deepstar_chevron-multiphase-design-guide-pt-1

PART I - MULTIPHASE PIPELINE & SLUG CATCHER DESIGN GUIDE

Multiphase Pipeline Design Guide

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PART I - MULTIPHASE PIPELINE & SLUG CATCHER DESIGN GUIDE

PART I

TABLE OF CONTENTS

SECTION 1.0 - INTRODUCTION 1.1

Objective and Scope..................................................................................................................................................... 1

1.2

Definition of Terms........................................................................................................................................................ 1

SECTION 2.0 – OVERVIEW OF MULTIPHASE FLOW FUNDAMENTALS 2.1

Design Criteria.............................................................................................................................................................. 11

2.2

Velocity Guidelines ....................................................................................................................................................... 11

2.3

Flow Regimes............................................................................................................................................................... 13

2.4

Pressure Gradient ......................................................................................................................................................... 16 2.4.1

Frictional Losses .......................................................................................................................................... 16

2.4.2

Elevational Losses........................................................................................................................................ 17

2.4.3

Acceleration Losses...................................................................................................................................... 18

2.4.4

Allowable Pressure Drop............................................................................................................................... 20

2.5

Pressure Gradient Calculations...................................................................................................................................... 20

2.6

Section Highlights......................................................................................................................................................... 21

SECTION 3.0 – STEADY STATE DESIGN METHODS 3.1

Pipeline Design Methods ............................................................................................................................................... 25

3.2

Steady State Simulators................................................................................................................................................ 26 3.2.1

Phase Equilibrium and Physical Properties.................................................................................................... 26

3.2.2

Pipeline Elevation Profile .............................................................................................................................. 28

3.2.3

Heat Transfer ............................................................................................................................................... 30

3.2.4

Recommended Methods for Pressure Drop, Liquid Holdup, and Flow Regime Prediction................................................................................................................................ 33

3.2.5 3.3

Interpretation of Results................................................................................................................................ 35

Section Highlights......................................................................................................................................................... 38

SECTION 4.0 – TRANSIENT FLOW MODELING 4.1

Transient Flow Modeling (General) ................................................................................................................................ 41

4.2

Use of Transient Simulators........................................................................................................................................... 42

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4.3

Section Highlights......................................................................................................................................................... 43

SECTION 5.0 – SLUG FLOW ANALYSIS 5.1

Slug Flow (General) ...................................................................................................................................................... 45

5.2

Slug Length and Frequency Predictions......................................................................................................................... 46

5.3

5.2.1

Hydrodynamic Slugging................................................................................................................................ 46

5.2.2

Terrain Slugging........................................................................................................................................... 51

5.2.3

Pigging Slugs............................................................................................................................................... 53

5.2.4

Startup and Blowdown Slugs........................................................................................................................ 55

5.2.5

Rate Change Slugs ...................................................................................................................................... 56

5.2.6

Downstream Equipment Design for Slug Flow............................................................................................... 56

Section Highlights......................................................................................................................................................... 59

SECTION 6 – EXAMPLE PROBLEMS 6.1

6.2

Example Problem – 1 Low Gas/Oil Line Between Platforms .......................................................................................... 63 6.1.1

Line Size...................................................................................................................................................... 65

6.1.2

Slug Length Prediction ................................................................................................................................. 75

6.1.3

Slug Frequency and Length by Hill & Wood Method ...................................................................................... 80

Example Problem – 2 Gas Condensate Line .................................................................................................................. 88 6.2.1

Table 1, Wellstream Composition ................................................................................................................. 89

6.2.2

Table 2, Pipeline Evaluation Profile ............................................................................................................... 90

6.2.3

Pipeline Simulation Comparison ................................................................................................................... 92

SECTION 7.0 – REFERENCES .................................................................................................................................................... 106

FIGURES I: 1-1

Flow Regimes in Horizontal Flow................................................................................................................................... 8

I: 1-2

Flow Regimes in Vertical Flow ...................................................................................................................................... 9

I: 2-1

Horizontal Flow Regime Map......................................................................................................................................... 23

