effect of gas-oil-ratio on oil production

EFFECT OF GAS-OIL-RATIO ON OIL PRODUCTION

A

THESIS

Presented to the Faculty

of the African University of Science and Technology

in Partial Fulfilment of the Requirements

for the Degree of

MASTER OF SCIENCE

By

PARKER, Ebenezer Sekyi

Abuja, Nigeria

November, 2010

i

ABSTRACT

Maximum production from an oil well can be achieved through proper selection of tubing size. The

selection of optimum tubing size must be evaluated when completing a well in any type of reservoir

especially solution gas drive reservoir since there is likelihood of producing more gas as the reservoir

pressure declines. The most widely used methods such as Tarner, Muskat and Tracy methods for

predicting the performance of a solution gas drive reservoir were discussed and used to estimate the

behaviour of producing GOR. A comparison was made between the results from each method. System

analysis approach was adopted for this study. The future IPR curves were determined by a

combination of Vogel and Fetkovich correlation. Beggs and Brill multiphase spreadsheet was used to

produce the TPR curves by estimating flowing bottomhole pressure for several tubing size using the

predicted GOR produced and a range of flowrates. The effect of water production was also considered

in this study. The results showed that for IPR5 as GOR increased from 1052 to 1453 scf/stb, oil

production rate for 2 7/8-in increased by 17.6% and 3.3% for a further increase in GOR at 2610

scf/stb. At a GOR of 2610 scf/stb oil production decreased by 3.17% at water-cut of 5% and 9.5% at

water-cut of 25%. All things being equal, the percentage reduction in production reduces as GOR

increases from 2610 to 5635 scf/stb for all the tubing sizes used.

ii

ACKNOWLEDGEMENT

I thank the Almighty God for giving me the strength and ability to complete my master programme

successfully. I would also like to thank the members of my graduate committee for their earnest

contribution, support and time.

I would like to acknowledge the advice, supervision, guidance and financial support of Professor Dulu

Appah throughout my entire work.

I thank the African University of Science and Technology for providing and making available the

necessary facilities which facilitated my research with much less stress.

Finally, I would like to thank my parents, Mr and Mrs Parker and my siblings, Adelaide, Benjamin and

Nancy for their unceasing prayers and encouragement.

iii

TABLE OF CONTENTS

Content Page

ABSTRACT .......................................................................................................................................... i

ACKNOWLEDGEMENT ................................................................................................................... ii

TABLE OF CONTENTS .................................................................................................................... iii

LIST OF FIGURES .............................................................................................................................. v

LIST OF TABLES .............................................................................................................................. vi

CHAPTER 1 ......................................................................................................................................... 1

INTRODUCTION ................................................................................................................................ 1

1.1 Vertical Lift Problems relating to tubing .................................................................................. 2

1.2 Pressure Drop across Production System ...................................................................................... 3

1.3 Inflow Performance Relationship ................................................................................................. 4

1.3.1 Single Phase Inflow Performance ........................................................................................... 5

1.3.2 Two Phase Inflow Performance Relationship ........................................................................ 5

1.3.3 Construction of IPR using Test Points ................................................................................... 6

1.3.4 Future inflow performance relationship for an oil well .......................................................... 7

1.4 Tubing Performance Relationship ................................................................................................. 8

1.5 Behaviour of Produced GOR ........................................................................................................ 8

1.6 Statement of Problem .................................................................................................................. 10

1.7 Objectives .................................................................................................................................... 11

1.8 Methodology ............................................................................................................................... 11

CHAPTER 2 ....................................................................................................................................... 12

LITERATURE REVIEW ................................................................................................................... 12

2.1 Overview of System Analysis Approach .................................................................................... 12

2.2 Applications of System Analysis Approach ............................................................................... 13

iv

2.3 Optimization Approach ............................................................................................................... 15

CHAPTER 3 ....................................................................................................................................... 16

METHODOLOGY ............................................................................................................................. 16

3.1 Prediction of produced GOR ....................................................................................................... 16

3.1.1 Tarner’s method .................................................................................................................... 16

3.1.2 Tracy’s Method..................................................................................................................... 17

3.1.3 Muskat Method ..................................................................................................................... 19

3.2 Future inflow performance relationship (IPR) for an oil well .................................................... 21

3.3 Construction of TPR curves ........................................................................................................ 23

CHAPTER 4 ....................................................................................................................................... 24

RESULTS AND DISCUSSION ........................................................................................................ 24

4.1 Results ......................................................................................................................................... 24

4.2 Discussion ................................................................................................................................... 44

4.2.1 Behaviour of Tubing curves at LGOR ................................................................................. 44

4.2.2 Behaviour of Tubing curves at HGOR ................................................................................. 45

4.2.3 Production profile of the various tubing sizes ...................................................................... 45

4.2.4 Effect of water cut in HGOR condition ................................................................................ 46

CHAPTER 5 ....................................................................................................................................... 47

CONCLUSION AND RECOMMENDATION ................................................................................. 47

5.1 CONCLUSION ........................................................................................................................... 47

5.2 RECOMMENDATION .............................................................................................................. 47

APPENDIX A .................................................................................................................................... 48

APPENDIX B .................................................................................................................................... 49

NOMENCLATURE ........................................................................................................................... 52

REFERENCES ................................................................................................................................... 54

v

LIST OF FIGURES

Page

Figure 1.1 Pressure Losses in a Simple Production System. .................................................................. 3

Figure 2.1 Node flow rate and pressure ................................................................................................. 12

Figure 4.1 Variation of GOR with Pressure using Tracy, Tarner and Muskat Methods. ..................... 25

Figure 4.2 GLR vrs GOR at varying water cut ratios. (Tracy’s method) ............................................. 26

Figure 4.3 GLR vrs GOR at varying water cut ratios. (Tarner’s Method) ........................................... 26

Figure 4.4 GLR vrs GOR at varying water cut ratios. (Muskat’s Method) .......................................... 27

Figure 4.5 Variation of GOR with reservoir pressure........................................................................... 31

Figure 4.6 Future Inflow Performance Relationships Curves .............................................................. 32

Figure 4.7 Effect of tubing size on production rate at a constant GOR (840 scf/stb) ........................... 33

Figure 4.8 Effect of tubing size on production rate at a constant GOR (1052 scf/stb) ......................... 34

Figure 4.9 Effect of tubing size on production rate at a constant GOR (1453 scf/stb) ......................... 35

Figure 4.10 Effect of tubing size on production rate at a constant GOR (2610 scf/stb) ....................... 36



Figure 4.13 Production profile for 2 3/8-in tubing size ........................................................................ 40



Figure 4.16 Production profile for 4-in tubing size .............................................................................. 42

Figure 4.17 Effect of water cut on flowrate at a GOR of 2610 scf/stb ................................................. 42



Figure A.1 Log-log graph of Kro vrs Sg ................................................................................................. 48

Figure A.2 Log-Log graph of Krg vrs Sg ............................................................................................... 48

Figure B.2 Variation of pressure and instantaneous GOR calculated by Tarner’smethod. ................... 49

Figure B.4 Variation of pressure and instantaneous GOR calculated by Muskat method. .................. 51

vi

LIST OF TABLES

Page

Table 4.2a Available PVT Data for predicting oil reservoir performance ........................................... 28

Table 4.2b Data generated from PVT data in table 4.2a ....................................................................... 29

Table 4.2c Continuation of Data generated from PVT data in table 4.2b ............................................ 30

Table 4.3a Operating point for various tubing diameters at a GOR of 840 scf/stb .............................. 33

Table 4.3b Operating point for various tubing diameters at a GOR of 1052 scf/stb ............................ 34

Table 4.3c Operating point for various tubing diameters at a GOR of 1453 scf/stb ............................ 35

Table 4.3d Operating point for various tubing diameters at a GOR of 2610 scf/stb ............................ 36

Table 4.3f Operating point for various tubing diameters at a GOR of 5635 scf/stb ............................. 38

Table 4.4a Variation in production rate and pressure with GOR range of 840-1052 scf/stb ............... 39

Table 4.4b Variation in production rate and Pressure with GOR range of 1052-1453 scf/stb ............. 39

Table 4.4c Variation in production rate and Pressure with GOR range of 1453-2610 scf/stb ............. 39

Table 4.4d Variation in production rate and pressure with GOR range of 2610-3444 scf/stb ............. 39

Table B.1 Data generated from PVT data in table 4.2a using Tarner method ...................................... 49

Table B.3a Data generated from PVT data in table 4.2a using Muskat method ................................... 50

Table B.3b Continuation of data generated from PVT data in table B.3a ............................................ 50

1

CHAPTER 1

INTRODUCTION

Production optimization identifies the opportunities to increase production and reduce operating

costs. The overall goal is to achieve the optimum profitability from the well. To achieve and

maintain this, it is essential to evaluate and monitor different sections of the production system

including, the wellbore sandface, reservoir, produced fluids, production equipment on surface

and downhole. Several methods are being used for production optimization. The most common

and widely used method is the system analysis approach commonly known as nodal analysis.

