Feasibility Condition for the Conventional Control Structure

Let us consider a reactor/separator/recycle process, where n reactants Aj give m products and intermediates Pk. The network of r reactions can be described by  

Let us assume that the separation section does not allow reactants Aj to leave the process. Then, the overall mass balance can be written as  

Obviously, the linear system (4.16) has at least one solution for any vector F0, if the following condition is fulfilled  

The flow rates of fresh reactants can be set at arbitrary values, but within stoichiometric constraints. Then, the internal flow rates and concentrations adjust themselves in such a way that, for each reactant, the net consumption rate equals the 

In Chapter 9, the butane/butene alkylation for isooctane production is discussed. The reactions can be represented by the following stoichiometry. 

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