A method of calculating pumping induced leakage Hongbin Zhan * , Aiguo Bian Department of Geology and Geophysics, Texas A&M University, College Station, TX 77843-3115, United States Received 12 October 2005; received in revised form 10 January 2006; accepted 17 January 2006 Summary We have discussed pumping induced leakage in a leaky-confined aquifer bounded by a relatively thin aquitard whose storage effect is neglected. Both constant-rate and constant- drawdown, fully penetrating vertical pumping wells are considered. We have derived closed- form analytical solutions of the steady-state leakage rates and volumes within any given radial distance from the well for both the constant-rate and constant-drawdown pumping wells. For the constant-rate well, we have derived the closed-form analytical solutions for the total leak- age rate and volume over the entire aquitard–aquifer boundary at a given time; and the semi- analytical solutions for calculating the leakage rate and volume within any radial distance from the pumping well at a given time. For the constant-drawdown well, we have further provided the analytical solutions of the leakage rate and volume in the Laplace domain; those solutions are numerically inverted to yield results in the real time domain. With the scale-invariant relation- ship of [Butler Jr., J.J., Tsou, M.-S., 2003. Pumping-induced leakage in a bounded aquifer: an example of a scale-invariant phenomenon. Water Resour. Res. 39(12), 1344, doi: 10.1029/ 2002WR001484.], the solutions of the total leakage rates and volumes can be generalized to finite size aquifers with lateral impermeable boundaries. These solutions are useful for managing multi-layer aquifers in which pumping induced water transfer across the aquitards can occur.  c 2006 Elsevier B.V. All rights reserved. KEYWORDS Leaky aquifer; Leakage rate; Leakage volume; Analytical solution; Aquifer management Introduction Many natural aquifers are semi-confined where aquitards separate them from adjacent aquifers. When groundwater is withdrawn from one aquifer, transfer of water from the adjacent aquifer to the pumped aquifer will occur, a pro- cess termed leakage. Pumping induced leakage across aqui- tards could be an important water budget component that must be considered in groundwater management. The early work on the semi-confined aquifer system was probably pio- neered by Hantush and Jacob (1955), Hantush (1964, 1967), and further developed by Neuman and Witherspoon (1969a,b), Bear (1972), Zlotnik and Zhan (2005), and many others. Petroleum engineers also have great interests in the subject because of the need to deal with oil migration across less permeable semi-confining layers (Streltsova, 1988). Most studies on this subject concern vertical pumping 0022-1694/$ - see front matter  c 2006 Elsevier B.V. All rights reserved. doi:10.1016/j.jhydrol.2006.01.010 * Corresponding author. Tel.: +1 979 862 7961; fax: +1 979 845 6162. E-mail address: zhan@geo.tamu.edu (H. Zhan). Journal of Hydrology (2006) 328, 659– 667 available at www.sciencedirect.com journal homepage: www.elsevier.com/locate/jhydrol