Advances in Water Resources 83 (2015) 89–101 Contents lists available at ScienceDirect Advances in Water Resources journal homepage: www.elsevier.com/locate/advwatres Semi-analytical solutions for flow to a well in an unconfined-fractured aquifer system Mohammad M Sedghi a , Nozar Samani b,∗ a Department of Geology, Payame Noor University, Tehran 19395-3697, Iran b Department of Earth Sciences, Shiraz University, Shiraz 71454, Iran article info Article history: Received 23 January 2015 Revised 20 May 2015 Accepted 20 May 2015 Keywords: Unconfined aquifer Fractured double porosity aquifer Leakage Laplace–Hankel transforms Numerical inversion abstract Semi-analytical solutions of flow to a well in an unconfined single porosity aquifer underlain by a fractured double porosity aquifer, both of infinite radial extent, are obtained. The upper aquifer is pumped at a con- stant rate from a pumping well of infinitesimal radius. The solutions are obtained via Laplace and Hankel transforms and are then numerically inverted to time domain solutions using the de Hoog et al. algorithm and Gaussian quadrature. The results are presented in the form of dimensionless type curves. The solution takes into account the effects of pumping well partial penetration, water table with instantaneous drainage, leakage with storage in the lower aquifer into the upper aquifer, and storativity and hydraulic conductivity of both fractures and matrix blocks. Both spheres and slab-shaped matrix blocks are considered. The effects of the underlying fractured aquifer hydraulic parameters on the dimensionless drawdown produced by the pumping well in the overlying unconfined aquifer are examined. The presented solution can be used to es- timate hydraulic parameters of the unconfined and the underlying fractured aquifer by type curve matching techniques or with automated optimization algorithms. Errors arising from ignoring the underlying fractured aquifer in the drawdown distribution in the unconfined aquifer are also investigated. © 2015 Elsevier Ltd. All rights reserved. 1. Introduction The interpretation of the time-drawdown data recorded during a pumping test has long been used to estimate aquifer hydraulic pa- rameters. To obtain accurate results an appropriate analytical model must be used. Theis [33] published the first transient well-test solu- tion for confined aquifers. Leakage from the overlying aquitard with- out storage was considered in the solution presented by Hantush and Jacob [7]. Elastic storage in the aquitard was considered in the Hantush [9] solution. In both the Hantush and Jacob [7] and Han- tush [9] solutions leakage is imposed to the whole aquifer thickness and the aquitard transmits water from a constant head source to the main aquifer. Hantush [8] considered two aquifers separated by an aquitard. He neglected horizontal flow and elastic storage in the aquitard and vertical flow in both aquifers. Neuman and Witherspoon [24] considered the same aquifer system configuration as in Hantush [8] taking into account the elastic storage in the aquitard. Moench [20] obtained a two-dimensional Laplace domain solution for flow to a fully penetrating well in an aquifer bounded between two aquitards with storage. In some analytical solutions (e. g. Hunt [11] and Sun and ∗ Corresponding author. Tel/fax.: +98 711 2284572. E-mail address: samani@susc.ac.ir, samanin@shirazu.ac.ir (N. Samani). Zhan [32]) leakage enters the main aquifer through its top boundary that is more realistic but a constant head source over the aquitard is assumed. Malama et al. [14] presented a semi-analytical solution for drawdown in leaky unconfined aquifer-aquitard systems. The uncon- fined aquifer is pumped by a fully penetrating well and is measured in a partially or fully penetrating observation well. The aquitard is bounded below by an impermeable boundary. Thus, the only source of leakage is the stored water in the aquitard. Theoretical results of the Malama et al. [14] solution show that leakage can cause signifi- cant departure, at both early and late times from the solution with no leakage. The semi-analytical solution for flow in a system con- sisting of unconfined and confined aquifers, separated by an aquitard was presented by Malama et al. [13]. The result of Malama et al. [13] shows low sensitivity to changes in radial hydraulic conductivity for the aquitard that is two or more orders of magnitude smaller than that of the aquifer, confirming the findings of Neuman and Wither- spoon [24]. Malama et al. [13,14] used the instantaneous drainage model of Neuman [23,25] to simulate the water table drainage. Grad- ual release of water from the unsaturated zone was considered by Moench [19]. Moench [21] used Laplace and Fourier cosine trans- forms to obtain an analytical solution for flow to a well in an uncon- fined aquifer considering both instantaneous and gradual release of water from the unsaturated zone. Sepulveda [29] obtained a three- dimensional analytical solution for flow in an aquifer bounded at http://dx.doi.org/10.1016/j.advwatres.2015.05.018 0309-1708/© 2015 Elsevier Ltd. All rights reserved.