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

Multiphase flow in porous media is important in a number of environmental and industrial applications such as soil remediation, CO2 sequestration, and enhanced oil recovery. Wetting properties control flow of immiscible fluids in porous media and fluids distribution in the pore space. In contrast to the strong and weak wet conditions, pore-scale physics of immiscible displacement under intermediate-wet conditions is less understood. This study reports the results of a series of two-dimensional high-resolution direct numerical simulations with the aim of understanding the pore-scale dynamics of two-phase immiscible fluid flow under intermediate-wet conditions. Our results show that for intermediate-wet porous media, pore geometry has a strong influence on interface dynamics, leading to co-existence of concave and convex interfaces. Intermediate wettability leads to various interfacial movements which are not identified under imbibition or drainage conditions. These pore-scale events significantly influence macro-scale flow behaviour causing the counter-intuitive decline in recovery of the defending fluid from weak imbibition to intermediate-wet conditions

Pore-network modelling of non-Darcy flow through heterogeneous porous media

A pore-network model (PNM) was developed to simulate non-Darcy flow through porous media. This paper investigates the impact of micro-scale heterogeneity of porous media on the inertial flow using pore-network modelling based on micro X-ray Computed Tomography (XCT) data. Laboratory experiments were carried out on a packed glass spheres sample at flow rates from 0.001 to 0.1 l/s. A pore-network was extracted from the 3D XCT scanned volume of the 50 mm diameter sample to verify the reliability of the model. The validated model was used to evaluate the role of micro-heterogeneity in natural rocks samples. The model was also used to investigate the effect of pore heterogeneity on the onset of the non-Darcy flow regime, and to estimate values of the Darcy permeability, Forchheimer coefficient and apparent permeability of the porous media. The numerical results show that the Reynold's number at which nonlinear flow occurs, is up to several orders of magnitude smaller for the heterogeneous porous domain in comparison with that for the homogeneous porous media. For the Estaillades carbonate rock sample, which has a high degree of heterogeneity, the resulting pressure distribution showed that the sample is composed of different zones, poorly connected to each other. The pressure values within each zone are nearly equal and this creates a number of stagnant zones within the sample and reduces the effective area for fluid flow. Consequently, the velocity distribution within the sample ranges from low, in stagnant zones, to high, at the connection between zones, where the inertial effects can be observed at a low pressure gradient

Trapping and hysteresis in two-phase flow in porous media: A pore-network study

Abstract: Several models for two-phase flow in porous media identify trapping and connectivity of fluids as an important contribution to macroscale hysteresis. This is especially true for hysteresis in relative permeabilities. The trapping models propose trajectories from the initial saturation to the end saturation in various ways and are often based on experiments or pore-network model results for the endpoints. However, experimental data or pore-scale model results are often not available for the trajectories, that is, the fate of the connectivity of the fluids while saturation changes. Here, using a quasi static pore-network model, supported by a set of pore-scale laboratory experiments, we study how the topology of the fluids changes during drainage and imbibition including first, main and scanning curves. We find a strong hysteretic behavior in the relationship between disconnected nonwetting fluid saturation and the wetting fluid saturation in a water-wet medium. The coalescence of the invading nonwetting phase with the existing disconnected nonwetting phase depends critically on the presence (or lack thereof) of connected nonwetting phase at the beginning of the drainage process as well as on the pore geometry. This dependence involves a mechanism we refer to as reversible corner filling. This mechanism can also be seen in laboratory experiments in volcanic tuff. The impact of these pore-network model results on existing macroscopic models is discussed.Keywords: hysteresis, trapping, two-phase flow, fluid topology, pore geometry, pore networ

Evaporation in capillary porous media at the perfect piston-like invasion limit: Evidence of non-local equilibrium effects

