Inverse modeling to estimate LNAPL plume release timing

Abstract

Methodologies are presented for dating releases of light nonaqueous phase liquids (LNAPLs) using an inverse modeling approach with simple analytical models. Models for LNAPL plume migration are presented to predict LNAPL plume velocity in the unsaturated and saturated zones as a function of basic soil and fluid properties. A relative mobility factor is introduced for LNAPL movement at the water table that depends primarily on the van Genuchten n parameter (related to the breadth of the soil pore size distribution) and the magnitude of water table fluctuations. Estimated LNAPL plume velocities compare reasonably with more rigorous numerical models, which may be used in cases where data availability warrant the greater effort entailed. Two methods of estimating release timing and its uncertainty are investigated. A direct estimation method is described that determines travel time for a single observed travel distance based on estimated soil and fluid properties. Release date uncertainty may be determined using the first order (FO) or Monte Carlo (MC) methods. The second method for estimating release date involves nonlinear parameter estimation utilizing distance vs. time measurements and other data. A case study is presented for a field site where independent estimates of release timing were obtained from a numerical modeling analysis. Release timing estimates based on direct inversion of the analytical timing model agree well with the numerical analysis. Results for a second field site indicate that release date confidence limits estimated by the FO method, assuming log-normally distributed travel times, are close to values determined by the MC method, which makes no assumption regarding the form of the travel time probability distribution. Results for a hypothetical problem indicate that LNAPL velocity and travel time may be accurately estimated if sufficient data on travel distance vs. time are available. Incorporating prior information on relevant soil and fluid properties into the objective function reduces the uncertainty in release date if prior estimates are accurate. However, biased prior estimates may lead to over- or underestimation of release date uncertainty. Simultaneous estimation of soil and fluid properties and release date is possible if prior information is available to condition the parameter estimates.