## Multiphase flow correlations

The primary purpose of a multiphase flow correlations is to predict the liquid holdup (and hence the flowing mixture density) and the frictional pressure gradient.  This article details the most widely used correlations for the prediction of the Vertical Lift Performance.

The oil and water are lumped together as one equivalent fluid. Thus flow correlations in common use consider liquid/gas interactions.  They are therefore more correctly termed two-phase flow correlations.  Depending on the particular correlation, flow regimes are identified and specialized holdup and friction gradient calculations are applied for each flow regime.

There is no universal rule for selecting the best flow correlation for a given application. When an outflow performance simulator is used, it is recommended that a Correlation Comparison always be carried out. By inspecting the predicted flow regimes and pressure results, the User can select the correlation that best models the physical situation.

## Multiphase flow correlations:

### Fancher & Brown:

• Fancher and Brown is a no-slip correlation, with no flow regime map. Therefore, this correlation cannot be recommended for general use and it is provided for use as a quality control (should not be used for quantitative work).
• It gives the lowest possible value of Vertical lift Performance (VLP). Therefore, Measured data falling to the left of Fancher Brown on the correlation comparison plot indicates a problem with fluid density (i.e PVT) or field pressure data.
• According to Brown, it is only suitable for 2-3/8 – 2-7/8 inch tubing.
• It is for GLR less than 5000 scf/bbl and flow rates less than 400 bpd.
• It has its own friction factor model, which is independent of pipe roughness.

## Vogel’s inflow performance relationship

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: