Steady Linear Gas Flow Through Porous Media
Authors: Dranchuk P.M. , Kolada L.J. 
Published: December 2007

American Institute of Mining, Metallurgical and Petroleum Engineers, Inc.

This paper was prepared for the 42nd Annual Fall Meeting of the Society of Petroleum Engineers of AIME, to be held in Houston, Tex., Oct. 1–4, 1967. Permission to copy is restricted to an abstract of not more than 300 words. Illustrations may not be copied. The abstract should contain conspicuous acknowledgment of where and by whom the paper is presented. Publication elsewhere after publication in the JOURNAL OF PETROLEUM TECHNOLOGY or the SOCIETY OF PETROLEUM ENGINEERS JOURNAL is usually granted upon request to the Editor of the appropriate journal provided agreement to give proper credit is made.

Discussion of this paper is invited. Three copies of any discussion should be sent to the Society of Petroleum Engineers office. Such discussion may be presented at the above meeting and, with the paper, may be considered for publication in one of the two SPE magazines.

In the field of core analysis, it is currently common practice to perform laboratory gas flow tests on a specimen to determine its permeability and inertial resistance coefficient. The interpretation procedure requires the use of Darcy's law, Forchheimer's equation and three graphical displays of the data. If properly employed, the procedure will yield the permeability, the visco-inertial resistance coefficient and Klinkenberg's parameter. Since this procedure is cumbersome and time consuming, simple alternatives are proposed for those who have access to a digital computer.

Specifically, the present work proposes the application of quasi-linearization to modified versions of the Forchheimer equation, which make allowance for slip at the gas-solid interface. These procedures permit the simultaneous estimation of the aforementioned three parameters. The techniques are demonstrated by means of application to a set of laboratory data.

Introduction

For some time now, the evaluation of permeability and visco-inertial resistance coefficients of cores has been effected through the plotting of laboratory gas flow data on Klinkenberg and visco-inertial flow plots respectively. Since both plots invariably exhibited appreciable departures from linearity, the application of this method of interpretation often resulted in large errors.

Recently, it has been demonstrated that in the case of the Klinkenberg plot, departures from linearity may be avoided, provided that the data used are confined to the viscous flow region. It has also been shown that, by modifying the Forchheimer equation to allow for molecular streaming, a modified visco-inertial flow plot may be made which indicates little if any departure from linearity. Although this modified interpretation technique has been found to yield good results it does require a large number of data points, a sufficient number of which must be in the viscous flow region to permit the accurate estimation of the Klinkenberg parameter b.

During the course of investigations currently underway at the U. of Alberta, an attempt was made to apply the above-mentioned modified interpretation technique to data taken by previous investigators.