Stochastic delineation of well capture zones

Abstract

In this work, we describe a stochastic method for delineating well capture zones in randomly heterogeneous porous media. We use a moment equation (ME) approach to derive the time-dependent mean capture zones and their associated uncertainties. The mean capture zones are determined by reversely tracking the non-reactive particles released at a small circle around each pumping well. The uncertainty associated with the mean capture zones is calculated based on the particle displacement covariances for nonstationary flow fields. The flow statistics are obtained either by directly solving the flow moment equations derived with a first-order ME approach or from Monte Carlo simulations (MCS) of flow. The former constitutes a full ME approach, and the latter is a hybrid ME-MCS approach. This hybrid approach is invoked to examine the validity of the transport component of the stochastic method by ensuring that the ME and MC transport approaches have the same underlying flow statistics. We compared both the full ME and the hybrid ME-MCS results with those obtained with a full MCS approach. It has been found that the three approaches are in excellent agreement when the variability of hydrologic conductivity is small (r 2 Y ¼ 0:16). At a moderate variability (r 2 Y ¼ 0:5), the hybrid ME-MCS and the full MCS results are in excellent agreement whereas the results from the full ME approach deviate slightly from the full MCS results. This indicates that the (first-order) ME transport approach renders a good approximation at this level of variability and that the first-order ME flow approximation may not be sufficiently accurate at this variability in the case of divergent/convergent flow. The first-order ME flow approach may need to be corrected with higher-order terms even for moderate r 2 Y although the literature results reveal that the first-order ME flow approach is robust for uniform mean flow (i.e., giving accurate results even with r 2 Y as large as four).

Quantifying flow and remediation zone uncertainties for partially opened wells in heterogeneous aquifers

“…Recent applications of first-order methods have been extended to the determinations of stochastic well capture zones (e.g. Kunstmann and Kinzelbach, 2000;Stauffer et al, 2002Stauffer et al, , 2004Lu and Zhang, 2003;Zhang and Lu, 2004;Lessoff and Indelman, 2004;Bakr and Butler, 2005;Riva et al, 2006;Kunstmann and Kastens, 2006;Indelman et al, 2006). Most studies on the subject dealt with depth-averaged two-dimensional problems (Kunstmann and Kinzelbach, 2000;Stauffer et al, 2002Stauffer et al, , 2004Lu and Zhang, 2003;Zhang and Lu, 2004;Bakr and Butler, 2005;Riva et al, 2006;Kunstmann and Kastens, 2006).…”

Recent advances in modeling of well hydraulics

“…Some studies have devoted to the assessment of the uncertainty about the delineation of well capture zones in heterogeneous aquifers. The stochastic approach based on the Monte Carlo simulations is widely adopted for characterizing the uncertainty about the capture zone delineation [324][325][326][327]. Instead of Monte Carlo simulations, Esling et al [328] attempted to reduce the capture zone uncertainty based on a systematic sensitivity analysis.…”

Capture zone between two streams

“…Scientists have used stochastic methods to study capture zones in heterogeneous aquifers (e.g. Zhang and Lu, 2004).…”