The use of Prosper in studying the Production Optimization of an Oil Well

TABLE OF CONTENTS

DEDICATIONIII

LIST OF TABLES

LIST OF FIGURES

ACKNOWLEDGEMEENT

ABSTRACT

NOMENCLATURE

CHAPTER ONE
1.0 GENERAL INTRODUCTION
1.1 SCOPE OF STUDY
1.2 OBJECTIVE OF STUDY
1.3 MODALITIES OF STUDY
1.4 RESTRICTION(S) OF STUDIES

CHAPTER TWO
2.0 NODAL ANALYSIS
2.1 NODAL ANALYSIS THEORY AND CONCEPT
2.2 INFLOW PERFORMANCE OF A WELL
2.2.1 DARCY’S EQUATION
2.2.2 PRODUCTIVITY INDEX (PI)
2.2.3 IPR CURVE
2.2.4 IPR IN SINGLE PHASE FLOW
2.2.5 IPR IN TWO PHASE FLOW
2.2.6 VOGEL’S EQUATION
2.2.7 FETKOVICH AND MULTIRATE FETKOVICH
2.2.8 JONES AND MULTI-RATE JONES
2.2.9 TRANSIENT
2.3 TUBING PERFORMANCE OF A WELL
2.4 CHOKE PERFORMANCE
2.5 GRADIENT CURVES
2.5.1 LIQUID FLOW RATE
2.5.2 GAS TO LIQUID RATIO (GLR)
2.6 OPERATING POINT
2.6.1 FAVOURABLE GLR
2.6.2 WATER CUT
2.7 MULTIPHASE FLOW
2.8 OVERVIEW OF THE GAS LIFT SYSTEM
2.8.1 FORMS OF GAS LIFT SYSTEMS
2.9 INJECTION GAS PRESSURE REQUIREMENT
2.9.1 GAS LIFT VOLUME REQUIREMENT

CHAPTER THREE
3.0 HISTORY OF WELL J-12T
3.1 METHODOLOGY
3.1.1 PROSPER’S SETUP FOR SENSITIVITY ANALYSIS
3.1.2 WORKING PROCEDURE FOR WELL MODEL SET-UP
3.1.3 OPTIONS SUMMERY
3.2 PVT DATA
3.2.1 PVT MATCHING PROCEDURES
3.2.2 REGRESSION
3.2.3 PARAMETERS
3.3 EQUIPMENT DATA
3.3.1 DEVIATION SURVEY
3.3.2 SURFACE EQUIPMENT
3.3.3 DOWNHOLE EQUIPMENT
3.3.4 GEOTHERMAL GRADIENT
3.3.5 AVERAGE HEAT CAPACITIES
3.4 GAS LIFT DATA
3.5 IPR DATA
3.6 MATCHING OF THE IPR MODEL
3.6.1 VLP MATCHING
3.6.2 IPR MATCHING

CHAPTER FOUR
4.0 INTERPRETATION AND DISCUSSION OF SENSITIVITY ANALYSIS
4.1 SIMULATE BASE CASE FORECAST
4.2 EVALUATION OF VARIOUS OPTIMIZATION PLANS
4.3 SHORT TERM OPTIMIZATION OF WELL J-12T
4.3.1 SENSITIVITY ON TUBING HEAD PRESSURE
4.3.2 SENSITIVITY ON TUBING SIZE
4.4 LONG TERM OPTIMIZATION OF WELL J-12T
4.4.1 GAS LIFT DESIGN
4.4.2 MODELLING WELL J-12T WITH GAS LIFT
4.5 OPTIMUM GAS INJECTION RATE
4.5.1POSITIONING OF VALVES
4.5.2 RESULTS FROM GAS LIFT DESIGN FOR WELL J-12T
4.6 SENSITIVITES ON GASLIFT INJECTION RATES
4.7 OIL PRODUCTION FORECAST FOR WELL J-12T GASLIFT
4.8 ECONOMIC EVALUATION
4.9 OPTIMIZATION RESULTS FOR WELL J-12T GASLIFT

CHAPTER FIVE
5.0 CONCLUSION AND RECOMMENDATIONS

REFERENCE

APPENDIX
APPENDIX 1
APPENDIX 2
APPENDIX 3

DEDICATION

This project is dedicated to the Almighty God whose gift of life, love, favor, strength, wisdom and grace saw me throughout my stay for this Five years programme.