I: 2-2

Vertical Flow Regime Map............................................................................................................................................. 24

I: 5-1

Taitel-Dukler Liquid Holdup Predictions.......................................................................................................................... 60

I: 5-2

Stages in Terrain Slugging ............................................................................................................................................ 61

I: 5-3

Pipeline Slugging.......................................................................................................................................................... 62

I: 6-1

Liquid Holdup for Example 1, Year 12 ............................................................................................................................ 101

I: 6-2

Inlet Pressure for Example 1, Year 12............................................................................................................................ 102

I: 6-3

Liquid Flowrate Out of Line, Example 1, Year 12............................................................................................................ 103

I: 6-4

Gas Flowrate Out of Line, Example 1, Year 12............................................................................................................... 104

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I: 6-5

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Liquid Holdup Predictions for Example 2........................................................................................................................ 105

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SECTION 1.0 - INTRODUCTION 1.1

Objective and Scope

The simultaneous flow of gas and liquid through pipes, often referred to as multiphase flow, occurs in almost every aspect of the oil industry. Multiphase flow is present in well tubing, gathering system pipelines, and processing equipment. The use of multiphase pipelines has become increasingly important in recent years due to the development of marginal fields and deep water prospects. In many cases, the feasibility of a design scenario hinges on cost and operation of the pipeline and its associated equipment. Multiphase flow in pipes has been studied for more than 50 years, with significant improvements in the state of the art during the past 15 years. The best available methods can predict the operation of the pipelines much more accurately than those available only a few years ago. The designer, however, has to know which methods to use in order to get the best results. Part I of this guide consists of seven sections. The fundamentals of multiphase flow in pipelines are discussed in Section 2.0. The third section describes the use of steady state simulation methods. This section of the guide helps the designer choose the best methods for the project, and it gives guidelines to use in designs. The fourth section of the report briefly describes transient flow modeling. The fifth section describes slug flow modeling, giving suggestions on the best methods to use in slug flow simulation. The sixth section includes two sample problems, based on actual designs, which illustrate the design steps used in analyzing the pipeline designs. 1.2

Definition of Terms

In discussing the design of multiphase pipelines, it is necessary to define several terms used repeatedly throughout this text. Near Horizontal and Near Vertical Angles The term "near horizontal" is used in this guide to denote angles of -10 degrees to +10

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degrees from horizontal. The term "near vertical" denotes upward inclined pipes with angles from 75 to 90 degrees from horizontal. Flow Regimes In multiphase flow, the gas and liquid within the pipe are distributed in several fundamentally different flow patterns or flow regimes, depending primarily on the gas and liquid velocities and the angle of inclination. Observers have labeled these flow regimes with a variety of names. Over 100 different names for the various regimes and subregimes have been used in the literature. In this guide, only four flow regime names will be used: slug flow, stratified flow, annular flow, and dispersed bubble flow. Figure I:1-1 shows the flow regimes for near horizontal flow, and Figure I:1-2 shows the flow regimes for vertical upward flow. Descriptions of the flow regimes 1. Stratified Flow - at low flowrates in near horizontal pipes, the liquid and gas separate by gravity, causing the liquid to flow on the bottom of the pipe while the gas flows above it. At low gas velocities, the liquid surface is smooth. At higher gas velocities, the liquid surface becomes wavy. Some liquid may flow in the form of liquid droplets suspended in the gas phase. Stratified flow only exists for certain angles of inclination. It does not exist in pipes that have upward inclinations of greater than about 1 degree. Most downwardly inclined pipes are in stratified flow, and many large diameter horizontal pipes are in stratified flow. This flow regime is also referred to as stratified smooth, stratified wavy, and wavy flow by various investigators. 2. Annular Flow - at high rates in gas dominated systems, part of the liquid flows as a film around the circumference of the pipe. The gas and remainder of the liquid (in the form of entrained droplets) flow in the center of the pipe. The liquid film thickness is fairly constant for vertical flow, but it is usually asymmetric for horizontal flow due to gravity. As velocities increase, the fraction of liquid entrained increases and the liquid film thickness decreases. Annular flow exists for all angles of inclinations. Most gas dominated pipes in high pressure vertical flow are in annular flow. This flow regime is referred to as annular-mist or mist flow by many investigators.

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3. Dispersed Bubble Flow - at high rates in liquid dominated systems, the flow is a frothy mixture of liquid and small entrained gas bubbles. For near vertical flow, dispersed bubble flow can also occur at more moderate liquid rates when the gas rate is very low. The flow is steady with few oscillations. It occurs at all angles of inclination. Dispersed bubble flow frequently occurs in oil wells. Various investigators have referred to this flow regime as froth or bubble flow. 4. Slug Flow - for near horizontal flow, at moderate gas and liquid velocities, waves on the surface of the liquid may grow to sufficient height to completely bridge the pipe. When this happens, alternating slugs of liquid and gas bubbles will flow through the pipeline. This flow regime can be thought of as an unsteady, alternating combination of dispersed bubble flow (liquid slug) and stratified flow (gas bubble). The slugs can cause vibration problems, increased corrosion, and downstream equipment problems due to its unsteady behavior. Slug flow also occurs in near vertical flow, but the mechanism for slug initiation is different. The flow consists of a string of slugs and bullet-shaped bubbles (called Taylor bubbles) flowing through the pipe alternately. The flow can be thought of as a combination of dispersed bubble flow (slug) and annular flow (Taylor bubble). The slugs in vertical flow are generally much smaller than those in near horizontal flow. Slug flow is the most prevalent flow regime in low pressure, small diameter systems. In field scale pipelines, slug flow usually occurs in upwardly inclined sections of the line. It occurs for all angles of inclination. Investigators have used many terms to describe parts of this flow regime. Among them are: intermittent flow; plug flow; pseudo-slug flow, and churn flow. Superficial Velocities The velocities of the gas and liquid in the pipe are prime variables in the prediction of the behavior of the multiphase mixture. Most multiphase flow prediction methods use the superficial gas and liquid velocities as correlating parameters. The superficial velocities are defined as the in situ volumetric flowrate of that phase divided by the total pipe crosssectional area. In oil field units, this corresponds to:

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Vsg

= Superficial Gas Velocity, ft/sec = (actual ft3/sec of gas) / (pipe cross-sectional area, ft2)

Vsl

= Superficial Liquid Velocity, ft/sec = (actual ft3/sec of liquid) / (pipe cross-sectional area, ft2)

Mixture Velocity The mixture velocity (Vm) is the volumetric average velocity of the gas-liquid mixture. It is equal to the sum of the gas and liquid superficial velocities. Vm = Vsg + V sl

Slip and Liquid Holdup Liquid holdup is defined as the volume fraction of the pipe that is filled with liquid. It is the most important parameter in estimating the pressure drop in inclined or vertical flow. It is also of prime importance in sizing downstream equipment, which must be able to operate properly when the liquid holdup in the line changes because of pigging or rate changes. If there was no slip between the gas and liquid phases, both phases would move through the pipe at the mixture velocity. The liquid would occupy the volume fraction equivalent to the ratio of the liquid volumetric flowrate to the total volumetric flowrate. In multiphase flow terminology, this equates to the liquid holdup being equal to the ratio between the superficial liquid velocity and the mixture velocity: Hlns = No-slip liquid holdup = Vsl / Vm Under most conditions, however, the liquid phase, which is more dense and viscous, moves more slowly than the gas. When this occurs, the liquid holdup (Hl) is greater than the no-slip holdup.

