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Chapter-3
Well Performance Analysis
Well performance analysis involves determination of optimum tubing size that will allow
obtain maximum production from a given completion design. A typical well completionis presented in Fig. 3.1.
Fig. 3.1: Perforated well completion.
The production tubing acts as a throttle for the reservoir. As shown in Fig. 3.2, larger theopening of the valve (larger tubing diameter) greater the bottomhole. The increase or
decrease in bottomhole flow has the following effects: one is the reservoir performance
and the other tubing performance (flow through tubing). The effect of bottomhole flowcan best be described in Fig. 3.3.
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Fig. 3.2: Drawdown of a gas cap expansion drive reservoir
From the plot 1 in Fig. 3.3 it can be seen that bottomhole flowing pressure (BHFP) isdirectly affected by production rate (flow rate, Q). For an oil well, the BHFP decreases
linearly with increase in bottomhole flow until it reaches bubble point pressure (BPP).
Below this pressure the relationship between BHFP and Q is non linear. One can obtainmaximum openhole flow (AOF) at zero BHFP. Plot 2 of the Fig. 3.3 describes tubing
performance. For a given tubing diameter, BHFP (which is required to initiate tubing
flow) initially decrease up to a point and then increases with increase in Q. It is also seen
that for each diameter there is a maximum production that can be obtained. Largestproduction rate can be obtained by having largest diameter of the tubing as shown in Fig.
3.3.
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Fig. 3.3: Tubing Performance Analysis
In this chapter the effect of bottomhole flow on both reservoir performance and thetubing performance will be discussed. A number of examples will be presented to provide
a better understanding of well performance.
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3.1 Inflow performance analysis
Several techniques have been proposed for determining the reservoir performance
analysis. Most of the techniques require data produced from the flow test. The data
includes the flow rates and bottomhole flowing pressure. Using this data authors havedeveloped different methods to carry reservoir performance analysis. Some of these
methods are listed below:
Vogels method, Wigginss method, Standings Method, Fetkovichs Method and the Klins Clark Method.
VOGELS METHOD
Vogel, 1966, using a computer based model, developed a generalised IPR referencecurves for saturated oil reservoirs. Using the generalised curves, a specific IPR curve can
be constructed for a well if the reservoir pressure and the bottomhole flowing pressure are
known. Vogel normalized the IPRs and expressed it in a dimensionless form as:
Dimensionless PressureR
wf
p
p=
Dimensionless flow ratemaxq
qo=
Where, maxq is the flow rate at zero bottomhole flowing pressure and known as
absolute open hole flow (AOF).
The dimensionless flow rate is expressed as:
2
max
8.02.01
=
R
wf
R
wfo
p
p
p
p
q
q(3.1)
Where qmax= maximum producing rate atpwf = 0
=
+
Sr
rB
phk
w
eoo
Ro
75.0ln2.141
8.1
1
qo= oil flow rate
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In order to use Vogels method the following data is required:
current average reservoir pressure, Rp , bubble point pressure,pb and
stabilized flow test data that include oq and wfp
Vogels method can be used to predict IPR curves for both Saturated and under saturated
oil reservoirs.
STANDINGS METHOD
By using Vogels method, it is obviously more difficult to predict the effects of formation
damage and/or the improvements to be expected from reservoir stimulation (hydraulic
fracturing). Standing, 1970 modified Vogels curve by taking in to account of the
changes in flow efficiency and introducing PI (productivity index).
FETKOVICHS METHOD
The most widely accepted method of estimating IPR curves is that developed by
Fetkovich, 1973. He simplified the approach given by Muskat and Evinger, 1942.
According to Darcys radial flow equation, the production rate of oil can be expressed as:
+
=
r
wf
p
P
w
e
o dppf
Sr
r
khQ )(
75.0ln2.141(3.2)
Where the pressure function f(p) is defined by:
oo
ro
B
kpf
=)(
Where,
rok =oil relative permeability,
o =oil viscosity and
oB =oil formation volume factor
Fetkovich suggested the pressure function can fall into one of the two regions:
1. Undersaturated Region,p >pb2. Saturated Region, p
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In the undersaturated region, oil relative permeability equals unity, therefore the pressure
function becomes:
pooB
pf
=
1)(
In the saturated region Fetkovich shows that f(p) changes linearly with pressure and the
line passes through the origin. This relationship is shown schematically in Fig. 3.4. Themathematical representation of this linear function is:
=
bpoop
p
Bpf
b
1)(
Where o and oB are evaluated at the bubble point pressure.
Pressure
Fig. 3.4: Pressure function concept, after Tarek Ahmed, 2002
In the case of the undersaturated region when we substitute the pressure function into Eq.
(3.2) we get:
+
=
r
wf
p
P oo
w
e
o dpB
Sr
r
khQ )
1(
75.0ln2.141
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Since )1
(ooB
is constant:
)(
75.0ln2.141
wfR
w
e
o pp
Sr
r
khQ
+
=
or
)(wfRoppJQ = (3.3)
In terms of reservoir parameters the productivity index is defined as:
+
=
S
r
rB
khJ
w
e
oo 75.0ln2.141 (3.4)
oB and o are evaluated at2
)( wfR pp +
For the saturated region Eq. (3.2) may be written as:
+
=
r
wf
b
p
P b
p
oo
w
e
o dpp
p
BS
r
r
khQ )()
1(
75.0ln2.141
The term )1
()1
(b
p
oo pBb
is a constant:
+
=
r
wf
b
p
Pb
p
oo
w
e
odpp
pBS
r
r
khQ )()
1()
1)(
75.0ln2.141
(
Introducing the productivity index gives:
))(2
1(
22
wfRpp
pJQ
b
o =
The term )2(
bp
Jis commonly referred to as theperformance co-efficientC:
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)(22
wfRppCQ
o = (3.5)
Fetkovich introduced an exponent n to the above equation accounting for non-Darcy flow(turbulent flow).
no wfR
ppCQ )( 22 = (3.6)
The exponent n and intercept Care usually determined from a multi-point or isochronal
back-pressure test, where )(22wfR pp is plotted against q on a log-log paper.
Example 3.1:Productivity Index in an undersaturated Oil Reservoir
A well is producing from an undersaturaed oil reservoir at an average reservoir pressure
of 2800 psi. The bubble point pressure is recorded as 1400 psi at 140 oF. The following
additional data are available:
stabilized flow rate = 300 STB/day stabilized wellbore pressure = 1800 psi h = 20 rw = 0.25 re = 600 s= 0.5 k= 55 md o at 2300 psi = 2.5cp
oB at 2300psi = 1.5 bbl/STB
Calculate the productivity index by using both reservoir properties and flow test data.
Solution:
Using the reservoir properties in Eq. (3.4) we have:
(55)(20)0.28
600141.2(2.5)(1.5) ln 0.75 0.5
0.25
J= = +
STB/day/psi
From Production data:
3000.3
2800 1800J= =
STB/day/psi
Results show a reasonable match between the two approaches.
