Stochastic determination of well capture zones

Abstract

Abstract. A stochastic approach is adopted for characterizing the uncertainty in well capture zones in heterogeneous formations. Transmissivity is modeled as a random space function and a Monte Carlo approach is used to infer the probability distribution of the resulting stochastic capture zones. Through several numerical experiments, the influence of the statistical parameters of transmissivity variation on the extent of uncertainty in the location of the capture zone is investigated. Two aquifer models are considered: a fully confined aquifer and a leaky-confined aquifer receiving recharge from above. A connection is made with previous work on transport theory, and the statistical parameters of the capture zone probability distribution are compared with those of a solute concentration plume.

On macrodispersion in uniform ? radial divergent flow through weakly heterogeneous aquifers

“…Bear and Jacobs, 1965;Lerner, 1992;Kinzelbach et al, 1992;van Kooten, 1995;van Herwaarden, 1994) or with numerical modeling of two-dimensional transport in formations of random transmissivity (e.g. Bair et al 1991;Varljen and Shafer, 1991;Franzetti and Guadagnini, 1996;Cole and Silliman, 1997;Vassolo et al 1998;van Leewen, 1998;Gaudagnini and Franzetti 1999;Feyen et al 2001). In the paper we consider formations of three-dimensional random conductivity and analyze the properties of the solute spread in protection zones by deriving the variance of the particle trajectory.…”

Final Report to the Subsurface Science Program - Impact of Measurement Instrument and Conceptual Model on Analysis of Subsurface Heterogeneity

“…The first invovles ; I trade-off between factors of safety and risk. As noted previously (van Leeuwen et al 1998;Bair et al 1991;, it may be possible to place confidence bounds on the capture zone (e.& a capture zone boundary that has a 10% or 50% probability of being violated). As shown in , the width of these capture zones tends to increase rapidly as one decreases the level of acceptable risk.…”

A Quantitative Groundwater Resource Management under Uncertainty Using a Retrospective Optimization Framework

“…The typical number of realizations range between a few tens and thousands, meaning more computer time, and hence high expenses [3]. For instance, van Leeuwen et al [24] used 1000 realizations; Wagner et al [25] used 100 realizations; while Wagner and Gorelick [26], Wagner et al [27], Ndambuki et al [14], and Ndambuki [3] used a total of 30 realizations. In this example, a total of 30 realizations of uncertain hydraulic conductivity fields (which leads to different aquifer water system responses (i.e., hydraulic heads/water table level drawdowns)) were generated for the heterogeneous aquifer system.…”