SlideShare a Scribd company logo
1 of 13
Download to read offline
1
Effect of Gas Injection Rate on Oil Production Rate: Details of Operating Mechanism
Asekhame U. Yadua, Nigerian Petroleum Development Company (NPDC)
Abstract
It is well known that, during gas lift operations, as the gas injection rate increases, the operating oil
production rate increases, gets to a peak, then begins to decline – resulting in the parabolic shape of the
gas lift performance curve. In this work, the mechanism behind this phenomenon is unravelled and
clearly explained, with the aid of mathematics and MS Excel. It is shown that, as gas injection rate
increases, the gravitational pressure drop in a producing oil well will keep decreasing while the frictional
pressure drop will keep increasing. During gas injection, oil production rate increases when the modulus
of the change in gravitational pressure drop is greater than the modulus of the change in frictional
pressure drop; and oil production rate declines when the modulus of the change in frictional pressure
drop is greater than the modulus of the change in gravitational pressure drop.
Keywords: Gaslift, production optimisation, well performance.
1. Introduction
At some point during the life of a well, the oil production rate may be less than what is desired, hence,
necessitating an artificial lift technique. Gaslift, the only artificial lift technique that does not require the
installation of a downhole pump is widely used in the industry because it is relatively more reliable, simpler
and more flexible in terms of production rates and depth of lift (Bellarby 2009). Gas lift entails the injection
of compressed gas into the lower section of the tubing, to enhance well productivity. The injected gas does
this in two ways:
 It mixes with the liquid column, reduces the density and viscosity of the column, thereby
making it easier for the liquid to get to the surface.
 It expands and displaces the liquid to the surface (Takacs 2005; Guo et al. 2007a).
It is well known that, as gas injection rate increases, oil production rate increases, gets to a peak, then
begins to decline. In this paper I present a detailed explanation of this phenomenon, with the aid of
mathematics. Numerical simulation with MS Excel was carried out to buttress and validate the analytical
model.
2. Well performance
The performance of a well is determined by the combination of the inflow performance relationship (IPR)
curve of the reservoir and the outflow performance relationship (OPR) curve of the wellbore, also known as
the Tubing Performance relationship (TPR). The point of intersection of the IPR and the TPR curve is the
operating point of the well.
2
2.1. IPR
Darcy’s Law for steady-state radial flow with formation damage will be used in this work. The equation is as
follows (Ahmed 2006; Bedrikovetsky et al. 2012):
………………………………………………………………………………..(1)
2.2. TPR
Considering the fact that flow properties vary in the three Cartesian coordinates and are unsteady, flow in
an oil well is an extremely complex problem. To develop some understanding of tubing performance, it is
convenient to simplify the flow to single-phase, one-dimensional flow (flow properties only vary along the
length of the tubing).
Consider oil flowing from the bottom to the top (wellhead) of a single-diameter tubing string of measured
depth and true vertical depth (see Fig. 1). The law of conservation of energy yields the equation for
pressure drop along a tubing string. The total pressure drop in a tubing string is the sum of gravitational
pressure drop, acceleration pressure drop, and frictional pressure drop. The general form of the equation is
. …………………………………………………………………...(2)
The explicit formula for the total pressure drop in the tubing is (Guo et al. 2007b)
. ………………………………………....................................(3)
The first, second and third terms of the right hand side of Eq. 3 are the gravitational pressure drop,
accelerational pressure drop, and frictional pressure drop respectively.
Assuming the flow is steady, homogeneous and turbulent; substituting for u and for A in the
third term of the right hand side of Eq. 3; and rearranging yields
.
Simplifying the above equation yields
. ………………………………………………(4)
Rearranging Eq. 4 yields
And
3
, ………….............................................(5)
where is the water cut and is the fractional flow for gas in the well.
. ………………………………………………………………………………………………(6)
Converting the unit to barrels per day, Eq. 5 becomes
. ……………………………….(7)
Eq. 7 is the TPR used for the simulation.
2.2.1. Effect of gas injection on TPR
When gas is injected into a producing oil well, the nature of the well fluid changes, resulting in a new TPR
curve. For example, the density of the liquid column changes from to
. ……………………………………………………………………...............................(8)
where .
Substituting value in Eq. 7 yields
. …..………………(9)
The above equation was used to calculate the various TPR curves. The fractional flow for gas is directly
proportional to gas injection rate, as shown below.
.
Rearranging the above equation yields
………………………………………………………………………………………………….(10)
But Gas/liquid ratio ,
……………………………………………………………………………....................................(11)
As gas injection rate increases, the gas occupies more space in the well, resulting in increasing gas/liquid
ratio. When , . As , .
4
. .……………………………………………………………………(12)
Therefore, as gas/liquid ratio tends to infinity, fractional flow for gas tends to unity. So, as the gas injection
rate increases, the gas/liquid ratio increases and the fractional flow for gas approaches unity. And as the
fractional flow for gas approaches unity (as ), the well effectively becomes a gas well and liquid
production rate declines. For a given gas injection rate there is a corresponding value of gas/liquid ratio and
fractional flow for gas. And a given value of fractional flow for gas has a corresponding TPR curve, given
that all other factors remain constant.
So, sensitizing on bottomhole flowing pressure (BHFP) will yield corresponding values of oil production
rate . The plot of BHFP versus oil production rate produces the TPR curve for a given value of fractional
flow for gas as shown in Fig. 2.
2.2.2. Effect of gas injection rate on gravitational pressure drop.
Consider the equation for gravitational pressure drop
. …………………………………………………………………………………………………..(13)
Since the acceleration due to gravity and the true vertical depth of the tubing are constant, the critical
factor here is the mixture density .
Eq. 8 can be rewritten as
.
At all times, the fractional flow for gas falls in the range and . Therefore, the
gravitational pressure drop will keep reducing as gas injection rate increases ( ).
2.2.3. Effect of gas injection rate on frictional pressure drop.
Consider the equation for frictional pressure drop
. …………………………………………….......................................(14)
To compare scenarios, we keep constant. Since other parameters (f, , and water cut) are kept
constant as well, the critical factor is:
5
. ………………………………………………………………………………………………....(15)
The minimum value of is 0 and the maximum value is 1. Using limits to sensitize on yields
and
. ..…………………………………………………………………………..(16)
Therefore, as the fractional flow for gas increases, the critical factor also increases. This shows that the
frictional pressure drop will keep increasing as more gas is injected into the well.
2.2.4. Effect of gas injection rate on operating point
Now it is clear that, as gas injection rate increases the gravitational pressure drop decreases, while the
frictional pressure drop increases. And it has been established that a given value of fractional flow for
gas will result in a unique TPR curve, given that all other factors remain constant. When increases, the
TPR changes position – it either moves westward or eastward (see Eq. 9 and Fig. 2). When the TPR
moves westward, the TPR-IPR point of intersection also moves westward, resulting in lower oil production
rate; and when the TPR moves eastward, the TPR-IPR point of intersection also moves eastward, resulting
in a higher oil production rate. When the TPR moves westward, it shows that a higher value of is
required for a given value of and and when it moves eastward, it shows that a lower value of is
required for a given value of and . In other words, an increase in the required due to increase in
, for a given and indicates a decline in oil production rate; while a decrease in the required due
