Coal Gasification Modeling in Fluidized Bed Reactors

I NTERNATIONAL J OURNAL OF C HEMICAL R EACTOR E NGINEERING Volume 9 2011 Article A2 Mathematical Modeling of Coal Gas...

Author: Pablo Cornejo

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I NTERNATIONAL J OURNAL OF C HEMICAL R EACTOR E NGINEERING Volume 9

2011

Article A2

Mathematical Modeling of Coal Gasification in a Fluidized Bed Reactor Using a Eulerian Granular Description Pablo Cornejo∗

∗

Oscar Far´ıas†

Universidad de Concepci´on, [email protected] Universidad de Concepci´on, [email protected] ISSN 1542-6580 c Copyright 2011 Berkeley Electronic Press. All rights reserved. †

Mathematical Modeling of Coal Gasification in a Fluidized Bed Reactor Using a Eulerian Granular Description Pablo Cornejo and Oscar Far´ıas

Abstract A three-dimensional computational model was developed to describe the coalgasification processes inside fluidized-bed reactors. The commercial multi-purpose CFD code FLUENT 6.3 was employed, taking into account drying, volatilization, combustion and gasification processes. Both gas phase and solid phase were described using a eulerian approach to model the exchanges of mass, energy and momentum between phases. The disperse phase was described using the kinetic theory of granular flows. The chemical model involved five heterogeneous and five homogeneous chemical reactions, tracking seven species in the gas phase (CO2 , CO, H2 O, CH4 , H2 , O2 and N2 ) and one specie in the solid phase (C(s) ). Drying and volatilization rates were estimated by mass conservation. Heterogeneous reaction-rates were determined by combining an Arrhenius kinetic-rate and a diffusion rate using the kinetics/diffusion Surface Reaction Model; the model was implemented within FLUENT through UDFs (User Defined Functions). Homogeneous reaction-rates were described by a turbulent mixing rate using the Eddy Dissipation Model available in FLUENT. Calibration and validation were performed by using existing experimental data from a benchmark coal-gasification case available in the literature. Results are in good agreement with experimental data, capturing known phenomena like fluidization-bed height, temperature distribution and species concentrations. The main contribution of the present work was implementing the necessary sub-models within the FLUENT code in order to handle reactive fluidized-beds in complex geometries. This allowed combining the flexibility of a commercial CFD code with the accuracy of simplified models developed in academic frameworks. KEYWORDS: coal gasification, fluidized bed, CFD modeling, eulerian granular model

Cornejo and Farías: Coal Gasification Modeling in Fluidized Bed Reactors

1

1

Introduction

The dependence of Chile from imported energy sources, the natural gas supply crisis and the high prices of natural gas, petroleum and its derivatives, all combine to make the study of solid fuel (coal and biomass) gasification technologies attractive due to the availability of these resources in Chile [CNE (2009)], and the clean and efficient nature of the gasification process [Yu, Lu, Zhang, and Zhang (2007); A.Ocampo, E.Arenas, J.Espineln, C.Londoo, J.Aguirre, and Perez (2003); Pohorely, Vosecky, Hejdova, Puncochar, Skoblja, Staf, Vosta, Koutsky, and Svoboda (2006); Azuhata, Hedman, and Smoot (1986); Gururajan, Agarwal, and Agnew (1992); Lv, Chang, Xiong, Huang, Wu, and Chen (2003)]. Numerical modeling is an essential design, optimization and scaling-up tool, of combustion [Yang, Goh, Zakaria, Nasserzadeh, and Swithenbank (2002); Fletcher, Haynes, Christo, and Joseph (2000); Mathur, Freeman, and ODown (2001a); Sijercic, Beloevic, and Stefanovic (2005); Saljnikov, Komatina, and Goricanec (2006)] and gasification [Yu et al. (2007); Chejne and Hernandez (2002); Lu, Lu, Zhang, Zhang, and Dai (2008); Kim, Lee, and Kim (2000); Di-Blasi (2004); Chen, H.Spliethoff, J.Andries, and Glazer (2004); Gururajan et al. (1992); Ma, Felder, and Ferrell (1988); Saffer, Ocampo, and Laguerie (1988); Weimer and Clough (1981); Zhou, feng Yan, xiang Guo, and shi Zhu (2006)] processes, in fixed bed [Di-Blasi (2004); Yang et al. (2002); Yang, Yamauchi, Nasserzadeh, and Swithenbank (2003)] and entrained bed [Lu et al. (2008); Fletcher et al. (2000); Zhou et al. (2006); Cornejo, Rodriguez, and Farias (2008)] reactors, as have been widely reported. The same is true for fluidized beds, as have been reported in studies on numerical simulation of inert fluidization [Ding and Gidaspow (1990); Taghipour, Ellis, and Wong (2003)] and reactive fluidization [O’Brien, Syamlal, and Guenther (2003); Gururajan et al. (1992); Hjertager, Solberg, and Hansen (2005)]. In the latter case, the numerical modeling of fluidized-bed gasification has basically followed two approaches. For continuous fluidized beds and low solid-phase volumefractions, the lagrangian approach is adopted for the description of the solid dispersedphase and the conservation equations are integrated along the particle trajectories [Lu et al. (2008); Fletcher et al. (2000); Hjertager et al. (2005)]. However, for high solid-phase volume fractions, or in the case of bubbling fluidized beds [Yu et al. (2007); Gururajan et al. (1992); Ma et al. (1988); Taghipour et al. (2003); Saffer et al. (1988)], where the bed is fluidized to a constant height, this modeling approach becomes impractical. In the simulation of bubbling fluidized-beds, two modeling approaches are typically adopted: the first one, based on the discrete element method (DEM), considers each one of the particles by using empirical coefficients of restitution, fric-

