the predictions of outlet gas compositions from the models using different values of θ are insignificant. It may be because in the modeling of biomass gasification, the outlet gas compositions are not just determined by char combustion; other reactions such as biomass pyrolysis, gas combustion, and the reaction of char and water vapor may also play important roles in the gas production.9 Accordingly, a change of θ may not be able to cause significant impact on the predictions of outlet gas compositions. 4.4.2. Impact of θ on the Predictions of Gasifier Temperatures (Cases 1−3). Parts a and b of Figure 7 demonstrate the temperature profiles of Cases 1−3. As seen in Figure 7a, for Case 1, the gasifier temperature increases more quickly to a peak than those of Cases 2 and 3 between the heights of 0−1.0 m, and after the peak point, the temperature drops quickly and continues to decrease along the gasifier. On the other hand, the temperature profiles of Cases 2 and 3 are very similar and overlap each other. Compared to the temperature of Case 1, the rates of temperature increases in Cases 2 and 3 are relatively slow between the heights of 0−1.0 m, and after reaching the peak temperature at around 1000 °C, the temperature tends to be constant between 1.0 and 2.0 m. However, above the height of 2.0 m, the temperature starts to drop, and keeps decreasing in the rest of the gasifier. Additionally, as demonstrated in Figure 7b, the high temperature area of Case 1 is much shorter than those of Cases 2 and 3. From the comparison above, it is observed that the value of θ can influence the predicted temperature profile. The reactor temperature for the Case 1 in which θ is set as 0.5 increases more rapidly in the lower region of the gasifier than those in Cases 2 and 3 in which the values of θ are 0.75 and 1.0, respectively. It

Figure 2. Comparison of gas composition distributions (366k grid vs 484k grid).

4.2. Comparison of Simulation Results and Experimental Data (Case 3). The simulation results are also compared with the experimental data.18 As shown in Figure 3,

Figure 3. Comparison of outlet gas composition (Case 3).

the predictions of gas compositions at the outlet are in a good agreement with the experimental data, and the differences between the gas composition predictions and the experimental data are acceptable. Additionally, as illustrated in Figure 4, the predicted temperature profile of Case 3 follows the trend described in

Figure 4. Predicted gasifier temperature profile (Case 3).

́ the experiment by Garcia-Ibañ ez, et al.18 It is found that the temperature increases sharply in the lower part of the gasifier and then reaches a peak. After this point, the temperature starts to drop and keeps decreasing in the rest of the gasifier. Furthermore, as indicated in the trend, the highest predicted temperature is found at the height of 2.0 m, which is the same as described in the literature.18 Since reaction rates vary with temperature, a properly predicted temperature profile may contribute to accurate predictions of reaction rates in the gasifier. Therefore, comparing both the outlet gas compositions and the 5558



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Figure 5. Gas composition distributions (Case 3).

Figure 6. Comparisons of outlet gas composition (Cases 1−3).

may be caused by the different stoichiometric coefficients of char combustion and the consequent changes of reaction rates. In Case 1, due to the setting of θ, only 0.5 mol of O2 is consumed in char combustion. So, compared to Cases 2 and 3, there would be more remaining O2 for the combustion of some gases such as CH4, C2H4, and syngas (CO + H2). Since gas combustion can generally happen more rapidly, the temperature may also increase dramatically in a very short period of time. Accordingly, a high peak temperature may then be predicted from Case 1, as shown in Figure 7a. However, since only a limited amount of air or O2 is supplied to the gasifier and after O2 is depleted, the reactor temperature then starts to drop. 4.4.3. Impact of θ on the Estimations of Gas Combustion Rates (Cases 1−3). Since reaction rates vary with temperature, the different temperature profiles, as described previously, may then lead to different estimations of reaction rates for Cases 1−3.

Figure 7. (a) Temperature profiles of Cases 1−3. (b) Temperature contours on the XZ plane (Cases 1−3).

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As shown in Figures 8−10, between the heights of 0−1.0 m, CO, CH4, and C2H4 combustion reactions in Case 1 are much

Figure 11. O2 and CO2 distributions (Cases 1−3). Figure 8. Rates of CO combustion in Cases 1−3.

Figure 9. Rates of CH4 combustion in Cases 1−3.

Figure 12. CH4 distributions of Cases 1−3.

Figure 10. Rates of C2H4 combustion in Cases 1−3.

