Interval-Analysis-Based Determination of Globally Optimal Total Annualized Cost for Compressor Sequences

In this work, the minimum total annualized cost (TAC) problem is studied for a series of non-isentropic compressors and coolers that brings a gas with constant compressibility factor from a specified initial pressure and temperature to a specified final pressure and the same temperature. For constant heat capacity, constant compressibility factor gases, additional properties of the globally optimal compressor sequence are analytically established. These properties permit development of an interval-analysis-based solution strategy that identifies compressor configurations yielding the globally-minimum TAC for varying network outlet pressures. Several case studies are presented to illustrate the developed theorems and solution strategy.