to increase in , for a given and indicates a boost in oil production rate (see Fig. 3).
3. How exactly does change as increases?
Consider the well pressure drop equation under steady-state flow and constant wellhead pressure at a
given value of oil production rate :
Starting from point 1;
, …………………………………………………………………………….(17)
at point 2,
. …………………………………………………………………………….(18)
Subtracting Eq. 17 from Eq. 18 yields
. ……………….................................(19)
6
. ……………………………………………………………………………………...(20)
As gas injection rate increases, will always be less than and will always be greater
than , as aforementioned. Therefore, and .
To have a boost in oil production rate, the TPR curve must move eastward (i.e. under constant
and a given value of must be less than zero). For this to happen, the following condition must be
fulfilled:
That is, the modulus of the change in gravitational pressure drop must be greater than the modulus of the
change in frictional pressure drop. In other words, the reduction in gravitational pressure drop must
dominate the increase in frictional pressure drop when gas injection rate increases.
And to have a decline in oil production rate, the TPR curve must move westward (i.e. under constant
and a given value of must be greater than zero). For this to happen, the following condition must be
fulfilled:
That is, the modulus of the change in gravitational pressure drop must be less than the modulus of the
change in frictional pressure drop. In other words, the increase in frictional pressure drop must dominate
the reduction in gravitational pressure drop when gas injection rate increases.
4. Simulation, results and discussions
Eqs. 1 and 9 were used for the IPR and TPR calculations respectively. MS Excel was used to run the
simulations. Apart from the density of water, other input data were arbitrarily chosen (see Tables 1 and 2).
Each TPR curve plotted corresponds to a given value of fractional flow for gas (see Fig. 4). All other
parameters in the TPR formula were kept constant. To determine the optimum fractional flow for gas , and
consequently the optimum gas injection rate, the operating oil production rate derived from Fig. 4 was
plotted against the corresponding value of (see Fig. 5).
From Fig. 4, it can be seen that as increases from 0 to 0.3, the TPR curve keeps moving eastward,
resulting in higher production rates. When was increased to 0.5, the TPR curve moved westward and this
trend continued as was increased to 1, resulting in lower production rates. Fig. 5 clearly illustrates the
explanation in the preceding section. At , the oil production rate is 2,340 bbl/day. As increases, the
oil production rate increases (when reduction in gravitational pressure drop dominates the increase in
frictional pressure drop), gets to the peak point = 0.26, = 2,475 bbl/day, then begins to decline to the
point = 1, = 0 bbl/day (as the increase in frictional pressure drop starts dominating the reduction in
gravitational pressure drop).
7
5. Conclusions
1. Gas injection into a producing oil well changes the TPR curve, resulting in new operating point(s).
2. As gas injection rate increases, the gravitational pressure drop keeps decreasing while the
frictional pressure drop keeps increasing.
3. When the modulus of the change in gravitational pressure drop is greater than the modulus of the
change in frictional pressure drop, oil production rate increases; and when the modulus of the
change in frictional pressure drop is greater than the modulus of the change in gravitational
pressure drop, oil production rate decreases.
4. On the gas lift performance curve (Fig. 5), the area to the left of the abscissa of the optimum point
is the area where reduction in gravitational pressure drop dominates the increase in frictional
pressure drop; and the area to the right of the abscissa of the optimum point is the area where
increase in frictional pressure drop dominates reduction in gravitational pressure drop.
5. The optimum fractional flow for gas is always in the range .
Nomenclature
Roman letters
Dt = tubing internal diameter, L, ft
fF = Fanning friction factor
g = acceleration due to gravity, L , ft/s
2
h = payzone thickness, L, ft
kO = effective permeability to oil, , mD
Lmd = measured depth of tubing, L, ft
Lv = true vertical depth of tubing, L, ft
pA = accelerational pressure drop, m , psi
pe = pressure at drainage radius, m , psi
pF = frictional pressure drop, m , psi
pG = gravitational pressure drop, , psi
pT = total pressure drop in tubing string, , psi
pwf = bottomhole flowing pressure, , psi
pwh = wellhead flowing pressure, , psi
8
qO = oil flow rate in the reservoir, , ft
3
/s [bbl/day]
QG = gas flow rate in the well, , ft
3
/s
QL = liquid flow rate in the well, , ft
3
/s [bbl/day]
QO = oil flow rate in the well, , ft
3
/s [bbl/day]
QT = total flow rate in the well, , ft
3
/s [bbl/day]
QW = water flow rate in the well, , ft
3
/s [bbl/day]
re = drainage radius, L, ft
rw = wellbore radius, L, ft
s = skin factor
u = velocity, L , ft/s
VG = volume of gas in the well, , ft
3
VL = volume of liquid in the well, , ft
3
Greek letters
= fractional flow for gas
= gas/liquid ratio
= change
= viscosity of oil, m , cp
= pi
= density, m , lbm/ft
3
= gas density, m , lbm/ft
3
= liquid density, m , lbm/ft
3
= gas-liquid mixture density, m , lbm/ft
3
= oil density, m , lbm/ft
3
= water density, m , lbm/ft
3
9
References
(1) Bellarby, J. 2009. Artificial Lift. In Developments in Petroleum Science, Vol. 56, 303 – 369. Elsevier.
(2) Takacs, G. 2005. Gas Lift Manual. Oklahoma: PennWell Corporation.
(3) Guo, B., Lyons, W.C., Ghalambor, A. 2007a. Gas Lift. In Petroleum Production Engineering, Chap. 13,
181-206. Burlington, Massachusetts: Gulf Professional Publishing/Elsevier.
(4) Ahmed, T. 2006. Reservoir Engineering Handbook, third edition. Burlington, Massachusetts: Gulf
Professional Publishing/Elsevier.
(5) Bedrikovetsky, P., Vaz, A., Machado, F. et al. 2012. Skin Due to Fines Mobilization, Migration, and
Straining During Steady-State Oil Production. Petroleum Science and Technology 30 (15): 1539-1547.
http://dx.doi.org/10.1080/10916466.2011.653702
(6) Guo, B., Lyons, W.C., Ghalambor, A. 2007b. Wellbore Performance. In Petroleum Production
Engineering, Chap. 4, 46-58. Burlington, Massachusetts: Gulf Professional Publishing/Elsevier.
TABLE 1—DATA OF IPR CALCULATION
ko (mD) h (ft) pe (psi) pwf (psi) re (ft) rw (ft) s qo (bbl/day)
120 120 5000 0 1.8 2932 0.3177 1.5 26641.36038
500 23977.22434
1000 21313.08831
1500 18648.95227
2000 15984.81623
2500 13320.68019
3000 10656.54415
3500 7992.408115
4000 5328.272077
4500 2664.136038
5000 0
TABLE 2—INPUT DATA FOR TPR CALCULATIONS
Dt (ft) QW/QL pwf (psi) pwh (psi)
(lbm/ft3
)
(lbm/ft3
) Lv (ft) fF Lmd (ft)
0.1875 0.6 0 120 0.072 58 7391 0.0065 8900
500
1000
1500
2000
2500
3000
3500
4000
4500
5000
10
Fig. 1—Flow along a tubing string (adapted from Guo et al. 2007b).
Fig. 2—Effect of gas injection rate on TPR curve.
11
Fig. 3—Effect of gas injection rate on operating oil production rate.
Fig. 4—Calculated IPR and TPR curves for various values of fractional flow for gas.
250
1250
2250
3250
4250
5250
0 500 1000 1500 2000 2500
BottomholeFlowingPressure,pwf,psi
Oil Production Rate, Qo, bbl/day
IPR
TPR 1 (beta = 0)
TPR 2 (beta = 0.1)
TPR 3 (beta = 0.2)
TPR 4 (beta = 0.3)
TPR 5 (beta = 0.5)
TPR 6 (beta = 0.7)
TPR 7 (beta = 0.9)
TPR 8 (beta = 1)
12
Fig. 5—Gas lift performance curve.
SI metric conversion factors
Bbl x 1.589873 E-01 = m
3
cp x 1.0
*
E-03 = Pa.s
ft x 3.048
*
E-01 = m
lbm x 4.535924 E-01 = kg
psi x 6.894757 E+00 = kPa
*
Conversion factor is exact.
Author
Asekhame U. Yadua is a graduate Facilities Engineer at the Nigerian Petroleum Development Company
(NPDC), a subsidiary of the Nigerian National Petroleum Corporation (NNPC). His research interests
include Petroleum Production Engineering, Process Engineering, and Reservoir Engineering. He holds a
BEng degree in Chemical Engineering (First Class Honours) from Covenant University, Nigeria, and an
MSc degree in Oil and Gas Engineering (Distinction) from the University of Aberdeen. He is a member of
the Society of Petroleum Engineers (SPE) and Energy Institute (EI).
Telephone numbers: +234 8183117508 and +234 8106853967
0
250
500
750
1000
1250
1500
1750
2000
2250
2500
2750
0 0.2 0.4 0.6 0.8 1
OilProductionRate,Qo,bbl/day
Optimum Point (0.26, 2475)
Fractional Flow for Gas,
13
E-mail addresses: aseyadua@gmail.com and yadua.au@npdc-nigeria.com
Office address: NPDC, 62/64 Sapele Road, Benin City, Nigeria