LIST OF TABLES

Table 3.1: Options summery data entry

Table 3.2: PVT data entry.

Table 3.3: Flash data entry.

Table 3.5: Geothermal gradient data entry

Table 3.4: Downhole equipments data entry

Table 3.6: Composite IPR model data entry

Table 3.7: gravel pack parameter entry

Table 3.8: Last well test data for well J-12T

Table 4.1: Showing base case parameters

Table 4.2: Showing base case forecast results

Table 4.3: Parameters for tubing head pressure sensitivity.

Table 4.4: Showing tubing head sensitivity results

Table 4.5: Parameters for tubing head pressure sensitivity.

Table 4.6: Showing tubing head sensitivity results

Table 4.7: Continuous gas lifts data entry

Table 4.8: Showing result from gas lift design

Table 4.9: Showing results of sensitivity on gas lift injection rates

Table 4.10: Showing parameter for forecast

Table 4.11: Showing forecast results for declining reservoir pressure on gas lifted well

Table 4.12: Showing the maximum economical water cut for well J-12T

Table 4.13: showing the optimization results

Table 4.14: Summary of optimization result for well J-12T

Table 4.15: comparison of actual and optimized results

LIST OF FIGURES

Figure 2.1: Showing the location of various pressure nodes on a well.

Figure 2.2: Determination of flow capacity

Figure 2.3: IPR Curve for Single Phase (Liquid) Flow

Figure 2.4: Phase Diagram for Two Phase Flow

Figure 2.5: IPR Curve for Two Phase Flow

Figure 2.6: Results of well testing and Simulation runs plotted in dimensionless form

Figure 2.7: System performance for various tubing size

Figure 2.8: System performance for various wellhead chokes

Figure 2.9: Effect of Increased Liquid Rate on Gradient Curves

Figure 2.10: Effect of GLR on Gradient Curves

Figure 2.11: Flowing BHP as a function of GLR for different flow rates and the same WHP

Figure 2.12: Operating point

Figure 2.13: Favorable GLR and corresponding liquid production rate with VLP Curve

Figure 2.14: Effect of Water cut on Gradient Curves

Figure 2.15: Flow regimes in horizontal flow

Figure 2.16: Flow regimes in vertical flow

Figure 2.17: General Gas lift system

Figure 2.18: Continuous and Intermittent lift

Figure 2.19: Injection pressure kick-off requirements - well dead.

Figure 2.20: The function of gas Lift valves and mandrels.

Figure 2.21: Estimating optimum gas lift rate

Figure 2.22: Gas lift well performance curve.

Figure 3.1: Production profile for well J-12T

Figure 3.2: Flow chart of system analysis using prosper

Figure 3.3: Menus and Options in Prosper Main Screen

Figure 3.4: PVT is matched

Figure 3.5: Deviation survey data for well J-12T. The well path is plotted to the right.

Figure 3.6: Down hole equipment data for well J-12T.Drawn by PROSPER on the right.

Figure 3.7: IPR plot for well J-12T

Figure 3.8: Well J-12T Correlation comparisons

Figure 3.9: Besting Tubing correlation comparison for well J-12T

Figure 3.10: Production point (VLP/IPR intersections) of well J-12T in 11/27/2005

Figure 4.1: Graphical representation of results for forecast

Figure 4.2: Graphical representation of results for THP sensitivity

Figure 4.3: Graphical representation of results showing the sensitivity on various tubing sizes at the current water cut of 50% of well J-12T

Figure 4.4: Gas lift design menu.

Figure 4.5: Gas lift performance curve for well J-12T

Figure 4.6: Valve spacing design for well J-12T

Figure 4.7: IPR vs. VLP plot for optimized gas lift well J-12T

ACKNOWLEDGEMENT

I would like to express my sincere gratitude to my supervisor Dr K.I. Idigbe for the fatherly role he played to make this work a success. I am also grateful to Mr. D.O Onaiwu who introduced me to the PROSPER software, Mr. Ala and Mr. Dolor of (Department of Petroleum Resources) DPR for their academic support during the period of this work.