Optimization of the wellbore is considered mainly during well completion stages. Tubing joints

vary in length from 18 to 35 feet although the average tubing joint is approximately 30 feet.

Tubing is available in a range of outer diameter sizes. The most common sizes are 2 3/8-in, 2

7/8-in, 3 1/2-in and 4 1/2-in. The API defines tubing as pipe from 1-in to 4 1/2-in OD. Larger

diameter tubulars (4 1/2-in to 20-in) are being termed casing. (Schlumberger, 2001)

The flow rate per well is the key parameter. It governs the number of wells that need to be drilled

to achieve the optimum economic output of the field. The first parameter that needs to be

considered in the tubing string selection is the nominal tubing diameter. The grades of steel and

nominal weight are chosen based on the stress the tubing will have to withstand during

production. Thirdly, depending on the how corrosive the existing and future effluents, the type of

connection and the metallurgy are selected. In fact the different stages mentioned above overlap

and sometimes make the choice of tubing a difficult job. In the determination of the nominal pipe

diameter, the nominal diameter through the weight governs the inside through diameter of the

pipe. The flows that can pass through it depend on the acceptable pressure losses but are also

limited by two parameters: the maximum flow rate corresponding to the erosion velocity and the

minimum flow rate necessary to achieve lifting of water or condensate. Tubings with diameter

less than 2 7/8-in are mostly reserved for operations on well using concentric pipe and are termed

macronic string. Note also that the space required by couplings of the tubing limits the nominal

tubing diameter that can be run into the production casing. (Perrin, et al., 1999)

2

1.1 Vertical Lift Problems relating to tubing

In lieu of the usefulness of tubing strings in oil and gas production, it can have some limitations.

Tubing wear occurs most often in pumping wells. It depends little upon whether the hole is

vertical or slanting, but it is much worse in dog-legged holes regardless of the deviation. It may

either be external or internal. If external, it is usually the couplings which are affected and the

cause is the rubbing against the inside of the casing in phase with the reversing strokes of the

sucker rods. If the wear is internal, it is caused by the sucker rods. There can be leakage from the

inside to the outside or vice versa. This can be attributed to the API thread shape used (the V-

shaped or round thread shape.) The tubing string can be flattened from wall to wall by either

having a higher hydrostatic pressure or as a result of diastrophic shifting of formation caused by

an earthquake. Since some 90 percent of all oil-well tubing is upset design, practically all failures

are in the body of the pipe. However, any tension failures are rare because tubing is almost

always run inside of casing and except for occasional trouble of unseating packers; it seldom

becomes stuck and therefore needs not be pulled on. As with upset casing, upset tubing will

stretch before failing. The tubing will burst when the pressure inside the tubing string is higher

than the pressure in that annulus. This tubing trouble is commonly seen in high pressure wells

and can be exceeding serious. (Hexter, 1955)

3

1.2 Pressure Drop across Production System

Figure 1.1 Pressure Losses in a Simple Production System.

Pwfs Pwf

f

1 2

STOCK TANK

Sales Line Gas

4 Pwh Psep

3 2

1

3

4

ΔPT

4

Integrating the production system component helps to design a well completion or predict the

production ratio properly. Since the tubing section in Figure 1.1 contributes to about 80% of the

total pressure drop in the production system, much research should be carried out in that area in

order to reduce the pressure drop. The pressure drops in the tubing section are mainly frictional

pressure drop and hydrostatic pressure drop. The last pressure drop which is due to acceleration

is usually neglected because it is negligible.

The general pressure gradient equation for a vertical well is:

(1.1)

Equation (1.1) can be written as the composite of the three component as

(1.2)

Many correlations have been developed in the last 30 and 40 years for predicting two-phase

flowing pressure gradient in producing wells. Due to the limitations and the availability of some

for these correlations, Beggs and Brill was used for prediction in this study. (Beggs, 2003)

The optimization process requires the knowledge of inflow performance relationship, the tubing

performance relationship and the behaviour of the produced gas-oil-ratio.

1.3 Inflow Performance Relationship

The inflow performance relationship of a well is a relationship between its producing bottomhole

pressure and it corresponding production rates under a given reservoir condition. The

preparations of inflow performance relationship curves for oil and gas wells are extremely

important in production system analysis. Unless some idea of the productive capacity of a well

can be established the design and optimization of the piping system of the well becomes difficult.

5

1.3.1 Single Phase Inflow Performance

In a single phase liquid flow, the pressure is above the bubble point pressure. The inflow

performance relationship is usually depicted by a straight line. The IPR equation for this phase is

given as: (Clegg, 2007)

(1.3)

1.3.2 Two Phase Inflow Performance Relationship

Solution gas escapes from the oil and becomes free gas when the reservoir pressure falls below

the bubble point pressure. During this state of pressure decline, oil and gas (two phase flow)

exists in the whole reservoir. The presence of free gas leads to reduced relative permeability and

increased oil viscosity. The synergies of these two effects result in lower oil production rates.

This makes the IPR curve deviate from linear trend below the bubble point pressure. The two

main widely used empirical correlations for modeling IPR of two phase reservoir are;

Vogel (1968) equation.

(1.4)

The can be theoretically estimated based on the reservoir pressure and productivity index

above the bubble point pressure. (BOYUN, et al., 2007)

The pseudo-steady state flow follows that

(1.5)

Fetkovich equation is written as

(1.6)

6

Where n is an empirical constant related to

1.3.3 Construction of IPR using Test Points

Due the unavailability of reservoir parameters for the determining productivity index in the IPR

model, test points are frequently used for constructing IPR curves. Constructing IPR curves

using test points involves back calculation of the constant in the IPR model for single phase

(under-saturated oil) reservoir. The model constant can be determined by using equation (1.3)

Where is the tested production rate at tested flowing bottomhole pressure

For a partial two-phase reservoir, the model constant in the generalized Vogel equation

(equation 1.4) must be determined on the range of tested flowing bottomhole pressure. If the

range of tested flowing bottomhole pressure is greater than bubble point pressure, the model

constant should be determined by equation (1.3). (Boyun, 2007)

If the tested flowing bottomhole pressure is less than bubble point pressure, the model constant

J* should be determined using

(1.7)

7

1.3.4 Future inflow performance relationship for an oil well

For saturated conditions many approximate methods to simulate the effects of depletion on

productivity index for saturated conditions. Usually those methods provide an equation relating

changes in the productivity index J* as a function of reservoir average pressure.

In essence the methods for future reservoir prediction express changes in J* as a function of

changes in average reservoir pressure. In this study a combination of Fetkovich and Vogel

equations were used to predict the future IPRs. (Prado, 2009)

Fetkovich expressed changes in productivity index as a function of changes in average reservoir

pressure as;

(1.8)

Fetkovich also expressed Absolute Open Flow (AOF) as a function of the average reservoir

pressure.

(1.9)

For under-saturated conditions, when the bottom hole flowing pressure is higher than the bubble

point pressure, the flow of fluids in the reservoir is single phase and the linear IPR is valid.

