Two‐phase flow in a variable aperture fracture

Abstract

In this paper a dynamic two-dimensional two-phase flow model for a single variable aperture fracture is developed. The model is based on a finite volume implementation of the cubic law and the conservation of mass for each liquid. The two-phase fracture flow system is represented by incompressible parallel plate flow within two-dimensional subregions of constant aperture. The fluid phase distribution is represented by an explicit definition of the phase presence at each location within the domain. To achieve this definition, a phase distribution is assigned to each fracture subregion. Knowledge of the phase distribution allows calculation of interface capillary pressure based on the fracture aperture. One-dimensional analytic solutions for two-phase flow are developed and used to verify the model's behavior in one dimension. The model is verified against the Sandia Waste-Isolation Flow and Transport III model for the case of two-dimensional single-phase flow. Two-dimensional two-phase flow verification is performed qualitatively because no suitable analytic or physical model is currently available. Two-dimensional flow phenomena are investigated for variable aperture fractures generated using geostatistical methods. Results from these simulations illustrate the flow processes of phase isolation, pinching off of nonwetting phase globules, nonwetting phase refusal at the edges of tight regions, and downslope migration of a fluid countercurrent to flow of a less dense fluid.

Experimental study of turbulent unconfined groundwater flow in a single fracture

“…That is because the rapid flow in the natural fractures makes it difficult to maintain a relatively large hydraulic gradient over a sustainable period of time except in circumstances such as near a fault, or a pumping well, or a dam, etc. This is probably one of the reasons why laminar flow is assumed in many previous studies (Snow, 1969;Neuzil and Tracy, 1981;Murphy and Thomson, 1993;Lapcevic et al, 1999). Under certain field conditions such as flow near a well, or a dam, the flow velocity could be high enough to justify the use of the non-Darcian relationship.…”

“…In the past several decades, numerous studies have provided significant insights into the hydrodynamics of flow in fractured media (Snow, 1969;Neuzil and Tracy, 1981;Long, 1982;Huyakorn et al, 1983;Tsang and Tsang, 1987;Moreno et al, 1988;Murphy and Thomson, 1993;Lapcevic et al, 1999). A general consensus of those studies is that realistic quantification of groundwater movement in fractured media is complicated by the uncertainty of characterizing fracture properties (Raven et al, 1988;Silliman, 1989;Durham and Bonner, 1994;Keller et al, 1995;Novakowski et al, 1995;Berkowitz et al, 2001).…”

Effective transmissivity of two-dimensional fracture networks

“…The conductance Ci of the ith individual fracture segment depends on geometrical features such as the mean aperture, the fracture wall roughness, the amount of contact area of the two rock faces, and the length of the segment [6-91. If the rock is only partially saturated, the conductance will also depend on the degree of liquid saturation [10,11]. In the present work, we consider only the problem of estimating the macroscopic conductivity of a network of fractures, assuming that the individual fracture segment conductances are known.…”

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

“…An active capillary pressure between the wetting and nonwetting phases was developed to simulate two-phase flow in rough-walled rock fractures, from which the relative permeability for the lognormal aperture distribution was calculated [5]. Based on a finite volume implementation of the cubic law and the conservation of mass, a conceptual model of two phases in a single fracture was developed, and the results of simulations were compared with a one-dimensional analytic solution [6]. A composition simulator based on Darcy's law and Brooks-Corey functional relationship was used to simulate the migration of dense NAPLs through a single fracture in a clay aquitard and to evaluate the effect of fracture aperture [7,8].…”