The Influence of an Immobile or Mobile Saturation Upon Non-Darcy Compressible Flow of Real Gases in Propped Fractures (includes associated papers 19901 and 21622 )

Abstract

The effects of immobile and mobile liquid saturations on the non-Darcy flow coefficient in propped fractures have been investigated. It was observed that an immobile liquid saturation of up to 20% PV can triple the non-Darcy flow coefficient and a small mobile liquid saturation will increase the non-Darcy flow coefficient by nearly an order of magnitude (over that of the dry case). The linear relationship between the logarithm of the non-Darcy flow coefficient and the logarithm of the proppant permeability for propped fractures, as proposed by Cooke, is shown to be invalid in the presence of an immobile or mobile liquid saturation. Constants are presented that can be used to obtain a more accurate approximation than has previously been available on the non-Darcy flow coefficient for single-phase flow in fractures propped with 10/20-and 20/40-mesh Ottawa sand. The experimental data obtained from this research are compared with those of others reported in the literature. Fig. 1-Slmulated hydraulic fracture. Nitrogen Sourc.

Two-Phase Inertial Flow in Homogeneous Porous Media: A Theoretical Derivation of a Macroscopic Model

“…These two tensors can be determined from the solution of periodic closure problems that are solved on a representative periodic unit cell of the porous medium. Several studies reported in the literature extend the Forchheimer equation to multiphase flow on an empirical basis and provide relationships for correlating non-Darcy flow coefficients under multiphasic conditions (Evans et al 1987;Evans and Evans 1988;Liu et al 1995). Similar models were also considered in nuclear safety applications (Buchlin and Stubos 1987;Lipinski 1980Lipinski , 1982.…”

Numerical Simulation of Two-Phase Inertial Flow in Heterogeneous Porous Media

“…In order to test Geertsma's proposition and to develop a general correlation for the non-Darcy flow coefficient, a large variety of single-and two-phase flow data were collected by these authors from various sources (Cornell and Katz 1953;Geertsma 1974;Evans et al 1987;Evans and Evans 1988;Whitney 1988) including studies on consolidated and unconsolidated porous media as well as an analysis of the effect of an immobile liquid saturation. On the basis of this, Liu et al (1995) proposed a more satisfactory correlation by including the tortuosity factor in the expression of the inertial coefficient given by…”

“…Empirical relationships correlating β α with porosity, effective permeability, and saturation were proposed in the literature (Geertsma 1974;Evans et al 1987;Evans and Evans 1988;Liu et al 1995).…”

Inertial Effects in Two-Phase Flow Through Fractures

“…So far, there is no correlation proposed in the literature. Other studies (Geertsma, 1974;Evans and Evans, 1986;Evans, Hudson and Greenlee, 1987;Martins, Milton-Taylor and Leung, 1990;Narayanaswamy, Sharma and Pope, 1998) attempted to find β G when the gas is flowing while the liquid remains immobile. The main correlation proposed in this case is the correlation of Geertsma (1974), where S is saturation and ε is porosity:…”