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H l > H ln s Under these conditions, the actual gas velocity is greater than the mixture velocity, and the actual liquid velocity is smaller than the mixture velocity. The expressions for the actual gas velocity (Ug) and actual liquid velocity (Ul) are: Ug =

Vsg 1 − Hl

V U l = sl Hl For small diameter, low pressure piping, there is frequently a vast difference between Ug and Ul. For field piping, there is generally less slip between the phases, and the flow may approximate no-slip flow in dispersed bubble and annular flows. It is possible to get conditions where the liquid holdup is less than no-slip, but this only occurs over a small range of flowrates in downwardly inclined pipes. Pressure Gradient Two definitions of the term "pressure gradient" are used in the literature. In this guide, the term "pressure gradient" will be used to describe the pressure drop per unit length of pipe, (Pin - Pout)/L. In many papers, the term "pressure gradient" is used to denote the pressure change per unit length (dp/dx = (Pout - Pin)/L). The magnitude of the pressure gradient is the same in either definition, but the sign of the pressure drop per unit length is usually positive, while the sign of dp/dx is usually negative. Most people prefer to work with positive numbers, so the majority of people use the pressure drop per unit length definition. The choice of the definition is somewhat arbitrary, but it should be noted when reading the multiphase flow literature, and working with some of the available software. 3-Phase Flow vs. 2-Phase Flow In most of this guide, the discussion will consider 2-phase flow, or gas-liquid flow. In the majority of oil field applications, there will actually be 3 phases present (gas, oil, and water). The rigorous prediction of 3-phase flow is in its infancy. 3-Phase flow methods

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are not generally available, so most simulators use 2-phase models with a mixed liquid stream using averaged properties for the oil and water. The use of 2-phase models with averaged properties generally gives acceptable results unless either: emulsions are present; or the flowrates are low enough to cause stratification of all three phases. These problems are discussed in more depth in Section 3.2.1 Mechanistic Models vs. Correlations The prediction of multiphase flow behavior has improved considerably during the 50+ years that the subject has been studied. For many years, multiphase flow prediction methods were correlations, based on curve fits of experimental data. The correlations frequently used arbitrarily selected variables and were based on limited databases, consisting almost entirely of low pressure, small diameter data. Extrapolations of these prediction methods to field conditions frequently proved to be seriously in error. In the 1960s and 1970s, several investigators undertook experimental studies to try to understand the fundamental mechanisms of the various flow regimes. In the past 15 years models have been developed, which are based on simulation of these mechanisms. These models, referred to as mechanistic models, have proven to extrapolate best to field conditions. Newtonian vs. Non-Newtonian Fluids Most condensates and crude oils follow Newton’s law of viscosity, which is defined as:

τ yx = µ where τyx

dv x dy

= shear stress

µ

= viscosity

vx

= velocity

y

= distance

Some liquids, however, exhibit behavior that is very different from Newton's law. These fluids are referred to as non-Newtonian. In the oil field, examples of non-Newtonian fluids are drilling muds, polymeric additives, and crude oils below their cloud point.

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Flowline simulators are based on Newtonian fluids. If a non-Newtonian liquid is present, the simulator must be “tricked” into giving a Newtonian viscosity equivalent to the actual viscosity at the given temperature and shear stress. The methods of doing this are beyond the scope of this guide.

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Figure I:1-1 Flow Regimes in Horizontal Flow

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Figure I:1-2 Flow Regimes in Vertical Flow

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SECTION 2.0 - OVERVIEW OF MULTIPHASE FLOW FUNDAMENTALS 2.1

Design Criteria

The majority of lines are sized by use of three primary design criteria: available pressure drop; allowable velocities; and flow regime. In some cases, a more optimal line size may be found that better suits the overall design of the pipeline system. These considerations will be discussed later in the transient modeling section of the guide. A description of each of the primary design criteria follows in Sections 2.2, 2.3, and 2.4. 2.2

Velocity Guidelines

The velocity in multiphase flow pipelines should be kept within certain limits in order to ensure proper operation. Operating problems can occur if the velocity is either too high or too low, as described in the following sections. It is difficult to accurately define the point at which velocities are "too high" or "too low". This section of the guide will try to quantify limits, but these limits should be considered as guidelines and not absolute values. Maximum Velocity For the maximum design velocity in a pipeline, API RP-14E recommends the following formula: Vmax =

C ρ ns

(Eqn. 2.1)

where Vmax = Maximum mixture velocity, ft/sec

ρns

= No-slip mixture density, lb/ft3 =

ρg

CPTC

(ρ

g

)

Vsg + (ρ l Vsl ) Vm

= Gas Density, lb/ft3

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ρl

= Liquid Density, lb/ft3

C

= Constant, 100 for continuous service, 125 for intermittent service.

