Improved forward and inverse analyses of saturated‐unsaturated flow toward a well in a compressible unconfined aquifer

[1] We present an analytical solution for flow to a partially penetrating well in a compressible unconfined aquifer that allows inferring its saturated and unsaturated hydraulic properties from drawdowns recorded in the saturated and/or unsaturated zone. We improve upon a previous such solution due to Tartakovsky and Neuman (2007) by (1) adopting a more flexible representation of unsaturated zone constitutive properties and (2) allowing the unsaturated zone to have finite thickness. Both solutions account for horizontal as well as vertical flows throughout the system. We investigate the effects of unsaturated zone constitutive parameters and thickness on drawdowns in the saturated and unsaturated zones as functions of position and time; demonstrate the development of significant horizontal hydraulic gradients in the unsaturated zone in response to pumping; validate our solution against numerical simulations of drawdown in a synthetic aquifer having unsaturated properties described by the van Genuchten-Mualem constitutive model; use our solution to analyze drawdown data from a pumping test conducted by the U.S. Geological Survey at Cape Cod, Massachusetts; and compare our estimates of van Genuchten-Mualem parameters with laboratory values obtained for similar materials in the area.

[1]  R. H. Brooks,et al.  Hydraulic properties of porous media , 1963 .

[2]  R. Kachanoski,et al.  Suitability of Parametric Models to Describe the Hydraulic Properties of an Unsaturated Coarse Sand and Gravel , 1998 .

[3]  D. LeBlanc.  Sewage plume in a sand and gravel aquifer , 1982 .

[4]  A. Moench,et al.  Estimation of hydraulic parameters from an unconfined aquifer test conducted in a glacial outwash deposit, Cape Cod, Massachusetts , 2000 .

[5]  S. P. Neuman,et al.  Effect of partial penetration on flow in unconfined aquifers considering delayed gravity response , 1974 .

[6]  A. N. Stokes,et al.  An Improved Method for Numerical Inversion of Laplace Transforms , 1982 .

[7]  S. P. Neuman,et al.  Three‐dimensional saturated‐unsaturated flow with axial symmetry to a partially penetrating well in a compressible unconfined aquifer , 2007 .

[8]  S. P. Neuman.  Theory of flow in unconfined aquifers considering delayed response of the water table , 1972 .

[9]  M. S. Hantush.  Hydraulics of Wells , 1964 .

[10]  Y. Mualem.  A New Model for Predicting the Hydraulic Conductivity , 1976 .

[11]  A. Moench.  Importance of the Vadose Zone in Analyses of Unconfined Aquifer Tests , 2004, Ground water.

[12]  W. R. Gardner.  SOME STEADY‐STATE SOLUTIONS OF THE UNSATURATED MOISTURE FLOW EQUATION WITH APPLICATION TO EVAPORATION FROM A WATER TABLE , 1958 .

[13]  A. Polyanin,et al.  Handbook of Exact Solutions for Ordinary Differential Equations , 1995 .

[14]  C. V. Theis.  The relation between the lowering of the Piezometric surface and the rate and duration of discharge of a well using ground‐water storage , 1935 .

[15]  M. Schaap,et al.  ROSETTA: a computer program for estimating soil hydraulic parameters with hierarchical pedotransfer functions , 2001 .

[16]  S. P. Neuman,et al.  Determination of Aquitard/Aquiclude Hydraulic Properties from Arbitrary Water‐Level Fluctuations by Deconvolution , 1989 .

[17]  David Russo,et al.  Determining soil hydraulic properties by parameter estimation: On the selection of a model for the hydraulic properties , 1988 .

[18]  D. LeBlanc,et al.  Ground-water resources of Cape Cod, Massachusetts , 1986 .

[19]  A. Moench,et al.  Analytical and numerical analyses of an unconfined aquifer test considering unsaturated zone characteristics , 2008 .

[20]  Van Genuchten,et al.  A closed-form equation for predicting the hydraulic conductivity of unsaturated soils , 1980 .

[21]  S. Mathias,et al.  Linearized Richards' equation approach to pumping test analysis in compressible aquifers , 2006 .

[22]  Donald A. Walter,et al.  Hydrogeologic framework of western Cape Cod, Massachusetts , 1996 .

[23]  Kenny S. Crump,et al.  Numerical Inversion of Laplace Transforms Using a Fourier Series Approximation , 1976, J. ACM.

[24]  Timothy J Kneafsey,et al.  Correspondence of the Gardner and van Genuchten–Mualem relative permeability function parameters , 2007 .

[25]  Allen F. Moench,et al.  Flow to a well of finite diameter in a homogeneous, anisotropic water table aquifer , 1997 .

[26]  Irene A. Stegun,et al.  Handbook of Mathematical Functions. , 1966 .