More Related Content

What's hot

Q913 re1 w5 lec 20
Q913 re1 w5 lec 20Q913 re1 w5 lec 20
Q913 re1 w5 lec 20AFATous
 
Introduction - Artificial lift
Introduction - Artificial liftIntroduction - Artificial lift
Introduction - Artificial liftAndi Anriansyah
 
Q922+de2+l08 v1
Q922+de2+l08 v1Q922+de2+l08 v1
Q922+de2+l08 v1AFATous
 
Q922+de2+l07 v1
Q922+de2+l07 v1Q922+de2+l07 v1
Q922+de2+l07 v1AFATous
 
Q913 re1 w4 lec 13
Q913 re1 w4 lec 13Q913 re1 w4 lec 13
Q913 re1 w4 lec 13AFATous
 
Overview of artificial lift technology and introduction to esp system
Overview of artificial lift technology and introduction to esp systemOverview of artificial lift technology and introduction to esp system
Overview of artificial lift technology and introduction to esp systemGiuseppe Moricca
 
Q913 re1 w4 lec 15
Q913 re1 w4 lec 15Q913 re1 w4 lec 15
Q913 re1 w4 lec 15AFATous
 
Integrated Historical Data Workflow: Maximizing the Value of a Mature Asset
Integrated Historical Data Workflow: Maximizing the Value of a Mature AssetIntegrated Historical Data Workflow: Maximizing the Value of a Mature Asset
Integrated Historical Data Workflow: Maximizing the Value of a Mature AssetSociety of Petroleum Engineers
 
13 artificial-lift
13 artificial-lift13 artificial-lift
13 artificial-liftjuanca0106
 
FinalProjectFall2014presentation
FinalProjectFall2014presentationFinalProjectFall2014presentation
FinalProjectFall2014presentationMichael Okuneye
 
Artificial Lift Whitepaper: Making Your ESP Talk To You
Artificial Lift Whitepaper: Making Your ESP Talk To YouArtificial Lift Whitepaper: Making Your ESP Talk To You
Artificial Lift Whitepaper: Making Your ESP Talk To YouDean Murphy
 
