Particle Reactions

Particle Chemistry

Particle Devolatilization

Devolatilization is a gasification process where a solid is converted to volatile matter and a residue.

For each devolatilization reaction, multiple solid components can be chosen as reactants. Any number of products can be chosen as long as there is at least one solid or one fluid-phase product in each reaction. The most general representation of a devolatilization reaction is:

$${A1}_{\left(s\right)}+\mathrm{...}+{An}_{\left(s\right)}\to {B1}_{\left(g\right)}+\dots +{Bn}_{\left(g\right)}+{C1}_{\left(s\right)}+\dots +{Cn}_{\left(s\right)}$$

(3755)

First Order Rate Formulation

In the First Order Rate method, the reaction rate coefficient $k_{devol}$ [1/s] is of the Arrhenius form given by:

$$k_{devol}=A{T}^{\beta }{e}^{\left(\frac{-E_a}{R_{u}T}\right)}$$

(3756)

The rate [kg/s] of consumption of the devolatilizing solid component is given by:

$$\frac{d{m}_i}{dt}=-k_{devol}{\alpha }_{i}m$$

(3757)

User Reaction Rate

In the User Reaction Rate method, you specify the reaction rate $r_{userrate}$ [kmol/m² s] directly, which is then multiplied internally by the molecular weight ${M_w}_i$ of species $i$ , the surface area of the particle $A_p$ , and the stoichiometric coefficient ${\nu }_i$ of species $i$ :

$$\frac{d{m}_i}{dt}=-r_{userrate}{M_w}_i{A}_p{\nu }_i$$

(3758)

Particle Reaction

The most general representation of particle reaction is:

$${A1}_{\left(s\right)}+\mathrm{...}+{An}_{\left(s\right)}+{D1}_{\left(g\right)}+\dots +{Dn}_{\left(g\right)}\to {B1}_{\left(g\right)}+\dots +{Bn}_{\left(g\right)}+{C1}_{\left(s\right)}+\dots +{Cn}_{\left(s\right)}$$

(3759)

For each particle reaction, multiple solid and fluid components can be chosen as reactants. At least one solid and one fluid reactant is required. Any number of products can be chosen as long as there is at least one solid or one fluid-phase product present in each particle reaction.

First-Order Combined Rate Formulation

In the First-Order Rate method, the reaction rate coefficient $k_{char}$ [m/s] is of the Arrhenius form given by:

$$k_{char}=A{T}^{\beta }{e}^{\left(\frac{-E_a}{R_{u}T}\right)}$$

(3760)

The rate of consumption of the solid component is dictated by the combined effect of the Arrhenius rate and gas-reactant diffusion rate to the particle surface given by [778]:

$$\frac{d{m}_i}{dt}=-\frac{k_m{k}_{char}}{k_{char}+k_m}\varphi C_g{M}_w{A}_p$$

(3761)

with:

$$k_m=\frac{\left(Sh\right)\left(D_m\right)}{d}$$

(3762)

where $\varphi$ is the Thiele modulus, $C_g$ is the concentration of the gas phase species, $M_w$ is the Molecular Weight of the gas species, $A_p$ is the Particle Surface Area, $Sh$ is the Sherwood number, $D_m$ is the Diffusion Coefficient of the gas reactant species, and $d$ is the Particle Diameter.

Half-Order Combined Rate Formulation

In the Half-Order Rate method, the reaction rate coefficient is of the Arrhenius form given by Eqn. (3365).

The rate of consumption of the solid component is dictated by the combined effect of the Arrhenius rate and gas-reactant diffusion to the particle surface given by:

$$\frac{d{m}_i}{dt}=k_m{C}_g{M}_w{\varphi A}_p-\frac{k_m{r}^2}{\left(M_w{\varphi A}_p\right)k_{char}^2}$$

(3763)

User Reaction Rate

In the User Reaction Rate method, you specify the reaction rate $r_{userrate}$ [kmol/m² s] directly, which is then multiplied internally by the molecular weight ${M_w}_i$ of species $i$ , the surface area of the particle $A_p$ , and the stoichiometric coefficient ${\nu }_i$ of species $i$ :

$$\frac{d{m}_i}{dt}=-r_{userrate}{M_w}_i{A}_p{\nu }_i$$

(3764)

Coal Combustion

Coal Moisture Evaporation

The moisture content of the coal particle is assumed to coat the particle. Moisture evaporation occurs rapidly before other mass transfer processes take place.

The continuity equation for the moisture component in particle $p$ is as follows:

$$\frac{{d\alpha }_{wp}{m}_p}{dt}=-r_{wp}$$

(3765)

The moisture evaporation rate $r_{wp}$ required in Eqn. (3765) is obtained by solving for both heat and mass transfer. The formulation for this evaporation rate is identical to that of the Quasi-Steady Single-Component Droplet Evaporation model. In coal combustion, the heat transfer rate commonly controls the evaporation rate.

Raw Coal Devolatilization

Using this mechanism is a reasonable compromise between a simple one-step mechanism, which does not account for the effect of particle history on volatile yield, and a more complex, multi-step mechanism which increases computational time.

The continuity equation for the raw coal component in particle p is described as:

$$\frac{{dm}_{cp}}{dt}={-r}_{cp}$$

(3766)

The net rate of raw coal consumption is given by:

$$r_{cp}=k_{pn}{\alpha }_{cp}{m}_p$$

(3767)

${\alpha }_{cp}$ is the mass fraction of the particle raw coal component.

For the User-Defined model, you specify $r_{cp}$ as the User Devolatilization Rate.

