Mechanistic Modeling of Multiphase Flow in Subsea Pipeline of Oil Field X for Wax Deposition Prediction

Mechanistic Modeling of Multiphase Flow in Subsea Pipeline of Oil Field X for Wax Deposition PredictionMechanistic Modeling of Multiphase Flow in Subsea Pipeline of Oil Field X for Wax Deposition PredictionMechanistic Modeling of Multiphase Flow in Subsea Pipeline of Oil Field X for Wax Deposition PredictionMechanistic Modeling of Multiphase Flow in Subsea Pipeline of Oil Field X for Wax Deposition PredictionMechanistic Modeling of Multiphase Flow in Subsea Pipeline of Oil Field X for Wax Deposition PredictionMechanistic Modeling of Multiphase Flow in Subsea Pipeline of Oil Field X for Wax Deposition PredictionMechanistic Modeling of Multiphase Flow in Subsea Pipeline of Oil Field X for Wax Deposition Prediction

VIETNAM NATIONAL UNIVERSITY HO CHI MINH CITY

HO CHI MINH CITY UNIVERSITY OF TECHNOLOGY FALCUTY OF GEOLOGY AND PETROLEUM ENGINEERING DEPARTMENT OF DRILLING AND PRODUCING PETROLEUM ENGINEERING

OFFICE OF INTERNATIONAL STUDY PROGRAM

A thesis submitted in accordance with the requirement for the degree of

BACHELOR OF ENGINEERING (Petroleum Engineering)

Mechanistic Modeling of Multiphase Flow in Subsea Pipeline of Oil

Field X for Wax Deposition Prediction

INSTRUCTOR: Dr MAI CAO LAN

Mr NGUYEN VIET VAN STUDENT’S NAME: VO NHAT LINH CLASS: CC17DK11

STUDENT ID: 1652347

HO CHI MINH CITY September, 2021

HO CHI MINH UNIVERSITY OF TECHNOLOGY

Faculty of Geology and Petroleum Engineering

Department of Drilling and Producing Petroleum Engineering

No _/BKĐT

SOCIALIST REPUBLIC OF VIETNAM Independence – Freedom – Happiness

FINAL YEAR PROJECT PROPOSAL

(This form must be appeared at the first page of the final report of the final year project)

Department: Drilling and Producing Petroleum Engineering

Topic:

“Mechanistic Modeling of Multiphase Flow in Subsea Pipeline of Oil Field X for Wax Deposition Prediction” Expected outcome:

• Definition and characteristic of multiphase flow in pipeline

• Determining criteria for evaluation, selection of pipeline diameter

• Mathematical calculating the thickness of insulation

• Establishing model and principle for calculating the wax deposition in pipeline

Engineering

100%

The proposal has been screened by the Head/Deputy Head of the Department

Ho Chi Minh City, ……… 2021

Head of Department Advisor Advisor Ph.D Mai Cao Lan M.Sc Nguyen Viet Van FOR OFFICIAL USE ONLY Faculty:

Department:

Date of defense:

Evaluation grade:

Archive place:

ACKNOWNLEDGE

I wish to express sincere appreciation to Dr Mai Cao Lan for allowing to pursue this thesis in the “Mechanistic Modeling and Wax Deposition in Multiphase Transportation Pipeline” I am extremely thankful for his personal guidance, assistant and supervision

I am most grateful to M.Sc Nguyen Viet Van and his friendly colleague in Hoan Long – Hoang Vu JOC for their unwavering support and understanding throughout this work Their continued support and understanding were instrumental to the success of this wok and greatly appreciated

Furthermore, I will like to show gratitude to all petroleum engineers in “Tôi là Người Dầu Khí” community for their advice throughout the evaluation and correction for calculation tools Additionally, I will like to show gratitude to Nguyen Huu Nhan, Nguyen Hoai Vu and Nga Duong for their personal guidance and advices over the course of study Finally, my warmest thanks go to my family, who constantly supported me during five years

DECLARATION

I declare that the thesis has been composed by myself The thesis is submitted for examination in consideration of graduation of bachelor degree of petroleum engineer in Ho Chi Minh City University of Technology Furthermore, I took reasonable care to ensure that the work is original, and to the best of my knowledge, and has not been taken from other sources except where such work, investigated data have been cited and acknowledge within the text

Therefore, it is necessary to develop a flow-assurance model to analyze and calculate optimal conditions for a stable production of gas and hydrocarbon liquids with water in which pressure and temperature profiles are two key factors There are two ways in which are commonly used They are

1) experimentally, through laboratory-sized investigation with appropriate instrumentation to address relative method applied for specific cases (normally called empirical correlation methods)

2) and theoretically, using mathematical equations and models for the flow which is known as mechanistic models Poettmann and Carpenter’s method which is a semi-empirical correlation are quietly used because its reliable and is generally accepted However, a limited range of flow rates and gas-liquid ratios have made this method less used in many cases Furthermore, many empirical models exhibit large discontinuities at flow pattern transitions which may cause convergence problem when are used for the simulation of practical cases

Mechanistic models, on the other hands, have become a perfect adjustment due to using mathematical equations based on fundamental laws which can be applied in full range of data with more accurate OLGA, a dynamic multiphase flow simulator, is one of well-known software which is widely used in oil and gas field And in this thesis, a computation program developed in VBA (a coding method created by Microsoft) applied those impressive models to predict the pressure and temperature distribution in seabed pipeline The program was compared with OLGA to correct the workflow and check its validation before it is applied in practical cases

In 2014, Thap Minh Thu introduced a model simulating oil and gas transportation pipeline from W2-WHP to CPP who applied on fundamental theory of flow assurance and OLGA to propose a suitable inner diameter, insulation materials and analyze factors relating to flow-assurance problems However, Thap Minh Thu only used OLGA to develop model, therefore, a gap between applicability of theorem proposed and practicality was created which might not well understand the fundamental background of OLGA software Hence, in order to overcome this disadvantage, this thesis proposes a comprehensive model based on fundamental theorem for predicting pressure and temperature profiles To do this, VBA, a programing language for Excel is used due to its simple and ease of access The program is then compared with OLGA’s sample results to verify the model which would be used to apply in a practical case collected from Thap Minh Thu’s master thesis and shows an impressive accurate

X1-Wax deposition problem is one of critical issues that Thap Minh Thu did not mention in his Master thesis To consolidate his contribution, the OLGA software is then used to investigate wax deposition in X field pipelines system

by using wax deposition module and his data set The task of this section is determining the paraffin wax thickness consider the maximum allowed inlet pressure to propose a necessary time of pigging operation to prevent blockages All necessary data such as pressure and temperature profiles, wax deposition rate and effects of surrounding environment are also a primary concern to confirm the objective of this section

