Thermal interactions in large irregular fields of geothermal boreholes: the method of equivalent boreholes

Abstract

A new method is presented to evaluate thermal interactions between vertical geothermal boreholes. The finite line source (FLS) solution is extended to consider thermal interactions between groups of boreholes. Groups of boreholes that share similar temperatures and heat extraction rates are identified using hierarchical agglomerative clustering, and each group is represented in the model as a single equivalent borehole. Each equivalent borehole is split into segments, and temporal and spatial superposition of the FLS solution are employed to calculate the total temperature change along the length of the equivalent boreholes. The new method is shown to provide an accurate calculation of the g-function, with a mean absolute percentage error below 0.612 % on the g-functions of regular borefields of up to 144 boreholes using only 3 to 5 equivalent boreholes. Calculation times are significantly reduced : the g-function of a borefield of 1024 randomly positioned boreholes is calculated in 3.65 seconds. KEYWORDSground-coupled heat pumps; geothermal boreholes; g-functions; finite line source; thermal interactions; hierarchical agglomerative clustering CONTACT Carlos Prieto.

Semi-Analytical Method for 3D Transient Heat Transfer in Thermally Interacting Fields of Ground Heat Exchangers

“…This solution is extended to consider time-dependent fluid temperatures inside the U-tube by means of a coefficient updating scheme. The radial and axial heat conduction in the soil around GHEs, and the interactions between GHEs, are modeled with the FLS solution by considering thermal interactions between equivalent boreholes as proposed by Prieto and Cimmino [19]. The transient multipole method is coupled to the FLS solution to consider both of the short-and long-term effects around GHEs, and to a discretized finite difference model of the advection heat transfer process inside the U-tubes.…”

“…The finite line source (FLS) solution can then be superimposed to evaluate a penalty on the temperatures predicted by the transient multipole method. Additionally, the equivalent borehole method of Prieto and Cimmino [19] is used to simplify the thermal interaction problem and obtain a computationally-efficient simulation model of the bore field by only requiring the simulation of a limited number G of equivalent boreholes instead of the entire field of N b boreholes.…”

“…Recently, Prieto and Cimmino [19] proposed a methodology to account for thermal interactions among boreholes as interactions between equivalent boreholes sharing similar borehole wall temperatures and heat extraction rates. The field is divided into G equivalent boreholes using a hierarchical aglomerative algorithm.…”

“…In the case of the imposed inlet fluid temperature, a system of equations must be built and solved to evaluate heat extraction rate profiles and borehole wall temperature profiles along all GHEs in the field. Prieto and Cimmino [19] proposed a method to limit the sizes of the systems of equations by forming groups of similarly behaving boreholes and modeling each of these groups using a single equivalent borehole. This results in an efficient and robust method that allows the study of geothermal fields composed of thousands of GHEs.…”

“…This paper introduces a new methodology to study the transient heat transfer for both the interiors and exteriors of GHEs, considering fluid flow inside the pipes, fluidto-soil heat conduction via grout, thermal interactions among GHEs and axial effects. The equivalent borehole method of Prieto and Cimmino [19] is used to model the exteriors of the GHEs, including thermal interactions between GHEs. The transient multipole method of Prieto and Cimmino [36] is used to model the interiors of the GHEs, including temperature penalization to account for thermal interactions.…”