Modelling And Simulation Of Coal Gasification Process In Fluidised Bed

Fuel 81 (2002) 1687±1702

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Modelling and simulation of coal gasi®cation process in ¯uidised bed q F. Chejne*, J.P. Hernandez Energy and Thermodynamics Institute, Universidad Ponti®cia Bolivariana, Circular 1#73-34 Medellin, AA 56006, Colombia Received 5 September 2001; revised 14 January 2002; accepted 23 January 2002; available online 22 February 2002

Abstract A one-dimensional steady state mathematical model and a numerical algorithm have been developed to simulate the coal gasi®cation process in ¯uidised bed. The model incorporates two phases, the solid and the gas. The gaseous phase participates in the emulsion (with the solid phase) and forms the bubble. The solid phase is composed of carbonaceous material, limestone and/or inert bed material. The model can predict temperature, converted fraction, and particle size distribution for the solid phase. For the gaseous phase, in both emulsion and bubble, it can predict pro®les of temperature, gas composition, velocities, and other ¯uid-dynamic parameters. In the feed zone, a Gaussian distribution for the solid particle size is considered. This distribution changes due to attrition, elutriation, consumption and drag inside the reactor. A system of 29 differential and 10 non-linear equations, derived from the mass, energy and momentum balances for each phase, at any point along the bed height, are solved by the Gear and Adams Method. Experimental data from the Universidad de Antioquia and Universidad Nacional-Medellin have been used to validate the model. Finally, the model can be used to optimise the gasi®cation process by varying several parameters, such as excess of air, particle size distribution, coal type, and geometry of the reactor. q 2002 Published by Elsevier Science Ltd. Keywords: Gasi®cation; Mathematical model; Fluidised beds

1. Introduction Coal has been used as one of the most important energy sources in Colombian industry over the years. Nearly 80% of all industries use coal; textile, food, beer, and steel industries are the most relevant for the coal market in Colombia. Some coal ®elds are situated near the main industrial cities, thus coal has a low price compared to other fuels. Although the sulphur and moisture percent in Colombian coal are relatively low, coal combustion can be a more critical process, from an environmental point of view, than other fuels or processes. Thus, Colombian government and universities are interested in developing technology to increase the use of coal in the country in a clean and ef®cient way. Gasi®cation technology is being developed to provide environmentally clean and ef®cient power generation from fuels such as coal, biomass and oil residues. Modelling and simulation tools are increasingly popular with plant operators and contractors to assist with design, analysis and optimisation of gasi®cation and combustion processes. The application of mathematical modelling in coal gasi®ca* Corresponding author. Tel.: 1574-412-5246; fax: 1574-411-1207. E-mail address: [email protected] (F. Chejne). q Published ®rst on the web via Fuel®rst.comÐhttp://www.fuel®rst.com 0016-2361/02/$ - see front matter q 2002 Published by Elsevier Science Ltd. PII: S 0016-236 1(02)00036-4

tion is fairly new compared to that in coal combustion processes. Moreea-Taha [1] described how mathematical modelling can help in understanding the combustion and gasi®cation processes, and the use of modelling as a predictive tool, such as in pollutant emission prediction. He used onedimensional and three-dimensional ¯uid dynamics models with some assumptions, such as simpli®ed chemical reactions. de Souza-Santos [2±4] developed a comprehensive mathematical model and computer program, to use as a tool for engineering design and operation optimisation, by predicting the behaviour of a real unit during steady-state operation. Chejne et al. [5] developed a comprehensive mathematical model to predict the behaviour of coal combustion and gasi®cation on stacks in non-stationary operation. Skala and Kuzmanovic [6] presented a paper with information about heterogeneous gas±solid reactions and a mathematical model of the coal gasi®cation reaction. The model by de Souza-Santos [2±4] is regarded as complete and it includes the conservation equations for the emulsion phase and bubbles, empirical equations for hydrodynamics, and it also includes a through mass balance which considers that both drying and volatilisation are not instantaneous. This latter aspect is not included in our present work because we have realised, based on experimental results, that both drying and volatilisation take

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F. Chejne, J.P. Hernandez / Fuel 81 (2002) 1687±1702

Nomenclature a aj A Adens;p Att;i Arr;i Bp bj;m cj;m C Cp dj;m D Dij Dj;M ej;m f fsvol F g h hm H Hy DHf0 K L Mi Mrem MT MMi n Nu nrgg nrgs O Pr Q Rp RT RmT rgg;i rgs;i Re S

speci®c area ¯uid-dynamic constants values area constants for the solid±gas reaction rate (p ˆ 1, 2) attrition fraction for i-level drag fraction for i-level devolatilisation kinetic coef®cient (p ˆ 1,¼,13) viscosity constants of the jth component conductivity constants of the jth component carbon fraction speci®c heat binary diffusion coef®cient constants of the jth component diameter binary diffusion coef®cient between the ith and jth component diffusion coef®cient of the jth component in the mixture speci®c heat constants of the jth component remaining solid fraction in the bed volumetric solid fraction ¯ow rate gravity acceleration convection heat transfer coef®cient convection mass transfer coef®cient enthalpy hydrogen fraction formation enthalpy kinetic coef®cient height of the reactor mass of i-level mass of solids in bed kinetic constant for the solid±gas reaction rate molecular mass total number of level in the particle size distribution Nusselt number total number of gas±gas reactions total number of gas±solid reactions oxygen fraction Prandt number heat ¯ux reaction rate for the p-reaction (p ˆ 1,¼,10) total heat resistance total mass resistance gas±gas reaction rate for each specie i gas±solid reaction rate for each specie i Reynolds number sulphur fraction