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Example 3.2:Productivity Index in a Saturated Oil Reservoir
A four point stabilized flow test was conducted on a well producing from a saturated
reservoir that exists at an average pressure of 3600 psi.
Qo (STB/day) pwf(psi)300 3.20E+03
380 3.70E+03
450 2.54E+03
540 2.40E+03
Using the information provided construct a complete IPR using the Fetkovich method.
Solution:
Part 1
Step 1: Construct the following table.
Qo (STB/day) Pwf(psi) (PR2- Pwf
2) x 10-6 (psi2)300 3.20E+03 2.72
380 3.70E+03 4.55
450 2.54E+03 6.508
540 2.40E+03 7.2
Step 2: Plot)( 22
wfRpp
vs. oQ
on log-log paper. Determine the exponent n:
6 6
ln(380) ln(300)0.459
ln(4.55 10 ) ln(2.72 10 )n
= =
(Values determined from graph below)
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1.00E+00
1.00E+01
100 1000
Step 3: Solve forC
6
3800.332
(4.55 10 )n
C= =
Step 4: Generate the IPR by assuming various values for pwf and calculating the
corresponding flow rate.
2 2 0.4590.332(3600 )
wfoQ p=
Pwf(psi) Qo (STB/day)3.40E+03 0
2.40E+03 469.206
1.80E+03 538.575
1.20E+03 582.301
600 606.777
0 614.681
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IPR Curve
0.00E+00
5.00E+02
1.00E+03
1.50E+03
2.00E+03
2.50E+03
3.00E+03
3.50E+03
4.00E+03
0 200 400 600 800
Flow rate (BBL/day)
Pressure(psi)
Oil well IPR
GAS WELL IPR
Gas well IPR can best be described by the exact solution to the differential form ofDarcys equation for compressible fluids under the pseudo steady state conditions and
can be expressed as:
+
=
Sr
rT
khQ
w
e
wfR
g
75.0ln1422
)(
(3.7)
Where,
gQ = gas flow rate, Mscf/day,
k= permeability, md,
R = average reservoir real gas pseudo pressure, psi2/cp,
T = temperature, oR,s = skin factor,h = thickness,
er = drainage radius and
wr = wellbore radius.
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The productivity of a gas well can be written as:
+
=
=
Sr
rT
khQJ
w
ewfR
g
75.0ln1422)( (3.8)
or
)( wfRg JQ = (3.9)
Eq. (3.9) may be expressed as:
gRwf QJ1=
This equation indicates that a plot of wf vrs. gQ would produce a straight line with a
slope ofJ
1and an intercept of R . If two different flow rates are available the line can
be extrapolated and the slope determined to estimate AOF, J, and wf .
Eq. (3.7) can be written as:
+
=
r
wf
p
P g
w
e
g dpzp
Sr
rT
khQ )2(
75.0ln1422
Note: )(z
p
gis directly proportional to )
1(
ggB.
p
zTBg 00504.0=
Where,
gB = gas formation volume factor, bbl/scf,z = gas compressibility factor andT = temperature, oR.
Substituting forBgwe get:
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+
=
r
wf
p
Pgg
w
e
g dpB
Sr
r
khQ )
1(
75.0ln
)10(08.76
Fig. 3.5 shows a typical plot of the gas pressure function versus pressure. The pressurefunction exhibits three individual pressure application regions.
Pressure
Fig. 3.5: Gas PVT Data, after Tarek Ahmed, 2002
Region I: High Pressure Region ( wfp and Rp > 3000 psi)
The pressure functions are nearly constant in this region. This suggests that the term
)1
(ggB
can be treated as a constant. So:
+
=
S
r
rB
ppkhQ
w
eavggg
wfR
g
75.0ln)(
)()10(08.7 6
(3.10)
gB And g are evaluated at2
)( wfR pp +
This method of determining gas flow rate is commonly referred to as the pressure-
approximation method.
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Region II: Intermediate Pressure Region (2000 psi < wfp , Rp < 3000 psi)
The pseudo-pressure gas pressure approach, Eq. (3.7), should be used to calculate the gas
flow rate in this region.
Region III:Low Pressure Region ( wfp and Rp < 2000 psi)
The pressure functions exhibit a linear relationship in this region. Golan and Whitson,
1986 suggested that the product zg is essentially constant for pressures below 2000
psi. Using this observation and integrating we get:
+
=
Sr
rzT
ppkhQ
w
eavgg
g
wfR
75.0ln)(1422
)(22
(3.11)
The z-factor and gas viscosity should be evaluated at the average pressure:
2
)( wfRavg
ppp
+=
This method of determining gas flow rate is commonly referred to as the pressure-squared approximation method.
If both pwf and pr are less than 2000 psi Eq (3.11) can be expressed in terms of the
productivity index,J:
)( 22wfR
ppJQg =
with
)()( 2max RpJAOFQg ==
+
=
Sr
rzT
khJ
w
e
avgg75.0ln)(1422
(3.12)
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Example 3.3: Comparison of Pressure Approximation methods and Exact Solution
The PVT properties of a gas sample taken from a dry gas reservoir are given in the
following table:
P (psi) g (cp) z (psi2/cp) Bg (rb/scf)0 0.01270 1.000 0 -
400 0.01286 0.937 1.32E+07 0.007080
1200 0.01530 0.832 1.13E+08 0.002100
1600 0.01680 0.794 1.98E+08 0.0015002000 0.01840 0.770 3.04E+08 0.011600
3200 0.02340 0.797 6.78E+08 0.000750
3600 0.02500 0.827 8.16E+08 0.0006954000 0.02660 0.860 9.50E+08 0.000650
4600 0.02860 0.890 1.13E+09 0.000601
The reservoir is producing under the pseudo steady state condition. The following
additional data is available:
k= 55 md, h = 15, T= 550oR, re= 600, rw = 0.25, S= 0.4
Calculate the gas flow rate under the following conditions:
1. Rp = 4600 psi and wfp = 3400 psi
2. Rp = 2000 psi and wfp = 1200 psi
Use the appropriate approximation method and compare results with the exact solution.
Part 1. Calculate gQ at Rp = 4600 psi and wfp = 3400 psi
Step 1: Select the approximation method. Because Rp and wfp are both greater than
3000 psi the pressure approximation method is used i.e. Eq. (3.10)
Step 2: Calculate the average pressure and determine the corresponding gas properties.
4600 34004000
2p
+= = psi
gB = 0.000650 and g = 0.02660
Step 3: Calculate the gas flow rate by applying Eq. (3.10).
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67.08(10 )(55)(15)(4600 3400)
600(0.02660)(0.000650) ln 0.75 0.4
0.25
gQ
= +
5.455E+4gQ = Mscf/day
Step 4: Recalculate gQ by using the pseudo pressure equation i.e. Eq. 3.7.
