Enhanced Steady-State Solution of the Infinite Moving Line Source Model for the Thermal Design of Grouted Borehole Heat Exchangers with Groundwater Advection

The objective of this study is to assess the suitability of the analytical infinite moving line source (MLS) model in determining the temperature of vertical grouted borehole heat exchangers (BHEs) for steady-state conditions when horizontal groundwater advection is present. Therefore, a numerical model of a grouted borehole is used as a virtual reality for further analysis. As a result of the first analysis, it has been discovered that established analytical methods to determine the borehole thermal resistance as a mean value over the borehole radius can also be applied to BHEs with groundwater advection. Furthermore, the deviation between a finite MLS and the infinite MLS is found to be only less than 5% for BHEs of a depth of 30 m or more, and Péclet numbers greater than 0.05. Finally, the accuracy of the temperature change calculated with the infinite MLS model at the radius of the borehole wall compared to the temperature change at a numerically simulated grouted borehole is addressed. A discrepancy of the g-functions resulting in a poor dimensioning of BHEs by the infinite MLS model is revealed, which is ascribed to the impermeable grouting material of the numerical model. A correction function has been developed and applied to the infinite MLS model for steady-state conditions to overcome this discrepancy and to avoid poor dimensioning of BHEs.

A Single Probe Transient Moving Line Source Method for Determining Thermal Conductivity, Thermal Diffusivity, and Superficial Flow Velocity of a Porous Material With Flow

This paper presents a method to determine the effective thermal conductivity and thermal diffusivity of a porous material, as well as the superficial flow velocity of fluid flowing through the porous matrix using a single probe transient moving line source method. The method transforms the transient analytical solution for a moving line source using differentiation to produce three independent equations to solve for the three unknowns. Empirical data are presented from a laboratory scale test apparatus for three test cases with known properties and flow rates to validate the method. The method is then applied to field data from a standing column well used in ground source heat pump systems to obtain the thermal and flow properties of the ground formation. The properties are inserted into the transient analytical solution for a moving line source and superimposed over the empirical data showing agreement between the model and the data. The method is more accurate than traditional methods for estimating thermal properties when flow conditions are present, and the implementation of the method does not require any additional thermal data.