Shj T tw u V Wi x y

Sherwood number for the jth component temperature reactor wall thickness velocity volume mass fraction of i-level molar fraction mass fraction

Greek letters a combustion kinetic coef®cient b combustion kinetic coef®cient 1 porosity G solid friability coef®cient l conductivity m viscosity r density r app coal apparent density r real coal real density n i;gg stoichiometric coef®cient of each specie i in the gas±gas reactions ni;gs stoichiometric coef®cient of each specie i in the gas±solid reactions Subscripts arf inert material ave average between diameters b bubble cal limestone e emulsion feed conditions at the feeding point g gaseous phase ge gas in emulsion inf relative to the inferior level in conditions inside the reactor i CO2, CO, O2, N2, H2O, H2, CH4, SO2, NOX, C2H6, H2S, NH3 in emulsion k CO2, CO, O2, N2, H2O, H2, CH4, SO2, NOX, C2H6, H2S, NH3 in bubble M average value mc carbonaceous material mf minimum ¯uidisation conditions or relative to the holes on the plate out conditions out the reactor p relative to the solid particles pl relative to the plate r reactor s solid sup relative to the superior level t terminal conditions w reactor wall

F. Chejne, J.P. Hernandez / Fuel 81 (2002) 1687±1702

place very quickly when the gasi®cation or combustion occurs in a ¯uidised bed. Therefore we decided to consider both processes as instantaneous and to include the species released [7] as a mass source term in the mass conservation equations. Ross et al. [8] investigated the time required for devolatilisation of large coal particle in a ¯uidised-bed operating at 750, 850, and 950 8C and in gas environments simulating pyrolysis, combustion, and gasi®cation conditions. From this work, we can see that the particle less than 6 mm need less than 10 s. Our experiments in pilot plant were performed with particles of average diameter of about 1 mm, so we expect even shorter volatilisation times. These works and other more recent ones such as the work by Ciesielcyk and Gawdzik [9], Guo and Chan [10], and Chen et al. [11] use the classical equations of continuity and energy in a way similar to that one described in the present work. The great majority of coal gasi®cation models in ¯uidised beds use empirical correlations to describe the ¯uid dynamics inside the reactor, thus they avoid the solution of the momentum equations as it is proposed in this paper. Darton et al. [12] described the phenomenon related with bubbles growth due to coalescence in ¯uidised bed by using a simple theory which gives an empirical equation for the bubble diameter. Coronella et al. [13] have studied the slugging of ¯uidised beds by using a new method based on detecting pressure drop ¯uctuations. We have tested several of these aforementioned empirical equations in order to avoid the solution of the momentum equation and to know the behaviour of the gasi®cation process. Our main contribution to the prediction of coal gasi®cation in ¯uidised beds is to develop an original proposal which includes the evolution of particles distribution inside the reactor starting from an initial Gaussian distribution of the ¯ow of coal fed into the equipment. Another important contribution made in the present work is to use the nonlinear conservation equations in compact form which have allowed us to obtain an ef®cient numerical solution with fast convergence and minimisation of the numerical error. In our algorithm for the numerical solution we have used the subroutine DIVPAG from the IMSL ver. 3.0 to evaluate the transport coef®cients such as the diffusivity of species in the mixture, the thermal conductivity of gases, and the viscosity of gases as a function of temperature. These calculations were performed for each of the chemical species and also for the mixture which has led to numerical predictions that agree very well with experimental results as can be seen in ®gures presented in the paper. Adanez [14] developed a model considering the hydrodynamic behaviour of a turbulent circulating ¯uidised bed, the kinetics of coal combustion and sulphur retained in the riser. They have also used empirical equations to include the hydrodynamics of a turbulent bed just as we had done in this paper.

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Adanez et al. [14] made a population balance of each family of char particles in order to perform the carbon mass balances in a bed with shrinking particles. In the present work, a distribution function (Fig. 3) which changed during the process due to several mechanisms such as attrition, elutration, drag, and chemical reaction processes was taken, thus achieving a better approach for modelling and understanding the actual combustion phenomena. Huilin et al. [15] developed a steady state model for a coal ®red circulating ¯uidised bed boiler which included the hydrodynamics, heat transfer and combustion and analysed both the dense zone and the dilute region in the furnace. They also used empirical equations for the hydrodynamics in the ¯uidised bed and a model of one ¯uid without taking into account the possible variation of gas temperature inside the furnace. Kim et al. [16] proposed a mathematical model to predict gasi®cation in an internally circulating ¯uidised bed reactor with draught tube, based on hydrodynamics, reaction kinetics and empirical correlations for pyrolysis. They were not able to predict neither the temperature pro®les nor the gas concentration inside the bed, nevertheless their results and predictions were reasonably accurate. The main characteristics and advantages of the coal gasi®cation model (MGC) described in this paper are: 1. One-dimensional and steady-state. 2. It includes two ¯uids; emulsion and bubble; and two phases; gas and solid. 3. The emulsion is formed by gas and solids. 4. The bubble is considered free of solid particles, therefore it is formed only by gas. 5. The solid is considered isothermal and the consumption uniform through the bed height. 6. The mass and heat transfer between solid and gas in the emulsion, are considered. This is also true for the mass and heat transfer between the emulsion gas and the bubble (mass or heat transfer between solid and bubble are NOT considered). 7. Attrition, elutriation and drag are included for solid phase. 8. Reaction models are used for homogeneous (gas±gas) and heterogeneous (gas±solid) chemical reactions. 9. Devolatilisation and drying are considered instantaneous in the feed zone. 10. The gasi®cation process can be achieved with stream (H2O) or with carbon dioxide (CO2). 11. A partial differential equation for mass and heat transfer, for each component in the gas and solid phases, is derived and solved. 12. Experimental correlations for the ¯uid-dynamic parameters are used. 13. Chemical reactions, convection and diffusion are included in the differential equations for the gas and solid phases. The energy equations for both phases are coupled by convection phenomena on the surface of the

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F. Chejne, J.P. Hernandez / Fuel 81 (2002) 1687±1702

Fig. 3. Phases, ¯uids and exchanges in the MGC.