(Prado, 2009)

When the bottom hole flowing pressure is below the bubble point pressure, a modified parabolic

equation is used for the IPR.

(1.10)

(1.11)

8

(1.12)

Productivity index for the saturated part of the IPR is defined as:

(1.13)

(1.14)

(1.15)

1.4 Tubing Performance Relationship

A tubing performance may be defined as the behaviour of a well in giving up the reservoir fluids

to the surface. The performance is commonly showed as a plot of flowrate versus bottomhole

flowing pressure. This plot is called the tubing performance relationship (TPR). For a specified

wellhead pressure, the TPR curves vary with diameter of the tubing. Also, for a given tubing

size, the curves vary with wellhead pressure. For single-phase liquid flow, pressure loss in tubing

can be determined using a simple fluid flow equation for vertical pipe, or using some graphical

pressure loss correlations where available with GLR = 0. Tubing performance curves are used to

determine the producing capacity of a well. By plotting IPR and TPR on the same graph paper, a

stabilized maximum production rate of the well can be estimated. (Lyon, 2010)

1.5 Behaviour of Produced GOR

Increasing GOR lightens the mixture density and thereby reduces the pressure loss due to

hydrostatic forces. Larger gas quantities usually result in larger pressure losses due to friction.

9

The GOR is considered critical when the producing GOR is equal to or greater than three times

the solution GOR (Rsi), that is (GOR ≥ 3Rsi) for producing oil well that is not on gas lift. (Slider,

1983)

The relationship between GLR and GOR can be expressed as

(1.16)

The produced GOR is constant above the saturation pressure. However, once the gas saturation

has reached a point that the free gas in the reservoir begins to flow, the behaviour of the gas-oil -

ratio becomes more complicated. The produced gas-oil-ratio, R at any particular time is the ratio

of the standard cubic feet of gas being produced at any time to stock-tank barrels of oil being

produced at that same instant. (Slider, 1983)

(1.17)

The term can be expanded using the radial flow equation as:

(1.18)

Writing and in terms of the above equation applied at the wellbore with the rates

corrected from reservoir volumes to scf and stb, respectively, yields an expression for reservoir

flowing GOR and the produced GOR:

(1.19)

10

(1.20)

(1.21)

The ratio of the effective permeabilities in the above equation is the same as the ratio of the

relative permeabilities which is a function of the liquid saturation. In order to determine the

relative permeability ratio and the produced gas oil ratio, it is necessary to evaluate the oil

saturation corresponding to any cumulative oil production. (Slider, 1983)

The oil saturation is the remaining reservoir barrels of oil in the reservoir, , divided

by the reservoir pore volume in barrels. The pore volume can be determined from the initial oil

saturation, and the original reservoir barrels of oil in the reservoir, . Thus the

material balance expression for the oil saturation is written as:

(1.22)

1.6 Statement of Problem

The proper selection, design, and installation of tubing string are critical parts of any well

completion. Tubing strings must be sized correctly to enable the fluids to flow efficiently or to

permit installation of effective artificial lift equipment. The optimum tubing size is selected to

obtain the desired production rates at the lowest capital and operating costs. This usually means

at the maximum initial flow rate and maintaining it as long as possible. Whatever the case, the

selection process inevitably involves analysis of the gross fluid deliverability and flow stability

under changing reservoir conditions to confirm that the production forecast can be met.

A tubing string that is too small causes large friction losses and limits production. It also may

severely restrict the type and size of artificial lift equipment. A tubing string that is too large may

11

cause heading and unstable flow, which results in loading up of the well and can complicate

workover operations. As previously mentioned, the changing conditions over the life of the well

must be considered when selecting tubing size. These changes are normally declining reservoir

pressure, increasing water cut and Gas Oil Ratio which will reduce flow rates. Water production

is rarely observed in the early and mid-stages of production. However GOR production is likely

to occur during the early stage as well as throughout the life of the well. High Gas Oil Ratio

(HGOR) is a situation where the produced GOR is equal to or three times higher than the initial

GOR. When this occurs it will lead to unstable flow and thus hinder production forecast. This

trend is downwards towards cessation of flow and, obviously the tubing selected for the start of

production will not be the optimum size after some period of time.

1.7 Objectives

1. To examine the effect of Low and High GOR on tubing performance.

2. To identify the critical points beyond which production begins to decline.

3. To observe the effect of water production at HGOR condition on production rate.

1.8 Methodology

1. Generation of GOR profile with respect to decreasing reservoir pressure.

2. Sensitivity Analysis (based on the GOR profile).

3. Determination of critical point of GOR.

4. Analysis of the effect of water production at HGOR condition on oil flowrate.

12

CHAPTER 2

LITERATURE REVIEW

2.1 Overview of System Analysis Approach

Systems analysis, which has been applied to many types of systems of interacting components,

consists of selecting a point or node within the producing system (well and surface facilities).

Equations for the relationship between flow rate and pressure drop are then developed for the

well components both upstream of the node (inflow) and downstream (outflow). The flow rate

and pressure at the node can be calculated since flow into the node equals flow out of the node

and only one pressure can exist at the node. Furthermore, at any time, the pressures at the end

points of the system (separator and reservoir pressure) are both fixed. Thus:

PR - (Pressure loss upstream components) = P node (2.1)

Psep + (Pressure loss downstream components) = P node (2.2)

Figure 2.1 Node flow rate and pressure

13

Typical results of such an analysis are shown in Figure 2.1 where the pressure-rate relationship

has been plotted for both the inflow (Equation 2.1) and outflow (Equation 2.2) at the node. The

intersection of these two lines is the (normally unique) operating point. This defines the pressure

and rate at the node. This approach forms the basis of all hand and computerized flow calculation

procedures. It is frequently referred to as Nodal analysis.

2.2 Applications of System Analysis Approach

The use of systems analysis to design a hydrocarbon production system was first suggested by

Gilbert (1954). Gilbert performed a sensitivity analysis to determine an approximate solution for

natural flow and gas-lift problems for 1.9-in, 2 3/8-in, 2.785-in and 3 1/2-in API tubing sizes and

crude oils with API gravity ranging from 25 to 40 API. He also explains the hydraulics of natural

flow as well as summarizing the methods for estimating individual well capabilities using the

same set of API tubing sizes. The author has prepared a very useful tool for the solution of

problems relative to flow of oil, gas, and water in a tubing string.

Brown and Lea run a production optimization using a computerized well model. This

computerized well model has contributed to improving completion techniques, for better

efficiency and higher production with many wells. The optimization was carried out for gravel

packed well as well as perforated wells.

Tubings were evaluated for a well to gravel packed. The IPR curve was prepared using Darcy’s

law including the additional turbulence pressure drops. The Gulf Coast well was considered for

this experiment. Tubing sizes of 2 7/8-in 3 1/2-in and 4 1/2-in are evaluated at the wellhead

pressure of 1200 psi needed to flow gas into the sales lines. From the analysis 4 ½-in tubing is

selected.

For the perforated well a sample oil well with low GOR, a low bubblepoint pressure, and

assumed single-phase liquid flow across the completion was analyzed. The reason for this

selection is that current technology has offered solutions only for single-phase flow across such

completions. When two-phase flow occurs across a gravel-packed or a standard perforated well,

relative permeability effects must be considered. The IPR curve was prepared with Darcy’s law,

14

assuming no pressure drop across the completion. Tubing performance curve was plotted for 2

3/8-in, 2 7/8-in and 3 1/2-in- -in tubing. Assuming 3 1/2-in-in tubing is selected, transfer it

pressure drop curve. Using the appropriated equations from Mcleod and as discussed by Brown

et al., the pressure drops across the available completions were determined. A final plot is

constructed to show the importance of perforating underbalanced.