6(55)(15)(1130 747) 10
60001422(550) ln 0.75 0.4
0.25
gQ
= +
5.435E+4gQ = Mscf/day
Part 2. Calculate gQ at Rp = 1600 psi and wfp = 1200 psi
Step 1: Select the approximation method. Because Rp and wfp are both less than or
equal to 2000 psi the pressure-squared approximation method is used
Step 2: Calculate the average pressure and determine the corresponding gas properties.
2 21600 1200
14142
p+
= = psi
zave = 0.771 g = 0.0163 cp
Step 3: Calculate the gas flow rate by applying Eq. (3.11).
2 2(55)(15)(1600 1200 )
6001422(550)(0.0163)(0.771) ln 0.75 0.4
0.25
gQ
= +
12647gQ = Mscf/day
Step 4: Compare gQ with the exact the exact value i.e. Eq. 3.7.
6(55)(15)(198 113.1) 10
6001422(500) ln 0.75 0.4
0.25
gQ
= +
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12062gQ = Mscf/day
The most common method of estimating gas well IPRs is the "back-pressure" method of
Rawlins and Schellhardt, 1936. From analysis of flow data from a large number of wellsRawlins and Schellhardt postulated the relationship between gas flow rate and pressure
can be expressed as:
n
wfRg ppCq )(22 = (3.12)
Where,
gq = gas flow rate, Mscf/day,
Rp = average reservoir pressure, psi,
n = exponent andC= performance co-efficient, Mscf/day/psi2.
The well is flowed for a fixed period at different rates. Using the bottomhole flowing
pressures at equal flow times, a plot of )log(22wfR pp vs. gqlog is prepared. The slope
gives a value for l/n (Fig. 3.5) and using this, Ccan be calculated. The exponent n variesfrom 1.0 for laminar flow to 0.5 for fully turbulent conditions.
Fig. 3.5: Plotfor a conventional well test example.
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It is important to remember that this IPR relationship is empirical and that Cis a function
of flow time; its value under semi steady state conditions must either be
calculated or determined from an extended flow period. At low rates, where n1.0, we may calculate C as:
+
=
Sr
rZT
khC
w
e 75.0ln1422 Mscf/d/psi2 (3.13)
or in the SI system:
+
=
Sr
rZT
khC
w
e75.0ln1300
m3/d/kPa2
Where,
= viscosity, mPas,
T= temperature, oR = oF + 460 (oK = oC + 273) and
Z= compressibility factor.
LIT (LAMINAR INERTIAL TURBULENT) APPROACH
LIT method includes:
Pressure squared method, Pressure Quadratic method and Pseudo Pressure Quadratic method.
Pressure squared method:
Another method of determining the IPR for a gas well is to plot )(22wfR pp /q versus q
from the generalized semi steady state flow equation
222)( FqBqpp wfR += (3.14)
The slope will give a value forF(non-Darcy orturbulence dependent coefficient) and the
intercept will give a value forB (Darcy coefficient). Dake (1978) provided formulas forestimatingB andFfrom core data or build-up analyses. More correctly, B andFshould
be calculated from pseudopressures (m(p)) to be independent of variations in gas
viscosity and deviation factor, at which point they can be used to predict future
performance accurately. Theoretically, this method is still not absolutely correct, but inthe majority of cases it is a perfectly adequate description of the inflow performance.
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Stimulation of gas wells will affect not only their skin factor ( S), their Darcy coefficient
(CorB) but also the non-Darcy coefficient (n orF).
This method can be employed based on few assumptions. The flow is restricted to single
phase and the reservoir is considered homogeneous and isotropic. Permeability in the
reservoir doesnt vary with the change in pressure and the product of gas viscosity andcompressibility factor (z) is assumed constant. It is recommended to use this method for
pressures less than 2000psi indicated as region III in Fig. 3.5.
Pressure Quadratic method (Pressure Approximation):
In this method of determining the IPR for a gas well is to plot ( )R wfp p /q versus q fromthe generalized semi steady state flow equation
2
1 1( )R wfp p B q F q = + (3.15)
The slope will give a value forF1 (non-Darcy or turbulence dependent coefficient) and
the intercept will give a value forB1 (Darcy coefficient).This method adopts similar
assumptions as stated in pressure squared method, except that it can be applied to
pressures greater than 3000psi.
Pseudo pressure Quadratic method (Pseudo Pressure):
In this method of determining the IPR for a gas well is to plot ( )R wf /q versus q fromthe generalized semi steady state flow equation
2
2 2(( )R wf B q F q = + (3.16)
Similar to the above equations the slope will give F2 which represents non-Darcy orturbulence dependent coefficient and the intercept will give a value forB2 (Darcycoefficient).
From a completion engineering viewpoint, the following concepts are fundamental toproper well design:
The inflow performance of a well is largely determined by reservoir parameters. Test results alone may not adequately describe the long-term inflow performance
of a producer unless corrected for : semisteady state conditions, curving of the IPR in oil wells below the bubble-point and in gas wells and
expected skin (this is a function of perforation length, perforation efficiency,stimulation, damage, etc.).
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Example 3.4: Gas well IPR example
A gas well was tested using a three-point conventional deliverability test. Data recordedduring the test are given below:
Pwf,psia wf, psi2
/cp Qg, Mscf/dayPr = 1952 316 x 10
6 0
1700 245 x 106 2642.6
1500 191 x 106 4154.7
1300 141 x 106 5425.1
Generate the current IPR by using the following methods:
a. Simplified back-pressure equation (Eqn 3.12)b. Laminar-inertial-turbulent (LIT) methods: (Eqn. 3.14 Eqn.3.16)
i. Pressure-squared approach
ii. Pressure-approachiii. Pseudo-pressure approach
c. Compare results of calculation.
Solution
a. Back-Pressure Equation:
Step 1: Prepare the following table:
Pwf P2wf, psi
2 x 103 (Pr2-P2wf), psi
2x 103 Qg, Mscf/day
Pr = 1952 3810 0 01700 2890 920 2642.6
1500 2250 1560 4154.7
1300 1690 2120 5425.1
Step 2:Plot (Pr2 Pwf
2) versus Qg on a log-log scale. Draw the best straight line throughthe points.
Step 3: Using any two points in the straight line, calculate the exponent n:
)600log()1500log(
)1800log()4000log(
=n n=0.87
Step 4: Determine the performance coefficient C by using the coordinate of any point on
the straight line, or:
( ) 87.000,600
1800=C C = .0169 Mscf/psi2
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Step 5:The back-pressure equation is then expressed as:
( )87.02000,810,30169. wfg pQ =
Step 6: Generate the IPR data by assuming various values of Pwfand calculating the
corresponding Qg.
