Abstract
A number of (semi-)analytical solutions are available to drawdown analysis and leakage estimation of shallow aquifer–aquitard systems. These solutions assume that the systems are laterally infinite. When a large-scale pumping from (or injection into) an aquifer–aquitard system of lower specific storativity occurs, induced pressure perturbation (or hydraulic head drawdown/rise) may reach the lateral boundary of the aquifer. We developed semi-analytical solutions to address the induced pressure perturbation and vertical leakage in a “laterally bounded” system consisting of an aquifer and an overlying/underlying aquitard. A one-dimensional radial flow equation for the aquifer was coupled with a one-dimensional vertical flow equation for the aquitard, with a no-flow condition imposed on the outer radial boundary. Analytical solutions were obtained for (1) the Laplace-transform hydraulic head drawdown/rise in the aquifer and in the aquitard, (2) the Laplace-transform rate and volume of leakage through the aquifer–aquitard interface integrated up to an arbitrary radial distance, (3) the transformed total leakage rate and volume for the entire interface, and (4) the transformed horizontal flux at any radius. The total leakage rate and volume depend only on the hydrogeologic properties and thicknesses of the aquifer and aquitard, as well as the duration of pumping or injection. It was proven that the total leakage rate and volume are independent of the aquifer’s radial extent and wellbore radius. The derived analytical solutions for bounded systems are the generalized solutions of infinite systems. Laplace-transform solutions were numerically inverted to obtain the hydraulic head drawdown/rise, leakage rate, leakage volume, and horizontal flux for given hydrogeologic and geometric conditions of the aquifer–aquitard system, as well as injection/pumping scenarios. Application to a large-scale injection-and-storage problem in a bounded system was demonstrated.
This is a preview of subscription content, log in via an institution to check access.
Similar content being viewed by others
References
Abramowitz M., Stegun I.A.: Handbook of Mathematical Functions with Formulas, Graphs, and Mathematical Tables. Dover Publications, Inc., New York (1972)
Batu V.: Aquifer Hydraulics: A Comprehensive Guide to Hydrogeologic Data Analysis. John Wiley, New York (1998)
Bear J.: Dynamics of Fluids in Porous Media. Dover Publications, New York (1972)
Birkholzer, J.T., Zhou, Q., Tsang, C.-F.: Large-scale impact of CO2 storage in deep saline aquifers: a sensitivity study on pressure response in stratified systems. Int. J. Greenh. Gas Control (2008). doi:10.1016/j.ijggc.2008.08.002
Butler J.J., Tsou M.: Pumping-induced leakage in a bounded aquifer: an example of a scale-invariant phenomenon. Water Resour. Res. 39(12), 1344 (2003). doi:10.1029/2002WR001484
Cheng A.H.D., Morohunfola O.K.: Multilayered leaky aquifer systems: pumping well solutions. Water Resour. Res. 29(8), 2787–2800 (1993). doi:10.1029/93WR00768
Cheng A.H.D.: Multilayered Aquifer Systems—Fundamentals and Applications. Marcel Dekker, New York (2000)
Cohen A.M.: Numerical Methods for Laplace Transform Inversion. Springer, New York (2007)
de Hoog F.R., Knight J.H., Stokes A.N.: An improved method for numerical inversion of Laplace transforms. SIAM J. Sci. Stat. Comput. 3, 357–366 (1982). doi:10.1137/0903022
Earlougher R.C.: Advances in Well Test Analysis. Henry L. Doherty Memorial Fund of AIME, New York (1977)
Hantush M.S.: Modification of the theory of leaky aquifers. J. Geophys. Res. 65(11), 3713–3725 (1960). doi:10.1029/JZ065i011p03713
Hantush M.S.: Hydraulics of wells. In: Chow, V.T.(eds) Advances in Hydroscience, Academic Press, New York (1964)
Hantush M.S., Jacob C.E.: Nonsteady radial flow in an infinite leaky aquifer. Eos Trans. AGU 36(1), 95–100 (1955)
Konikow L.F., Neuzil C.E.: A method to estimate groundwater depletion from confining layers. Water Resour. Res. 43, W07417 (2007). doi:10.1029/2006WR005597
Moench A.F.: Transient flow to a large-diameter well in an aquifer with storative semicofining layers. Water Resour. Res. 21(8), 1121–1131 (1985). doi:10.1029/WR021i008p01121
Moridis G.: Semianalytical solutions for parameter estimation in diffusion cell experiments. Water Resour. Res. 35, 1729–1740 (1999). doi:10.1029/1999WR900084
Neuman S.P., Witherspoon P.A.: Theory of flow in a two-aquifer system. Water Resour. Res. 5(4), 803–816 (1969). doi:10.1029/WR005i004p00803
Ramakrishnan T.S., Kuchuk F.J.: Pressure transients during injection: constant rate and convolution solutions. Transp. Porous Media 10, 103–136 (1993). doi:10.1007/BF00617004
Stehfest H.: Numerical inversion of Laplace transforms. Commun. ACM 13(1), 47–49 (1970). doi:10.1145/361953.361969
Streltsova T.D.: Well Testing in Heterogeneous Formations. Wiley, New York (1988)
Theis C.V.: The relation between the lowering of the piezometric surface head and the rate and duration of discharge of a well using ground-water storage. Eos Trans. AGU 16, 519–524 (1935)
USEPA (U.S. Environmental Protection Agency): Determination of Maximum Injection Pressure for Class I wells, United States Environmental Protection Agency Region 5—Underground Injection Control Section Regional Guidance #7. EPA, Washington, DC (1994). http://www.epa.gov/R5water/uic/r5guid/r5_07.htm
Vukovic M., Soro A.: Hydraulics of Water Wells: Theory and Application. Water Resources Publications, Littleton, CO (1992)
Zhan H., Bian A.: A method of calculating pumping-induced leakage. J. Hydrol. (Amst.) 328, 657–667 (2006). doi:10.1016/j.jhydrol.2006.01.010
Zhou Q., Bensabat J., Bear J.: Accurate calculation of specific discharge in heterogeneous porous media. Water Resour. Res. 37(12), 3057–3070 (2001). doi:10.1029/1998WR900105
Zhou Q., Liu H.-H., Molz F.J., Zhang Y., Bodvarsson G.S.: Field-scale effective matrix diffusion coefficient for fractured rock: Results from literature survey. J. Contam. Hydrol. 93, 161–187 (2007). doi:10.1016/j.jconhyd.2007.02.002
Zhou Q., Birkholzer J.T., Tsang C.-F., Rutqvist J.: A method for quick assessment of CO2 storage capacity in closed and semi-closed saline formations. Int. J. Greenh. Gas Control. 2, 626–639 (2008). doi:10.1016/j.ijggc.2008.02.004
Author information
Authors and Affiliations
Corresponding author
Rights and permissions
About this article
Cite this article
Zhou, Q., Birkholzer, J.T. & Tsang, CF. A Semi-Analytical Solution for Large-Scale Injection-Induced Pressure Perturbation and Leakage in a Laterally Bounded Aquifer–Aquitard System. Transp Porous Med 78, 127–148 (2009). https://doi.org/10.1007/s11242-008-9290-0
Received:
Accepted:
Published:
Issue Date:
DOI: https://doi.org/10.1007/s11242-008-9290-0