Benchmarking numerical codes for tracer transport with the aid of laboratory-scale experiments in 2D heterogeneous porous media

Abstract

We present a combined experimental and numerical modeling study that addresses two principal questions: (i) is any particular Eulerian-based method used to solve the classical advection-dispersion equation (ADE) clearly superior (relative to the others), in terms of yielding solutions that reproduce BTCs of the kind that are typically sampled at the outlet of a laboratory cell? and (ii) in the presence of matches of comparable quality against such BTCs, do any of these methods render different (or similar) numerical BTCs at locations within the domain? To address these questions, we obtained measurements from carefully controlled laboratory experiments, and employ them as a reference against which numerical results are benchmarked and compared. The experiments measure solute transport breakthrough curves (BTCs) through a square domain containing various configurations of coarse, medium, and fine quartz sand. The approaches to solve the ADE involve Eulerian-Lagrangian and Eulerian (finite volume, finite elements, mixed and discontinuous finite elements) numerical methods. Model calibration is not examined; permeability and porosity of each sand were determined previously through separate, standard laboratory tests, while dispersivities are assigned values proportional to mean grain size. We find that the spatial discretization of the flow field is of critical importance, due to the non-uniformity of the domain. Although simulated BTCs at the system outlet are observed to be very similar for these various numerical methods, computed local (point-wise, inside the domain) BTCs can be very different. We find that none of the numerical methods is able to fully reproduce the measured BTCs. The impact of model parameter uncertainty on the calculated BTCs is characterized through a set of numerical Monte Carlo simulations; in cases where the impact is significant, assessment of simulation matches to the experimental data can be ambiguous.

Porous Medium Typology Influence on the Scaling Laws of Confined Aquifer Characteristic Parameters

“…Although these configurations can be defined as homogeneous, as highlighted previously, an evident heterogeneity remains in the aquifer due to the different dimensions and shape of the grains, their arrangement within the porous medium and, consequently, the different interconnections of the voids, as well as to the variation of tortuosity. Especially in field investigations but also in laboratory models if there are doubts about the homogeneity of the porous medium and to better investigate some particular aspects, such as the interconnection of the pore voids, the carrying out of tracer tests and geophysical tests can be very useful [41][42][43]. The hydraulic conductivity values thus obtained are shown in Table 3, for each configuration and for all the values of the injection volume considered; Table 3 also reports the corresponding radius of influence values determined experimentally during the tests.…”

HESS Opinions: Chemical transport modeling in subsurface hydrological systems – Space, time, and the holy grail of “upscaling”

“…Subsequent flow cell experiments demonstrated, for example, that the dispersivity constants are not actually constant, and change with length scaleeven over a tens of centimetersto achieve even approximate fits to the measurements (e.g., Silliman and Simpson, 1987). Moreover, solutions of the ADE appear inadequate when compared to transport in laboratory flow cells with distinct regions of different hydraulic conductivities (e.g., Maina et al, 2018). In a sense, then, it can be considered somewhat surprising that this form of the ADE was subsequently assumed to apply, over several decades, in a rather sweeping fashion for a wide range of hydrogeological scenarios and length scales.…”

Numerical Benchmark Studies on Flow and Solute Transport in Geological Reservoirs

“…They illustrate the accuracy of the numerical simulators for single-phase flow in porous or fractured porous media by comparing established analytical solutions. Most of the software user manuals or reference books (e.g., [2,3]) include such examples of benchmark problems demonstrating solution accuracy or as an independent study to simulated breakthrough concentration (BTCs) at the outlet in column or lab scale porous media (e.g., [8,9]). Further, some developers present and document user experiences on their web pages or newsletters.…”

“…Konikow [11] described that solute transport at different flow boundaries significantly varies depending on the software and methods used. Although many codes have a long history of application in field problems, revealed good agreement with the field data might not necessarily imply numerical solution efficiency [12] and may fail to converge in basic transport simulation (e.g., [9]). Further aspects, such as financial costs (e.g., purchasing licenses), should also be considered, making it even more difficult for the user to decide on the numerical simulator for a particular problem.…”