Modeling of Two-Phase Flow in Rough-Walled Fracture Using Level Set Method

Abstract

To describe accurately the flow characteristic of fracture scale displacements of immiscible fluids, an incompressible two-phase (crude oil and water) flow model incorporating interfacial forces and nonzero contact angles is developed. The roughness of the two-dimensional synthetic rough-walled fractures is controlled with different fractal dimension parameters. Described by the Navier-Stokes equations, the moving interface between crude oil and water is tracked using level set method. The method accounts for differences in densities and viscosities of crude oil and water and includes the effect of interfacial force. The wettability of the rough fracture wall is taken into account by defining the contact angle and slip length. The curve of the invasion pressure-water volume fraction is generated by modeling two-phase flow during a sudden drainage. The volume fraction of water restricted in the rough-walled fracture is calculated by integrating the water volume and dividing by the total cavity volume of the fracture while the two-phase flow is quasistatic. The effect of invasion pressure of crude oil, roughness of fracture wall, and wettability of the wall on two-phase flow in rough-walled fracture is evaluated.

Benchmarking NAPL Redirection and Matrix Entry at Fracture Intersections Below the Water Table

“…Water Resources Research (e.g., see recent summaries in Berre et al (2018) and Glaser et al (2017)) for networks. Other numerical methods, which incorporate inertial, viscous, and capillary effects more robustly, include pore network modeling (e.g., Jiang et al, 2017), the level-set method (e.g., Dai et al, 2017), or the numerical manifold method (e.g., Ma et al, 2017). However, these detailed techniques are limited to small numbers of fractures.…”

“…Numerical simulation of two‐phase flow in discrete “many fracture” networks, and discrete fracture‐matrix (DFM) domains has been accomplished for many years by finite volume, finite element, and hybrid schemes (e.g., see recent summaries in Berre et al () and Glaser et al ()) for networks. Other numerical methods, which incorporate inertial, viscous, and capillary effects more robustly, include pore network modeling (e.g., Jiang et al, ), the level‐set method (e.g., Dai et al, ), or the numerical manifold method (e.g., Ma et al, ). However, these detailed techniques are limited to small numbers of fractures.…”

Darcy model with optimized permeability distribution (DMOPD) approach for simulating two-phase flow in karst reservoirs

“…An another challenge that arises when modelling two-phase flows through open channels using the Stokes/Brinkman equation is to manage the interface between two phases as there is a sharp change between the density and viscosity of fluid on either side of the interface. Two main methods that are used to model the moving interface are the volume of fluid (VOF) method and the level-set method (Bilger et al 2017;Dai et al 2017;Olsson and Kreiss 2005). An additional auxiliary equation is required to track the interface.…”

Three‐Dimensional Numerical Modeling of Large‐Scale Free Surface Flows with Heat and Contaminant Transfer in Reservoirs

“…e flows with an obvious three-dimensional (3D) convection-diffusion mechanism shall be simulated by more promising 3D methods. Typically, 3D numerical methods for simulating LS-FS flows are mainly based on gas-liquid two-phase flow models [9], interface tracking models [10][11][12], and interface capturing models [13][14][15]. Nevertheless, the flow problems in the field of hydraulic projects are usually complicated because of the large-scale and complex boundary conditions, which not only results in a dramatic amount of computing resource consumption but also makes the stable and accurate simulation challengeable [16].…”