Rafiqul Awal et al develop a new nodal analysis technique which helps improve well completion

of matured oil field. They proposed the use of a simple, tapered tubing string completion (using

larger internal diameter ID tubing pipes in the upper sections) that can be customized for specific

reservoirs. They employed nodal analysis technique to develop an equivalent tubing diameter

(ETD) concept. The ETD allow for comparing the well performance for single – ID tubing. The

procedure also seeks an optimum length for the larger tubing ID in the upper section. This

method had limitations as it was suitable for wells with moderate to high open flow potential. It

is suited for low GOR wells with high future water-cut. The technique was to reduce or eliminate

the high capital cost of investing into waterflooding or any other Enhanced oil recovery method.

The experiment was carried out by firstly using a mono tubing completion using five tubing ID

sizes: 1.995-in, 2.441-in, 2.992-in, 3.476-in and 3.958-in. The well performance graphs produced

showed that for water-cut ranging from 50% to 60%, the stabilized gross liquid rate increase with

tubing size until 3.476-in. The reserve at 3.958-in indicating the optimum tubing diameter lies

between the 3.476-in and 3.958-in

Next, we show the nodal analysis results for the Duplex Tapered Internal Diameter Tubing

Completion TIDC realizations. The TIDC realizations shown were very simple, i.e., the depth

intervals for various tubing sizes in a TIDC completion are equal. The result showed that the

Duplex TIDC gives significantly higher gross liquid rates at all three water-cut values. The

optimization process was carried out by choosing several values for length of the upper tubing

section, and comparing the stabilized flow rates. It reveals the optimum length of the upper

section (larger ID, 3.958-in.) to be 3,600-ft, which much shorter than the smaller ID (3.476-in.),

lower section: (9,990 – 3,600) ft = 6,390-ft.

In the foregoing duplex TIDC optimized solution, the economic gains are significant, given the

high oil price. The duplex TIDC gives increased gross fluid rates as follows:

15

• 10 to 15% compared to the 3.476-in. mono tubing completion, and

• 10 to 30% compared to the 3.958-in. mono tubing completion, over the water-cut range of

50 to 70%

2.3 Optimization Approach

This work looks closely at the application of nodal analysis to oil wells with high GOR. Analysis

of the behaviour of GOR produced on production rate is coupled with variation of water-cut at

HGOR conditions.

16

CHAPTER 3

METHODOLOGY

3.1 Prediction of produced GOR

Planning the development of a reservoir with respect to sizing equipment and planning for

artificial lift as well as evaluating the project form an economics point of view, requires the

ability to predict reservoir performance in the future. The reservoir PVT data must be available

in order to predict the primary recovery performance of a depletion-drive reservoir in terms of

Np and Gp. These data are: initial oil-in-place, hydrocarbon PVT, initial fluid saturation, and

relative permeability. All the methods used to predict the future performance of a reservoir are

based on combining the appropriate material balance equation (MBE), with instantaneous GOR

using a proper saturation equation. However the prediction is narrowed only to the instantaneous

GOR. The calculations are repeated at a series of assumed reservoir pressure drops. There are

several techniques that were specifically developed to predict the performance of the solution gas

drive reservoir. These methods include Tarner’s method, Tracy’s method and Muskat method,

3.1.1 Tarner’s method

Tarner (1944) pointed out that the Np1 and Gp1 are set equal to zero at the initial reservoir

pressure that is at bubble point pressure. He computed based on the assumed using

equation (3.1)

– – (3.1)

For each of Npn assumed, a corresponding So was determined using equation (2.7). From the So

determined, calculate Sg using equation (3.2) and using the field data Sgversus kg/koin appendix

A determine kg/ko

(3.2)

17

Calculate the instantaneous Gas Oil ration (Rn) using equation (2.6)

Checking the validity of the assumed Np necessitates the need to calculate the Gp again using

equation. (3.3). if the new calculated Gp agrees with the previous Gp then the assumed Np is

correct. This sequence is repeated for the subsequent pressures.

(3.3)

If there are difficulties in the guessing of the cumulative oil production equation (3.4) can be

used.

(3.4)

3.1.2 Tracy’s Method

Tracy (1955) suggests that the general material balance equation can be rearranged and

expressed in terms of two functions of PVT variables for depletion drive reservoir without water

influx. Following equation is based on an initial oil in place of 1 STB

(3.5)

Where

(3.6)

(3.7)

The following Procedure was adopted for the prediction

1. Select an average reservoir pressure

2. Calculate values of the PVT functions

3. Estimate the GOR at assumed reservoir pressure from PVT data

18

4. Calculate the average instantaneous GOR using equation (3.8)

(3.8)

5. Calculate the incremental oil production from equation 3.9

(3.9)

6. Calculate the cumulative oil production using equation (3.10)

(3.10)

7. Calculate the oil and gas saturation at selected average reservoir pressure

8. Obtain relative permeability ratio Krg/kroat Sg

9. Calculate the Instantaneous GOR from equation (2.6)

10. Compare the estimated GOR in step (3) with the calculated GOR in step (10). If the

values are within acceptable tolerance proceed to next step. If not within the tolerance set

the estimated GOR equal to the calculated GOR and repeat the calculation from step (2).

11. Calculate the cumulative gas production

(3.11)

12. Since results of the calculations are based on 1 STB of oil initially in place, a final check

on the accuracy of the prediction should be made on the MBE and repeat the calculation

from step 1

= 1±Tolerance (3.12)

19

3.1.3 Muskat Method

Muskat (1946) expressed the material balance equation for a depletion-drive reservoir in

following differential form:

(3.13)

Craft, Hawkins, and Terry (1991) suggested the calculations can be greatly facilitated by

computing and preparing in advance in graphical form the following pressure dependent groups:

(3.14)

(3.15)

(3.16)

Introducing the above pressure dependent terms into Equation (3.14) gives

(3.17)

20

Craft et al, 1991 proposed the following procedure for solving Muskat’s equation for a given

pressure drop.

The following procedure was adopted

1. Prepare a plot of krg/kro versus gas saturation

2. Plot Rs, Bg and (1/Bg) versus pressure and determine the slope of each plot at selected

pressures , that is dBo/dp, dRs/dp and d(1/Bg)/dp

3. Calculate the pressure dependent terms X(p), Y(p) and Z(p) that correspond to the

selected pressures in step 2.

4. Plot the pressure dependent terms as a function of pressure.

5. Graphically determine the values of X(p), Y(p) and Z(p) that corresponds to the pressure

p.

6. Solve equation (3.17) for (dSo/dp) by using the oil saturation So* at the beginning of the

pressure drop interval p*

7. Determine the oil saturations So at the average reservoir pressure using equation (3.18)

(3.18)

8. Using the So from Step 7 and the pressure p, recalculate (dSo/dp) from equation 3.17

9. Calculate the average value for (dSo/dp) from the two values obtained in step 6 and 8 or;

(3.19)

10. Using solve for oil saturation So from

(3.20)

This value of So becomes for the next pressure drop interval.

21

11. Calculate gas saturation Sg by

(3.21)

12. From equation (2.7) , solve for the cumulative oil production

(3.22)

13. Calculate the cumulative gas production Gp using equation (3.22) and repeat steps 5

through 13 for all pressure drops.

(3.23)

These prediction methods were compared and series of graphs were constructed to select the best

method. A plot of GLR versus GOR was constructed using various water cut ratios (15%, 20 %

and 25%).

3.2 Future inflow performance relationship (IPR) for an oil well

Several correlations have been developed for predicting future inflow performance relationships

curves (IPRs). In this study a combination of Fetkovich and Vogel Equation was used to predict

the future IPRs.

The following steps were used to construct the IPRs.

1. Using Beggs and Brill (1978 ), estimate the bubble point pressure, Pb for the current GLR

22

2. Calculate and it corresponding using the equations (3.24) and (3.25) respectively

at the average reservoir pressure.

(3.24)

(3.25)

The qb below the bubble point pressure and at the bubble point pressure is zero. Above the

bubble point pressure, is determined by using equation (3.24). Below the bubble point

pressure the is based on previous and pressure and determined by using equation

(3.25)

3. Calculate for the average reservoir pressure

(3.26)

4. Calculate for the productivity index J* and for the bubble point pressure Pb

(3.27)

5. Generate a pressure profile below the bubble point pressure and calculate the

corresponding and J* using Fetkovich correlations.

