10.1.1.476.6482 tesis de dr carlos oropeza vasquez

8/20/2019 10.1.1.476.6482 Tesis de Dr Carlos Oropeza Vasquez

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T H E U N I V E R S I T Y O F T U L S A

THE GRADUATE SCHOOL

MULTIPHASE FLOW SEPARATION IN LIQUID-LIQUID CYLINDRICAL

CYCLONE AND GAS-LIQUID-LIQUID CYLINDRICAL CYCLONE

COMPACT SEPARATORS

by

Carlos Oropeza-Vazquez

A dissertation submitted in partial fulfillment of

the requirements for the degree of Doctor of Philosophy

in the Discipline of Petroleum Engineering

The Graduate School

The University of Tulsa

2001


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ABSTRACT

Carlos Oropeza (Doctor of Philosophy in Petroleum Engineering).

Multiphase Separation in Liquid-Liquid Cylindrical Cyclone and Gas-Liquid-Liquid

Cylindrical Cyclone Compact Separators (120 pp. - Chapter VI).

Directed by Dr. Ovadia Shoham and Dr. Ram Mohan

(411 words)

The hydrodynamics of multiphase flow in Liquid-Liquid Cylindrical Cyclone

(LLCC©1) and Gas-Liquid-Liquid Cylindrical Cyclone (GLLCC©

2) compact separators

have been studied experimentally and theoretically for evaluation of their performance as

free water knockout devices. In both GLLCC and the LLCC configurations, no complete

oil-water separation occurs. Rather, both separators perform as free water knockouts,

delivering a clean water stream and an oil rich stream.

A new state-of-the-art, two-inch, three-phase, fully instrumented flow loop has

been designed and constructed. Experimental data on oil-water separation efficiency in

the LLCC and the GLLCC have been acquired.

A total of 260 runs have been conducted for the LLCC for water-dominated flow

conditions. Four different flow patterns in the inlet have been identified, namely,

Stratified flow, Oil-in-Water Dispersion – Water Layer flow, Double Oil-in-Water

1 LLCC - Liquid-Liquid Cylindrical Cyclone - Copyright, The University of Tulsa, 1998.2 GLLCC – Gas-Liquid-Liquid Cylindrical Cyclone – Copyright, The University of Tulsa, 2000.


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Dispersion flow and Oil-in-Water Dispersion flow. For all runs, an optimal split ratio

exists, where the flow rate in the water stream is maximum with 100% water cut. The

value of the optimal (maximum) split ratio depends upon the existing flow pattern. For

the Stratified and Oil-in-Water Dispersion - Water Layer flow patterns, this maximum

split ratio is about 60%. For the Double Oil-in-Water Dispersion and Oil-in-Water

Dispersion flow patterns, the maximum split ratio ranges from 50% to 20%, decreasing

with the increase of oil content in the inlet stream.

Experimental data on oil-water separation efficiency in the GLLCC have been

acquired. A total of 220 experimental runs have been conducted, including the oil-water

separation efficiency for different combinations of oil and water superficial velocities,

and varying the split ratio for each combination. The GLLCC separation efficiency data

reveal that it performs, in addition to the separation of the gas phase, also as a free water

knockout. This occurs only for very low oil concentrations at the inlet, below 10%.

Also, lower separation efficiencies are observed, as compared to the LLCC configuration.

Novel mechanistic models have been developed for the prediction of the complex

flow behavior and the separation efficiency in the LLCC and GLLCC. The models

consist of several sub-models, including inlet analysis, nozzle analysis, droplet size

distribution model, and separation model based on droplet trajectories in swirling flow.

Comparisons between the experimental data and the LLCC and GLLCC model

predictions show excellent agreement. The models are capable of predicting both the

trend of the experimental data as well as the absolute measured values. The developed

models can be utilized for the design and performance analysis of the LLCC and

GLLCC.


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ACKNOWLEDGMENTS

I acknowledge Dr. Ovadia Shoham and Dr. Ram Mohan for their personal support

and encouragement as well as their supervision and guidance in this study. I also thank

Dr. Mauricio Prado and Dr. Leslie Thompson, for their willingness to serve as members

of the dissertation committee and for their useful suggestions and assistance.

I am very grateful to PEMEX Exploración y Producción for this once-in-a-

lifetime opportunity, as well as the U. S. Department of Energy (Grant No. DE-FG26-

97BC15024) for supporting this project. I thank the TUSTP members and graduate

students for their valuable assistance during this project, especially to Jinli Liu and

Rajkumar Mathiravedu for their assistance in the experimental data acquisition. My

appreciation is extended to Ms. Judy Teal also.

This dissertation is dedicated to my beloved wife Carolina and my children Carlos

and Carolina. I fully appreciate their love and encouragement during my graduate studies

at The University of Tulsa. I dedicate this work to my family, especially to my mother

Teresa.


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vi

TABLE OF CONTENTS

TITLE PAGE i

APPROVAL PAGE ii

ABSTRACT iii

ACKNOWLEDGMENTS v

TABLE OF CONTENTS vi

LIST OF FIGURES ix

LIST OF TABLES xii

CHAPTER I: INTRODUCTION 1

CHAPTER II: LITERATURE REVIEW 6

2.1 GLCC Development 6

2.2 LLCC Development 8

2.3 Swirling Flow Field 9

2.4 Oil-Water Pipe Flow Pattern Prediction 10

2.5 Droplet Size Distribution 15

CHAPTER III: EXPERIMENTAL PROGRAM 16

3.1 Experimental Facility 16

3.1.1 Metering and Storage Section 17

3.1.2 Modular Test Section 18

3.1.3 Instrumentation, Control and Data Acquisition System 19

3.1.4 GLLCC Design 20

3.1.5 LLCC Design 21


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3.2 Experimental Results 22

3.2.1 LLCC Experimental Results 22

Inlet Flow Patterns 23

Separation Efficiency 28

3.2.2 GLLCC Experimental Results 32

CHAPTER IV: MECHANISTIC MODELING 40

4.1 LLCC Mechanistic Model 40

4.1.1 Inlet Analysis 41

Inlet Flow Pattern Prediction 42

Stratified Flow Model 44

Oil-in-Water Dispersion - Water Layer Model 48

Oil-in-Water Dispersion Model 50

Double Oil-in-Water Dispersion Model 51

Nozzle Analysis 52

4.1.2 Separation Analysis 55

Entry Region Analysis 55

Flow Field 58

Droplet Trajectory 61

4.2 GLLCC Mechanistic Model 69

4.2.1 Physical Phenomena 70

4.2.2 Inlet Analysis 71

4.2.3 Nozzle Analysis 74

4.2.4 Oil-Water Separation Analysis 77


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Equilibrium Split Ratio 81

Water-cut in Water Outlet 83

CHAPTER V: RESULTS AND DISCUSSION 84

5.1 LLCC Comparison Study 84

5.2 GLLCC Comparison Study 89

CHAPTER VI: CONCLUSIONS AND RECOMMENDATIONS 94

NOMENCLATURE 99

REFERENCES 104

APPENDIX A: LLCC EXPERIMENTAL DATA 110

APPENDIX B: GLLCC EXPERIMENTAL DATA 115


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Figure 3-18. GLLCC Experimental Results (Set 1) 35

Figure 3-19. GLLCC Experimental Results (Set 2) 36

Figure 3-20. GLLCC Separation Efficiency Results (Set 3) 37

Figure3-21. GLLCC Experimental Results (vSW = 0.3 m/s) 38

Figure 3-22. GLLCC Experimental Results (vSW = 0.5 m/s) 38

Figure 4-1. LLCC Schematic 41

Figure 4-2. Trallero (1995) Flow Pattern Prediction Model and Experimental Data 43

Figure 4-3. Modified Trallero (1995) Model Flow Pattern Map 44

Figure 4-4. Stratified Flow Model Geometry and Variables 45

Figure 4-5. Nozzle Schematic and Variables 53

Figure 4-6. Local Split at Entry Region and Reverse Flow 56

Figure 4-7. Fluid Transfer from Oil Leg to Water Leg for qunder > q50 58

Figure 4-8. Droplet Size Distribution 66

Figure 4-9. Schematic of Water Leg Separation Calculation Procedure 67

Figure 4-10. Oil Removal Based on Separated Oil Droplet Diameter 69

Figure 4-11. GLLCC Schematic 70

Figure 4-12. Two-Fluid Model Schematic and Variables for GLLCC Inlet 72

Figure 4-13. Nozzle Schematic and Variables 75

Figure 4-14. GLLCC Liquid Leg Separation: Calculation Procedure 80

Figure 5-1. LLCC Comparison Study: Stratified Flow 84

Figure 5-2. LLCC Comparison Study: DO/W–Water Layer Flow (Runs 4, 7, 10) 85


Figure 5-4. LLCC Comparison Study: DO/W–Water Layer Flow (Runs 1, 25, 26, 27) 86


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Figure 5-6. LLCC Comparison Study: Double DO/W Flow (Runs 14, 17, 19, 21) 88

