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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 4.11 Effect of tubing size on production rate at a constant GOR (3444 scf/stb) ....................... 37
Figure 4.12 Effect of tubing size on production rate at a constant GOR (5653 scf/stb) ....................... 38
Figure 4.13 Production profile for 2 3/8-in tubing size ........................................................................ 40
Figure 4.14 Production profile for 2 7/8-in tubing size ........................................................................ 41
Figure 4.15 Production profile for 3 1/2-in tubing size ........................................................................ 41
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 4.18 Effect of water cut on flowrate at a GOR of 3444 scf/stb ................................................. 43
Figure 4.19 Effect of water cut on flowrate at a GOR of 5635 scf/stb ................................................. 43
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
Figure 4.8 Effect of tubing size on production rate at a constant GOR (1052 scf/stb)
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
Figure 4.9 Effect of tubing size on production rate at a constant GOR (1453 scf/stb)
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
Figure 4.10 Effect of tubing size on production rate at a constant GOR (2610 scf/stb)
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
Figure 4.11 Effect of tubing size on production rate at a constant GOR (3444 scf/stb)
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
Figure 4.12 Effect of tubing size on production rate at a constant GOR (5653 scf/stb)
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
Production decrease %
(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
Production decrease %
(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
Figure 4.14 Production profile for 2 7/8-in tubing size
Figure 4.15 Production profile for 3 1/2-in tubing size
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
Figure 4.18 Effect of water cut on flowrate at a GOR of 3444 scf/stb
Figure 4.19 Effect of water cut on flowrate at a GOR of 5635 scf/stb
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
3444 scf/stb and IPR5
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
5635 scf/stb and IPR5
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
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