The distribution of an additive in a chemical process: An application of input-output theory

This paper deals with a chemical process interpreted as a paper mill. In order to improve certain properties of the process, an additive is injected at various points in the process flows. At certain stages there are diverging feedback flows leading back to earlier stages, occasionally via storage tanks. Also there may be feedback flows coming from other externally connected processes. The problem treated is to determine the concentration of the additive in different process flows. For this purpose, the process is interpreted as a general linear input-output system. It is shown that the solution can be obtained by computing two inverse matrices, both related to the Leontief inverse.