Pwf, psia Qg, Mscf/day
1952 0
1800 1720
1600 3406
1000 6891
500 8465
0 8980 = AOF = (Qg)max
IPR, Back-pressure Method
0
500
1000
1500
2000
2500
0 2000 4000 6000 8000 10000
Qg, Mscf/day
Pwf,psia
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b. LIT Method
i.Pressure-squared method:
Step 1: Construct the following table:
Pwf, psia (P2r P
2wf), psi
2x103 Qg, Mscf/day (P2r-Pwf
2)/Qg1952 0 0 -
1700 920 2624.6 351
1500 1560 4154.7 375
1300 2120 5425.1 391
Step 2: Plot (P2
r P2
wf)/Qg versus Qg on a Cartesian scale and draw the best straight lineas shown below:
Pressure-squared method
345
350
355
360
365
370
375
380
385
390
395
0 1000 2000 3000 4000 5000 6000
Flow Rate
Differential
PressureOve
Flow
Rate
Step 3: Determine the intercept and slope of the straight line to give:
Intercept a = 314.04Slope b = 0.0143
Step 4: The quadratic from of the pressure-squared approach can be expressed as:
2201333.0318)000,810,3( ggwf QQp +=
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Step 5: Construct the IPR data by assuming various values for Pwf and solving for Qg.
Pwf (Pr2-Pwf
2), psi2x103 Qg, Mscf/day
1952 0 0
1800 570 1675
1600 1250 34361000 2810 6862
500 3560 8304
0 3810 8763
IPR, Pressure-squared Method
0
500
1000
1500
2000
2500
0 2000 4000 6000 8000 10000
Qg, Mscf/day
Pwf,psia
ii.Pressure-approximation method:
Step 1: Construct the following table:
Pwf, psia (Pr Pwf) Qg, Mscf/day (Pr-Pwf)/Qg1952 0 0 -
1700 252 262.6 .090
1500 452 4154.7 .109
1300 652 5425.1 .120
Step 2: Plot (Pr Pwf)/Qg versus Qg on a Cartesian scale and draw the best straight line as
shown below:
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Pressure-approximation Method
0
0.02
0.04
0.06
0.08
0.1
0.12
0.14
0 1000 2000 3000 4000 5000 6000
Flow Rate
DifferentialOverFlowR
at
Step 3: Determine the intercept and slope of the straight line to give:
Intercept a = 0.06
Slope b = 1.111x10-5
Step 4: The quadratic from of the pressure-squared approach can be expressed as:
25 )10(111.106.)1952( ggwf QQp+=
Step 5:Construct the IPR data by assuming various values for Pwf and solving for Qg.
Pwf (Pr2-Pwf
2), psi2x103 Qg, Mscf/day
1952 0 0
1800 152 1879
1600 352 3543
1000 952 6942
500 1452 9046
0 1952 10827
24
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IPR, Pressure-approximation Method
0
500
1000
1500
2000
2500
0 2000 4000 6000 8000 10000 12000
Qg, Mscf/day
Pwf,psia
iii.Pseudopressure method:
Step 1: Construct the following table:
Pwf , psi2/cp (r - wf) Qg, Mscf/day (r-wf)/Qg1952 316x106 0 0 -
1700 245x106 71x106 262.6 27.05x103
1500 191x106 125x106 4154.7 30.09x103
1300 141x106 175x106 5425.1 32.26x103
Step 2: Plot (r wf)/Qg versus Qg on a Cartesian scale and draw the best straight line as
shown below:
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Pseudopressure Method
2.60E+04
2.70E+04
2.80E+04
2.90E+04
3.00E+04
3.10E+04
3.20E+04
3.30E+04
0 1000 2000 3000 4000 5000 6000
Flow Rate
DifferentialPressureOve
FlowR
ate
Step 3: Determine the intercept and slope of the straight line to give:
Intercept a = 22.28 x 103
Slope b = 1.727
Step 4: The quadratic from of the pressure-squared approach can be expressed as:
236 727.11028.22)10316( ggwf QQxx +=
Step 5:Construct the IPR data by assuming various values for Pwf and solving for Qg.
Pwf Qg, Mscf/day
1952 316x106 0
1800 270x106 1794
1600 215x106 3503
1000 100x106 6331
500 40x106 7574
0 0 8342
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IPR, Pseudopressure Method
0
500
1000
1500
2000
2500
0 2000 4000 6000 8000 10000
Flow Rate
DiffernetialPressureOve
FlowR
ate
d. Compare the gas flow rates as calculated by the four different methods. Resultsof the IPR calculation are documented below:
Pressure Back-
pressure
p-Squared p-Approximate -Approach
1952 0 0 0 0
1800 1720 1675 1879 1794
1600 3406 3436 3543 3503
1000 6891 6862 6942 6331
500 8465 8304 9046 7574
0 8980 8763 10827 8342
IPR for all Methods
0
500
1000
1500
2000
2500
0 2000 4000 6000 8000 10000 12000Flow Rate (Mscf/day)
Pressure(psia)
Back-pressure
Pressure-squaredPressure-approximationPseudopressure
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3.2 Tubing performance analysis
Performance of tubing is directly related to the summation of pressure drop in the
completion system which includes:
production tubing, sub-surface choke, surface choke, flow line, separator and gathering line to sale point.
In a single phase flow, the calculation of pressure loss is relatively simple and the
pressure values can be determined accurately by using well established methods. Formultiphase flow same procedure can be applied, however, the parameters for pressure
terms can not be accurately determined at an acceptable level. Problem of calculating
pressure loss in multi phase flow is that the phase behaviour and flow pattern aretemperature and pressure dependant which can vary from bottomhole to the surface. The
flow from reservoir to the well is single phase as long as the reservoir pressure remains
above the bubble point pressure. Due to the change in pressure and temperature inside
tubing, the pressure might fall below the bubble point. This will result in liberation of gasfrom liquid (oil). As pressure continues to drop, the gas phase expands and additional gas
comes out of the solution. This could change fluid stream from single phase liquid at the
bottomhole to mostly gas phase at the near surface. Typical flow regimes in a tubing areillustrated in Fig. 3.6.
Fig. 3.6: Flow regimes, after
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Empirical and semi-empirical analysis:
The process of estimating pressure loss when multiphase flow exist through tubing iscomplex. Because of this complexity, empirical and semi-empirical analysis techniques
have been used to develop relationships among the producing conditions listed in Fig.3.6.
There are a number of correlations incorporated in commercial software (e.g.VIRTUWELLTM) or published as gradient curves. Since these correlations give somewhat
different results, the engineer should establish a match with field test data and choose the
most appropriate correlation.
Three of the most commonly used correlations are: Hagedorn and Brown, Griffith and Beggs and Brill.
Hagedorn & Brown / Griffith:
An effort was made by Hagedorn and Brown to determine a correlation which would
include all practical ranges of flow rate, a wide range of gas-liquid ratios, all ordinary
used tubing sizes and the effects of fluid properties. The heart of the Hagedorn andBrown correlation is a correlation for liquid holdup. This correlation is selected based on
the flow regime as follows. Bubble flow exists if g
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n= no-slip mixture density, lb/ft3 and
m
nf
2
= .
