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

摘要

This study presents a numerical first-order spectral model to quantifytransient flow and remediation zone uncertainties for partially opened wellsin heterogeneous aquifers. Taking advantages of spectral theories in solvingunmodeled small-scale variability in hydraulic conductivity (K), thepresented nonstationary spectral method (NSM) can efficiently estimate flowuncertainties, including hydraulic heads and Darcy velocities in r- andz-directions in a cylindrical coordinate system. The velocity uncertaintiesassociated with the particle backward tracking algorithm are then used toestimate stochastic remediation zones for scenarios with partially openedwell screens. In this study the flow and remediation zone uncertaintiesobtained by NSM were first compared with those obtained by Monte Carlosimulations (MCS). A layered aquifer with different geometric mean of K andscreen locations was then illustrated with the developed NSM. To compare NSMflow and remediation zone uncertainties with those of MCS, three differentsmall-scale K variances and correlation lengths were considered forillustration purpose. The MCS remediation zones for different degrees ofheterogeneity were presented with the uncertainty clouds obtained by 200equally likely MCS realizations. Results of simulations reveal that thefirst-order NSM solutions agree well with those of MCS for partially openedwells. The flow uncertainties obtained by using NSM and MCS show identicallyfor aquifers with small ln K variances and correlation lengths. Based on thetest examples, the remediation zone uncertainties (bandwidths) are notsensitive to the changes of small-scale ln K correlation lengths. However,the increases of remediation zone uncertainties (i.e. the uncertaintybandwidths) are significant with the increases of small-scale ln K variances.The largest displacement uncertainties may have several meters ofdifferences when the ln K variances increase from 0.1 to 1.0. Suchconclusions are also valid for the estimations of remediation zones inlayered aquifers.