Dst (Drill Stem Test)
Dst (Drill Stem Test)Dst (Drill Stem Test)
Dst (Drill Stem Test)Mubarik Rao
 
MEB and Wellbore Performance
MEB and Wellbore PerformanceMEB and Wellbore Performance
MEB and Wellbore PerformanceAjay Suri
 
Underbalance drilling equipment
Underbalance  drilling equipmentUnderbalance  drilling equipment
Underbalance drilling equipmentshivan abdalrahman
 

What's hot (20)

Q913 re1 w5 lec 20
Q913 re1 w5 lec 20Q913 re1 w5 lec 20
Q913 re1 w5 lec 20
 
Introduction - Artificial lift
Introduction - Artificial liftIntroduction - Artificial lift
Introduction - Artificial lift
 
Kick t1
Kick t1Kick t1
Kick t1
 
Gas lift design
Gas lift designGas lift design
Gas lift design
 
Q922+de2+l08 v1
Q922+de2+l08 v1Q922+de2+l08 v1
Q922+de2+l08 v1
 
Q922+de2+l07 v1
Q922+de2+l07 v1Q922+de2+l07 v1
Q922+de2+l07 v1
 
Q913 re1 w4 lec 13
Q913 re1 w4 lec 13Q913 re1 w4 lec 13
Q913 re1 w4 lec 13
 
Overview of artificial lift technology and introduction to esp system
Overview of artificial lift technology and introduction to esp systemOverview of artificial lift technology and introduction to esp system
Overview of artificial lift technology and introduction to esp system
 
Q913 re1 w4 lec 15
Q913 re1 w4 lec 15Q913 re1 w4 lec 15
Q913 re1 w4 lec 15
 
Integrated Historical Data Workflow: Maximizing the Value of a Mature Asset
Integrated Historical Data Workflow: Maximizing the Value of a Mature AssetIntegrated Historical Data Workflow: Maximizing the Value of a Mature Asset
Integrated Historical Data Workflow: Maximizing the Value of a Mature Asset
 
Hydraulic fracturing
Hydraulic fracturingHydraulic fracturing
Hydraulic fracturing
 
13 artificial-lift
13 artificial-lift13 artificial-lift
13 artificial-lift
 
Drill stem testing
Drill stem testingDrill stem testing
Drill stem testing
 
FinalProjectFall2014presentation
FinalProjectFall2014presentationFinalProjectFall2014presentation
FinalProjectFall2014presentation
 
Artificial Lift Whitepaper: Making Your ESP Talk To You
Artificial Lift Whitepaper: Making Your ESP Talk To YouArtificial Lift Whitepaper: Making Your ESP Talk To You
Artificial Lift Whitepaper: Making Your ESP Talk To You
 
Reservoir
ReservoirReservoir
Reservoir
 
Dst (Drill Stem Test)
Dst (Drill Stem Test)Dst (Drill Stem Test)
Dst (Drill Stem Test)
 
MEB and Wellbore Performance
MEB and Wellbore PerformanceMEB and Wellbore Performance
MEB and Wellbore Performance
 
Underbalance drilling equipment
Underbalance  drilling equipmentUnderbalance  drilling equipment
Underbalance drilling equipment
 
Formation Damage and Acid Stimulation Presentation 2.
Formation Damage and Acid Stimulation Presentation 2.Formation Damage and Acid Stimulation Presentation 2.
Formation Damage and Acid Stimulation Presentation 2.
 

Viewers also liked

Omar-Omrane-Final-report
Omar-Omrane-Final-reportOmar-Omrane-Final-report
Omar-Omrane-Final-reportOmar Omrane
 
Production Optimization
Production OptimizationProduction Optimization
Production OptimizationWin Nyunt Aung
 
A Study Of Production Optimization Of An Oil Copy
A Study Of Production Optimization Of An Oil   CopyA Study Of Production Optimization Of An Oil   Copy
A Study Of Production Optimization Of An Oil Copyaadrish
 
Tubing Performance Relation (TPR)
Tubing Performance Relation (TPR)Tubing Performance Relation (TPR)
Tubing Performance Relation (TPR)James Craig
 
Well Test Design and Analysis
Well Test Design and Analysis Well Test Design and Analysis
Well Test Design and Analysis petroEDGE
 
Larry Shultz presents TexasEOR.com Exhaust Gas Injection CO2 Enhanced Oil Rec...
Larry Shultz presents TexasEOR.com Exhaust Gas Injection CO2 Enhanced Oil Rec...Larry Shultz presents TexasEOR.com Exhaust Gas Injection CO2 Enhanced Oil Rec...
Larry Shultz presents TexasEOR.com Exhaust Gas Injection CO2 Enhanced Oil Rec...Larry Shultz
 
Reservoir evaluation method 101
Reservoir evaluation method 101Reservoir evaluation method 101
Reservoir evaluation method 101bachhva
 
1053 tubing%20 performance1
1053 tubing%20 performance11053 tubing%20 performance1
1053 tubing%20 performance1Dani Garnida
 
Nodal Analysis introduction to inflow and outflow performance - next
Nodal Analysis   introduction to inflow and outflow performance - nextNodal Analysis   introduction to inflow and outflow performance - next
Nodal Analysis introduction to inflow and outflow performance - nextgusgon
 
Material balance Equation
  Material balance Equation  Material balance Equation
Material balance EquationAshfaq Ahmad
 
Enhanced Oil Recovery EOR using flooding polymer ( Polyacrylamide )
Enhanced Oil Recovery EOR using flooding polymer ( Polyacrylamide )Enhanced Oil Recovery EOR using flooding polymer ( Polyacrylamide )
Enhanced Oil Recovery EOR using flooding polymer ( Polyacrylamide )Al Mo'taz Bellah
 
Crude oil Production System
Crude oil Production System Crude oil Production System
Crude oil Production System Tobiloba Omitola
 

Viewers also liked (18)

Omar-Omrane-Final-report
Omar-Omrane-Final-reportOmar-Omrane-Final-report
Omar-Omrane-Final-report
 
Production Optimization
Production OptimizationProduction Optimization
Production Optimization
 
