INTERROGATING THE ACCURACY OF PERMEABILITY AND NON-DARCY COEFFICIENT MEASUREMENT USING COMPRESSIBLE FLOW IN LABORATORY SETTINGS

Abstract

Laboratory measurements of gas permeability and the non-Darcy inertial resistance coefficient β are fundamental inputs to reservoir engineering models, yet the dependence of these quantities on the length of the core sample used for measurement has received limited systematic attention. This study investigates the effect of sample length on laboratory-measured gas permeability and β for Berea sandstone under compressible nitrogen flow. Measurements were conducted using a Hassler-type core holder with a novel dual pressure transducer configuration that allowed inline and separate line pressure measurements to be made simultaneously on every sample and at every flow condition. The separate line configuration, which measures pressure directly at the core face through dedicated end cap ports, was found to be substantially more reliable than the inline configuration. The divergence between the two configurations grew systematically with decreasing sample length and increasing sample diameter, with the inline configuration overestimating β by factors of up to 10 for the shortest samples tested. Across all three rock sets and both diameter sets examined, after careful calibration and accounting for rock heterogeneity, Darcy permeability was found to be broadly stable across lengths and to average predictably using the harmonic mean, with differences between calculated and measured values of less than 4%. The inertial resistance coefficient β, by contrast, consistently increased as sample length decreased regardless of the measurement configuration used, and did not average predictably using a weighted mean, with differences between calculated and measured values ranging from -44% to 241%. A systematic investigation of core holder design effects identified two experimental factors responsible for the apparent length dependence: the restrictive geometry of the narrow bore spacer face, and the inline pressure measurement configuration. The Forchheimer model is confirmed as an accurate description of high-velocity gas flow in this Berea sandstone, and β is confirmed as a true intrinsic rock property independent of sample length when measurements are made with appropriately designed apparatus.