Figure 5-7. LLCC Comparison Study: Double DO/W Flow (Runs 30, 31) 88

Figure 5-8. LLCC Comparison Study: DO/W Flow 89

Figure 5-9. GLLCC Comparison Study for Data Set 1 90

Figure 5-10. GLLCC Comparison Study for Data Set 2 91

Figure 5-11. GLLCC Comparison Study for Data Set 3 (vSW = 0.5 m/s) 92





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LIST OF TABLES

Table 2-1. Exponents and Coefficients for Trallero (1995) Model 14

Table 4-1. Modified Coefficients for LLCC Inlet Flow Pattern Prediction 43

Table 4-2. Inlet Momentum Flux Ratio and Initial Water-cut Calculation 62

Table A-1. LLCC Experimental Data 111

Table B1. GLLCC Experimental Data Set 1: Oil Finder @ 30 inches Below Inlet 116

Table B2. GLLCC Experimental Data Set 2: Oil Finder @ 36 inches Below Inlet 116

Table B3. GLLCC Experimental Data Set 3 117


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CHAPTER I

INTRODUCTION

The presence of water along with the hydrocarbons produced from the reservoir is

a common phenomenon in the petroleum production. The amount of produced water

usually increases and tends to be the main product as the field becomes more mature. The

volume of produced water that must be processed in the separation facilities often

exceeds that of the produced hydrocarbons, increasing size and cost of the equipment.

The production of water also increases with secondary recovery methods, such as water

flooding and steam injection.

The oil -water-gas separation technology in the petroleum industry has been based

in the past on conventional vessel-type separators. These separators are bulky, heavy and

expensive. With the new trend in the petroleum industry toward hydrocarbons production

from offshore fields and economic challenges to reduce production costs, the petroleum

industry has recently shown keen interest in compact separators that are low weight, low

cost and efficient.

Gas-Liquid Separation: One alternative for gas-liquid separation, which is

economically attractive, is the Gas Liquid Cylindrical Cyclone (GLCC©

)3. The GLCC is

a simple, compact and low-cost separator. It is a vertical pipe section, with a downward

inclined, tangential inlet located approximately at the middle. Neither moving parts nor

internal devices are used, reducing the need for maintenance. The separation in this


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equipment is achieved by centrifugal and gravity effects. The inclined inlet promotes a

gravity driven pre-separation and the tangential inlet creates a swirling motion in the

vertical pipe, forcing the liquid toward the pipe wall and to the bottom, while the gas

moves to the center of the pipe and exits from the top. Control valves on both gas and

liquid outlets maintain the liquid level constant inside the vertical section. Mechanistic

models for design and performance prediction of the GLCC are now available. In these

models, the oil-water mixture is treated as a single liquid phase flow. The GLCC has

recently gained popularity in the industry, with more than 150 units installed in the field

around the world.

Liquid-Liquid Separation: Most of the studies on liquid-liquid separation have

been focused on conical liquid hydrocyclones (LLHC). The main application of the

hydrocyclone is to clean produced oily water for disposal, reducing oil concentrations to

the order of ppm in the effluent. This equipment is suitable only for water with very low

oil content. During the development of the conical hydrocyclone, attempts were made to

utilize cylindrical geometries. The use of cylindrical hydrocyclones for liquid-liquid

separation has not been deeply investigated primarily due to the fact that at high

velocities they perform as mixers rather than separators. However, by operating at

moderate velocities, the cylindrical hydrocyclone can be used to perform at least partial

liquid-liquid separation (free water knockout).

A pioneering study has been conducted by Afanador (1999) on the performance

of the cylindrical cyclone as a free water knockout. In that study the regular configuration

of the GLCC was used, i.e., a vertical pipe with an inclined tangential inlet. This

3 GLCC - Gas-Liquid Cylindrical Cyclone - Copyright, The University of Tulsa, 1994


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equipment is referred to as the Liquid-Liquid Cylindrical Cyclone (LLCC). The reported

results indicated the capability of this device to provide a water-rich stream from the

bottom and an oil-rich stream from the top by using low and moderate liquid velocities.

Gas-Liquid-Liquid Separation: In order to extend the cylindrical cyclone

technology to three-phase gas-oil-water separation, two geometrical configurations are

proposed in this study.

3-phase

Flow

Oil + Water

Gas

Oil

Water

Figure 1-1. Two-Stage System (GLCC and LLCC)

The first configuration is called the Two-Stage System and it is shown in Figure

1-1. The Two-Stage System consists of a regular GLCC, as the first stage, to remove the

gas from the liquid, with the liquid outlet connected to a second stage LLCC to separate

the liquid mixture. In this configuration, the three-phase gas-oil-water mixture enters

through the inclined tangential inlet of the GLCC. The gas flows to the top and exits out

of the system. The liquid, an oil-water mixture, flows through the GLCC liquid leg into


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the second stage LLCC.

The LLCC horizontal inlet promotes oil-water segregation and the liquid phases

enter the vertical section through a reducing area nozzle, increasing their velocity. The

swirling motion in the LLCC produces a centrifugal separation, thus, an oil-rich stream

exits through the top (overflow) and a water-rich stream leaves the system through the

bottom (underflow).

Gas

Water-Rich

Oil-Rich

3-Phase

Flow

Oil Finder

Figure 1-2. Gas-Liquid-Liquid Cylindrical Cyclone (GLLCC)

Figure 1-2 shows the second configuration. This configuration is a single stage

system called the Gas-Liquid-Liquid Cylindrical Cyclone (GLLCC). It consists of a

regular GLCC body with an inner concentric pipe extended through the bottom, called

the oil finder. In this case, the three-phase mixture enters through the inclined tangential

inlet, which promotes gas-liquid pre-separation by segregating the gas and the liquid

forming a stratified flow pattern. The tangential entry of the fluid produces a swirling


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motion in the vertical pipe. The gas flows upwards to the gas outlet and leaves the

GLLCC, while the liquid swirls in the lower section of the vertical pipe. Due to the

difference in density, the centrifugal effect segregates the oil-water mixture,

concentrating the oil at the center of the pipe, while the water is thrown towards the wall

region. The oil-rich core formed at the center is taken out through the oil finder. The

water-rich liquid, present at the wall region, flows to the annulus between the pipe wall

and the oil finder and leaves the GLLCC through the tangential outlet.

Objective and Dissertation Structure: The objective of the present study is to

investigate experimentally and theoretically oil-water separation performance of the

LLCC; and the oil-water separation performance of the GLLCC, while performing gas-

liquid separation.

The next chapter presents a review of the literature relevant to this study. In

Chapter III, the new experimental facility is described as well as the experiments carried

out in the GLLCC and the LLCC. The developed models are presented in Chapter IV.

Chapter V includes the comparison between the experimental results and the modeling

predictions. Conclusions and recommendations are found in Chapter VI.


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CHAPTER II

LITERATURE REVIEW

The Liquid-Liquid-Cylindrical Cyclone (LLCC) and the Gas-Liquid-Liquid

Cylindrical Cyclone (GLLCC) are new technologies for multiphase flow separation that

followed the advances in the Gas-Liquid Cylindrical Cyclone (GLCC) separator

development at The University of Tulsa. Pertinent literature on the GLCC and LLCC,

along with three other related topics, namely, swirling flow, oil-water flow patterns and

oil droplet size distribution, are given below.

2.1 GLCC Development

Previous experimental attempts using cylindrical hydrocyclones for gas-liquid

separation found in the literature include Davies and Watson (1979) and Davies (1984)

who studied compact separators for offshore production, where low size and weight of

the equipment are important. They showed several advantages of using a cyclone

separator instead of conventional separator, such as compactness and low cost, while

improving the separation performance.

Nebrensky et al. (1980) developed a cyclone for gas-oil separation that included a

tangential rectangular inlet with a special arrangement to change the inlet area. Zhikarev

et al. (1985) developed a cyclone separator with a rectangular, tangential inlet located

near the bottom.


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Based on experimental results, Fekete (1986) suggested the use of a vortex tube

separator due to its low weight and size. Another study by Oranje (1990) also showed

that cyclone type separators are suitable for applications on offshore platforms due to

their small size and weight.

