Mathematical Models for Multiphase Flow
Knut‐Andreas Lie · Cambridge University Press eBooks · 2019
This chapter introduces the basic equations used to describe multiphase flow. It also introduces key concepts such as saturation, wettability, relative permeability, and capillary pressure. Combining the multiphase extension of Darcy's law with mass conservation of fluid phases or chemical components gives a system of parabolic PDEs. The chapter derives the so-called fractional flow formulation and discusses several special cases of two-phase flow equations. The chapter ends with a discussion of various analytical and semi-analytical 1D solutions, including the classical Buckley–Leverett problem.