Analytical Solutions for Pressure Perturbation and Fluid Leakage through Aquitards and Wells in a Multilayered System

Large-scale groundwater pumping or deep fluid injection in a multilayered system may generate pressure perturbation not only in the target formation(s), but also in over- and underlying units. Hydraulic communication in the vertical direction may occur via diffuse leakage through aquitards and/or via focused leakage through leaky wells. Existing analytical solutions for pressure perturbation and fluid flow in such systems consider either diffuse leakage or focused leakage, but never in combination with each other. This study presents generalized analytical solutions for pressure buildup and fluid leakage rates in a multilayered system consisting of any number of aquifers, alternating aquitards, injection wells, and leaky wells. The equations of horizontal groundwater flow in the aquifers are coupled by the equations of vertical flow in the aquitards and by the continuity equations in the leaky wells. The general solutions were obtained by applying the Laplace Transform method and eigenvalue analysis to the governing equations. Accuracy of the solutions was demonstrated by comparison with other analytical solutions as well as with detailed numerical predictions. Example applications to hypothetical CO2 injection scenarios (without consideration of two-phase flow) demonstrate that the new solutions are an efficient tool for analyzing pressure buildup in multilayered systems with leakage through multiple aquitards and multiple leaky wells. The solutions are particularly useful when a large number of calculations need to be performed, i.e., for uncertainty quantification, parameter estimation, or for the optimization of pressure management schemes.