Well_Completion_and_Stimulation——Chapter_3_Well_Performance_Analysis-New

7/27/2019 Well_Completion_and_StimulationChapter_3_Well_Performance_Analysis-New

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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:


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


Intercept a = 0.06

Slope b = 1.111x10-5


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

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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:


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


Intercept a = 22.28 x 103

Slope b = 1.727


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.

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