This equation attempts to indicate the velocity at which erosion-corrosion begins to increase rapidly. Many people think this equation is an oversimplification of a highly complex subject, and as a result, there has been considerable controversy over its use. For wells with no sand present, values of C have been reported to be as high as 300 without significant erosion/corrosion. For flowlines with significant amounts of sand present, there has been considerable erosion-corrosion for lines operating below C = 100. The use of the API equation has been the subject of several research projects. It has been generally agreed that the form of the equation is not sophisticated enough, and should include additional parameters. Unfortunately, no other equation has been proposed which has gained acceptance in the industry as an alternative to the API equation. As a result, the recommended maximum velocity in the pipeline is the value calculated from Equation 2.1 with a C value of 100. It should be noted that Equation 2.1 is also used by many people as an estimate of the maximum velocity for noise control. For additional guidance on the use of the API equation, refer to Chevron’s Piping Manual. Minimum Velocity The concept of a minimum velocity for the pipeline is an important one and should be considered in the design of the line. Turndown conditions frequently govern the design of the downstream equipment. Velocities that are too low are frequently a greater problem than excessive velocities, so that the designer’s natural tendency to add "a bit of fat" to the design by increasing pipe diameter can cause severe problems in the operation of the line and the downstream facilities. At low velocities, several operating problems may occur: a) Water may accumulate at low spots in the line. If there is an appreciable amount of CO2 or H2S in the well stream, this water may be very corrosive.

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b) Liquid holdup may increase rapidly at low mixture velocities. A large accumulation of liquid may cause problems in downstream separators or slug catchers if the line is pigged or the rate is changed rapidly. c) Low velocities may cause terrain induced slugging in hilly terrain pipelines and pipeline-riser systems. It isn’t possible to give a simple formula quantifying the velocity when the phenomena discussed above will occur. The minimum velocity depends on many variables, including: topography; pipeline diameter; gas-liquid ratio; and operating conditions of the line. A ball-park value for the minimum velocity would be a mixture velocity of 5-8 ft/sec. The actual value of the minimum velocity can only be quantified by simulation of the system using the methods discussed in Section 5.2.2. 2.3

Flow Regimes

As discussed in Section 1, the gas and liquid in the pipe are distributed differently in each of the four major flow regimes (stratified, annular, slug, and dispersed bubble flows). The prediction of the correct flow regime is important for several reasons. The flow regime prediction can show whether the line will operate in a stable flow regime or an unstable regime. The prediction of liquid holdup and pressure drop are highly dependent on the flow regime, with each regime exhibiting different behavior when the design variables are changed. The transitions between the flow regimes are frequently depicted in a flow regime map, such as that shown in Figure I:2-1. The flow regime map typically has the superficial gas velocity (Vsg) on the X-axis and the superficial liquid velocity (Vsl) on the Y-axis. As discussed later in this section, the flow regime map is only valid for a single point in the pipeline. As the angle of inclination, pressure and temperature change with position in the pipeline, the flow regime map also changes. Some general comments, however, can be made about the flow regime transitions. Stratified flow occurs at low superficial gas and liquid velocities. Dispersed bubble flow occurs at high superficial liquid velocities. Annular flow occurs at high superficial gas

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velocities. Slug flow occurs at moderate superficial gas and liquid velocities. Figure I:2-2 shows a typical flow regime map for vertical flow. Many experimental studies of the transitions between the flow regimes for various systems have been made, and many flow regime transition prediction methods have been published. Some of these methods work fairly well, but most are poor. The designer needs to carefully choose the method that will work best for the set of conditions. The best methods are discussed in the remainder of this section. Experimental studies of flow regime transitions have shown that each of the flow regime boundaries reacts differently to changes in the system variables. The following table shows the sensitivity of the transitions to changes in the major system variables:

