Limitations and inherent assumptions of the law of mass action

A formulation for a law of mass action is central to any reaction equilibrium calculations. This equation, which is required for each reaction happening inside the system, relates the composition of the reactants and the products.

The general form of the law of mass action is as follows:

where

Keq is the equilibrium coefficient

fProducts is a generalized measure of composition for the reaction products (for example, molar fraction, mass fraction, activity, fugacity, or partial pressure)

fReactants is a generalized measure of composition for the reactants

We typically calculate Keq as a function of temperature, and we can calculate it from an empirical formula or from the heats of formation of the reaction participants. The following empirical formula is a typical example:

where

A, B, C, and D are regressed coefficients

From a numerical point of view, two problems may arise during the solution of the equation system:

• When Keq assumes a very high value at the solution, the composition measures for reactants are very small. This can lead to convergence issues.

• When reactants are not present in the feed, the law of mass action exhibits a singularity due to a division by zero.

To mitigate this issue, you can write the law of mass action without the fraction by multiplying both side of the equation by PfReactants.

This reformulation circumvents the division-by-zero problem but does not solve the root problem (that is, the assumption that equilibrium is violated when reactants are not present). However, for many practical applications, this formulation is stable enough in a wide variety of conditions to be generally useful. For that reason, we prefer this formulation in the reaction equilibrium models that we provide as part of AVEVA Process Simulation.