Challenges in modeling unstable two-phase flow experiments in porous micromodels
Résumé
The simulation of unstable invasion patterns in porous media flow is challenging since small perturbations tend to grow in time, so that slight differences in geometry or initial conditions potentially give rise to significantly different solutions. Here we present a detailed comparison of pore scale simulations and experiments of unstable primary drainage in porous micromodels. The porous medium consists of a Hele-Shaw cell containing cylindrical obstacles. Two experimental flow cells have been constructed by soft lithography, with different degrees of heterogeneity in the grain size distribution. To model two-phase flow at the pore scale, we solve Navier-Stokes 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. During drainage, if the defending fluid is the most viscous, viscous forces destabilize the interface, giving rise to the formation of preferential flow paths, in the form of a branched fingering structure. We test different numerical models (a 2D vertical integrated model and a full 3D model) and different initial conditions, studying their impact on the simulated spatial distributions of the fluid phases. Although due to the unstable nature of the invasion, small discrepancies between the experimental setup and the numerical model can result in different fluids patterns (see figure), simulations show a satisfactory agreement with the structures observed experimentally. To estimate the ability of the numerical approach to reproduce unstable displacement, we compare several quantities in both the statistical and deterministic sense. We demonstrate the impact of three main sources of uncertainty : i) the uncertainty on the pore space geometry, ii) the interface initialization and ii) three dimensional effects [1]. Simulations in weakly heterogeneous geometries are found to be more challenging because uncertainties on pore neck widths are on the same order of magnitude as the pore to pore variability of those widths.[1] A. Ferrari, J. Jimenez-Martinez ,T. Le Borgne , Y. Méheust, and I. Lunati (2014), Challenges in modeling unstable two-phase flow experiments in porous micromodels, submitted.