Published by Berkeley Electronic Press, 2011

2

International Journal of Chemical Reactor Engineering

Vol. 9 [2011], Article A2

tion, stiffness and damping. But industrial applications typically include millions of particles, and therefore the required computational resources and calculation times of DEM methods are quite high. Due of this problem, other numerical modeling approaches have been developed. These are based on multi-phase flows which includes the disperse solid phase in an eulerian framework; the properties and stresses resulting from particle collisions are modeled by the kinetic theory of granular flows [Yu et al. (2007); Chejne and Hernandez (2002); Ding and Gidaspow (1990); Gururajan et al. (1992); Hjertager et al. (2005); Ma et al. (1988); Taghipour et al. (2003); Saffer et al. (1988)]. This approach not only requires lower computational resources and calculation times, but also allows a detailed analysis of the disperse phase flowfield, which is convenient for engineering design applications. Numerical models for gasification processes in bubbling fluidized-bed reactors generally adopt a similar approach for the multi-phase description. However, there is no unique chemical model capable of describing the chemical reactions in volatilization, combustion and gasification processes. This is due to the variability in the composition of solid fuels: coal [Yu et al. (2007); Chejne and Hernandez (2002); Lu et al. (2008); Kim et al. (2000); Radulovic, Ghani, and Smoot (1995); Gururajan et al. (1992); Ma et al. (1988); Saffer et al. (1988); Weimer and Clough (1981)], biomass [Di-Blasi (2004); Chen et al. (2004); Fletcher et al. (2000); Yang et al. (2003)] and waste [Yang et al. (2002); Yang et al. (2003)], and the nature of the fluid flow itself. In flows controlled by turbulent fluctuations, kinetics do not play an explicit rol in the homogeneous reaction rates [Yu et al. (2007); Lu et al. (2008); Fletcher et al. (2000)]; therefore, reactions are controlled by turbulent mixing. The description of heterogeneous reactions is generally carried out by weighting a diffusion-controlled rate with an Arrhenius kinetic rate [Lu et al. (2008); Mathur et al. (2001a); Saveliev, Korytni, Perelman, Spitz, and Bar-Ziv (2007); Mathur, Gera, and Freeman (2001b); Saljnikov et al. (2006)]. Several models for gasification in bubbling fluidized beds have been reported in the literature. However, these are mostly one-dimensional models [Chejne and Hernandez (2002); Luo, Aoki, Uemiya, and Kojima (1998); Radulovic et al. (1995); Chen et al. (2004); Ferreira, Rodrigues, Secchi, Trierweiler, Lansarin, Marczak, and Mendes (2005); Rodrigues, Lansarin, Secchi, and T.F.Mendes (2005)] and bidimensional models [Yu et al. (2007); Chejne and Hernandez (2002); Ding and Gidaspow (1990); Taghipour et al. (2003)], generally developed within an academic framework, even though the geometry and operational conditions are highly tridimensional. No gasification three-dimensional models of solid fuels in fluidized-beds reactors, developed within the framework of commercial Computational Fluid Dynamics (CFD) codes, have been found in the literature. Commercial CFD codes can

http://www.bepress.com/ijcre/vol9/A2


3

be used in a wide range of problems. But in some very specific cases, like granular flows with chemical reactions, their use is restricted by the lack of the sub-models needed for these types of flows. One of the most popular commercial CFD codes is the FLUENT code. This code incorporates a robust framework for modeling combustion and gasification of solid fuels, using a lagrangian approach. However, it does not have a modeling methodology to describe the solid-fuel gasification processes in fluidized beds, where it is necessary to use an eulerian modeling approach coupled with heterogeneous chemical-reactions. The objective of the present work is to develop a modeling methodology within the framework of the commercial CFD code FLUENT to describe the coalgasification processes in bubbling fluidized bed reactors.

