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.
Highlights
Compatibility of the Thermal Borehole Resistance Model for borehole heat exchangers (BHEs) with Groundwater Advection steady-state conditions can be calculated using Equations (9) and (13) as follows: To implement the infinite moving line source (MLS) model in design programs, it has to be assessed if f g, the non-radial temperature θ, distribution
The BHE is considered to be perfectly sealed for horizontal groundwater advection in the surrounding subsurface so that only heat conduction occurs within the grouting material of the borehole
It can be concluded that the multipole method for the determination of the thermal borehole resistances is applicable to BHEs with groundwater advection
Summary
Ground source heat pump (GSHP) systems represent a valuable CO2 -emission-reducing alternative for heating and cooling of residential and commercial buildings compared to conventional systems [1,2,3]. A typical GSHP system consists of a heat pump coupled with horizontal or, more commonly, vertical borehole heat exchanger (BHEs). Compared to air source heat pump systems, the efficiency of GSHP systems is better and their environmental impact is lower [5,6]. Installation costs are significantly higher, which affects their economic competitiveness [1,7]. For the design of cost-optimized systems, it is important to consider all relevant heat transfer effects of the ground source and to include as many geological characteristics for site-specific system tuning as possible
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