The Unsteady-State Gas Permeameter
Authors: Ruth D.W. , Kenny J. 
Published: March 2010

Abstract
This paper presents a numerical simulator-based analysis of the performance of an unsteady-state gas permeameter. The influence of both slippage and inertial effects on the response of the instrument are calculated, and discussed in the context of experimental errors. It is shown that, for certain permeability ranges, it is difficult if not impossible to measure Klinkenberg and/or Forchheimer coefficients. When measuring these parameters, it is essential to determine that the Klinkenberg and/or Reynolds numbers are greater than 0.1 or the calculated values may be due entirely to experimental error.

Introduction
Even though first identified by Henry Darcy 130 years ago, methods for determining the permeability of porous media are still being developed today. Recently, there has been considerable interest in using the unsteady-state (pulse) technique to measure gas permeability. The method also allows evaluation of the effects of gas slippage (Klinkenberg phenomena) and inertia (Forchheimer phenomena). The experimental method and, in particular, the data analysis procedures for these measurements are based largely on the work of Jones(1). The attraction of the method is that it promises a rapid and accurate means of determining all three gas flow parameters (permeability, k; Klinkenberg coefficient, b; Forcheimer coefficient, β). As will be discussed in this paper, this promise is not always fulfilled. A schematic diagram of an unsteady-state gas permeameter is presented in Figure 1. The components of the system comprise a core holder, in which to confine the sample, a pulse valve, a gas source chamber and a differential pressure transducer. There are two basic configurations, one in which the exhaust from the core sample is vented directly to the atmosphere (exit pressure ambient), and one in which the core sample is vented to a vacuum (exit pressure zero).
The operation of the system is straightforward. A sample is mounted in the core holder, the pulse valve is closed and the source chamber is charged with gas. At time zero, the pulse valve is opened. The differential pressure is then recorded as a function of time.
In a steady-state gas permeameter, data interpretation is simple: a pressure drop and a flow rate are measured, and Darcy's law is used to calculate the permeability. In order to determine Klinkenberg and/or Forchheimer coefficients, several tests, at varying flow rates and varying mean pore pressures, are required. The unsteady-state technique provides these varying conditions within one test. However, because only differential pressure is measured, data interpretation is considerably more complicated.
Jones' method of data analysis (henceforth referred to as the approximate method) is based on a number of assumptions including that the gas is ideal and the mass flow rate through the core is essentially constant (a correction method is provided for non-constant mass flow). The method relies on solving the equation
Equation (1) Available In Full Paper.
where Vt is the volume of the source chamber, p is the density of the gas, t is the time and Qout is the mass flow rate through the core. This mass flow rate is given by Darcy's law.