The raw coal, that is, the dry, ash-free portion of the coal, undergoes devolatilization to form volatiles and char by one or more reactions. The nth reaction is represented by:

$$\begin{array}{c}{{\left(rawcoal\right)}_p\stackrel{k_{pn}}{\to }YY}_{pn}{\left(volatilematter\right)}_g+\left({1-YY}_{pn}\right){\left(char\right)}_p\end{array}$$

(3768)

The volatile matter consists of combustible hydrocarbons and oxygen, and may also contain inorganic species (for example, N, Cl, and S). This is represented by the CoalVolatile component in the gas phase.

The kinetic rate of production of volatiles from the nth reaction (Eqn. (3768)) is given by:

$$r_{\nu pn}=k_{pn}{YY}_{pn}{\alpha }_{cp}{m}_p$$

(3769)

where the reaction rate constant $k_{pn}$ is given by:

$$k_{pn}=A_{pn}{e}^{\left(-\frac{E_{pn}}{R_u{T}_p}\right)}$$

(3770)

The two-step mechanism [751] is recommended for computing the devolatilization rate.

Char Oxidation

Raw coal devolatilization produces char according to Eqn. (3768). The continuity equation for the char component in particle p is as follows:

$$\frac{{dm}_{hp}}{dt}={-r}_{hp}$$

(3771)

Char reacts heterogeneously, after diffusion of the reactants (that is, O2, CO2 and H2O) to the particle surface, by one or more reactions of the form:

$$\begin{array}{c}{\left(char\right)}_l+{\left(oxidizer\right)}_l{\stackrel{k_{pl}}{\to }\left(products\right)}_l\end{array}$$

(3772)

Depending on the char oxidation model that is selected, the oxidation reaction is assumed to be first-order or half-order with respect to the oxidizer concentration. Three oxidizers are currently considered for char reactions: $O_2$ , $H_{2}O$ and $C{O}_2$ . These correspond to the following reactions:

$$\phi C+O_2\to \left(2\phi -2\right)CO+\left(2-\phi \right)C{O}_2$$

(3773)

$$C+H_{2}O\to CO+H_2$$

(3774)

$$C+{CO}_2\to 2CO$$

(3775)

First-Order Char Oxidation

A simple mass balance results in an expression for the rate of formation of char from particle p of the nth devolatilization reaction as shown below:

$$r_{hpn}={r_{\nu pn}\left({1-YY}_{pn}\right)/YY}_{pn}$$

(3776)

The net rate of raw coal consumption is the rate of char oxidation plus volatile formation.

Char is assumed to react heterogeneously with gaseous oxidizers that diffuse to the particle surface from the bulk gas phase. Two rate-limiting steps are considered for this process:

• Gas phase diffusion
• Heterogeneous reaction

The surface reaction is assumed to be first-order in the surface concentration of the oxidizer. The Arrhenius expression for the rate constant is then given by:

$$k_{pl}=A_{pl}{T}_p^n{e}^{\left(-\frac{E_{pl}}{R_u{T}_p}\right)}$$

(3777)

The overall combined char reaction rate is calculated from the following implicit equation [778]:

$$r_{hpl}=\frac{{A_p{M}_w}_{hp}{\phi }_l{k}_{pl}{\zeta }_{pl}{C}_g}{{\zeta }_{pl}{k}_{pl}+k_{cpl}}$$

(3778)

The mass transfer coefficient without the correction from blowing, $k_{cpl}$ , is computed from the Sherwood number, which in turn is based on the Ranz-Marshall correlation. The value of particle pore area coefficient, ${\zeta }_{pl}$ , has been chosen as 1.0. Since the char oxidation reaction is zero-order with respect to char concentration, heterogeneous ignition is permitted.

Half-Order Char Oxidation

Char is assumed to react heterogeneously with gaseous oxidizers that diffuse to the particle surface from the bulk gas phase. Two rate-limiting steps are considered for this process:

• Gas phase diffusion
• Half-Order Heterogeneous reaction

The surface reaction is assumed to be half-order in the surface concentration of the oxidizer. The Arrhenius expression for the rate constant is then given by:

$$k_{pl}=A_{pl}{T}_p^n{e}^{\left(-\frac{E_{pl}}{R_u{T}_p}\right)}$$

(3779)

The overall half-order combined char reaction rate for reaction $l$ is calculated from the following implicit equation:

$$r_{hpl}={{\varphi }_{l}k}_{cpl}{A}_p{M_w}_{hp}\left[C_{olg}-{\left(\frac{r_{hpl}}{{\varphi }_l{k}_{pl}{A}_p{M_w}_{hp}{\zeta }_{pl}}\right)}^2\right]$$

(3780)

The mass transfer coefficient without the correction from blowing, $k_{cpl}$ , is computed from the Sherwood number, which in turn is based on the Ranz-Marshall correlation. The value of particle pore area coefficient, ${\zeta }_{pl}$ , has been chosen as 1.0.

Effect of Particle Porosity

Simcenter STAR-CCM+ also provides the optional Lagrangian model, Particle Porosity, which allows you to define how the porosity of particles which burn internally changes through the course of a coal combustion reaction. The porosity of a particle, $\theta$ , determines how the diameter and surface area of the particle changes throughout a reaction. When the surface area of a particle changes, the overall reaction rate is affected. Using the Particle Porosity model, you can control how the reacting particle varies by specifying the exponent $\alpha$ which is used to determine porosity according to Eqn. (3240). The porosity is then used to calculate the particle volume, Eqn. (3241), which is used to calculate the particle diameter, Eqn. (3242), using the apparent density Eqn. (3243). Particle diameter, $d_p$ , is then used to calculate the surface area of the particle, $A_p$ .