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On the upscaling of mass transfer rate expressions for interpretation of source zone partitioning tracer tests

Analysis of partitioning tracer tests conducted in dense nonaqueous phase liquid (DNAPL) source zones relies on conceptual models that describe mass exchange between the DNAPL and aqueous phases. Such analysis, however, is complicated by the complex distribution of entrapped DNAPL mass and formation heterogeneity. Due to parameter uncertainty in heterogeneous regions and the desire to reduce model complexity, the effect of mass transfer limitations is often neglected, and an equilibrium‐based model is typically used to interpret test results. This work explores the consequences of that simplifying assumption on test data interpretation and develops an alternative upscaled modeling approach to quantify effective mass transfer rates. To this end, a series of partitioning tracer tests is numerically simulated in heterogeneous two‐dimensional PCE‐DNAPL source zones, representative of a range of hydraulic conductivity and DNAPL mass distribution characteristics. The effective mass transfer coefficient corresponding to each test is determined by fitting an upscaled model to the simulated data, and regression analysis is performed to explore the correlation between various source zone metrics and the effective mass transfer coefficient. Results suggest that vertical DNAPL spreading, Reynolds number, pool fraction, and the effective organic phase saturation are the most significant parameters controlling tracer partitioning rates. Finally, a correlation for prediction of the effective (upscaled) mass transfer coefficient is proposed and verified using existing experimental data. The developed upscaled model incorporates the influence of physical heterogeneity on the rate of tracer partitioning and, thus, can be used for the estimation of source zone mass distribution characteristics from tracer test results.