Analysis of Flow Characteristics in Porous Media with Heterogeneity at Microscale and Macroscale

Abstract

Hydrodynamic or oilfield scale models are needed to predict long-term the production process, to design and optimise well placement and evaluate the outcomes of different enhanced recovery practises. These models operate using continuum medium approximations and upscaled effective porous media properties such as permeability, relative permeability and capillary curves and are conventionally based on (multiphase generalization of) Darcy and continuity equations. In this work we explored the difference between flow patterns on the Darcy scale depending on how we parameterized the model – using scalar permeability values, or based on pore-scale simulations on 3D pore geometries of real rock samples. In the latter case two permeabilities were utilized – conventional directional permeability (in three directions) and full permeability tensor. Our results strongly support the idea that full tensors are needed to accurately represent fluxes at Darcy scale then upscaling from core-scale measurements or simulations, or even if using geologic/geostatistical model (with spatial heterogeneous distribution of flow properties). More specifically, our upscaled Darcy scale model parameterized using hypothetical scalar or pore-scale simulated permeabilities revealed: even a simple scalar permeability field, if heterogeneous, produces significant off-diagonal terms in tensorial permeability results; using tensoral permeabilities when upscaling from the core-scale results in significant difference in upscaled (tensorial) permeabilities compared to conventional directional simulation framework.