TABLE OF CONTENTS

ACKNOWNLEDGE i

DECLARATION ii

ABSTRACT iii

TABLE OF CONTENTS iv

TABLE OF FIGURES vi

TABLE OF TABLES vii

INTRODUCTION 1

1 Background 1

2 Problem Statement 1

3 Purpose and Scope 1

4 Thesis Organization 2

CHAPTER 1 LITERATURE REVIEW 3

1 Motivation of Study 3

2 Relevant Researches 5

CHAPTER 2 FUNDAMENTAL BACKGROUND 9

2.1 PVT Properties Of Oil And Gas 9

2.1.1 Pseudo-Critical Quantities 9

2.1.2 Direct Calculation of Compressibility Factor 9

2.1.3 Gas Density 9

2.1.4 Gas Formation Volume Factor 10

2.1.5 Gas Viscosity 10

2.1.6 The Bubble-point Pressure 11

2.1.7 Oil Formation Volume Factor 12

2.1.8 Isothermal Compressibility Coefficient of Crude Oil 13

2.1.9 Oil Density 14

2.1.10 Oil Viscosity 14

2.2 Multiphase-Flow In Subsea Pipeline 15

2.2.1 The Main Parameter of Multiphase-Flow 15

2.2.2 Flow Regimes in Pipeline 16

2.2.3 Pressure Drop Along Multiphase Flow Pipeline 17

2.2.4 Mechanistic Model for Predicting Flow Regimes and Pressure Distribution 20

2.2.5 Heat Transfer in Pipes 36

2.2.6 Temperature Prediction Along Multiphase-Flow Pipeline 40

2.3 Basic Concepts of Wax Deposition and Wax Deposition Mechanisms 41

2.3.1 Cloud Point or Wax Appearance Temperature (WAT) 41

2.3.2 Pour Point 41

2.3.3 Mechanisms of Wax Deposition 41

CHAPTER 3 PREDICTING TEMPERATURE AND PRESSURE FOR SEABED PIPELINE IN X FIELD 43

3.1 Computational Workflow for Pressure and Temperature Prediction 43

3.2 Validation of Computational Workflow 45

3.2.1 Preparation 45

3.2.2 Results and Discussions 47

3.3 Application of The Computational Workflow for The Gathering Pipeline in Field X 49

3.3.1 Background 49

3.3.2 Data Preparation 49

3.3.3 Results and Discussion 53

CHAPTER 4 WAX DEPOSITION MODELING FOR SEABED PIPELINE IN X FIELD 57

4.1 Factors Affecting The Wax Deposition 57

4.1.1 Temperature Difference And Cooling Rate 57

4.1.2 Crude Oil Composition 57

4.1.3 Flow Rate 57

4.1.4 Pressure 58

4.1.5 Pipe Surface Properties 58

4.2 Wax Control Strategies For The Field 58

4.3 Computational Workflow for Deposited Wax Prediction 59

4.4 Application of OLGA for Wax Thickness Prediction in The Gathering Pipeline, Field X 62

4.4.1 Construction of OLGA Wax Module for Wax Thickness Prediction 62

4.4.2 Methodology of Wax Deposition Simulation 62

4.4.2 Results and Discussions 63

CONCLUSIONS AND RECOMMENDATIONS 66

1 Conclusions 66

2 Recommendations 66

NOMENCLATURE 67

REFERENCE 69

APPENDIX 71

Appendix A Newton-Raphson Iterative Procedure and the Existence of the Solution For Slug Flow Model 71

Appendix B Stratified Flow Model 72

Appendix C The Derivation Of Equations For Temperature Prediction 75

TABLE OF FIGURES

Figure 2-1 Gas-solubility pressure diagram [24] 12

Figure 2-2 Oil formation volume factor versus pressure [24] 12

Figure 2-3 Major flow patterns in horizontal flow [12] 17

Figure 2-4 Major flow patterns in vertical flow [13] 17

Figure 2-5 Control volume and relevant variable describe a system for flow through a pipe section [9] 19

Figure 2-6 Workflow of flow regime prediction 25

Figure 2-7 Physical model for bubble flow [11] 27

Figure 2-8 Equilibrium stratified flow 29

Figure 2-9 Physical model for slug flow [11] 33

Figure 2-10 Physical model for annular flow [11] 35

Figure 2-11 A cylinder with conduction surface condition [18] 36

Figure 2-12 Composite hollow cylinder with convection both surface: a) Temperature distribution and b) Equivalent thermal circuit [18] 39

Figure 3-1 An illustration of computational workflow presented in Figure 3-2 in which the pressure and temperature is calculated in each incremental length of pipe 43

Figure 3-2 The flow chart for the pressure and temperature prediction 44

Figure 3-3 Flow chart for inner diameter selection when pressure and temperature is predicted 45

Figure 3-4 Pipeline profile from OLGA_sample_case 46

Figure 3-5 Temperature distribution predicted by OLGA and computational program along 400-m pipeline 48

Figure 3-6 Pressure distribution predicted by OLGA and computational program along 400-m pipeline 48

Figure 3-7 Pipeline Profile between X2-WHP to X1-CPP, X field 51

Figure 3-8 A PT phase diagram of hydrocarbon components generated by Multiflash software 51

Figure 3-9 Temperature distribution comparison between TMT’s data and calculation 54

Figure 3-10 Pressure distribution comparison between TMT’s data and calculation 54

Figure 4-1 Summary of general wax deposition and control methodologies 58

Figure 4-2 The flow chart for wax thickness prediction in seabed pipeline 61

Figure 4-3 An illustration of Figure 4-2 about application of wax deposition model to calculate the wax thickness in seabed pipeline over a period of time ∆𝑡 62

Figure 4-4 Schematic flow line diagram in the OLGA software 63

Figure 4-5 Pressure profiles in pipeline after 50 days in X field’s pipeline 63

Figure 4-6 Temperature profiles in X field’s pipeline after 50 days 64

Figure 4-7 Thickness of wax deposition in X field’s pipeline after 50 days 64

Figure 4-8 Deposited wax thickness after 50 days in PIPE-50 and PIPE-51 section, X field’s pipeline 65

Figure 4-9 Temperature at the pipe wall of seabed pipeline in X field 65

TABLE OF TABLES

Table 2-1 Important Dimensionless Group in convection heat transfer 37

Table 2-2 Constants for the Hilpert Correlation for Circular (Pr≥0.7) and Noncircular (Gases only) Cylinders 38

Table 3-1 Bathymetry data for the production pipeline from OLGA_sample_case 46

Table 3-2 Input parameter for OLGA_sample_case 46

Table 3-3 Pipeline details for OLGA_sample_case 47

Table 3-4 Material properties for OLGA_sample_case 47

Table 3-5 Material/Coating thickness for OLGA_sample_case 47

Table 3-6 Statistical analysis of results compared between OLGA_sample_case and computational program 47

Table 3-7 Major programming verification activities 48

Table 3-8 Bathymetry Data for the Production Pipeline from the X2-WHP to the X1-CPP, X field 49

Table 3-9 Hydrocarbon components of oil and gas gathering in seabed pipeline, X field 51

Table 3-10 Critical parameters which require for gathering oil and gas in pipeline, X field 52

Table 3-11 Pipeline details to gathering oil and gas in X field 52

Table 3-12 Material properties of X field’s pipeline 52

Table 3-13 Material/Coating thickness of X field’s pipeline 53

Table 3-14 Seawater temperature - Surface 53

Table 3-15 Seawater temperature - Seabed 53

Table 3-16 Air temperature 53

Table 3-17 Air velocity 53

Table 3-18 Other parameters 53

Table 3-19 Production data 53

Table 3-20 Results of temperature distribution prediction calculated by Thap Minh Thu and computational program in pipeline from X2-WHP to X1-CPP 54

