Modelling of Critical Gas Velocities based on the Entrained Droplet Model for Gas Wells and the Effect of Heat Loss on Gas Production

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Chair of Petroleum and Geothermal Energy Recovery, Montanuniversität Leoben

Master Thesis

Modelling of Critical Gas Velocities based on the Entrained Droplet Model for Gas Wells and the Effect

of Heat Loss on Gas Production

Written by: Advisors:

Gernot Schwaiger, BSc Univ.-Prof. Dipl.-Ing. Dr.mont. Herbert Hofstätter

m0835141 Dipl.-Ing. Dr.mont. Rudolf K. Fruhwirth

Leoben, Austria; February 24, 2016

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EIDESSTATTLICHE ERKLÄRUNG ii

EIDESSTATTLICHE ERKLÄRUNG

Ich erkläre an Eides statt, dass ich die vorliegende Diplomarbeit selbständig und ohne fremde Hilfe verfasst, andere als die angegebenen Quellen und Hilfsmittel nicht benutzt und die den benutzten Quellen wörtlich und inhaltlich entnommenen Stellen als solche erkenntlich gemacht habe.

Datum Unterschrift

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AFFIDAVIT iii

AFFIDAVIT

I hereby declare that the content of this work is my own composition and has not been submitted previously for any higher degree. All extracts have been distinguished using quoted references and all information sources have been acknowledged.

Date Signature

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Acknowledgement iv

Acknowledgement

For their efforts and assistance, a special Thank You to the Chair of Petroleum and Geothermal Energy Recovery and its head, Univ.-Prof. Dipl.-Ing. Dr.mont. Herbert Hofstätter.

Dipl.-Ing. Dr.mont. Rudolf K. Fruhwirth (Chair of Petroleum and Geothermal Energy Recovery) has been the ideal thesis supervisor. His advice and patient encouragement aided the writing of this thesis in innumerable ways. He has set an example of excellence as a mentor and instructor.

Finally, I dedicate this work to my parents. Their support, love and encouragement from the beginning of my studies up until now have been invaluable. I am forever grateful and I could not have done this without you - Thank You!

To each of the above, I extend my deepest appreciation.

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Abstract v

Abstract

Natural gas is one of the most important energy sources. In 2014, it accounted for about a quarter of the world energy consumption. Accordingly, gas production operations take place on a global level, and potential improvements of these operations may possibly have a significant effect. This holds especially true when those improvements are straightforward and easy to implement. Additionally, if these measures eliminate or postpone the need for workover interventions, there is a reduced risk of incidents which directly leads to an improved health, safety and environment record.

Thus, this thesis aims to investigate the ubiquitous issue of liquid loading which at some point affects every gas well. The liquid loading of gas wells occurs in many cases due to heat loss into the surrounding formation and decreasing flow velocities within the production tubing. Heat loss into the formation is facilitated by the circumstance that the use of appropriately insulated tubings is usually neglected. The absence of insulation permits unnecessary heat loss and thus a subsequent reduction in gas temperature. The reduced temperature in turn may lead to condensation of liquids, adding to the possibly already existing amount of fluids in the reservoir.

Moreover, flow velocities decrease due to two main causes. One is the inevitable decline of reservoir pressure. The other is the reduced gas volume which is caused by the reduced gas temperature. Therefore, the understanding of heat flow and methods to reduce loss are desirable to tackle this issue.

In this thesis, the leading formula for the determination of critical gas flow velocities which must not be undercut by the actual flow velocity is investigated. This formula is colloquially known as ”Turner’s equation” and allows the calculation of the minimum flow velocity needed to lift liquid droplets all the way up to the surface. This “entrained droplet model” contains several parameters which ultimately depend on the prevailing pressure and temperature conditions.

Hence, a heat transfer model was built in order to formulate and determine the pressure and temperature values for every point within the wellbore. The heat transfer model builds on concepts such as equation of state correlations, heat capacity models, density models, viscosity models, the Joule-Thomson coefficient and water density and water surface tension models.

As a result, it was found that insulated tubings lead to higher temperature and pressure readings, and that these effects can be quantified for different types and thicknesses of insulation materials. Moreover, the temperature increase also leads to higher actual gas velocities. Thus, critical gas velocities are exceeded more easily and for a longer period of time, and the margin between them is more pronounced. In the end, this allows an increased amount of gas production and the postponing of the economic limit of a gas well.

