A model to simulate pumping tests in wells with high loss and backflow

Traditional methods of analyzing pumping tests in single wells fail when the well loss is very high due to a low transmissivity skin. Because of the restricted rate at which water can enter a high loss well from the aquifer, well casing storage becomes a significant factor. Additionally, if a slug of water enters the well from the pump column immediately after the pump is switched off, it has a long-lasting significant effect on the recovering water level in the well because it cannot be absorbed rapidly by the aquifer. A theoretical model is derived here that simulates the water level in a well in these circumstances. In the model, the continuously changing rate of water inflow from the aquifer to the well is approximated by a step function with a finite difference time step. It is demonstrated by a real example that the model can be applied easily to analyze pumping tests, including tests with a varying pumping rate. The analysis confirms suspected high well loss, calculates the unknown rate of backflow, and determines the aquifer's transmissivity.