Table 3-21 Results of pressure distribution prediction calculated by Thap Minh Thu and computational program in pipeline from X2-WHP to X1-CPP 55

Table 4-1 𝑁𝑆𝑅 expressed for each flow pattern proposed in Matzain model 59

INTRODUCTION

1 BACKGROUND

Over recent decades, large amounts of oil and gas are found in extreme conditions as they are buried at thousand meters deep with special reservoir characteristics This situation raises new challenges within the field of petroleum exploration, production, and transportation Low reservoir pressure, low seabed temperature, or far from shoreland are some of the field challenges

In Vietnam, the substantial development of the petroleum industry has been made a great contribution to the construction of the country Many reservoirs with large potential reserves have been producing and exploring Besides, some small reservoirs are also considered and produced but they are hard to be developed separately due to small scale and low recovery enhance In these cases, therefore, the development option by connecting with the existing reservoir

is often chosen because of the possibility of higher economic efficiency than the independent development option

2 PROBLEM STATEMENT

The main objective in the transportation of oil and gas is to ensure efficient production, profitability, and safety One

of the biggest challenges preventing those factors which occur flow instabilities in the seabed pipeline system is wax deposition on the tube walls due to heat transfer from the environment Hence, it is very important to understand the flow behaviors, fluid properties as well as in-situ performance in the intra-reservoir area, and connection between neighboring reservoirs to propose a proper production plan To achieve that, a thorough interpretation of current system conditions such as pressure and temperature is regularly evaluated

Moreover, modeling wax deposition is a complex task that involves several disciplines, such as, thermodynamics, phase equilibrium, mass/heat transfer, and fluid mechanics The precipitation and deposition rate can significantly influence to stabilization of the whole system and the economy of the field because operational and remedial costs are increased on account of product reduction Therefore, the ability to accurately predict wax deposition is an invaluable tool that would help in the design stages of the pipeline, as well as, in the scheduling of interventions

3 PURPOSE AND SCOPE

Successful development of the seabed hydrocarbon transportation project requires engineering designs of the facilities that can handle the flow assurance challenges such as wax deposit problems A robust can only be obtained with an accurate prediction of pressure and temperature, which are two factors causing wax precipitation To accomplish this, physical approaches are used to predict the drop of pressure and temperature distribution in multiphase flow along the pipeline and defines potential wax problems, and estimates the pigging frequency

In this thesis, mechanistic models for multiphase flow are used to predict pressure drop and flow behavior in pipes Those models are based on Petalas and Aziz’s method [20] which are proved that can take into account a wide range of data and all types of fluids and conditions where exhibit large discontinuities that empirical models often show their limits On the other hand, it was found that their mechanistic model for predicting flow patterns could improve the capability of calculating pressure gradients along the pipeline These new empirical correlations were applied to all fluid properties and pipe geometries

Alves et al [2] proposed a method that improved Ramey’s model to predict the flowing temperature distribution in pipes This method shows a closure relationship of pressure and temperature in multiphase flow which takes into account thermodynamic laws and the Joule-Thomson effect and adapts changes in well or pipeline deviation and variable thermal properties The use of unified equations could obtain the entire range of inclination angles make this method applicable

in pipelines and wellbores

In the second part of the thesis, the main issue of transporting gas and hydrocarbon fluids paraffin components Matzain develop a wax deposition model based on mechanisms that are dominant factors for the accumulation of waxy crystal This model shows that wax deposition depends on flow patterns which the build-up trends for deposition are similar to the observation of flow regimes

The Thesis Objectives

The purpose of the project is to provide an applicable workflow for predicting the pressure and temperature in a seabed pipeline Many researches also investigate the pressure and temperature distribution (e.g Thap Minh Thu (2014) – “Tính Toán Đảm Bảo Dòng Chảy Trong Quá Trình Vận Chuyển Sản Phẩm Khai Thác Từ Giàn X2-WHP Về X1-CPP”, Dang Van Hoi (2020) – “Tính Toán Đảm Bảo Vận Chuyển Dầu Khí Bằng Đường Ống Từ Đầu Giếng Giàn X Đến Giàn Xử Lý Y“) However, using the software makes them dependent and they might not understand the root of the phenomenon

Therefore, EXCEL was used to program and predict the pressure and temperature distribution in the seabed pipeline The investigated pipeline consists of a 7,500 m seabed pipeline connected to a wellhead platform (WHP) and a central processing platform (CPP) through risers in that the data set was collected from Thap Minh Thu’ Master thesis The program was emphasized from a three-step procedure They are:

b) Pressure drop and liquid holdup prediction

Once the flow pattern has been determined, the pressure distribution and flow behavior can be predicted from physical models The model involves mass, momentum, and energy balance for multiphase flow

c) Temperature prediction

Pressure gradient alone pipe is a crucial key to enter the temperature determination Developed algorithms enable to simulate steady-state pressure and temperature profiles in the system This will involve the use of an energy equation in terms of enthalpy

However, it must be verified by trusted commercial software before raising any recommendation for any practical cases The software OLGA, hence, was used In addition, the OLGA was used to develop a wax deposition model to investigate how deposited wax acts to the pipeline system of the X field and showed the amount of deposited wax over

a time period in the pipe wall Finally, an analysis of the pressure buildup at WHP was conducted to propose a suitable pigging operation schedule for the pipeline OLGA was applied to determine the choice of maximum operation period

4 THESIS ORGANIZATION

Chapter 1 (Literature Review) introduces fundamental studies that the thesis uses to develop the computational

workflow and program Besides, the introduction of relevant researches in Vietnam as well as in other countries shows the importance of pressure and temperature investigation and wax deposition in the study of flow assurance problems

Chapter 2 (Fundamental Background) comprises some of the main empirical correlations for PTV measurements

and mathematical equations to develop a model It accounts for hydrocarbon property analysis with the selection of flow patterns possibly existing in the pipeline As a result, a predicted flow condition in terms of pressure and temperature is established

Chapter 3 (Predicting Temperature and Pressure for Seabed Pipeline in X Field) gives an overview of developing a

computational program for predicting pressure and temperature profiles Once the program satisfies some crucial requirements to check its validity and accuracy of results, it will be used to propose the operability of the pipeline including pressure and temperature profile from field data include pipeline material properties, hydrocarbon components, and environmental data

Chapter 4 (Wax Deposition Modeling for Seabed Pipeline in X Field) addresses the use of OLGA in the analysis of

wax deposition along pipe walls The chapter provides a theoretical recommendation of pigging operation schedule to

enhance the operability

CHAPTER 1 LITERATURE REVIEW

CHAPTER ONE OVERVIEW

In this chapter, a brief outline of three papers explains the fundamental of this thesis which includes purposes and scopes, general methods and results to evolve the flow assurance statements, and the growing wax deposition in the hydrocarbon pipelines

The understanding of the wax deposition problems and a combination of mathematic models would support the aims and objectives of this study

1 MOTIVATION OF STUDY

TOPIC 01: A Mechanistic Model for Multiphase Flow in Pipes - 2000

Authors: N Petalas, K Aziz

Problem Statement and Objectives

The flow of liquid and gas through petroleum wells and pipes is a complex phenomenon One factor which needs to take into account is the existence of several flow regimes along the well or pipe for a given operating condition Due to the complex nature of two-phase flows, many predictive models through empirical or semiempirical methods may not suitable during transient periods for predicting pressure and liquid holdup variations Mechanistic models, on the other hand, are based on fundamental laws and can offer more accurate modeling of the geometric and fluid property variations

