TITLE : MODELLING of COAL GASIFICATION

BY : Dr S V Zhubrin, CHAM Ltd

DATE : March 2002

FOR : Demonstration case for CHAM-Japan

INTRODUCTION

The case presents the implementation in PHOENICS of an IPSA based model for non-equilibrium two-phase reactive flow of coal particles particles finely dispersed in the carrying air-steam stream. The model uses the Eulerian description of the two interpenetrating continua with the transfer of heat, mass and momentum between them. The processes accounted for are the volatilisation of dispersed phase material, gaseous exothermic oxidation of volatile products, heterogeneuos oxidation of particle char, steam reforming, shift conversion and carbon monoxide reduction.

The devolatilisation of particulate phase is considered as kinetically driven. Turbulent oxidation of volatiles is modelled via two-step reaction of hydrocarbon oxidation, in which carbon monoxide is an intermediate product. The reaction rates are considered as a blend of EBU model and Arrhenius kinetics. The char oxidation is represented by blended mechanism of the oxygen diffusion to the particle and chemical kinetic. The relative amount of char oxidation products are assumed to be dependent on the particle temperature. The reaction rates of steam reforming, shift conversion and carbon monoxide reduction are represented through exemplary EBU/Arrhenius-kinetics blends.

The turbulence is accounted for by conventional K-e model.

The model is applied to the pulverized coal gasification in a wall-fed pressurized reaction chamber.

MODELLING CONSIDERATIONS

Conservation equations

The independent variables of the problem are the three components of cartesian coordinate system.

The main dependent (solved for) variables are:

• Three velocity components of gas flow, U1,V1 and W1
• Three velocity components of particulate flow, U2, V2 and W2
• Pressure, P1.
• Volume fractions of gas and particulate phases, R1 and R2
• "Shadow" volume fraction, RS
• Kinetic energy of gas turbulence, KE, and
• its dissipation rate, EP
• Specific gas enthalpy, H1
• Specific particle enthalpy, H2
• Mass fraction of hydrogen, YH2.
• Mass fraction of oxygen, YO2.
• Mass fraction of volatiles, YCH4
• Mass fraction of carbon monoxide, YCO
• Mass fraction of carbon dioxide, YCO2
• Mass fraction of water vapour, YH2O
• Mass fraction of raw coal, COL2
• Mass fraction of char, CHA2

• Interphase mass transfer, CMDOT
• Densities of gas, RHO1, and particles, RHO2
• Specific heats of gas, CP1, and particles, CP2
• Temperatures of gas, T1, and particles, T2
• Mass fractions of nitrogen, YN2
• Mass fractions of ash, ASH2
• Particle diameter, SIZE
• Particle Reynolds number, REYN
• Volumetric interphase heat transfer coefficient, HCOF

Main features of the model

For the second, particulate, phase, raw coal, COL2, is consumed during devolatilisation, and char, CHA2, solid, combustible residue of volatilisation, appears as COL2 disappears. The char then disappears as it burnt in the char oxidation. The ash contents of the phase, ASH2, increase to value 1 in a completely reacted particles.

For the first, gas, phase volatile fuel, YCH4, appears as a consequence of volatilisation and carbon monoxide reduction, and then disappears as it oxidized in gas-phase reaction with oxygen and consumed in steam reforming. The water steam along with its vapour, YH2O, appear as a consequence of external supply and volatile oxidation, and then are consumed in steam reforming and shift conversion producing hydrogen, YH2, carbon monoxide, YCO, and carbon dioxide, YCO2. The hydrogen can also dissapear through carbon dioxide reduction releasing methane, YCH4, and water vapour. The carbon monoxide and dioxides are also the products of char and volatile oxidations. The oxygen contents, YO2, decrease as it is consumed in both latter reactions.

Volatilisation mechanism

The volatilisation of solid-fuel, raw coal, particles, is presumed to follow the one-step irreversible reaction type mechanism:

1 Kg Coal = Y_VKg Volatiles + ( 1 - Y_V ) Kg Char

where Y_V stands for the mass fraction of volatiles in coal which is coal-rank dependent and is, normally, the user specified input.

As a consequence, the rate of coal consumption, R_coal, in kg m^-3s^-1, is readily related to the rate of volatiles released through associated stoichiometric coefficient as follows:

R_coal = R_V/Y_V

where R_V is mass source of volatiles originating from the coal particles into the gas phase, kg m^-3s^-1.

The rate of char formation, R_char, in kg m^-3s^-1, is also calculated through the volatilisation rate as:

R_char = ( 1 - Y_V )R_V/Y_V

Devolatilisation kinetics

Volatilisation kinetics are coal-rank dependent. The volatilisation rate is modelled through an Arrhenius-type expression:

R_V = 2.10³e^-2829/T2m_V2M_VPV

Here

• m_V2 is the mass fraction of remaining volatiles in particulate phase and
  
• M_VPV is volumetric mass of volatiles, kg/m³

m_V2 = Y_VCOL2

The mass of voilatiles per unit of reaction volume is given as:

M_VPV = RHO2 Y_VR2

Volatiles oxidation (combustion)

The volatiles are taken as 100% methane. Combustion of the volatiles is treated as a two-step irreversible chemical reaction of methane oxidation as follows:

Step 1: CH₄ + 1.5 ( O₂ + 3.76N₂) = CO + 2H₂O + 5.64N₂

Step 2: CO + 0.5( O₂ + 3.76N₂ ) = CO₂ + 1.88N₂

The reaction rates of combustion are obtained as the harmonic blend of a Arrhenius kinetics and eddy-dissipation rates:

R^com_CH4 = - [ ( R^k_CH4)^-1 + (R^e_CH4 )^-1 ]^-1 and

R^com_CO = - [ ( R^k_CO )^-1 + ( R^e_CO )^-1 ]^-1

where R^k and R^e, in kg/m³s, are the kinetic and eddy-dissipation rates:

R^e_CH4 = 4 RHO1 EP/KE min( YCH4, YO2/3)
R^e_CO = 4 RHO1 EP/KE min( YCO, YO2/0.57)
R^k_CH4 = 1.15 10⁹RHO1²e^-24444/T YCH4^-0.3YO2^1.3
R^k_CO = 5.42 10⁹RHO1²e^-15152/T YO2^0.25YH2O^0.5YCO

The remaining rates are defined through associated stoichiometric coefficients:

Step 1:
R¹_O2 = 3 R^com_CH4
R¹_CO = -1.75 R^com_CH4
R¹_H2O = -2.25 R^com_CH4

Step 2:
R²_O2 = 0.57 R^com_CO
R²_CO2 = -1.57 R^com_CO

The net rates of species generation in volatile combustion are the balances of formation and combustion as appropriate:

R_V,CH4 = R^com_CH4
R_V,CO = R^com_CO + R¹_CO
R_V,O2 = R¹_O2 + R²_O2
R_V,CO2 = R²_CO2
R_V,H2O = R¹_H2O

Combustion of char

The particle char burns creating carbon oxides according to the reaction:

C + 0.5(1 + w) O₂ = ( 1 - w)CO + wCO₂

where w is the mole fraction of carbon oxides formed as CO₂ which is related to the mass fractions as follows:

w = M_COYCO2/( M_COYCO2 + M_CO2YCO )

where M_CO = 28 and M_CO2 =44, are the molecular masses of carbon monoxide and carbon dioxide, respectively.

The mass split between carbon oxides is assumed to depend on the particle temperature as:

YCO/YCO2 = 2500e^-6249/T2

The char burnout rate, R_C, in kg m^-3s^-1, is obtained as an harmonic blend of a kinetic- and diffusion-controlled mass-transfer rates:

R_C = A_p [ ( K^k_C)^-1 + (K^d_C )^-1 ]^-1P_O2

where

A_p = 6R2/SIZE, is volumetric particle surface area, 1/m, and P_O2 is partial pressure of O₂, N/m².

The partial pressure P_O2 is calculated using Dalton's law:

P_O2 = x_O2P1

Wherein, the mole fraction of O₂, x_O2, is related to mass fraction, YO2, through molecular masses of O₂, M_O2, and the mixture, M_mix, as

x_O2 = M_mix/M_O2YO2

Kinetic mass transfer coefficient, K^k_C, in s/m, is calculated as:

K^k_C = 0.1309 e^-26850/T2

Diffusion mass transfer coefficient, K^d_C, in s/m, is calculated as follows:

K^d_C = Sh D_O2M_C/ ( R_gasT₂SIZE )

where

• Sh is a particle Sherwood Number ;
  
• D_O2 is the diffusion coefficient of O₂ in air, m₂/s ;
  
• M_C = 12, is the molecular mass of C, kg/mol ;
  
• R_gas = 8314, is universal gas constant, J mol^-1K^-1 ; and
  
• T₂ is particle temperature, K.

