Posterior Assessment of Parameters in a Time Domain Random Walk Model of Partitioning Tracer Tests in Two‐Phase Flow Scenarios

Abstract

AbstractWe provide a reliable and efficient methodological framework for the interpretation of laboratory‐scale partitioning tracer test data under uncertainty. The proposed approach rests on a Time domain random walk (TDRW) particle tracking methodology. The range of applicability of the latter is extended to include transport of partitioning tracers upon considering retardation and trapping mechanisms. A classical maximum likelihood (ML) approach is applied considering the extensive set of experimental observations of Dwarakanath et al. (1999, https://doi.org/10.1021/es990082v). This yields best estimates of model parameters, including residual immobile phase saturation, the partition coefficient and the parameters of the memory function employed to simulate the impact of solute trapping. Experimental observations of the partition coefficient are included in the objective function upon relying on a regularization term. We show that considering these types of information, which are typically obtained through batch experiments, is important to attain joint estimates of the partition coefficient and of residual immobile phase saturation. Sample probability distributions of model parameters conditional on available data are then assessed through a stochastic inverse modeling approach. This step poses a significant challenge in terms of computational effort and is performed through a reduced order surrogate model. Our results show that the TDRW‐based approach can effectively capture the key features of the observed breakthrough curves of the various partitioning tracers analyzed and provide satisfactory estimates of residual immobile phase saturation.