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VA – GP - OA: Numerical Multiphase PTA
p 15/29
3.2. Analysis of the sources of oscillations
The development of oscillations during production of black oil is a more complex process than
in the case of water injection. However, it can still be related to the discretization in presence
of a moving saturation front.
Let us consider a simple continuous model, using a 1-D pressure profile (Figure 19). From this
profile, the corresponding pseudo-permanent saturation profile can be deduced: it is such that
the flowing composition is constant everywhere, i.e. CFout=CFin on Figure 19.
Note that while the flowing composition is uniform in this model, the local compositions and
saturations are not uniform.
When the pressure profile evolves slowly due to depletion, the saturation profile evolves
accordingly in order to stabilize and ensure constant flowing compositions. Note also that the
gas saturation profile exhibits a strong discontinuity while P decreases below Pb.
Figure 19
Although not clear on this Figure, it is interesting to point out that this simplified model leads
to a saturation profile giving higher gas saturation values for a given P<Pb, compared to the
saturations predicted by constant mass depletion of the original oil at the same pressure P.
This point was confirmed by the results of our simulations, and will be useful further in the
document, when we analyze the evolution of the GOR and the evolution of saturation maps
during build-ups.
Let us now discretize our model, and focus on a cell where the saturation front is present.
This
front cell was initially undersaturated, and at a given time, its pressure
P
becomes lower than
the entering oil saturation pressure
Pb
. The oil entering into this cell during a time step flashes
and gives a free gas quantity, which is unmovable as long as the gas saturation is below the
critical saturation
Sgr
. In this case, the produced fluid is no more the injected fluid: it is the
saturated oil of the cell, eventually completed by an insufficient quantity of gas. As a
consequence, this introduces a transient behavior, until the saturation value corresponding to
the constant flowing composition is reached. This process occurs each time the gas front
appears in a new cell, explaining the development of pressure derivative oscillations.
Understanding this phenomenon, it is suspected that the value of the residual saturation may
have a strong influence on these oscillations. This is confirmed by examining the results of
Figure 20.