R_C,O2 = - 0.5(1 + w) M_O2/M_C

The rate of CO produced by char combustion, in kg m^-3s^-1, is related to R_C through its own stoichiometric coefficient:

R_C,CO = (1 - w) M_CO/M_C

The rate of CO₂ produced by char combustion, in kg m^-3s^-1, is related to R_C through the stoichiometry as follows:

R_C,CO2 = wM_CO2/M_C

Carbon monoxide emerging from char further burns to carbon dioxide in the gas phase as a participant of the second step of volatile combustion.

Steam reforming reaction

The volatile methane reacts with water vapour creating carbon monoxide and hydrogen according to the reaction:

CH₄ + H₂O = CO + 3H₂

The reaction rates are obtained, in exemplary manner, as the minimum blend of an Arrhenius kinetics and eddy-dissipation rates:

R^ref_CH4 = - min( R^k_ref, R^e_ref) and

where R^k and R^e, in kg/m³s, are the kinetic and eddy-dissipation rates:

R^e_ref = 4 RHO1 EP/KE min( YCH4, 16/18.YH2O)
R^k_ref = 3.21 10²RHO1e^-468/T YH2O^1.3YCH4

The net rates of species generation in steam reforming are as follows:

R_SR,CH4 =R^ref_CH4
R_SR,H2O = 18/16.R_SR,CH4
R_SR,CO = -28/16.R_SR,CH4
R_SR,H2 = -6/16.R_SR,CH4

Shift conversion reaction

The carbon monoxide reacts with water vapour creating carbon dioxide and hydrogen according to the reaction:

CO + H₂O = CO₂ + H₂

The reaction rates are obtained, in exemplary manner, as the minimum blend of an Arrhenius kinetics and eddy-dissipation rates:

R^con_CO = - min( R^k_con, R^e_con) and

where R^k and R^e, in kg/m³s, are the kinetic and eddy-dissipation rates:

R^e_con = 4 RHO1 EP/KE min( YCO, 28/18.YH2O)
R^k_con = 3.21 10²RHO1e^-468/T YH2O^1.3YCO

The net rates of species generation in steam reforming are as follows:

R_SC,CO = R^con_CO
R_SC,H2O = 18/28.R_SC,CO
R_SC,CO2 = -44/28.R_SC,CO
R_SC,H2 = -2/28.R_SC,CO

Carbon monoxide reduction reaction

The carbon monoxide reacts with hydrogen creating methane and water vapour according to the reaction:

CO + 3H₂ = CH₄ + H₂O

The reaction rates are obtained, in exemplary manner, as the minimum blend of an Arrhenius kinetics and eddy-dissipation rates:

R^red_CO = - min( R^k_red, R^e_red) and

where R^k and R^e, in kg/m³s, are the kinetic and eddy-dissipation rates:

R^e_red = 4 RHO1 EP/KE min( YCO, 28/6.YH2O)
R^k_red = 3.21 10²RHO1e^-468/T YH2^1.3YCO

The net rates of species generation in steam reforming are as follows:

R_CR,CO = R^red_CO
R_CR,H2 = 6/28.R_CR,CO
R_CR,CH4 = -16/28.R_CR,CO
R_CR,H2O = -18/28.R_CR,CO

COMPUTATIONAL DETAILS

Model sources

Only the compilation of the model sources which required non-standard settings is provided below.

Interphase mass transfer, kg/s

CMDOT = V_cell( R_V + R_C )

Wherein V_cell is a cell volume, m³

2nd phase composition, kg m^-3s^-1

• Char: S_CHA2 = R_char - R_C
• Coal: S_COL2 = - R_coal

1st phase composition, kg m^-3s^-1

• Methane fuel: S_YCH4 = R_V + R_V,CH4 + R_CR,CH4 + R_CR,CH4
• Carbon dioxide: S_YCO2 = R_V,CO2 + R_C,CO2 + R_SC,CO2
• Carbon monoxide: S_YCO = R_V,CO + R_C,CO + R_SR,CO + R_SC,CO + R_CR,CO
• Oxygen: S_YO2 = R_V,O2 + R_C,O2
• Water vapour: S_YH2O = R_V,H2O + R_SR,H2O + R_SC,H2O + R_CR,H2O
• Hydrogen: S_YH2 = R_SR,H2 + R_SC,H2 + R_CR,H2

1st phase energy, W m^-3

The reaction heats, i.e. the heats of combustions for volatile methane, H°_CH4, carbon monoxide, H°_CO, and char, H°_C, are released with the rates of their consumptions.