Cowie (1992) tested vertical caisson slug catchers comparing radial and tangential

inlets. The tangential inlet configuration provided the best performance. Bandyopadhyay

et al. (1994) studied the separation of helium bubbles from water using cyclone

separators.

Weingarten et al. (1995) developed and tested the auger separator which is a

cylindrical cyclone with internal spiral vanes.

Based on experimental and theoretical studies performed at The University of

Tulsa, a mechanistic model for the GLCC was developed by Arpandi et al. (1995). This

model is able to predict the general hydrodynamic flow behavior in a GLCC, including

simple velocity distributions, gas-liquid interface shape, equilibrium liquid level, total

pressure drop, and operational envelop for liquid carry-over. Marti et al. (1996)

attempted to develop a mechanistic model to predict gas carry-under in GLCC separators.

This model predicts the separation efficiency based on bubble trajectory analysis. Gomez

(1998) developed a state-of-the-art computer code integrating improved models for the

different sections of the GLCC.

The models developed at the University of Tulsa have allowed the application of

the GLCC to real field cases as detailed by Kouba and Shoham. (1996) and Gomez et al.

(2000)


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Movafaghian et al. (2000) reported the effects of fluid properties, inlet geometry

and pressure on the behavior of the GLCC. Gomez, L.E. (2001) developed a model to

predict the gas carry-under in this separator.

2.2 LLCC Development

Most of the published work on liquid-liquid separation in hydrocyclones has been

done on conical hydrocyclones (LLHC) consisting of mainly experimental studies. A

review of the important references on the LLHC is given by Gomez, C.H. (2001).

Very few studies have been published on the Liquid-Liquid Cylindrical Cyclone

separator. Listewnik (1984) reported oil-water separation efficiency in a cylindrical

hydrocyclone with four inlets. Gay et al. (1987) presented a comparison between a static

conical hydrocyclone and a rotary cylindrical cyclone. Bednarsky and Listewnik (1988)

analyzed the effect of the inlet diameter on the separation efficiency of a hydrocyclone.

They concluded that small inlets cause droplet break-up and big inlets do not produce

enough swirl intensity. Seyda (1991) simulated numerically the separation of oil-water

dispersions in a small cylindrical tube.

Afanador (1999), at the University of Tulsa, performed a pioneering experimental

study on the separation efficiency of oil and water by using the LLCC separator. She used

a two-inch cylindrical cyclone with an inclined tangential inlet, similar to the GLCC

configuration. The mixture entered through the inclined tangential inlet and swirled

inside the vertical pipe providing an oil-rich stream from the top and a water-rich stream

from the bottom.


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2.3 Swirling Flow Field

Nissan and Bressan (1961) measured experimentally the axial and tangential

velocities of swirling flow in pipes. They injected water through two tangential inlets and

used impact probes to measure the velocities. The axial velocity distribution showed a

flow reversal region near the center of the pipe.

Ito et al. (1979) studied the swirl intensity decay by using water and multi-

electrode probes. The measured tangential velocity distribution showed a forced vortex

structure near the pipe axis and a free vortex structure close to the wall. The swirl was

found to decrease with the axial distance.

Millington and Thew (1987) used Laser Doppler Anemometry to measure the

velocity inside a cylindrical cyclone section and reported the tangential velocity profile to

be a forced vortex structure. Algifri et al. (1988) conducted experiments on turbulent

swirling pipe flow using air and hot-wire probes. They concluded that the tangential

velocity distribution could be described as a Rankine-type vortex.

Kitoh (1991) measured the flow field in swirling flow by using hot wire

anemometers and found that the swirl intensity decays exponentially with the axial

distance. Chang and Dhir (1994), using air and hot-wire anemometers, studied the

turbulence in a swirling flow. It was found that the swirl intensity decays as a function of

the axial distance and the Reynolds number.

Using Laser Doppler Velocimetry and Pitot tube, Kurokawa (1995) located three

regions in the pipe swirling flow: a jet region in the center of the pipe with a forced

vortex structure, an intermediate region of reverse flow and a free vortex region near the


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wall. He reported that when the pipe is long enough, the swirl intensity becomes weak

and the reverse flow disappears, leading to regular pipe flow.

By using published data and CFD simulation, Mantilla et al. (1999) developed

correlations for the axial and tangential velocities that take into account the reverse flow

region. Erdal (2001) presented experimental data on swirling flow of a single-phase

liquid in a vertical cylindrical pipe with tangential, horizontal and inclined inlets. He used

Laser Doppler Velocimetry, and glycerin and water as working fluids. Based on the

experimental results, he modified Mantilla’s correlations.

2.4 Oil-Water Pipe Flow Pattern Prediction

An extensive literature review on oil-water flow in pipes can be found in Trallero

(1995). Trallero (1995) acquired experimental data on oil-water flow patterns in

horizontal pipes. He proposed a new classification to standardize oil-water flow patterns

and developed a mechanistic model for their prediction. The model is based on the

stability analysis of the oil-water interface and droplet diameters comparison. The new

classification includes the following flow patterns.

• Stratified Flow (ST). In this pattern the two liquid phases flow as layers with the

heaviest, usually the water, at the bottom and the lighter (usually oil) at the top.

Some waviness can be observed at the interface.

• Stratified Flow with Mixing at the Interface (STMI). In this case the system tends

to be stratified, but the turbulence generates a mixing zone about the interface.

The mixing zone can be significant, but still pure fluids exist at the top and the


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bottom of the pipe.

• Dispersion of Oil in Water with a Water Layer (DO/W&W). The water is

distributed across the entire pipe. A layer of clean water is flowing at the bottom

and dispersed droplets of oil in water flow at the top.

• Dispersion of Water in Oil with an Oil Layer (DW/O&O). This case occurs for

high oil content. The oil is distributed across the entire pipe, forming a pure oil

layer at the top and the water exists as droplets dispersed in oil in the lower

section of the pipe.

• Dispersion of Oil in Water (DO/W). In this case, all the pipe area is occupied by

water containing dispersed oil droplets.

• Dispersion of Water in Oil (DW/O). The oil is the continuous phase and the water

is present as droplets across all the pipe area.

• Dual Dispersion (DO/W&DW/O). In this flow pattern, two different layers can be

identified. Both phases are present across the entire pipe, but at the top, the

continuous phase is the oil and it contains droplets of water. In the lower region of

the pipe, the continuous phase is the water and the oil exists as droplets.

Trallero’s model predicts the flow pattern by performing both inviscid and

viscous stability analyses of the oil-water interface under equilibrium stratified flow

conditions. If the flow conditions comply with both stability criteria, the flow pattern is

stratified with a clean interface. If some of these criteria are not satisfied, a comparison

between transitional velocities based on different droplet size definitions and the


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continuous phase properties is performed to predict the flow pattern.

The inviscid stability criterion is accomplished when

( ) ( )0

2,

2

2

≤−−−−=im

inwo

im

owin

mow

owinow

S

A

S

g A

A A

vv ACRI

ρ

ω σ

ρ

ρ ρ

ρ

ρ ρ . (2 - 1)

The viscous stability criterion is accomplished when:

( ) 011073.0

2

2

2

2

2

≤

++−+

+−+=

owm

inow

o

oo

w

ww

m

in

A A

Avv

A

v

A

v A

B

E CRI CRV

ρ ρ

ρ ρ

ρ , (2 - 2)

where ω is a wave number defined as 2π/(100d ). B is a dispersion coefficient calculated

by means of a small disturbance in the water height level and E is a dispersion coefficient

obtained by small perturbations of the oil and water velocities. The value of ! is the

density of the faster moving phase.

The different transitional velocities considered in Trallero (1995) model are as

follows:

• Transitional velocity of the oil based on the maximum water droplet diameter and

using the mixture velocity to calculate the friction factor:

m

o

wmaxwd

maxwd mo f

g d

v3

18 ,

,,,

−

= ρ

ρ

. (2 - 3)

• Transitional velocity of the oil based on the maximum water droplet diameter and

using the oil velocity to calculate the friction factor:


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o

o

wmaxwd

maxwd oo f

g d

V 3

18 ,

,,,

−

= ρ

ρ

. (2 - 4)

• Transitional velocity of the water based on the maximum oil droplet diameter and

using the water velocity to calculate the friction factor:

w

w

omaxod

maxod ww f

g d

V 3

18 ,

,,,

−

= ρ

ρ

. (2 - 5)

• Transitional velocity of the water based on the minimum oil droplet diameter and

using the water velocity to calculate the friction factor:

w

w

ominod

minod ww f

g d

V 3

18 ,

,,,

−

= ρ

ρ

. (2 - 6)

• Transitional velocity of the water based on the maximum oil droplet diameter and

using the mixture velocity to calculate the friction factor:

m

w

omaxod

maxod mw f

g d

V 3

18 ,

,,,

−

= ρ

ρ

. (2 - 7)

Figure 2-1 shows the flow chart for the liquid-liquid flow pattern prediction

using Trallero’s model.

