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

Abstract

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.

How a sensitive analysis on the coupling geology and borehole heat exchanger characteristics can improve the efficiency and production of shallow geothermal plants

“…(2020b) . According to many authors ( Wang et al., 2009 ; Casasso and Sethi, 2014 ; Van de Ven et al., 2021 ; Chen et al., 2022 ), during transient groundwater conditions the advection process is verified, and the BHE performance greatly improves. Therefore, with and without a steady state groundwater flow, the worst condition due to the higher impact in increasing the thermal disturbance of the ground around the BHE is verified.…”

“…On the other hand, more detailed studies based on numerical simulations show how specific types of grouts behave and how they can improve the overall BHE performances ( Li et al., 2018 ; Kim and Ho, 2018 ; Badenes et al., 2020b ; Van de Ven et al., 2021 ): in particular Kim and Ho (2018) proved how the GHE performances can increase with an increased thermal conductivity and specific heat capacity values of different types of grouting mixtures, during both continuous and intermittent GSHP operations.…”

Estimation of Groundwater Flow Rate by an Actively Heated Fiber Optics Based Thermal Response Test in a Grouted Borehole

“…Current research has solved the ground thermal conductivity estimation problem when only considering heat conduction based on ILS theory. On the other hand, for estimating the groundwater flow rate from TRTs, the moving infinite line source (MILS) theory has been suggested instead (Angelotti et al, 2018;Van de Ven et al, 2021;Verdoya et al, 2018;Wagner, Bayer, et al, 2014;Wagner et al, 2013). MILS theory was proposed by Sutton et al (2003) and Diao et al (2004) with a moving heat source assumption.…”

“…The drive rod was installed by direct‐push in direct contact with surrounding strata to meet the linear heat source assumption (direct contact between heat source and ground), and the MILS was employed to calculate the groundwater flow rate at various depths. Borehole effects such as by grout in borehole heat exchangers hamper the application of the MILS (Van de Ven et al., 2021; Wagner, Bayer, et al., 2014). The applicability of direct‐push, however, is limited to unconsolidated sediments and shallow depths.…”

Analytic expressions for the moving infinite line source model

“…Hu (2017) and Erol and François (2018) proposed models to take into account the multilayer case, thus lifting the assumption of a homogeneous media. Finally, Van de Ven et al (2021) recently developed a correction function to the MILS model to take into account the impervious grout put in place in GHEs.…”