Taitel and Dukler (1976) “A model for predicting flow regime transitions in the horizontal and near horizontal liquid flow” – A theoretical model was developed to predicts the flow regimes based on their relationship with mass flow rates, fluid properties, pipe diameter, and angle of inclination The process of analyzing pressure drop is using an overall momentum balance over a flow unit in a horizontal pipeline Later, a mechanistic model for predicting flow transition for a whole range of pipe inclinations was proposed by Barnea (1986) “A unified model for predicting flow-pattern transitions for the whole range of pipe inclinations” which were modified and extended to consider the effect of small deviations from vertical cases

gas-All of the models presented above are either incomplete, as they only consider flow pattern determination, or are limited in their applicability to only some pipe inclinations Therefore, Petalas and Aziz suggested a mechanistic model for all flow regimes which could improve the capability of predicting pressure gradient and liquid holdup along pipes These new empirical correlations were developed for all fluids properties and pipeline geometries

Methods

A large amount of experimental data has been collected through the use of a Multiphase Flow Database developed

at Stanford University Based on subsets of these data, the previously proposed models, and new correlations, a new model has been developed

Results

The flow behaviors were examined over a wide range of flow rates and fluid properties This was done over the complete range of upward and downward pipe inclinations and both pressure gradient and liquid holdup were analyzed The model was then compared with experimental observations which were extracted from Stanford Multiphase Flow Database for which pressure gradient, holdup, and flow pattern gave reliable results The model was then analyzed compared with existing methods and showed that it exhibits a generally smooth behavior and consistent trends between flow patterns

TOPIC 02: A Unified Model for Predicting Flowing Temperature Distribution in Wellbores and Pipelines - 1992

Authors: I Alves, F Alhanati, O Shoham

Problem Statements and Objectives

This paper presents a general and unified equation for flowing temperature prediction that is applicable for the entire range of inclination angles The equation degenerate from Ramey’s equation for ideal gas or Coulter and Bardon's equation for incompressible liquid Furthermore, the Joule-Thomson coefficient was taken into account due to the thermodynamic behavior of the multiphase flow fluids

The model can be applied to pipelines or production and injection wells, under single- or two-phase flow over the entire inclination angle range from horizontal to vertical, with compositional and black-oil fluid models The prediction

of temperature profiles shows a remarkable agreement of errors compared with five different methods

Results

The prediction of temperature profiles shows a remarkable agreement of errors compared with five different methods Especially, the results show excellent values for the high flow rates where the Joule-Thomson effect becomes substantial

compared to the Ramey equation which did not predict the right trend

TOPIC 03: Multiphase Flow Wax Deposition Modeling – 2001

Authors: A Matzain, M Apte, H Zhang et al

Problem Statement and Objectives

The world demand for energy has led oil companies to expand their operation in a deeper reservoir and far from shoreland Wax deposition is a significant operational and economic concern leading to reduce production rates, equipment breakdowns, and production shutdowns Hence, a measurement of wax deposition places an important factor

A semi-empirical kinetic model was developed for the wax deposition tests that predicted wax thickness with acceptable accuracy, especially at high flow rates The rate of wax build-up is calculated by a modification of Fick’s law

Results are presented from two-phase flow wax tests using high pressure and multiphase flow test facility carried out

by using South Pelto oil provides an insight for future model development A steady-state simulator was developed for simulating paraffin deposition in a multiphase flow environment It consists of four main modules that perform the following tasks:

• Multiphase flow hydrodynamic calculations

• Multiphase flow heat transfer calculations

• Wax and fluid thermodynamic calculations

• Wax deposition rate calculation

This modular structure is currently applied in the Flow assurance module in OLGA (a dynamic multiphase flow simulator developed by Schlumberger)

TOPIC 04: Calculation of Flow Assurance During Transporting Hydrocarbon Production from X2-WHP to

X1-CPP - 2014

Authors: Thap Minh Thu

Problem Statements and Objectives

Once the practical observations and database, such as fluid components, pipeline, material details, and environmental condition, were collected from X field, Cuu Long Basin, Thap Minh Thu used theoretical approaches of flow assurance and OLGA software to select an appropriate pipe size, insulation coating for the pipeline, and analyze problems related

to flow assurance such as fluid plug formation and calculate the starting pressure after the shutdown time Finally, it is proposed a reasonable production and transportation plan to ensure safety and economic efficiency

Methods

The objective of this thesis will be solved by collected input data and parameter from the field X:

• Compositions and fluid properties

• Production fluid rates

• Technical parameters such as pressure and temperature

• Pipeline and coating parameter and seabed geometry

• Properties of the surrounding environment

The model was carried out by using PVTsim to investigate hydrocarbon properties and OLGA:

• Hydraulic analysis to determine pipe size

• Thermal analysis to determine the insulation requirements to prevent wax deposition in pipeline

• Analysis of instantaneous thermo-hydraulic properties including shutdown time, slug formation to propose safe operation plans

Results

From the results generated by OLGA, Thap Minh Thu proposed that:

• A 10-inch-diameter pipeline is suitable to transport gas and hydrocarbon fluid from X2-WHP to X1-CPP

• An overall heat transfer coefficient of insulation is 0.25 𝐵𝑇𝑈

𝑓𝑡 2 ℎ𝑟℉ to ensure the fluid temperature higher than wax appearance temperature

• Analysis of instantaneous thermo-hydraulic properties determines the fluid temperature reduce to pour point temperature after 34 days

• Liquid surge volume at X1-CPP is determined to propose slug catcher specifications

Author: Faisal Abdullah Aladwani

Problem Statements and Objectives

Underbalanced drilling is the drilling process where the effective bottom hole circulation pressure of the fluid system

is less than the formation pressure Performing UBD operations on deviated or horizontal wells requires controlling the drilling parameters in order not to damage the formation and to achieve the maximum rate of penetration To optimize

the use of UBD in any well, successful control of the bottom-hole pressure and fluid flowing through the formation is necessary

During UBD operations, a complex fluid system occurs both inside the drill string and the annulus Two-phase flow prediction techniques are used to predict several parameters such as pressure drops (both inside the drill string and through the annulus), flow patterns, velocities, liquid holdup, and other parameters To achieve this task, a set of mechanistic two-phase flow models are used Specifically, a current model is modified to include the effects of wellbore deviation Simulation results are compared with data from a deviated well drilled with UBD technology

Methods

A computer algorithm was coded into a macro which can be run using MS EXCEL to calculate the pressure distribution in the drilling string and in the annulus and through bit nozzles by using mechanistic models The macro was written in VBA (Visual Basic for Applications)

The computer program described above has been used to simulate the behavior of a deviated well while drilling underbalanced To demonstrate the validity of the model, a field case was simulated and results were compared with measurements and a commercial simulator

Result

After running the program for the two cases, the results have a good match with the measured value where the average absolute error 𝐸𝑎 has an average value of less than 10% For the second run, the pressure difference between the calculated by empirical correlations and measured did not distribution correctly along the wellbore and gave a large injection pressure The author concludes that the use of different mechanistic models shows that they can capture the behavior of the flow during different combination of flow rates and pipe geometries, unlike the empirical correlations where they reported not to work well in oil field cases

