Analytical solutions for pressure perturbation and fluid leakage through aquitards and wells in multilayered-aquifer systems



[1] Large-scale groundwater pumping or deep fluid injection in a multilayered subsurface 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. In this study, we developed generalized analytical solutions that account for the combined effect of diffuse and focused leakage. The new solutions solve for pressure changes in a system of N aquifers with alternating leaky aquitards in response to fluid injection/extraction with any number, NI, of injection/pumping (active) wells, and passive leakage/recharge in any number, NL, of leaky wells. The equations of horizontal groundwater flow in the aquifers are coupled by the vertical flow equations in the aquitards and by the flow continuity equations in the leaky wells. The solution methodology, described in detail in this paper, involves transforming the transient flow equations into the Laplace domain; decoupling the resulting ordinary differential equations (ODEs) coupled by diffuse leakage via eigenvalue analysis; solving a system of NL × N linear algebraic equations for the unknown rates of flow through leakage wells; and superposing the solution of pressure buildup/drawdown in aquifers and aquitards resulting from flow in the NI active and NL leaky wells. Verification of the new methodology was achieved by comparison with existing analytical solutions for diffuse leakage and for focused leakage, and against a numerical solution for combined diffuse and focused leakage. Application to an eight-aquifer system with leaky aquitards and one leaky well demonstrates the usefulness and efficiency of the approach, and illustrates the pressure behavior over a spectrum of leakage scenarios and parameters.