Fig. 1. Schematic diagram of the reactor.

particles. Inside each equation, the mass and heat transfer coef®cients are also calculated.

2. Mathematical model The proposed model is applied to solid particles submerged in a ¯uidiser gas. The solids (coal, limestone, inert material) enter into the reactor at the feed point; the type of coal, initial particle size distribution and composition of solids; i.e. coal, limestone and sand percentages; are given at this point. The gas (air, stream, carbon dioxide) enters through the bottom of the reactor, its inlet composition and temperature must be speci®ed (Fig. 1). At the feeding point a Gaussian distribution is assumed for the solid material; for each element an average diameter is calculated. Inside the reactor, the shape of the distribution

is conserved but the average diameter changes due to attrition, elutriation, consumption, and drag. Attrition only affects the size of the particles, on the other hand, elutriation, consumption and drag also affect the total mass of the element (Fig. 2). The bubble is considered a ¯uid, that increases the energy and mass transfer inside the reactor. The bubble helps the solids homogenisation and its presence increases the process ef®ciency and performance. The bridge between the solid and bubble is the gas in the emulsion, because it exchanges mass and energy with both solids and bubble; while these only exchange mass and energy with the gas in the emulsion (Fig. 3). A system of several chemical reactions for the solid and gaseous phase were included. The drying, devolatisation and limestone reactions are considered as instantaneous phenomena at the feeding point. The solid phase is considered independent of the axial co-ordinate. As a consequence, temperature, consumption fraction and composition are constant in the reactor. The gaseous phase changes at any point along the bed height. This consideration allows the mass and energy equations to be derived. The mass and heat transfer coef®cients are calculated using experimental correlations from several references. Speci®c heat, conductivity, viscosity and binary diffusion

Fig. 2. Schematic view of the particle size distribution.

F. Chejne, J.P. Hernandez / Fuel 81 (2002) 1687±1702

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Table 1 Equations for the physical properties Equation hm;k ˆ 2

Unit umf 12 1 3=2 Db Db



Dk;M 1mf ub p

1=2

1s

!1=2

Reference

21

[2±4]

±

[2±4]

W m 22 K 21

[20]

W m 22 K 21

[2±4]

 2=3 Re Nu ˆ 0:4 Pr1=3 1

±

[2±4]

ln…mj † ˆ bj;0 1 bj;1 ln…Tg † 1 bj;2 ln…Tg †2 1 bj;3 ln…Tg †3

N s m 22

Shj ˆ 21mf 1

4Dp 1mf ub pDj;M

hg±b ˆ

  umf rge Cpg;M lg;M 1mf ub rge Cpg;M 1=2 12 3 Db

hg±s ˆ

Nulg;M Dp

2

ln…lj † ˆ cj;0 1 cj;1 ln…Tg † 1 cj;2 ln…Tg † 1 cj;3 ln…Tg †

3

2

Wm 3

ln…Dij † ˆ dij;0 1 dij;1 ln…Tg † 1 dij;2 ln…Tg † 1 dij;3 ln…Tg † 2

3

Cpj ˆ ej;0 1 ej;1 …Tg † 1 ej;2 …Tg † 1 ej;3 …Tg † 1 ej;4 …Tg †

mg;M ˆ

12 X iˆ1

11

mi X xk k±i

lg;M ˆ

12 X iˆ1

11

X k±i

xi

4

2

21

J kg

21

m s

Nsm

[17,31]

K

21

[17,31] [17,31]

K

21

[32]

22

[17,31]

F ik

li xk 1:065F ik

1 2 wi DM i ˆ X xk k±i

21

W m 21 K 21

[17,31]

m 2 s 21

[17,31]

±

[17,31]

Dik

   1=2   !2 1 M 1=2 mi Mi 1=4 F ik ˆ p 1 1 i 11 Mk mk Mk 2 2

coef®cients, for each component in the gas phase are calculated as a function of temperature at each point, and the mixture's properties are then calculated. Table 1 summarises the most important coef®cients of the MGC model.

where the reaction rate for each species i due to gas±gas and gas±solid reactions (Table 2) can be expressed like, nrgg

rgg;i ˆ

2.1. Basic equations The mass balance for the gas phase in the emulsion requires that the variation of each component along the axial direction is equivalent to the generation (or consumption) from the heterogeneous and homogeneous reaction and the exchange by convection with the bubble, d…rge uge yi † dVg dA dA ˆ rgg;i 1 hm;i ‰ye;i 2 yb;i Šrg b 1 rgs;i s dz dz dz dz …1†

rgs;i ˆ

X

ggˆ1 nrgs X gsˆ1

rgg;i ni;gg MMi

…2†

rgs;i ni;gs MMi

…3†

For the gas in the bubble, the variation in the composition is due to the generation (or consumption) from the homogeneous reaction and by the exchange through convection with the gas in the emulsion, d…rb ub yk † dV dA ˆ rgg;k b 2 hm;k ‰ye;i 2 yb;k Šrg b dz dz dz

…4†

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F. Chejne, J.P. Hernandez / Fuel 81 (2002) 1687±1702