Figure 13. C2H4 distributions of Cases 1−3.

faster than those of Cases 2 and 3 due to the higher temperature predicted from Case 1. However, it is also observed that between the heights of 1.0−4.0 m, the rates of CH4 and C2H4 combustion for Case 1 are eventually exceeded by those in Cases 2 and 3 due to the quick depletion of O2 in Case 1. As discussed above, the different temperature profiles can cause the different estimations of reaction rates for Cases 1−3. As a result of different reaction rates in these cases, the gas composition distributions may also vary from one to another. In the following section, the effect of θ on the distributions of gas compositions in the gasifier will be addressed. 4.4.4. Impact of θ on the predictions of Gas Composition Distributions (Cases 1−3). In Figure 11, it is observed that O2 in Case 1 is consumed more rapidly in the bottom region of the gasifier than those in Cases 2 and 3 due to faster reaction rates. Meanwhile, as a main product of gas combustion, CO2 in Case 1 is also generated faster in the same region. Figures 12 and 13 demonstrate the distributions of CH4 and C2H4. As shown in the figures, the gas compositions first increase in the bottom area due to biomass pyrolysis, then gradually drop due to gas combustion reactions, and finally reach a constant value when O2 is depleted in the gasifier.

It is also seen that in the middle and upper parts of the gasifier, the compositions of CH4 and C2H4 are higher than those of Cases 2 and 3. On the other hand, Figure 14 shows that for Case 1, the composition of syngas (CO + H2) is lower than those of Cases 2 and 3 in the same region. The higher predictions of CH4 and C2H4 and the lower predictions of syngas for Case 1 may be caused by the different predictions of gasifier temperature and combustion rate in Cases 1−3.

Figure 14. Syngas distributions of Cases 1−3. 5560



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In Figures 9 and 10, the combustion rates of CH4 and C2H4 in Case 1 drop dramatically above the height of 1.0 m due to the rapid decrease of combustion reactants such as CH4, C2H4, and O2, and the combustion rates become less than those of Cases 2 and 3. Meanwhile, Figure 8 indicates that the rate of CO combustion in Case 1 also drops quickly above the height of 1.0 m, but it still remains at the same level as those of Cases 2 and 3. It may be due to the fact that the temperature between the heights of 1.0−2.3 m is much higher than those of Cases 2 and 3, as illustrated in Figure 7a, and unlike CH4 and C2H4, CO is not only produced from pyrolysis, it can also be continuously generated from the reaction of char and water vapor (R4) along the gasifier. Thus, because of the higher reaction temperature and continuous production of syngas, more syngas is consumed in combustion, and consequently, the composition of syngas becomes less than those of Cases 2 and 3, as shown in Figure 14. On the contrary, since the amount of air supplied to the gasifier is limited, CH4 and C2H4 of Case 1 are then consumed less in combustion than those of Cases 2 and 3, and the compositions of CH4 and C2H4 become higher, as displayed in Figures 12 and 13. It is noted that, although the cases using various values of θ present different temperature and gas composition profiles, the difference between the predictions of outlet gas compositions is still small. It is mainly because apart from char combustion, other reactions such as pyrolysis and the reaction of char and water vapor (R4) also play important roles in the gas production. Varying the value of θ for char combustion may affect the distribution of gas composition to some extent, but it might not be able to cause significant impact on the predictions of outlet gas compositions. 4.5. Effect of Air Flow Rate (Cases 4−9). In this section, case studies using different air flow rates (Cases 4−6 and 7−9) are implemented to further examine the impact of θ on the predictions of gas composition and reactor temperature. Figures 15 and 16 demonstrate the predictions of outlet gas compositions for Cases 4−6 (air flow rate: 120 Nm3/h), and 7−9

Figure 16. Outlet gas compositions of Cases 7−9.

Figure 17. Temperature distributions of Cases 4−6.

Figures 18−20 show the distributions of CH4, C2H4, and syngas for Cases 4−6. As displayed in the figures, the gas

Figure 18. CH4 distributions of Cases 4−6.

Figure 15. Outlet gas compositions of Cases 4−6. Figure 19. C2H4 distributions of Cases 4−6.

(air flow rate: 147 Nm3/h), respectively. It is observed that the differences between the outlet gas compositions from the cases using different values of θ are insignificant. It therefore confirms the conclusion of section 4.4.1 that the coefficient of θ has minor influence on the predictions of outlet gas compositions. Figure 17 demonstrates the temperature profiles from Cases 4−6, and the peak temperature predicted from Case 4 appears earlier than those of Cases 5 and 6. As mentioned in section 4.4.2, it may be caused by faster gas combustion.

composition distributions of Cases 4−6 follow the trends analogous to those of Cases 1−3. According to our model, the similar results of temperature and gas composition comparisons are also found in Cases 7−9. Thus, the impacts of θ on the temperature and gas composition profiles discovered in sections 4.4.2 and 4.4.4 are again confirmed with the comparison results from other cases by increasing air supply to the gasifier. 5561