A Study Of Production Optimization Of An Oil Copy
A Study Of Production Optimization Of An Oil   CopyA Study Of Production Optimization Of An Oil   Copy
A Study Of Production Optimization Of An Oil Copy
 
Tubing Performance Relation (TPR)
Tubing Performance Relation (TPR)Tubing Performance Relation (TPR)
Tubing Performance Relation (TPR)
 
Cmg presentation
Cmg presentationCmg presentation
Cmg presentation
 
Well Test Design and Analysis
Well Test Design and Analysis Well Test Design and Analysis
Well Test Design and Analysis
 
Larry Shultz presents TexasEOR.com Exhaust Gas Injection CO2 Enhanced Oil Rec...
Larry Shultz presents TexasEOR.com Exhaust Gas Injection CO2 Enhanced Oil Rec...Larry Shultz presents TexasEOR.com Exhaust Gas Injection CO2 Enhanced Oil Rec...
Larry Shultz presents TexasEOR.com Exhaust Gas Injection CO2 Enhanced Oil Rec...
 
Reservoir evaluation method 101
Reservoir evaluation method 101Reservoir evaluation method 101
Reservoir evaluation method 101
 
1053 tubing%20 performance1
1053 tubing%20 performance11053 tubing%20 performance1
1053 tubing%20 performance1
 
Cpf nilepet
Cpf nilepetCpf nilepet
Cpf nilepet
 
Oil and gas separators
Oil and gas separatorsOil and gas separators
Oil and gas separators
 
Oil and gas separators
Oil and gas separatorsOil and gas separators
Oil and gas separators
 
Nodal Analysis introduction to inflow and outflow performance - next
Nodal Analysis   introduction to inflow and outflow performance - nextNodal Analysis   introduction to inflow and outflow performance - next
Nodal Analysis introduction to inflow and outflow performance - next
 
Material balance Equation
  Material balance Equation  Material balance Equation
Material balance Equation
 
Enhanced Oil Recovery EOR using flooding polymer ( Polyacrylamide )
Enhanced Oil Recovery EOR using flooding polymer ( Polyacrylamide )Enhanced Oil Recovery EOR using flooding polymer ( Polyacrylamide )
Enhanced Oil Recovery EOR using flooding polymer ( Polyacrylamide )
 
Separator
SeparatorSeparator
Separator
 
Crude oil Production System
Crude oil Production System Crude oil Production System
Crude oil Production System
 
Three Phase Separators
Three Phase SeparatorsThree Phase Separators
Three Phase Separators
 

Similar to Effect of Gas Injection Rate on Oil Production Rate

Axial Flow and Radial Flow.pdf
Axial Flow and Radial Flow.pdfAxial Flow and Radial Flow.pdf
Axial Flow and Radial Flow.pdfethiopianart2020
 
Evaluation of steam jet ejectors
Evaluation of steam jet ejectorsEvaluation of steam jet ejectors
Evaluation of steam jet ejectorsBhaskar Social
 
M.Sc.Thesis-Reda Ragab-2008
M.Sc.Thesis-Reda Ragab-2008M.Sc.Thesis-Reda Ragab-2008
M.Sc.Thesis-Reda Ragab-2008Reda Ragab
 
Steam Turbines & Gearing (GJ ROY).pdf
Steam Turbines & Gearing (GJ ROY).pdfSteam Turbines & Gearing (GJ ROY).pdf
Steam Turbines & Gearing (GJ ROY).pdfNitinChaurasia15
 
Flash Steam and Steam Condensates in Return Lines
Flash Steam and Steam Condensates in Return LinesFlash Steam and Steam Condensates in Return Lines
Flash Steam and Steam Condensates in Return LinesVijay Sarathy
 
Fundamentals of Centrifugal Compressor - Head (revised)
Fundamentals of Centrifugal Compressor - Head (revised)Fundamentals of Centrifugal Compressor - Head (revised)
Fundamentals of Centrifugal Compressor - Head (revised)Sudhindra Tiwari
 
Effect of flow coefficient and loading coefficient on
Effect of flow coefficient and loading coefficient onEffect of flow coefficient and loading coefficient on
Effect of flow coefficient and loading coefficient oneSAT Publishing House
 
Effect of flow coefficient and loading coefficient on the radial inflow turbi...
Effect of flow coefficient and loading coefficient on the radial inflow turbi...Effect of flow coefficient and loading coefficient on the radial inflow turbi...
Effect of flow coefficient and loading coefficient on the radial inflow turbi...eSAT Journals
 
Economic benefits of compressor analysis
Economic benefits of compressor analysisEconomic benefits of compressor analysis
Economic benefits of compressor analysisglyn learmonth
 
3.4 pascal principle answer
3.4 pascal principle answer3.4 pascal principle answer
3.4 pascal principle answerSuriyati Yusoff
 
391861703-Mod-5-Fan-Measurement-and-Testing.pdf
391861703-Mod-5-Fan-Measurement-and-Testing.pdf391861703-Mod-5-Fan-Measurement-and-Testing.pdf
391861703-Mod-5-Fan-Measurement-and-Testing.pdfBlentBulut5
 
FUEL INJECTION AND SPRAY FORMATION
FUEL INJECTION AND SPRAY FORMATIONFUEL INJECTION AND SPRAY FORMATION
FUEL INJECTION AND SPRAY FORMATIONAhmed Hamza
 
R&ac lecture 21
R&ac lecture 21R&ac lecture 21
R&ac lecture 21sayed fathy
 

Similar to Effect of Gas Injection Rate on Oil Production Rate (20)

Axial Flow and Radial Flow.pdf
Axial Flow and Radial Flow.pdfAxial Flow and Radial Flow.pdf
Axial Flow and Radial Flow.pdf
 
Evaluation of steam jet ejectors
Evaluation of steam jet ejectorsEvaluation of steam jet ejectors
Evaluation of steam jet ejectors
 
0 4
0 40 4
0 4
 
M.Sc.Thesis-Reda Ragab-2008
M.Sc.Thesis-Reda Ragab-2008M.Sc.Thesis-Reda Ragab-2008
M.Sc.Thesis-Reda Ragab-2008
 
Ip3314661469
Ip3314661469Ip3314661469
Ip3314661469
 
Steam Turbines & Gearing (GJ ROY).pdf
Steam Turbines & Gearing (GJ ROY).pdfSteam Turbines & Gearing (GJ ROY).pdf
Steam Turbines & Gearing (GJ ROY).pdf
 