I would not forget to show appreciation to my friends and colleagues amongst whom are Adebayo Otadotun, Okoh Victor Ugochukukwu, Uzezi Orivri, Obaseki Ebarumeifo, Claraphina Dudun , Emeka Amaechi and others so many to mention for their love, care, prayers and support which cannot be quantified.Also to appreciate is the Evangelical fellowship in the Anglican Communion (EFAC) for their prayers, encouragement and assistance.

Finally, I am highly indebted to my parents Mr. and Mrs. Dudun and my siblings Ama, Ayo, Glory, and Felicia for their undying love, continual prayers, financial support and care.

ABSTRACT

Crude oil production is a major requirement to sustaining the well begins of any petroleum company. This will entail the effective placement of all facilities and equipment; surface or subsurface in order to achieve optimum volume of crude oil production, this is usually called production optimization.

In this study, the software prosper was utilized to case study well J-12T. Well J-12T, a natural producer was producing at its peak oil rate at 6137 STB/d at 0% water-cut by mid-1973 but since then production has been on the decline due to increasing water-cut and decreasing reservoir pressure. But to date, the well is producing at an oil rate of 1431 STB/d at a water-cut of 50%.The VLP/IPR data were matched to well test flow rate measurement with a deviation of about 0.0534%, thereafter a short and long term optimization plan scenarios such as sensitivity runs on the well head pressure, tubing sizes, and gas lift technique respectively etc for the well, were simulated in PROSPER and then evaluated.

The results of this work suggests that; by lowering the Christmas tree pressure from 180 to 120psi the well’s life can be extended to 70% water-cut, also increasing the tubing size from 2.992" to 3.958" ID is also recommended. The gas lift method was found to be more economical as it can produce up to a maximum economic water cut of 90% with optimum gas injection rate of 3.3MMscf/d and oil production rates will increased from 1431 STB/d to about 3000 STB/d at 50% water-cut.

NOMENCLATURE

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CHAPTER ONE

1.0 GENERAL INTRODUCTION

Petroleum production involves two distinct but intimately connected general systems; the reservoir, which is a porous medium with unique storage and flow characteristics and the surface gathering separation and storage facilities. During their transportation from the reservoir to the surface, these fluids require energy to overcome friction losses and to lift products to the surface. The production system in use in an oil or gas field consists of several components where pressure losses may occur, thus affecting the well performance in terms of production rate.

In order to optimize production performance and determine the exact effect of each component on the production rate, it is important to analyze the entire production system from the reservoir to the surface network; hence this process of analysis is called nodal analysis or system analysis. Oil and gas production optimization ensures that wells and facilities are operating at their peak performance at all times to maximize production. Too often, production engineers face problems due to ill-sized tubing or ill-sized chokes when the selection of the values of those parameters that will best fit their field properties and production demand, is incorrect. It includes a good understanding about production systems and reservoir fluid. It is therefore imperative to select the best values for parameters such as the tubing size, the wellhead pressure, and the choke size and the surface flow-line diameter.

Nodal analysis is the application of systems analysis to the complete well system from the outer boundary of the reservoir to the sand face, across the perforations and completion section to the tubing intake, up the tubing string including any restrictions and down hole safety valves, the surface choke, the flow line and separator. It uses a combination of; well inflow performance, well outflow performance or down hole multipurpose flow conduit performance, surface performance (including choke, horizontal or inclined flow performance and separator).

The nodal analysis procedure can be applied to both flowing and artificial lift wells if the effect of the artificial lift method on the pressure can be expressed as a function of flow rate. The procedure can also be applied to the analysis of injection well performance by appropriate modification of the inflow and outflow expressions. A partial list of possible applications is given as follows:

1. Selection tubing size and flow line size.
2. Gravel pack design.
3. Surface choke sizing.
4. Subsurface safety valve sizing.
5. Artificial lift design.
6. Allocating injection gas among gas lift wells.
7. Determining the effect of compression gas well performance.
8. Predicting the effect of compression on gas well performance.etc.

1.1 SCOPE OF STUDY

This study was conducted on a single string natural producer well (well J-12T) located in the XX-field in the Niger delta. The nodal analysis of the well through the aid of a PRO duction and S ystem PER formance analysis software (PROSPER) was carried out on the well’s subsurface i.e. From the pressure node at the reservoir to the pressure node at the bottom (sand face) of the well (assumed solution node) up to the pressure node at the subsurface safety valve (SSSV) and finally to the pressure node at the well head. Once the solution node is selected, the pressure drops or gains from the starting point are added until the solution node is reached.

