Environmental Engineering Reference
In-Depth Information
Here we present a general model for the simulation of a three-phase fluid flow in
a deformable formation. The balance equations governing the problem are
formulated directly and their solution is obtained through the finite element method.
The interested reader can find the development of these equations in [LEW 98b].
Even though in reservoir engineering the finite difference method is still widely
used, the finite element method is chosen here because of its flexibility and ease in
handling the boundary conditions. This is also true in complex geological situations,
which often characterize hydrocarbon reservoirs. A fully coupled solution is
presented here that fairly accurately models the real behavior of a reservoir and its
overburden. Such a coupled solution can be obtained quite easily with the
computers currently available.
Several examples will be shown in this chapter: the first one deals with a
petroleum reservoir and hence involves the three fluid phases mentioned above. In
the second case, the pollution is with polychlorobiphenyl (PBC) oil with a density
greater than one,
while
the case of a pollutant transported in pore water and pore air
concludes the chapter. For the simulation of the third case, part of the general model
is used together with a diffusion advection equation.
14.3.1.
The physical model
Here we consider the flow of three immiscible and compressible fluid phases in
a deformable porous medium. The initial conditions of such a reservoir in
equilibrium where there is no fluid-flow are presented in Figure 14.3: oil is very
often confined above by gaseous hydrocarbons and below by a heavier salt water
layer. For a reservoir under isothermal conditions, the properties of each fluid phase
are given according to the pressure, volume and temperature (PVT) data. The
interfaces between oil and water and between oil and gas can be obtained from
petro-physical and geological data or by experimental tests in the laboratory on
samples taken from the reservoir.
The separation surface between two fluids is not as sharp as shown in Figure
14.3; in fact there are capillary fringes, where more than one fluid phase is present.
These effects must be included in a mathematical and numerical model to make the
model more stable and ensure the results are closer to reality.