Slug to Dispersed Bubble

Slug to Annular

Slug to Stratified

Stratified to Annular

Angle of Inclination

Small Effect

Moderate Effect

Strong Effect

Strong Effect

Gas Density

Small Effect

Strong Effect

Strong Effect

Strong Effect

Pipeline Diameter

Small Effect

Small Effect

Strong Effect

Moderate Effect

Liquid Physical Properties

Moderate Effect

Small Effect

Moderate Effect

Moderate Effect

Transition Variable

Many people have attempted to develop simple flow regime maps, usually using some arbitrary dimensionless parameter on each axis (e.g. Baker, Beggs & Brill). These methods are inherently inaccurate since no single parameter can model the sensitivity effects shown in the previous table. The only flow regime map prediction methods that have been effective for a wide range of conditions are those using mechanistic models to estimate the flow regime transitions.

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In 1976, Taitel and Dukler published a landmark article describing a method of predicting flow regime transitions by modeling the mechanism of each transition. By modeling each transition, this method can show the same type of behavior observed in the experimental work. The original Taitel-Dukler paper covered flow regime transitions in near horizontal flow only, and one of the transitions (slug-dispersed bubble) is very much in error. Taitel and his co-workers at the University of Tel Aviv have subsequently published several articles that expand the range of angles of inclination and correct the errors in the original paper. The Taitel-Dukler paper and the latest paper from Tel Aviv model flow regime transitions for all angles of inclination. The Taitel, et al. methods give reasonably good predictions of the various flow regime transitions, and the accuracy of the predictions has improved with each revision. Another approach to the modeling of flow regime transitions is the method used in the OLGAS method. It employs mechanistic models of each flow regime and links the models by the assumption that the flow regime giving the lowest liquid holdup is the correct one. This assumption holds up well in practice. The OLGAS method predicts flow regime transitions with similar accuracy to the Taitel, et al. models. Within Chevron, there are several programs available for flow pattern prediction. Pipephase will print a flow regime map based on the Taitel-Dukler method for near horizontal flow and the Taitel-Dukler-Barnea model for near vertical flow. Unfortunately, these methods are the oldest and weakest of this family of methods. Two programs are available within CPTC that incorporate the latest versions of the Taitel, et al. models. These programs are FLOPAT, developed by Tulsa University, and FLEX, developed by Advance Multiphase Technology. CPTC should be consulted if it is desired to use these programs. As in many aspects of multiphase flow, the flow regime prediction methods are not exact. Errors of +/- 25% for the transition velocities are typical, even for the best prediction methods. If the Taitel-Dukler map is used, the designer should be aware of the gross errors in the slug to dispersed bubble transition. The errors for this transition can be 1000%. The dispersed bubble to slug transition typically occurs at a superficial liquid velocity of about 10 ft/sec. Taitel-Dukler frequently predicts this transition velocity to be 50-100 ft/sec.

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2.4

Pressure Gradient

In most pipelines, the pipeline diameter is determined by the allowable pressure drop in the line. The overall pressure gradient is composed of three additive elements: a) pressure drop due to friction;

b) pressure changes due to elevational effects; c) accelerational losses. The calculation of the constituent parts of the pressure gradient will be discussed in the next three sections. The Chevron Fluid Flow Manual contains a good discussion of these pressure loss terms for single phase flow and can be consulted as a reference. 2.4.1

Frictional Losses

In multiphase flow, frictional losses occur by two mechanisms: friction between the gas or liquid and the pipe wall; and frictional losses at the interface between the gas and liquid. The friction calculations, therefore, are highly dependent on the flow regime, since the distribution of liquid and gas in the pipe changes markedly for each regime. In stratified flow, there is wall friction between the gas and the pipe wall at the top of the pipe, and wall friction between the liquid and the wall at the bottom of the pipe. There is also friction between the gas and liquid at the gas-liquid interface. The interfacial friction can be similar in magnitude to the wall friction if the interface is smooth, or it can be considerably higher if waves are present. In annular flow, there is friction between the liquid film and the wall. There is also considerable interfacial friction between the gas in the core of the pipe and the liquid film. The interfacial friction is usually the larger component. In dispersed bubble flow, friction occurs between the liquid and the wall. There is negligible interfacial friction between the gas and liquid.

