Analytical model of well leakage pressure perturbations in a closed aquifer system

Deep saline aquifers are commonly used for disposal and storage of various surface fluids. The target injection zone must be hydraulically isolated from overlying zones in order to ensure containment of the injected fluids. Improperly plugged nonoperational abandoned wells that penetrate the injection zone are the main potential leakage pathways. Leakage through such wells may cause an observable pressure signal in a zone overlying the injection zone; such a signal can be used to detect the leakage. In this paper we develop an analytical model to evaluate the pressure change induced by leakage through a well in a multilayer system. Unlike previous analytical models on the topic, our model uses a closed system, which may significantly affect the strength and behavior of the pressure signal induced by leakage. The analytical model is first presented for a two-layer system centered at the leaky well location. We evaluate the leakage-induced pressure change using the Laplace transform of Duhamel’s superposition integral, yielding the solution in the Laplace domain. We then derive a late-time asymptotic solution using the final value theorem, which suggests that the leakage rate becomes constant after sufficient time. We then obtain the multilayer solution by extending the two-layer solution and presenting it in matrix form in the Laplace domain. We apply the solution to three examples. In the first example, we apply the analytical model to a two-layer system, investigating its behavior and comparing the results with a numerical solution. In order to demonstrate behavior and potential applications of the multilayer analytical model, we present two multilayer examples: one with identical layers and another, replicating a CO2 storage site, with dissimilar layers. The leakage-induced pressure change does not necessarily decrease as the distance increases from the injection zone toward the surface.