On the contrary, there are other methods of production optimization tools but are not accounted for in the course of this study. Moreover, it should be noted that there is nothing inherent in PROSPER that makes feasible all the time; rather its reliability is a direct function of the available data and the competence and integrity of the analyzer (production Engineer).

1.2 OBJECTIVE OF STUDY

Oil reserves are depleting everyday and oil prices are peaking, thus the role of production optimization cannot be neglected. Hence the objective of this project work is;

1. To optimize the well J-12T performance in order to maximize the production rate using the nodal analysis tool: PROSPER software.
2. To carry out a short term optimization plan to optimize well J-12T oil production, by doing sensitivity runs on the well head pressure, chokes sizes, tubing sizes.
3. To carry out a long term optimization plan to optimize well J-12T oil production, through the use of gas lift technique.
4. Finding out the optimum gas injection rate for well J-12T, to achieve the maximum oil production.
5. Evaluation of economical water cut for selected optimization technique.

1.3 MODALITIES OF STUDY

Chapter 1 highlighted a brief introduction of the production systems and production optimization using nodal analysis. The Objectives, scope of study, and limitations to the studies were highlighted.

Chapter 2 discusses relevant literature such as: the nodal analysis concept, reservoir and inflow performance, well productivity, multiphase flow correlations and finally concluded with an overview of the gas lift system

Chapter 3 discusses the history of the case study well, and the methodology used in obtaining the IPR/VLP of the case study well, and sensitivity run calculations on the well.

Chapter 4 discusses and interpretes the sensitivity analysis results for well J-12T.

Finally, Chapter 5 concludes the studies and gives further recommendations necessary for the optimization of the well.

1.4 RESTRICTION(S) OF STUDIES

1) Lack of complete field data to do a full scale optimization on the well, from the well subsurface up to the storage tank of the processing facilities.
2) Inability to give a real time optimization result due to non availability of a dynamic reservoir simulation software like the eclipse (schlumberger) software at the time of conducting this studies. For example, one could estimate the rate of oil production at a particular water cut and at a given reservoir pressure using the prosper software, but can’t actually tell the time frame at which that oil production rate will be sustainable.
3) Non availability of data to give a full scale economic analysis for both the short and long term optimization plan of the well, so as to know the profitability of the plan.

CHAPTER TWO LITERATURE REVIEW

2.0 THE NODAL ANALYSIS (SYSTEM ANALYSIS)

Traditionally and conventionally, the hydrocarbon industry has employed the simulation tool of the NODAL production systems analysis, originally developed by Schlumberger, to address the optimization of production systems design and per evolved into such a common adoption over the years, close to a household name within the industry, to the extent that the approach is referred to simply as ‘nodal analysis’ nowadays (Beggs, 1991). Dating back to (Gilbert) as early as 1954 that propose the use of this technique (Nind 1964), (Brown and Lea, 1985), nodal analysis generally refers to the systems approach for the optimization of the production operations of oil and gas wells via a thorough evaluation of the complete well production system. It involves employing correlations to predict multiphase flow behavior through pipes, well completions, restrictions and the reservoir in order to analyze the flow behavior in the entire production (Brill, 1987). This is accomplished by repetitively varying the associated optimization variables to simulate the underlying system.

Ultimately, nodal analysis determines the daily operating policy by forecasting the performance of the various elements that make up a completion and production system. This is executed with the objective of optimizing the completion design to suit the reservoir deliverability, to identify restrictions or limitations present in the production system and subsequently, to determine any means of improving the production efficiency (Schlumberger Oilfield Glossary, 2006). However, Kosmidis et al. (2004) point out that nodal analysis is limited only to oilfields with a small number of wells due to its trial-and-error nature.

In nodal analyses, all components beginning with the static reservoir pressure, and ending with the separator were analyzed. Important completion parameters can be entered, and varied, to enable the assessment of their contribution to the overall performance of the completion system. Selection of correct tubing size is important for maintaining an economical flow rate for the desired production period. Several correlations for tubing performance are in use in the petroleum industry. Brown, in a widely used work, outlined the procedure for pressure drop calculations in production strings. The choke was designed to control the production rate from a well. Sachdeva modeled the wellhead choke as a pipe restriction. This model is capable of modeling critical and subcritical flow. Wellhead choke is usually selected so that the fluctuations in the line pressure downstream of the choke have no effect on the well flow rate. Whenever two fluids with different physical properties flow simultaneously in a pipe, there is a wide range of possible flow patterns. Many investigators such as Mukherjee and Brill have attempted to predict the flow pattern that will exist for various flow conditions. This is particularly important as the liquid holdup is found to be dependent on the flow pattern.

2.1 NODAL ANALYSIS THEORY AND CONCEPT

The Nodal analysis concept consists of selecting a division point or node in the well and dividing the system at that point. All of the components upstream of the node comprise the inflow section, while the out flow section consists of all of the components downstream of the node. A relationship between flowrate and pressure drop must be available for each component in the system. The flowrate through the system can be determined once the following requirements are satisfied:

1. Flow into the node equals flow out of the node.
2. Only one pressure can exist at a node.

At a particular time in the life of the well, there are always two pressures that remains fixed and are not functions of flow rate. One of these pressures is the average reservoir pressure and the other is the system outlet pressure. The outlet pressure is usually the separator pressure if the well is controlled by a surface choke the fixed outlet pressure may be the wellhead pressure . Once the node is selected; the node pressure is calculated from both directions starting at the fixed pressures.

Inflow to the node:

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Outlet from the node:

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The pressure drop , in any component, varies with flow rate, q. Therefore a plot of node pressure versus flow rate will produce two curves, the intersection of which will give the conditions satisfying requirements 1and 2, given previously. The procedure is illustrated graphically in Fig 2.2.The effect of a change in any of the components can be analyzed by recalculating the node pressure versus flow rate using the new characteristics of the component that was changed, if a change was made in an upstream component. The outflow curve will remain unchanged. However, if either curve is changed, the intersection will be shifted and a new flow capacity and node pressure will exist. The Curve will also be shifted if either of the fixed pressures is changed, which may occur with depletion or a change in separation conditions.

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Fig 2.1: showing the location of various pressure node on a well

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Fig 2.2: determination of flow capacity

Finally, repeat this same procedure for each component that is to be optimized.

For production optimization and gas lift allocation of different wells, it is truly necessary to have conceptions of well hydraulics and inflow and outflow performances of wells. In the following sections, relevant theories and concepts have been outlined on which basis the project work had been performed.

2.2 INFLOW PERFORMANCE OF A WELL

The ability of a well to lift up fluid represents its inflow performance. Inflow performance of a well with the flowing well pressure above the bubble point pressure can be expressed by Darcy’s equation for a single well located in the centre of a drainage area, produces at steady state condition.

2.2.1 Darcy’s equation

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2.2.2 Productivity Index (PI) PI is one of the important characteristics of a well’s inflow performance. It depends on the reservoir and fluid properties. From Equation, we find;

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If the PI is known, evaluation of the expected inflow rate under specified flowing well pressure is straightforward:

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2.2.3 IPR Curve

The relation between the production rate and the drawdown pressure is called Inflow Performance Ratio or IPR curve. Production rates at various drawdown pressures are used to construct the IPR curve. It reflects the ability of the reservoir to deliver fluid to the well bore.

2.2.4 IPR in Single Phase Flow

In case of a single phase flow, the relation between the production rate and the pressure drop is a straight line. As follows from the figure, slope of the IPR is inversely proportional to the PI value; i.e. Slope = = constant

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Figure 2.3: IPR Curve for Single Phase (Liquid) Flow

Equations (2.3) and (2.4) cannot be used if the flowing well pressures is below the bubble point pressure . At this condition ( ), the IPR is no longer a straight line. It has been illustrated in Phase diagram (figure6) which states that at such bottom hole conditions, a two phase flow occurs in a reservoir where both oil and gas flow together towards the well. This type of flow is called solution gas drive.

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Figure 2.4: Phase Diagram for Two Phase Flow

2.2.5 IPR in Two Phase Flow

A two phase flow has effect on the IPR curve. It deviates from a straight line resulting in reduced values of the productivity index corresponding to reduced values of the flowing well pressure.

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Figure 2.5: IPR Curve for Two Phase Flow

2.2.6 Vogel’s Equation

There are many models for predicting the well’s inflow performance. One of the methods of predicting well’s inflow performance under a solution gas drive (two phase flow) conditions (e.g. ) was developed by Vogel. In 1968, Vogel suggested the following equation for IPR for the solution gas drive conditions;

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Here = Average reservoir pressure or bubble point pressure, whichever is lower.

However a similar expression for Vogel’s back-pressure equation was suggested by Fetkovich in 1973:

It is important that Vogel’s equation gives the best fit for the results of well testing and simulation runs. Plotting these results on dimensionless form gives almost the same curve in all cases, as illustrated in figure 2.6:

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Figure 2.6: Results of Well Testing and Simulation Runs Plotted in Dimensionless Form

2.2.7 Fetkovich and Multirate Fetkovich

The Fetkovich equation for oil is a modified form of the Darcy equation, which allows for two phase flow below the bubble point .the equation, can be expressed as:

The skin can be entered either by hand or calculated using Locke’s, Macleod’s or the Karakas and Tariq method.

While, the Multi rate Fetkovich method uses a non-linear regression to fit the Fetkovich model for up to 10 points. The model is expressed as:

The fit value of C and n are posted on the IPR plot.

2.2.8 Jones and Multi-rate Jones

The Jones equation for oil is a modified form of the Darcy equation, which allows for both Darcy and non Darcy pressure drops. Jones equation can be expressed in the form:

Where “a” and “b” are calculated from reservoir properties or can be determined from a multi-rate test. The same data as for the Darcy model plus the perforated interval is required. Skin can be directly entered or calculated using the available methods.

While the multi-rate jones method uses anon-linear regression to fit up to 10 test point for the Jones model.

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2.2.9 Transient

This IPR method takes into account the change of deliverability with time. The method can be particularly important for tight reservoirs. Both the Darcy and Jones equations assume that the will has reached pseudo-steady state flow conditions. In tight reservoirs, the transient equation can be used to determine the inflow performance as a function of flowing time. Once the flowing time is long enough for pseudo-steady state flow to develop within the drainage radius, the Darcy inflow model is then used.

The transient IPR equation is:

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2.3 TUBING PERFORMANCE OF A WELL

An increase in production rate can be achieved by increased tubing size. However if the tubing is too large, the velocity of the fluid moving up the tubing may be too low to efficiently lift the liquid to the surface .this could be caused by either large tubing or low production rate. A quantitative example of selecting the optimum tubing size for a well that is producing both gas and liquid is show in the figure below

Analysis of a Tubing performance or vertical lift performance (VLP) of a well is an important part of the well design. It allows selecting the well completion correctly corresponding to lifting methods and to evaluate well’s performance.

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FIG 2.7

2.4 CHOKE PERFORMANCE

Placing a choke at the wellhead can mean fixing the wellhead pressure and thus flowing bottom hole pressure and production rate It can be shown theoretically, assuming a knife edge choke and making several simplifying assumption with regards to the pressure –volume characteristics of the oil and gas , that from Gilbert (1954) empirical formula,

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Where,

= tubing head pressure,psia. R=gas/liquid ratio, mcf/bbl. q =gross liquid rate bbl/day. S= bean size 1/64 in.

This equation is derived using regularly reported daily individual well production data from Ten Section Field in California. In the type of formula used, it is assumed that actual mixture velocities through the bean exceed the speed of sound, for which condition the downstream, or flow line, pressure has no effect upon the tubing pressure. Thus, the equation applies for tubing head pressure of at least 70% greater than the flow line pressure.

A reduction in the choke size causes an increased back pressure on the tubing, which causes a decreased flow rate through the tubing.

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Fig 2.8: system performance for various wellhead chokes

2.5 GRADIENT CURVES

The pressure gradient in a pipe line or well bore is the summation of following components:

- Hydrostatic head
- Friction head

Thus the total pressure gradient can be written as:

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The hydrostatic component is due to the density of fluid mixture at each point in the system and is a complex function of the relative velocity of the present phases. The gravity head loss is proportional to the fluid density corrected for slip. The slip correction to be applied depends on the flow regime and fluid viscosity.

Friction component is controlled by fluid viscosity and geometric factors such as pipe diameter and roughness. In the majority of the oil field application, the gravitational component s normally accounts for around 90% of the overall head loss. Therefore the total pressure drop function is not particularly sensitive to the value of friction loss coefficient.