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Slug flow has several frictional components. In the slug, the friction losses are caused by the friction between the liquid and the pipe wall. In the gas bubble, the frictional components are the same as in stratified flow, namely gas and liquid friction with the pipe walls and interfacial friction between the gas and liquid. The friction loss in the slug is usually much higher than the losses in the bubble. 2.4.2

Elevational Losses

Elevational losses may be the major pressure loss component in vertical flow and flow through hilly terrain. The calculation of elevational losses is governed by the following equation:

ρ g sinα  dp    = mix  dx  elev 144g c where: (dp/dx)elev = Pressure gradient due to elevation, psi/ft

ρmix

= Mixture Density, lb/ft3 = (ρl) (Hl) + (ρg) (1-Hl)

Hl

= Liquid Holdup

g

= Acceleration due to gravity, 32.2 ft/sec2 α

gc

= Angle of inclination = Gravitational conversion factor, 32.2 lb-ft/(lbf-sec2)

In order to calculate the elevational gradient, the liquid holdup must be determined. The holdup in each flow regime has its own sensitivity to the important operating variables. A summary of the effect of the major operating variables on the liquid holdup is:

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Slug Flow

Annular Flow

Stratified Flow

Dispersed Bubble Flow

Superficial Gas Velocity

Strong

Strong

Strong

Strong

Superficial Liquid Velocity

Strong

Strong

Strong

Strong

Gas Density

Moderate

Strong

Strong

None

Pipeline Diameter

Moderate

Weak

Weak

Weak

Angle of Inclination

Moderate

Weak

Very Strong

None

Liquid Properties

Moderate

Moderate

Moderate

Weak

As seen in the previous table, the influence of the major variables on the holdup is very different for each of the flow regimes. As a result, it is impossible to develop a general holdup correlation that will apply to all the flow regimes. Unfortunately, almost all of the commonly used holdup methods available in commercial software try to do this. They work poorly over much of the operating range as a result. The only way to accurately predict liquid holdup is to use mechanistic models for each of the flow regimes. The accuracy of available holdup methods is discussed further in Section 3.2.4. 2.4.3

Acceleration Losses

Although acceleration losses are present for all flow regimes, they are only significant for two flow regimes: annular flow and slug flow. The mechanisms for the losses in these two flow regimes are very different and will be discussed separately. In single phase flow, acceleration losses can be calculated from Bernoulli’s equation. Acceleration losses represent the change in kinetic energy as the fluid flows down the pipe. The expression for acceleration gradient is:  ρ V   dV   dp     =   dx  accel  144 g c   dx 

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where: ρ

= Density, lbm/ft3

V

= Velocity, ft/sec

For multiphase flow, the same type of relationship holds except that it refers to the flow of the mixed phase fluid. Most methods assume a no-slip mixture and use the no-slip mixture density (ρns) and the mixture velocity (Vm) in the calculation of acceleration losses. The kinetic energy acceleration losses are small for most oil industry applications. The main exception is high velocity flow through low pressure piping. Flare systems would be an example of piping that has high acceleration losses. Acceleration may account for 3050% of the overall pressure loss in such lines. For a typical high pressure gathering system line, acceleration is usually less than 1% of the total drop and is frequently ignored. Please note that the present version of Pipephase, 6.02, does not properly account for acceleration losses, and, as a result, is not suitable for use in flare system design. In slug flow, another source of acceleration contributes significantly to the total pressure drop. As a slug propagates down the pipeline, it overruns and entrains the slower moving liquid from the film ahead of the slug front. Accelerating the liquid from the film velocity to the slug velocity can produce significant pressure losses. The acceleration loss may be anywhere from