6. Plug in the first average reservoir pressure and it corresponding in the IPR

program.xls to generate the IPR.

7. Repeat steps 6 and 7 for all the generated in 5 to generate their IPR’s.

23

3.3 Construction of TPR curves

Using the Beggs and brill spreadsheet, the generated flowrates and it corresponding pressures

were used to construct the outflow performance relationship (OPR) or TPR curve. To achieve

that, a range of tubing sizes (2 3/8-in, 2 7/8-in, 3 1/2-in and 4 -in) were selected. The tubing

diameter, estimated GOR, depth of the well, wellhead pressure, reservoir pressure and fluid

properties were kept constant while changing the oil flowrate. The watercut was assumed to be

zero in the first instance and later varied with equal interval. For each flowrate used a pressure is

recorded at the node. This method was used to construct TPR curves for all the tubing string

sizes considered in this study.

24

CHAPTER 4

RESULTS AND DISCUSSION

In this chapter the nodal analysis described in chapter two is applied for various instantaneous

GORs and water cuts. The results obtained from the sensitivity analysis are presented in this

chapter.

4.1 Results

Tables 4.4a to 4.4e show the variation in oil production rate as well as pressure for a particular

range of GOR. The red coloured numbers in Tables 4.3a to 4.3f signify an increase in either the

production rate or bottomhole flowing pressure. The blue coloured numbers in Tables 4.3a to

4.3f signify a decrease in either the production rate or bottomhole flowing pressure. Tables 4.3a

to 4.3f show the operating points of the various tubing sizes at specific reservoir pressure and

GOR.

25

A comparison of GOR estimated by the three predictive methods as described in chapter 3 is

presented in Figure 4.1.

Figure 4.1 Variation of GOR with Pressure using Tracy, Tarner and Muskat Methods.

0

1000

2000

3000

4000

5000

6000

7000

050010001500200025003000

GO

R (

SCF/

STB

Pressure, Psi

Tracey

Tarner

Muskat

26

Figure 4.2 GLR vrs GOR at varying water cut ratios. (Tracy’s method)

Figure 4.3 GLR vrs GOR at varying water cut ratios. (Tarner’s Method)

0

1000

2000

3000

4000

5000

6000

0 1000 2000 3000 4000 5000 6000

GLR

(SC

F/ST

B)

GOR (SCF/STB)

Tracy

Tracy 15%

20%

25

wc (15%)

wc (20%)

wc (25%)

0

1000

2000

3000

4000

5000

6000

0 1000 2000 3000 4000 5000 6000

GLR

(SC

F/ST

B)

GOR (SCF/STB)

Tarner

Tarner 15%

20%

25

wc (15%)

wc (20%)

wc (25%)

27

Figure 4.4 GLR vrs GOR at varying water cut ratios. (Muskat’s Method)

Table 4.1 Estimated GLR at varying water cut with all the prediction methods

Tracy Tarner Muskat Calculated Difference

wc

(%)

GOR

(scf/stb)

GLR

(scf/stb)

25% 2000 1500 1500 1500 1500 0

20% 2000 1700 1700 1700 1600 100

15% 2000 1900 1900 1900 1700 200

25% 5000 3700 3700 3700 3750 50

20% 5000 4200 4200 4200 4000 200

15% 5000 4700 4700 4700 4250 450

From Table 4.1 all the prediction methods yielded approximately the same GLR at a specific

GOR and water cut. The results presuppose that either of the methods can be used to predict the

instantaneous gas oil ratio for the oil well with much accuracy. Tracy method was selected due to

the fact, the error margin between the estimated and calculated GOR was very small and a zero

0

1000

2000

3000

4000

5000

6000

7000

0 1000 2000 3000 4000 5000 6000 7000

GLR

(SC

F/ST

B)

GOR (SCF/STB)

Muskat

Muskat 15%

20%

25%

wc (15%)

wc (20%)

wc (25%)

28

tolerance was observed for each pressure drop. The only exception is that Muskat method

predicted a much higher GOR of 6304 scf/stb as opposed to the 5800 and 5635 scf/stb of Tarner

and Tracy methods respectively.

Following Tracy’s steps in Chapter three for prediction of produced GOR, the GOR was

estimated. Table 4.2b shows the generated data based on input PVT data in Table 4.2a. A plot of

the produced or instantaneous GOR versus pressure is also showed in Figure 4.3

The following data applies to a solution gas drive reservoir

Initial oil in place is 3.7 MMSTB

Connate Water Saturation is 35%

Oil Saturation is 0.65

Bubble Point Pressure is 2500 psi

Abandonment Pressure is 700 psi

Table 4.2a Available PVT Data for predicting oil reservoir performance

P Bo Bg Rs Uo/Ug

psi bbl/STB bbl/scf scf/bbl

2500 1.2 0.00069 840

2300 1.195 0.00071 820 28.7

2100 1.19 0.00074 770 32.4

1900 1.185 0.00078 730 36.7

1700 1.18 0.00081 680 42.6

1500 1.175 0.00085 640 47.1

1300 1.17 0.00089 600 53.5

1100 1.165 0.00093 560 60.8

900 1.16 0.00098 520 69.2

700 1.155 0.00102 480 78.6

29

Table 4.2b Data generated from PVT data in table 4.2a

P

Psi Фo Фg Rav ΔNp Np ΔGp

2500 840

2300 66.6087 0.077174 828 0.007664 0.007664 6.343198

2100 14.83732 0.017703 879 0.025465 0.033129 22.37774

1900 8.694915 0.011017 1052 0.0195 0.052629 20.51226

1700 5.740876 0.007391 1453 0.020264 0.072893 29.45321

1500 4.351724 0.005862 1942 0.01408 0.086973 27.33743

1300 3.464052 0.004847 2610 0.011466 0.098439 29.92334

1100 2.85803 0.004126 3444 0.009242 0.107681 31.82911

900 2.377193 0.003582 4444 0.007821 0.115502 34.75197

700 2.065177 0.003166 5635 0.006045 0.121546 34.06302

30

Table 4.2c Continuation of Data generated from PVT data in table 4.2b

Gp So Sg kro krg krg/kro

GOR

(Scf/stb) Tolerance

840

6.343198 0.642331 0.007669 0.459029 7.27E-05 0.000158 828 0.00000

28.72093 0.623229 0.026771 0.370921 0.000774 0.002087 879 0.00000

49.23319 0.608094 0.041906 0.313289 0.001807 0.005769 1052 0.00000

78.68641 0.592576 0.057424 0.263483 0.00328 0.01245 1453 0.00000

106.0238 0.581104 0.068896 0.231827 0.00463 0.019972 1941 0.00000

135.9472 0.571364 0.078636 0.207956 0.005946 0.028593 2610 0.00000

167.7763 0.563091 0.086909 0.189618 0.007185 0.037893 3444 0.00000

202.5283 0.55576 0.09424 0.174727 0.008375 0.047932 4444 0.00000

236.5913 0.549583 0.100417 0.16309 0.009444 0.057906 5635 0.00000

31

The produced GOR using Tracy’s method in Table 4.2c is plotted against it respective

bottomhole pressure pressure in Figure 4.5

Figure 4.5 Variation of GOR with reservoir pressure

The data generated for Muskat and Tarner methods using the same data in Table 4.1a are

presented in appendix B. Plots of GOR versus pressure for both methods are also presented in

appendix B.

0

1000

2000

3000

4000

5000

6000

50010001500200025003000

GO

R S

CF/

STB

Pressure Psi

32

The Inflow performance relationship curves in Figure 4.4 were produced by following the

procedure in section 3.2.

Figure 4.6 Future Inflow Performance Relationships Curves

0

500

1000

1500

2000

2500

3000

3500

0 500 1000 1500 2000 2500 3000

Pre

esu

re, p

si

Production rate, stb/day

IPR 1

IPR 2

IPR 3

IPR 4

IPR 5

IPR 6

IPR 7

IPR 8

IPR 9

IPR 10

IPR 11

33

Figure 4.7 to 4.12 shows plots of IPR and TPR for various tubing sizes at specific GOR at a

water cut of zero.

