CHEMICAL_REACTION_MODEL

Type

AcuSolve Command

Syntax

CHEMICAL_REACTION_MODEL("name") {parameters...}

Qualifier

Parameters

reaction_type (enumerated) [=homogeneous]

Type of the chemical reaction model.

homogeneous

Use when all reacting materials are gaseous.

heterogeneous

Use when both solid and gaseous materials are reacting.

homogeneous_model_type (enumerated) [=none]

Type of the chemical reaction model.

none

No homogeneous model.

finite_rate

The exponential temperature-dependent Arrhenius equation is used to determine the rate of reaction. For reaction:

$${{\displaystyle \sum }}_{i=0}^n{r}_i{R}_i\to {{\displaystyle \sum }}_{i=0}^m{p}_i{P}_i$$

The rate of reaction is expressed as $k=A T^{\beta }{e}^{\left(-E/RT\right)}$ , where A is the pre-exponential factor and E is the activation energy. R and T are the universal gas constant and temperature, respectively. The rate of consumption and production of fields can be described as:

$$\frac{1}{r_i}\frac{d\left[R_i\right]}{dt}=-\frac{1}{p_i}\frac{d\left[P_i\right]}{dt}= k {\Pi }_{i=0}^{n}k{\left[R_i\right]}^{a_i}$$

$\left[R_i\right]$ and $\left[P_i\right]$ represent the concentrations ( $\text{mole}/m^3$ ) of the reactant and products fields. The unit of the A is (${\left(\text{mole}/m^3\right)}^{1-{{\displaystyle \sum }}_{i=0}^n{a}_{i }})/\text{sec}$ .

eddy_dissipation

The Eddy Dissipation model is used to calculate the rate of reaction. In this model the rate of reaction is a function of the turbulent time scale. A two-equation turbulence model is needed for this approach. The chemical reaction time scale for different turbulent models can be expressed as: $\frac{ϵ}{k}$ or $\omega$ .

The rate of reaction for this model is calculated as:

$$k=\rho \frac{ϵ}{k} \text{Min}\left(A\frac{Y\left(R_i\right)}{M{W}_i}, AB\frac{{{\displaystyle \sum }}_{i=0}^{n}Y\left(P_i\right) }{{{\displaystyle \sum }}_{i=0}^{n}M{W}_i }\right)$$

Here, A and B are model constants, Y and MW are the mass fraction and the molecular weights, respectively. The rate of consumption and production of fields is determined:

$$\frac{1}{r_i}\frac{d\left[R_i\right]}{dt}=-\frac{1}{p_i}\frac{d\left[P_i\right]}{dt}= k$$

finite_rate_eddy_dissipation

The rate of reaction is calculated using the finite_rate approach but the maximum value is constrained by the eddy_dissipation model.

heterogeneous_model_type (enumerated) [=none]

Type of the chemical reaction model.

none

No heterogeneous model.

surface_reaction

In this model, the gas surrounding the solid reacts on the solid’s surface. While new gas is produced, the internal composition of solid remains unchanged. For example, the surface reaction of solid S and gaseous reactant R to produce gaseous product P can be represented as:

$$\text{S}+\text{Rgas }\to \text{Pgas}$$

The combined effects of chemical kinetics and diffusion are used to determine the rate of reaction:

$$k=S_s{P}_{Rgas}{\left(\frac{1}{\text{kin}}+\frac{1}{\text{dif}}\right)}^{-1}$$

where S is the surface area of solid and P is the partial pressure of reactant R. kin and dif are modeled as:

$$\text{kin}=A T_s{}^{\beta }{e}^{\left(-E/R{T}_s\right)}$$

$$\text{dif}=\frac{Dc}{d}\left((T_s+T_g\right)/2{)}^{0.75}$$

here Dc and d are the mass diffusion rate coefficient and solid particle diameters, respectively.

