Gas lift system is optimized by use of PVT data combined with fluid and multiphase flow correlations. The aim of project is to develop a generalized program that eliminate the use of synthetic Gradient curves and sensitivity of system with respect to each parameter can be analyzed easily. The project is mainly based on two pressure gradient models; one is single phase flow of compressible fluids (gas) and second is multi-phase correlation developed by Hagedorn and Brown3 including Griffith correction4 of bubble flow particularly for vertical wellbores. Different but appropriate PVT correlations are adopted to suit the condition. The project is divided into two parts, first is developing single Gas lift diagram and second is multiple Gas lift diagrams which facilitate to derive Equilibrium curve, usually use to have idea of unloading valves at different depths with varying flowrates

1. Page 1 of 13
Continuous Gas Lift in Oil Wells, Computer Assisted Design
SPE Trondheim - April 2005.
Abstract
Gas lift system is optimized by use of
PVT data combined with fluid and multiphase
flow correlations. The aim of project is to
develop a generalized program that eliminate
the use of synthetic Gradient curves and
sensitivity of system with respect to each
parameter can be analyzed easily.
The project is mainly based on two
pressure gradient models; one is single phase
flow of compressible fluids (gas) and second is
multi-phase correlation developed by
Hagedorn and Brown3
including Griffith
correction4
of bubble flow particularly for
vertical wellbores. Different but appropriate
PVT correlations are adopted to suit the
condition.
The project is divided into two parts,
first is developing single Gas lift diagram and
second is multiple Gas lift diagrams which
facilitate to derive Equilibrium curve, usually
use to have idea of unloading valves at
different depths with varying flowrates.
Introduction
Here continuous gas lift system is
discussed, usually gas injection results in
reduction in the natural flowing gradient of the
reservoir fluid, and thus reducing the
hydrostatic component of the pressure
difference from the bottom to the top of the
well. The purpose is to bring the fluids to the
top at a desirable wellhead pressure while
keeping the bottomhole pressure at a value that
is small enough to provide good driving force
in the reservoir. This pressure drawdown must
not violate restrictions for sand control and
water or gas coning.
Other considerations also contribute in
designing. First, the gas that is injected is
produced with the reservoir fluid into the low
pressure system. Therefore, the low-pressure
separator must have sufficient gas separation
capacity to handle gas lift as well as formation
gas. If gas lift is to be used, it is even more
important from a production standpoint that
the low pressure separator be operated at the
lowest practical pressure.
Second, there exists a limit gas-liquid ratio
(GLR) above which the pressure difference in
the well will begin to increase because the
reduction in the hydrostatic pressure will be
offset by the increase in the friction pressure.
This phenomenon is elaborated in figure-4,5
and 6 with dummy data of Table-3 and 4.
Project Categorization
The project is divided into two
modules,
1. First module; develops the single point gas
lift diagram. For this purpose two pressure
gradient models are utilized,
a) Single phase (gas) compressible flow
model used for injected gas in annulus
with assumption of unlimited gas supply
and known surface injection pressure.
b) For two phase flow in tubing well known
multi-phase model by Hagedorn and
Brown3
is utilized in con-current direction.
For simplicity Linear IPR for
undersaturated oils is assumed.
)( wfRo ppjq −= .................(1)
j
q
pp o
Rwf −= .......................(2)
2. Methodology for Second module, is
adopted from Book of Well performance
by Michael Golan1
chapter-5, page-558,
the procedure is simple with tracing paper
but enough to get puzzle while
implementing in programming as it is
difficult to define depths prior to analysis,
but key sentence mentioned on page-557
i.e. development of several lift diagrams
thus gives good idea to understand physics

