Arthur W. Westerberg

Studies in process synthesis—II: Evolutionary synthesis of optimal process flowsheets☆

Abstract The method most often used by process designers to solve the formidable task of synthesizing a process flowsheet is probably the evolutionary approach. The method is easily based on the previous experience of the designer and involves moving to better and better flow-sheets by making a succession of small improvements to an existing one. This paper presents a first step to organize the evotutionary synthesis of process flowsheets. In general terms it discusses the rules to make modifications and their desired properties, strategies to use these rules, and the various means to compare flowsheets. Specific rules and strategies are then proposed and successfully demonstrated on the evolutionary synthesis of multicomponent separation flowsheets. Where appropriate, proofs are given that these specific modification have the stated desired properties.

Studies in process synthesis—I: Branch and bound strategy with list techniques for the synthesis of separation schemes

Abstract The synthesis of a good flowsheet for a multicomponent separation problem constitutes a formidable task even for a small scale problem. The number of alternate, feasible separator sequences increases rapidly as the number of components in the mixture and the number of allowed separation methods increase. Some methods to select a sequence are almost purely heuristic to permit rapid screening among the alternatives without a guarantee of optimality. Another is based on dynamic programming and for special problems can in principle locate the best sequence, but it is notably time consuming. This paper uses primal and dual bounds in a branch and bound strategy to develop a procedure for locating a small number of nearly optimal separation sequences; furthermore, the optimal sequence must be among those found. Restrictions necessary for the dynamic programming approach can be relaxed (serial structure, high product purity), and in principle the method should generally be significantly faster. Two examples illustrate the approach.

Computer-aided design, Part 1 enhancing convergence properties by the choice of output variable assignments in the solution of Sparse equation sets

Abstract Techniques to guide one in choosing calculational schemes for sparse equation sets are being developed so a computer system can produce its own solution procedure—or subroutine—given a set of equations to be solved and the numbers occurring in the problem of interest. Previous work in this area has generally dealt only with the structural properties of the equation set. This paper presents a technique permitting the derived solution procedure to account directly for the problem numbers also. An algorithm results which also leads to a new method of obtaining structural information about the equation set.

Structural sensitivity analysis in design synthesis

Abstract Structural sensitivity analysis is an analysis procedure developed for use in process structural synthesis (flow sheet synthesis). The primary problem treated is that of determining, without reoptimizing the modified system, whether a feasible structural modification (generated automatically by a computer or manually by an engineer) to a given feasible structure appreciates return. The method proposed is to generate alternately dual (using generalized dual bounding procedures) and primal bounds for the modified system until a decision is possible on the value of the modification. Based on this approach, the paper presents a strategy which fully exploits dual bounding information to select the best of several proposed modifications at each step in the synthesis of a process flow sheet. Thus it is a local procedure for use in synthesis. It is demonstrated on three heat exchanger network synthesis problems.

Computer-Aided Design, Part 2 An approach to convergence and tearing in the solution of sparse equation sets

Abstract This paper is a sequel to the previous one on enhancing of convergence properties by a proper choice of output variable assignment for sparse equation sets. A new criterion for the output set assignment selection is presented. Two algorithms—one based on dynamic programming and the other on branch and bound techniques—implement this selection criterion. The paper also indicates that the resulting dynamic programming network is a compact structural representation for the equation set and can be used to obtain tearing information for all output set assignments for the equations directly.

Computer-aided design: Part 3 decision variable selection to avoid hidden singularities in resulting recycle calculations

Abstract The chemical engineer is often faced with the task of choosing an appropriate set of variables to be used as input information in the analysis of a process design. The problem can be considered as solving a set of N equations with M variables ( M ≥ N ). The engineer must therefore choose MN variables to be decision variables, and these must then be externally fixed to allow calculation of the remaining N state variables. In design each equation will contain only a few of the system variables. Such sparse systems of equations lend themselves to precedence ordering and tearing techniques as effective solution procedures. The concept of an output variable assignment for each equation is basic to these techniques. This paper presents an algorithm for automatically choosing an appropriate set of decision variables. It chooses a set which avoids leaving singular or nearly singular N × N equation sets for solution. Simultaneously the algorithm also chooses an output set for each N × N system so that the solution of any cyclic subset of equations by the iterative method of successive substitutions has good convergence properties. This technique extends earlier work by the authors on locating output sets for N × N cyclic equation sets. This extension is an effective method for evaluating sparse embedded systems of determinants thus permitting one to avoid singularities. The paper concludes with two examples including a binary flash distillation system.