Stochastic analysis of concentration measurements in the transport experiment at Twin Lake Site

Abstract

A procedure to identify the parameters characterizing flow and transport in heterogeneous aquifers with the aid of concentration measurements in tracer field experiments is developed. Unlike previous studies, which employed the measured plume spatial moments at different times and their theoretical expressions, we rely here on breakthrough curves and temporal moments in order to analyze the field tests at Chalk River Site. In these experiments, breakthrough curves of a radioactive tracer were measured continuously at a large number of points in parallel control planes. We derive theoretical expressions of the temporal moments of the breakthrough curves by the same Lagrangian approach that was used previously for spatial moment. We assume a stationary random velocity field of constant mean and relate it to the axisymmetric log conductivity covariance by a first‐order approximation in the variance, with neglect of the effect of pore‐scale dispersion. The final theoretical results relate the temporal moments to U (the mean velocity), σY2 (the log conductivity variance), IYh (the horizontal integral scale), and b(e) (a function of the anisotropy ratio e=IYυ/IYh). By assuming ergodicity, we identify the temporal moments at the Chalk River Site experiment from measured breakthrough curves. With the aid of the theoretical results and by a best fit we could estimate U, σY2, IYh, and IYh/b(e). An attempt to identify the vertical and transverse integral scales from temporal‐spatial moments in the control planes was not successful. We took advantage of the dense measurements of breakthrough curves along vertical transects (at intervals of 1 cm) in order to identify the experimental concentration two‐point covariance. We derived a simplified theoretical expression for its dependence on the log conductivity vertical integral scale IYυ, which was identified by a best fit with experimental results. This procedure, applied for the first time to analysis of field tests, led to the identification of the estimates of σY2 and IYh, as well as of their variances of estimation.