Impact of Representative Elemental Volume on Steady-State and Unsteady-State Relative Permeability

The comparison between steady-state relative permeability (SSRP) and unsteady-state relativepermeability (USRP) is essential for accurately characterizing fluid flow in porous media. Under conditionsdominated by capillary forces and a low capillary number, SSRP and USRP are generally expected to alignclosely, as both methods are governed by similar physical mechanisms. However, this agreement iscontingent upon the sample being a Representative Elemental Volume (REV), which ensures that the samplecaptures the statistical homogeneity and relevant structural features of the porous medium. In this study, amultiphase lattice Boltzmann model (LBM) is employed to numerically measure both SSRP and USRP inthe sample of Berea sandstone and carbonate as well as heterogeneous samples with rich clay content andfracture. A screening process to determine sample REV is introduced for quality check. Our results suggestthat, when the samples do not represent an REV, the match between SSRP and USRP deteriorates due toscale effects and heterogeneity. Steady-state measurements fail to account for dynamic changes in fluiddisplacement over time, which are captured by unsteady-state methods. These findings emphasize theimportance of using REV-scale samples to ensure the validity and reliability of permeability measurements.The mismatch between SSRP and USRP in non-REV samples presents challenges in the interpretation ofpermeability data and may lead to inaccurate predictions of fluid flow behavior. In addition, it is observedthat the screening process in this study is good indicator to evaluate sample representativeness.