Estimation of spatially variable residual nonaqueous phase liquid saturations in nonuniform flow fields using partitioning tracer data

Abstract

Estimates of spatially variable residual NAPL saturations SN are obtained in heterogeneous porous media using first temporal moments of breakthrough curves (BTCs) obtained from multilevel samplers during in situ partitioning tracer tests. An approach is adopted in which the distribution of the log NAPL/water volumetric ratio (Y = ln [SN/(1 − SN∥]) and log hydraulic conductivity (F = ln K) are treated as spatially correlated random fields. A nonlinear Gauss‐Newton search technique is used to identify the spatial distribution of Y that minimizes the weighted sum of the deviation of the temporal moment predictions from their measured values and the deviation of the estimate of Y from its prior estimate obtained from the temporal moments of extraction well BTCs. Sensitivities required for the algorithm are obtained using a coupled flow and transport adjoint sensitivity method. In addition to obtaining optimal estimates for the spatial distribution of Y, the method also provides the estimation error covariance. The estimation error covariance can be used to evaluate the information that may be obtained from alternate pumping and monitoring configurations for tracer tests designed to detect NAPL in the subsurface. To this end, we tested the method using two different NAPL distributions (one with a random spatially correlated field and a second that was a block of NAPL) and three different pumping configurations (a double five‐spot pattern, an inverted double five‐spot pattern, and a line‐drive pattern). The results show that measured temporal moments are more sensitive to Y in the double five‐spot and inverted double five‐spot patterns, and estimates produced in these configurations are slightly superior to those produced in the line‐drive pattern.