Flash Steam and Steam Condensates in Return Lines
Flash Steam and Steam Condensates in Return LinesFlash Steam and Steam Condensates in Return Lines
Flash Steam and Steam Condensates in Return Lines
 
Fundamentals of Centrifugal Compressor - Head (revised)
Fundamentals of Centrifugal Compressor - Head (revised)Fundamentals of Centrifugal Compressor - Head (revised)
Fundamentals of Centrifugal Compressor - Head (revised)
 
Effect of flow coefficient and loading coefficient on
Effect of flow coefficient and loading coefficient onEffect of flow coefficient and loading coefficient on
Effect of flow coefficient and loading coefficient on
 
Effect of flow coefficient and loading coefficient on the radial inflow turbi...
Effect of flow coefficient and loading coefficient on the radial inflow turbi...Effect of flow coefficient and loading coefficient on the radial inflow turbi...
Effect of flow coefficient and loading coefficient on the radial inflow turbi...
 
Axial flow compressors
Axial flow compressorsAxial flow compressors
Axial flow compressors
 
Steam engine
Steam engineSteam engine
Steam engine
 
Economic benefits of compressor analysis
Economic benefits of compressor analysisEconomic benefits of compressor analysis
Economic benefits of compressor analysis
 
Axial Flow Compressor.
Axial Flow Compressor. Axial Flow Compressor.
Axial Flow Compressor.
 
3.4 pascal principle answer
3.4 pascal principle answer3.4 pascal principle answer
3.4 pascal principle answer
 
Flumping
FlumpingFlumping
Flumping
 
FlowTypesRE.pdf
FlowTypesRE.pdfFlowTypesRE.pdf
FlowTypesRE.pdf
 
391861703-Mod-5-Fan-Measurement-and-Testing.pdf
391861703-Mod-5-Fan-Measurement-and-Testing.pdf391861703-Mod-5-Fan-Measurement-and-Testing.pdf
391861703-Mod-5-Fan-Measurement-and-Testing.pdf
 
FUEL INJECTION AND SPRAY FORMATION
FUEL INJECTION AND SPRAY FORMATIONFUEL INJECTION AND SPRAY FORMATION
FUEL INJECTION AND SPRAY FORMATION
 