2. Page 2 of 13
of the system rather then tracing lines on
synthetic gradient curves, although the
second module develops the multi-balance
points from several gas list diagrams at
different assumed oil rates, thus giving the
equilibrium curve. This curve is
particularly important in getting idea of
placing valves specially unloading valves,
for this purpose multi-phase model is used
in two directions (con-current and
Counter-current) with respect to flow as
follows;
a) Con-current calculation uses the linear
IPR, and with that bottomhole flowing
pressure (Pwf) including only formation or
natural GLR, wellhead pressure is
determined along the depth of Well.
b) Counter-current calculations uses the
known tubing head pressure, injection gas
rate, from which injected GLR is derived
to be used in counter-current calculations;
( ) lnaturalinjectedg qGLRGLRq −= ........ (3)
natural
l
g
injected GLR
q
q
GLR += ………..(4)
Intersection of con-current and counter-
current two phase calculations thus defines
equilibrium point or node at each flowrate.
c) From that Point of Balance and
corresponding Pressure, again Gas
injection in annulus using single
compressible model, in con-current
direction is performed to give surface
injection pressure for each flowrate.
Cross-checking for the authenticity of
second module is validated with first module
at particular oil rate, and point of balance
derived by both is in considerable agreement.
Key Details
Here I will demonstrate briefly, key
equations and important procedures for flow
models and PVT correlations.
Single-Phase Compressible Flow Model
For injection of gas in annulus (counter-
current and con-current directions), the
pressure drop calculation is based on
mechanical energy balance equation; which
consists of three contributions to total pressure
drop i.e. potential (hydrostatic), kinetic energy
(velocity), friction (slippage).
FKEPE PPPP ++= ……….. (5)
where
Z
gc
g
PPE =  …………………………(6)
)(
2
2
u
g
P
c
KE =

…………………… (7)
Dg
Luf
P
c
f
F
2
2 
= …………………….… (8)
To calculate friction factor, an explicit
equation derived by chen2
based on colebook-
White implicit equation with similar accuracy
is the chen2
equation:






















+−−=
8981.0
1098.1
149.7
8257.2
log
0452.5
7065.3
log4
1
REREf
NNf
 …… (9)
Equivalent diameter while for gas injection in
annulus is defined as:
222
sin TubingODgIDCaDe
−= …… (10)
TubingODgIDCaDe
−= sin …… (11)
Two Phase Flow Model
Usually along the wellbore path
towards up, the flow segregates into two or
three phases, especially when surface pressure
or pressure at certain depth gets below bubble
point in undersaturated reservoirs. Many Gas
wells also behave in similar manner if there

3. Page 3 of 13
exits condensates or enough water (either
having dissolved gas in water or as free water).
Two-phase flow behavior depends
strongly on the distribution of the phases in the
wellbore, holdup phenomenon in which in-situ
denser phase being heldup relative to fast
moving lighter phase, described by holdup
V
V
y

 = …………………….… (12)
V
V
y 
 = …………………….… (13)
 yy −= 1 …………………… (14)
Where;
y
= holdup of denser phase
y = holdup of lighter phase (void fraction of
gas if gas-liquid)
V
= volume of denser phase in pipe segment
V = volume of lighter phase in pipe segment
V = Volume of pipe segment
Another measure of the holdup phenomenon is
the slip velocity, defined as the difference
between the average velocities of the phases,
actually it is not independent property from
holdup but another way of representing
holdup, superficial velocities relates slip and
holdup also. In General superficial velocities
are given by;
A
q
us

 = …………………..…… (15)
A
q
us

 = …………………..…… (16)
Hagedorn and Brown Correlation3
This correlation being widely used in
industry also Brown’s15
famous Gradient
curves were basically developed using HB
correlation. But today Mechanistic Models
provides good results then even HB.
The Hagedorn and Brown Correlation3
(now called other then bubble flow Hagedorn
and Brown Correlation3
as Griffith correlation4
is substituted as flow pattern converts to
bubble flow) were developed for vertical,
upward flow and are recommended only for
near-vertical wellbores. Details for whole
correlations can be found in original paper in
references.
The form of energy balance equation used in
Hagedorn-Brown Correlation3
is
( )
z
gu
Dg
uf
g
g
dz
dp cm
c
m
c 

++=
2/2 22


 ..…… (17)
sgslm uuu += …………………………..…… (18)
To calculate the pressure gradient with
eq-17, the liquid holdup is obtained from a
graphical correlation by Hagedorn-Brown
which is digitized for programming and the
friction factor is based on mixture Reynolds
number. The liquid holdup and hence the
average density is obtained from series of
charts using dimensionless numbers i.e. liquid
velocity number, gas velocity number, pipe
diameter number, liquid viscosity number.
The values of group numbers from
charts are then digitized to be used in program
using linear interpolation.
Checks for single phase is considered
that if computed solution GOR is greater then
producing GLR along the path then holdup
will be one, and program will eliminate using
dimensionless charts accounting for two-phase
behavior.
Griffith (Bubble flow) Correlation4
As the heart of the Hagedorn and
Brown Correlation3
is using the no-slip hold
when empirical correlation predicts a liquid
holdup value less than the no-slip holdup, then
Griffith correlation is used for bubble flow
regime.

