The black-oil equations are a set of partial differential equations that describe fluid flow in a petroleum reservoir, constituting the mathematical framework for a black-oil reservoir simulator.
[1] The term black-oil refers to the fluid model, in which water is modeled explicitly together with two hydrocarbon components, one (pseudo) oil phase and one (pseudo-)gas phase.
This is in contrast with a compositional formulation, in which each hydrocarbon component (arbitrary number) is handled separately.
are saturations of liquid ("oil") and vapor ("gas") phases in the reservoir,
The oil and gas at the surface (standard conditions) could be produced from both liquid and vapor phases existing at high pressure and temperature of reservoir conditions.
is a solution of gas in oil phase (ratio of volume of gas to the volume of oil at standard conditions obtained from some amount of liquid phase at reservoir conditions),
is a vaporized oil in gas phase (ratio of volume of oil to the volume of gas at standard conditions obtained from some amount of vapor phase at reservoir conditions).
Last updated by Jesse Gabriel, June 2021 Koma Kange