TOPIC 06: A Study on Heat Loss from Offshore Pipelines Depending on the Thermal Conductivity of

Backfills and Burial Depth - 2018

Author: Dong-Su Park, and Young-Kyo Seo

Problem Statements and Objectives

Subsea pipelines are designed to transport mixtures of oil, gas, and their associated impurities from the wellhead that can have temperatures as high as 100℃, while the external temperature can be as low as 5℃ Heat can be lost from the subsea pipeline containing high-temperature fluid to the surrounding environment owing to the generation of hydrates and wax, which causes significant economic loss To prevent hydrates and wax from being generated, it is essential to identify a period in which the crude and natural gas reach extreme temperatures This paper presents a comparison between numerical analyses and existing theoretical formulas for different backfills and burial depths The results were compared with the Carlsaw & Jaeger formula and OTC23033 formula for the calculation of the overall heat transfer coefficient

Methods

ANSYS CFX v13.0, a commercial numerical analysis program with proven accuracy of heat transfer analysis, was used as a comparative study In the numerical analysis, the overall heat transfer coefficient is calculated by using the mean temperature of the outlet, inlet, and surface of the subsea pipe in burial depth of the pipe varied as 200%, 100%, 80%, 60%, 40% and 20% when the temperature of the whole model reaches the steady-state by a certain temperature of internal fluid And compared with the theoretical formulas

Results

In this study, the results of the calculation of the overall heat transfer coefficient show potential application into economically fabricate or design insulating materials as well as burial depth due to the average errors were slightly below 9% when comparing them with the results obtained by Carslaw’s and Jeager’s formula and the OTC 23033 formula The errors decreased with the increase of burial depth

TOPIC 07: Temperature Profile in Subsea Pipeline and Effect of Paraffin Wax Deposition on The Overall

Heat Transfer Coefficient - 2011

Author: Håkon Eidem Christiansen

Problem Statements and Objectives

The temperature profile along a subsea pipeline is decided by the heat flow in the pipeline, the overall heat transfer coefficient of the pipeline, and the ambient temperature The drop of temperature leads to decrease in the solubility of the components and precipitate paraffin wax Furthermore, the water molecules can form hydrates with small hydrocarbon molecules This can lead to a lower flow rate, higher pressure loss, and clogging the pipeline This project tried to identify the parameters that affect the temperature profile along a subsea pipeline And, the main objective is to find out whether paraffin wax deposits on the pipe wall will affect the total heat transfer coefficient of the subsea pipeline The results will be used to identify if a pipeline has the potential of wax deposition and promote a pigging frequency

Methods

The author indicated that the deposit was a buildup of a continuous phase of wax and a discontinuous phase of oil which means the deposit could be looked at as a porous medium with a discontinuous phase Therefore, the thermal conductivity could be calculated by the use of the Maxwell-Eucken model

The heat transfer coefficient of oil describes how well heat is transferred from the oil to the environment outside the pipeline It is claimed that the estimation would be difficult due to the heat transfer coefficient depends on many factors (e.g., wall’s geometry, material, or flow condition), so that the author used semi-empirical correlations with dimensionless numbers to calculate The dimensionless numbers were used are the Nusselt number, the Reynolds number, and the Prandtl number

To find values for the volatile oil, its composition was entered into HYSYS, together with pressure, temperature, and calculated volume flow rate The values of heat capacity, viscosity, density, and thermal properties with respected pressure and temperature were generated by PVTsim

To investigate the effect of deposited paraffin wax on the overall heat transfer coefficient, the wax deposit was assumed to be uniformly distributed throughout the whole pipeline The deposition thickness and oil entrainment were plotted with seven cases of the buried pipeline

For a clean pipe, it is necessary to identify the temperature profile with the use of the boundary layer temperature corresponding to wall temperature to find out where in the pipeline wax crystals would start to precipitate The frequency and rate of pigging operation depend on the deposition rate and the rate of aging

TOPIC 08: Calculation of Flow Assurance for Transporting Hydrocarbon in Pipeline from Well Head Platform X to Central Processing Platform Y

Author: Dang Van Hoi

Problem Statements and Objectives

In Vietnam, the expansion of petroleum exploitation to the marginal and deep-water fields is a very practical and urgent, effective, and strategic issue due to the energy demand However, flow assurance problems become a primary concern when transport and gathering oil and gas in the subsea pipeline, especially for a pipeline with tens of kilometer long Besides, Heat can be lost from the subsea pipeline containing high-temperature fluid to the surrounding environment owing to the generation of hydrates and wax This phenomenon would make the operation more difficult, even shut down the system Therefore, the objective of this thesis is to investigate the flow assurance problems in the gathering pipeline from wellhead platform X to central processing platform Y in order to promote a safe operating condition and minimizing unintended costs

Methods

In this study, the effects of wax deposition and slug formation on seabed pipelines were investigated by using the OLGA The collected data, such as hydrocarbon components, pipeline, environment conditions, were used to build the model and simulation

Based on data obtained from the X field, hydrodynamic analysis was developed to validate the model built by OLGA The uncertain factors and their influence on the simulation results were analyzed to correct the input parameters With the support of the Solver add-in in EXCEL, the empirical constant term in the Matzain model is modified to apply the wax deposition model for the X field

Results

The simulation results showed that the model built by OLGA gave results close to the data obtained from reality During operation, the producing parameters changed to match the system, leading to the actual parameters being different from the simulation results The author claimed that these differences are caused by the overall heat transfer coefficient, environment conditions, pipe, and insulation materials

From the production data in the period of February 2020, the wax deposition rate was simulated by using the OLGA wax deposition simulation module to show a mass of deposited paraffin wax was 16 kg which is acceptable

From the Cold Finger experiment and field data collected, the empirical constant 𝐶1, 𝐶2 and 𝐶3 is adjusted to be applicable for X field The wax thickness obtained at temperature 30℃ us 0.117 mm after 30 days

CHAPTER 2 FUNDAMENTAL BACKGROUND

CHAPTER TWO OVERVIEW

The chapter two presents the use of empirical correlations to estimate necessary parameters for further calculation These correlations are used to describe the way where hydrocarbon would behave in the specific volume with a variety

of pressure and temperature The parameters, normally, are determined from lab experiments In this thesis, they are described in flow simulation software

This chapter also presents hydraulic and thermal analyses which describe the fundamental theorem and their combination in predicting flow regimes, pressure, and temperature in the pipeline

2.1 PVT PROPERTIES OF OIL AND GAS

The industry standard is to measure the gas and oil properties, Pressure – Volume – Temperature (PVT), in laboratory using reservoir samples However, it is sometimes expensive and time-consuming when analyses PVT behaviors Therefore, empirical correlations, which are established by a mathematical relation based on experiments, will be used

to predicts the oil and gas properties

The following parameters will normally be measure

where pseudo-critical pressure is in 𝑝𝑠𝑖 and pseudo-critical temperature is in °𝑅

These correlations are applicable for mixture with impurities such as 𝑁2, 𝐶𝑂2 and 𝐻2𝑆 The pseudo-reduced pressure and temperature are dimensionless parameters and is expressed as:

