Use of Cross g-functions to Calculate Interference Between Ground Heat Exchangers Used in Ground-source Heat Pump Systems

Abstract

Ground-source heat pump systems are increasingly popular for providing single-family home heating in Nordic countries. As the density of installations increase, questions sometimes arise as to the influence of new systems on existing systems. These questions cannot be readily answered, as design and simulation techniques developed over the last 35 years have focused on analysis of individual systems without regard to the influences of other systems. Response factor models of ground heat exchangers utilize pre-computed response functions known as g-functions. These g-functions give the response of the ground heat exchanger (non-dimensionalized temperature) to the past and current heat rejection or extraction of the ground heat exchanger. We might call this a "self-g-function." In this paper, we define a "cross g-function" that gives the response of one ground heat exchanger to heat rejection or extraction of another ground heat exchanger. With this formulation, it is possible to determine the impact of a neighboring ground heat exchanger with a different load profile and history. This has many possible applications, but we demonstrate its use to study the sensitivity of nearby residential ground heat exchangers upon one another.