4. Page 4 of 13
This correlation used a different holdup
correlation, bases the frictional pressure
gradient on the in-situ average liquid velocity,
and neglects the kinetic energy pressure
gradient, for this correlation energy balance
takes the form as;
Dg
uf
g
g
dz
dp
c
ll
c
2
2 
 += ..…………… (19)
Further details can be seen in original paper in
references4
.
PVT correlations
Gas
Here non-hydrocarbons are not taken
into account. Critical pressure and temperature
are calculated using standing5
dry hydrocarbon
correlations. For gas compressibility Factor
(Z-Factor) Dranchuk, P.M, & Abu. Kassem
J.H6
and for gas viscosity Dempsey, J.R7
correlations are used.
Oil
Bubble point pressure is determined by
standing8
. Solution GOR i.e. Rs by standing8
Dead oil viscosity by Begg16
and Beggs and
Robinson9
.Bubble point viscosity by chew and
connally10
using functional relation of Beggs
and Robinson9
. Undersaturated oil viscosity by
Vazquez and Beggs11
. Bubble point oil
formation volume factor by Standing12
California crude oils, undersaturated oil FVF
by Vazquez and Beggs11
, while undersaturated
oil compressibility is computed by standing13
.
Water
Water is not taken into account but can
be included in program, as program has option
but commented for simplicity.
Modules Description and Examples
Module-1:
This module with first sheet as INPUT DATA
gets data from user as in table-1 and calculates
the parameters for Gas lift Diagram by
pressing button “Calculate single Injection
point”
Here dummy well is defined by taking some
data from examples of Well performance by
Michael Golan1
chapter-5 and Petroleum
Production Systems by M.J.Economides14
.
Results of the calculations are generated by
program in RESULTS sheet. The figure-1 for
Gas lift is then updated accordingly, that
defines key parameters as required in any Gas
Lift diagram specially tubing head pressure,
Point of balance and point of injection for
which linear interpolation is used.
Note: here ∆Pvalve is parameter input from user,
as it depends on manufacturers supplied values
and considered beyond the scope for this time,
but can be implemented using orifice through
put equations.
Module-2:
This module gets data in sheet INPUT
DATAEQ as in table-2, in table user have to
provide appropriate assumed values for
different flowrates on which system has to be
analyzed. After entering data calculations can
be performed using button “Calculate
EQUILIBRIUM Points” Results will be
printed in sheet RESULTSEQ, and based on
those results Figure-2 defining several Lift
diagrams will be demonstrated, while based on
those values figure-3 will define the
equilibrium curve i.e. this curve displays the
relationship between the downhole injection
depth and the corresponding pressure
downstream of the downhole orifice.
Note: here option for ∆ Pvalve is provided which
can be neglected as being not good option as
far as calculation procedure is concern.
In input table Gas flowrate and
formation GLR must be provided that uses Eq-
3 to calculate injected GLR and thus from
provided tubing head pressure finds the two-

