Well Drainage Management in Abandoned Mines: Optimizing Energy Costs and Heat Use Under Uncertainty

In this study, we investigate how pump control optimized with respect to the prevailing electricity prices (temporal arbitrage conditions) impacts the “eternal” operating costs of well drainage in an abandoned mine. Such a drainage system can be seen as a small-scale underground pumped storage hydro plant. The mathematical optimization of the well takes the dependency of electrical power with the water volume lifted and the changing water level into account. The non-linear dependency is transformed into a linear optimization problem in multiple stages. First, a superstructure optimization is used. Second, the characteristic pump profiles are linearized piecewise, resulting in a simplified problem where only the multiplication of a binary and a positive real variable remain. The multiplication of the two variables is replaced by a new variable, transforming the optimization problem into a mixed integer linear optimization problem. The results of the superstructure optimization yield the optimal pump size and the minimal costs incurred, which are then used to optimize the maintenance strategy. We find that well drainage costs can be reduced markedly by the optimization proposed, and that the economic potential for using mine water as a heat source for a local district heating network is rather limited.