2

Computational model

The computational model was implemented within the framework of the commercial multi-propose CFD code FLUENT 6.3. The model is multi-phase (two phases: gas and solid), where the solid phase is modeled by an eulerian granular model. Furthermore, both phases exchange heat by convection, momentum (due to the drag between gas phase and solid phase) and mass (due to the heterogeneous chemical reactions). After the coal particle is heated and the coal humidity reaches its vaporization temperature, it is dried and subjected to continuous heating until a temperature around 400 C - 500 C is reached. At this temperature the coal particle is volatilized, remaining the char particle dry and free of volatile matter. Usually this type of reactors operates at temperatures above 700 C [Yu et al. (2007); Chejne and Hernandez (2002)]. Therefore the drying and volatilization processes may be considered as occurring instantaneously at the feed region. Once the drying and volatilization processes have been completed, the char particle is burnt and gasified, and the resulting gas phase reacts according to the homogeneous chemical-reactions described on the following sections. To reduce the nonlinear characteristics of the computational model, so as to improve convergence within acceptable calculation times and computational resources, some simplifying assumptions were incorporated to the models describing the fluid-dynamics and chemical processes involved on the coal gasification, as follows: 1. The intensity of particles collision does not vary with temperature, i.e., exothermic or endothermic reactions has no impact on the fluctuation of solid phase



4

2.

3. 4.

5.

2.1


velocity and hence the temperature variations of the solid phase will no alter the granular temperature [Yu et al. (2007)]. The solid phase is dense and continuous in the bed and in contact with the walls, and the mean free path of radiation is much smaller than the solid particle dimensions so as to limit the contribution of radiative heat transfer between the bed and reactor walls. The gas phase can be assumed transparent, so that the radiative energy is neither absorbed nor emitted [Yu et al. (2007)]. As a result the bed temperature will become rapidly uniform due to the strong agitation of the particles. With these assumptions, it is reasonable to consider the radiative heat losses negligible compared with convection heat transfer. Therefore, this mechanism will be the main heat-transfer mechanism within the reactor. Coal particles are modeled as mono-dispersed, smooth, inelastic and isothermal (internal thermal resistance negligible) spheres [Yu et al. (2007)]. Drying and volatilization are assumed occurring instantaneously in the feed region of the gasifier [O’Brien et al. (2003); Yu et al. (2007); Weimer and Clough (1981)]. The ash content of coal particles is not considered as a constitutive specie [Yu et al. (2007)].

Hydrodynamics

The fluid-flow nature in the fluidization process correspond to a multi-phase flow, where both phases interpenetrate each other exchanging momentum, energy and, in the case of a reactive fluidized bed, mass. As mentioned before, to describe the fluid-dynamics of the fluidization process the lagrangian approach to describe the solid phase dynamics is not feasible due to its high computational cost, since for these applications the volume fraction of the solid phase (> 11 %), and hence the number of particles are quite high. Therefore, the eulerian approach, as described in the following sections, is the most-common approach for the numerical modeling of fluidized beds, with the disperse solid phase described by using the kinetic theory of granular flows. The description of a multi-phase flow as interpenetrating continua incorporates the concept of phase volume fractions αq . Volume fractions represent the space occupied by each phase, and the conservation equations of mass, momentum, energy and chemical species, are satisfied by each single phase. The volume of phase q, Vq , is defined by Z

Vq =

V

(αq )dV


(1)


5

where n

∑ (αq) = 1

(2)

ρbq = αq ρq

(3)

q=1

The effective density of phase q is

The volume fraction for each phase is obtained from the following continuity equation: n 1 ∂ (αq ρq ) − (( + ∇ · (αq ρq → υq )) = ∑ (m˙pq − m˙qp )) ρrq ∂ (t) p=1

(4)

~q is the velocity of phase q, m˙pq and m˙qp characterizes the mass transfer where υ from the pth to qth phase and from qth to pth phase respectively, and ρrq is the reference density, or the density of the phase qth averaged in the solution domain. This equation is solved for each secondary phase, and the volume fraction of the primary phase is calculated from the condition that the volume fraction of all phases involved must sum to unity. The momentum conservation equation for the phase qth is ~q ) ∂ (αq ρq υ ~q υ ~q ) = −αq ∇(p) − ∇(pq ) + ∇ · (τ¯q ) + ∇ · (αq ρq υ ∂ (t)

(5)

+ αq ρq~g + ∑np=1 (K pq (~υ p − ~υq ) + m˙pq υ~pq − m˙qp~υqp ) + (~Fq + ~Fvm,q ) where τ¯q is the stress tensor of phase qth , given by 2 τ¯q = αq µq (∇(~υq )∇(~υqT )) + αq (λq − µq )∇ · ~υq I¯ (6) 3 Here µq and λq are the shear viscosity and bulk viscosity of phase qth respectively, ~Fq is an external body force, ~Fvm,q is a virtual mass force, which allows to include the virtual mass effect that occurs when phase qth feels a relative acceleration to phase pth and the inertia of the primary phase mass encountered by the accelerating particles exerts a virtual mass force, p is the pressure shared for all phases, pq is the solid pressure in the case of a granular solid phase, ~υqp is the interface velocity, which is equal to ~υ p if mass is being transferred from pth to qth or equal to ~υq on the opposite. K pq is the momentum exchange coefficient between phases and n the total number of phases.



