The equations that define the chemical process are shown below. The reactants, A and B, are mixed together while carbon dioxide is continuously added to produce a desired third compound C. In the interest of commercial competition, the names of the chemical species have been changed.

We can define the above reaction scheme as a mathematical system, using the equation below:

,

with and

The matrix, M, is of rank 5 and given by:

and the function f by:

where the and are auxiliary variables given by:

The variables , , , , , and , are the concentrations of the following compounds , , , , and , respectively. The partial pressure of is given by and H is Henry's law constant.

Using the information above, we can derive the system of nonlinear differential-algebraic equations (DAEs) that models the chemical process described above.

| (1) |

Rearranging the equations derived above, we end up with a stiff system of 6 non-linear DAEs of index 1. Although there is no single formulation, stiffness is usually defined as an equation (or system of equations) with terms that can lead to rapid variations in the solution.

=

=

=

=

=

=

We now create a system model containing the equations derived above and the initial conditions.

| (2) |