Modeling Fluid Flow Through Single Fractures Using Experimental, Stochastic and Simulation Approaches

Abstract

A fracture is usually assumed as a set of smooth parallel plates separated by a constant width. However, the flow characteristics of an actual fracture surface would be quite different, affected by tortuosity and the impact of surface roughness. Though several researchers have discussed the effect of friction on flow, their efforts lack corroboration from experimental data and have not converged to form a unified methodology for studying flow on a rough fracture surface. In this study, we have shown an integrated methodology, involving experiments, stochastics and numerical simulations that incorporate the fracture roughness and the friction factor, to describe flow on a rough fracture surface. Laboratory experiments were performed to support the study and the flow contributions from the matrix and the fracture were matched through modified cubic law. Observations suggest that the fracture apertures need to be distributed to accurately model the experimental results. The methodology successfully modeled fractured core experiments, which were earlier not possible through parallel plate approach. A gravity drainage experiment using an X-ray CT scan of a fractured core has also validated the methodology. Introduction The search for hydrocarbons has been expanded into harder-to-evaluate formations, where potential and profitable hydrocarbon reserves are located. The prime candidate among those is the naturally fractured reservoirs, where large quantities of reserves are still left unexplored because of the complexities associated with a fractured reservoirs. Understanding the fluid flow characteristics of fractures is very important to model flow through fractures. This requires basic knowledge of flow from core studies. This research is aimed at studying fluid flow though a single fracture from simple core experiments and provide an effective methodology to simulate the flow behavior. Previous Research Efforts Early investigators based their idea that a parallel plate concept would be utilized to understand the concept of fluid flow through fractures. The first comprehensive work on flow through open fractures was by Lomize1. He used parallel glass plates and demonstrated the validity of the cubic law as long as the flow was laminar. He introduced the concept of defining the impact of surface roughness based on empirical data. Later he developed a flow regime chart that takes into account the effects of roughness and turbulent flow in open fractures. It was Snow 2 who used this concept to simulate real fractures. Iwai 1 conducted a comprehensive study of fluid flow through a single fracture and investigated the validity of the cubic law of fluid flow through a single natural fracture. One of the important features of his experiments was that the fracture planes had contact area as well as roughness.

Simulating stress-dependent fluid flow in a fractured core sample using real-time X-ray CT data

“…Similar, but more simplified, deformation procedures were performed for statistically derived aperture distributions (Pyrak-Nolte and Morris, 2000), profilometer measurements (Kim et al, 2003), laser-scan data (Nemoto et al, 2009;Watanabe et al, 2008Watanabe et al, , 2009) and a conceptual 2-D model (Liu et al, 2010). Furthermore, Dicman et al (2004) described changes in aperture distribution by combining laboratory data and stochastic approaches. Considering this study and further information provided in Table 1, most of the used fracture geometries can be assumed to be not directly correlated to the actual fracture geometries under loading conditions used for validation.…”

A new friction factor correlation for laminar, single-phase flows through rock fractures

“…An extensive review of flow though fractured media was reported by Berkowitz (2002). More recently, Oron and Berkowitz (1998), Dicman et al (2004) and Muralidharan et al (2004) studied flows through rough fractures. Lespinasse and Sausse (2000) studied the fluid flow in realistic fractures using a finite difference formulation.…”

A Well Performance Analysis about Vertically Fractured Well with a Non-Uniform Conductivity Hydraulic Fracture in Tight Sandstone Gas Reservoirs Based on Discrete Fracture-Matrix model

“…We use the Probability density function of lognormal distribution that is expressed by the following equation [24][25][26] , and the relevant functions are shown in the below:…”