Globally optimal computer aided design of chemical processes

Process network synthesis is of fundamental importance to the chemical engineering discipline. With today's revolution in digital computers, there is an increased opportunity to address synthesis problems by employing mathematical programming based approaches. Although there have been significant advances in this research field, the fundamental difficulty associated with the solution of nonlinear nonconvex optimization formulations has stifled progress. In recent years, the I&barbelow;nfinite D&barbelow;imE&barbelow;nsionA&barbelow;l S&barbelow;tate-space (IDEAS) work was introduced as a unified approach to globally optimal process network synthesis. The IDEAS methodology has been used to address a number of process network synthesis problems including heat/mass exchange networks, distillation networks and reactor networks. The IDEAS framework results in an infinite optimization problem formulation that requires an approximation scheme for its solution. In previous IDEAS works, the convergence of the approximation scheme has been verified numerically. In this work, novel IDEAS convergence results are presented. In the continuing effort of IDEAS development, we also develop a number of novel properties for the IDEAS formulation for reactor network synthesis. These properties are then employed to construct an algorithm that is capable of identifying the attainable region to any desired degree of accuracy, with excellent computational results. Due to the structural similarity between the IDEAS and the state-space (SS) frameworks, similar properties are derived for the SS formulation for reactor network synthesis. These properties are further developed based on the finiteness of the SS framework by employing classical results from linear algebra which give additional insights to the meaning of these properties. The results on the SS framework are employed to quantify the novel concept of a fixed number/type of reactors attainable region (FN/TR-AR). In the last part of this work, we employ the IDEAS framework to address the total annualized cost (TAC) network synthesis problem. We show that some economies of scale (EOS) behavior of sizing process equipment can be captured using a linear objective function within the IDEAS framework. Economies of scale that do not lead to linear objective functions within the IDEAS framework, motivate us to propose a finite branch and bound algorithm for the global solution of programs with a linear feasible region and a concave, separable objective function with special power-law characteristics.