Find Chemical Equilibrium for Networks of Reactions
Chemical reaction systems that have equilibrium can typically be directly modeled as a polynomial system of equations. These problems are defined by conservation and reaction equations. The example below is from combustion chemistry and models the burning of fuel in a combustion chamber such as in a car engine. The goal is to find out what chemical components and compounds are in the combustion chamber at various stages. The system of reactions being studied is given by , , , , , , .
Introduce a variable for the quantity of each component. Here is treated as a component, since does not occur on its own.
Also introduce a variable for the quantity of each compound.
If you assume a closed chemical system, quantities are conserved, which leads to conservation equations shown in their chemical and algebraic notation.
Give the equations for equilibrium.
Give parameter values.
Solve the system over the reals, and select only non-negative solutions.
Compute a higher-precision solution.