Stability in optimal design: Synthesis of complex reactor networks

A systematic methodology applicable to the optimal design of stable process systems is presented. It is based on the formulation of a parametric problem that provides bounds on the optimal stable solution and an iterative algorithmic approach that attains convergence of the bounds in a finite number of iterations. The bounds on the optimal stable solution are based on analytical expressions of bounds on the eigenvalues of the Jacobian matrix using the concept of the measure of the matrix. When extended to the synthesis problem of reactor networks, the approach is able to couple the optimization problem with stability issues even in cases where the number of reactors is large and the reaction mechanism is described by a general complex reaction scheme. Furthermore, since at the synthesis level the reactor network represents an exhaustive superposition of the existing structural and operational alternatives, the approach fully exploits these alternatives and coordinates a weighted optimal search that improves the objective and accommodates a stable reactor network. This approach is not restricted to the synthesis of reactor networks and can be applied to the design of total process flowsheets.