6


Using the drag model of Wen and Yu (1966) , the momentum exchange coefficient takes the following form 3 αs αl ρl |~υs − ~αl | −2.65 Ksl = CD αl 4 ds

(7)

24 [1 − 0.15(αl Res )0.687 ] αl Res

(8)

ρl ds |~υs − ~υl | µl

(9)

where CD = with the Res defined by Res =

For incompressible granular flows, i.e., when volume fractions are lower than the maximum allowable value, a solid pressure for the granular solid phase is estimated in an independent way and used to calculate the term ∇(pq ) in the momentum conservation equation of granular solid phase, equation 5. The granular pressure will be composed by one kinetic term and a second term due to particle collisions ps = αs ρs Θs + 2ρs (1 + ess )αs2 g0,ss Θs

(10)

where ess is the restitution coefficient for particle collisions, Θs the granular temperature and g0,ss is the radial distribution function. The radial distribution function g0,ss drives the transition from the compressibility condition α < αs,max , where the spacing between solid particles can continuously decrease, to the incompressibility condition α = αs,max , where no additional decrease can takes place. In practise, the radial distribution function is a correction factor that modifies the probability of particle collisions when the granular phase becomes denser. This function may also be interpreted as a non-dimensional distance between spherical particles s + dp (11) s where s and d p are the distance between particles and particle diameter respectively. In the literature no single formulation for the radial distribution function exists. When there is only one solid phase in the domain, FLUENT (2006) proposes the following empirical relation: g0 =

g0 = [1 − (

αs αs,max

1

) 3 ]−1


(12)


2.2

7

Turbulence model: κ − ε per phase

The κ − ε Per Phase turbulence model solves a set of turbulent kinetic-energy and turbulent kinetic-energy dissipation-rate conservation equations for each phase. The selection of this turbulence model is appropriate when the turbulence transfer between phases plays a predominant rol as in the case of gasification in fluidized beds. The turbulence model is given by the κ − ε conservation equations: ∂ ~ q kq ) = ∇ · (αq µt,q ∇kq ) + (αq Gk,q − αq ρq εq )+ (αq ρqU ∂t σk

(13)

N N ~ ~ µt,i ~ ~ µt,q ∑N i=1 Kiq (Ciq ki −Cqi kq ) − ∑i=1 Kiq (Ui − Uq ) αi σi ∇αi +∑i=1 Kiq (Ui − Uq ) αq σq ∇αq

∂ ~ q εq ) = ∇ · (αq µt,q ∇εq ) + εq [C1ε αq Gk,q −C2ε αq ρq εq + (αq ρqU ∂t σε kq

(14)

~ i −U ~ q ) µt,i ∇αi +∑Ni=1 Kiq (U ~ i −U ~ q ) µt,q ∇αq ] C3ε (∑Ni=1 Kiq (Ciq ki −Cqi kq )− ∑Ni=1 Kiq (U αi σi αq σq The terms Ciq and Cqi can be approximated as Ciq = 2 Cqi = 2(

(15)

ηiq ) 1 + ηiq

(16)

where ηiq is the characteristic time ratio related with the particle dispersion. Finally, turbulent viscosity µt can then calculated by combining k y ε by the following equation µt = ρCµ

κ2 ε

(17)

where Cµ = 0.09 (FLUENT (2006)). Then the Reynolds stress tensor is calculated using the equation 6.

2.3

Granular eulerian model

In the granular eulerian model, stresses in the granular solid phase are obtained by analogy with the random particle-motion and the thermal motion of molecules within a gas, and accounting for the inelasticity of solid particles. As in a gas, the



8


intensity of the velocity fluctuations determines the stresses, viscosity and pressure of the granular phase. The kinetic energy associated with velocity fluctuations is described by a pseudo-thermal temperature or granular temperature, which is proportional to the norm of particle velocity fluctuations. The conservation equation for the granular temperature, obtained from the kinetic theory of gases, takes the following form: 3 ∂ (ρs αs Θs ) [ + ∇ · (ρs αs~υs Θs ))] = (−ps I¯ + τ¯s ) : ∇(~υs )+ 2 ∂ (t)

(18)

+ ∇ · (kΘs ∇(Θs )) − γΘs + φls where (−ps I¯ + τ¯s ) : ∇(~υs ) : generation of energy by the solid stress tensor kΘs ∇(Θs ) : the diffusion of energy (kΘs is the diffusion coefficient) γΘs : the collisional dissipation of energy φls : the energy exchange between the l th fluid phase and the sth solid phase Equation 18 contains the term kΘs ∇(Θs ) describing the diffusive flux of granular energy. The diffusion coefficient for granular energy kΘs was modeled using the following expression from M.Syamlal, W.Rogers, and T.J. (1993) √ 15ds ρs αs θs π 12 16 [1 + η 2 (4η − 3)αs g0,ss + (41 − 33η)ηαs g0,ss ] (19) kθs = 4(41 − 33η) 5 15π

where 1 η = (1 + ess ) 2

(20)

