(78d) Globally Optimal TAC for Compressors and Coolers in Series

In this work we explore the minimum total annualized cost problem for a series of nonisentropic compressors and coolers in series that brings an ideal gas from a specified initial temperature and pressure to a specified final temperature and pressure, subject to constraints on the compressor maximum operating temperature and the minimum temperature of the gas stream. We will explore cases for which (1) the heat capacity of the gas is constant, and (2) the heat capacity is a function of temperature. Through mathematical proof, the existence of an optimum and regularity of all feasible points for both cases will be established. This permits development of a solution strategy involving simultaneous identification of the number of compressors/coolers required and minimization of compressor work and coolant flow rate. This will be illustrated in a case study involving hydrogen compression.