Minimum Cost (Operating/Capital/Total Annualized) for Chemical Process Sequences: Reactor/Compressor Processes

In this work we formulate and solve minimum cost problems for two processes: (1) a system of n compressors and n coolers alternating in series that brings an ideal gas from a specified initial temperature and pressure to a specified final temperature and pressure and (2) a series of n CSTRs in which a reaction of general form mA→B takes place.

The former considers the heat capacity of the gas as a function of temperature, and compressors that operate nonisentropically. Constraints in the formulation are as follows: each compressor has a specified maximum operating temperature, and each cooler cannot cool the gas stream to lower than the initial temperature. Solution of the minimum cost problem involves determination of the number of compressors and coolers required, as well as simultaneous minimization of compressor work and coolant flow rate in the coolers.

The latter formulation seeks to minimize the concentration of species A leaving the last CSTR (that is, maximize the production of the desired species B). The problem assumes the CSTRs operate at steady state and that the concentrations of all material streams are constant. Constraints used in this formulation are as follows: Each CSTR has a finite specified maximum volume and finite residence time. Solution of this minimum cost problem involves determination of the number of CSTRs along with a set of volumes and residence times that maximize the extent of the reaction for a minimum capital cost.