The term γΘs represents the granular energy dissipation rate within the sth solid phase due to collisions between particles. This term is represented by the expression derived by Lun, S.B.Savage, Jeffrey, and N.Chepurniy (1984)



γΘs =

2.4

9

3 12(1 − e2ss )g0,ss √ ρs αs2 θs2 ds π

(21)

Energy conservation

For energy conservation, the following energy conservation equation must be solved for each phase ∂ (αq ρq hq ) ∂ (pq ) + ∇ · (αq ρq~uq hq ) = −αq + τ¯q : ∇(~uq ) ∂ (t) ∂ (t)

(22)

~ pq + m˙ pq h pq − m˙ qp hqp ) -∇ ·~qq + Sq + ∑np=1 (Q where hq is the specific enthalpy of phase qth , ~qq is the heat flux, Sq is a source term due to chemical reactions, Q pq is the heat-transfer intensity between phases pth and qth , and h pq is the enthalpy of the interface (in the case of evaporation it would be the steam enthalpy at the water droplets temperature). The rate of energy transfer is assumed to be a function of the temperature difference between phases Q pq = h pq (Tp − Tq ) (23) where h pq is the heat-transfer coefficient between the fluid phase pth and the solid phase qth . Provided convection is the main heat-transfer mechanism within the flow, the heat-transfer coefficient is related to the Nusselt number of phase qth by h pq =

6κ p αq α p Nuq d 2p

(24)

Here, κ p is the thermal conductivity of phase pth . The Nusselt number is typically calculated from one of the many correlations existing in the literature. In the case of fluidized bed, Gunn (1978) proposes the correlations of equation 25, which can be used for a range of bed porosity of 0.35 − 1.0 and a particle Reynolds Number up to 105 1

3 Nuq = (7 − 10α p + 5α p2 )(1 + 0.7Re0.2 q Pr )

(25)

1

+ (1.33-2.4α p + 1.2α p2 )Re0.7 q Pr 3 with the phase qth Prandtl number Pr and the Reynolds number Req defined by the following equations:



10

(c p ) p µ p κp

(26)

ρl d p |~υq − ~υl | µl

(27)

Pr = Req =


where (c p ) p is the heat capacity of phase pth at constant pressure.

2.5

Coal drying and volatilization

According to experimental results [Yu et al. (2007); Chejne and Hernandez (2002)], coal drying and volatilization processes occur instantaneously once the fuel enters the reactor. For such reason, coal drying and volatilization processes could be assumed already completed in the feed zone. Then char, ash, volatile matter and steam are produced following equation 28 and its reaction rate computed from mass conservation. In the equation 28 ash appears for illustration only. The simulation does not consider ash content in the solid phase. Coals → Chars +Volatiless + Steamg + Ashs

(28)

There is no unique chemical reaction describing coal volatilization due to the complex and variable nature of coal composition. In the present work, the chemical reactions proposed by Di-Blasi (2004) and Lu et al. (2008), equations 29 and 30, have been adopted to describe the coal volatilization and Tar decomposition. Volatiles → α1CH4 + α2CO + α3CO2 + α4 H2

(29)

+α5 H2 O + α6 Tar Tar → β1CO + β2CO2 + β3CH4

(30)

For simplification, the overall volatilization process has been described as a combination of the two above reactions in a single reaction represented by equation 31 [Lu et al. (2008)]. Volatiles → (α1 + α6 β3 )CH4 + (α2 + α6 β1 )CO

(31)

+(α3 + α6 β2 )CO2 + α4 H2 + α5 H2 O + α6 Tar If there is no available experimental data regarding the chemical-species distribution in the coal volatile matter, then the correlations of Weimer and Clough (1981)



11

can be used to predict the species distribution in the volatile matter, given by equations 32 to 37: CH4 = 0.21 − 0.469VOL + 0.241VOL2 (32) H2 = 0.157 − 0.868VOL + 1.338VOL2

(33)

CO2 = 0.135 − 0.9VOL + 0.196VOL2

(34)

CO = 0.425 − 2.653VOL + 1.906VOL2

(35)

H2 O = 0.409 − 2.389VOL + 4.554VOL2

(36)

Tar = −0.325 − 7.279VOL − 12 − 880VOL2

(37)

where VOL is the mass fraction of coal volatile-matter in dry/ash free basis. The species distribution in the Tar decomposition was obtained from Di-Blasi (2004).

