Maximizing the spatial potential of thermal groundwater use by mixed-integer PDE-constrained optimization

Groundwater heat pump systems are one of the key technologies for the energy transition of the heating and cooling sectors. These systems alter the groundwater temperature and cause thermal plumes, which propagate downstream according to the natural groundwater flow. The plumes can reach neighboring systems and deteriorate their efficiency. For this reason, already existing downstream users are legally protected against a severe change of natural groundwater conditions. Hence, it is important to optimally position these systems to avoid negative interactions and simultaneously maximize the spatial potential of thermal groundwater use. Processes that take place in groundwater, i.e. flow and heat transport, are described with a system of nonlinear coupled PDEs. Therefore, the underlying problem is a PDE-constrained optimization problem, which includes control (spatial coordinates of wells) and state (groundwater temperature) constraints. The decision to install a particular groundwater heat pump can be modeled with binary variables. In this talk, we will introduce an adjoint-based approach to solve this mixed-integer PDE-constrained optimization problem. The approach is tested with various numbers of heat pumps and applied to real case scenarios, where the geothermal potential within a city district is maximized.     «

Groundwater heat pump systems are one of the key technologies for the energy transition of the heating and cooling sectors. These systems alter the groundwater temperature and cause thermal plumes, which propagate downstream according to the natural groundwater flow. The plumes can reach neighboring systems and deteriorate their efficiency. For this reason, already existing downstream users are legally protected against a severe change of natural groundwater conditions. Hence, it is important to...     »