Table 2 Chemical reactions Reaction

Type

Chemical reaction

Reference

1 2

Solid±gas Solid±gas

[2±4] MGC model

3

Solid±gas

4 5 6 7 8 9 10

Solid±gas Gas±gas Gas±gas Gas±gas Gas±gas Gas±gas Gas±gas

C 1 aO2 ! …2b 2 1†CO2 1 …2 2 2b†CO C 1 H2 O ! CO 1 H2 C 1 CO2 ! 2CO Volatile ! B1 CO2 1 B2 CO 1 B3 O2 1 B4 N2 1 B5 H2 O 1 B6 H2 1 B7 CH4 1 B8 SO2 1 B9 NO 1 B10 C2 H6 1 B11 H2 S 1 B12 NH3 1 B13 Tar Carbonaceous material ! C 1 H2 O CO 1 H2 O $ CO2 1 H2 O 2CO 1 O2 ! 2CO2 2H2 1 O2 ! 2H2 O CH4 1 2O2 ! CO2 1 2H2 O 2C2 H6 1 7O2 ! 4CO2 1 6H2 O 4NH3 1 5O2 ! 4NO 1 6H2 O

Due to the homogeneity and isothermal conditions for the solid phase (coal, limestone and/or inert material), the mass balance is global and is integrated over the volume of the reactor. For the coal, the difference between the inlet and outlet ¯ow is equivalent to the oxygen and gasi®cation reactions in the reactor, Fmc;out 2 Fmc;in ˆ

ZL 0

i Vol rsg;mc …1 2 1†Ar fmc dz

…5†

The mass balance for the limestone requires that the rate of generation (or consumption) due to sulphur reactions is equivalent to the differences between the inlet and outlet ¯ow, Fcal;out 2 Fcal;in ˆ

ZL 0

i Vol rsg;cal …1 2 1†Ar fcal dz

…6†

Finally, the inlet and outlet ¯ow for the inert material are equal, Farf;out 2 Farf;in ˆ 0

…7†

For the gaseous phase; in both emulsion and bubble; the differential energy balance considers that the change in enthalpy along the axial direction is equivalent to the exchange by convection with the solid phase, with the other ¯uid (either emulsion or bubble) and the energy losses through the reactor wall. In consequence, the energy balance for the gas in emulsion is d…rge uge Hge † dA dA ˆ hg±b ‰Tb 2 Tge Š b 1 hg±s ‰Ts 2 Tge Š s dz dz dz 1

‰Tge 2 Tout Š RT

(8)

where the equivalent resistance for heat transfer includes convection inside and outside the reactor and the conduction

[2±4] [2±4] [2±4] [2±4] [2±4] [2±4] [2±4] [2±4]

through the reactor wall, RT ˆ

1 ln……Dr 1 tw †=Dr † 1 pDzNuin lg;M 2pDzlw 1 pDz…Dr 1 tw †hout

1

…9†

For the gas in the bubble the balance is d…rb ub Hb † dA ˆ 2hg±b ‰Tb 2 Tge Š b dz dz

…10†

The enthalpy in Eqs. (8) and (10) consider changes in temperature and consumption (or generation) due to the chemical reactions [17] from the mass balance represented by the formation enthalpy of each component, Hj ˆ

X m

  X 0 ym DHf;m 1 Cp;m Tj ˆ ym Hm

…11†

m

where j represents the gas in emulsion or bubble, and m represents the ith or kth component of the speci®c ¯uid. Expanding the left hand side of Eqs. (8) and (10) and by substitution of the enthalpy de®nition (Eq. (11)) in the resulting expression, we obtain the reaction energy term. See appendix 1 for details. v.g. The energy generated due to chemical reactions is appreciated by taking the derivative of Eq. (8),

d…rge uge Hge † ˆ dx ˆ

X i

Hi

d rge uge

X

dx

i

! yi Hi

d…rge uge yi † X dH 1 …rge uge yi † i dx dx i

…12†

By using mass balance equation (e.g. Eq. (1)), enthalpy equation (Eq. (11)) and by introducing in the latter

F. Chejne, J.P. Hernandez / Fuel 81 (2002) 1687±1702

equations we obtain, d…rge uge Hge † dx  X  dVg dAb dAs ˆ 1 hm;i ‰ye;i 2 yb;i Šrg 1 rgs;i Hi rgg;i dz dz dz i 1

X i

…rge uge yi †

dH dx

(13)

also, d…rge uge Hge † dx  X  dVg dA dA ˆ 1 hm;i ‰ye;i 2 yb;i Šrg b 1 rgs;i s Hi rgg;i dz dz dz i 1

X i

…rge uge yi †

d…Cpi T† dx

(14)

In this way we have proved that the heat of reaction is included in our model. A similar approach can be made for Eq. (10). The global energy balance for the solid phase considers the inlet and outlet ¯ow plus the total of the chemical reactions inside the reactor, ZL  …FH†mc;out 2 …FH†mc;in ˆ Qsg dz Ar fmc …15† 0

where the inlet enthalpy of the carbonaceous material is a function of the coal's chemical characterisation [18,19],     …O† Hmc;in ˆ 80:8…C† 1 344 …Hy† 2 1 22:2…S† 4186:8 8 …16†

different sources. The most important parameters in the ¯uidisation process are the velocities and diameters of the different phases and ¯uids. In order to maintain a ¯uidised bed, the conditions of minimum ¯uidisation must be satis®ed. This means that the drag force, from the ¯uid in motion, has to overwhelm the weight of the solid particles. In this way, levitation of the solids is achieved. The minimum gas velocity for ¯uidisation is de®ned when drag force and weight of the solid particles are equivalent. This is the limit between a ®xed and the ¯uidised bed. To ®nd this velocity, the minimum ¯uidisation Reynolds number has to be calculated. Here in the MGC model the Wen and Yun [4] correlation is used,   10:5 0 a2 D3p rg g…rmc 2 rg † A 2a1 …19† Remf ˆ @a21 1 m2g where a1 ˆ 25:25 and a2 ˆ 0:0651 from the experimental work with coals by Babu [20]. Using this Reynolds number, the minimum ¯uidisation velocity can be obtained by: umf ˆ