Pressure gradients associated with these both terms can be written as:

Hydrostatic force:[Abbildung in dieser Leseprobe nicht enthalten]

Frictional force:[Abbildung in dieser Leseprobe nicht enthalten]

The type of flow is determined from the Reynolds number:

Re = [Abbildung in dieser Leseprobe nicht enthalten]

Where: μ = fluid viscosity

The boundary between flow regimes are:

Re ≤ 2000: Laminar flow

2000 < Re ≤ 4000: Transition between laminar and turbulent flow

4000 < Re: Turbulent flow

For laminar flow f = 64/Re (Moody friction factor). However, finding the friction factor is more complicated for turbulent flow, and there are several ways to calculate the friction factor.

2.5.1 Liquid flow rate

As follows from equation (16), increased liquid rate (higher values of velocity um) results in friction losses increase. Rearranging equation [15],

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We find from equation [17], hydrostatic pressure also increases with the increased liquid production. This effect has been illustrated by the following figure.

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Figure 2.9: Effect of Increased Liquid Rate on Gradient Curves

2.5.2 Gas to liquid ratio (GLR)

Rearranging equation [17] we find,

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Equation [18] shows that increased in gas to liquid ratio results in reduction of the pressure gradient. It mostly affects the hydrostatic component. Increase in GLR while keeping a constant liquid rate ql, reduces the hydrostatic component resulting in the reduced bottomhole pressure to a certain degree. On the other hand, increased GLR increases friction forces and has a counter effect on the bottom hole pressure. When contribution of the friction forces higher than that of hydrostatic forces, the actual bottom hole pressure ( ) begins to grow. This effect has been illustrated by the following figure.

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Figure 2.10: Effect of GLR on Gradient Curves

Combining figure 2.9 and 2.10 and expressing the flowing BHP as a function of GLR for different liquid rates, we obtain the following figure.

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Figure 2.11: Flowing BHP as a function of GLR for different flow rates and the same WHP

2.6 Operating Point

To calculate the well production rate, the bottom-hole pressure that simultaneously satisfies both the IPR and VLP relations is required. By plotting the IPR and VLP in the same graph the producing rate can be found. The system can be described by an energy balance expression, simply the principle of conservation of energy over an incremental length element of tubing. The energy entering the system by the flowing fluid must equal the energy leaving the system plus the energy exchanged between the fluid and its surroundings.

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Figure 2.12: Operating point

Combining the tubing performance curve with a curve reflecting the inflow performance identifies the operating point. Optimum liquid production is achieved in this point.

2.6.1 Favourable GLR

Re-plotting the figure 2.10 in addition to VLP/IPR curve, the crossing point of these two curves gives a value of the maximum possible liquid rate as illustrated in following figure.

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Figure 2.13: Favorable GLR and Corresponding Liquid Production Rate with VLP Curve

2.6.2 Water Cut

Effect of water cut on gradient curve is expressed by the following equations

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Here, is water cut. It is follows from equation [19] that increased water cut results in increased water density which in its turn, increases hydrostatic forces. As a result, pressure gradient and bottom hole pressure increases, as illustrated in the following figure.

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Figure 2.14: Effect of Water cut on Gradient Curves

2.7 MULTIPHASE FLOW

Oil wells normally produce a mixture of fluids and gases to the surface while phase conditions usually change along the path. At higher pressures, especially at the well bottom, flow may be single phase. But going up in the well the continuous decrease of pressure causes dissolved gas to gradually escape from the flowing liquid, resulting in multiphase flow. Gas injection into a well is also an example of multiphase flow.

In single phase flow we discriminate between laminar and turbulent flow. In two-phase flow we discriminate in addition between flow regimes that are characteristic for the time and space distribution of gas and liquid flow. In horizontal flow we discriminate between the flow regimes

- Stratified flow
- Slug flow
- Dispersed bubble flow
- Annular flow

These are shown in figure 2.15. At low velocities the gas and liquid are separated as in stratified flow. At high velocities gas and liquid become mixed. Slug flow is an example of a flow regime in between, representing both separation and mixing. Slug flow is consequently referred to as an intermittent flow regime.

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Figure 2.15: Flow regimes in horizontal flow

In vertical flow we discriminate between the flow regimes

- Slug flow
- Churn flow
- Dispersed bubble flow
- Annular flow

Figure 2.16 illustrates the flow regimes in vertical flow. The same comments that apply to horizontal flow are valid in vertical flow. The big difference is that in vertical (concurrent upward) flow it is not possible to obtain stratified flow. The equivalent flow regime at identical flow rates of gas and liquid is slug flow with very slow bullet shaped Taylor bubbles.

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Figure 2.16: Flow regimes in vertical flow

The superficial velocities are defined by:

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They are also referred to as apparent velocities or volumetric fluxes. From the definition we see that the volumetric flowrates and the pipe cross section A is known, from the superficial velocities follow directly. The phase velocities are the real velocities of the flowing phases. They may be defined locally (at a certain position in the pipe cross section) or as a cross sectional average for the pipe. They are defined by:

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Gas and liquid in general flow with different phase velocities in pipe flow. The relative phase velocity or the slip velocity is defined by:

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The slip velocity thus has the same unit as the phase velocities. In addition the slip

ratio is commonly used:

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Note that the slip ratio is dimensionless. Slip effect is seen in inclined flow and is caused by the density difference between the gas and liquid, which in turn causes a velocity difference; the gas will rise through the liquid.“Hold up” is a consequence of slip and is defined as the proportion of the pipe that is occupied by liquid.

Multiphase flow correlations are used to predict the liquid holdup and frictional pressure gradient. Correlations in common consider the oil and gas lumped together as one equivalent fluid. They are therefore more correctly termed 2-phase flow correlations. Depending on the particular correlation, flow regimes are identified and specialized holdup and friction gradient calculations are applied for each flow regime.

Some of the correlations most widely accepted for oil wells are:

1) Duns and Ros (1963): it usually performs well in mist flow cases and should be used in high GOR oil and condensate wells. It tends to over-predict VLP in oil wells. Despite this, the minimum stable rate indicated by the minimum of the VLP curve is often a good estimate.
2) Hagedorn and Brown (1963): it performs well in oil wells for slug flow at moderate to high production rates (well loading is poorly predicted). Hagedorn Brown should not be used for condensates and whenever mist flow is the main flow regime. It under predicts VLP at low rates and should not be used for predicting minimum stable rates.
3) Orkiszewski (1967): its correlation often gives a good match to measured data. However, its formulation includes a discontinuity in its calculation method. The discontinuity can cause instability during the pressure matching process, therefore we do not encourage its use.
4) Beggs and Brill (1973): it is primarily a pipeline correlation. It generally over-predicts pressure drops in vertical and deviated wells.
5) Fancher Brown (1963): it is a no-slip hold-up correlation that is provided for use as a quality control. It gives the lowest possible value of VLP since it neglects gas/liquid slip it should always predict a pressure which is less than the measured value. Even if it gives a good match to measured downhole pressures, Fancher Brown should not be used for quantitative work. Measured data falling to the left of Fancher Brown on the correlation comparison plot indicates a problem with fluid density (i.e. PVT) or field pressure data.

2.8 OVERVIEW OF THE GAS LIFT SYSTEM

The need of artificial lift is required when the pressure of well is not enough as to maintain the oil production with satisfactory economic return, thus the gas lift system is one form of artificial lift. Gas lift is a method of lifting fluid where relatively high pressure gas is used as the lifting medium through a mechanical process. In a typical gas lift system, compressed gas is injected through gas lift mandrels and valves into the production string. The injected gas lowers the hydrostatic pressure in the production string to re-establish the required pressure differential between the reservoir and well bore, thus causing the formation fluids to flow to the surface.

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Fig 2.17: General Gas lift system

2.8.1 FORMS OF GAS LIFT SYSTEMS

Basically there are the continuous gas lift and the intermittent gas lift systems.

Continuous gas lift: The continuous injection of relative high pressure gas to reduce the flow gradient.

Intermittent gas lift: Injection of gas below an accumulated liquid slug in a relatively short time period to lift the slug to surface.

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Fig 2.18: Continuous and Intermittent lift

2.9 INJECTION GAS PRESSURE REQUIREMENT

The surface gas injection pressure required at the wellhead to achieve kick-off depends on the pressure profile in the well. The well may be full of kill fluid or dead oil, or it may be flowing at a rate lower than the rate obtainable with gas lift.

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Fig 2.19: Injection pressure kick-off requirements - well dead.

After injection of gas has been established, the flowing bottom hole pressure, and therefore the surface injection pressure required, will decrease until the minimum intake pressure corresponding to the gas lift injection rate is reached.

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