2.1.2 Direct Calculation of Compressibility Factor

One of the best correlations for evaluation of the z- factor was given by Beggs and Brills [6] The Dranchuk and Abu-Kassem’s correlation [10] determined z-factor from Standing and Katz charts using the pseudocritical gas pressure and temperature at low pressure But this correlation showed more accurate compared to Beggs and Brill’s but gives large errors at high pressure The error in estimating z-factor will lead to big error in estimating all other gas properties such as density, gas viscosity, and gas compressibility Therefore, Mohamed Mahmoud [17] develops a new z-factor correlation which in turn gives less errors at high pressure

𝑇 is the absolute temperature, °𝑅

2.1.4 Gas Formation Volume Factor

The gas formation volume factor is defined as the ratio of the volume of gas at specific pressure and temperature to the volume of gas at standard condition The gas formation volume factor can be described as:

𝐵𝑔 =𝑉𝑔,(𝑃,𝑇)

where:

𝐵𝑔 is the gas formation volume factor, 𝑓𝑡3/𝑠𝑐𝑓

𝑉𝑔,(𝑃,𝑇) is the volume of gas at the interest pressure and temperature, 𝑓𝑡3

𝑉𝑔,𝑆𝐶 is the volume of gas at standard condition (14.7 𝑝𝑠𝑖𝑎 and 60℉), 𝑠𝑐𝑓

If the Equation (2-10) combines with the real gas equation of state and substitute for the volume The gas formation volume factor is:

𝑧𝑛𝑅𝑇𝑃

where compressibility factor at standard condition is 1.0 (𝑧𝑠𝑐 = 1.0)

Since 𝑃𝑠𝑐 = 14.7 𝑝𝑠𝑖 and 𝑇𝑠𝑐 = 520 °𝑅, the above equation would be:

be used for any hydrocarbon-gas production or transportation operations

and the viscosity of gas mixture at 1 atm is generated by this relation

The numerical values of the parameters for viscosity at 1 atm in Equation (2-24) are given by

where 𝑇 is the temperature in ℉ and viscosity of gas mixture is in unit of centipoise (𝑐𝑃)

2.1.6 The Bubble-point Pressure

The bubble-point pressure of a hydrocarbon system is defined as the highest pressure at which the first bubble of gas

is liberated from the oil This is an important property that can be measured by experiments In the absence of the experimentally measured bubble-point pressure, it is necessary to make an estimate of this crude oil properties The bubble-point pressure is based on a function of gas solubility 𝑅𝑠, gas gravity 𝛾𝑔, oil gravity 𝐴𝑃𝐼, and temperature 𝑇

2.1.6.1 Gas Solubility 𝑹𝒔

The gas solubility 𝑅𝑠 is defined as the number of cubic feet of gas in standard condition that will dissolve in one stoke-tank barrel of crude oil at 60℉ and 14.7 𝑝𝑠𝑖𝑎 Standing [23] proposed an equation for determining the gas solubility as a function of pressure in 𝑝𝑠𝑖, temperature in ℉, gas specific gravity and API gravity:

Figure 2-1 Gas-solubility pressure diagram [24]

2.1.6.2 The Bubble-point Pressure

Standing expressed the bubble-point pressure of crude oil systems by the following equation:

where 𝑇 is the system temperature in ℉

2.1.7 Oil Formation Volume Factor

The oil formation volume factor is defined as the ratio of the volume of oil at specific pressure and temperature to the volume of oil at standard condition The oil formation volume factor can be described as:

Figure 2-2 Oil formation volume factor versus pressure [24]

Standing presented the oil formation volume factor in form of mathematic that is a function of gas solubility 𝑅𝑠, specific gravity of oil and gas and the system temperature in ℉

𝐵𝑜= 0.917 + 0.000147 [𝑅𝑠(𝛾𝑔

)

0.5+ 1.25𝑇]

1.175

(2-28)

It should be notice that the Equation (2-28)is only applied at pressure below the bubble-point at which the volume

of oil increases due to gas elements dissolved compared to the compression of the oil as the increasing pressure

Above the bubble point pressure, the formation volume factor must be calculated from

where 𝑐𝑜 is the oil compressibility coefficient at undersaturated hydrocarbon systems, Equation (2-35)

2.1.8 Isothermal Compressibility Coefficient of Crude Oil

Isothermal compressibility coefficient, in general, is defined as the relative change in the volume of a substance with respect to the change in pressure at constant temperature It is expressed in units of reciprocal pressure (usually 𝑝𝑠𝑖−1)

By definition, the isothermal compressibility is expressed mathematically as:

𝜕𝑉

At pressures above the bubble-point, the isothermal compressibility coefficient of the oil phase is described by the

following equivalent expression:

T: the system temperature, ℉

𝑅𝑠𝑏: the gas solubility at the bubble point pressure, 𝑠𝑐𝑓/𝑆𝑇𝐵

At pressures below the bubble-point, the Equation (2-36) describes the isothermal compressibility coefficient:

where:

𝑃 is the interested pressure, 𝑝𝑠𝑖𝑎

𝑇 is the system temperature, ℉

𝑅𝑠 is the gas solubility at pressure 𝑃, 𝑠𝑐𝑓/𝑆𝑇𝐵

𝐵𝑔 is the gas formation volume factor at pressure 𝑃, 𝐵𝐵𝐿/𝑠𝑐𝑓

𝐵𝑜 is the oil formation volume factor at pressure 𝑃, 𝐵𝐵𝐿/𝑆𝑇𝐵

𝛾𝑜, 𝛾𝑔 are the specific gravity of oil and gas, respectively

2.1.9 Oil Density

Calculation of oil density at interested conditions is necessary in predicting pressure losses in pipeline For saturated

hydrocarbon system, the oil density is shown in the following expression:

(2-40) where:

𝜌𝑜 is the density of oil at pressure 𝑃 and temperature 𝑇, 𝑙𝑏𝑚/𝑓𝑡3

Above the bubble point pressure, the oil density must be calculated from Equation (2-41) which is expressed from Equation (2-33)

𝜌𝑜 is the density of oil at pressure 𝑃 and temperature 𝑇, 𝑙𝑏𝑚/𝑓𝑡3

𝑐𝑜 is the oil compressibility coefficient at undersaturated system, 𝑝𝑠𝑖−1

𝑍 = 3.0324 − 0.02023𝛾𝑜 (2-45) For saturated oil viscosity where the hydrocarbon system exists dissolved gas, the equation is expressed as

2.2 MULTIPHASE-FLOW IN SUBSEA PIPELINE

The most distinguishing aspect of studying multiphase flow is the variation in the physical distribution of the phases

in the conduit – a characteristic known as flow pattern or flow regime During multiphase flow through pipes, the flow pattern depends on the relative magnitudes of the forces that act on the fluids Buoyancy, turbulence, inertia, and surface-tension forces vary significantly with the flow rates, pipe diameter, inclination angle, and fluid properties of the phases Several different flow patterns can exist in a given well as a result of the large pressure and temperature changes The important factor is the significant variation in pressure gradient with flow pattern Therefore, the way of predicting flow pattern as a function of a flow parameter is a primary concern

2.2.1 The Main Parameter of Multiphase-Flow

2.2.1.1 Superficial Velocity, 𝒗𝒔

Flow velocities of the gas and liquid phases greatly influence the particle velocity Superficial velocity is an artificial flow velocity calculated as the given phase or fluid were the only one flowing or present in a given cross section area Therefore, the superficial velocities are the volumetric flow rates per unit are of the pipe as shown in Equations (2-49) and (2-50)