The mixture velocity is the sum of the superficial velocities of each phase ( vsg and vsl)which can be calculated using:
slsgm vvv += (3.21)
A
qv
g
sg = (3.22)
and
A
qv lsl = (3.23)
Where,
qg and ql are the gas and liquid flow rates respectively.
The no-slip liquid hold-up and density are calculated as follows:
m
sl
Lv
v= (3.24)
( )LgLLn += 1 (3.25)
whereL andg are liquid and gas densities respectively.
The liquid holdup is obtained from a correlation and the friction factor is based on a
mixture Reynolds number. Using the following dimensionless numbers we can determinethe liquid holdup from a series of charts and are defined as:
Liquid velocity number:
4938.1
lslvl vN = (3.26)
Gas velocity number:
4938.1
gsgvg vN = (3.27)
Pipe diameter number:
lD dN 872.120= (3.28)
Liquid viscosity number:
43
115726.0
l
lLN = (3.29)
Where,
Superficial velocities are in ft/sec
Density in lbm/ft3,
Surface tension, ( ) in dynes/cm viscosity in cp and diameter in ft.To obtain holdup first calculateNL and read the value ofCNLfrom Fig. 3.11.
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Fig. 3.11 Hagedorn and Brown correlation forCNL (from Hagedorn and Brown, 1965)
Then the following group is calculated
Davg
Lvl
NpN
CNpN
1.0575.0
1.0)(
(3.30)
Pis the absolute pressure at the location where the pressure gradient is wanted and pa is
the atmospheric pressure
A value forLH , whereHL is the holdup factor, can be obtained using this group and
Fig. 3.12.
Fig. 3.12 Hagedorn and Brown correlation forly (from Hagedorn and Brown, 1965)
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Finally calculate the following group and use it and Fig. 3.13 to get
14.2
380.0
D
Lvg
N
NN(3.31)
Fig. 3.13 Hagedorn and Brown correlation for(from Hagedorn and Brown, 1965)
The liquid holdup is defined as:
)(
= LLH
H (3.32)
The mixture density is calculated below as :( )LgLLm HH += 1 (3.33)
The frictional pressure gradient is based on the Fanning friction factor. To obtain this
value Reynolds number must be calculated:
m
mnm
dvN
1488Re = (3.34)
Where, mixture viscosity, cp, is defined as:( )LL H
g
H
Lm
= 1 (3.35)
The friction factor is obtained using the Moody diagram or from the following equation:
2
9.0
Re
25.21log214.1
1
+
=
mNd
f
(3.36)
Where, = pipe roughness, ft
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Bubble flow, the Griffith correlation:
The Griffith correlation uses Eq 3.37 to calculate pressure gradient.
2510
2
10413.7144
ll
l
yd
mf
dz
dp
+=
(3.37)
Where lm is the mass flow rate of the liquid only and lv is the in situ average liquid
velocity defined as:
l
l
l
sll
Ay
q
y
vv == (3.38)
++=
s
sg
s
m
s
ml
v
v
v
v
v
vy 4)1(1
2
11 2 (3.39)
Where vs= 0.8 ft/sec (vs is the slip velocity). Reynolds number can be calculated using:
ld
mN
2
Re
102.2 = (3.40)
Beggs and BrillThe Beggs and Brill correlation was developed from experimental data obtained in a
small scale test facility. It differs significantly from Hagedorn and Brown. Beggs and
Brill correlation is applicable to any pipe inclination and flow direction. The overall
pressure gradient can be calculated using:
k
FPE
E
dh
dp
dh
dp
dh
dp
+=
1
)()(
)( (3.41)
The kinetic energy contribution to the equation is accounted for by theEk parameter:
pg
vvE
c
msgm
k
= (3.42)
The potential energy pressure gradient is:
sin)( sc
PEg
g
dh
dp= (3.43)
and the frictional pressure gradient can be calculated using:
dg
vf
dh
dp
c
mntp
F2
)(
2= (3.44)
Where,
gglln += , (3.45)tpf = Two phase friction factor,
sgv = Superficial gas velocity (ft/sec),
= The angle between the horizontal and direction of flow ,
l = Input liquid fraction,
g = Input gas fraction,
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g = gravitational acceleration (32.2 ft/s2) and
( )LgLls HH += 1 (3.46)The two phase friction factor,ftp is determined using:
Sntp eff = (3.47)
Where,
( )2.12.2ln = xS for1
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Distributed flow exists when:
l < 0.4 and FRN 1L or l 0.4 and FRN > 4L (3.62)
For segregated, intermittent and distributed flow the following equations are used to
calculate liquid holdup and hence average density:)( )0(LL HH = (3.63)
c
FR
b
l
LN
aH
=)0( ( )0(LH must be greater than LH ) (3.64)
)8.1(sin333.0)8.1sin(1 3 += C
(3.65)
( ) gFRfvl
ell NNdC ln1=
(3.66)
Where a, b, c, d, e, f and g are dependent on the flow regime. Values for these constantsare specified in Table 3.1.
Table 3.1 Beggs and Brill Holdup Constants
Beggs & Brill Holdup Constants
Flow Regime a b c
Segregated 0.98 0.4846 0.0868
Intermittent 0.845 0.5351 0.0173Distributed 1.065 0.5824 0.0609
Flow Regime d e f g
Segregated Uphill 0.011 -3.5868 3.519 -1.614
Intermittent Uphill 2.96 0.305 -0.4473 0.0978
Distributed Uphill No Correlation C=0, =1
All regimes dowhill 4.7 -0.3692 0.1244 -0.5056
For transition flow the liquid holdup is calculated using both the segregated and the
intermittent equations and interpolated using the following:
)()( ntintermitteBHsegregatedAHH LLL += (3.67)
Where,
23
3
LL
NLA
FR
= (3.68)
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and
AB =1 (3.69)
These correlations are used to calculate pressure gradient which can be applied to a well
at random locations. However our objective is to calculate the overall pressure drop pover a considerable distance. Over large distances the pressure gradient in two phase flowwill vary significantly as the downhole flow properties change with temperature and
pressure. For example in a single phase flow oil well, if pressure drops below the bubble
point gas comes out of solution. This will cause gas-liquid bubble flow and as the
pressure continues to drop other flow regimes may occur farther up the tubing. Since bothtemperature and pressure are varying over the length of the tubing, the calculation for
total pressure drop will generally be iterative. An algorithm to calculate the pressure loss
using the empirical methods which are explained above is illustrated in Fig. 3.10
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Fig. 3.10Algorithm for pressure traverse calculation using either Hagedorn
& Brown/Griffith or Beggs & Brill correlation.