pyrolysis_reaction

In this model, solid particles undergo internal decomposition at high temperatures without the need for surrounding gases. It is assumed that the solid has two initial compositions: one part remains unchanged, while the other part is released as gas during the reaction. For example, in coal particles, volatile matters are released, leaving behind charcoal. To model this, the first order reaction is used as:

$$\frac{dm}{dt}=-m A T^{\beta }{e}^{\left(-E/RT\right)}$$

shrinking_core

In this model, solid particles undergo both surface and core reactions. The gas surrounding the particle reacts with it, changing the internal composition of the solid and potentially producing new gas. The combined effect of gas diffusion through the particle’s film layer, gas diffusion through the ash layer on the particle surface, and chemical kinetics are modeled. During the reaction, the particle will have a core with radius Rc, and an ash layer on top of the core with a radius equal to the particle radius Rp. The gas layer is on top of the ash layer. As an example, the shrinking core reaction of solid S1 and gaseous reactant R to produce solid S2 and gaseous product P can be represented as:

$$\text{S}1+\text{Rgas }\to \text{S}2+\text{Pgas}$$

Gas diffusion in the particle film layer is modeled as:

$$\text{dif}=S_s\left[\text{Rgas}\right]0.00225e^{\left(-14700/82.06T_s\right)}$$

$$\text{ash}=S_s\left[\text{Rgas}\right]\frac{ {ϵ}_{s}D}{{\tau }_s}\frac{1}{\left(1/Rc-1/\text{Rp }\right)}$$

where D, ${ϵ}_s$ and ${\tau }_s$ are gas diffusion coefficient, porosity and the tortuosity of the particles. $S_s$ and $\left[\text{Rgas}\right]$ are particle surface area and reactant concentration, respectively. Chemical kinetics in the core are modeled as:

$$\text{kin}=\left[S1\right]A{e}^{\left(-E/R{T}_s\right)}$$

where A and E are the pre-exponential and the activation energy, respectively.

reactant_fields (list) [={}]

Names of the reacting fields for homogeneous and heterogeneous reactions. reactant_fields will lead to the production of product_fields.

product_fields (list) [={}]

Names of the production fields for homogeneous and heterogeneous reactions. reactant_fields lead to the production of product_fields.

reactant_stoichiometric_numbers (array) [={}]

Stoichiometric numbers of the reactants. In the general form of the reaction mentioned in finite_rate model, reactant_stoichiometric_numbers will be $r_i$ values. The dimension of the array should match the number of reactant fields and the values should be provided in the same order as the reactant_fields.

product_stoichiometric_numbers (array) [={}]

Stoichiometric numbers of the product fields. In the general form of the reaction mentioned in finite_rate model, product_stoichiometric_numbers will be $p_i$ values. The dimension of the array should be equal to the number of product fields and the values should be provided in the same order as product_fields.

reactant_rate_exponents (array) [={}]

Exponents of the reactant fields in finite_rate reaction. In the general form of reaction mentioned in finite_rate model, reactant_rate_exponents will be $a_i$ values. The dimension of the array should match the number of reactant fields and values should be provided in the same order as reactant_fields. Used when reaction_type = homogeneous.

solid_reactant_fractions (array) [={}]

Initial mass fraction of the solid field within the reacting particle. If the particle composition is uniform, this value should be set to 1. For coal particles, this can be used to set initial mass fraction of volatile and solid coal. For coke and ore particles, the values can be set to 1. The dimension of the array should match the number of reactant fields and values should be provided in the same order as reactant_fields. Gaseous field values should be set to 0. Used when reaction_type = heterogeneous.

pre_exponential_factor (real) [=0.0]

The pre-exponential factor in the Arrhenius equation. Used when reaction_type = homogeneous or heterogenous and used with finite_rate or finite_rate_eddy_dissipation.

pre_exponential_temperature_exponent (real) [=0.0]

The pre-exponential factor temperature exponent in the Arrhenius equation. Used when reaction_type = homogeneous or heterogenous and used with finite_rate or finite_rate_eddy_dissipation.

activation_energy (real) [=0.0]

The activation energy in the Arrhenius equation. Used when reaction_type = homogeneous and used with finite_rate or finite_rate_eddy_dissipation.

include_reverse_reaction (boolean) [=off]

Flag specifying whether to calculate the reverse reaction for the given forward reaction. Used when reaction_type = homogeneous and used with finite_rate.

reverse_reactant_rate_exponents (list) [={}]

List of reverse_reactant_rate exponents. Used when reaction_type = homogeneous and used with finite_rate or finite_rate_eddy_dissipation.

reverse_pre_exponential_factor (real) [=0.0]

The pre-exponential factor in the Arrhenius equation for the reverse reaction. Use when include_reverse_reaction = on. Used when reaction_type = homogeneous and used with finite_rate or finite_rate_eddy_dissipation.