Figure 4.7 Effect of tubing size on production rate at a constant GOR (840 scf/stb)

Table 4.3a Operating point for various tubing diameters at a GOR of 840 scf/stb

IPR/OD 2 3/8-in 2 7/8-in 3 1/2-in 4-in

Q P Q P Q P Q P

1 1310 2090 1650 1800 1983 1550 2100 1375

2 950 1780 1170 1590 1310 1400 1370 1350

5 - - - - - - - -

0

500

1000

1500

2000

2500

3000

3500

0 500 1000 1500 2000 2500 3000

Bo

tto

mh

ole

Flo

win

g P

ress

ure

psi

Flowrate, stb/day

GOR of 840 scf/stb

IPR 1

IPR 2

IPR 3

IPR 4

IPR 5

IPR 6

IPR 7

IPR 8

IPR 9

IPR 10

IPR 11

2.375"

2.875"

3.5"

4"

34


Table 4.3b Operating point for various tubing diameters at a GOR of 1052 scf/stb

IPR/OD 2 3/8-in 2 7/8-in 3 1/2-in 4-in

Q P Q P Q P Q P

1 1310 2090 1700 1695 2000 1500 2150 1300

2 960 1750 1200 1500 1400 1330 1480 1230

5 490 1300 510 1200 510 1200 - -

0

500

1000

1500

2000

2500

3000

3500

0 500 1000 1500 2000 2500 3000

Bo

tto

mh

ole

Flo

win

g P

ress

ure

,psi

Flowrate,stb/day

GOR at 1052 scf/stb

IPR 1

IPR 2

IPR 3

IPR 4

IPR 5

IPR 6

IPR 7

IPR 8

IPR 9

IPR 10

IPR 11

2.375"

2.875"

3.5"

4"

35


Table 4.3c Operating point for various tubing diameters at a GOR of 1453 scf/stb

IPR/OD 2 3/8-in 2 7/8-in 3 1/2-in 4-in

Q P Q P Q P Q P

1 1290 2100 1700 1800 2030 1480 2200 1280

2 970 1850 1240 1500 1450 1250 1560 1100

5 520 1160 600 1050 630 980 - -

0

500

1000

1500

2000

2500

3000

3500

0 500 1000 1500 2000 2500 3000

Bo

tto

mh

ole

Flo

win

g P

ress

ure

,psi

Flowrate,stb/day

GOR at 1453 scf/stb

IPR 1

IPR 2

IPR 3

IPR 4

IPR 5

IPR 6

IPR 7

IPR 8

IPR 9

IPR 10

IPR 11

2.375"

2.875"

4"

3.5"

36


Table 4.3d Operating point for various tubing diameters at a GOR of 2610 scf/stb

IPR/OD 2 3/8-in 2 7/8-in 3 1/2-in 4-in

Q P Q P Q P Q P

1 1150 2230 1570 1900 1980 1520 2240 1200

2 880 1850 1190 1550 1440 1250 1620 1000

5 520 1180 630 950 700 820 720 760

6 - - 490 800 510 700 520 700

0

500

1000

1500

2000

2500

3000

3500

0 500 1000 1500 2000 2500 3000

Bo

tto

mh

ole

Flo

win

g P

ress

ure

,psi

Flowrate, stb/day

GOR at 2610 scf/stb

IPR 1

IPR 2

IPR 3

IPR 4

IPR 5

IPR 6

IPR 7

IPR 8

IPR 9

IPR 10

IPR 11

2.375"

4"

3.5"

2.875"

37


Table 4.3e Operating point for various tubing diameters at a GOR of 3444 scf/stb

IPR/OD 2 3/8-in 2 7/8-in 3 1/2-in 4-in

Q P Q P Q P Q P

1 1050 2300 1450 2000 1900 1600 2200 1300

2 800 1900 1120 1600 1420 1300 1620 1050

5 510 1200 620 950 700 800 730 800

6 - - 490 800 510 600 510 600

0

500

1000

1500

2000

2500

3000

3500

0 500 1000 1500 2000 2500 3000

Bo

tto

mh

ole

Flo

win

g P

ress

ure

,psi

Flowrate, stb/day

GOR at 3444 scf/stb

IPR 1

IPR 2

IPR 3

IPR 4

IPR 5

IPR 6

IPR 7

IPR 8

IPR 9

IPR 10

IPR 11

2.375"

2.875"

3.5"

4"

38


Table 4.3f Operating point for various tubing diameters at a GOR of 5635 scf/stb

IPR/OD 2 3/8-in 2 7/8-in 3 1/2-in 4-in

Q P Q P Q P Q P

1 850 2400 1250 2020 1680 1780 2040 1450

2 700 2000 970 1750 1300 1420 1540 1150

5 500 1400 580 1050 690 710 740 700

6 - - 490 900 510 600 590 500

0

500

1000

1500

2000

2500

3000

3500

0 500 1000 1500 2000 2500 3000

Bo

tto

mh

ole

Flo

win

g P

ress

ure

,psi

Flowrate, stb/day

GOR at 2610 scf/stb

IPR 1

IPR 2

IPR 3

IPR 4

IPR 5

IPR 6

IPR 7

IPR 8

IPR 9

IPR 10

IPR 11

2.375"

4"

3.5"

2.875"

39

Table 4.4a Variation in production rate and pressure with GOR range of 840-1052 scf/stb

Production Increase %

(840-1052 scf/stb)

Pressure reduction

psi

OID/IPR 1 2 5 ID/IPR 1 2 5

2 3/8” 0 1.1 N/A 2 3/8” 0 30 N/A

2 7/8” 3.0 2.6 N/A 2 7/8” 105 90 N/A

3 1/2” 0.9 6.9 N/A 3 1/2” 50 70 N/A

4” 2.4 8.0 N/A 4” 75 120 N/A

Table 4.4b Variation in production rate and Pressure with GOR range of 1052-1453 scf/stb

Production Increase %

(1052-1453 scf/stb)

Pressure reduction

psi

OD/IPR 1 2 5 ID/IPR 1 2 5

2 3/8” 1.5 1.0 6.1 2 3/8” 10 100 140

2 7/8” 0.00 3.3 17.6 2 7/8” 105 0 150

3 1/2” 1.5 3.6 23.5 3 1/2” 20 80 220

4” 2.3 5.4 N/A 4” 20 130 N/A

Table 4.4c Variation in production rate and Pressure with GOR range of 1453-2610 scf/stb

Production decrease %

(1453-2610 scf/stb)

Pressure increase

psi

ID/IPR 1 2 5

ID/IPR 1 2 5

2 3/8” 10.9 9.3 1.9 2 3/8” 130 0 20

2 7/8” 7.65 4.0 5.0 2 7/8” 100 50 100

3 1/2” 2.46 0.7 11.1 3 1/2” 40 0 160

4” 1.82 3.8 N/A 4” 80 100 N/A

Table 4.4d Variation in production rate and pressure with GOR range of 2610-3444 scf/stb


(2610-3444 scf/stb)

Pressure increase

psi

ID/IPR 1 2 5 6

ID/IPR 1 2 5 6

2 3/8” 8.7 9.1 3.8 N/A 2 3/8” 70 50 20 N/A

2 7/8” 7.64 5.9 1.6 0 2 7/8” 100 50 0 0

3 1/2” 4.04 1.4 0.0 0.0 3 1/2” 80 50 20 100

4” 1.79 1.6 1.4 1.9 4” 100 50 40 100

40

Table 4.4e Variation in production rate and Pressure with GOR range of 3444-5635 scf/stb


(3444-5635 scf/stb)

