Heterogeneity factor model for fluid/meso-structure coupling simulations of nonlinear seepage

Nonlinear seepage plays a crucial role in various engineering applications, yet an accurate prediction remains challenging. By incorporating the concept of the heterogeneity factor ${\zeta }_u$, an efficient one-field multiscale approach for seepage prediction has been proposed based on the fundamental principle of fluid/meso-structure interactions. The impact of flow and structural details (including Reynolds number, specific surface area of solid grain, and porosity of porous structure) on such factor are studied in detail. Results show that ${\zeta }_u$ is proportional to the square of specific surface area and reciprocal to the quadratic polynomial of porosity, and it has a sharp increase followed by a linear change with the increase of Reynolds numbers. A reduced model of ${\zeta }_u$ fitted from 105 pairs of simulation data is then proposed for performing macroscopic simulations of nonlinear seepage. This model in three-dimension heterogeneous porous media achieves a phenomenal gain of over $10^5$ speed-up compared to pore-scale simulation with a maximum prediction error of only 7.8%, demonstrating an exceptional performance-to-accuracy trade-off. Evidently, it attains a substantially higher degree of accuracy compared to the traditional method that utilizes the Kozeny–Carman permeability model. The present work provides an improved understanding of heterogeneous structure effect on nonlinear seepage, and provides a high-fidelity reduced model needed in large-scale nonlinear seepage simulations.