The steam reforming is supposed to be endothermic reaction with the reaction heat H°_SR. The heats of the reactions for shift conversion and carbon monoxide reduction are taken as H°_SC and H°_CR.

The heat is also transfered from the 2nd phase via interphase heat transfer.

In terms of the transport equation for H1, the resulting source term is:

S_H1 = S_H1,rea + S_H1,int

The contribution from the heats of reactions is:

S_H1,rea = R^com_CH4H°_CH4 + R^com_COH°_CO + R_CH°_C + R^ref_CH4H°_SR + R^con_COH°_SC + R^red_COH°_CR

The interphase heat transfer contribution is:

S_H1,int = HCOF( T₂ - T₁ )

2nd phase energy, W m^-3

The source term for 2nd phase specific enthalpy, H2, is caculated as:

S_H2 = S_H2,int

where

S_H2,int = HCOF( T₁ - T₂ )

Temperature calculations

The specific enthalpies are related to the phase temperatures and specific heats:

H1 = C_P,1T₁ and
H2 = C_P,2T₂

Densities, specific- and reaction-heats

The solid-phase density is taken as constant, as the ideal gas law is used for the gas phase as follows:

RHO1 = M_mixR^-1_gasT₁^-1P1

where the molecular mass of the mixture is composition-dependent:

M^-1_mix = YCH4/16+YO2/32+YN2/28+YCO/18+YCO2/44+YH2O/18+YH2/2

The solid-phase specific heats are taken as constant, and the gas-phase specific heat, C_P,1, is assumed to be equal for all gas components and is a linear function of gas temperature and the operating pressure as follows:

C_P,1 = (1059 + 0.25( T₁ - 300 )) (1.+ 0.005(P1/P_o-1)

wherein P_o stands for the datum pressure.

The combustion heats of volatiles and carbon monoxide, reaction heats for steam reforming, shift conversion and CO reduction are taken as constants. The heat of combustion for char is assumed to depend on the product split ratio:

H°_C = wH°_C2CO2 + (1 - w)H°_C2CO

where H°_C2CO2 and H°_C2CO are the heats of carbon oxidation to CO₂ and CO, J/kgC, respectively.

Interphase heat transfer

Interphase particle heat transfer is represented by a sphere-law correlation:

NUSS = 2. +0.65 REYN^0.5

Volumetric heat transfer coefficient, HCOF, in W m^-3 K^-1, is then evaluated as:

HCOF = A_pk_gasSIZE^-1NUSS

where, k_gas is gas heat conductivity taken as constant.

CASE STUDY

Geometry

The pressurised reaction chamber chosen for the present computations, idealised though, retains some features of real-life industrial equipment: twenty four coal-supply openings are located at the lower part on the chamber front wall; steam/air-pulverised coal particles are injected axially into the chamber; reaction products flow towards the outlet at the upper part of the chamber.

The chamber is symmetrical, and only half of it is simulated and represented.

Boundary conditions

At all inlets, values are given of all dependent variables together with the prescribed flow rates.

At the outlet, the fixed exit pressure is set equal to zero and the computed pressures are relative to this pressure.

At the walls, the condition of zero flux is assumed for all dependent variables.

THE IMPLEMENTATION NOTES

The problem setting-up has been made via VR-menu.

The model sources are coded in GROUND.FOR. They are activated via PATCH/COVAL commands in Q1 file.

In-Form has been used for the specification of the properties, RHO1 and CP1, calculations of chemical rection rates and related auxiliary variables.

The specific-to-model user inputs are:

• RHO2A - mass fraction of volatiles in coal
• TMP1A - heat of volatile combustion, J/kgCH4
• TMP1B - heat of CO combustion, J/kgCO
• TMP2A - heat of carbon oxidation to CO, J/kgC
• TMP2B - heat of carbon oxidation to CO2, J/kgC
• CMDTA - heat of steam reforming, J/kgCH4
• CMDTB - heat of shift conversion,J/kgCO
• CMDTC - heat of CO reduction,J/kgCO