reverse_pre_exponential_factor_temperature_exponent (real) [=0.0]

The pre-exponential factor temperature exponent in the Arrhenius equation for the reverse reaction. Use when include_reverse_reaction = on. Used when reaction_type = homogeneous and used with finite_rate or finite_rate_eddy_dissipation.

reverse_activation_energy (real) [=0.0]

The activation energy in the Arrhenius equation for the reverse reaction. Use when include_reverse_reaction = on. Used when reaction_type = homogeneous and used with finite_rate or finite_rate_eddy_dissipation.

mass_diffusion_rate_coefficient (real) [= 5.0e-12]

Mass diffusion rate coefficient in the surface reaction. Used with surface-reaction diffusion model. Used when reaction_type = heterogeneous.

reacting_particle_porosity (real) [=0.5 ]

Reacting particle porosity value. Used with shrinking_core gas film layer diffusion model. Used when reaction_type = heterogeneous and used with heterogeneous_model_type = shrinking_core.

reacting_particle_tortuosity (real) [=2.0]

Reacting particle tortuosity value. Used with shrinking_core gas film layer diffusion model. Used when reaction_type = heterogeneous and used with heterogeneous_model_type = shrinking_core.

solid_reaction_heat_rate_type (enumerated) [=formation]

Type of the heat release rate calculation for solid particles. Used when reaction_type = heterogeneous.

formation

If selected, heat rate will be calculated using the enthalpy of formation of the reactant and product fields.

isothermal

Reaction heat will be ignored.

polynomial

Temperature dependent polynomial correlation will be used to calculate heat of reaction. Δ $H={{\displaystyle \sum }}_{i=0}^m{c}_i{T}^i$

Coefficients of the polynomial should be provided by solid_reaction_heat_rate_coefficients.

solid_reaction_heat_rate_coefficients (array) [={}]

Polynomial coefficients to be used when solid_reaction_heat_rate_type = polynomial.

eddy_disspation_coefficient_A (real) [=4.0]

Coefficient A to be used when the homogeneous reaction is set to eddy_dissipation.

eddy_disspation_coefficient_B (real) [=4.0]

Coefficient B to be used when the homogeneous reaction is set to eddy_dissipation.

finite_rate_eddy_disspation_coefficient (real) [=4.0]

Coefficient to be used in the eddy dissipation part when the homogeneous reaction is set to finite_rate_eddy_dissipation.

Description

EQUATION {
    flow = navier_stokes
    temperature = advective_diffusive
    multi_field = euler
    edem_coupling = on
    fields = { "Particle", "CO", "CO2" }
    absolute_temperature_offset = 0.0
    gravitational_acceleration = { 0.0, 0.0, -9.81; }
}

MATERIAL_MODEL(  "CO2" ) {
    type = "fluid"
    density_model = "CO2"
    specific_heat_model = "CO2"
    conductivity_model = "CO2"
    viscosity_model = "CO2"
    gas_kinetic_model = "CO2"
}

DENSITY_MODEL(  "CO2" ) {
    type = ideal_gas
    gas_constant = 287.058
    isothermal_compressibility = 0.0
}

SPECIFIC_HEAT_MODEL( "CO2" ) {
     type = piecewise_polynomial_enthalpy
     piecewise_polynomial_variable = temperature
     piecewise_polynomial_values = {
                                                    +2.98000000E02, +1.00000000E03,
                                                    -4.83731400E04*188.922273259,
                                                    +2.27572400E00/1*188.922273259,
                                                    +9.92207200E-03/2*188.922273259,
                                                    -1.04091130E-05/3*188.922273259,
                                                    +6.86668600E-09/4*188.922273259,
                                                    -2.11728000E-12/5*188.922273259 ;
                                                    +1.00000000E03, +5.00000000E03,
                                                    -4.89669600E04*188.922273259,
                                                    +4.45362300E00/1*188.922273259,
                                                    +3.14016800E-03/2*188.922273259,
                                                    -1.27841050E-06/3*188.922273259,
                                                    +2.39399600E-10/4*188.922273259,
                                                    -1.66903330E-14/5*188.922273259 }
}
CONDUCTIVITY_MODEL(  "CO2" ) {
    type = gas_kinetic
}
VISCOSITY_MODEL(  "CO2" ) {
    type = gas_kinetic
}

