Description:
<jats:p> The optimization of complicated nonlinear systems, involving many variables and constraints, is a familiar problem in the chemical and petroleum industries. A typical example occurred in trying to find the optimum operating conditions for a fluid catalytic cracking unit. As a first step in investigating this particular problem, an elaborate mathematical model of the catalytic cracking operation was developed. When programmed on a large-scale digital calculator, this model permitted convenient simulation of both the engineering and economic aspects of the system. However, the number of variables subject to control, and the complicated relationships between them, precluded the use of any haphazard approach to finding the optimum operating conditions. The method of steepest ascents (taken from a part of the Box-Wilson technique for designed experiments) and linear programming were used to develop a rational sequential method for solving this problem. These methods optimized six key variables, subject to various operating constraints. The study was completed in a reasonable time and at a moderate cost. A substantial economic advantage was indicated between the final solution and the base case chosen to initiate the study. </jats:p>