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5. CONCLUSIONS In this paper, a 3D unsteady-state model was built to simulate biomass gasification using a CFB reactor. The RNG k-epsilon turbulence model was coupled with the enhanced wall treatment to describe turbulent flows in the gasifier. The equations of mass, momentum, and energy conservation were applied to model mass and energy transfer in the reactor. The simulation results were compared and validated with experimental data. Nine cases were set up to examine the effect of product distribution coefficient of char combustion. According to the comparison of outlet gas compositions from these cases, the product distribution coefficient showed minor impact on the prediction of outlet gas composition. It might be because, except for char combustion, other chemical reactions such as pyrolysis and char gasification reactions also play major roles in producing gases. On the other hand, it was found that this coefficient could affect the predictions of the gasifier temperature and gas composition distributions inside the gasifier. The reactor temperature from the cases with the value of 0.50 for the coefficient increased more quickly than those in the cases using the values of 0.75 and 1.0, due to higher rates of gas combustion.

Figure 20. Syngas distributions of Cases 4−6.

Figure 21 shows the profiles of syngas and CH4 for Cases 1, 4, and 7. As seen in the figures, for the cases using the same value of

■

APPENDIX: GIDASPOW’S DRAG MODEL AND FLUCTUATING ENERGY EQUATION Gidaspow drag model:20 Figure 21. Syngas and CH4 distributions of Cases 1, 4, and 7.

⎛ α 2μ ⎞ ρ α |v − vs| s g ⎟ + 1.75 g s g for αg ≤ 0.8 β = 150⎜⎜ 2⎟ dp ⎝ αgd p ⎠

θ, the mole fractions of syngas and CH4 decrease when the air flow rate increases from 109 to 147 N m3/h. According to our model, the same trend also applies to C2H4. It is mainly because when more air or O2 is supplied to the gasifier, more combustible gases such as CH4, C2H4, and syngas will react with O2. As a result of more gas combustion, the gasifier temperature also rises, while the air flow rate increases, as shown in Figure 22.

β=

Cd =

−2.65 3 ρg αsαg|vg − vs|αg Cd for αg > 0.8 4 dp

ρg |vg − vs|d p 24 [1 + 0.15(αgRep)0.687 ], Rep = αgRep μg

Fluctuating energy equation:20,21 ⎤ 3 ⎡ ∂αsρs Θ + ∇·(αsρs Θvs)⎥ ⎢ ⎦ 2 ⎣ ∂t = ( −ps I + τs): ∇vs − ∇·(κ ∇Θ) − γ

where (−psI + τs):∇vs is the generation of energy by the solid stress tensor, κ∇Θ is the energy diffusion, and λ is the collisional energy dissipation. Figure 22. Comparison of temperature distributions of Cases 1, 4, and 7.

ps = αsρs Θ + 2αsρs Θ(1 + e)g0αs

where e is particle−particle restitution coefficient. Syngas is generally a valuable gas, and high concentration of syngas is desirable for the operation of biomass gasifiers. Therefore, higher air flow rate is not preferable for biomass gasification, due to lower concentration of syngas. However, since the heat of combustion is the main heat source to maintain biomass gasification, a lower rate of air flow may cause lower conversion of biomass fuel, which may also lead to a lower production rate of syngas.38,39 Consequently, an optimum air flow rate is required. For fluidized bed gasifiers, the air flow rate that corresponds to a value of equivalence ratio between 0.20 and 0.30 was recommended by Basu.40

g0 =

1 ⎡ 1− ⎣⎢

⎤1/3 ⎦⎥

( ) αs

αs max

μs = μs,collision + μs,kinetic

5562

μs,collision =

⎛ Θ ⎞1/2 4 2 (αs ρs d pg0 + αs 2ρs d pg0e)⎜ ⎟ ⎝π⎠ 5

μs,kinetic =

10 π ρs d pΘ1/2 ⎡ ⎤2 4 ⎢⎣1 + (1 + e)g0αs⎥⎦ 96(1 + e)g0 5 dx.doi.org/10.1021/ie404239u | Ind. Eng. Chem. Res. 2014, 53, 5554−5563

Industrial & Engineering Chemistry Research ξs =

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Article

⎛ Θ ⎞1/2 4 (αsρs d pg0 + αsρs d pg0e)⎜ ⎟ ⎝π⎠ 3

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AUTHOR INFORMATION

Corresponding Author

*E-mail: [email protected] Notes

The authors declare no competing financial interest.

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ACKNOWLEDGMENTS We greatly acknowledge the support of the Agricultural Bioproducts Innovation Program (ABIP) by the Agricultural Bioproducts Innovation Network (ABIN), Natural Science and Engineering Research Council of Canada (NSERC), and High Performance Computing Virtual Laboratory (HPCVL).

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REFERENCES

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Effect of Char Combustion Product Distribution Coefficient on the CFD

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