2.6

Char combustion and gasification

For the char combustion and gasification chemical-reactions, the chemical model of Weimer and Clough (1981) was used. This model involves the heterogeneous reactions show below: equations 38 to 40. Char combustion: C(s) + O2 → CO2

(38)

C(s) + H2 O → CO + H2

(39)

H2 O char gasification:

CO2 char gasification: C(s) +CO2 → 2CO

(40)

To model the heterogeneous reaction-rates the Kinetic/Diffusion Surface Reaction Model (KDSRM) of Baum and Street. (1971) and Field (1969) was used. This model assumes that the surface reaction proceeds at a reaction rate determined from the weighting of an Arrehnius rate and a diffusion rate accounting for the oxidant diffusion at the surface of the particle. Diffusion rate coefficient D0 = C1

[(TP + T∞ )/2]0.75 dp

(41)



12


Arrehnius rate Rdi f f = C2 e−(E/RTp )

(42)

Reaction rate: weighting of diffusion and Arrehiuns rates dm p ρRT∞Yox D0 Rdi f f = −A p dt Mw,ox D0 + Rdi f f

(43)

Since the above model is not available in FLUENT when the eulerian model is enabled, it was implemented by the author by means of a UDF. The model coefficients are shown in table 1. Table 1: Kinetic/Diffusion Surface Reaction Model (KDSRM) coefficients.

2.7

Chemical Reaction

C1

C2

E

C(s) + O2 → CO2 C(s) + H2 O → CO + H2 C(s) +CO2 → 2CO

4e − 4 3e − 6 2e − 5

6.51e8 −0.9e5 6.2e8 −1.1e5 3.5e4 −1.5e5

Homogeneous reactions

Homogeneous reactions taking place in the gasifier include those proposed by Weimer and Clough (1981): equations 44 to 47. Following Yu et al. (2007), the methane (CH4 ) combustion, equation 47, was also included. Water gas shift reaction: CO + H2 O ↔ CO2 + H2

(44)

CO + O2 → 2CO2

(45)

2H2 + O2 → 2H2 O

(46)

CO combustion:

H2 combustion:



13

CH4 combustion: CH4 + 2O2 → CO2 + 2H2 O

(47)

The species mass fractions Yi are described through the solution of a convectiondiffusion equation. This equation takes the following general form: ∂ (ρYi ) + ∇ · (ρ ~υ Yi ) = −∇ · J~i + Ri + Si (48) ∂ (t) where Ri is the net production-rate of specie i due to homogeneous reactions, and Si is a source term describing the specie i production rate from the solid-phase heterogeneous reactions. The above equation is solved for the N − 1 species, where N is the total number of fluid species present in the system. In fluid flows controlled by turbulent fluctuations, chemical kinetics does not play an explicit role in the calculation of homogeneous reaction-rates and these are assumed to be controlled by the turbulent mixing rate Yu et al. (2007). Based on the work of Magnussen and Hjertager (1976), the Eddy Dissipation Model (EDM) was used. In this model, the production of the specie i due to the homogeneous reaction r, Ri,r , is given by the smaller value (limit value) of the following two expressions: ε YR 0 Ri,r = νi,r Mw,i Aρ minR ( 0 ) κ νR,r Mw,R 0 Ri,r = νi,r Mw,i ABρ

ε ∑P YP κ ∑Nj ν 00j,r Mw, j

(49) (50)

2.8 Numerical scheme The present computational model uses a three-dimensional steady-state solver, with first-order discretization schemes where gradients and derivatives are evaluated through the Green-Gauss method. Table 2 summarizes the characteristics of the solver. For the discretization of all conservation equations (momentum, continuity, energy, volume fraction, granular temperature, turbulent kinetic energy, turbulent kinetic energy dissipation rate and mass fraction of chemical species), a first-order upwind scheme was used. In this discretization scheme, quantities at the cell faces are determined by assuming that the cell-center values represent an average value and hold throughout the entire cell; the face quantities are identical to the cell quantities. Thus when first-order upwinding is selected, the current face value is taken equal to the cell-center value of the upstream cell in the N − 1 iteration.



14


Table 2: Solver parameters. Characteristic

Value

Pressure Based Formulation Space Velocity Formulation Gradient Option Porous Formulation Pressure-Velocity Coupling Discretization Under-Relaxation Factor

Enable Implicit 3D Absolute Green-Gauss Cell Based Superficial Velocity Phase Coupled SIMPLE First Order Upwind 0.1 all variables

The evaluation of gradients and derivatives is carried out by means of Green-Gauss Cell Based Gradient Evaluation method. Gradients ∇φ of a given variable φ is used to discretize the convection and diffusion terms in conservation equations. When the Green-Gauss theorem is used to calculate the gradient of some scalar φ at the cell-center c0, its discrete form is written as (∇φ )c0 =

1 − → φf Af ∑ v f

(51)

where φ f is the value of φ at the cell face centroid, computed with the following equation: φc0 + φc1 2 The summation is over all the faces enclosing the cell. φf =

3

(52)

Results

To calibrate and validate the model, a laboratory-scale fluidized bed gasifier designed and built to perform studies on Colombian coal gasification [Ocampo, Arenas, Chejne, Espinel, Londoo, Aguirre, and Perez (2003)] was chosen, since it has extensive experimental data available: figure 1. This gasifier have also been used as a benchmark case to validate other computational models in the literature [Yu