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Kurzfassung vi

Kurzfassung

Erdgas ist eine der wichtigsten Energiequellen. Im Jahr 2014 war es verantwortlich für rund ein Viertel des Weltenergieverbrauchs. Dementsprechend findet Gasproduktion weltweit statt und mögliche Verbesserungen dieser Produktionsmethoden können erhebliche Auswirkungen haben. Dies gilt insbesondere dann, wenn diese Verbesserungen überschaubar und einfach zu implementieren sind. Weiters kann das Unfallrisiko reduziert werden, wenn diese Maßnahmen Workover-Tätigkeiten verhindern oder verzögern. Somit wird auch die Gesundheit-, Sicherheit- und Umwelt-Bilanz einer Firma verbessert.

Diese Arbeit beschäftigt sich mit der allgegenwärtigen Problematik von Flüssigkeitsansammlungen, welche jede Gasbohrung früher oder später betreffen. Die Flüssigkeitsansammlungen in Gasbohrungen entstehen in den meisten Fällen durch Wärmeverlust in die umliegende Gesteinsformation und durch abnehmende Fließgeschwindigkeiten im Förderstrang. Der Wärmeverlust wird begünstigt durch die Tatsache, dass die Verwendung von angemessen isolierten Fördersträngen meist vernachlässigt wird. Das Fehlen dieser Isolierung erlaubt unnötigen Wärmeverlust und daher eine Reduzierung der Gastemperatur. Die reduzierte Temperatur wiederum führt zur Kondensation von Flüssigkeiten, die zusätzlich zu den möglicherweise bereits existierenden Lagerstätten-Flüssigkeiten hinzukommen. Zudem nimmt die Fließgeschwindigkeit aus zwei Gründen ab. Einer ist der unvermeidliche Abfall des Lagerstätten-Drucks. Der andere ist das reduzierte Gasvolumen aufgrund der verringerten Temperatur. Daher sind das Verständnis des Wärmeflusses und Methoden zur Verringerung dieser Verluste wünschenswert, um diese Problematik zu bekämpfen.

Diese Arbeit untersucht die führende Formel zur Bestimmung der kritischen Gas- Geschwindigkeiten, welche nicht durch die tatsächlichen Gas-Geschwindigkeiten unterschritten werden dürfen. Diese Formel ist umgangssprachlich als „Turner-Gleichung“

bekannt und erlaubt die Berechnung der minimal benötigten Fließgeschwindigkeit, um Flüssigkeits-Tropfen bis zur Oberfläche zu befördern. Dieses „Mitgerissene Tröpfchen Modell“

beinhaltet mehrere Parameter, welche letztendlich von Druck und Temperatur abhängig sind.

Daher wurde ein Wärmeübertragungs-Modell kreiert, um die vorherrschenden Druck- und Temperatur-Bedingungen im gesamten Förderstrang berechnen zu können. Das Wärmeübertragungs-Modell baut auf Konzepte auf wie Zustandsgleichungen, Wärmekapazitäts-Modelle, Dichte-Modelle, Viskositäts-Modelle, dem Joule-Thomson Koeffizient und Wasser-Dichte- und Wasser-Oberflächenspannungs-Modelle.

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Kurzfassung vii

Das Modellieren hat schlussendlich gezeigt, dass isolierte Förderstränge höhere Temperaturen und Drücke ermöglichen und dass diese Auswirkungen berechenbar sind für verschiedene Arten und Dicken von Isolierungen. Weiters führt der Temperaturanstieg zu höheren Gas-Geschwindigkeiten. Daher wird die kritische Gas-Geschwindigkeit leichter und für einen längeren Zeitraum von der tatsächlichen Gas-Geschwindigkeit überschritten und die Differenz zwischen den beiden ist stärker ausgeprägt. Dies ermöglicht eine höhere Produktionsrate und verlängert die Wirtschaftlichkeit einer Gasbohrung.

