Journal
WATER
Volume 12, Issue 11, Pages -Publisher
MDPI
DOI: 10.3390/w12113041
Keywords
Darcy’ s law; two-phase flows; phases coupling; fractional flow; Buckley– Leverett theory; capillary pressure
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Funding
- TAMUQ start-up fund [482202-50120]
- Qatar Foundation
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The theory of two-phase immiscible flow in porous media is based on the extension of single phase models through the concept of relative permeabilities. It mimics Darcy's law for a fixed average saturation through the introduction of saturation-based permeabilities to model the momentum exchange between the phases. In this paper, we present a model of two-phase flow, based on the extension of Darcy's law including the effect of capillary pressure, but considering in addition the coupling between the phases modeled through flow cross-terms. In this work, we extend the Buckley-Leverett theory to the subsequent model, and provide numerical experiments shading the light on the effect of the coupling cross-terms in comparison to the classical Darcy's approach.
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