Due to differences in flow behaviors in multiphase flow, the particle velocities may be different for different flow regimes For example, the particle velocity in annular flow depends on the annular liquid film velocity and gas core velocity In bubble flow, it may depend on the superficial liquid and gas velocities In slug flow, the particle velocity is affected by liquid slug velocity and liquid holdup in the liquid slug

2.2.1.2 Liquid and Gas Holdup, 𝑯𝑳 & 𝑯𝒈

Liquid holdup 𝐻𝐿 is defined as the fraction of a pipe cross-section or volume increment that is occupied by the liquid phase The value of 𝐻𝐿 ranges from 0 (total gas) to 1 (total liquid) The liquid holdup is defined by

where 𝐴𝐿 is the pipe area of the liquid occupied by the liquid phase and 𝐴 is pipe cross-sectional area

The term void fraction 𝛼 or gas hold up 𝐻𝑔 is defined as the volume fraction occupied by the gas

When two fluids travel at different velocities, the flow is referred to “slip” flow For the homogeneous equilibrium model represented for “no slip”, fluid properties are taken as the average of the gas and liquid phases and frictions are calculated using the single-phase Moody correlation

Hence, the no-slip liquid holdup is defined as the ratio of the volume of the liquid in a pipe segment to the volume

of the pipe segment which would exist if the gas and liquid traveled at the same velocity

where:

𝐻𝑛𝑠𝐿, 𝐻𝑛𝑠𝑔: No-slip liquid and gas holdup, dimensionless

𝑄𝐿𝑎, 𝑄𝑔𝑎: The actual flow rate of gas and liquid in a pipe segment, 𝑓𝑡3

2.2.2 Flow Regimes in Pipeline

The flow regimes describe how the two phases, gas and liquid, are distributed in the pipe This feature is presented

by the volumetric flow rate of each phase and the inclination angle Flow regimes and flow regime maps for horizontal, vertical are illustrated in Figure 2-3 and Figure 2-4, respectively

2.2.2.1 Flow Regimes in Horizontal Pipe

Flow regimes observed in a horizontal pipe depend on gas and liquid velocities Several classifications are defined

in the below literature for horizontal flow as shown in Figure 2-3

Bubble flow: At very slow injection rate, gas moves in the pipe as small bubbles This flow pattern is dispersed

bubble flow Gas bubbles do not have the same size Due to lighter density, gas bubbles tend to move on the upper part

of pipes

Stratified smooth flow: At low liquid and gas velocities in a horizontal pipe, gas and liquid separate and gas moves

on the top and liquid on the bottom The liquid-gas interface surface is smooth

Stratified wavy flow: Increasing the gas injection from stratified smooth flow cause turbulence to liquid-gas

interface surface, causing a wavy interface

Slug flow: If gas flow rate keeps increase from stratified wavy flow, the wavy motion of interface increases till it

reaches the upper side of the pipe and blocks the gas continuity in the system In slug flow, the flow regime is not uniform in the pipe Gas phase moves in separate spaces which are divided by columns (slugs) of the liquid phase

Annular flow: If gas injection rate further increases, gas moves as a core in the pipe surrounded by liquid Liquid

phase is thicker at the bottom due to gravity

Figure 2-3 Major flow patterns in horizontal flow [12]

2.2.2.2 Flow Regimes in Vertical Pipe

Flow regimes observe in vertical pipe are illustrated in Figure 2-4 Flow patterns created in vertical conduit are:

Bubble flow: Bubble flow occurs at low gas injection rates Gas bubble discrete in the continuous liquid phase and

moving in a continuous curve around the central of pipes

Slug flow: Increase the gas injection rate, large bubbles coalesce with smaller bubbles, generating larger bubbles

When large bullet-shape bubbles are present in the pipe, the flow is slug flow and the bubble is a Taylor bubble Taylor bubbles do not have enough pressure to support the liquid phase Therefore, liquid slips down the Taylor bubble and concentrate under the bubble until the next Taylor bubble arrives

Churn flow: Churn flow pattern is chaotic slug flow Churn flow occurs at higher gas injection than slug flow

Taylor bubble is deformed and the slug has an oscillatory motion This flow pattern exists in upward flow only

Annular flow: At high gas injection rates, gas flows as a continuous phase in the middle of pipe surrounded by

liquid film A small amount of liquid is entrained in the gas core Annular flow occurs at high gas superficial velocity with relatively little liquid present

Figure 2-4 Major flow patterns in vertical flow [13]

2.2.3 Pressure Drop Along Multiphase Flow Pipeline

Pressure drop occurs simultaneously with temperature drop in pipelines and wells While temperature drop is the primary reason for solids precipitation and deposition, simultaneous pressure drop and associated fluid velocity are also

important Many different flow situations are found in oil and gas production The situation ranges from simple-phase flow to complex multiphase flow

2.2.3.1 Energy Balance

The mechanistic model was developed from the general energy equation which expresses an energy balance between two points in a fluid system It follows the law of conservation of energy which states that change in amount of energy contained within the system during an interval of time is equal to the net amount of energy transfer in across the system boundary by heat transfer minus the net amount of energy transferred out the system boundary by work The energy balance equation is given in the following form:

Conservation of mass means that the total of any isolated material system (defined volume such as a segment of pipe)

is neither increased nor decreased by any reactions It is simply that the mass get in a system minus the mass out must equal to zero The equation is expressed by Reynold transport theorem, Equation (2-62)

In the control volume and relevant variable defined in Figure 2-5, the conservation of linear momentum can be expressed as

when 𝑁𝑅𝑒 < 2300 and the roughness has no effect

The turbulent flow regime, the relationship between Reynolds number and the friction factor is more complex The

roughness can have a significant effect on the friction factor and, thus the pressure gradient The relative roughness is a function of absolute roughness and inside diameter of the pipe, 𝜀/𝑑 One model for this relationship is Zigrang and Sylverster’s equation which is one of the most accurate and simple to use

Normally in seabed pipeline system, the transition flow regime is not considered due to high flow rate

The second component in Equation (2-70) is the pressure gradient caused by the change in elevation For the vertical pipeline or well, it is normally the predominant factor

2.2.4 Mechanistic Model for Predicting Flow Regimes and Pressure Distribution

The methods used to predict pressure drop along pipeline segment can be classified as empirical correlations and mechanistic models

Multiphase flow correlations were developed the general energy equation which expresses an energy balance between two points in a fluid flow system They are divided into 3 main parts, which consider slip or no-slip condition, the flow patterns and others parameters like liquid holdup and friction factor to support for predict flow patterns They started with simple pressure drop predictions for single phase flow, turn to multiphase flow correlation that do not consider the flow patterns or slip velocity, to accounted for slip and flow patterns, to complicated application of 2 and 3-phase mechanistic models

According to Petalas and Aziz et al.’s description [20], empirical models show large discontinuities at the flow pattern transitions which can lead to unexpected problems regards to the use of models for the simulation of reservoir and associated production facilities as they are limited by the range of data about types of fluids and conditions in oil and gas fields Hence, mechanistic models, for multiphase flow, can improve the prediction of pressure drop and liquid holdup in pipes, especially in situations that the reliable empirical correlations are not available