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Table of Content viii

Table of Content

Page

1 INTRODUCTION ... 1

1.1 Problem Statement ... 1

2 LITERATURE REVIEW ... 6

2.1 Turner et al. [1969] ... 6

2.2 Coleman et al. [1991] ... 10

2.3 Nosseir et al. [1997] ... 12

2.4 Li et al. [2002] ... 14

2.5 Lea and Nickens [2004] ... 16

2.6 Luan and He [2012] ... 18

2.7 Li et al. [2014] ... 20

2.8 Dimensionless Quantities ... 22

2.8.1 Reynolds Number ... 22

2.8.2 Friction Factor ... 22

2.8.3 Drag Coefficient ... 25

2.8.4 Weber Number ... 26

2.8.5 Grashof Number ... 27

2.8.6 Prandtl Number ... 27

2.8.7 Nusselt Number ... 27

3 METHODOLOGY ... 28

3.1 Entrained Droplet Model ... 28

3.2 Heat Transfer Model ... 30

3.3 Gas Correlations and Models ... 35

3.3.1 Equation of State ... 35

3.3.2 Specific Heat Capacity ... 41

3.3.3 Density ... 44

3.3.4 Dynamic Viscosity ... 45

3.3.5 Joule-Thomson Coefficient ... 47

3.3.6 Formation Volume Factor ... 49

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Table of Content ix

3.4 Water Correlations and Models ... 49

3.4.1 Specific Heat Capacity ... 49

3.4.2 Density ... 50

3.4.3 Dynamic Viscosity ... 51

3.4.4 Surface Tension ... 51

3.4.5 Formation Volume Factor ... 52

3.4.6 Solubility ... 52

3.5 Two Phase Flow Model ... 53

3.5.1 Linking Gas and Water Properties ... 53

3.5.2 Two Phase Flow Rates ... 54

3.5.3 Velocities ... 55

3.5.4 Flow Patterns ... 57

4 RESULTS ... 63

4.1 Constant Flow Rate ... 66

4.2 Constant Wellhead Pressure ... 70

4.3 Scenario Variations ... 72

4.3.1 Scenario 1 ... 73

4.3.2 Scenario 2 ... 78

4.3.3 Scenario 3 ... 83

4.3.4 Scenario 4 ... 88

4.3.5 Scenario 5 ... 93

4.3.6 Scenario 6 ... 99

5 CONCLUSION ... 104

6 DISCUSSION ... 106

7 REFERENCES ... 107

NOMENCLATURE ... 110

APPENDICES ... 113

Appendix A ... 113

Appendix B ... 116

Appendix C ... 117

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List of Tables x

List of Tables

Table 1: Coefficients for the Dranchuk and Abou-Kassem [1975] z-Factor Correlation. [37] . 40

Table 2: Coefficients for the Specific Isobaric Heat Capacity Departure. [41] ... 42

Table 3: Coefficients determined by Chen and Ruth [1993] for the Gurbanov and Dadash-Zade [1986] Viscosity Model used in Equations (99) and (100). [44] ... 46

Table 4: Coefficients for the Specific Isobaric Heat Capacity of Water. ... 49

Table 5: Coefficients for the Saturated Water Density Formula. [46] ... 50

Table 6: Flow Regimes and the Definition of their Limits. [67] ... 62

Table 7: Parameters calculated by the MS Excel Tool. ... 63

Table 8: Input Parameters required by the MS Excel Tool. ... 64

Table 9: Summary of Data. ... 66

Table 10: Setup of Properties for Scenario 1. ... 73

Table 16: Matching Tubing Size with Production Casing Size for Oil and Gas Wells. [71] .. 117

Table 17: Comparison of Nominal Tubing Sizes. [71] ... 117

Table 18: Comparison of Nominal Production Casing Sizes. [71] ... 117

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List of Figures xi

List of Figures

Figure 1: Worldwide Energy Consumption in 2014. [1, p. 42; modified] ... 1

Figure 2: Schematic of a Gas Well. [3] ... 2

Figure 3: Typical Gas/Water Production Profile. [4] ... 3

Figure 4: Production Behaviour of a Gas Well with Liquid Loading. [4] ... 4

Figure 5: Simplified Illustration of the Working Principle of a Plunger Lift System. [13] ... 5