…17†

In addition to the balance equations the gas volume variation and the surface area of the solids and bubble (with respect to the axial co-ordinate) are used. These parameters are connected with the area of each ¯uid, diameters and porosity in the following way, dVg ˆ Ae 1ge ; dz dAb 6 ˆ Ab Db dz

dAs ˆ Ae …1 2 1ge †afsvol ; dz

…18†

2.2. Fluid dynamics The ¯uid-dynamic phenomena involved in the process is too complicated to be studied in analytic form. Therefore, equations in the model are experimental correlations from

Remf mg D p rg

…20†

The diameters of the solid particles inside the reactor will decrease due to combustion, gasi®cation, and attrition. Some diameters will be so small that the ¯uid will arrive at the terminal velocity of these particles. The terminal velocity is de®ned as the gas velocity that pushes the particles of a determined diameter out of the reactor. In other words, the drag force will be higher than the weight of those particles. Assuming that the particles are spherical, and using the minimum ¯uidisation Reynolds number Levenspiel [21] proposed the following correlation: ut ˆ

and, dA Qsg ˆ hg±s …Ts 2 Tge † s dz

1693

g…rmc 2 rg †D2p Remf # 0:4 18mg !1=3

ut ˆ

4g2 …rmc 2 rg †2 225mg rg

ut ˆ

3:1g…rmc 2 rg †Dp rg

Dp 500 # Remf $ 200 000 …21† !1=2 Remf $ 200 000

Inside the reactor, there are two ¯uids and phases, so it is very important to know the fraction of the gas phase forming the bubble and the fraction in the emulsion. It is also important to know the average velocity of the gas phase and the porosity involved in the ¯uidisation phenomena, because, as will be explained later, the bubble diameter and velocity depend of these parameters. At the bottom of the reactor, the inlet gas ¯ow is known and MGC considers that the gas in the emulsion at this point has minimum ¯uidisation conditions. In other words, the emulsion gas velocity is obtained using Eq. (20) and the porosity is equal to the minimum ¯uidisation porosity, which is a constant value according to de Souza-Santos [4] and equal to 0.52.

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F. Chejne, J.P. Hernandez / Fuel 81 (2002) 1687±1702

The gas velocity in the emulsion is related to the area and density by: uge ˆ

Fge rge Ae

…22†

The emulsion area fraction (Ae) is a function of the bed expansion coef®cient [4,12], Ae ˆ

fexp ˆ

Ar fexp

To complete the set of ¯uid-dynamic parameters the bubble area fraction and porosity can be obtained with the following relations [4], Ab ˆ A r 2 A e

8 1:032…ug 2 umf †0:57 rga > > > 11 > 0:445 < rp u0:063 mf Dr

for Dr , 0:0635

> > 14:314…ug 2 umf †0:738 D1:006 r0:376 > p p > :11 0:126 0:937 rga umf

for Dr $ 0:0635

…24† Using mass conservation, the ¯ow of the gaseous phase is the sum of the ¯ow of the gas in the emulsion and in the bubble, Fg ˆ Fge 1 Fb

…25†

As mentioned earlier, for the bottom of the reactor, the ¯ow of gas in the emulsion is known equal to the minimum ¯uidisation ¯ow. From Eq. (25), the ¯ow for the bubble can be obtained. From here, the ¯ows in this equation are given from the mass balance equation for each ¯uid, and the ¯ow of the gaseous phase is calculated. The average gas velocity is then calculated as follows: Fg ug ˆ Ar r g

…26†

where the average density of the gasses is Fge rge 1 Fb rb r g ˆ Fg



…32†

1=6:7

1e ˆ 1mf

Ue Umf

1b ˆ 1 2

121 1 2 1e

…33† …34†

2.3. Particle size distribution The MGC model considers a Gaussian distribution for the initial size distribution. Inside the reactor, the shape is conserved but the average diameter changes due to attrition, elutriation, drag, and consumption. The average diameter at the feed point and inside the reactor is calculated as, 1

Dp;M ˆ

nX 21

…35†

Wi Di;ave

where M Wi ˆ X i Mj

…36†

j

Di;ave ˆ …27†

1 2 1e fexp

1ˆ12

…23†

…31†

Di11 1 Di 2

…37†

The bubble diameter and velocity can be calculated from the gas velocity. The bubble results from the difference between the minimum ¯uidisation condition in the emulsion and the ¯ow of the gaseous phase. For the bubble diameter, a perforated plate was considered and the correlation of Mori and Wen [22] is used,   20:3Dz Db ˆ Db;max 2 …Db;max 2 Db;or †exp …28† Dr

At the feeding point the initial diameter and mass of each level in the distribution are given, and with Eq. (36) the mass fraction of each level is found. The model manipulates these three vectors (diameter, mass, and fraction) with the elutriation fraction, and new values are obtained. From these vectors, the diameters and masses are affected by the consumption fraction, while the fractions remain constant. In other words, the mass fraction of each level is not affected by the consumption, but its value will be affected by attrition and drag. The mass fraction of each level in the distribution inside the reactor is obtained by:

where the bubble diameter in the plate (Db,or) and the maximum diameter (Db,max) are de®ned as,

Wi;in ˆ

Db;max ˆ 1:638…Ar …ug 2 umf ††0:4  Db;or ˆ 0:872

Ar …ug 2 umf † Nor

0:4

…29†

ub ˆ ug 2 umf 1 0:711…gDb †

…30†

…38†

where the attrition and drag ¯ows are given by [2,4,24,25]: 0 1 X vol Att;i ˆ G s Mrem …ug 2 umf †fs Wi @ Wj A …39† i±j

