On the necessary conditions of optimality of water utilization systems in process plants with multiple contaminants

This paper presents necessary conditions of optimality for multicomponent water allocation systems in refineries and process plants. We extend the necessary conditions of optimality proved for single component by Savelski and Bagajewicz (Chem. Eng. Sci. 55(21) (2000) 5035). In particular, it is shown that at least one component reaches the maximum concentration at the outlet of a freshwater user process. A necessary condition of monotonicity is also proven. In this particular case, monotonicity only holds for certain components called "key" components.