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EFFECTS OF SOME IMPORTANT PARAMETERS ON BOTTOMHOLE
FLOWING PRESSURE
Parameters affecting pressure loss inside tubing include:
tubing diameter (D), flow rate (q), gas-liquid ratio (GLR), water cut, fluid density , viscosity , pressure and temperature
Effect of GLR:
Unlike single phase reservoirs, the GLR (gas liquid ratio) will vary with time as the
pressure in the reservoir changes. As GLR increases, the density of produced fluiddecreases, which will result in decrease in BHP (bottomhole pressure).Usage of GLR curves is illustrated in Fig. 3.7. The important thing to remember is enter
the curve at a point defined by the rate, GLR and flowing tubing pressure, or BHP (THP
equivalent to 1,000 ft in Fig. 3.8), and then move along the appropriate GLR line by anincrement equivalent to the depth (i.e., from 1,000 to 8,000 ft for a 7,000-ft deep well).
Do not just read the BHP conditions at a given depth - this merely corresponds to a value
of 0 THP. The other important considerations are that you use the correct water cut and
adjust the GOR to a GLR:
GLR = (1 WC) xGOR (3.17)
For deviated wells, it may be necessary to use a computer or to interpolate between true
vertical depth and measured depth by deducting the additional head effects using anaverage effective density.
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Fig. 3.7: Vertical flowing pressure gradient, (from Brown, 1982)
Effect of Liquid Density:
As liquid density decreases, required flowing bottomhole pressure decreases. Fig. 3.8compares the effect of API gravity crude to fresh and salt water.
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Fig. 3.8: Effect of API gravity on required flowing BHP, (from Brown, 1982).
Effect of Liquid Viscosity:
As liquid viscosity increases, higher flowing bottomhole pressures are required.
Effect of Liquid Surface Tension:
The required flowing bottomhole pressure increases with increased surface tension.
Effect of Kinetic Energy:
The kinetic energy effect on flowing pressure can become important for small diameter
tubing with high gas/liquid ratios and low pressure levels.
Effect of Subsurface and Surface Choke Size:
These two chokes contribute to substantial amount of pressure loss within the producingequipment. Subsurface chokes are installed at specific depths depending on their
functioning .The pressure loss at subsurface choke is comparatively greater when they are
installed at a shallow depth than at deeper locations.
To study the effect of surface chokes on pressure drops, a plot of pressure drop vsupstream pressures is plotted with different sizes of chokes. It is observed that the
pressure drop decreases with increase in the upstream pressures for a constant flow rate.
This is illustrated in Fig. 3.9.
Effect of Flow line:
At a specific length it is observed that as the size of the flow line increases the pressure
drop decreases.
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Effect of Separator pressure:
Usually this pressure is maintained constant level at the separator. As the separator back
pressure varies at given conditions, it will alter the flow rate substantially.For more detail study in regards to effects of individual factors mentioned above please
referProduction operations -1, by Allen and Roberts (1989) andProduction operations
course -1 by L.E. Buzarde et.al.(1972)
Fig. 3.9: Effect of surface choke size and upstream pressure, (from Brown, 1982).
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VERTICAL LIFT PERFORMANCE ANALYSIS
In process of well design a plot of flowing bottomhole pressure (pwf) versus rate (q) for
various tubing sizes and gas liquid ratios would be most useful in presenting the
performance of the tubing.For a selected tubing size, there is a minimum flow rate which is required to attain
production of hydrocarbons from the well. This is the rollover point in the tubing
performance curves, which is not easily recognized without a computer simulation. Inpractice a fluid velocity of at least 5 ft/s is required for production. Below this rate the
well will be unstable. This phenomenon is referred to as liquid holdup and is due to
slippage of the gas phase through the liquid. The larger the tubing diameter, the higher
will be the liquid holdup rate.
Matching Completion and Reservoir Performance:
The objective of this analysis is to calculate the maximum productivity of the system.
The output of the analysis is the complete drilling design. We determine a size of tubingwhich can deliver maximum performance at a specific GOR. And thus allowing us to
determine the maximum size of the casing needed to complete the well. This analysis isperformed at the development drilling planning phase so that an adequate casing size is
planned. In obtaining this plot, the well head pressure and about 5 flow rates that are
likely to be within the extent of productivity are assumed.
The steps involved in determining the tubing size are given below:
I. Plot the IPR of the reservoir.II. Plot the VLP of different tubing sizes.
III. The final step is to combine them and identify the intersection points that indicate
the maximum productivity of the system.IV. While this requirement is obvious for flowing wells, gas-lift operations, and
injection wells, it is often forgotten when other artificial lift systems are used.
V. The production target rate and the expected water cut and GLR behavior will alsobe constraining factors that will be evaluate.
VI. Combination of VLP(Vertical lift performance) and IPR
Example 3.5: Calculation of VLP for single phase fluid and combination with IPR
For a 8000 ft oil well (oil gravity, = 0.88) with a tubing I.D of 2 in and the following
properties what would be the expected production rate and corresponding bottomholepressure if the wellhead pressure is 0 psi? Assume the bubble point pressure is zero. The
reservoir operates under steady state conditions. Ignore any kinetic energy losses.
k= 8.2 md,
h = 53 ft,
pR= 5651 psi,
= 1.7 cp,
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B = 1.1 rb/STB,
rw = 0.328 ft,
s = 0,re= 2980 ft,
= 55 lb/ft3 and
= 0.0006.For steady state flow:
kh
Sr
rqB
ppw
eoo
Rwf
+
=
ln2.141
The IPR curve may be represented as:qpwf 54.55651=
To calculate the potential energy pressure loss we have:zPPE = 433.0
3048)8000)(88.0(433.0 == PEP psi
Since the well is considered to be single phase and the fluid is considered to be
incompressible the potential energy drop will be the same regardless of flow rate.Pressure losses due to friction can be calculated using:
dg
zvfP
c
f
F
=
22
Where,
2
4
d
qv
=
and
)))149.7(8257.2
log(0452.57065.3
log(41 8981.0
Re
1098.1
Re NNff+=
To construct a VLP curve we need to find pwfat different flow rates:
Forq = 100 STB/day
2400)7.1)(2(
)55)(100(48.1Re ==N
0117.0=ff
( )2.1173
)
12
2)(17.32(
)8000()3.0)(55)(0117.0(2
2
2
==
=ft
lbzP
f
F psi
The total pressure drop will be the sum of the potential energy drop and the frictional
pressure loss. Sinceptp= 0 this is also equal to flowing bottomhole pressure,pwf30492.13048 =+=wfp psi
The following table provides the values forpwfat different flow rates using similarcalculations:
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qo (STB/day) pwf(psi)
100 3049
300 3056
500 3068
700 3083
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3.3 Well Performance Analysis using VirtuwellTM
The calculation of pressure drops through different production scenarios can be very timeconsuming. These calculations can be particularly tedious in cases in which multiphase
flow is expected. For this reason, many companies in the oil industry rely on computer
software to model and predict the pressure drops in tubulars for a given flow mixture.
The software can also be used to predict the productivity index and tubing performance.
