Whenever a fluid flows through a conduit pressure loss occurs. Many methods are available to calculate frictional pressure losses. They range from simple empirical equations to rigorous mechanistic multiphase flow models.

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The Darcy-Weisbach flow equation is theoretically sound equation derived from the Conservation of Mass and Conservation of Momentum laws. Named after Henry Darcy and Julius Weisbach, it relates the pressure loss due to friction along a given length of pipe to the average velocity of the fluid flow for an incompressible fluid.

The Darcy-Weisbach equation contains a dimensionless friction factor, known as the Darcy friction factor. This is also variously called the Darcy—Weisbach friction factor, friction factor, resistance coefficient, flow coefficient, or Moody friction factor.

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.

Therefore, this correlation cannot be recommended for general use and should not be used for quantitative work.

This is why Fancher Brown no slip and Duns and Ros Modified can serve only as quality check boundaries for downhole measurements. 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.

## Multiphase Flow Regimes in Pipes

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. For oil wells, the main component of pressure loss is the gravity or hydrostatic term. Calculation of the hydrostatic pressure loss requires knowledge of the proportion of the pipe occupied by liquid holdup and the densities of the liquid and gas phases.

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Gas, being less dense than liquid flows with a greater vertical velocity than liquid. The difference in velocity between the gas and liquid is termed the slip velocity.

The effect of slip is to increase the mixture density and hence the gravity pressure gradient. In the next paragraphs, two-phase flow properties holdup, densities, velocity, and viscosity will be detailed.

As well as, the two-phase flow procedure to calculate the outlet pressure is detailed. In multiphase flow, each fluid moves at a different speed due to different gravitational forces and other factors, with the heavier phase moving slower, or being more held up, than the lighter phase.

The sum of the holdups of the fluids present is unity. H L is defined as the ratio of the volume of a pipe segment occupied by the liquid to the volume of the pipe segment.

The remainder of the pipe segment is of course occupied by gas, which is referred to as H g. Multiphase correlations References:.

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.

Therefore, Measured data falling to the left of Fancher Brown on the correlation comparison plot indicates a problem with fluid density i.

## Two Phase Flow

It has its own friction factor model, which is independent of pipe roughness. Follow us on Facebook :. International Journal Heat Mass Transfer 18 ,