Similarity Problems for Steady State Geothermal Systems

Abstract

Increasing energy efficiency of the geothermal systems (GS) is an important task for further development and implementation of the geothermal energy for industrial and domestic heating and cooling. Achieving the higher efficiency, in its turn, requires insight into thermodynamic interaction of all elements of GS. Mathematical modeling of such systems, as well as the development of similarity methods for such modeling is highly relevant because of the high cost of the GS. The presented in the paper mathematical model of a strongly non-equilibrium thermodynamic systems Ground - Borehole Heat Exchanger - Ground Source Heat Pump has been elaborated to describe the energy exchange between the ground, BHE and GSHP. Based on this model a stationary problem of such system operation has been solved. A new type of non-equilibrium spatial scales for this problem, not depending on its geometric parameters and that are determined by energy characteristics of GS are introduced. It is shown that in the special variables considered problem is characterized by a unique dimensionless parameter - the ratio of the thermal conductivity of the ground and brine. This allows us to formulate new approaches to GS modeling.The physical interpretation of the received results is provided.