Use of ko-b Plot to Interpret Gas Permeability Measurements in Low-Permeability Reservoirs
Authors:   University of Houston, Song Wenxiu , Myers Michael T. ,   University of Houston, Hathon Lori ,   University of Houston, Aldin Munir ,   Metarock Laboratories
Published: November 2024

Klinkenberg (1941) proposed that gas permeability is a function of the intrinsic permeability (ko) and a slippage factor (b), which is proportional to the reciprocal mean pore pressure (1/Pm). This work investigates the use of Klinkenberg corrections to understand the applicability to low-permeability samples. This is done by generating ko-b plots at multiple mean pore pressures to examine the physics of transport in shale gas reservoirs. For a 100-psi pressure drop applied to gas flow, there are no unique ko and b values that fit the time-dependent pressure profiles of the inlet and outlet pressure chambers in a pulse decay measurement. For any assumed ko, there is a corresponding value of b which fits the chamber data within experimental error. A ko-b curve of equivalent fits may therefore be generated. To determine both ko and b, at least two significantly different mean pore pressures are required. Included in the figure is an example of a ko-b plot and a detail of the intersections of the curves, which give the unique values of ko and b at the mean pressure of the two measurements. The objective is to understand the applicability of a Klinkenberg-type correction. The permeability is measured on 1-in. diameter by 1-in. length core plugs using the pulse decay technique. The samples are measured at several different mean pore pressures, ranging from 250 to 1,450 psi, while the effective stress is kept at a constant 1,000 psi. The range of data spans the critical pressure for room temperature measurements. The pressure change in the upstream and downstream chambers are monitored, and these data are modeled using COMSOL Multiphysics® software to obtain the ko-b curve for each separate test. The b value is assumed, and then the best-fit value of ko is determined. The figure shows an example of the inability to determine a unique value of ko-b. By plotting the optimum fit values at each measured mean pore pressure, the ko-b plot is generated. The results are shown in the figure for the ko and b values of a pyrophyllite outcrop sample. Pyrophyllite has been used as a standard because it is observed to be uniform and microfracture free. The values of both ko and b are both a strong function of mean pore pressure. The intersections of the ko-b plots illustrate that as mean pressure increases, the gas slippage factor decreases. The simple inverse pressure relationship commonly assumed for the Klinkenberg correction does not hold. The ko-b values follow different trends above and below the critical pressure. The two trends observed intersect at the critical pressure, which validates the physical interpretation of the measured values. Further work will be aimed at developing an improved understanding of the controls determining these pressure-dependent ko and b values Previous studies have often neglected the slippage effects when calculating the gas permeability, often assuming a b value of zero. This study determines the ko-b values as a function of mean pore pressure. The values of b are large, as expected, but decrease with increasing mean pore pressure. The values are significant even above the critical pressure.