Trallero modified the Hinze (1955) and Levich (1962) models for maximum and

minimum droplet diameters respectively, by taking into account the dispersed phase

concentration as follows:


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d vv

vC d

n

SOSW

SW mod

+

= . (2 - 8)

The constants and exponents utilized in Equation 2-8 are presented in Table 2-1.

Table 2-1. Exponents and Coefficients for Trallero (1995) Model

Droplet

DiameterFriction factor C n

dod,max f m 2 -3.5

dod,max f w 15.1 2

dod,min f w 2.2 -7

dwd,max f m 744 1.832

dwd,max f o 0.9 0

CRI < 0

CRV < 0vo < vw vo vo,m,wd,max

vo > vo,o,wd,maxvw > vw,w,od,max

vw vw,w,od,max

vo > vo,o,wd,maxvw > vw,w,od,max

vo > vo,m,wd,max

vw > vw,w,od,maxS

DW/O&DO/W

DW/O

DW/O&DO/W

DW/O

DW/O&O

DW/O&DO/W

STMI

DO/W

STMI DO/W&W

ST

N

Y

Y

N

N

N

Y

Y

N

N

N

Y

Y

Y

N

Y

N

Y

Y

N

Y N

N

Y

Figure 2-1. Trallero (1995) Model Flow Chart


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2.5 Droplet Size Distribution

Hinze (1955) published a model to calculate the maximum stable droplet size in

turbulent pipe flow. His model is based on the equilibrium between turbulent forces and

interfacial tension forces.

Levich (1962) showed that the Hinze (1955) model cannot predict the stable

droplet size in the region close to the pipe wall, and developed a new model that is

capable of predicting the minimum droplet size in the flow.

The Hinze (1955) and Levich (1962) models take into account the breakup

phenomenon, but not the coalescence. Trallero (1995) proposed the modification of these

models by using empirical functions of the dispersed phase concentration in order to take

into account the coalescence phenomenon.

Few works have been published on droplet size distribution when two

immiscible fluids flow in a pipe. Karabelas (1978) measured droplet size distributions

and found that the Rosin-Rammler and the log-normal distributions can describe his

experimental results. Crowe et al. (1998) states that the size distribution function

frequently used to correlate droplet size measurements is the Rosin-Rammler distribution.

The above literature review reveals a lack of systematic data and mechanistic

models for the LLCC and GLLCC. This is the scope and contribution of the present

study.


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CHAPTER III

EXPERIMENTAL PROGRAM

3.1 Experimental Facility

A new experimental flow loop has been constructed in the College of Engineering

and Natural Sciences Research Building, located in the North Campus of The University

of Tulsa. This indoor facility enables year around data acquisition and simultaneous

testing of different compact separation equipment. Figure 3-1 shows an overview of the

facility.

Figure 3-1. Experimental Flow Loop

The new oil-water-air three-phase flow facility is a fully instrumented state-of-

the-art, two-inch flow loop, enabling testing of single separation equipment or combined

separation systems. The three-phase flow loop consists of a metering and storage section


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and a modular test section. Following is a brief description of both sections.

3.1.1 Metering and Storage Section

Air is supplied from a compressor and is stored in a high-pressure gas tank. The

air flows through a one-inch metering section, consisting of Micromotion® mass flow

meter, pressure regulator and control valve. The liquid phases (water and oil) are pumped

from the respective storage tanks (400 gallons each), and are metered with two sets of

Micromotion® mass flow meters, pressure regulators and control valves. The pumping

station, shown in Figure 3-2, consists of a set of two pumps (10 HP and 25 HP equipped

with motor speed controllers) for each liquid phase. Each set of pumps has an automatic

re-circulating system to avoid high pressures. Several mixing points have been designed

to evaluate and control the oil-water mixing characteristics.

Figure 3-2. Tanks, Pumping Station and Metering Section


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The liquid and gas phases are then mixed at a tee junction and sent to the test

section. Downstream of the test sections, the gas, oil-rich and water-rich streams flow

through three Micromotion® net oil computers to measure the outlet gas flow rate, and

total flow rate and water-cut of the two liquid streams. The three streams then flow into a

three-phase conventional horizontal separator (36-inch diameter and 10 feet long), where

the air is vented to the atmosphere and the separated oil and water flow back to their

respective storage tanks. A technical grade white mineral oil type Tufflo® 6016 with a

specific gravity of 0.857 and a viscosity of 27 cp. (@ 75 °F) is used as the experimental

fluid along with tap water.

Figure 3-3. Test Section

3.1.2 Modular Test Section

The metered three-phase mixture coming from the metering section can flow into


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any of the four different test stations. This flexibility enables the testing of single

separation equipment, such as a GLLCC, LLCC, Liquid-Liquid Hydrocyclones (LLHC)

or conventional separators and any combination of these, in parallel or series, forming a

compact separation system. Two 10-feet x 15-feet x 8-feet frames are installed in the test

section in order to support the equipment. Figure 3-3 shows a picture of the modular test

section.

3.1.3 Instrumentation, Control and Data Acquisition System

Control valves placed along the flow loop control the flow into the test sections.

The flow loop is also equipped with several temperature sensors and pressure transducers

for measurement of the in-situ pressure and temperature conditions. All output signals

from the sensors, transducers, and metering devices are collected at a central panel. A

state-of-the art data acquisition system, built using LabView®

, is used to both control the

flow into and out of the loop and to acquire data from the analog signals transmitted by

the instrumentation. The program provides variable sampling rates. The sampling rate is

set at 2 Hz for a 2 minutes sampling period. The final measured quantity results from an

arithmetic averaging of the 240 readings, when steady-state condition is established. A

regular calibration procedure, employing a high-precision pressure pump, is performed

on each pressure transducer on a regular schedule to guarantee the precision of

measurements. The temperature transducers consist of a Resistive Temperature Detector

(RTD) sensor, and an electronic transmitter module.


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3.1.4 GLLCC Design

The GLLCC, shown in Figure 3-4, is a 7 feet, 3-inch ID vertical pipe, with a 5

feet, 3-inch ID, 27 degrees inclined inlet. The inlet slot area is 25% of the inlet full bore

cross sectional area and is connected tangentially to the vertical pipe. The inlet is located

3 feet below the top of the vertical section. The 2-inch ID gas outlet is located radially at

the top of the vertical pipe. The water 2-inch ID outlet is located tangentially at the

bottom of the vertical pipe. The oil finder is a movable, 3 feet, 1.5-inch ID pipe that

enters the lower end of the vertical pipe through a special seal arrangement. Four pins at

the top of the oil finder keep it concentric to the vertical pipe, allowing its up and down

movement. The oil finder is attached to an electromechanical lift device.

1.5

2

57

3

36

27°

3

6

44

4

8

2105

Nozz le

84

2

*Units in inches

*Not to scale

3-Phase

Mixture

3612 27

2

Gas

Oil

Water

Hose 1.52

Figure 3-4. GLLCC Design

Because single-phase meters are used to quantify the flow rates and water-cuts

downstream of the test section, traps are provided to remove any entrained liquid in the


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gas outlet and the entrained gas in both liquid outlets, as shown in Figure 3-4. The liquid

trap is a slightly downward inclined 6-inch ID pipe connected to the 2 inch ID gas outlet.

The liquid being carried over settles in this trap by reducing the gas velocity, and a

vertical 1-inch ID drain is provided to measure and remove the trapped liquid.

The gas trap in the water outlet consists of a vertical 4 feet, 8-inch ID pipe with a

2-inch ID tangential inlet located at the upper end. The water exits the trap through a

tangential 2-inch ID pipe at the bottom. The gas being carried by the liquid is separated

inside the trap by reducing the velocity and swirling the liquid, and it goes to the top of

the trap. A conical reduction 8 to 2 inches extends the upper end of the gas trap, and a 1

foot, 2-inch ID pipe with a ¼ inch valve is located at the top, enabling the measurement

and the relief of the trapped gas. A similar trap is used in the oil outlet, but the inlet is a 2-

inch ID tangential pipe connected with a 2-inch flexible hose to the 1.5-inch ID oil finder

to allow its movement inside the GLLCC body. Pressure and temperature transducers are

located at the inlet and pressure transducers are located on each of the three outlets.