GAS_KINETIC_MODEL(  "CO2" ) {
    geometrical_configuration_index = 1
    molecular_weight = 0.044
    Lennard_Jones_potential_well_depth = 244.00
    Lennard_Jones_collision_diameter = 3.763
    dipole_moment = 0.0
    polarizability = 2.650
    rotational_relaxation_collision_number = 2.1
    enthalpy_of_formation = -393546.0
}

MATERIAL_MODEL(  "CO" ) {
    type = "fluid"
    density_model = "CO"
    specific_heat_model = "CO"
    conductivity_model = "CO"
    viscosity_model = "CO"
    gas_kinetic_model = "CO"
}


DENSITY_MODEL(  "CO" ) {
    type = ideal_gas
    gas_constant = 287.058
    isothermal_compressibility = 0.0
}

SPECIFIC_HEAT_MODEL( "CO" ) {
     type = piecewise_polynomial_enthalpy
     piecewise_polynomial_variable = temperature
     piecewise_polynomial_values = {
                                                    +2.98000000E02, +1.00000000E03,
                                                    -1.43105390E04*296.833150367,
                                                    +3.26245100E00/1*296.833150367,
                                                    +1.51194090E-03/2*296.833150367,
                                                    -3.88175500E-06/3*296.833150367,
                                                    +5.58194400E-09/4*296.833150367,
                                                    -2.47495100E-12/5*296.833150367 ;
                                                    +1.00000000E03, +5.00000000E03,
                                                    -1.42683500E04*296.833150367,
                                                    +3.02507800E00/1*296.833150367,
                                                    +1.44268850E-03/2*296.833150367,
                                                    -5.63082700E-07/3*296.833150367,
                                                    +1.01858130E-10/4*296.833150367,
                                                    -6.91095100E-15/5*296.833150367 }
}
CONDUCTIVITY_MODEL(  "CO" ) {
    type = gas_kinetic
}

VISCOSITY_MODEL(  "CO" ) {
    type = gas_kinetic
}


GAS_KINETIC_MODEL(  "CO" ) {
    geometrical_configuration_index = 1
    molecular_weight = 0.028
    Lennard_Jones_potential_well_depth = 244.00
    Lennard_Jones_collision_diameter = 3.763
    dipole_moment = 0.0
    polarizability = 2.650
    rotational_relaxation_collision_number = 2.1
    enthalpy_of_formation = -110500.00
}

MATERIAL_MODEL( "Coke" ) {
    Type = "solid"
    density_model = "Coke"
    specific_heat_model = "Coke"
    conductivity_model = "Coke"
    gas_kinetic_model = "Coke"
}

DENSITY_MODEL( "Coke" ) {
    type = constant
    density = 920 
    isothermal_compressibility = 0      
}

SPECIFIC_HEAT_MODEL( "Coke" ) {
    type = constant
    specific_heat = 1380      
    latent_heat_type = none
}

CONDUCTIVITY_MODEL( "Coke" ) {
    type = constant
    conductivity = 237      
    turbulent_prandtl_number = 0.91
}

GAS_KINETIC_MODEL(  "Coke" ) {
    molecular_weight = 2.378
}

FIELD( "Particle" ) {
    material_model = "Coke"
}
FIELD( "Coke" ) {
    material_model = "Coke"
}
FIELD(  "CO2" ) {
    material_model = "CO2" 
}

CHEMICAL_REACTION_MODEL( "Coke-CO2" ) {
    reaction_type = heterogeneous
    heterogeneous_model_type = surface_reaction
    edem_reacting_particle = "Coke"
    reactant_fields = { "Coke", "CO2" }
    reactant_stoichiometric_numbers = { 1.0, 1.0 }
    solid_reactant_fractions = { 1.0, 0.0 }
    product_fields = { "CO" }
    product_stoichiometric_numbers = { 2.0 }
    pre_exponential_factor = 242 
    activation_energy = 8.314*2.84e4 ;
}
FIELD_INTERACTION_MODEL(  "Interaction_Mixture" ) {
    type = euler
    dispersed_field = "Particle"
    carrier_field = "CO2"
    drag_model = Gidaspow
    fields = { "CO", "CO2" }
    turbulent_schmidt_number = 0.85
    diffusion_matrix_type = gas_kinetic
    chemical_reaction_models = { "Coke-CO2" }
    edem_multi_species_carrier = on
}