Finally, for the bubble velocity, the recommended expression by Davidson and Harrison [12,23] is used, 0:5

…Fmc;i 1 Att;i;sup 2 Att;i;inf 1 Arr;i † Mrem

Arr ˆ

0:5 2:5 …3:07e 2 9†A2r Db r3:5 g g …ug 2 umf † Wi m2:5

…40†

F. Chejne, J.P. Hernandez / Fuel 81 (2002) 1687±1702 Table 3 Reaction rates for the homogeneous (gas±gas) reactions " # yCO2 yH2 R5 (kg m 23 s 21) R5 ˆ K5 yCO yH2 O 2 K5p R6 (kg m 23 s 21)

j k 1:5 R6 ˆ K6 yCO y0:5 O2 rg

R7 (kg m 23 s 21)

R7 ˆ

i K7 h 1:5 yH2 yO2 r2:5 g 1:5 Tg

R8 (kg m 23 s 21)

R8 ˆ

K8 y y r2 Tg CH4 O2 g

R9 (kg m 23 s 21)

R9 ˆ

K9 y y r2 Tg C2 H6 O2 g

1:04 1:9 R10 ˆ K10 y0:86 NH3 yO2 rg

R10 (kg m 23 s 21)

1695

2.4. Chemical reactions At the feeding point a simultaneous and instantaneous devolatilisation and drying processes are presented, for the remaining coal combustion and gasi®cation reactions are considered, in other words reactions with oxygen, stream and carbon dioxide. For devolatilisation and drying the kinetic coef®cients are calculated from the mass balance principle, while for the combustion, gasi®cation and limestone reactions the kinetic coef®cients are function of temperature and composition. For limestone and homogeneous reactions (gas±gas) the kinetic coef®cients were calculated with different expressions from several references. For combustion and gasi®cation reactions, the kinetic coef®cients were obtained with experimental techniques in the Universidad de Antioquia laboratories. Tables 2±4 summarise reactions, reaction rates for the homogeneous reactions, and kinetic coef®cients used in the MGC model. The exposed particle model was chosen for combustion

Table 4 Kinetic coef®cients Reaction 1

2a

2b

5

5

6

7

8

9

10

Equation " k1 ˆ 17:9 exp

213 750 Tp "

k2a ˆ 5:95 £ 1025 exp

#

"

k2b

226 927 ˆ 3:92 exp Tp "

k5 ˆ 2:78 £ 103 exp 2 " k5p ˆ 0:0265 exp

3968 Tg "

k6 ˆ 1:0 £ 1015 exp 2

#

1510 Tg

#

#

16 000 Tg

" k7 ˆ 5:159 £ 1015 exp 2

#

3430 Tg

#

"

k8 ˆ 3:552 £ 10

14

#

213 650 Tp

15 700 exp 2 Tg "

k9 ˆ 3:552 £ 1014 exp 2 " k10 ˆ 9:78 £ 1011 exp 2

15 700 Tg 19 655 Tg

#

#

#

Units

Reference

Pa 21 s 21

2±4

Pa 21 s 21

MGC model

Pa 21 s 21

MGC model

kmol 21 m 3 s 1

2±4

±

2±4

kmol 20.75 m 2.25 K 1.5 s 21

2±4

kmol 21.5 m 4.5 K 1.5 s 21

2±4

kmol 20.9 m 2.7 s 21

2±4

kmol 20.9 m 2.7 s 21

2±4

kmol 21 m 3 s 21 k

2±4

1696

F. Chejne, J.P. Hernandez / Fuel 81 (2002) 1687±1702

and gasi®cation reactions, while for the limestone reaction the unreacted core model was used. The rates include reaction and diffusion resistance. The rates of combustion, gasi®cation and limestone reactions are then calculated as follows: Ri ˆ

2 ri Dp;feed RmT;i

…41†

where i is the type of reaction (combustion, gasi®cation or limestone). The mass resistance for the exposed core are, RmT;i ˆ

1 1 Shi Di;M

Dp =Dp;feed Di;M A2dens;1

Dp M A 21 Dp;feed T;i dens;2

!

…42† while for the unreacted core, RmT;i ˆ

1 2 Dp =Dp;feed 1 1 Dp Shi Di;M D Dp;feed i;M Dp =Dp;feed

1

Dp M A 21 Dp;feed T;i dens;2

Di;M A2dens;1

!

…43†

MT;i ˆ 0:5 Dp

!0:5

A2dens;1

…45†

The consumption factor does not affect the mass fraction of each level in the particle size distribution. This implies that the consumption is assumed equal for all particles. In order to better approximate the consumption, an average rate is calculated as a function of each mass fraction and diameter as follows: 1 Ri;M ˆ X Wj j Ri;ave

…46†

where Ri;ave ˆ

Ri;sup 1 Ri;inf 2

² Generalisations of the Runge±Kutta method, like the Rosenbrock methods or the Kaps±Rentrop method [26,27]. ² Generalisations of the Bulirsch±Stoer method, in particular a semi-implicit extrapolation method due to Bader and Deu¯hard [26,27]. ² Multi-step, Predictor±corrector methods, like Gear's backward differentiation method and the Adams±Bashfoth±Moulton scheme [26,28,29]. Normally, the integral of a function is easy to ®nd because the integrand has a known dependence on the independent variable x, but in an ordinary differential equation the integrand depends both on x and on the dependent variable y. Thus to ®nd the solution of y 0 ˆ f …x; y† from xn to x the following equation has to be solved: Zx y…x† ˆ yn 1 f …x 0 ; y†dx 0 …48† xn