Sampling ports are also provided on each outlet.

3.1.5 LLCC Design

The LLCC is a 6.4 feet, 2-inch ID vertical pipe, with a 5 feet, 2-inch ID horizontal

inlet. The inlet slot area is 25% of the inlet full bore cross sectional area. The inlet is

attached to the vertical section 3.3 feet below the top. A 1.5-inch ID concentric pipe

located at the top is used as the oil outlet, and the water outlet is a radial, 1.5-inch ID pipe

located at the bottom of the vertical section.


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A temperature sensor is located at the inlet and a pressure sensor is located on

each outlet. Sampling ports are provided on each outlet as well as the inlet. Figure 3-5

shows a schematic of the LLCC. Valves in both the oil outlet and the water outlet allow

the control of the flow rates leaving the separator, namely, the split ratio.

40

Oil-Water

Mixture

Oil-rich

Water-rich

*Units in inches

*Not to scale

1.5

2

60

40

37

2

1.5 1 Nozzle

Figure 3-5. LLCC Design

3.2 Experimental Results

The experimental data acquired for both the LLCC and the GLLCC are presented

in the following section.

3.2.1 LLCC Experimental Results

Experiments on the LLCC have been conducted by Mathiravedu (2001) in order

to develop control strategies to maximize the free water knockout. The results of some


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experiments are used in this study. Only the water-dominated case (superficial water

velocity greater than superficial oil velocity) is considered. The maximum total liquid

mixture superficial velocity used is around 1.3 m/s, since beyond this velocity the oil-

water system forms a stable emulsion. Under this condition, no free water exists and the

LLCC only splits the entering emulsion into two distinct emulsions with different oil

concentrations. Table A-1 in Appendix A includes the 37 experimental runs analyzed in

this study. Several combinations of oil and water superficial velocities are used, within

the studied region, varying the split ratio for every combination of oil and water

superficial velocities.

Inlet Flow Patterns

During the experiments, four flow patterns were observed in the horizontal inlet,

as shown in Figure 3-6.

• At low superficial velocities (vSW < 0.2, vSO < 0.1 m/s), the oil enters the inlet

through the upstream vertical pipe section in the form of large droplets. These oil

droplets immediately move to the top of the pipe forming a continuous oil layer.

The water remains at the bottom. This flow pattern is called “Stratified” (Figure

3-6.A).

• When the superficial water velocity increases (0.2< vSW < 0.8 m/s) and the oil

content is low (vSO < 0.2 m/s), the droplets entering the inlet are smaller. They still

are able to move to the top of the pipe, but they do not form a continuous oil

phase. Thus, an oil in water dispersion flows at the top of the pipe and a free-


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water layer flows at the bottom. This configuration is called “Oil-in-water

Dispersion with Water Layer” (DO/W&W) (Figure 3-6.B).

Figure 3-6. Horizontal Inlet Flow Patterns

• At intermediate superficial water velocities (0.2< vSW < 0.8 m/s), but increasing

the oil content (vSO > 0.2 m/s), the bigger oil droplets move to the top and the

small ones remain at the bottom, and no free-water layer is observed. However,

the oil concentration is increasing from the bottom to the top of the pipe. Dividing

the pipe by a horizontal plane parallel to the pipe axis, it can be considered that

two dispersions with different oil content are flowing in the inlet. This flow

pattern is called “Double Oil in Water Dispersion” (Double DO/W) (Figure 3-

6.C).

A

B

C

D


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• At higher superficial water velocities (vSW > 0.8 m/s), the oil droplets are small

and they are evenly distributed in the entire cross sectional area of the pipe. This

flow pattern is called “Oil-in-Water Dispersion” (DO/W), as seen in Figure 3-6.D.

Figure 3-7 shows the inlet flow pattern map obtained during the experimental data

acquisition. The superficial oil velocity is plotted in the horizontal axis and the superficial

water velocity is plotted in the vertical axis. The dashed line divides the water-dominated

region and the oil-dominated region. As can be observed, all the experimental data points

are located in the water-dominated region, and their location define well separated

regions according to their flow pattern.

0.0

0.2

0.4

0.6

0.8

1.0

1.2

0.0 0.2 0.4 0.6 0.8 1.0 1.2

Vso (m/s)

V s w

( m / s )

DO/W

DO/W & W

ST

D DO/W

Figure 3-7. Experimental Flow Pattern Map for LLCC Inlet

Effect of Inlet Inclination: Afanador (1999) performed experiments on partial

separation of oil and water using a 2-inch ID LLCC with an inclined inlet. Figure 3-8

shows a plot of the water-cut in the water outlet versus the split ratio for a superficial


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water velocity of 1 m/s and different oil contents at the inlet. The split ratio is defined as

the ratio between the underflow liquid flow rate and the inlet liquid flow rate, namely SR

= qunder /qin. It can be observed that there is a tendency to reduce the oil content in the

underflow as the split ratio decreases. However, no tendency of the lines to cross the

100% water-cut value is shown, for which clean water would be obtained at the

underflow.

75

80

85

90

95

100

25 35 45 55 65

Split Ratio, SR , %

W a t e r c u t U n d e r %

20%

15%

8%

4%

Oil @ Inlet

Afanador (1999)

Figure 3-8. LLCC with Inclined Inlet (vSW = 1 m/s)

In order to investigate the effect of the inlet inclination angle, a qualitative

analysis of flow patterns in the inlet is performed. For this purpose, the model of Trallero

(1995) is used. The analysis shows that the horizontal inlet promotes better oil-water

segregation than the inclined inlet.

Figure 3-9 is a visual comparison between the two inlet configurations for the

same flow conditions. In the inclined inlet, a significant initial water layer is observed.


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The height of the water layer decreases as the liquid advances through the pipe. On the

contrary, the horizontal inlet shows a significant initial water layer height and this layer

grows as the liquid moves towards the vertical LLCC section. In this case the water layer

entering the vertical section is bigger than in the inclined case, so a better separation

efficiency can be expected.

Figure 3-9. Horizontal vs. Inclined Inlets Comparison

Experimental results for a water superficial velocity of 1 m/s using the horizontal

inlet are presented in Figure 3-10. As it can be seen the lines are steeper than in the

inclined inlet case under same flow conditions (Figure 3-8) and even more important, the

lines reach the 100% water cut value, showing the presence of clean water in the

underflow at significant split ratios. This means that an important fraction of the

incoming liquid goes to the underflow as pure water, enabling this device to be

successfully used as a free water knockout. Thus, a horizontal inlet has been used

throughout this study.

vSW = 0.4 m/s

vSO = 0.025 m/s

vSW = 0.4 m/s

vSO = 0.025 m/s


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75

80

85

90

95

100

25 35 45 55 65

Split Ratio, SR , %

W a t e r c u t U n d

e r %

20%

15%

8%

4%

This Study

Oil @ Inlet

Figure 3-10. LLCC with Horizontal Inlet (vSW = 1 m/s)

Separation Efficiency

Figure 3-11 shows the effect of the split ratio on the purity of the underflow by a

sequence of photographs of the lower section of the LLCC (water leg) for stratified flow

pattern at the inlet.

The superficial water velocity at the inlet is 0.1 m/s and the superficial oil velocity

at the inlet is 0.05 m/s yielding a water-cut of 67%. Under these conditions, the water

level in the inlet pipe is 50% of the inlet diameter. For a split ratio of 50%, only clean

water is observed in the water leg. When the split ratio is increased to 55%, oil droplets

are entering the water leg, but they are separated and go up to the oil leg. At 60%, more

oil is entrained, but still only clean water is leaving the water leg. At a split ratio of 65%

the entrained oil in the water leg increases even more and some quantity of oil leaves

with the underflow.


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Figure 3-11. LLCC Separation Behavior as a Function of the Split Ratio(vSW = 0.1, vSO = 0.05 m/s)

0

20

40

60

80

100

0 20 40 60 80 100

Split Ratio, SR , %


LLCC Run 37

Stratified Flow

v SW = 0.1 m/s

v SO = 0.05 m/s

Figure 3-12. Experimental Results for Stratified Flow

The experimental results for this case of Stratified Flow are shown in Figure 3-12.

The water cut in the underflow outlet is plotted as a function of the split ratio. As can be

observed, for split ratios smaller than 62%, clean water is obtained in the underflow.