The classical continuum modeling of evaporation in capillary porous media is revisited from pore network simulations of the evaporation process. The computed moisture diffusivity is characterized by a minimum corresponding to the transition between liquid and vapor transport mechanisms confirming previous interpretations. Also the study suggests an explanation for the scattering generally observed in the moisture diffusivity obtained from experimental data. The pore network simulations indicate a noticeable nonlocal equilibrium effect leading to a new interpretation of the vapor pressure‐saturation relationship classically introduced to obtain the one‐equation continuum model of evaporation. The latter should not be understood as a desorption isotherm as classically considered but rather as a signature of a nonlocal equilibrium effect. The main outcome of this study is therefore that nonlocal equilibrium two‐equation model must be considered for improving the continuum modeling of evaporation

X-ray micro-tomography and pore network modeling of single-phase fixed-bed reactors.

A three-dimensional (3D) irregular and unstructured pore network was built using local topological and geometrical properties of an isometric bead pack imaged by means of a high-resolution X-ray computed micro-tomography technique. A pore network model was developed to analyze the 3D laminar/inertial(non-Darcy) flows at the mesoscopic (pore level) and macroscopic (after ensemble-averaging) levels. The non-linear laminar flow signatures were captured at the mesoscale on the basis of analogies with contraction and expansion friction losses. The model provided remarkably good predictions of macroscopic frictional loss gradient in Darcy and non-Darcy regimes with clear-cut demarcation using channel-based Reynolds number statistics. It was also able to differentiate contributions due to pore and channel linear losses, and contraction/expansion quadratic losses. Macroscopic mechanical dispersion was analyzed in terms of retroflow channels, and transverse and longitudinal Péclet numbers. The model qualitatively retrieved the Péclet-Reynolds scaling law expected for heterogeneous networks with predominance of mechanical dispersion. Advocated in watermark is the potential of pore network modeling to build a posteriori constitutive relations for the closures of the more conventional macroscopic Euler approaches to capture more realistically single-phase flow phenomena in fixed-bed reactor applications in chemical engineering

Pore-scale Modeling of Viscous Flow and Induced Forces in Dense Sphere Packings

We propose a method for effectively upscaling incompressible viscous flow in large random polydispersed sphere packings: the emphasis of this method is on the determination of the forces applied on the solid particles by the fluid. Pore bodies and their connections are defined locally through a regular Delaunay triangulation of the packings. Viscous flow equations are upscaled at the pore level, and approximated with a finite volume numerical scheme. We compare numerical simulations of the proposed method to detailed finite element (FEM) simulations of the Stokes equations for assemblies of 8 to 200 spheres. A good agreement is found both in terms of forces exerted on the solid particles and effective permeability coefficients

Water and Methane in Shale Rocks: Flow Pattern Effects on Fluid Transport and Pore Structure

Using molecular dynamics simulations we study the two-phase flow of water and methane through slit-shaped nano-pores carved from muscovite. The simulations are designed to investigate the effect of flow patterns on the fluids transport and on the pore structure. The results indicate that the Darcy’s law, which describes a linear relation between flow rate and pressure drop, can be violated when the flow pattern is altered. This can happen when the driving force, i.e., the pressure drop, increases above a pore-size dependent threshold. Because the system considered here contains two phases, when the fluid structure changes, the movement of methane with respect to that of water changes, leading to the violation of the Darcy’s law. Our results illustrate the importance of the capillary force, due to the formation of water bridges across the model pores, not only on the fluid flow, but also on the pore structure, in particular its width. When the water bridges are broken, perhaps because of fast fluid flow, the capillary force vanishes leading to significant pore expansion. Because muscovite is a model for illite, a clay often found in shale rocks, these results advance our understanding regarding the mechanism of water and gas transport in tight shale gas formations

Two-phase porous media flows with dynamic capillary effects and hysteresis: Uniqueness of weak solutions

In this paper, we obtain the uniqueness of weak solutions for a two phase flow model in a porous medium. A particularity of the model is that the dynamic effects and hysteresis are included in the capillary pressure. Keywords: Dynamic capillary pressure, two-phase flow, hysteresis, weak solution, uniqueness