1、翻译部分Effective Correlation of Apparent Gas Permeability in Tight Porous MediaFaruk CivanAbstract:Gaseous flow regimes through tight porous media are described by rigorous application of a unified HagenPoiseuille-type equation. Proper implementation is accom-plished based on the realization of the pre
2、ferential flow paths in porous media as a bundle of tortuous capillary tubes. Improved formulations and methodology presented here are shown to provide accurate and meaningful correlations of data considering the effect of the charac-teristic parameters of porous media including intrinsic permeabili
3、ty, porosity, and tortuosity on the apparent gas permeability, rarefaction coefficient, and Klinkenberg gas slippage factor.Keywords:Tight porous media Apparent gas permeability Rarefaction coefficient Klinkenberg gas slippage factor Tortuosity1 IntroductionDescription of various gaseous flow regime
4、s through tight porous media has drawn con-siderable attention because the convetional Darcys law cannot realistically describe the variety of the relevant flow regimes other than the viscous flow regime. For example, Javadpour et al. ( 2007) have determined that gas flow in shales deviates from beh
5、avior described by the conventional Ficks and Darcys laws. Therefore, many attempts have been made in describing the transfer of gas through tight porous media under various regimes. Such efforts are of utmost practical importance when dealing with extraction of hydro-carbon gases from unconventiona
6、l gas reservoirs, such as shale-gas and coal-bed methane reservoirs. Skjetne and Gudmundsson (1995), and Skjetne and Auriault (1999) theoretically investigated the wall-slip gas flow phenomenon in porous media based on the Navier-Stokes equation, but did not offer any correlation for the Klinkenberg
7、 effect. Wu et al. (1998)developed analytical procedures for determination of the Klinkenberg coefficient from laboratory and well tests, but did not provide any correlation. Having reviewed the vari-ous correlations available, Sampath and Keighin (1982) proposed an improved correlation for the Klin
8、kenberg coefficient of the N2 gas in the presence of water in porous media, expressed here in the consistent SI units aswhere bk is in Pa, K is in m2, and is in fraction. The significance of this correlation is that its exponent is very close to the 0.50 exponent value obtained by theoretical analys
9、is in this article.Beskok and Karniadakis (1999) developed a unified HagenPoiseuille-type equation covering the fundamental flow regimes in tight porous media, including continuum fluid flow, slip flow, transition flow, and free molecular flow conditions. Ability to describe all four flow regimes in
10、 one equation alone is an outstanding accomplishment. However, the empirical correlation of the available data of the dimensionless rarefaction coefficient is a mathe-matically complicated trigonometric function. As demonstrated in this article, much accu-rate correlation of the same data can be acc
11、omplished using a simple inverse-power-law function.Florence et al. ( 2007) made an attempt at utilizing the HagenPoiseuille-type equation of Beskok and Karniadakis ( 1999) to derive a general expression for the apparent gas perme-ability of tight porous media and correlated some essential parameter
12、s by means of exper-imental data, including the Klinkenberg gas slippage factor and the Knudsen number by ignoring the effect of tortuosity, although it is an important factor especially in tight porous media. Therefore, although their overall methodology is reasonable, their formulation and data an
13、alysis procedure require some critical improvements as pointed out in this article when attempting to apply the HagenPoiseuille-type equation, originally derived for pipe flow to tight-porous media flow. Their treatment neglects a number of important issues. The HagenPoiseuille-type equation of Besk
14、ok and Karniadakis ( 1999) has been derived for a single-pipe flow. When the bundle of tortuous tubes realization of the preferential flow paths in tight-porous media ( Carman 1956) is considered, the number and tortuosity of the pref-erential flow paths formed in porous media should be taken into a
15、ccount as the important parameters.Further, the approach taken by Florence et al. ( 2007) for correlation of the Klinkenberg gas slippage factor is not correct and consequently their correlation cannot represent the data over the full range of the gas molecular mass (commonly called weight). These e
16、rrors are corrected in this article by a rigorous approach which leads to a very accurate correlation of their data with a coefficient of regression almost equal to 1.0. In addition, the present analysis lends itself to a practical method by which tortuosity of tight porous media can be determined using the flow data obtained by conventional gas flow tests. To the authors knowledge, such a method does not presently exist in the literature
