Black-oil equations


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.

The term black-oil refers to the fluid model, in which water is modeled explicitly together with two hydrocarbon components, one oil phase and one gas phase.
This is in contrast with a compositional formulation, in which each hydrocarbon component is handled separately
The equations of an extended black-oil model are
where
is a porosity of the porous medium,
is a water saturation,
are saturations of liquid
and vapor phases in the reservoir,
are
Darcy velocities of the liquid phase, water phase and vapor phase in the reservoir.
The oil and gas at the surface could be produced from both liquid and vapor phases existing at high pressure and temperature of reservoir conditions. This is characterized by the following quantities:
is an oil
formation volume factor
,
is a water formation volume factor
,
is a gas formation volume factor
,
is a solution of gas in oil phase
,
is a vaporized oil in gas phase
.