5. Page 5 of 13
phase pressure gradient from wellhead to total
depth.
While as mentioned earlier Pwf will be
used from IPR equation-2 with provided
natural GLR and then pressure gradient will be
find in con-current direction to tubing head.
Finally after interpolating balance point
values from above two-phase curves, program
will find Gas injection Gradient from solution
node (point of balance) to surface. Thus
completing the Gas Lift Diagram.
Iterative procedure Adopted
Pressure
In all programs Newton-Raphson
iterative (set tolerance) procedure is used.
Rung-Kutta and Euler may be implemented
but avoided at this time.
Temperature
For simplicity and lack of data, linear
relation between top and bottom temperatures
is used. Model has the capacity to utilized
famous correlation by Shiu. K.S. and Beggs17
flowing temperature in oil wells.
Program Authenticity
Validity of program is checked with
synthetic data of book well performance1
example 5.7-5.8, and of book Petroleum
Production Systems by M.J.Economides14
examples 19.1 to 19.6.
Table-1 and Table-2 are data from worked
examples while figure-1, figure-2 and figure-3,
are outputs which are in good agreement but as
the books uses the gradient curves so
difference is acceptable.
Different checks are provided in the
program to tackle erroneous input data and to
avoid overflow. Especially the digitized chart
values of Hagedorn and Brown Correlation3
are avoided to be extrapolated ahead and
beyond the chart’s start and end point values
as this gives erroneous results specially for
calculating Holdup with dimensionless
numbers i.e. holdup factor, liquid viscosity
number (corrected) and pipe diameter number
charts.
Limit GLR Example
This phenomenon is shown from both
Modules, with input data in Table-3 and
Table-4, while figure-4, figure-5 and figure-6,
provides inset how large values of GLR can
cause hydrostatic component dominated by
friction pressure drop.
Nomenclature
PVT = Pressure-Volume-Temperature
IPR = Inflow Performance Relation
Pwf = Bottomhole flowing pressure
GLR = Gas-Liquid Ratio, SCF/STB
GOR = Gas-Oil Ratio, SCF/STB
injectedGLR =Injected Gas-Oil Ratio, SCF/STB
naturalGLR = Natural (Formation) Gas Liquid
Ration, SCF/STB
=P Total pressure drop, psi
= PEP Potential energy pressure drop, psi
= KEP Kinetic Energy Pressure drop, psi
= FP Friction pressure drop, psi
=g Earth’s Gravitational acceleration, 32.174
ft/sec2
=cg Earth’s Gravitational constant, 32.174
ft/sec2
= Density, Ibm/ft3
=Z Elevation Difference, FT
2
u = Velocity difference, ft/sec
2
u = Velocity, ft/sec
ff =Fanning Friction Factor
L = Length, FT
D= conduit diameter, inch
ε = relative roughness factor, dimensionless
NRE = Reynolds number
De = Equivalent Diameter, inch
De2
= Equivalent Diameter, inch
CasingID=inside Diameter of Casing, inch
TubingOD= Outside Diameter of tubing, inch

6. Page 6 of 13