SR

50%

SR

55%

SR

60%

SR

65%


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Increasing the split ratio beyond 62% the oil phase starts flowing into the underflow

along with the water. It can be observed that as the split ratio increases, the water-cut in

the underflow decreases, and about a split ratio of 80% the water-cut in the underflow

reaches the same value as the inlet water-cut. At this point no separation is occurring.

Increasing the split ratio, beyond 80%, the underflow water-cut continues decreasing, so

for this split ratios the underflow water-cut is smaller than the inlet water-cut. Finally, at

the split ratio of 100%, all the liquid is flowing down so the water-cut in the underflow is

the same as the inlet water-cut.

0

20

40

60

80

100

0 20 40 60 80 100

Split Ratio, SR , %


LLCC Run 26

DO/W - WL Flow

v SW = 0.40 m/s

v SO = 0.15 m/s

Figure 3-13. Experimental Results for DO/W – Water Layer Flow

Figure 3-13 shows a representative case of separation for the Oil-in-water

Dispersion - Water Layer flow pattern. The water-cut in the underflow stream is plotted

as a function of the split ratio. Similar behavior is observed; at low split ratios, the water-

cut in the underflow is 100%; i.e. only clean water is obtained from the underflow. For

this case, the maximum split ratio for clean water is 55%.


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The separation behavior in the LLCC for the Double Oil-in-Water Dispersion

flow pattern is shown in Figure 3-14. A similar behavior is observed, but the maximum

split ratio for 100% water-cut decreases to 18%. In all the experiments on this flow

pattern the maximum split for clean water was observed at low values. The maximum

split decreases as the oil content in the inlet increases.

0

20

40

60

80

100

0 20 40 60 80 100

Split Ratio, SR , %

W a t e r c u t U n d e r

%

LLCC Run 31

Double DO/W Flow

v SW = 0.7 m/s

v SO = 0.4 m/s

Figure 3-14. Experimental Results for Double DO/W Flow

The behavior of the oil-water separation in the LLCC when the Oil-in-Water

Dispersion flow pattern occurs at the inlet is presented in Figure 3-15. At low split ratios,

the underflow outlet provides clean water. For the present case, a maximum split ratio for

clean water of 48% can be reached. This maximum value is also affected strongly by the

oil content and the velocity of the mixture. For low oil content, maximum split ratios

around 50% are observed, but values of maximum split ratio around 20% occur for high

oil content. For a similar case, as the one shown here, but increasing the mixture velocity


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to 1.15 m/s the maximum split ratio falls to 40%.

0

20

40

60

80

100

0 20 40 60 80 100

Split (q_inderflow / q_inlet) %


LLCC Run 32

DO/W Flow

v SW = 0.9 m/s

v SO = 0.1 m/s

Figure 3-15. Experimental Results for DO/W Flow

In summary, from the experimental observations, it can be concluded that better

separation efficiency is achieved for the Stratified and the DO/W & W inlet flow

patterns. The Double Dispersion cases show good efficiency near the DO/W & W region,

but the efficiency decreases as the oil content increases. The Oil-in-Water Dispersion

flow pattern is very efficient for very low oil content (less than 10%) and this efficiency

decreases, as the oil content in the inlet is higher. This last flow pattern is limited by the

emulsification phenomenon.

3.2.2 GLLCC Experimental Results

The oil-water-gas separation phenomenon in the GLLCC is shown in Figure 3-16.

As can be seen, the gas-liquid separation occurs as in a regular GLCC. However, in the


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liquid section, due to centrifugal forces, the oil is segregated from the water forming an

oil core at the center of the pipe. The oil finder captures this oil core, which is an oil-rich

stream. Moreover, clean water flows downward through the annulus formed between the

oil finder and the pipe wall and exits through the water outlet.

Preliminary data have shown that for oil-dominated mixtures the swirl decays

rapidly in the liquid section of the GLLCC, and no good separation effect has been

observed. Based on those results, it was decided to work only into the water-dominated

region. Since the behavior of a gas-liquid mixture is known from previous studies, the gas

superficial velocity is kept constant at 0.75 m/s in all the experiments. This value was

chosen experimentally to achieve Stratified Flow at the inlet, for the range of liquid

velocities used.

Figure 3-16. Three-Phase Separation Feasibility

The superficial water velocity is varied from 0.1 to 0.5 m/s. The oil superficial

velocity is varied from 0.025 to 0.5 m/s. The GLLCC pressure is varied between 22 and

Oil Finder


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27 psia and the temperature is in the range of 68 - 75 ˚F. Figure 3-17 shows the data

region that includes only water-dominated conditions.

0

0.1

0.2

0.3

0.4

0.5

0 0.1 0.2 0.3 0.4 0.5

Vso (m/s)

V s w ( m / s )

Figure 3-17. GLLCC Experimental Data Range

Two limiting phenomena have been observed. At low liquid velocities, the flow in

the inlet is unstable due to churning in the vertical pipe that feeds the separator. Due to

these disturbances and a weak swirling effect, no oil core is formed, and poor separation

is obtained. On the other hand, at high liquid velocities, a gas core is formed all the way

through the liquid phase, providing a channel for the gas to be carried to the underflow.

In this case, even though the oil-water separation is efficient, the gas-liquid separation is

not accomplished. The points located between the two dashed lines in Figure 3-17 are

points where oil-water separation is achieved under the operational envelope of the gas-

liquid separation (with no gas carry-under).

Two hundred and twenty nine experimental points divided in three sets have been

acquired as presented in Appendix B. The first set of data has been taken at a constant


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split ratio of 40%. The split ratio in the GLLCC is defined as the ratio between the liquid

flow rate leaving the GLLCC through the water outlet to the total liquid flow rate at the

inlet. For these experiments the oil finder was located 30 inches below the inlet. These

experimental results are summarized in Table B-1 in Appendix B and they are shown in

Figure 3-18. The water-cut in the water outlet is plotted as a function of the water

superficial velocity for different superficial oil velocities.

As can be observed from Figure 3-18, the GLLCC is capable of delivering clean

water at the water outlet only at very low oil content and high water velocity. All the

curves indicate that, for the same superficial oil velocity at the inlet, cleaner water is

obtained by increasing the superficial velocity of the water. On the other hand, as the oil

content in the incoming liquid increases, the purity of the water delivered through the

water outlet decreases.

0

20

40

60

80

100

0 0.1 0.2 0.3 0.4 0.5

Vsw (m/s)

W a t e r O u t l e t W a t e r c u t %

0.025

0.050

0.100

0.150

Figure 3-18. GLLCC Experimental Results (Set 1)

GLLCC Set 1

Split Ratio = 40%

Oil Finder @ 30 inches below inlet

vSG = 0.75 m/s

Vso (m/s)


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0

20

40

60

80

100

0.00 0.10 0.20 0.30 0.40 0.50

Vsw (m/s)

W a t e r O u t l e t W a t e

r c u t %

0.025

0.050

0.100

0.150

0.200

Figure 3-19. GLLCC Experimental Results (Set 2)

The second set of experiments has been acquired at the same split ratio, namely

40%, but the oil finder has been placed 36 inches below the inlet, to investigate the effect

of the oil finder position on the separation efficiency. The experimental results are

presented in Table B-2 in Appendix B. Figure 3-19 is a graphical representation of these

data. Comparison between Figure 3-18 and Figure 3-19 shows a slight improvement for

the oil finder location at 36 inches below the inlet.

The third set of experiments has been carried out with the oil finder located at 36

inches below the inlet. The superficial water velocity is varied from 0.1 to 0.5 m/s and the

oil superficial velocity is varied from 0.025 to 0.5 m/s. The split ratio is varied from 10%

to 100%. The experiments are summarized in Table B-3 in Appendix B.

Figure 3-20 shows the measured water-cuts in both liquid outlets of the GLLCC

as functions of the split ratio for superficial water and oil velocities of 0.5 m/s and 0.15

Vso (m/s)

GLLCC Set 2

Split Ratio = 40%

Oil Finder @ 36 inches below inlet

vSG = 0.75 m/s


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m/s, respectively. The horizontal line indicates the water-cut in the inlet, which is kept

constant during these experiments. The upper line is the water-cut in the water outlet

stream. As can be seen, this line is always located above the inlet water-cut line,

indicating the decrease of the oil fraction in this liquid stream. On the other hand, the

lower line, corresponding to the water-cut in the oil outlet, is always below the inlet

water-cut line, indicating the increase in oil content in the oil stream outlet. A similar

behavior has been observed in all the experiments.