Figure 6: Forces at Work in the Entrained Droplet Model. [3] ... 7

Figure 7: Entrained Droplet Model after Turner et al. [1969]. [8] ... 9

Figure 8: 8-day L-10 Production Chart of a Gas Well. [11] ... 11

Figure 9: Plot of Data Points comparing Observed and Calculated Critical Rates. [11] ... 12

Figure 10: Comparison between four different Calculation Models. [57, modified] ... 14

Figure 11: Spherical Drop (left side) being deformed into a Flattened Shape (right side) in a High-Velocity Gas Stream due to pressure differences. [12] ... 15

Figure 12: Comparison of the Coefficients by Turner et al. [1969] and Li et al. [2002]. [12] .. 16

Figure 13: Comparison of Li et al.’s [2002] model and Turner et al.’s [1969] model. [12] ... 16

Figure 14: Flow Regime Chart. [7] ... 17

Figure 15: Decline Curve with and without Liquid Loading. [13] ... 17

Figure 16: Inflow Performance Relationship (IPR) vs. Tubing Performance Curve (TPC) for three different Tubing Diameters. [13] ... 18

Figure 17: Comparison of Critical Flow Rates. [14] ... 19

Figure 18: Pipe Deviated by Angle α from the Vertical Axis. [15] ... 20

Figure 19: Flow Reversal of the Liquid Film Adhering to the Tubing Wall. [15] ... 21

Figure 20: Influence of Deviation Angles on the Critical Gas Velocity. [15] ... 21

Figure 21: Moody [1944] Diagram. [20] ... 23

Figure 22: Nikuradse [1933] Diagram. [20] ... 23

Figure 23: Drag Coefficient vs. Reynolds Number. [21] ... 25

Figure 24: Experiment Conducted to determine Critical Weber Numbers. [23] ... 26

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List of Figures xiii

Figure 50: Simulation Results of Minimum Gas Velocity for Constant Wellhead Pressure .... 71 Figure 51: Flow Pattern Chart of the Reference Case according to Duns and Ros [1963]. ... 74 Figure 52: Temperature, Pressure, Velocity and Density Curves of the Reference Case. .... 75 Figure 53: Duns and Ros [1963] Flow Pattern Chart of all Scenario Variations. ... 76 Figure 54: Pressure Losses vs. Water Production Rate. ... 77 Figure 55: Wellhead Fluid Temperature and Bottomhole Flowing Pressure vs. Water

Production Rate. ... 77 Figure 56: Flow Pattern Chart of the Reference Case according to Duns and Ros [1963]. ... 79 Figure 57: Temperature, Pressure, Velocity and Density Curves of the Reference Case. .... 80 Figure 58: Duns and Ros [1963] Flow Pattern Chart of all Scenario Variations. ... 81 Figure 59: Pressure Losses vs. Gas Production Rate. ... 82 Figure 60: Wellhead Fluid Temperature and Bottomhole Flowing Pressure vs. Gas Production

Rate. ... 82 Figure 61: Flow Pattern Chart of the Reference Case according to Duns and Ros [1963]. ... 84 Figure 62: Temperature, Pressure, Velocity and Density Curves of the Reference Case. .... 85 Figure 63: Duns and Ros [1963] Flow Pattern Chart of all Scenario Variations. ... 86 Figure 64: Pressure Losses vs. Gas Production Rate. ... 87 Figure 65: Wellhead Fluid Temperature and Bottomhole Flowing Pressure vs. Gas Production

Rate. ... 87 Figure 66: Flow Pattern Chart of the Reference Case according to Duns and Ros [1963]. ... 89 Figure 67: Temperature, Pressure, Velocity and Density Curves of the Reference Case. .... 90 Figure 68: Duns and Ros [1963] Flow Pattern Chart of all Scenario Variations. ... 91 Figure 69: Pressure Losses vs. Insulation Thickness (P* = perfect insulation). ... 92 Figure 70: Wellhead Fluid Temperature and Bottomhole Flowing Pressure vs. Insulation

Thickness (P* = perfect insulation). ... 92 Figure 71: Flow Pattern Chart of the Reference Case according to Duns and Ros [1963]. ... 94 Figure 72: Temperature, Pressure, Velocity and Density Curves of the Reference Case. .... 95 Figure 73: Duns and Ros [1963] Flow Pattern Chart of all Scenario Variations. ... 96

