Drainage in Open Rough-walled Fractures – Comparison of experimental and numerical results

Displacement of a wetting by a non-wetting fluid in fractured media is a process with relevance for many applications, such as fluid storage in the subsurface or oil and gas exploitation. How to capture the flow in open rough-walled fractures on the large length scales required for such applications is an open question. It is highly questionable if the two-phase flow equations can be simplified to continuum approaches, such as established for porous media, which would allow for coarse spatial resolutions of a model. For this reason, it is necessary to develop a good understanding of how flow regimes and fracture geometry influence the properties of the fluid distributions during a displacement process that determine the macroscopic behavior. Such properties are, for example, fluid that is immobilized behind the displacement front. While there has been extensive investigation of this question in the context of porous media, studies on rough fractures are relatively scarce.

It is well established that in horizontal settings, the displacement is governed by capillary and viscous forces, resulting in the emergence of various displacement patterns (compact, viscous fingering or capillary fingering). Numerical simulations of the flow process could be helpful to relate the flow conditions and geometrical properties of the aperture field to characteristics of fluid distributions. However, such numerical simulations are not straight forward, as capturing the fluid-fluid surfaces and contact lines requires very fine grids and poor representations of the interfaces can cause large numerical errors. It is thus crucial to validate numerical models with well controlled experiments. As it is necessary to have well controlled conditions for boundary conditions and precise knowledge of the geometrical properties of the fracture aperture, such experiments are challenging.

In this contribution, we compare numerical results to recent results from experiments carried out in a setup featuring a fracture flow cell with self-affine rough walled surfaces and a precisely controlled mean aperture. Different viscosity ratios are obtained by altering the viscosities of both the displacing and the displaced fluids and different capillary numbers are obtained by varying the flow rate imposed through the cell. We compare the experimental findings to Direct Numerical Simulation (DNS) results obtained by solving the Navier–Stokes equations within the fracture pore space, employing the Volume of Fluid (VOF) method to track the evolution of the fluid-fluid interface.  We systematically confront the numerical predictions to the experimental results, in terms of various morphological properties of the displacement patterns such as Euler number, cluster size distribution, interfacial length, typical finger width, trapped cluster size distributions or fluid-fluid interface length. From this we infer a range of capillary numbers and viscosity ratios for which the numerical model can be validated as properly predicting the experiments.