This study presents a numerical first-order spectral model to quantify transient flow and remediation zone uncertainties for partially opened wells in heterogeneous aquifers. Taking advantages of spectral theories in solving unmodeled small-scale variability in hydraulic conductivity (K), the presented nonstationary spectral method (NSM) can efficiently estimate flow uncertainties, including hydraulic heads and Darcy velocities in r- and z-directions in a cylindrical coordinate system. The velocity uncertainties associated with the particle backward tracking algorithm are then used to estimate stochastic remediation zones for scenarios with partially opened well screens. In this study the flow and remediation zone uncertainties obtained by NSM were first compared with those obtained by Monte Carlo simulations (MCS). A layered aquifer with different geometric mean of K and screen locations was then illustrated with the developed NSM. To compare NSM flow and remediation zone uncertainties with those of MCS, three different small-scale K variances and correlation lengths were considered for illustration purpose. The MCS remediation zones for different degrees of heterogeneity were presented with the uncertainty clouds obtained by 200 equally likely MCS realizations. Results of simulations reveal that the first-order NSM solutions agree well with those of MCS for partially opened wells. The flow uncertainties obtained by using NSM and MCS show identically for aquifers with small In K variances and correlation lengths. Based on the test examples, the remediation zone uncertainties (bandwidths) are not sensitive to the changes of small-scale In K correlation lengths. However, the increases of remediation zone uncertainties (i.e. the uncertainty bandwidths) are significant with the increases of small-scale In K variances. The largest displacement uncertainties may have several meters of differences when the In K variances increase from 0.1 to 1.0. Such conclusions are also valid for the estimations of remediation zones in layered aquifers.