Review of Petroleum and Hydrogeology Equations for Characterizing the Pressure Front Diffusion during Pumping Tests

Abstract

In hydrogeology, the pressure front diffusion equation is crucial for the interpretation of pumping tests. It describes the displacement around the pumping well of the pressure front generated by a hydraulic disturbance, such as pumping or injection. This equation serves to physically locate the hydraulic objects (the recharge boundary, impermeable boundary, fault and hydraulic connection) that are able to influence the hydrodynamic behaviour of aquifers during a transient hydraulic test. However, several authors who have attempted to characterize this equation have come up with different expressions because the pressure front has been defined according to different approaches. This paper first clarifies the origin of the divergence between authors before reviewing seven approaches used to characterize the diffusion equation. In addition, a new approach is proposed, which is more practical and which defines the pressure front using the logarithmic derivative of the drawdown. Finally, all these reviewed approaches, plus the new one, are unified into a single general approach that defines the pressure front according to a general criterion, which is the critical drawdown, noted as sc. To do this, the pressure front criteria of each existing approach, including the new one, were converted into equivalent critical drawdowns. The ultimate goal of this study is to enable hydrogeologists to use all these approaches correctly in order to improve the accuracy of the interpretation of pumping test data for the better characterization of the geometry of aquifers.