15

et al. (2007); Chejne and Hernandez (2002)]. Detailed information about the experimental installation can be found in: Chejne and Hernandez (2002); Ocampo et al. (2003). Only the basic elements will be described here. The core of the reactor is a 22 cm internal diameter and 200 cm total height fluidized bed reactor, which is built in AISI 310 stainless steel. It is internally covered by a 10 cm layer of refractory brick and externally by a 15 cm layer of ceramic fiber in order to reduce the heat losses. Coal is fed by a screw feeder located 30 cm above the air distributor. The latter has 142 holes of 1 mm diameter, arranged in a circular pattern. At the air and steam inlet a uniform-velocity condition was assumed; this is an acceptable assumption due to the use of the air distributor. The outlet pressure is fixed at its atmospheric value. Since the coal drying and volatilization processes are assumed to occur instantaneously at the feed zone, it was assumed that char and volatile mater enter into the domain independently. Heat losses are considered negligible, so reactor walls are assumed adiabatic. The domain was discretized by a 3508 hexahedral-cells computational grid: figure 1. Experimental tests were carried out using a Colombian coal. The coal analysis and properties are summarized in table 3.

Figure 1: Experimental installation and simulation grid.


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Table 3: Colombian coal analysis and properties: Chejne and Hernandez (2002). Parameter Ultimate analysis (wt%) C H O N S Proximate analysis (wt%) Ash Moisture Volatile matter Fixed carbon Others Mean particles size (mm) Density (kgm−3 ) High heating value, (kJkg−1 )

Value, %

71.38 5.12 17.62 1.36 0.22 4.3 22.3 47.1 48.6 0.62 1250 21.5

Operating conditions used for the model calibration: case 1, and validation: case 2, case 3 and case 4, are summarized in table 4. The bed was initially filled with fuel particles up to a height of 1 m, with a solid-phase volume-fraction of 0.48 [Chejne and Hernandez (2002)]. The simulated cases are denoted as case 1, case 2, case 3 and case 4, and correspond to operating conditions 1, 2, 3 and 4 respectively. The calibration was carried out using the operating conditions and experimental results of case 1. Submodels and their parameters were chosen in order to obtain the best-possible fit between experimental and simulated operating temperatures. Calibration results show a good fit with the available experimental data: figure 2. Predicted operating temperature and chemical-species molar-fractions show an agreement with data, similar to that of existing models developed as academic codes one-dimensional [Chejne and Hernandez (2002)], two-dimensional [Yu et al. (2007)] and three-dimensional [O’Brien et al. (2003)].



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Figure 2: Calibration, case 1 - experimental and predicted species molar fractions.

Figure 3: Calibration, case 1 - species molar fraction distributions.


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For the validation, the error in the temperature predictions with respect to the experimental data is less than 1%, table 5. Regarding chemical-species, the highest error correspond to the CH4 concentration; this error reached 70%. From the remaining species, the computed CO concentration reached a 33% error. All other species were kept below an 11% error. For the CH4 (which only appears in the combustion reaction), the high error found, were the predicted value underestimates the experimental data, is presumed to be caused by the fact that volatilespecies distributions are given by correlations, and are not specific to the coal used in the current experiments. Furthermore, since the absolute values of molar fraction of CH4 present in the experimental data and numerical results are very low, a small difference will be reflected in a high relative error. This characteristic of the prediction of CH4 is a known phenomena and has been reported in other models [O’Brien et al. (2003); Yu et al. (2007)]. Figure 3 shows the distributions of chemical species in an axial plane. A high CO2 concentration was found in the bed zone due to the the char combustion-reaction. Regarding CO and H2 , these species present a high concentration in the feed region, were the volatilization process takes place. Fluidization is an unsteady process. Therefore, although variables like species molar-fractions and reactor temperature appear to have converged, the solid phase volume fraction represents only an instantaneous state which may give some qualitative idea of the bed fluidization. However, it does not represent a converged state. Figure 4 shows the solid phase volume fraction distribution in an axial plane of the reactor. The bubble formation (gas-rich areas) and the fluidization height (around 1 m) can be observed; the latter agrees well with the experiment.

Figure 4: Calibration, case 1 - solid phase volume fraction.



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Table 4: Operating condition: Chejne and Hernandez (2002). Operating condition

1

Coal feed (kgh−1 ) 8.0 −1 Air supply (kgh ) 21.9 Steam supply (kgh−1 ) 4.6 Air and steam T 420 at the entrance (C) H2 (%) 8.53 CO2 (%) 19.31 N2 (%) 60.37 CH4 (%) 0.84 CO (%) 10.94

