Challenges in modeling unstable two‐phase flow experiments in porous micromodels

Abstract

The simulation of unstable invasion patterns in porous media flow is very challenging because small perturbations are amplified, so that slight differences in geometry or initial conditions result in significantly different invasion structures at later times. We present a detailed comparison of pore-scale simulations and experiments for unstable primary drainage in porous micromodels. The porous media consist of HeleShaw cells containing cylindrical obstacles. By means of soft lithography, we have constructed two experimental flow cells, with different degrees of heterogeneity in the grain size distribution. As the defending (wetting) fluid is the most viscous, the interface is destabilized by viscous forces, which promote the formation of preferential flow paths in the form of a branched finger structure. We model the experiments by solving the NavierStokes equations for mass and momentum conservation in the discretized pore space and employ the Volume of Fluid (VOF) method to track the evolution of the interface. We test different numerical models (a 2-D vertical integrated model and a full-3-D model) and different initial conditions, studying their impact on the simulated spatial distributions of the fluid phases. To assess the ability of the numerical model to reproduce unstable displacement, we compare several statistical and deterministic indicators. We demonstrate the impact of three main sources of error: (i) the uncertainty on the pore space geometry, (ii) the fact that the initial phase configuration cannot be known with an arbitrarily small accuracy, and (iii) three-dimensional effects. Although the unstable nature of the flow regime leads to different invasion structures due to small discrepancies between the experimental setup and the numerical model, a pore-by-pore comparison shows an overall satisfactory match between simulations and experiments. Moreover, all statistical indicators used to characterize the invasion structures are in excellent agreement. This validates the modeling approach, which can be used to complement experimental observations with information about quantities that are difficult or impossible to measure, such as the pressure and velocity fields in the two fluid phases.

New insights on the complex dynamics of two-phase flow in porous media under intermediate-wet conditions

“…The final arrangement of these elements was almost unstructured, near the grain surface it was split-hexahedrals and hexahedrals elsewhere 16 . The meshing algorithm employed in this research has been successfully used by Ferrari et al .…”

Validation of model predictions of pore-scale fluid distributions during two-phase flow

“…Systematic studies of whether an image-based model of a rock captures the appropriate physics or merely suffers from uncertainties on the experimental input properties are lacking, due to the complexity of extracting comprehensive information from such a comparison. Valuable progress has been made to provide pore-scale validation with micromodels [23,[28][29][30], yet these simple two-dimensional pore structures do not capture the three-dimensional structural complexity of natural rocks.…”

“…In this experiment, the repeated flooding sequences were all performed on the same sample, and so there is no variability due to using different cores of the same rock type. However, two-phase flow is very sensitive to perturbations in the boundary conditions [28,54]. Also, small differences in the initial saturations for imbibition at the end of drainage may have led to discrepancies in the observed fluid distributions.…”

Pore-scale modeling of phase change in porous media

“…Popular approaches for the direct simulation of immiscible flow in the pore space inferred from three-dimensional images include the lattice Boltzmann method [5][6][7][8][9][10], the volume-of-fluid method [11][12][13][14][15], which solves the Navier-Stokes equations together with a relatively straightforward advection and reconstruction of fluid-fluid interfaces, and the level set method [16][17][18]. Porescale modeling based on diffuse-interface, or phase-field, modeling is emerging as a promising alternative to traditional approaches.…”