--Development of a mechanistic model for theprediction of slug length in horizontalmulti phase flowMGOPALCorrosion in Multiphase Systems Center, Ohio University, Athens, USA

Synopsis

A mechanistic model for the prediction of slug length in multi phase flow is presented based ona unique concept involving the Froude number. It is shown that the Froude number in the liquidfilm ahead of the slug is greater than unity. It decreases to values less than unity inside themixing zone of the slug and then gradually increases within the body of the slug. The slug tailoccurs as the Froude number tends to unity once more. Agreement with experimental data isgood. The model also closely predicts the data of other researchers in large diameters pipes.

Notation

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area occupied by the gas above the stratified layer of liquidarea occupied by the stratified layer of liquidperimeter of liquid contact with wall over which shear stress acts.perimeter of gas contact with wall over which gas phase shear stress acts.width of gas-liquid interface.wall shear stress for liquid and gas respectivelyshear stress at gas-liquid interface.density of liquid and gas respectivelypipe inclination (small values, close to horizontal).interfacial friction factorgas phase friction factortranslational velocity of the slug.liquid film velocityeffective film height ahead of the slug

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Several flow regimes occur in multiphase flows, including, stratified, slug, and annular flows.The production rates from the wells are such that these multiphase flow pipelines are expectedto be in slug flow at some time in their lives. This is a highly turbulent flow regime, leading toincreased pipe damage from internal corrosion and mechanical impacts. This is related to theslug length. It is therefore, important to obtain a detailed, mechanistic understanding of slug flowcharacteristics, and to determine the overall slug length.

Mathematical models have been developed that describe the relationship between differentvariables as knowledge of slug flow features have increased over the last decade. However, adetailed understanding of the motion of gas within the slug, and the distribution of phases in thedifferent zones of the slug is not known. This is essential information that may be used todevelop a complete mathematical model to predict slug length.

This paper describes a mathematical model that has been developed to predict slug lengthutilizing the phase distribution and velocity profiles within the slug. The experimental techniqueshave been described elsewhere (Gopal and Jepson, 1997, 1998a,b).

2BACKGROUND

Figure I shows the profile of a slug. Waves form on the liquid film, that grow to bridge the pipe.This causes the liquid to be accelerated by the gas. As the slug front moves through the pipe,it overruns the slow moving liquid film ahead of it and accelerates it to the velocity of the slug.A mixing vortex is created in this process. This leads to a scouring mechanism on the pipe wallwith high rates of shear. Also, as the liquid is assimilated by the slug, a considerable amount ofgas is entrained (Jepson, 1987). This leads to the creation of a highly frothy, turbulent regionbehind the slug front called the mixing zone.

Beyond the mixing region of the slug, the level of turbulence is reduced, and buoyancy forcesmove the gas towards the top of the pipe. The cross sectional area available for liquid flowincreases, a boundary layer develops, and the liquid velocity decreases. This is the slug body.Eventually a point is reached where the liquid velocity is no longer sufficient to sustain thebridging of the pipe, and the slug body is curtailed. This is called the slug tail. The liquidvelocity decreases in the liquid film, its height rebuilds with waves forming on its surface, andthe next slug is initiated.

Dukler and Hubbard (1975) published the first realistic mechanistic model for slug flowcharacteristics. They established fundamental equations that could predict several slug flowcharacteristics. The agreement with experimental data was good and a better understanding ofthe mechanisms was achieved. However, many parameters, such as slug frequency and the voidfraction within the slug, were required to complete the calculation. Also, their definition of themixing zone is not adequate (Gopal and Jepson, 1998b). The slug lengths in their studies variedfrom 12 to 25 pipe diameters.

Nicholson et al. (1978) found a non-zero gravity induced drift velocity, even for horizontalpipes, and determined that this velocity needed to be incorporated in the calculation of the slugtranslational velocity. They modified and extended the model of Dukler and Hubbard to apply

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to the entire intermittent flow regime. The slug lengths in their case varied from 10 to 60 pipdiameters. It is to be noted that the model ignores any slip between gas and liquid within thslug. It has been found (Jepson, 1987) that for large diameter pipes, this is not true for hightslug velocities.

Maron et al. (1982) derived a model for slug flow based on periodic distortion of thhydrodynamic boundary layer followed by a recovery process. As the slug front overruns thliquid film, the boundary layer is destroyed by the mixing eddy. At the end of the mixing zon,this boundary layer begins to redevelop. The model considered two separate types of slug, onwith aeration and the other without. In the first case, the entrained gas bubbles in the slug lea"the boundary layer region due to buoyancy effects and tend to agglomerate in the upper portioof the pipe. The slug length is the distance required for complete separation of the gas from thliquid. In the second case, the slug length is given by the distance required for the boundarlayer to fully develop and reach the center of the pipe. They developed their boundary laytanalysis in a coordinate system moving with the slug front and introduced a one-seventh POWIlaw model to describe the velocity profile within the boundary layer. They showed that thmodel could be applied to predict pressure drop for a wide quasi-steady frequency range (slugs. However, stability analysis indicated that the slug pattern stabilized over a narro'frequency range corresponding to a minimum pressure drop. It is to be noted that no informatioabout the pipe diameter or working fluids were given.

Dukler et.al. (1985) applied the concepts developed by Maron et al. (1982) and formulatea generalized model for the prediction of the minimum stable slug length for horizontal anvertical slug flow. The model utilized the velocity profile developed by Maron et al. (1982) ithe boundary layer, and combined this with an inviscid potential core. An assumption was madthat a flat velocity profile resulted at the end of the mixing zone. The velocity at the center WIallowed to decrease due to frictional effects predicted by a Blasius-type equation. The slulength was predicted by the distance required for the complete development of the boundarlayer. The results of the model were applied to 5 cm I.D. vertical and horizontal, and 3.8 CIhorizontal pipes, with air and water as the working fluids. It was found that the experiment..,- ...~ ~~..; ./ ./ ;>:1 .:.-_------ --:--/// -'

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References

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Nydal, O. J., Pintus, S., and Andreussi, P., "Statistical Characterization of Slug Flow inHorizontal Pipes", Int. 1. Multiphase Flow, 18, 3, pp. 439, (1992).

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Zhou, x., and Jepson, W. P., "Corrosion in Three-Phase Oil/Water/Gas Slug Flow inHorizontal Pipes", Corrosion/94, Paper no. 94026, (Houston, TX: NACE International,1994).

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