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The Composite Inflow Performance Relationship

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The Composite Inflow Performance Relationship is based on the combination of PI model, presented in the previous articles “Well Inflow Performance”, and “Vogel’s inflow performance relationship”. As per the aforementioned articles, PI model could be used if the well producing a single phase flow with no gas in the solution (Pwf > Pb). In the other hand, Vogel’s IPR could be used when the well’s flowing bottomhole pressure (Pwf) is below the bubble point pressure (Pb) and if the produced fluid is pure oil.

If the Pwf is below Pb and well’s produced fluids is a mixture of oil, water, and gas, the inflow performance could be described by the Composite IPR. In this case, IPR curves are somewhere between the curves valid for pure oil (Vogel model) and the one valid for Pwf > Pb (PI model).

The following graph shows the differences between these methods in graphical form:

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Vogel’s inflow performance relationship

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In 1968, Vogel established an empirical relationship ( Vogel’s inflow performance relationship )for flowrate prediction of a solution gas-drive reservoir in terms of the wellbore pressure based on reservoir simulation results.

Vogel’s Model compared to PI Model…

The PI model works very well for single phase fluid (water, oil, or water/oil) flowing into a wellbore, even though water and oil are two separate phases, they are considered as a single phase since they are both liquid.

But what happens when gas comes out of solution?

” The flow velocity of a fluid in a porous medium is inversely proportional to the fluid viscosity. Typically, gas viscosity in the reservoir is about fifty times smaller than for liquid oil and consequently, the gas flow velocity is much greater. As a result, it is normal, when producing from a reservoir in which there is a free gas saturation, that gas will be produced in disproportionate amounts in comparison to the oil “. (Dake, fundamentals of reservoir engineering).

Compared to liquid, gas has much higher permeability and much lower viscosity. These two factors will give the gas a much higher flow rate than liquid inside the reservoir, so that:

QG >> QL

Below the bubble point pressure, the solution gas escapes from the oil and become free gas. The free gas occupies some portion of pore space and reduces flow of oil. This effect is quantified by:

  • A decrease of oil Relative permeability
  • An increase of oil viscosity (as its solution gas content drops)

Therefore, the combination of the relative permeability effect and the viscosity effect results in lower oil production rate at a given bottom-hole pressure.

Graphically, it would looks like this:

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