=gq Gas Phase Flow Rate, CF/day
=lq Liquid Phase Flow Rate, bbl/day
y
= holdup of denser phase
y = holdup of lighter phase (void fraction of
gas if gas-liquid)
V
= volume of denser phase in pipe segment
V = volume of lighter phase in pipe segment
V = Volume of pipe segment
=su Superficial Velocity, Gas (light) Phase,
ft/sec
=su Superficial Velocity, Oil (Dense) Phase,
ft/sec
q = Light Phase Flow rate. CFT/day
q = Dense Phase Flow rate. CFT/day
A = Area of Conduit, sq-ft
HB = Hagedorn and Brown
=
dz
dp
Pressure gradient, psi/ft
= In-situ average density, Ibm/ft3
f =friction factor
mu =mixture velocity, ft/sec
=sgu Superficial Velocity, Gas (light) Phase,
ft/sec
=slu Superficial Velocity, Oil (Dense) Phase,
ft/sec
l = In-situ liquid density,Ibm/ft3
lu = In-situ average liquid velocity
∆ Pvalve = Pressure Drop across Gas Lift Valve
List of Figures
Figure 1: Single Gas Lift Diagram................... 9
Figure 2: Multiple Gas Lift Diagram............... 9
Figure 3: Equilibrium Curve.......................... 10
Figure 4: Very High GLR leads Flattening of
Tubing Gradient Curves.......................... 12
Figure 5: High GLR effect in Multiple Gas
Lift Diagram............................................ 13
Figure 6: Equilibrium Curve shifts Balance
Points to total Depth................................ 13
List of Tables
Table 1: Input table for Single Gas Lift
Diagram.....................................................8
Table 2: Input table for Equilibrium curve.......8
Table 3: Input for Limit GLR check from
Single Gas Lift diagram...........................11
Table 4: Input for Limit GLR check in multi
Gas Lift Diagram .....................................11
References
1. Golan, M. and Whitson, C.H.,”Well
Performance, 2nd
Ed, prentice Hall,
Englewood cliffs, NJ, 1991.
2. Chen, N.H.,”An Explicit Equation for
Friction Factor in pipe,
Ind.Eng.Chem.Fund” 18:296, 1979.
3. Hagedorn, A.R., and Brown, K.E.,”
Experimental Study of pressure Gradients
occurring during continuous Two-phase
flow in small diameter vertical conduits,”
JPT, 475-484, April, 1965.
4. Griffith, P ., Willis, B. B., ”Two-Phase
Slug Flow,” J. Heat Transfer, trans.
ASME,Ser.D,83,307-320,
5. Standing, M.B, .:Volumetric and Phase
behavior of oil Field Hydrocarbon
Systems, SPE, Richardson, Texas (1981)
6. Dranchuk, P.M, & Abu. Kassem J.H.,
“Calculation of Z – Factor for natural
gases using equation of state”, JCPT, July
– Sept., 1975, PP, 34-36.
7. Dempsey, J.R., “Computer Routine Treats
Gas Viscosity as a Variable”, Oil & Gas
Journal, Aug. 16, 1965, PP.141-143.
8. Standing.M.B.: Oil-System Correlations,
P.P Hankbook (ed.),McGraw-Hill Books
Co.Inc., Newyork City (1962)
9. Beggs, H.D. and Robinson, J.R.:”
Estimating the Viscosity of crude oil
Systems,” JPT (September 1975)1140.
10. Chew,J.N and Connally,C.A,:”A Viscosity
Correlation for Gas-Saturated Crude
Oils,” Trans.,AIME (1959)216,23