2

3

4

8.0 17.0 4.6 413

8.0 19.4 4.6 422

8.0 21.9 4.6 435

8.84 18.38 61.1 1.07 10.59

9.63 14.4 64.62 1.34 9.97

7.88 15.6 64.52 1.01 10.94

Once the model was calibrated, the validation process was carried out using the operating conditions and results of case 2, case 3 y case 4, table 4. Results are in good agreement with the experimental data given in Ocampo et al. (2003). Figures 6, 8 and 10 show the comparisons between predicted and experimental species molar-fractions. In all cases, temperature predictions errors were kept lower than 1% (table 5), and temperature distributions were found mostly constant within the reactor in agreement with experimental data, figure 5. Besides the CH4 concentration, where a high error existed (59% of average error) due to reasons explained before, within the remaining species the highest error corresponds to the predicted CO concentration, reaching 32% of average error. The average error in the prediction of the other species concentration, CO2 , H2 and N2 , was found to be 12%, 14% and 4% respectively; in all cases the error between predictions and experiments was under 23%. As previously explained, the errors found in the predictions of chemicalspecies with respect to experimental data are presumably attributable to the fact that the correlations used to calculate species distribution within the volatile gas do not correspond to the current coal, predicting a low CO and CO2 concentration and overestimating the H2 O concentration. A second possible cause of these errors is that the Tar decomposition-equation also is not specific to the current coal. Figures 7, 9 and 11 show the contour plot of species molar-fractions in an axial plane of the gasifier. All plots show a similar tendency: high CO2 concentrations in the bed due to char combustion and high CO and H2 concentration in the near feed region where coal volatilization takes place.


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Table 5: Predicted and experimental temperature. Case 1 Case 2 Case 3 Case 4

Model T (K) 855 807 839 865

Experimental T (K) 851 812 841 866

Figure 5: Validation, temperature predictions. Axial distribution.




21

Figure 6: Validation, case 2 - experimental and predicted species molar fractions.

Figure 7: Validation, case 2 - species molar fraction distributions.


22







23





24


Figure 12 shows the solid-phase volume-fraction distribution for the three validation cases. In comparison to one- and two-dimensional models available in the literature [Chejne and Hernandez (2002); Yu et al. (2007)], the present model takes into account three-dimensional effects of the fluid flow. Unlike those models, the three-dimensionality of the present model allows the modeler to include geometrical modifications and/or alterations in the operating and boundary conditions and capture their effects. This allows the model to be used in the analysis and optimization of existing gasifiers and to study new designs with reasonable turnaround times, regardless of the complexity of reactor geometry and operating conditions.

Figure 12: Validation, case 2, case 3 and case 4 - solid phase volume fraction.

4

Conclusions 1. A modeling methodology to describe the coal gasification in fluidized bed reactors was developed within the framework of the commercial CFD code FLUENT, including the drying, volatilization, combustion and gasification processes. Both phases, gas and solid, were described using an eulerianeulerian approach exchanging mass, energy and momentum. The solid disperse phase was described by the kinetic theory of granular flows. The heterogeneous reaction taking place within the reactor were modeled using the Kinetics Diffusion Surface Reaction Model implemented within the FLUENT framework through a User Defined Function (UDF). Calculation times are approximately two days in a 3.2 GHz, 8 Gb RAM desktop computer.



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2. The model was calibrated and validated using operating conditions and experimental data from a benchmark fluidized-bed coal-gasifier available in the literature. Numerical results are in good agreement with the experimental data. 3. The model is capable of describing the fluid-dynamics and chemical processes taking place in the overall gasification process, capturing know phenomena like fluidization bed-height, temperature distribution and chemicalspecies concentrations. The predictions errors are similar to those of oneand two-dimensional models existing in the literature for the same experiment. However, since the model was developed in the framework of a multipropose commercial code, it can handle more complex geometries and operating and boundary conditions. Therefore, it can be used for the analysis and optimization of existing gasifiers and for relatively-quick evaluations of new designs.

Nomenclature Notation A, B Ap C1 C2 CD Cp E → − F H K Mw Nu P Pr Re S

calibration constants eddy dissipation model EDM surface of coal particle, m2 diffusion coefficient KDSRM pre-exponential factor Arrehnius reaction rate KDSRM,s−1 drag coefficient J calorific capacity, kgK activation energy Arrehnius J reaction rate KDSRM, kgmol force, N J enthalpy, kgmol momentum transfer coefficient kg molecular weight, kmol Nusselt number pressure, Pa Prandtl number Reynolds number source term



26

T V Y d ess f g0 h k → − q s vr → − v

temperature, K volume, m3 mass fraction coal particle diameter, m restitution coefficient drag function radial distribution function J specific enthalpy, kmolkg W thermal conductivity, mK heat flux, mW2 distance between particles, m terminal velocity magnitude, ms velocity, ms

Greek letters αn ρb ρ ρr µ λ θ κ ε µt ν0

volume fraction of n-phase effective density, mkg3 density, mkg3 reference density, mkg3 kg molecular viscosity, ms kg bulk viscosity, ms 2 granular temperature, ms2 2 turbulent kinetic energy, ms2 turbulent kinetic energy 2 dissipation rate, ms3 kg turbulent viscosity, ms stequiometric coefficient

Subscripts p, q s P R

fluid phase solid phase products in chemical reactions reactants in chemical reactions




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Abbreviations AISI CFD DEM EDM KDSRM UDF

American Iron and Steel Institute Computational Fluid Dynamics Discrete Element Method Eddy Dissipation Model Kinetic Diffusion Surface Reaction Model User Defined Function

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