Pressure increase

psi

ID/IPR 1 2 5 6

ID/IPR 1 2 5 6

2 3/8” 19.0 12.5 2.0 N/A 2 3/8” 100 100 200 N/A

2 7/8” 13.8 13.4 6.5 0 2 7/8” 20 150 100 100

3 1/2” 11.6 8.5 1.4 0.0 3 1/2” 180 120 90 0

4” 7.3 3.8 1.4 15.7 4” 150 100 100 100

Figure 4.13 Production profile for 2 3/8-in tubing size

0

200

400

600

800

1000

1200

1400

600 1600 2600 3600 4600 5600 6600

Flo

wra

te, s

tb/d

ay

GOR, scf/stb

2 3/8" TUBING SIZE

IPR1

IPR2

IPR5

41



0

200

400

600

800

1000

1200

1400

1600

1800

600 1600 2600 3600 4600 5600 6600

Flo

wra

te, s

tb/d

ay

GOR, scf/stb

2 7/8" TUBING SIZE

IPR1

IPR2

IPR5

0

500

1000

1500

2000

2500

600 1600 2600 3600 4600 5600 6600

Flo

wra

te, s

tb/d

ay

GOR, scf/stb

3 1/2" TUBING SIZE

IPR2

IPR5

IPR1

42

Figure 4.16 Production profile for 4-in tubing size

Figure 4.17 Effect of water cut on flowrate at a GOR of 2610 scf/stb

0

500

1000

1500

2000

2500

600 1600 2600 3600 4600 5600 6600

Flo

wra

te, s

tb/d

ay

GOR, scf/stb

4" TUBING SIZE

IPR1

IPR2

IPR5

IPR6

400

450

500

550

600

650

700

750

2 2.5 3 3.5 4 4.5

Flo

wra

te s

tb/d

ay

Tubing diameter , in

2610 scf/stb and IPR5

wc = 0

wc = 20%

wc = 5%

wc = 25%

43



400

450

500

550

600

650

700

750

2 2.5 3 3.5 4 4.5

Flo

wra

te, s

tb/d

ay

Tubing diameter, in


wc = 0

wc = 5%

wc = 20%

wc = 25%

400

450

500

550

600

650

700

750

800

2 2.5 3 3.5 4 4.5

Flo

wra

te, s

tb/d

ay

Tubing diameter, in


wc = 0

wc = 5%

wc = 20%

wc = 25%

44

4.2 Discussion

The two major components of production optimization (cost and reduction in pressure losses)

can be positively influenced by acting on the analysis and recommendation of this study. In the

analysis of the behaviour of the produced GOR on tubing performance, equal numbers of Low

and High GOR values were selected.

4.2.1 Behaviour of Tubing curves at LGOR

From Figure 4.5, tubing performance curves for (2 3/8-in, 2 7/8-in, and 3 1/2-in) tubing sizes

intersect IPR1 and IPR4 curves making tubing selection feasible. The 4-in tubing performance

curve intersect IPR1 to IPR3 curves. Moving closer to IPR5, the TPR curves for (2 3/8-in, 2 7/8-

in, and 3.1/2-in) tubing sizes converge. The bigger tubing size (4-in) cannot be used to produce

the well at lower IPR curves (IPR4 and IPR5). Considering the IPR1 curve, the 4-in tubing size

can produce as high as 2100 stb/day at a bottomhole pressure of 1375 psi whereas the 2 3/8-in

produces 1310 stb/day at a much higher bottomhole pressure of 2090psi. The bottomhole

pressure tends to decrease with increasing tubing diameter.

As GOR increases from 840 scf/stb to 1052 scf/stb in Figure 4.6, a shift in the tubing curves to

the right is observed associated with an increase in oil production. From table 4.4a it can be seen

that for all the tubing sizes used the more bottomhole pressure reduces the greater the percent

increase in oil production rate. Considering the IPR1 curve, 2 7/8-in tubing size experienced the

highest pressure drop associated with the highest percent increment in production.

The same trend was observed when the GOR increased from 1052 to 1453 scf/stb. The only

exception was 1.5% reduction in production rate at for 2.3/8-in tubing size when it intersect the

IPR1 curve. Considering IPR2 and for the same range of GOR, 4-in has the highest production

rate increase followed by 3 1/2-in with a corresponding pressure drop of 80psi and 130psi

respectively. There was no pressure drop using 2 7/8-in yet there was a potential gain in

production.

45

From table 4.4a to 4.4b, it was observed that as GOR increases, bottomhole pressure decreases

associated with an increase in oil production rate. This phenomenon is mainly valid for low GOR

cases.

4.2.2 Behaviour of Tubing curves at HGOR

From Figure 4.8, a slight shift of the tubing curves to the left side is observed. This is associated

with decrease oil production. At a GOR of 2610 scf/stb, production can be feasible and extended

to the IPR5 curve.

Moving from the region of LGOR to HGOR a decrease in production rate is observed due to the

increase in bottomhole pressure. For a GOR range of 1453 to 2610 scf/stb and IPR5 curve, there

is a percent decrease in production using 2 3/8-in, 2 7/8-in and 3 1/2-in tubing sizes. As the GOR

increases further, the more the rise in bottomhole pressure causing much more decrease in

production. For a GOR ranges of 2610 to 3444 scf/stb and 3444 to 5635 scf/stb, the 4-in tubing

size can be still be used to produce a substantial quantity of the oil at lower reservoir pressures.

From table 4.4d to 4.4e, it is observed that as GOR increases, bottomhole pressure increases with

an associated decrease in oil production rate. This phenomenon is mainly valid for HGOR cases.

4.2.3 Production profile of the various tubing sizes

The analysis of the two cases of GOR condition shows that there is a point for each tubing size

where production rate begins to decline. Considering IPR1 and IPR 2 in Figure 4.13 there is a

sharp gradual increase in production rate. The production rate tends to decrease when the GOR

increases beyond 1500 scf/stb. The production rate beyond the critical point for IPR5 seems to be

fairly constant. From Figure 4.14, the same trend in Figure 4.13 was observed for 2 7/8” tubing

size. From Figures 4.15 and 4.16 the critical point for 3 1/2” and 4” tubing sizes varies for

different IPR curves and the critical point is also not distinct. Production using 4” tubing size

with the Lower IPR curves (IPR5 and IPR6) will be only possible beyond a GOR of 2600 scf/stb.

46

4.2.4 Effect of water cut in HGOR condition

The onset of water production can affect the production rate. The extend to which it affect

production rates depends on the operation GOR, and the water cut as well as the tubing size

used. From Figure 4.17 to 4.19, production rate tends to decrease with increasing water cut

ratios. The 2 3/8-in tubing size can no longer produce the well at a water cut of 25% and a GOR

of 2610 scf/stb. Production with 2 3/8-in tubing size is hindered as GOR increases from 2610

scf/stb to 5635 scf/stb. On the other hand, the tubing sizes ranging from 2 7/8-in to 4-in can

comfortably produce the well in these conditions.

47

CHAPTER 5

CONCLUSION AND RECOMMENDATION

5.1 CONCLUSION

The results for the oil production trends indicate that GOR production adds some value to

production. It is obvious that the GOR produced as the reservoir pressure declines cannot be

controlled and as such it is imperative to run a sensitivity analysis for all the available tubing

sizes ascertain which tubing sizes gives an appreciable potential gain in production. Tracy’s

method was selected as the best among the three produced GOR prediction methods. The result

from this study will also serve as a guide in choosing the optimum tubing size during completion

stages or at a point in the life of the well and in the gas lift planning.

In HGOR case, potential gain in oil production is hindered and as such the necessary measures

can be adopted to remedy or mitigate the situation.

The results from this sensitivity analysis showed that there is always a critical point beyond

which there is a net decrease in the oil production rate for all the tubing sizes. The critical point

is a function of the tubing size used as well as the current well condition (GOR).

Finally the production of water at any stage of the well irrespective of the percentage also

contributes adversely to reducing the oil production rate. All things being equal, the percentage

reduction in production reduces as GOR increases from 2610 to 5635 scf/stb for all the tubing

size used.

5.2 RECOMMENDATION

Due to the limitations of Beggs and Brill, new nodal analysis software such as PROSPER,

Wellflo and Snap can be used to carry out this sensitivity analysis with higher level of accuracy.