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List of Figures xiv

Figure 74: Pressure Losses vs. Water Production Rate. ... 97

Figure 75: Wellhead Fluid Temperature vs. Water Production Rate. ... 97

Figure 76: Gas Production Rate vs. Water Production Rate. ... 98

Figure 77: Flow Pattern Chart of the Reference Case according to Duns and Ros [1963]. . 100

Figure 78: Temperature, Pressure, Velocity and Density Curves of the Reference Case. .. 101

Figure 79: Duns and Ros [1963] Flow Pattern Chart of all Scenario Variations. ... 102

Figure 80: Pressure Losses vs. Flowing Bottomhole Pressure. ... 103

Figure 81: Wellhead Fluid Temperature and Flowing Pressure vs. Flowing Bottomhole Pressure. ... 103

Figure 82: Movement of Liquid Film with Thickness h. [8] ... 113

Figure 83: Continuous Film Model after Turner et al. [1969]. [8] ... 115

Figure 84: Setup of MS Excel Tool. ... 116

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Abbreviations xv

Abbreviations

BHFP Bottom Hole Flowing Pressure

BWR Benedict-Webb-Rubin

CFM Continuous Film Model

EDM Entrained Droplet Model

EoS Equation of State

GFK Glass fiber reinforced plastic

HC Hydrocarbons

HSE Health, Safety and Environment

HTM Heat Transfer Model

ID Inner Diameter

IPR Inflow Performance Relationship

JT Joule-Thomson

OD Outer Diameter

ppm Parts per million

t.b.d. To be determined

TPC Tubing Performance Curve

WHFP Wellhead Flowing Pressure

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Chapter 1 – Introduction 1

1 Introduction

Natural gas is one of the world’s most important energy sources. The demand is continuously growing and in 2014, natural gas accounted for about a quarter of the the entire world energy consumption, as shown in Figure 1. [1, p. 42]

Figure 1: Worldwide Energy Consumption in 2014. [1, p. 42; modified]

The situation in Austria is very similar: about 22 % of the primary energy usage were supplied by natural gas in 2012. These 22 % are composed of about 5 % which were produced domestically and of 17 % which were imported, mainly from Russia and Norway. [2, pp. 6-7]

Thus, given this important status, a great deal could potentially be gained by having a closer look at how natural gas is produced and whether there is room for improvement in today’s worldwide production practices.

1.1 Problem Statement

An area that traditionally has been neglected in the design of wellbore completions is the occurrence of heat loss from the media within the production tubing into the surrounding formation. Hydrocarbons are typically found in reservoirs which have a depth of several kilometers (Figure 2) and accordingly, exhibit pressures ranging from about 150 to 1000 bar und temperatures ranging from about 60 to 230 °C. During the production of these hydrocarbons to the surface, the surrounding rock formation (or, in the case of offshore production, the surrounding sea water) becomes considerably cooler than the media in the tubing string due to the temperature reduction associated with the geothermal gradient. If the tubing and the surrounding completion are not insulated, heat loss into the surrounding formation is facilitated.

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Figure 2: Schematic of a Gas Well. [3]

While surface facilities are usually built in such a way that heat losses are minimized, these heat preserving considerations are often not conveyed to the design of wellbore completions (such as casing and cement) and tubings (see Figure 2). This potentially represents large areas of improvement.

Since gas production is always accompanied by the presence of liquids, these heat preserving considerations should be heeded much more rigorously. Liquids may already be present in the reservoir or start to occur during production due to condensation. Other possible sources include water horizons, residuals from interventions, leaking packers and channelling behind the casing. [4]

The condensation process is caused by the decreasing temperature which occurs mostly due to the aforementioned heat loss into the formation (the Joule-Thomson effect is at work as well, see Chapter 3.3.5) and is ultimately facilitated by neglected insulating properties of the installed completion. Therefore, at the dew point of the gas, any decrease in temperature or increase in pressure will cause evaporated liquids to condense. Moreover, condensed water is low in total chlorides (less than 500 ppm) which can pose the additional problem of damaging formations containing swelling clays. [11]

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Typical liquids are water or condensate; the latter is composed of liquefied higher hydrocarbons such as propane and butane. While at the beginning of gas production both of these liquids are being removed from the wellbore without further difficulty by being entrained in the gas stream, the inevitable decreases in tubing pressure and temperature have a negative impact on the removal abilities of the well.

