Basics of COP Maximum of Wastewater Heat Recovery System using an Analytical Optimization Method

This article presents the basics of the mathematical analysis for determining the COP (coefficient of performance) optimum of a heat recovery system. A new sizing method is introduced to determine the optimal mass flow of hot water and well water and thus the optimal performance of the circulating pump. The optimal pump performance ensures maximum energy efficiency of the system, i.e. maximum coefficient of performance (COP) of the heat pump recovery system with using the chosen type of heat pump. The mathematical model of the heat recovery system is stationary, consisting of algebraic equations with lumped parameters. By using the analytical optimization procedure and the objective function, the local energy optimum conditions can be defined as a result, with respect to the mass flow. The governing equations for local optimization of the COP are presented in this paper. The resulting system of algebraic functions can only be solved numerically. For this purpose, Newton linearization and Gauss elimination methods should be used, which will be presented in the upcoming papers.