R&ac lecture 21
R&ac lecture 21R&ac lecture 21
R&ac lecture 21
 

Effect of Gas Injection Rate on Oil Production Rate

  • 1. 1 Effect of Gas Injection Rate on Oil Production Rate: Details of Operating Mechanism Asekhame U. Yadua, Nigerian Petroleum Development Company (NPDC) Abstract It is well known that, during gas lift operations, as the gas injection rate increases, the operating oil production rate increases, gets to a peak, then begins to decline – resulting in the parabolic shape of the gas lift performance curve. In this work, the mechanism behind this phenomenon is unravelled and clearly explained, with the aid of mathematics and MS Excel. It is shown that, as gas injection rate increases, the gravitational pressure drop in a producing oil well will keep decreasing while the frictional pressure drop will keep increasing. During gas injection, oil production rate increases when the modulus of the change in gravitational pressure drop is greater than the modulus of the change in frictional pressure drop; and oil production rate declines when the modulus of the change in frictional pressure drop is greater than the modulus of the change in gravitational pressure drop. Keywords: Gaslift, production optimisation, well performance. 1. Introduction At some point during the life of a well, the oil production rate may be less than what is desired, hence, necessitating an artificial lift technique. Gaslift, the only artificial lift technique that does not require the installation of a downhole pump is widely used in the industry because it is relatively more reliable, simpler and more flexible in terms of production rates and depth of lift (Bellarby 2009). Gas lift entails the injection of compressed gas into the lower section of the tubing, to enhance well productivity. The injected gas does this in two ways:  It mixes with the liquid column, reduces the density and viscosity of the column, thereby making it easier for the liquid to get to the surface.  It expands and displaces the liquid to the surface (Takacs 2005; Guo et al. 2007a). It is well known that, as gas injection rate increases, oil production rate increases, gets to a peak, then begins to decline. In this paper I present a detailed explanation of this phenomenon, with the aid of mathematics. Numerical simulation with MS Excel was carried out to buttress and validate the analytical model. 2. Well performance The performance of a well is determined by the combination of the inflow performance relationship (IPR) curve of the reservoir and the outflow performance relationship (OPR) curve of the wellbore, also known as the Tubing Performance relationship (TPR). The point of intersection of the IPR and the TPR curve is the operating point of the well.
  • 2. 2 2.1. IPR Darcy’s Law for steady-state radial flow with formation damage will be used in this work. The equation is as follows (Ahmed 2006; Bedrikovetsky et al. 2012): ………………………………………………………………………………..(1) 2.2. TPR Considering the fact that flow properties vary in the three Cartesian coordinates and are unsteady, flow in an oil well is an extremely complex problem. To develop some understanding of tubing performance, it is convenient to simplify the flow to single-phase, one-dimensional flow (flow properties only vary along the length of the tubing). Consider oil flowing from the bottom to the top (wellhead) of a single-diameter tubing string of measured depth and true vertical depth (see Fig. 1). The law of conservation of energy yields the equation for pressure drop along a tubing string. The total pressure drop in a tubing string is the sum of gravitational pressure drop, acceleration pressure drop, and frictional pressure drop. The general form of the equation is . …………………………………………………………………...(2) The explicit formula for the total pressure drop in the tubing is (Guo et al. 2007b) . ………………………………………....................................(3) The first, second and third terms of the right hand side of Eq. 3 are the gravitational pressure drop, accelerational pressure drop, and frictional pressure drop respectively. Assuming the flow is steady, homogeneous and turbulent; substituting for u and for A in the third term of the right hand side of Eq. 3; and rearranging yields . Simplifying the above equation yields . ………………………………………………(4) Rearranging Eq. 4 yields And
  • 3. 3 , ………….............................................(5) where is the water cut and is the fractional flow for gas in the well. . ………………………………………………………………………………………………(6) Converting the unit to barrels per day, Eq. 5 becomes . ……………………………….(7) Eq. 7 is the TPR used for the simulation. 2.2.1. Effect of gas injection on TPR When gas is injected into a producing oil well, the nature of the well fluid changes, resulting in a new TPR curve. For example, the density of the liquid column changes from to . ……………………………………………………………………...............................(8) where . Substituting value in Eq. 7 yields . …..………………(9) The above equation was used to calculate the various TPR curves. The fractional flow for gas is directly proportional to gas injection rate, as shown below. . Rearranging the above equation yields ………………………………………………………………………………………………….(10) But Gas/liquid ratio , ……………………………………………………………………………....................................(11) As gas injection rate increases, the gas occupies more space in the well, resulting in increasing gas/liquid ratio. When , . As , .
  • 4. 4 . .……………………………………………………………………(12) Therefore, as gas/liquid ratio tends to infinity, fractional flow for gas tends to unity. So, as the gas injection rate increases, the gas/liquid ratio increases and the fractional flow for gas approaches unity. And as the fractional flow for gas approaches unity (as ), the well effectively becomes a gas well and liquid production rate declines. For a given gas injection rate there is a corresponding value of gas/liquid ratio and fractional flow for gas. And a given value of fractional flow for gas has a corresponding TPR curve, given that all other factors remain constant. So, sensitizing on bottomhole flowing pressure (BHFP) will yield corresponding values of oil production rate . The plot of BHFP versus oil production rate produces the TPR curve for a given value of fractional flow for gas as shown in Fig. 2. 2.2.2. Effect of gas injection rate on gravitational pressure drop. Consider the equation for gravitational pressure drop . …………………………………………………………………………………………………..(13) Since the acceleration due to gravity and the true vertical depth of the tubing are constant, the critical factor here is the mixture density . Eq. 8 can be rewritten as . At all times, the fractional flow for gas falls in the range and . Therefore, the gravitational pressure drop will keep reducing as gas injection rate increases ( ). 2.2.3. Effect of gas injection rate on frictional pressure drop. Consider the equation for frictional pressure drop . …………………………………………….......................................(14) To compare scenarios, we keep constant. Since other parameters (f, , and water cut) are kept constant as well, the critical factor is:
  • 5. 5 . ………………………………………………………………………………………………....(15) The minimum value of is 0 and the maximum value is 1. Using limits to sensitize on yields and . ..…………………………………………………………………………..(16) Therefore, as the fractional flow for gas increases, the critical factor also increases. This shows that the frictional pressure drop will keep increasing as more gas is injected into the well. 2.2.4. Effect of gas injection rate on operating point Now it is clear that, as gas injection rate increases the gravitational pressure drop decreases, while the frictional pressure drop increases. And it has been established that a given value of fractional flow for gas will result in a unique TPR curve, given that all other factors remain constant. When increases, the TPR changes position – it either moves westward or eastward (see Eq. 9 and Fig. 2). When the TPR moves westward, the TPR-IPR point of intersection also moves westward, resulting in lower oil production rate; and when the TPR moves eastward, the TPR-IPR point of intersection also moves eastward, resulting in a higher oil production rate. When the TPR moves westward, it shows that a higher value of is required for a given value of and and when it moves eastward, it shows that a lower value of is required for a given value of and . In other words, an increase in the required due to increase in , for a given and indicates a decline in oil production rate; while a decrease in the required due to increase in , for a given and indicates a boost in oil production rate (see Fig. 3). 3. How exactly does change as increases? Consider the well pressure drop equation under steady-state flow and constant wellhead pressure at a given value of oil production rate : Starting from point 1; , …………………………………………………………………………….(17) at point 2, . …………………………………………………………………………….(18) Subtracting Eq. 17 from Eq. 18 yields . ……………….................................(19)