0

20

40

60

80

100

0 20 40 60 80 100

Split Ratio, SR , %

W a t e r c u t %

Figure 3-20. GLLCC Separation Efficiency Results (Set 3)

Since the purpose of the GLLCC is to obtain a water-rich stream (as rich as

possible) in the water outlet, a plot of the water-cut in this outlet versus the split ratio is

an appropriate way to present the separation efficiency. As a sample of the results, Figure

3-21 shows a plot of the water-cut in the water outlet as a function of the split ratio.

These experiments are acquired for a superficial water velocity of 0.3 m/s and the oil

superficial velocity is varied from 0.025 to 0.3 m/s. The split ratio is varied for every pair

Oil Outlet

Inlet

Water Outlet

GLLCC

vSW = 0.50 m/s

vSO = 0.15 m/s

v = 0.75 m/s


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of superficial velocities. It can be observed that the water-cut in the water-rich stream

increases as the split decreases. It can also be observed that the separation is better for

low inlet oil contents.

0

20

40

60

80

100

0 20 40 60 80 100

Split Ratio, SR , %

W a t e r O

u t l e t W a t e r c u t %

0.025

0.050

0.100

0.150

0.200

0.250

0.300GLLCC Set 3v SW = 0.30 m/s

v SG = 0.75 m/s

Figure 3-21. GLLCC Experimental Results (vSW = 0.3 m/s)

0

20

40

60

80

100

0 20 40 60 80 100

Split Ratio, SR, %

W a t e r O u t l e t W a t e r c u t %

0.025

0.050

0.100

0.150

0.200GLLCC Set 3

v SW = 0.5 m/s

v SG = 0.75 m/s

Figure 3-22. GLLCC Experimental Results (vSW = 0.5 m/s)

vSO (m/s)

vSO (m/s)


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Figure 3-22 presents a similar plot for a superficial water velocity of 0.5 m/s. A

similar behavior is observed but the curves are shifted upwards, indicating higher

separation efficiency due to increasing liquid velocity, and the resulted increase of the

centrifugal force.

It is important to notice that the experimental data presented for the GLLCC in

this study are partial. Several effects are not studied, namely, the change of the liquid

level in the liquid leg, which is kept constant at the inlet. The gas superficial velocity is

kept constant at 0.75 m/s. Consequently, the flow pattern in the inlet is not varied, and all

the experiments are for the stratified flow case only.


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CHAPTER IV

MECHANISTIC MODELING

This chapter presents the mechanistic models developed for the LLCC and

GLLCC, respectively.

4.1 LLCC Mechanistic Model

The LLCC consists of a vertical pipe section (the separator) and a horizontal pipe

section (the inlet), as shown in Figure 4-1. Both pipes are attached through a reducing

area nozzle. The vertical pipe is divided by the nozzle into two sections. The upper

section is called the “Oil Leg” as it delivers oil-rich stream into the oil outlet or overflow.

The lower section is called the “Water Leg” and it delivers water-rich stream into the

water outlet or underflow. Valves in the oil and water outlets are used to control the flow

rates leaving the LLCC.

The ratio between the water outlet (underflow) flow rate to the total inlet flow rate

is defined as the “Split Ratio” (SR). The separation efficiency of the LLCC depends

strongly on the split ratio. To date, no simple and general definition of the liquid-liquid

separation efficiency has been developed. In this study, the separation efficiency is

described by means of the split ratio and the water fraction in the water leg. These two

parameters give information about how much liquid exits through the water outlet, and

the purity of this liquid stream. The purity and the flow rate in the oil leg can be


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determined from continuity relationships between the inlet, water leg and the oil leg.

Inlet

Water Leg

Oil Leg

Underflow

Overflow

ModeledRegion

Figure 4-1. LLCC Schematic

In order to develop a model for the entire LLCC system, it is necessary to develop

sub-models for the different components of the separator, namely, the horizontal inlet

pipe, the reducing area nozzle (inlet analysis), and the water leg (separation analysis).

Note that by analyzing only the water leg, the system behavior is well defined, as the

flow into the oil leg is the difference between the flows of the inlet and the water leg.

These sub-models are given in the following sections.

4.1.1 Inlet Analysis

The inlet consists of the horizontal pipe and the nozzle. Different flow patterns

can occur in the inlet, depending upon the oil and water flow rates combination, pipe

diameter and fluid properties. The determination of the existing flow pattern for a given


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set of flow conditions is essential for the analysis, since all the design parameters of the

flow depend on the existing flow pattern. These include the spatial distribution of the

phases and their corresponding velocities. Models to predict the flow pattern in the inlet

pipe, individual models for each of the flow patterns and the nozzle analysis are

presented next.

Inlet Flow Pattern Prediction

The starting point for the LLCC modeling is the prediction of the occurring flow

pattern in the horizontal inlet. Trallero (1995) developed a mechanistic model for liquid-

liquid flow pattern prediction, applicable for horizontal and near horizontal pipes, as

presented in Chapter II. This model is adapted and modified in the present study for the

inlet section analysis.

Figure 4-2 shows the LLCC experimental data and the flow pattern boundaries

predicted by Trallero’s (1995) model, considering only the water-dominated region. The

superficial oil velocity is plotted in the horizontal axis, while the superficial water

velocity is plotted in the vertical axis. The points represent the flow patterns observed

during the experiments and the lines are the predicted flow pattern boundaries.

As can be observed in Figure 4-2, the boundaries predicted by the model, except

the stratified – non-stratified boundary, do not agree with the experimental data. This

discrepancy is because Trallero’s (1995) model considers fully developed flow, while the

LLCC inlet is a short pipe section. Thus, there is not enough length to form fully

developed flow patterns. Moreover, only four flow patterns have been observed in the


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43

water-dominated region during the experimental work (see Chapter III), as compared to

five defined by Trallero (1995).

Trallero (1995) Model0.0

0.2

0.4

0.6

0.8

1.0

1.2

0.0 0.2 0.4 0.6 0.8 1.0 1.2v SO (m/s)

v S W ( m / s )

ST

DO/W &

DW/O

STMI

DO/W & W

ST

DO/W & W

D DO/W

DO/W

Data Points

Figure 4-2. Trallero (1995) Flow Pattern Prediction Model and Experimental Data

In order to improve the prediction of the observed flow patterns, the coefficients

in Equation 2-8 and Table 2-1 are modified for the present study, as follows.

Table 4-1. Modified Coefficients for LLCC Inlet Flow Pattern Prediction

Droplet

DiameterFriction factor C n

dod,max f m 0.33 -3.5

dod,max f w 0.9 2

dod,min f w 0.174 -7

dwd,max f m 37.39 1.832

dwd,max f o 0.043 0


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In order to use the modified model to predict the four flow patterns observed in

the LLCC inlet, the Stratified with Mixing flow pattern is considered as Oil-in-Water

Dispersion – Water Layer, and the Oil-in-Water and Water-in-Oil Dual Dispersion flow

pattern is considered as the Oil-in-Water Double Dispersion flow pattern. Figure 4-3

shows the LLCC experimental data and the boundaries predicted by the modified model.

As can be observed, the flow pattern boundaries predicted agree very well with the

experimental data.

LLCC Flow Pattern Map

Modified Trallero (1995) Model

0

0.2

0.4

0.6

0.8

1

1.2

0 0.2 0.4 0.6 0.8 1 1.2

Vso (m/s)

V s w ( m / s )

DO/W

DO/W

& W

ST

Double

DO/W

Figure 4-3. Modified Trallero (1995) Model Flow Pattern Map

Stratified Flow Model

For low liquid velocities, stratified flow pattern is observed in the inlet. The

water flows at the lower section of the pipe, and a layer of oil travels at the top. A

suitable model for this flow configuration is the two-fluid model. Figure 4-4 shows the

geometry and the variables of the stratified flow pattern.


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! o

vo

S w

S o

S i

hw

Ao

Aw

d in

! w

! i

vw

∆∆∆∆ x

Figure 4-4. Stratified Flow Model Geometry and Variables

A momentum balance on each phase results in the following equations:

0=−−− iiwww S S dx

dP A τ τ , (4 - 1)

0=+−− iiooo S S dxdP A τ τ . (4 - 2)

Eliminating the pressure gradient from Equations 4-1 and 4-2, the combined

momentum equation is obtained:

011

=

+−−

wo

ii

w

ww

o

oo

A AS

A

S

A

S τ

τ τ . (4 - 3)

The combined momentum equation (Equation 4-3) is an implicit function of the

water layer height, hw.

