### 9.1.2. Reaction Rate Types

On the Reaction Rate tab of a reaction definition, the following types of reaction rate may be available:

- Arrhenius

- Arrhenius with Temperature PDF

- Expression

- Equilibrium

#### 9.1.2.1. Arrhenius

Two forms of the Arrhenius dependency are supported in CFX. The first is given by:

| (9–2)

where is reaction rate coefficient, is the pre-exponential factor, is the activation energy, is the universal gas constant, is the temperature exponent and is the temperature. A modified form:

| (9–3)

where is the activation temperature.

The pre-exponential factor may be an expression in space, time, absolute or static pressure, turbulence quantities (), molar mass or mixture composition (species mass fractions, molar fractions, mass concentrations, molar concentrations).

The units of the pre-exponential factor are:

| (9–4)

where n is the sum of the number of reaction orders, (plus 1 for a third body term, if present). As an example, for a reaction with two reactants, both with a reaction order of 1, and a third body term, n = 2+1 = 3. The physical dimensions for the pre-exponential factor in this case are:

| (9–5)

#### 9.1.2.2. Arrhenius with Temperature PDF

Similar instructions apply here as for Arrhenius, except that a temperature limit list is required to describe the probability density function. For details, see Arrhenius. The probability density function is a mathematical model that describes the probability of events occurring over time. This function is integrated to obtain the probability that the event time takes a value in a given time interval.

The temperature limit list requires the entry of the upper and lower bounds for temperature integration range (2 values).

#### 9.1.2.3. Expression

To enter an expression, click the enter expression icon and type the name of the expression into the box. For details, see Expressions in the CFX-Pre User's Guide.

#### 9.1.2.4. Equilibrium

For any reversible reaction, :

| (9–6)

where and represent the number of moles of materials A and B in the reaction. While quantities [A] and [B] represent the molar concentrations and , the equilibrium constant (which is dependent on temperature, enthalpy, entropy). The forward and backward reaction rates are defined as:

| (9–7)

and

| (9–8)

At equilibrium, , and therefore:

| (9–9)

Where is the forward rate and is the backward rate. When applied, the Arrhenius Reaction Model calculates the rate according to the following:

| (9–10)

The equilibrium option is only available if the forward reaction rate is set to Arrhenius.

A reaction is reversible when, for each reactant or production component, the reaction order is equal to the stoichiometric coefficient.

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