7. Page 7 of 13
11. Vazquez,M. and Beggs,H.D.:”Correlations
for fluid Physical Property
Prediction,”JPT (june 1980) 968
12. Standing. M.B.: “Pressure-Volume-
Temperature Correlation for Mixtures of
California Oils and Gases,” Drill & Prod.
Prac. (1947) 275.
13. Standing, M.B.: Petroleum Engneering
Data Book, Norwegian Inst of Technology,
Trondheim Norway (1974)
14. M.J.Economides, A.Daniel Hill, Christine
Ehlig-Economides., ”Petroleum
Production Systems”, prentice Hall,
Englewood cliffs, NJ, 07632 (1994).
15. Brown, K.E., The Technology of Artificial
Lift Methods, Vol.1, Pennwell Books,
Tulsa, OK1977.
16. Beggs, H.D.:”Oil System Correlations,”
Petroleum Engineering Handbook, SPE,
Richardson, TX (1987) Chap.22.
17. Shiu, K.C. and Beggs, H.D.:”Predicting
Temperatures in Flowing oil Wells,”
J.Energy Res.Tech., (March 1980);
Trans.AIME.

8. Page 8 of 13
Table 1: Input table for Single Gas Lift Diagram
Table 2: Input table for Equilibrium curve

9. Page 9 of 13
900
1131 2550
266
1021, 5322
635
913, 4982
5660
2000
4000
6000
8000
10000
0 500 1000 1500 2000 2500 3000
Pressure, psia
Depth,ft
Gas Gradient Line
Dead Tubing Fluid Gradient
Tubing fluid Gradient from Point of Balance
Tubing Fluid Gradient from Point of Injection
Single Gas Lift Diagram
Color Code for Numbers:
OOO =Surface Gas Injection Pressure, psia
OOO =Bottomhole Gas Injection Pressure, psia
OOO =Wellhead Pressure, psia (from Point of Balance, after injection)
OOO =Wellhead Pressure, psia (from Point of Injection, after injection)
OOO =Wellhead Pressure, psia (before Injection, Dead Gradient)
OOO =Pressure(psia), & Depth(ft) @ Point of Balance
OOO =Pressure(psia), & Depth(ft) @ Point of Injeciton
OOO =Bottomhole flowing Pressure(psia),@ Total depth, or Mid perfs
Figure 1: Single Gas Lift Diagram
Multiple Gas Lift Diagram
0
1000
2000
3000
4000
5000
6000
7000
8000
9000
10000
11000
0 500 1000 1500 2000 2500 3000
Pressure, psia
Depth,FT
Tubing Lifted Traverse TPR @Qo
(stb/day)= 200
Tubing Lifted Traverse TPR @Qo
(stb/day)= 400
Tubing Lifted Traverse TPR @Qo
(stb/day)= 600
Tubing Lifted Traverse TPR @Qo
(stb/day)= 800
Tubing Lifted Traverse TPR @Qo
(stb/day)= 1000
Inflow Dead Traverse IPR @Qo
(stb/day)= 200
Inflow Dead Traverse IPR @Qo
(stb/day)= 400
Inflow Dead Traverse IPR @Qo
(stb/day)= 600
Inflow Dead Traverse IPR @Qo
(stb/day)= 800
Inflow Dead Traverse IPR @Qo
(stb/day)= 1000
Inj.Gas Gradient from
POB,psia@STB/day= 200
Inj.Gas Gradient from
POB,psia@STB/day= 400
Inj.Gas Gradient from
POB,psia@STB/day= 600
Inj.Gas Gradient from
POB,psia@STB/day= 800
Inj.Gas Gradient from
POB,psia@STB/day= 1000
Figure 2: Multiple Gas Lift Diagram

10. Page 10 of 13
Equilibrium Curve
0
1000
2000
3000
4000
5000
6000
7000
8000
9000
10000
11000
0 500 1000 1500 2000 2500
Equilibrium Pressure, psia
EquilibriumDepth,FT
0 500 1000 1500 2000 2500
Oil Rates (assumed), STB/Day
Equilibrium Curve
@Balanced Points
Equilibrium Curve
@Injection Points
(DP Valve included)
Oil Rates
Corresponding to
Balance Points
Oil Rates
corresponding to
Injection Points (DP
valve included)
Figure 3: Equilibrium Curve

11. Page 11 of 13
Table 3: Input for Limit GLR check from
Single Gas Lift diagram
Table 4: Input for Limit GLR check in
multi Gas Lift Diagram

12. Page 12 of 13
Figure 4: Very High GLR leads Flattening of Tubing Gradient Curves

13. Page 13 of 13
Multiple Gas Lift Diagram
0
1000
2000
3000
4000
5000
6000
7000
8000
9000
10000
11000
0 500 1000 1500 2000 2500 3000 3500 4000
Pressure, psia
Depth,FT
Tubing Lifted Traverse TPR @Qo
(stb/day)= 200
Tubing Lifted Traverse TPR @Qo
(stb/day)= 400
Tubing Lifted Traverse TPR @Qo
(stb/day)= 600
Tubing Lifted Traverse TPR @Qo
(stb/day)= 800
Tubing Lifted Traverse TPR @Qo
(stb/day)= 1000
Inflow Dead Traverse IPR @Qo
(stb/day)= 200
Inflow Dead Traverse IPR @Qo
(stb/day)= 400
Inflow Dead Traverse IPR @Qo
(stb/day)= 600
Inflow Dead Traverse IPR @Qo
(stb/day)= 800
Inflow Dead Traverse IPR @Qo
(stb/day)= 1000
Inj.Gas Gradient from
POB,psia@STB/day= 200
Inj.Gas Gradient from
POB,psia@STB/day= 400
Inj.Gas Gradient from
POB,psia@STB/day= 600
Inj.Gas Gradient from
POB,psia@STB/day= 800
Inj.Gas Gradient from
POB,psia@STB/day= 1000
Figure 5: High GLR effect in Multiple Gas Lift Diagram
Equilibrium Curve
9000
10000
11000
2600 2650 2700 2750 2800 2850 2900 2950 3000
Equilibrium Pressure, psia
EquilibriumDepth,FT
0 500 1000 1500 2000 2500 3000
Oil Rates (assumed), STB/Day
Equilibrium
Curve
@Balanced
Points
Equilibrium
Curve
@Injection
Points (DP
Valve
included)
Oil Rates
Correspond
ing to
Balance
Points
Oil Rates
correspondi
ng to
Injection
Points (DP
valve
included)
Figure 6: Equilibrium Curve shifts Balance Points to total Depth