As a result of these pressure and temperature decreases, the gas density decreases and the upward flow velocity of the natural gas in the production tubing continuously decreases as well.

Once this upward velocity falls short of a certain so-called critical gas velocity, the gas stream loses its ability to carry the liquids all the way to the surface. Thus, liquids are not being removed from the wellbore any longer and they start to accumulate at the bottom of the well, creating a backpressure which is adversely affecting the production capacity of the reservoir (Figure 3). In the worst case, this liquid column can exert such an amount of backpressure that the gas well is effectively killed and production ceases. This happens when the remaining reservoir pressure is smaller than the backpressures caused by the liquid column, hydrostatic losses, friction losses and acceleration losses.

As an example, Figure 3 shows that after a continuous increase in surface water production, the water production rate starts to decline at a certain point (about 8 months). Also, the gas rate decreases and severe decline occurs. This means that the well is loading up and affecting the flowing capabilities of the well. Once the gas production stops after 12 months, no more lifting energy is supplied to the water in the wellbore and thus, production of gas and water ceases completely.

Figure 3: Typical Gas/Water Production Profile. [4]

1 5 12

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This concept of liquid loading was formulated by Turner et al. [1969]. Based on the balance of the forces acting on a liquid droplet, they stated a formula which yields the required velocity for continuous liquid removal out of the wellbore: the aforementioned critical gas velocity. This formula consists of several parameters which ultimately are all dependent on the prevailing pressure and temperature conditions.

Thus, an improved conservation of heat within the tubing influences these parameters and would therefore also affect the gas velocity. This in turn could help in postponing the phenomenon of liquid loading and lead to an improved ultimate recovery factor of gas reservoirs. Moreover, the postponed occurrence of liquid loading would also delay the need for workover interventions.

This also contributes directly to the health, safety and environment (HSE) record of the operator by eliminating the need for or reducing the amount of workover interventions which always include a certain safety risk. Other problems associated with liquid loading are formation damages and increased corrosion. [4]

Figure 4 shows an example of the influence of liquid loading and the resulting need for liquid removal. On three occasions, the gas production stopped due to liquid loading. As counter- measures, a plunger lift system, compression and gas recirculation had to be installed. If possible, it would be desirable to be able to forgo these costly and potentially hazardous measures by preventing or delaying liquid loading.

Figure 4: Production Behaviour of a Gas Well with Liquid Loading. [4]

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Well-established indications for the onset of liquid loading are e.g. stop of liquid production, erratic gas production behaviour, significant pressure changes in gradient curves and increasing differences in tubing and casing pressure. Possible deliquification techniques include installing a velocity string; installing artificial lift methods that can be adapted to the removal of relatively small amounts of unwanted liquids (such as gas lift); using surfactants to decrease the droplet’s surface tension; adopting intermittent production with a plunger lift system (Figure 5); increasing the gas rate; removing unnecessary bottlenecks; and heating the tubing. [4]

It is worth mentioning that artificial lift methods and deliquification methods might seem similar, yet are profoundly different in that the first is designed to get the desired product to the surface, while the latter is only concerned with getting liquids out of the way. As an example, evaporation by a significant reduction of wellhead pressure is an additional efficient deliquification technique which is unacceptable for artificial lift, however. [5]

Figure 5: Simplified Illustration of the Working Principle of a Plunger Lift System. [13]

Another possibility is the previously mentioned reduction of the wellhead pressure which on one hand evaporates liquids, increases the flow rate and improves liquid lift capabilities but on the other hand creates the need for compressor stations to meet the pressure requirements of the sales line. [7, p. 60]

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Chapter 2 – Literature Review 6

2 Literature Review

Following the publication of the paper by Turner et al. [1969], a multitude of authors used it as a starting point for their own investigations. This chapter aims to give an overview of the original work, additional findings and the contributions of the respective authors.

