A hierarchy of models for simulating experimental results from a 3D heterogeneous porous medium

Abstract

In this work we examine the dispersion of conservative tracers (bromide and fluorescein) in an experimentallyconstructed three-dimensional dual-porosity porous medium. The medium is highly heterogeneous (σ 2 Y = 5.7), and consists of spherical, low-hydraulic-conductivity inclusions embedded in a high-hydraulic-conductivity matrix. The bi-modal medium was saturated with tracers, and then flushed with tracer-free fluid while the effluent breakthrough curves were measured. The focus for this work is to examine a hierarchy of four models (in the absence of adjustable parameters) with decreasing complexity to assess their ability to accurately represent the measured breakthrough curves. The most information-rich model was (1) a direct numerical simulation of the system in which the geometry, boundary and initial conditions, and medium properties were fully independently characterized experimentally with high fidelity. The reduced models included; (2) a simplified numerical model identical to the fully-resolved direct numerical simulation (DNS) model, but using a domain that was one-tenth the size; (3) an upscaled mobile-immobile model that allowed for a time-dependent mass-transfer coefficient; and, (4) an upscaled mobile-immobile model that assumed a space-time constant mass-transfer coefficient. The results illustrated that all four models provided accurate representations of the experimental breakthrough curves as measured by global RMS error. The primary component of error induced in the upscaled models appeared to arise from the neglect of convection within the inclusions. We discuss the necessity to assign value (via a utility function or other similar method) to outcomes if one is to further select from among model options. Interestingly, these results suggested that the conventional convection-dispersion equation, when applied in a way that resolves the heterogeneities, yields models with high fidelity without requiring the imposition of a more complex non-Fickian model.

Measuring, imaging and modelling solute transport in a microporous limestone

“…c/c 0 ≈ 0.01%, as shown in Figure 8b. This concentration range is comparable, if not wider than values reported in the literature for BTCs measured experimentally [16,51]. While radiotracers provide a higher sensitivity to low concentrations as compared to conductivity measurements, other tracers (e.g., Uranine [52]) allow extending this range even further and resolving concentration tails at late times, which can appear in rocks containing microporosity [53].…”

3D non-conforming mesh model for flow in fractured porous media using Lagrange multipliers

“…However, flow through fractured rock formations is governed by 3D effects, as strong heterogeneities affect flow properties in the fracture and porousmedium domains [52,16,54,53]. To apply the Lagrange multiplier method to 3D fracture networks, the variational transfer between fractures and matrix for non-conforming methods needs to be implemented both accurately and with parallel processing capabilities.…”