The shear stresses are calculated as:


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2

2

oooo

v f ρ τ = , (4 - 4)

2

2

www

w

v f ρ τ =

, (4 - 5)

( )

2

owowii

i

vvvv f −−=

ρ τ . (4 - 6)

If vw > vo, f i = f w and ρ i = ρ w ; for vo > vw f i = f o and ρ i = ρ o.

Friction factors are calculated as:

on

o

ooooo

vd C f

−

=

µ

ρ , (4 - 7)

wn

w

wwwww

vd C f

−

=

µ

ρ . (4 - 8)

For laminar flow C w = C o = 16 and nw = no = 1. For turbulent flow C w = C o = 0.046 and

nw = no = 0.2.

The hydraulic diameters depend on the relative velocity between the phases, as

follows:

For vo > vw

w

ww

io

oo

S

Ad

S S

Ad

4;

4=

+= . (4 - 9)

For vo < vw


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iw

ww

o

oo

S S

Ad

S

Ad

+==

4;

4 . (4 - 10)

For vo = vw

w

ww

o

oo

S

Ad

S

Ad

4;

4== . (4 - 11)

The geometrical variables are functions of hw, as follows:

−−= − 1

2cos 1

in

winw

d

hd S π , (4 - 12)

−= − 1

2cos 1

in

wino

d

hd S , (4 - 13)

2

12

1

−−=

in

wini

d

hd S , (4 - 14)

−−

−+

−−= −

2

12

12

112

12

cos4 in

w

in

w

in

winw

d

h

d

h

d

hd A π , (4 - 15)

−−

−−

−= −

2

12

12

112

12

cos4 in

w

in

w

in

wino

d

h

d

h

d

hd A . (4 - 16)

The actual velocities are calculated as:

sw

w

w v A

Av = , (4 - 17)


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so

o

o v A

Av = . (4 - 18)

The combined momentum equation, Equation 4-3, and the auxiliary relationships,

can be solved using the operational variables (oil and water superficial velocities), the

geometry (pipe diameter), and the fluids properties (density and viscosity of oil and

water) that are known, to determine the water layer height hw and the actual velocity of

each phase vo and vw.

Oil droplet size distribution: The oil droplets are generated in the LLCC vertical

pipe section, just in front of the inlet slot. However, the oil droplet size distribution is

correlated with the horizontal pipe inlet flow conditions. The same model developed for

Oil-in-Water Dispersion –Water Layer flow (to be presented in next section) is used, but

considering the velocity, properties and geometry of the oil layer, instead of the

dispersion layer.

Oil-in-Water Dispersion – Water Layer Model

The most common flow pattern observed in the horizontal inlet during the

experiments is an oil-in-water dispersion flowing at the top of the pipe with a layer of

free water flowing at the bottom. Considering the free water layer as a phase and the

dispersion as a second phase, this flow pattern can be analyzed as the case of stratified

flow, applying the two-fluid model. However, the dispersion must be characterized

through the determination of its properties, namely, average density and viscosity. In this

case, the combined momentum equation becomes


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011

=

+−−

wd

ii

w

ww

d

d d

A AS

A

S

A

S τ

τ τ . (4 - 19)

The dispersion properties can be calculated by assuming a no-slip condition

between the oil droplets and the water in the dispersion phase (which is a sound

assumption for horizontal flow), as follows:

( )d wod wwd ,, 1 λ ρ λ ρ ρ = , (4 - 20)

( )d wod wwd ,, 1 λ µ λ µ µ = , (4 - 21)

where λ w,d is the local no-slip water holdup in the dispersion. Several attempts to use the

two-fluid model to describe the Oil-in-Water Dispersion-Water Layer flow pattern can be

found in the literature, but none provides a method to predict λ w,d . In this study, a

correlation for λ w,d is developed, based on the experimental data, as follows:

( )

2

, 1

wh

SOSW w

SOind w

vv Av A

+−=

λ . (4 - 22)

Equation 4-22 is a function of the water and oil superficial velocities, which are

known, and the height of the water layer. Thus, simultaneous solution of the equation for

λ w,d and the combined momentum equation, yields the water layer height hw and the

actual velocities of the dispersion layer vd , and the water layer vw.

Oil droplet size distribution: The determination of the maximum and minimum

oil droplet diameters in the dispersion is performed by using modified Hinze (1955) and

Levich (1962) models, respectively, and considering the velocity and geometry of the


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dispersion layer and its average properties, as follows:

4.03

6.0

,

5.0

,

,

2725.0

9.1

−

=

d

d d

d

woinw

maxod d

v f d

ρ

σ λ , (4 - 23)

( )

2

1

5.132

,

5.0

,

,5.025

25.2

=

d d d

d woinw

minod f v

d ρ

µ σ λ , (4 - 24)

where λ w,in is the no-slip holdup of the water in the inlet flow, and d d , the hydraulic

diameter of the dispersion, is calculated as given in equations 4-9 to 4-11.

Oil-in-Water Dispersion Model

For high liquid velocities, the oil droplets entering the inlet pipe cannot coalesce

and they move along with the water phase and no water layer is observed. For this flow

pattern, the homogeneous no-slip model is applicable. The oil and water velocities are the

same, namely, SOSW mow vvvvv === , and the dispersion properties are averaged based

on λ w,in, the inlet no-slip water holdup.

Oil droplet size distribution: Determination of the maximum and minimum oil

droplet diameters for this flow pattern is performed by using modified Hinze (1955) and

Levich (1962) models, respectively, and considering the mixture velocity and properties,

as follows:

4.03

6.0

,

max,

2725.0

14.2

1−

=

in

mm

m

wo

od d

v f d

ρ

σ , (4 - 25)


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51

( )

2

1

5.132

,

min,5.025

243.1

1

=

mmm

mwo

od f v

d ρ

µ σ . (4 - 26)

Double Oil-in-Water Dispersion Model

At intermediate liquid velocities and high oil contents, the bigger oil droplets are

able to move to the top while the smaller ones remain at the bottom. Under these

conditions, the local water holdup increases gradually from the top to the bottom of the

pipe. It is assumed that the flow can be divided into two layers of dispersion with

different oil concentrations. The division plane is located at the middle of the pipe and the

velocities of both layers are considered the same, equal to the mixture velocity.

The water fraction in the upper and lower dispersions is calculated, respectively,

as:

+−=

SW SO

SOuw

vv

va21,λ , (4 - 27)

( )

+

−−=SW SO

SOl w

vv

va121,λ , (4 - 28)

where the parameter a, varying in the range [0, 1], is the fraction of oil in the upper

dispersion and is correlated with the mixture velocity as follows:

mva 4.01= . (4 - 29)

The maximum and minimum oil droplet diameters are calculated in the same way


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as in the Oil-in-Water Dispersion model, i.e., by using the mixture velocity and the

mixture properties, averaged with λ w,in, the inlet no-slip water holdup.

Nozzle Analysis

The inlet pipe delivers the liquid into the LLCC vertical section through a

reducing area tangential nozzle. The effect of the nozzle is to increase the velocity of the

flow. Also, it affects the height of the water layer in the Stratified and in the Oil-in-Water

Dispersion- Water Layer flow patterns, before entering into the LLCC.

In the Oil-in-Water Dispersion and the Oil-in-Water Double Dispersion flow

patterns no water layer exists, so the effect of the nozzle is only to increase the velocity as

follows:

( )

is

inSOSW is

A

Avvv = . (4 - 30)

Next, the nozzle analysis for the Stratified flow pattern is presented. The same

model is applied to the Oil-in-Water Dispersion – Water Layer case, but the oil phase is

replaced with the dispersion phase.

Figure 4-5 shows a schematic of the nozzle geometry and the variables considered

in the model. The nozzle is formed by a vertical plate located inside the horizontal inlet.

The plate forms the nozzle from the full inlet bore to the reduced inlet-slot-area tangential

to the LLCC vertical pipe section. The inlet slot has the shape of a circular sector. In this

model, however, it is considered as a rectangle, keeping the same height of a circular


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sector and the same area, which is 25% of the inlet cross sectional area.

vw Water Layer

d in

hw

hw,isvw,is

vo

vo,is

Lis

W is

Figure 4-5. Nozzle Schematic and Variables

The height of the inlet slot is calculated from:

2

12

1

−−=

in

is

d

y L , (4 - 31)

where y is the solution of

−−

−+

−−= −

2

11

211

21

2cos

1

inininin

is

d

y

d

y

d

y

A

Aπ

π . (4 - 32)

The inlet slot width is

is

is

is L

AW = . (4 - 33)

Application of the Bernoulli’s equation to the top of the water layer, between the


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in

10.1.1.476.6482 tesis de dr carlos oropeza vasquez

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