2.1 Turner et al. [1969]

Turner et al. [1969] tackled the issue of liquid loading by trying to analyse the involved parameters and to find a formula to predict the minimal flow rate required for a continuous removal of liquids. In their study, they examined two different models which account for the upward transport of liquids: the Continuous Film Model (CFM) and the Entrained Droplet Model (EDM).

The Continuous Film Model deals with liquid phases that accumulate on the surface of the tubing and are being moved upward due to the shear force of the gas acting on the liquid film.

The main interest is finding the minimum gas rate that is needed to provide enough lift to the film to prevent a gas well from loading up. The approach used by Turner et al. [1969] follows Hewitt [1961] and his analysis of Dukler’s [1960] work. The forces at work are the interfacial shear between the moving gas and the liquid adhering to the tubing, counteracted by gravity and friction (see Appendix A). However, after tests with independent field data from gas wells that produced liquids were completed, the forecasts of the continuous film model did not show a good match with this data. In some cases, while the wells were in fact unloading liquids, the film model falsely predicted the gas rates as being too low. Moreover, the theoretical framework behind the film model suggests dependency on the gas liquid ratio of the well. Turner et al.

[1969] therefore drew the conclusion that the continuous film model is not the commanding mechanism for liquid unloading. Finally, a downward moving liquid film starts to thicken at certain points due to the countercurrently moving gas and forms a bridge across the tubing.

The breakdown of this bridge then causes the formation of entrained droplets which require an entirely different transport mechanism, namely the EDM.

The Entrained Droplet Model is based on the occurrence of liquid drops within the gas stream.

In other words, a liquid drop is falling under its own weight through a fluid until it reaches its terminal velocity. This terminal, or threshold, velocity can be expressed as the maximum velocity the droplet can reach due to the force of gravity, while simultaneously being counteracted by the drag force and the buoyancy force (as is shown in Figure 6).

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Figure 8: 8-day L-10 Production Chart of a Gas Well. [11]

When Coleman et al. [1991] plotted this data (Figure 9), they found that it matched Turner et al.’s [1969] predictions better without the 20 % upward adjustment and drew six conclusions from this result. First, they concur with the assumption that in most cases the WHFP has a controlling influence on the beginning of liquid loading. Secondly, they revealed that in some tests the WHFP had to be increased significantly to force load-up. Thirdly, wells that exhibitied slugging behaviour plotted well below the theoretical line and should be considered anomalies.

Fourthly, the liquid to gas ratio ranged from 1 to 22.5 bbl/MMscf and in this analysis, it did not have any effect concerning liquid load-up. This means that the amount of liquid which is present in the tubing does not influence the onset of liquid loading, only the gas flow rate does;

a finding that is consistent with Turner et al.’s [1969] results. Fifth, in most cases the main source of loading fluid was condensed water; A finding that significantly strengthens the postulation that heat losses into the formation during production should be minimized as vigorously as possible.

And finally, as their sixth finding, Coleman et al. [1991] observed during the utilisation of three- phase separators a complete stop in liquid production once the well went into load-up behaviour. The reason for this is that the critical velocity was equal or larger than the actual gas velocity and thus, the liquid droplets were being held up in the tubing string.

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Figure 10: Comparison between four different Calculation Models. [57, modified]

As Figure 10 shows, the data used by Coleman et al. [1991] shows a good fit with the (unadjusted) Coleman et al. [1991] formula. For Coleman et al. [1991] themselves, their unadjusted model is rather unaccurate which is improved by the upward correction of 20 %.

The model by Nosseir et al. [1997] which uses the appropriate equation depending on the flow regime shows an even further improvement in match quality.

2.4 Li et al. [2002]

According to Li et al. [2002], many gas wells in China produce at rates which are lower than the minimum flow rates necessary to prevent liquid loading as determined by Turner et al.’s [1969] equation. The engineers responsible for these wells found that reducing the required critical rate by two-thirds yielded more accurate results. Thus, Li et al. [2002] set out to find the underlying causes for this apparent mismatch and they started to examine the deformation falling droplets experience due to the forces acting on the droplet. These forces cause the change from a spherical shape to a flat shape (Figure 11).