One such program used in industry is VirtuwellTM. This software incorporates empirically
derived mathematical models to predict the flow behavior and pressure drop throughtubulars for single and multiphase flow. It can be used for vertical or deviated wells. The
correlations used will vary for the composition of the fluid. For this reason, it uses one set
of correlations for single-phase liquid or gas flow, and another set for multiphase flow.The correlations used in VirtuwellTM to model single-phase and multiphase flows are now
discussed in the following section.
VirtuwellTM Single-Phase Flow Correlations:
Generally it is easier to calculate pressure drops for single-phase flow than it is for
multiphase flow. There are three single-phase correlations that are available and they are:
Fanning - This correlation is divided into two sub categories Fanning Liquid and
Fanning Gas. The Fanning Gas correlation is also known as the Multi-Step Cullender and
Smith when applied for vertical well bores.
Panhandle:
This correlation was developed originally for single-phase flow of gas through horizontalpipes. In other words, the hydrostatic pressure difference is not taken into account. We
have applied the standard hydrostatic head equation to the vertical elevation of the pipe to
account for the vertical component of pressure drop. Thus our implementation of the
Panhandle correlation includes both horizontal and vertical flow components, and thisequation can be used for horizontal, uphill and downhill flow.
Modified Panhandle:
This is a variation of the Panhandle correlation that was found to be better suited to some
transportation systems. Thus, it also originally did not account for vertical flow.
VirtuwellTM applies the standard hydrostatic head equation to account for the vertical
component of pressure drop. Hence, the implementation of the Modified Panhandlecorrelation includes both horizontal and vertical flow components, and this equation can
be used for horizontal, uphill and downhill flow.
Weymouth:
This correlation is of the same form as the Panhandle and Modified Panhandle
correlations. It was originally developed for short pipelines and gathering systems. As aresult, it only accounts for horizontal flow and not for hydrostatic pressure drop.
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VirtuwellTM applies the standard hydrostatic head equation to account for the vertical
component of pressure drop. Thus, the implementation of the Weymouth equation
includes both horizontal and vertical flow components, and this equation can be used forhorizontal uphill and downhill flow.
In this software, for cases that involve a single-phase flow, the Gray, Hagedorn & Brownand Beggs & Brill correlations revert to the Fanning single-phase correlations. For
example, if the Gray correlation was selected but there was only gas in the system, the
Fanning Gas correlation would be used. Similarly, for single-phase flow, the Flaniganand Modified Flanigan correlations devolve to the single-phase Panhandle and Modified
Panhandle correlations respectively. The Weymouth (Multiphase) correlation devolves to
the single-phase Weymouth correlation.
VirtuwellTM Multiphase Flow Correlations:
Many of the published multiphase flow correlations are applicable for "vertical flow'
only, while others apply to "horizontal flow" only. Other than the Beggs and Brill
correlation, there are not many correlations that were developed for the whole spectrumof flow situations that can be encountered in oil and gas operations; namely uphill,
downhill, horizontal, inclined and vertical flow. VirtuwellTM has adapted all of thecorrelations (as appropriate) so that they apply to all flow situations. The following is a
list of the multiphase flow correlations that are available:
Gray:
The Gray Correlation (1978) was developed for vertical flow in wet gas wells.
FASTWELL uses a modified version of it so that it applies to flow in all directions by
calculating the hydrostatic pressure difference using only the vertical elevation of thepipe segment and the friction pressure loss based on the total pipe length.
Hagedorn and Brown:
The Hagedorn and Brown Correlation (1964) was developed for vertical flow in wells.
FASTWELL uses a modified version of this correlation so that it applies to flow in all
directions by calculating the hydrostatic pressure difference using only the verticalelevation of the pipe segment and the friction pressure loss based on the total pipe length.
Beggs and Brill: The Beggs and Brill Correlation (1973) is one of the few published
correlations capable of handling all of the flow directions. It was developed usingsections of pipe that could be inclined at any angle.
Flanigan:
The Flanigan Correlation (1958) is an extension of the Panhandle single-phase
correlation for multiphase flow. It incorporates a correction for multiphase Flow
Efficiency, and a calculation of hydrostatic pressure difference to account for uphill flow.There is no hydrostatic pressure recovery for downhill flow. In this software, the
Flanigan multiphase correlation is also applied to the Modified Panhandle and Weymouth
correlations. It is recommended that this correlation not be used beyond +1- 10 degrees
from the horizontal.
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Modified-Flanigan:
The Modified - Flanigan is an extension of the Modified Panhandle single-phase equationfor multiphase flow. It incorporates the Flanigan correction of the Flow Efficiency for
multiphase flow and calculation of hydrostatic pressure difference to account for uphill
flow. There is no hydrostatic pressure recovery for downhill flow. In this software, theFlanigan multiphase correlation is also applied to the Panhandle and Weymouth
correlations. It is recommended that this correlation not be used beyond +/- 10 degrees
for the horizontal.
Weymouth (Multiphase):
The Weymouth Correlation is an extension of the Weymouth single-phase equation for
multiphase flow. It incorporates the Flanigan correction of the Flow Efficiency formultiphase flow and calculation of hydrostatic pressure difference to account for uphill
flow. There is no hydrostatic pressure recovery for downhill flow. In this software, the
Flanigan correlation is also applied to the Panhandle and Modified Panhandle
correlations. It is recommended that this correlation not be used beyond +/- 10 degreefrom the horizontal.
Each of these correlations was developed for it's own unique set of experimental
conditions, and accordingly results will vary between them.
In the case ofsingle-phase gas, the available correlations are the Panhandle, Modified
Panhandle, Weymout and Fanning Gas. These correlations were developed for horizontal
pipes, but have been adapted to vertical and inclined flow by including the hydrostatic
pressure component. In vertical flow situations, the Fanning Gas calculation is equivalentto a multi-step Cullender and Smith calculation.
In the case ofsingle-phase liquid, the available correlation is the Fanning Liquid. It hasbeen implemented apply to horizontal, inclined and vertical wells.
Formultiphase flow in essentially horizontalpipes, the available correlations are Beggs& Brill, Gray, Hagedorn & Brown, Flanigan, Modified-Flanigan and Weymouth
(Multiphase). All of these correlations are accessible on the Pipe Module and the
Comparison Module of the program.
Warning:The Flanigan, Modified-Flanigan and Weymouth (Multiphase) correlations
can give erroneous results if the pipe described deviates substantially (more than 10
degrees) from the horizontal. The Gray and Hagedorn & Brown correlations were derivedfor vertical wells and may not apply to horizontal pipes.
Formultiphase flow in essentially vertical wells, the available correlations are Beggs &Brill, Gray and Hagedorn & Brown. If used for single-phase flow, these three correlations
devolve to the Fanning Liquid correlation.
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When switching from multiphase flow to single-phase flow, the correlation will default to
the Fanning. When switching from single-phase flow to multiphase flow, the correlation
will default to the Beggs and Brill.