Petalas and Aziz modified the Barnea [5] model to apply for the entire range of inclination angles, from upward vertical flow to downward vertical flow (−90° ≤ 𝜃 ≤ 90°) The procedure depicted in Figure 2-6 is a composed model for predicting flow pattern in a pipe segment

2.2.4.1 Flow pattern prediction

Transition from Dispersed bubble flow

Dispersed bubble flow usually appears at very high liquid flow rate There are conditions where small discrete bubbles also appear at low liquid rate These bubbles are called bubble or bubbly flow The distinction between bubbly flow and dispersed bubble flow is that the dispersed bubble flow is observed in whole range of pipeline inclination whereas the bubbly flow is only observed in vertical flow with large diameter pipes

The flow is bounded by two criteria:

1) Taitel et al [25] presented a criterion where the flow can exist This condition is satisfied in large-diameter pipes:

1/2

(2-76) where

𝑑 is the pipe diameter

𝜌𝐿, 𝜌𝑔 are the liquid and gas densities

𝜎𝐿 is the surface tension of liquid

2) In horizontal pipe, the angle of inclination 𝜃 must be large enough to prevent migration of bubbles to the top of wall of the pipe The critical inclination angle can be obtained by the following equation:

where 𝛼 = 𝛼𝑐 = 0.25 The sin 𝜃 is positive for the upward flow and negative for downward flow

At high liquid flow rate where the gas void fraction 𝛼 > 0.25, the turbulence causes bubbles to breakup and prevent agglomeration Taitel at al proposed a transition mechanism from dispersed bubble flow for upward vertical flow and recently modified by Barnea [4] to account for inclination angle The dispersed bubble flow can exist provided by one

of two below conditions:

1) The first transition mechanism from dispersed bubble flow was proposed by Taitel et al The flow pattern only exists when turbulent forces are strong enough to overcome the interfacial tension that disperse the gas phase into small bubbles This condition satisfies when the pipeline diameter is smaller than the maximum stable diameter:

1 2

(2-81) and 𝑑𝐶𝐵 is the critical bubble size which migration of bubbles to the upper part of the pipe is prevented

2) However, the transition boundary describe above is valid for 0 ≤ 𝛼 ≤ 0.52 At a high gas flow rate, the boundary

is terminated by another mechanism called the maximum volumetric packing coalescence occurs even at high turbulent levels The transition curve that characterizes this condition is

where the void fraction 𝛼 = 0.52

Transition from Stratified Flow

Determining the stability of the stratified flow pattern requires the calculation of liquid height ℎ𝐿 which can be obtained from momentum balance equations for the gas and liquid phases These calculations are expressed in the

Appendix B in terms of the dimensionless liquid height ℎ𝐿= ℎ𝐿/𝐷

Barnea [5] noted that any changes in the angle of inclination could have a major effect on the stratified or stratified flow regimes For slight-upward inclination, the stratified flow shrinks substantially and practically disappears

non-at intermedinon-ate angles of inclinnon-ation The downward inclinnon-ation of angles also has a significant effect on the strnon-atified flow regime which will expands considerably as the angle of inclination increases

At downward inclination angles (𝜃 ≤ 0), if the stratified liquid level ℎ𝐿 is small and the liquid velocity 𝑣𝐿 is very high, it will generate wavy turbulent interface and be deposited on the upper wall, resulting in an annular film The condition for this type of annular flows is described as below expression:

Transition from Churn flow

The churn-flow pattern is created when the gas in the Taylor bubble starts to penetrate into the liquid slug or the liquid in the liquid slug start to dominate the Taylor bubble region if the gas flow rate is increased to a critical value in the slug flow

Tengesdal et al.[28] presented a new transition criterion approaching for vertical and inclined pipeline which is called the “global” void fraction based on a drift flux concept and can be expressed by the following equations:

Tengesdal and Kaya [27] proposed the void fraction of about 0.78 in the Taylor bubble Substitute 𝛼 = 0.78 into Equation (2-93) and solving for 𝑣𝑆𝑔:

The Taylor bubble rise velocity 𝑣𝑠 is given by Bendiksen [7] for the inclination of angle

Transition from Annular flow

In annular flow, the gas flows along the center of the pipe and liquid flows as a film around the pipe wall Transition from annular flow to churn flow (or slug flow) will occur when this structure is collapsed by blocking of gas core by liquid lumps The blockage of the gas core may result from two mechanism:

1) The annular flow cannot keep the stable configuration due to the accumulation of liquid at low liquid flow rates Instability of the film occurs when

where 𝑌𝑀 and 𝑋𝑀 are the modified Lockhart-Martinelli [15] parameters, 𝐻𝐿𝐹 is the fraction of the pipe cross section that

is occupied by liquid film and is expresses in term of minimum dimensionless thickness, 𝛿 = 𝛿/𝑑, as

and the entrainment fraction 𝐹𝐸 were introduced by Wallis [19]

2) At high liquid flow rates, the liquid film becomes large enough to cause spontaneous blockage and bridge the gas core The mechanism criterion shown in Equation (2-101) is based on the minimum liquid holdup to form a liquid slug proposed by Ansari et al [3]

where 𝜆𝐿𝐶 is the no-slip liquid holdup caused by the entrained liquid in the gas core with respect to core cross section

Figure 2-6 Workflow of flow regime prediction

Begin Mechanistic Model

SLUG FLOW

BUBBLE FLOW YES

2.2.4.2 Pressure-gradient Prediction

Bubble Flow Model

The calculation of the liquid volume fraction in dispersed bubble flow is describe by the following procedure Assuming that a turbulent velocity profile for the mixture with rising bubbles concentrated more at the center than pipe wall, then the slip velocity can be expressed as

Figure 2-7 Physical model for bubble flow [11]

Dispersed-Bubble-Flow Model

Because there is a uniform distribution of gas bubbles in the liquid, dispersed-bubble flow can be treated as a homogeneous flow The pressure drop is estimated by treating the two phases as a single phase due to the absence of any slippage between the phases By using this simplification

All dimensionless variables depend only on ℎ𝐿 which are described through Equations (2-132) - (2-136) are explained clearly at Appendix B

Since the slug flow is one of the most complex flow patterns as its unsteady characteristics, Petalas recommends a model which assumes a uniform liquid level in the Taylor bubble zone A schematic of a typical unit cell under slug flow is shown in Figure 2-9

From an overall mass balance for the gas phase in a slug unit, the superficial velocity of gas can be expressed as

and

where 𝛽 is the ratio of the length occupied by the Taylor bubble 𝐿𝑇𝐵 to the entire length of the slug unit 𝐿𝑆𝑈

where 𝑑 is expressed in 𝑖𝑛𝑐ℎ and 𝐿𝐿𝑆 is in 𝑓𝑡

The mass balance for the gas phase relative to the Taylor bubble translational velocity to the liquid slug is as follow:

Under certain downflow condition, value of 𝑣𝑔𝐿𝑆 becomes negative In these situations, 𝑣𝑔𝐿𝑆 is set to zero (𝑣𝑔𝐿𝑆 = 0) The void fraction in the liquid slug 𝐻𝑔𝐿𝑆 is given as

1 2

The derivative of Equation (2-163) with respect to 𝐻𝑔𝑇𝐵 yields