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Figure 12: Comparison of the Coefficients by Turner et al. [1969]and Li et al. [2002]. [12]

They then proceeded to test their formula on 16 wells, and subsequently to compare it to Turner et al.’s [1969] formula as well. Figure 13 is set up in such a way that the datum points will plot on the diagonal if the well’s actual flow rate matches the critical flow rate (squares). If the actual flow rate is lower and liquid loading occurs (triangles), the points will plot below; if the flow rate is larger than the critical rate, the points should be located above the diagonal (rhombi). As is suggested in Figure 13, the model of Li et al. [2002] on the left side appears to yield much better results than Turner et al.’s [1969] model on the right side.

Figure 13: Comparison of Li et al.’s [2002] model and Turner et al.’s [1969] model. [12]

2.5 Lea and Nickens [2004]

Lea and Nickens [2004] start by discussing the total flowing-pressure drop which can be expressed as the sum of friction, acceleration and elevation pressure losses. For gas wells with low production rates, the friction and acceleration terms are likely to be small.

However, the elevation, or gravity, term increases with liquid loading and can reach unfavorable dimensions. They also discuss the influence of the prevailing flow regimes. The flow regimes are a function of superficial gas and liquid velocities (see Chapter 3.5), and Lea and Nickens [2004] used Figure 14 to illustrate this parameter:

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Figure 14: Flow Regime Chart. [7]

During mist flow, the well may experience only a slight increase in pressure drop. With decreasing gas velocity, however, the flow becomes more sluggish and finally reaches bubble flow. At this stage, a large fraction of the wellbore is filled with liquid and the production capability of the reservoir is hindered significantly.

Thus, it is highly advisable to try to stay in mist flow. Lea and Nickens [2004] list several ways to achieve this. They recommend creating a lower wellhead pressure, increasing the flow velocity by using a smaller tubing, getting the liquids out via the use of pump or gas lift and the sealing off of water zones.

To detect liquid loading, Lea and Nickens [2004] propose to closely observe the behaviour of the decline. As seen in Figure 15, sharp drops usually are a clear indication for liquid loading.

Other symptoms include liquid slugs arriving at the surface and sharp gradient changes on a flowing-pressure survey.

Figure 15: Decline Curve with and without Liquid Loading. [13]

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(36)

Figure 19: Flow Reversal of the Liquid Film Adhering to the Tubing Wall. [15]

Moreover, the influence of deviation angles on the critical gas velocity was explored as well.

The critical velocity increases up to a deviation of 60° and then decreases while the deviation increases to 90° (Figure 20).

Figure 20: Influence of Deviation Angles on the Critical Gas Velocity. [15]

The result of Li et al.’s [2014] work is a two-variable curve-fit model to predict the critical gas rate based on the deviation angle and the liquid superficial velocity. As a limitation, they note that the simulation was performed with air-water tests under atmospheric pressure. Moreover, in this work, the focus will lie on the Entrained Droplet Model including the deviation angle as proposed by Li et al. [2014] in Eq.(22).

(37)

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Figure 21: Moody [1944] Diagram. [20]

Figure 22: Nikuradse [1933] Diagram. [20]

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(44)

Chapter 3 – Methodology 29

As mentioned in Chapter 2.1, these are the parameters which make up the critical velocity formula and for which Turner et al. [1969] decided to use average values:

• drag coefficient

• surface tension of water

• surface tension of condensate

• density of water

• density of condensate

• critical Weber number

These simplified assumptions are likely to be the culprits for the mismatch which Turner et al.

[1969] and the other authors found when comparing their respective calculated critical velocities with actual field data, and also for the limitation to certain pressure and temperature conditions. Thus, in this approach, the implementation of models for each of these parameters is proposed instead of the use of constant values. Therefore, the ability to calculate the prevailing pressure and temperature conditions for every point in the tubing is absolutely necessary for a representative Entrained Droplet Model since all these parameters ultimately depend on and are influenced by those conditions (see Figure 26).

Figure 26: Required Models for the Entrained Droplet Model (EDM). [3]

Thus, a Heat Transfer Model has to be formulated which takes into account the conditions of the wellbore and which can be used for the determination of the current pressure within the tubing and the temperature of the gas stream. This model is described in the next chapter.

It must be emphasized that the Entrained Droplet Model by Turner et al. [1969] is designed for mist flow as the prevailing flow regime in the tubing string, as elaborated in Chapter 3.5.

(45)

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