  • 6. 6 . ……………………………………………………………………………………...(20) As gas injection rate increases, will always be less than and will always be greater than , as aforementioned. Therefore, and . To have a boost in oil production rate, the TPR curve must move eastward (i.e. under constant and a given value of must be less than zero). For this to happen, the following condition must be fulfilled: That is, the modulus of the change in gravitational pressure drop must be greater than the modulus of the change in frictional pressure drop. In other words, the reduction in gravitational pressure drop must dominate the increase in frictional pressure drop when gas injection rate increases. And to have a decline in oil production rate, the TPR curve must move westward (i.e. under constant and a given value of must be greater than zero). For this to happen, the following condition must be fulfilled: That is, the modulus of the change in gravitational pressure drop must be less than the modulus of the change in frictional pressure drop. In other words, the increase in frictional pressure drop must dominate the reduction in gravitational pressure drop when gas injection rate increases. 4. Simulation, results and discussions Eqs. 1 and 9 were used for the IPR and TPR calculations respectively. MS Excel was used to run the simulations. Apart from the density of water, other input data were arbitrarily chosen (see Tables 1 and 2). Each TPR curve plotted corresponds to a given value of fractional flow for gas (see Fig. 4). All other parameters in the TPR formula were kept constant. To determine the optimum fractional flow for gas , and consequently the optimum gas injection rate, the operating oil production rate derived from Fig. 4 was plotted against the corresponding value of (see Fig. 5). From Fig. 4, it can be seen that as increases from 0 to 0.3, the TPR curve keeps moving eastward, resulting in higher production rates. When was increased to 0.5, the TPR curve moved westward and this trend continued as was increased to 1, resulting in lower production rates. Fig. 5 clearly illustrates the explanation in the preceding section. At , the oil production rate is 2,340 bbl/day. As increases, the oil production rate increases (when reduction in gravitational pressure drop dominates the increase in frictional pressure drop), gets to the peak point = 0.26, = 2,475 bbl/day, then begins to decline to the point = 1, = 0 bbl/day (as the increase in frictional pressure drop starts dominating the reduction in gravitational pressure drop).
  • 7. 7 5. Conclusions 1. Gas injection into a producing oil well changes the TPR curve, resulting in new operating point(s). 2. As gas injection rate increases, the gravitational pressure drop keeps decreasing while the frictional pressure drop keeps increasing. 3. When the modulus of the change in gravitational pressure drop is greater than the modulus of the change in frictional pressure drop, oil production rate increases; and when the modulus of the change in frictional pressure drop is greater than the modulus of the change in gravitational pressure drop, oil production rate decreases. 4. On the gas lift performance curve (Fig. 5), the area to the left of the abscissa of the optimum point is the area where reduction in gravitational pressure drop dominates the increase in frictional pressure drop; and the area to the right of the abscissa of the optimum point is the area where increase in frictional pressure drop dominates reduction in gravitational pressure drop. 5. The optimum fractional flow for gas is always in the range . Nomenclature Roman letters Dt = tubing internal diameter, L, ft fF = Fanning friction factor g = acceleration due to gravity, L , ft/s 2 h = payzone thickness, L, ft kO = effective permeability to oil, , mD Lmd = measured depth of tubing, L, ft Lv = true vertical depth of tubing, L, ft pA = accelerational pressure drop, m , psi pe = pressure at drainage radius, m , psi pF = frictional pressure drop, m , psi pG = gravitational pressure drop, , psi pT = total pressure drop in tubing string, , psi pwf = bottomhole flowing pressure, , psi pwh = wellhead flowing pressure, , psi
  • 8. 8 qO = oil flow rate in the reservoir, , ft 3 /s [bbl/day] QG = gas flow rate in the well, , ft 3 /s QL = liquid flow rate in the well, , ft 3 /s [bbl/day] QO = oil flow rate in the well, , ft 3 /s [bbl/day] QT = total flow rate in the well, , ft 3 /s [bbl/day] QW = water flow rate in the well, , ft 3 /s [bbl/day] re = drainage radius, L, ft rw = wellbore radius, L, ft s = skin factor u = velocity, L , ft/s VG = volume of gas in the well, , ft 3 VL = volume of liquid in the well, , ft 3 Greek letters = fractional flow for gas = gas/liquid ratio = change = viscosity of oil, m , cp = pi = density, m , lbm/ft 3 = gas density, m , lbm/ft 3 = liquid density, m , lbm/ft 3 = gas-liquid mixture density, m , lbm/ft 3 = oil density, m , lbm/ft 3 = water density, m , lbm/ft 3
  • 9. 9 References (1) Bellarby, J. 2009. Artificial Lift. In Developments in Petroleum Science, Vol. 56, 303 – 369. Elsevier. (2) Takacs, G. 2005. Gas Lift Manual. Oklahoma: PennWell Corporation. (3) Guo, B., Lyons, W.C., Ghalambor, A. 2007a. Gas Lift. In Petroleum Production Engineering, Chap. 13, 181-206. Burlington, Massachusetts: Gulf Professional Publishing/Elsevier. (4) Ahmed, T. 2006. Reservoir Engineering Handbook, third edition. Burlington, Massachusetts: Gulf Professional Publishing/Elsevier. (5) Bedrikovetsky, P., Vaz, A., Machado, F. et al. 2012. Skin Due to Fines Mobilization, Migration, and Straining During Steady-State Oil Production. Petroleum Science and Technology 30 (15): 1539-1547. http://dx.doi.org/10.1080/10916466.2011.653702 (6) Guo, B., Lyons, W.C., Ghalambor, A. 2007b. Wellbore Performance. In Petroleum Production Engineering, Chap. 4, 46-58. Burlington, Massachusetts: Gulf Professional Publishing/Elsevier. TABLE 1—DATA OF IPR CALCULATION ko (mD) h (ft) pe (psi) pwf (psi) re (ft) rw (ft) s qo (bbl/day) 120 120 5000 0 1.8 2932 0.3177 1.5 26641.36038 500 23977.22434 1000 21313.08831 1500 18648.95227 2000 15984.81623 2500 13320.68019 3000 10656.54415 3500 7992.408115 4000 5328.272077 4500 2664.136038 5000 0 TABLE 2—INPUT DATA FOR TPR CALCULATIONS Dt (ft) QW/QL pwf (psi) pwh (psi) (lbm/ft3 ) (lbm/ft3 ) Lv (ft) fF Lmd (ft) 0.1875 0.6 0 120 0.072 58 7391 0.0065 8900 500 1000 1500 2000 2500 3000 3500 4000 4500 5000
  • 10. 10 Fig. 1—Flow along a tubing string (adapted from Guo et al. 2007b). Fig. 2—Effect of gas injection rate on TPR curve.
  • 11. 11 Fig. 3—Effect of gas injection rate on operating oil production rate. Fig. 4—Calculated IPR and TPR curves for various values of fractional flow for gas. 250 1250 2250 3250 4250 5250 0 500 1000 1500 2000 2500 BottomholeFlowingPressure,pwf,psi Oil Production Rate, Qo, bbl/day IPR TPR 1 (beta = 0) TPR 2 (beta = 0.1) TPR 3 (beta = 0.2) TPR 4 (beta = 0.3) TPR 5 (beta = 0.5) TPR 6 (beta = 0.7) TPR 7 (beta = 0.9) TPR 8 (beta = 1)
  • 12. 12 Fig. 5—Gas lift performance curve. SI metric conversion factors Bbl x 1.589873 E-01 = m 3 cp x 1.0 * E-03 = Pa.s ft x 3.048 * E-01 = m lbm x 4.535924 E-01 = kg psi x 6.894757 E+00 = kPa * Conversion factor is exact. Author Asekhame U. Yadua is a graduate Facilities Engineer at the Nigerian Petroleum Development Company (NPDC), a subsidiary of the Nigerian National Petroleum Corporation (NNPC). His research interests include Petroleum Production Engineering, Process Engineering, and Reservoir Engineering. He holds a BEng degree in Chemical Engineering (First Class Honours) from Covenant University, Nigeria, and an MSc degree in Oil and Gas Engineering (Distinction) from the University of Aberdeen. He is a member of the Society of Petroleum Engineers (SPE) and Energy Institute (EI). Telephone numbers: +234 8183117508 and +234 8106853967 0 250 500 750 1000 1250 1500 1750 2000 2250 2500 2750 0 0.2 0.4 0.6 0.8 1 OilProductionRate,Qo,bbl/day Optimum Point (0.26, 2475) Fractional Flow for Gas,
  • 13. 13 E-mail addresses: aseyadua@gmail.com and yadua.au@npdc-nigeria.com Office address: NPDC, 62/64 Sapele Road, Benin City, Nigeria