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

Abstract

[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, N I , of injection/pumping (active) wells, and passive leakage/recharge in any number, N L , 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 N L Â 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 N I active and N L 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.Citation: Cihan, A., Q. Zhou, and J. T. Birkholzer (2011), Analytical solutions for pressure perturbation and fluid leakage through aquitards and wells in multilayered-aquifer systems, Water Resour. Res., 47, W10504,

Impact-driven pressure management via targeted brine extraction—Conceptual studies of CO2 storage in saline formations

“…The calculations presented in Section 3 are conducted for an idealized example using an analytical solution for single-phase flow in a system of multiple aquifers and aquitards with multiple injection/pumping wells and multiple leaky wells (Cihan et al, 2011). …”

“…Because we focus on the changes in the far-field fluid pressure outside of the expected CO 2 plume domain, we can make the same approximation in our IDPM concept study and use an efficient analytical solution developed for single-phase flow in multi-layer aquifer and aquitard systems (Cihan et al, 2011). This solution captures most of the geometrical and flow features relevant for the idealized example shown in Figure 1; i.e., it can handle aquifer-aquitard systems with any number of layers involving slow brine migration into low-permeability aquitards (also referred to as diffuse leakage) and any number of injection/pumping and leaky wells (see Section 2.2).…”

A harmonic pulse testing method for leakage detection in deep subsurface storage formations

“…For the leak scenario, a leaky well is present at a distance r I from the injector, and the distance between the leaky well and observation well is denoted by r L . Such a problem setting has been widely used in analytical and numerical studies for leakage modeling [e.g., Avci, 1994;Birkholzer et al, 2011;Cihan et al, 2011;Nordbotten et al, 2004;Sun and Nicot, 2012;Sun et al, 2013b;Zeidouni, 2014]. Most of the previous analytical studies assume constant injection rates.…”

“…A primary environmental concern of these practices is the potential migration of injected fluids through connected pathways (e.g., abandoned wells or geologic faults) into underground sources of drinking water. A number of previous works have focused on forward and inverse modeling of leakage from deep subsurface storage formations [e.g., Avci, 1994;Cihan et al, 2011;Javandel et al, 1988;Nordbotten et al, 2004;Sun and Nicot, 2012]. Most of these analyses assume passive monitoring, in which pressure gauges are simply used to ''listen'' for possible leak signals.…”

Multi-Aquifer Parameterization with well loss in Vertical Flows

“…Miyake et al (2008) [28] carried out multi-aquifer pumping tests, in multi-screen pumping well and multi-level piezometers in multi-layered confined aquifers to estimate parameters in aquifers, and also for low permeability layers between the aquifers, using the Cooper-Jacob method and a finite element groundwater model. Cihan et al (2011) [9] developed analytical solutions accounting for the combined effect of diffuse and focused leakage to solve for pressure changes in a system of N aquifers with alternating leaky aquitards in response to fluid injection/extraction from any number of layers. Basic ingredient to the mathematical formulations of the above-stated solutions remained a minimum boundary condition of leakage face.…”