Optimization of Closed-Loop Shallow Geothermal Systems Using Analytical Models

Abstract

Closed-loop shallow geothermal systems are one of the key technologies for decarbonizing the residential heating and cooling sector. The primary type of these systems involves vertical borehole heat exchangers (BHEs). During the planning phase, it is essential to find the optimal design for these systems, including the depth and spatial arrangement of the BHEs. In this work, we have developed a novel approach to find the optimal design of BHE fields, taking into account constraints such as temperature limits of the heat carrier fluid. These limits correspond to the regulatory practices applied during the planning phase. The approach uses a finite line source model to simulate temperature changes in the ground in combination with an analytical model of heat transport within the boreholes. Our approach is demonstrated using realistic scenarios and is expected to improve current practice in the planning and design of BHE systems.

Figures (7)

• Figure 1: Cross section of a 1U borehole consisting of two pipe components and two grout zones (modified from DIERSCH20111122).
• Figure 2: Progression of the Modified Lloyd's Algorithm in a non-convex domain $\Omega$. Sub-figure (a) shows the initial clustering, (b) demonstrates the state after 20 iterations as generators approach equilibrium, and (c) presents the final converged configuration of the generators and their corresponding Voronoi cells.
• Figure 3: Annual Ground Load Profile with Hourly Discretization. This profile indicates how much thermal energy the BHE system must exchange at each hourly time interval over the period of a year. Positive values mean that heat is being extracted (heating demand), while negative values mean that heat is being rejected (cooling demand).
• Figure 4: Soil temperature distribution at BHE mid-depth after a 20-year simulation period. Black crosses denote the positions of the BHEs, and the rectangle indicates the property boundary. The temperature field exhibits symmetric diffusion, consistent with the symmetry of the BHE array and the property borders, with the highest thermal accumulation concentrated around the centroid of the BHE field.
• Figure 5: Soil temperature distribution at BHE mid-depth for varying property dimensions. A clear correlation is observed between property size and thermal saturation, with peak temperatures increasing as the property area is constrained. In all cases, the red contour line delineates a temperature increase of $3\,\text{K}$ relative to the initial ground temperature.