Four sets of nonreactive solute transport experiments were conducted with micromodels. Each set consisted of three experiments with one variable, i.e., flow velocity, grain diameter, pore-aspect ratio, and flow-focusing heterogeneity. The data sets were offered to pore-scale modeling groups to test their numerical simulators. Each set consisted of two learning experiments, for which all results were made available, and one challenge experiment, for which only the experimental description and base input parameters were provided. The experimental results showed a nonlinear dependence of the transverse dispersion coefficient on the Peclet number, a negligible effect of the pore-aspect ratio on transverse mixing, and considerably enhanced mixing due to flow focusing. Five pore-scale models and one continuum-scale model were used to simulate the experiments. Of the pore-scale models, two used a pore-network (PN) method, two others are based on a lattice Boltzmann (LB) approach, and one used a computational fluid dynamics (CFD) technique. The learning experiments were used by the PN models to modify the standard perfect mixing approach in pore bodies into approaches to simulate the observed incomplete mixing. The LB and CFD models used the learning experiments to appropriately discretize the spatial grid representations. For the continuum modeling, the required dispersivity input values were estimated based on published nonlinear relations between transverse dispersion coefficients and Peclet number. Comparisons between experimental and numerical results for the four challenge experiments show that all pore-scale models were all able to satisfactorily simulate the experiments. The continuum model underestimated the required dispersivity values, resulting in reduced dispersion. The PN models were able to complete the simulations in a few minutes, whereas the direct models, which account for the micromodel geometry and underlying flow and transport physics, needed up to several days on supercomputers to resolve the more complex problems.
Yoon, Hongkyu; Lee, Jonghyun; Kitanidis, Peter K.; Werth, Charles J.; Valocchi, Albert J.
Characterizing subsurface properties is crucial for reliable and cost-effective groundwater supply management and contaminant remediation. With recent advances in sensor technology, large volumes of hydrogeophysical and geochemical data can be obtained to achieve high-resolution images of subsurface properties. However, characterization with such a large amount of information requires prohibitive computational costs associated with “big data” processing and numerous large-scale numerical simulations. To tackle such difficulties, the principal component geostatistical approach (PCGA) has been proposed as a “Jacobian-free” inversion method that requires much smaller forward simulation runs for each iteration than the number of unknown parameters and measurements needed in the traditional inversion methods. PCGA can be conveniently linked to any multiphysics simulation software with independent parallel executions. In this paper, we extend PCGA to handle a large number of measurements (e.g., 106 or more) by constructing a fast preconditioner whose computational cost scales linearly with the data size. For illustration, we characterize the heterogeneous hydraulic conductivity (K) distribution in a laboratory-scale 3-D sand box using about 6 million transient tracer concentration measurements obtained using magnetic resonance imaging. Since each individual observation has little information on the K distribution, the data were compressed by the zeroth temporal moment of breakthrough curves, which is equivalent to the mean travel time under the experimental setting. Only about 2000 forward simulations in total were required to obtain the best estimate with corresponding estimation uncertainty, and the estimated K field captured key patterns of the original packing design, showing the efficiency and effectiveness of the proposed method.