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

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