48

APPENDIX A

Figure A.1 Log-log graph of Kro vrs Sg

Figure A.2 Log-Log graph of Krg vrs Sg

y = 0.500035e-11.157176x

R² = 1.000000

0.1

1

0 0.02 0.04 0.06 0.08 0.1 0.12

kro

Expon. (kro)

Kro

Sg

y = 0.730678x1.892000

R² = 1

0.00001

0.0001

0.001

0.01

0.1

1

0 0.02 0.04 0.06 0.08 0.1 0.12

Krg

Power (Krg)Krg

Sg

49

APPENDIX B

Table B.1 Data generated from PVT data in table 4.2a using Tarner method

P Np

Gp

(MMSCF) So Sg kro krg krg/kro R obs R cal

2500 840 840

2300 117502 143.768 0.626558 0.023442 0.038496 0.000602 0.015643 1576 1576

2100 103061 286.469 0.626474 0.023526 0.03846 0.000606 0.015765 1600 1591

1900 88457 397.463 0.626397 0.023603 0.038427 0.00061 0.015876 1600 1616

1700 99916 564.210 0.621758 0.028242 0.036488 0.000857 0.023479 2100 2139

1500 95734 686.960 0.619849 0.030151 0.035719 0.00097 0.027144 2400 2409

1300 96146 814.354 0.61714 0.03286 0.034656 0.001141 0.032922 2912 2914

1100 98207 943.993 0.614148 0.035852 0.033518 0.001345 0.040141 3600 3615

900 101382 1076.776 0.610968 0.039032 0.03235 0.00158 0.048844 4500 4518

700 104113 1208.654 0.607869 0.042131 0.03125 0.001826 0.058427 5800 5682

Figure B.2 Variation of pressure and instantaneous GOR calculated by Tarner’smethod.

800

1800

2800

3800

4800

5800

50010001500200025003000

GO

R, S

CF/

STB

Pressure psi

50

Table B.3a Data generated from PVT data in table 4.2a using Muskat method

P X(p) Y(p) Z(p) sg kro Krg Krg/kro

2500

2300 0.000125 0.000624 0.00019 0.024644 0.379828 0.000662 0.001743

2100 0.000131 0.000708 0.000198 0.020263 0.398857 0.000457 0.001146

1900 0.000138 0.000806 0.000208 0.03667 0.332136 0.001404 0.004228

1700 0.000144 0.00094 0.000216 0.052719 0.277682 0.002791 0.01005

1500 0.000152 0.001043 0.000227 0.066902 0.237042 0.00438 0.018477

1300 0.00016 0.001188 0.000238 0.078993 0.207128 0.005997 0.028955

1100 0.000168 0.001356 0.000248 0.089014 0.185219 0.007518 0.04059

900 0.000177 0.00155 0.000262 0.097377 0.168717 0.00891 0.052812

700 0.000185 0.00177 0.000272 0.104534 0.155768 0.01019 0.065416

Table B.3b Continuation of data generated from PVT data in table B.3a

P (Δso/Δp) So (Δso/Δp)So (Δso/Δp)avg So(new) Rcal Np

2500 0.65 840

2300 0.000123 0.625356 7.94E-05 0.000101 0.629737 904 124316.9

2100 8.31E-05 0.608738 8.1E-05 8.2E-05 0.61333 830 204000.7

1900 8.12E-05 0.592489 7.93E-05 8.02E-05 0.597281 966 282245.9

1700 7.17E-05 0.578153 7.01E-05 7.09E-05 0.583098 1304 350181.9

1500 6.1E-05 0.56595 5.99E-05 6.05E-05 0.571007 1844 406395.3

1300 5.05E-05 0.555852 4.97E-05 5.01E-05 0.560986 2635 450903.5

1100 4.21E-05 0.547435 4.15E-05 4.18E-05 0.552623 3649 486028.7

900 3.6E-05 0.540237 3 .56E-05 3 .58E-05 0.545466 4843 514331.4

700 3.11E-05 0.534012 3.08E-05 3.1E-05 0.539271 6304 537177.8

51

Figure B.4 Variation of pressure and instantaneous GOR calculated by Muskat method.

0

1000

2000

3000

4000

5000

6000

7000

50010001500200025003000

GO

R, S

CF/

STB

Pressure, psi

52

NOMENCLATURE

API American Petroleum Institute

AOF absolute open flow, stb/day

Area of the well, ft-squared

is the vogel empirical constant

Initial Oil Formation Volume Factor, rb/stb

Oil Formation Volume Factor, rb/stb

Gas Formation Volume Factor, bbl/scf

d = pipe diameter, L, in

= friction factor, dimensionless

g = gravitational acceleration, L/t2, ft/sec

2

= conversion facto, dimensionless, 32.2 ft-Ibm/Ibf-sec2

GLR is Gas Liquid Ratio, (SCF/STB)

GOR is Gas oil ratio, (SCF/STB)

Permeability of gas, md

Permeability of Oil, md

Gas-Oil Relative permeability, dimensionless

Effective Permeability

LGOR is Low GOR

Initial Oil in Place, STB

Cumulative Oil Production, stb/day

outer diameter, inches

is the bubble point pressure, psi

53

is the average reservoir pressure, psi

Bottomhole flowing pressure, psi

Pressure at the sand surface, psi

Wellhead Pressure, psi

Separator pressure, psi

is the flowrate at the bubble point pressure, stb/day

is an empirical constant, its value represent AOF, stb/day

R is Gas oil ratio (scf/stb)

= Flowing gas-oil ratio in the reservoir, scf/stb

Gas Oil Ratio at a specific reservoir pressure, scf/stb

Initial Solution Gas oil ratio, scf/stb

Gas Saturation

Oil Saturation

Saturation of Connate water

gas viscosity, cp

Viscosity of Oil, cp

= velocity, L/t, ft/sec

wc is water cut (percentage, %)

= angle of the well from vertical

1 Pressure loss in the reservoir, psi

2 Pressure loss across completion, psi

3 Pressure loss in the tubing, psi

4 Pressure loss in flowing, psi

Total Pressure loss, psi

54

REFERENCES

Ahmed T., Reservoir Engineering Handbook, Third Edition, 2006.

Awal M.R. et al., A New Nodal Analysis Technique Helps Improve Well Completion and

Economic Performance of Matured Oil Fields, 2009.

Beggs, D.H., Production Optimization using Nodal Analysis, Second Edition, OGCI and

Petroskills Publications Tulsa, Oklahoma, pp.92 – 95, 2003.

BOYUN G., et al., Petroleum Production Engineering, A Computer–Assisted Approach,

2007.

Brown K.E. et al., Production Optimization of Oil and Gas Wells by Nodal Systems Analysis,

Technology of Artificial Lifts methods, Pennwell Publishing Co, Tulsa, 1984.

Brown K.E. and Lea J.F., Nodal Analysis of Oil and Gas Wells, 1985.

Clegg, D. J., Petroleum Engineering Handbook, Volume IV Production Engineering

Operation, 2007.

ENI S.p.A., Agip Division, Completion design manual, 1999.

Gilbert W.E., Flowing and Gas-Lift well performance, 1954.

Heriot Watt University, Production Technology 1 lecture notes.

Lea J.F. and Brown K.E., Production Optimization using a computerized well model, 1986.

Mcleod, H. O., The Effect of Perforating conditions on well Performance. J. Pet. Tech.,

January, 1983.

Perrin, D., Caron, M. and Gaillot, G., Well completion and servicing: oil and gas field

development techniques, 1999.

Prado M., IPR Two Phase Flow, the University of Tulsa, 2009.

Schlumberger, Completion Primer, pp 3-3 to 3-4, Rev A January 19, 2001.

55

Slider, H, Worldwide Practical Petroleum Reservoir Engineering Method, pp. 457-458,

1983.

Texter, H.G., Oil-well Casing and Tubing, 1955.

William C. LYONS, Working Guide to Petroleum and Natural Gas Production Engineering,

pp. 177, 2010.

effect of gas-oil-ratio on oil production

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