Game theoretic approach to multiobjective designs: Focus on inherent safety

Abstract

A method for designing processes that are inherently safer—with the primary focus on disturbances having the potential for unbounded hazardous responses—is introduced. In cases where safety is not threatened (as in isothermal fermentation reactors), but product quality can rapidly degrade, this method provides designs that ensure high product quality (as in pharmaceutical processes). Using game theory, the method accounts for the trade-offs in profitability, controllability, safety and/or product quality, and flexibility. For nonlinear processes that are hard to control; that is, have an unstable and/or nonminimum-phase steady state, over a wide range of operating conditions, extended bifurcation diagrams are introduced. When a steady state is nonminimum phase, the process may exhibit inverse response. The steady states of processes are classified on the basis of instability and nonminimum-phase behavior to segregate the operating regimes into distinct zones. Locally optimal designs, one corresponding to each zone, are obtained first. These are compared with other locally optimal designs at alternate operating conditions, and/or process reconfigurations, to obtain the globally optimal design using game theory. Four indices—profitability, controllability, safety and/or product quality, and flexibility—characterize the optimality of a design. A novel index for safe operation and/or product quality at a steady state is formulated as a function of the eigenvalues of the Jacobian of the process model and the Jacobian of the process zero dynamics, providing a quantitative measure of instability and nonminimum-phase behavior. The application of the proposed method to an isothermal, continuous stirred-tank reactor (CSTR) with van der Vusse reactions, an exothermic CSTR, and an anaerobic fermentor with substrate and product inhibition is presented. © 2005 American Institute of Chemical Engineers AIChE J, 2006