Immiscible two-phase flow in porous media: Effective rheology in the continuum limit

Abstract

It is becoming increasingly clear that there is a regime in immiscible two-phase flow in porous media where the flow rate depends of the pressure drop as a power law with exponent different than one. This occurs when the capillary forces and viscous forces both influence the flow. At higher flow rates, where the viscous forces dominate, the flow rate depends linearly on the pressure drop. The question we pose here is what happens to the linear regime when the system size is increased. Based on analytical calculations using the capillary fiber bundle model and on numerical simulations using a dynamical network model, we find that the non-linear regime moves towards smaller and smaller pressure gradients as the system size grows.

Pore‐Scale Fluid Dynamics Resolved in Pressure Fluctuations at the Darcy Scale

“…This result suggests that the onset of non-linear flow dynamics may occur at lower capillary numbers in larger samples. This assertion agrees with dynamic pore network modeling observations showing that the onset of non-linear flow regimes start at lower flow rates as system size increases (Hansen et al, 2023;Pedersen & Hansen, 2023;Roy et al, 2019).…”

Quantification of Nonlinear Multiphase Flow in Porous Media

“…From a theoretical perspective, Sinha and Hansen (2012) suggested that the exponent a was around 0.5 and confirmed this behavior using a dynamic pore-scale model. Roy et al (2019) proposed a size dependence of the non-linear regime, such that for larger systems, the transition from intermittency to linear flow occurred for lower Ca in a high flow rate regime. In the limit of an infinite system, this suggests that there is no linear Darcy regime at all.…”