The additional constants in Eqs. (42) and (43) are de®ned as follows: ! rapp Dp Adens;1 ˆ 1 2 …44† ; Adens;2 ˆ coth M rreal Dp;feed T;i Ki

the bed as functions of composition and temperature. Thus, the MGC model deals with a non-linear and stiff set of equations. Stiffness occurs when there are two or more very different scales of an independent variable, which in turns affects the dependent variable. There are several highorder methods for the solution of stiff problems, the most important are:

…47†

3. Numerical method The MGC model includes a total of 29 differential equations with non-constant and non-linear coef®cients. As mentioned earlier, the transport coef®cients, physical properties, reactions rates are calculated at each point of

In a single-step method like Runge±Kutta or Bulirsch± Stoer, the value yn11 at xn11 depends only on yn. In a Multi-step method, f …x; y† is approximated by a polynomial passing through several previous points xn ; xn21 ; ¼ and possibly also through xn11 : The result of evaluating the integral Eq. (48) at x ˆ xn11 is then of the form, yn11 ˆ yn 1 h…b0 y 0n11 1 b1 y 0n 1 b2 y 0n21 1 b3 y 0n22 1 ¼† …49† where y 0 n denotes f …xn ; yn †; and so on. If b0 ˆ 0; the method is explicit; otherwise it is implicit. The order of the method depends on how many previous steps are used to get the new value of y. The MGC model uses the implicit Adams±Moulton method, or backward differentiation formulas: BDF or Gear's method. In both cases, the basic formulas are implicit, so a system of non-linear equations must be solved at each step. Newton's method is used for the iteration scheme. Several matrix±vector operations subroutines from the IMSL [30] were used. 4. Basic description of the algorithm The MGC program was programmed in double precision in FORTRAN 90 language, with three iteration processes. The external iteration concerns the solid temperature, the middle the coal consumption fraction, and the internal the diameter distribution. Fig. 4 shows a schematic diagram of the simulation program.

F. Chejne, J.P. Hernandez / Fuel 81 (2002) 1687±1702

1697

Fig. 4. MGC program diagram.

At ®rst, the solid temperature, coal consumption fraction and the new diameter distribution is given as an initial guess, and the Adams or Gear's method are used in order to obtain the temperatures and composition of the different phases. With equations for the attrition, elutriation and drag, a new diameter distribution is found and compared with the initial guess. When this distribution is equal to the guess, the solid reactions rates are integrated over the bed height, a new coal consumption fraction is obtained and compared with the initial guess. Finally, when the coal consumption fraction iteration process is ®nished, the energy equation of the solid phase is integrated, thus the solid temperature is found and compared with the initial guess. The necessary input data for the MGC program are the following: (a) Coal and limestone particle size distribution data; number of different levels, diameter and weight of each level.

(b) Reactor geometry parameters; i.e. reactor diameter, bed length, wall thickness. (c) Distributor plate type and geometry data; number of holes, hole diameter. (d) Inlet gaseous phase conditions; temperature, composition, moisture. (e) Inlet solid phase conditions; percentages of coal, limestone and inert material, temperature, densities, friability constants. (f) Complete characterisation of the coal; i.e. ®xed carbon, volatile material, moisture, carbon, sulphur, etc. (g) Combustion, gasi®cation (CO2 and H2O) and limestone reaction constants. (h) Numerical data; i.e. number of nodes, tolerances, iterations. 5. Results All the calculations presented in this paper were done on

1698

F. Chejne, J.P. Hernandez / Fuel 81 (2002) 1687±1702

Fig. 5. Fluid-dynamic results as a function of the bed height.

a COMPAQ Deskpro with 500 MHz Pentium II processor, 64MB RAM and 5GB of virtual memory. The convergence criterion for the diameter and the coal consumption fraction was taken as, uxnew 2 xold u # 1026 xold

…50†

while for the temperature, uTnew 2 Told u # 1022 Told

…51†

The typical computer time for a case with 1000 nodes and the above tolerances was 20 min. The number of iterations for the solid temperature and diameters were between 2 and

4, while for the coal consumption fraction were between 5 and 10. In Fig. 5 several ¯uid-dynamic parameters are shown as a function of the bed height. For these results, the feed point was ®xed at 0.3 m. The strong in¯uence of the feed point position can be observed in the results. The gas ¯ow rate increases, due to the combustion and gasi®cation reactions at every point of the bed, but it reaches its maximum at the feed point due to the devolatilisation, drying and limestone reactions. The velocities and porosity increase in the same way. The bubble increases its diameter and at the end, the bubble area is greater than that of the gas in the emulsion. It is important to remark that the emulsion phase reaches a porosity value of 0.9 because the solid material feeding is not enough to raise the participation. The curve of minimum

F. Chejne, J.P. Hernandez / Fuel 81 (2002) 1687±1702

1699

Fig. 6. Temperatures and molar composition as functions of the bed height.

