Effective rheology of two-phase flow in a capillary fiber bundle model

Abstract

We investigate the effective rheology of two-phase flow in a bundle of parallel capillary tubes carrying two immiscible fluids under an external pressure drop. The diameter of each tube varies along its length and the corresponding capillary threshold pressures are considered to be distributed randomly according to a uniform probability distribution. We demonstrate through analytical calculations that a transition from a linear Darcy regime to a non-linear behavior occurs while decreasing the pressure drop $\Delta P$, where the total flow rate $⟨Q⟩$ varies with $\Delta P$ with an exponent $2$. This exponent for the non-linear regime changes when a lower cut-off $P_m$ is introduced in the threshold distribution. We demonstrate analytically that, in the limit where $\Delta P$ approaches $P_m$, the flow rate scales as $⟨Q⟩\sim (|\Delta P|-P_m{)}^{3/2}$. We have also provided some numerical results in support to our analytical findings.

arXiv comment6 pages, 2 figures

References in corpus (2)

• Growth activity during fingering in a porous Hele Shaw cell
• Effective Rheology of Bubbles Moving in a Capillary Tube

Cited by in corpus (4)

• A statistical mechanics for immiscible and incompressible two-phase flow in porous media
• Rheology of immiscible two-phase flow in mixed wet porous media: Dynamic pore network model and capillary fiber bundle model results
• Pressure drop-flow rate nonlinearity in bubble trains through a capillary bundle
• A Dynamic Network Simulator for Immiscible Two-Phase Flow in Porous Media