I mentioned previously (8/2/2015) that I used fractional extent of reaction to obtain initial guesses for solving systems of equations. Example applications are CSTR reactors and Gibbs free energy minimization. This post will show how the initial guesses can be obtained.
Extending the fractional extent to multiple reactions
The formula for the outlet composition previously developed for one reaction can be modified easily for multiple reactions.
The example reaction system and feed composition
The first reaction has all of the reactants present in the feed and the second reaction needs the product of the first reaction to proceed.
Example 1: Extents needed to achieve maximum conversion
All of the reactants have been converted except the second which was fed in excess.
Example 2: A non feasible guess for the extent vector
Suppose I had guessed the following for the fractional extent vector.
Any guess for the fractional extent of the second reaction > 0.5 will result in negative values in the outlet composition. Since it can be difficult to determine the maximum extents by visual inspection of a multiple reaction system, I just do trial-and-error until the guess for the outlet composition has all positive elements.
Using this method, it is easy to arrive at an initial guess that is feasible, i.e. it satisfies the atom balances.