Time-related capture zones for radial flow in two dimensional randomly heterogeneous media

Abstract. We consider the effect of randomly heterogeneous hydraulic conductivity on the spatial location of time-related capture zones (isochrones) for a non-reactive tracer in the steady-state radial flow field due to a pumping well in a confined aquifer. A Monte Carlo (MC) procedure is used in conjunction with FFT-based spectral methods. The log hydraulic conductivity field is assumed to be Gaussian and stationary, with isotropic exponential correlation. Various degrees of domain heterogeneity are considered and stability and accuracy of the MC procedure is examined. The location of an isochrone becomes uncertain due to heterogeneity, and it is strongly influenced by hydraulic conductivity variance. The probability that a particle released at a point in the aquifer is pumped by the well within a given time is identified. We propose a new expression for the probabilistic spatial distribution of isochrones, which is formally similar to the analytical solution for a uniform medium and takes into account the effects of heterogeneity.

[1]  J. Bear,et al.  On the movement of water bodies injected into aquifers , 1965 .

[2]  Erik H. Vanmarcke,et al.  Random Fields: Analysis and Synthesis. , 1985 .

[3]  Alberto Guadagnini,et al.  Time‐Related Capture Zones for Contaminants in Randomly Heterogeneous Formations , 1999 .

[4]  L. Gelhar.  Stochastic Subsurface Hydrology , 1992 .

[5]  G. Dagan.  Flow and transport in porous formations , 1989 .

[6]  Yoram Rubin,et al.  Stochastic analysis of boundaries effects on head spatial variability in heterogeneous aquifers: 2. Impervious boundary , 1989 .

[7]  Alberto Guadagnini,et al.  Probabilistic estimation of well catchments in heterogeneous aquifers , 1996 .

[8]  John M. Shafer,et al.  Reverse Pathline Calculation of Time-Related Capture Zones in Nonuniform Flow , 1987 .

[9]  J. M. Shafer,et al.  Assessment of Uncertainty in Time‐Related Capture Zones Using Conditional Simulation of Hydraulic Conductivity , 1991 .

[10]  David N. Lerner,et al.  Well catchments and time‐of‐travel zones in aquifers with recharge , 1992 .

[11]  Stephen E. Silliman,et al.  Capture Zones for Passive Wells in Heterogeneous Unconfined Aquifers , 1997 .

[12]  William H. Press,et al.  The Art of Scientific Computing Second Edition , 1998 .

[13]  A. Rinaldo,et al.  Simulation of dispersion in heterogeneous porous formations: Statistics, first‐order theories, convergence of computations , 1992 .

[14]  G. Dagan,et al.  Stochastic analysis of boundaries effects on head spatial variability in heterogeneous aquifers: 1. Constant head boundary , 1988 .

[15]  Mark Bakker,et al.  Capture Zone Delineation in Two-Dimensional Groundwater Flow Models , 1996 .

[16]  Wolfgang Kinzelbach,et al.  Determination of groundwater catchment areas in two and three spatial dimensions , 1992 .

[17]  V. Zlotnik.  Effects of Anisotropy on the Capture Zone of a Partially Penetrating Well , 1997 .

[18]  Chin-Fu Tsang,et al.  CAPTURE-ZONE TYPE CURVES: A TOOL FOR AQUIFER CLEANUP , 1986 .