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Example 3.6 : VirtuwellTM
Use VirtuwellTM and the following data to answer the questions below:
Tubing size = 2.875" OD, 2.441" ID
Casing size =7" OD, 6.049" IDOil production=4000 bbl/day
Water production= 400 bbl/day
Gas production: 0.5 MMcfdOil API gravity: 35 deg API
Water SG: 1.038
Gas SG:0.65
Bubble point of produced fluid =1200 psiReservoir pressure =4000 psi
Tubing head temperature=80oF
Bottomhole temperature=260oF
Total length of tubing=6500 ftTotal depth of hole=7090 ft
Perforated interval=6610 - 6625 ft
A) What is the bottomhole flowing pressure if the wellhead pressure is 900psi? Use the
following correlations:
i) Beggs & Brill
ii) Gray
iii) Hagedorn &Brown
B) Plot the pressure profile for this tubing.
i) Change the gas production from 0.5 MMcfd to 5 MMcfd. What happens to
the plot?
ii) What correlations are most applicable for calculations on gas wells?
C) Plot the Oil IPR/TPR curve for this tubing (with gas production set back to 0.5
MMcfd).
i) Plot IPR/TPR curves for the following tubing sizes:
OD 3.56, ID 3.5534
OD 4.5, ID 4.090OD 5.5, ID 5.120
ii) Of these tubings, which one gives the highest production?
Solution:
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Part A
In the Wellbore module, input the data parameters as shown in the sample screen below.
Given the temperature, flow rates, composition, and fluid properties, this module lets ususe different empirical correlations to determine the sandface pressure given the wellhead
pressure - or vice-versa. This particular screen shows the results for the Hagedorn &
Brown Correlation.
After placing the inputs in, we can select another correlation. The results for thisparticular completion scenario are the same for all three correlations - they all predict a
sandface pressure of 3487.9 psi. This is because the correlations will revert to the
Fanning single-phase correlations when single-phase flow is encountered.
Part B
Virtuwell
TM
can also be used to predict the pressure profile of fluids flowing through aspecified tubing. To do this we use the Comparison Module of the program (shown in
VirtuwellTM screen below for the given case in this example).
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We can see from the results of this module that all the correlations predict the same
pressure profile. This is primarily attributed to the flow conditions and composition. For
all intensive purposes, we have single-phase flow of liquid for the given conditions, and
the empirical correlations will default to the Fanning correlations for single-phase flow.If we now change the gas production from 0.5 MMcfd to 5 MMcfd, we can see a
significant change in the pressure profile. This is shown in the VirtuwellTM screen below:
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We can see that there is a significant change in the pressure profile plot, simply because
now we have multiple phase flow, and the Fanning correlation for single phase can no
longer be used. Multiphase flow in vertical wells can be best modeled by the Gray, Beggs
& Brill, or Hagedorn & Brown correlations.
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Part C
We can use the Oil IPR/TPC module in this software to generate tubing performance
curves (TPC curves) and productivity index curves (IPR curves). This module is shownin the screen below:
From this module we can see that the rate of production will increase with the size of the
tubing. Hence, the largest tubing will have the highest production. However, we noticethat the incremental increase in production when using larger tubing is only marginal.
Therefore, we may wish to consider using the 3.56" tubing to complete this well. This
example illustrates how computers are used in the oil industry in the design andsimulation of tubing performance.
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Review questions
1. What is the main difference between the Hagedorn & Brown correlation and the
Beggs & Brill correlation?
2. What is liquid holdup?
3. When can kinetic energy effects become significant on bottom hole flowing
pressure?
4. A 7000-ft well is to be produced with a target of 15,000 bbl/Day. What tubing
intake pressure must be achieved to meet this target? Estimate tubing size andmake an educated guess as to whether artificial lift will be needed to produce
against a wellhead pressure of 400 psi. The well encountered 170 ft of oil-
bearing formation with pressure of 3000 psia. The hydrocarbon saturation is 80%and the net-to-gross pay ratio is 50%. These development wells are being drilled
with a spacing of 3000 ft between wells (200-acre spacing). The productioncasing is 9 5/8 set in a 12 hole. The oil has a GOR of 500 scf/bbl, a formation
volume factor of 1.2, and a viscosity under reservoir conditions of 1.1 cp. Coretests have shown that the average permeability to air is 435 md and the average
porosity from both cores and log data is 28%. Experience has shown that the
average well can be expected to have a skin of +2. Relative permeability data areas follows:
Sw (%) k ro (%) k rw (%)
10 90 0
20 70 030 60 5
50 36 20
70 12 50
80 0 70
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REFERENCES
1. Allen, TO and Roberts, AP, Well Completion Design- Production Operations-1, 3 rd
edition, 1989, pp 151-165.
2. Buzarde Jr,L.E.,1972:Production Operations Course -1,SPE
3. Brown, K.E., 1982: Overview of Artificial Lift Systems. SPE 9979. SPE-AIME.
4. Dake, L.P., 1978:Fundamentals of Reservoir Engineering. NY: Elsevier.
5. Elkins, L.F., Skov, A.M. and Liming, H.F.: A Practical Approach to Finding andCorrecting Perforation Inadequacies, Preprint of paper 2998 presented at 45 th Annual
Fall Meeting of SPE (Oct. 4-7, 1970), Houston, Texas.
6. Fetkovich, M.J., 1973: The Isochronal Testing of Oil Wells. SPE 4529. SPE-AIME.
7. Fetkovich, M.J., 1975: Multipoint Testing of Gas Wells. SPE Mid-continent section
Continuing Education Course of Well Test Analysis, March 17 1975.
8. Gilbert, W.E., 1954: Flowing and Gas-Lift Well Performance, API Paper 801-30H.
9. Golan, M. and Whitson, C., 1986: Well Performance, International Human Resources
Development Corporation (1986).
10. Hagedorn and Brown, et al : Experimental study of pressure gradients occurring
during continous two phase flow in small diameter conduits, JPT,1965.
11. Muskat, M. and Evinger, H.H: Calculations of Theoretical Productivity Factor,Trans. AIME, (1942), 126-139, 146.
12. Muskat, M.:Physical Principles of Oil Production, McGraw-Hill Book Co., Inc., NY(1949), 210-214.
13. Rawlins, E.L. and Schellhardt, M. A.,: Back-Pressure Data on Natural Gas Wellsand Their Application to Production Practices,, US Bureau of Mines Monograph 7
(1936)
14. Standing, M.B., 1970: Inflow Performance Relationships for Damaged WellsProducing by Solution-Gas Drive.JPT, (Nov. 1970), 1399-1400.
15. Standing, M.B., 1971: Concerning the Calculation of Inflow Performance of WellsProducing From Solution-Gas Drive Reservoirs.JPT, 1141-1142.
16. Tarek Ahmed, 2000: Reservoir Engineering Handbook, Gulf Publishing Co.
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17. Vogel, J.V., 1966: Inflow Performance Relationships for Solution-Gas Drive Wells.
SPE 1476. SPE-AIME.