Klinkenerg-Corrected Permeability Measurements in Tight Gas Sands: Steady-State Versus Unsteady-State Techniques

Abstract

Abstract This paper presents results from a laboratory study comparing Klinkenberg-corrected permeability measurements in tight gas sands using both a conventional steady-state technique and two commercially-available unsteady-state permeameters. We also investigated the effects of various rate and pressure testing conditions on steady-state flow measurements. Our study shows the unsteady-state technique consistently overestimates the steady-state permeabilities, even when the steady-state measurements are corrected for gas slippage and inertial effects. The differences are most significant for permeabilities less than about 0.01 md. We validated the steady-state Klinkenberg-corrected permeabilities with liquid permeabilities measured using both brine and kerosene. Although gas slippage effects are more pronounced with helium than with nitrogen, we also confirmed the steady-state results using two different gases. Moreover, we show results are similar for both constant backpressure and constant mass flow rate test conditions. Finally, our study illustrates the importance of using a finite backpressure to reduce non-Darcy flow effects, particularly for ultra low-permeability samples. Introduction Permeability measurements in core samples are based on the observation that, under steady-state flowing conditions, the pressure gradient is constant and is directly proportional to the fluid velocity. This constant of proportionality, as defined by Darcy's law, Equation 1 is the absolute core permeability, k8. This relationship has been validated for a wide range of flow velocities. For cores with permeabilities less than about 0.1 md, steady-state flow is difficult to achieve in a reasonable test time, especially when liquid is the flowing fluid. Consequently, gas is routinely used in low-permeability core samples. However, gas flow in tight gas sands is often affected by several phenomena that may cause deviations from Darcy's law. Failure to account for these non-Darcy effects, principally gas slippage and inertial flow, may cause significant measurement errors. Gas slippage is a non-Darcy effect associated with non-laminar gas flow in porous media. These effects occur when the size of the average rock pore throat radius approaches the size of the mean free path of the gas molecules, thus causing the velocity of individual gas molecules to accelerate or "slip" when contacting rock surfaces.1 This phenomenon is especially significant in tight gas sands that are typically characterized by very small pore throats. Klinkenberg,2 who was one of the first to study and document gas slippage effects in porous media, showed the observed permeability to gas is a function of the mean core pressure. Furthermore, he observed that the gas permeability approaches a limiting value at an infinite mean pressure. This limiting permeability value, which is sometimes referred to as the equivalent liquid permeability1 or the Klinkenberg-corrected permeability, is computed from the straight-line intercept on a plot of measured permeability against reciprocal mean pressure. In equation form, the line is defined by Equation 2 where k is the Klinkenberg-corrected permeability and b is the gas slippage factor. Experimental studies by Krutter and Day,3 Calhoun and Yuster4 and Heid, et al.,5 extended and validated the work of Klinkenberg.2