Physical quantity transport in 1D two-phase flow through porous media: The general case

<jats:p>Physical quantity profiles in 1D two-phase flow through porous media change with time. In the classical theory, in some special cases, the points on saturation or fractional flow profiles are transported during two-phase flow. However, in general cases, whether and how the points on profiles of all physical quantities are transported is unknown. To describe the physical quantity transport in a more general case introduced in this paper, here we propose a four-variable form of phase flow rate function, derive the general transport equations of physical quantities and explain their physical meanings. We found that, in this general case, the profile evolutions of all physical quantities can be explained by physical quantity transport, and the profiles at a given time are related to total flow rate history.</jats:p>