A simple solution to tunnel or well discharge under constant drawdown

A simple analytical formula is developed to calculate transient discharge inflow rates into a tunnel or a well under constant drawdown. The agreement with the classical, but cumbersome diffusion-equation-based solution of Jacob and Lohman is excellent throughout the range of dimensionless times. By using only a straightforward logarithmic function, this explicit solution may therefore be used with great computational benefits in practice, and also when further mathematical manipulations such as differentiation or integration are require

Assessing the impact of thermal feedback and recycling in open-loop groundwater heat pump (GWHP) systems: a complementary design tool

Thermal feedback and thermal recycling in open-loop groundwater heat pump (GWHP) systems occurs when a fraction of the injected water in a well doublet returns to the production well. They reflect two different mathematical representations of the same physical process. Thermal feedback assumes a constant injection temperature, while thermal recycling couples the injection and production temperatures by a constant temperature difference. It is shown that thermal feedback, commonly used in GWHP design, and recycling reflect two thermal end-members. This work addresses the coupled problem of thermal recycling, which is, so far, the missing link for complete GWHP assessment. An analytical solution is presented to determine the return-flow fraction in a well doublet and is combined with a heat-balance calculation to determine the steady-state well temperatures in response to thermal feedback and recycling. This is then extended to advective-dispersive systems using transfer functions, revealing that the well temperatures in response to thermal feedback and recycling are functions of the capture probability. Conjunctive interpretation of thermal feedback and recycling yields a novel design approach with which major difficulties in the assessment of the sustainability of GWHP systems can be addresse