¯uidisation is related to the velocity and Reynolds number required to attain minimum ¯uidisation. The temperature pro®le along the bed does not show any modi®cations within the reactor as it was expected in a ¯uidised bed where the distribution of solid particles is uniform. On the other hand, the temperature of the bubbles and the emulsion are very akin for the conditions with which the computer programme was run. This behaviour is basically due to the heat transfer coef®cients between both parts and the coal particles which are uniformly distributed along the bed. The in¯uence of the feed point is also clear in the left part of Fig. 6, where the gas phase temperatures and composition are shown for both ¯uids (emulsion and bubble). The temperature of both ¯uids at each point of the bed is similar due to the higher convection coef®cients presented in the

¯uidisation conditions. The temperatures drop at the feed point due to the energy necessary for the drying and devolatilisation processes. The gasi®cation process is presented through the bed height but it has a different behaviour after the feed point, where the H2 has a higher molar fraction than the CO, due to devolatilisation. The right part of Fig. 6 shows how the temperature of the gas phase increases in a short distance, due to the convection inside and the large and fast combustion processes, which consumes oxygen a few millimetres beyond the inlet point of gasses. Finally in Fig. 7, the comparison between experimental data, from the Universidad Nacional-Medellin (A. Ocampo et al., 2000. Proyecto COLCIENCIAS CoÂdigo No. 1118-06192-95, BogotaÂ, Colombia), and the MGC model are shown. The input data for the MGC program were changed

1700

F. Chejne, J.P. Hernandez / Fuel 81 (2002) 1687±1702

Fig. 7. Comparison between MGC and experimental data.

according to the conditions of the UN reactor, and the coal characterisation (Tables 5±7) and reaction rates represented the different coals used in the reactor, we also, changed the inlet gas ¯ow rate, temperature, composition; in order to predict the behaviour of the UN reactor. The reaction rates for the coals were obtained with experimental procedures at the laboratories of the Universidad de Antioquia (A. Ocampo et al., 2000. Proyecto COLCIENCIAS CoÂdigo No. 1118-06-192-95, BogotaÂ, Colombia). The pilot gasi®cation plant of ¯uidised coal bed at the Universidad Nacional-MedellõÂn is made of the following parts: The gasi®cation reactor, air compressor, air preheated, a small electric boiler, a feeding system of the mixture coal±lime,a combustion system of propane, an elimination system of particulate material and a chromatograph on line for the analysis of gases.

The ¯uidised bed gasi®cation reactor has an internal diameter of 0.22 m, a total height of 2 m and it has three main modules. The distribution plate is made of a 3 mm thick stainless steel plate with 142 1 mm holes. Six different experiments and numerical results are compared (Table 7), and the results are satisfactory. The dashed lines represent 20% calculation error. It can be observed that most of the results are within the 20% range. The higher differences are presented in the H2 molar composition, due to the fact that the devolatilisation rates were not changed for each coal, due to the dif®culty of ®nding data for Colombian coals. This is a research project at the Universidad Ponti®cia Bolivariana and once the rates are known the MGC model is easy to modify due to the modular form of the program.

F. Chejne, J.P. Hernandez / Fuel 81 (2002) 1687±1702

data thus proving the ef®ciency and accuracy of both the mathematical and numerical model. The presented model is being used recently for designing a new reactor which will produce gases with enough energy for drying bricks in industry.

Table 5 Proximate and elemental analysis of coal TitiribõÂ coal (%) Moisture 2.6 Volatile material 41.8 Fixed coal 54.1 Ash 1.5 Coal density 23 X TitiribõÂ coal: 1250 kg m 23 X Venice coal: 1328 kg m 23 X Lime: 2700 kg m Element TitiribõÂ coal (%) C 75.28 H 5.36 N 1.82 O 15.67 S 0.37

1701

Venice coal (%) 9.3 40.0 44.8 5.9

Acknowledgements In a huge project like the one presented in this paper there are a lot of institutions and people the authors wish to thank. In particular, COLCIENCIAS (Instituto Colombiano para el desarrollo de la Ciencia y Tecnologia Francisco Jose Caldas), MINERCOL (Minerales de Colombia), Universidad Ponti®cia Bolivariana, Universidad Nacional-MedellõÂn and Universidad de Antioquia for their logistic and economic support. Alonso Ocampo, Erika Arenas, John Jairo Ramirez, Jorge Espinel, Carlos LondonÄo, Leonardo Velasquez and J. Fredy Escobar who helped with the experiments at the UN reactor, to Fannor Mondragon for the reaction rate constants and to Marcio L. Sousa-Santos for technical support. The author apologise, if due to size of the project, someone is missed in the list of acknowledgements.

Venice coal (%) 64.95 5.33 1.95 21.46 0.41

6. Conclusions We have developed a gasi®cation model using the basic conservation equations in compact form in order to obtain an adequate and accurate numerical solution. The numerical results presented here agree very well with the experimental Table 6 Particle size distribution Grid

Diameter (mm)

14 16 20 25 30 50 Collector

1.412 1.180 0.850 0.710 0.595 0.295 ±

Average particle diameter (mm)

Differential analysis (%) TitiribõÂ coal

Venice coal

Lime

1.08 28.53 12.70 28.18 10.90 17.57 1.04

1.82 33.36 12.83 27.95 10.43 13.30 0.31

0.02 0.08 31.76 22.97 41.59 2.40 1.17

0.62

0.68

0.64

Table 7 Operation conditions and results Exp. N 0 21

Coal feed (kg h ) Air supply (kg h 21) Lime feed (kg h 21) Steam supply (kg h 21) Air and steam temperature at entrance (8C) Temperature of reactor (8C) H2 (%) CO2 (%) N2 (%) CH4 (%) CO (%)

1

2

3

4

5

6

8.0 21.9 0.8 4.6 420

8.0 17.0 0.8 4.6 413

8.0 19.4 0.8 4.6 422

8.0 21.9 0.8 4.6 435

8.0 28.4 0.8 4.6 368

6.6 14.8 0.66 4.0 336

855 8.53 19.31 60.37 0.84 10.94

812 8.84 18.38 61.10 1.07 10.59

841 9.63 14.40 64.62 1.34 9.97

866 7.88 15.60 64.52 1.01 10.94

826 6.48 14.86 71.54 1.29 5.80

829 10.80 21.59 56.60 0.86 10.14

1702

F. Chejne, J.P. Hernandez / Fuel 81 (2002) 1687±1702

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