Comparison of optimization approaches for the well placement of groundwater heat pumps

Groundwater heat pumps (GWHP) use the thermal energy stored in groundwater. Therefore, GWHP systems extract groundwater via extraction wells and, after heat exchange, return it to the same aquifer via injection wells. The returned water has a lower temperature than the pumped water since the GWHP extracts heat for domestic heating. This causes the development of so-called thermal plumes in the aquifer. The thermal plume dissipates downstream according to the local groundwater flow direction and can reach the extraction wells of neighboring systems. Depending on their mode of operation, this altered water can significantly reduce their efficiency. To ensure optimal use of geothermal potential, such negative interactions between neighboring systems must be avoided and are legally constrained to a maximum temperature change of 1K in downstream extraction wells. One way to avoid the negative interactions and to maximize the spatial utilization is the optimal placement of GWHPs and their wells. In addition, the optimal placement of wells is important within a system to avoid significant thermal recycling. To determine the optimal placement of wells, estimations of thermal plumes are required. These calculations can be performed using analytical or numerical (PDE-based) models.

In this contribution, we compare two different optimization approaches for the placement of GWHP wells. The first approach is based on the linear advective heat transport model (LAHM), which is an analytical model, and integer linear programming. The second approach is based on numerical simulation of groundwater flow and heat transport and the adjoint optimization method. We first present these two recently developed optimization approaches and then analyze their potential applications (optimal management of the geothermal resource, optimal system design, urban energy planning, etc.), limitations, and future possibilities. We use real case studies to analyze and compare the approaches.