Tarek Ahmed. Reservoir engineering handbook

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In order to apply the equation, at least three stabilized flow tests are

required to evaluate the three unknowns (Q

)

max

, V, and n at any given

average reservoir pressure p

–

. However, Bendakhlia and Aziz indicated

that the parameters V and n are functions of the reservoir pressure or

recovery factor and, thus, the use of Equation 7-61 is not convenient in a

predictive mode.

Cheng (1990) presented a form of Vogel’s equation for horizontal

wells that is based on the results from a numerical simulator. The pro-

posed expression has the following form:

Example 7-14

A 1,000-foot-long horizontal well is drilled in a solution gas drive

reservoir. The well is producing at a stabilized flow rate of 760 STB/day

and wellbore pressure of 1242 psi. The current average reservoir pressure

is 2145 psi. Generate the IPR data of this horizontal well by using

Cheng’s method.

Solution

Step 1. Use the given stabilized flow data to calculate the maximum flow

rate of the horizontal well.

)

max

= 1052 STB/day

Step 2. Generate the IPR data by applying Equation 7-62.

2145 0

1919 250

1580 536

1016 875

500 1034

0 1052

760

1 0 2055

1242

2145

1 1818

1242

2145

(

)

max

1.0 0.2055

1.1818

(7 62)

max

()

=+ - -

528 Reservoir Engineering Handbook

Reservoir Eng Hndbk Ch 07 2001-10-24 16:50 Page 528

PROBLEMS

1. An oil well is producing under steady-state flow conditions at 300

STB/day. The bottom-hole flowing pressure is recorded at 2500 psi.

Given:

h = 23 ft k = 50 md m

= 2.3 cp r

= 0.25 ft

= 1.4 bbl/STB r

= 660 ft s = 0.5

Calculate:

a. Reservoir pressure

b. AOF

c. Productivity index

2. A well is producing from a saturated oil reservoir with an average

reservoir pressure of 3000 psig. A stabilized flow test data indicates

that the well is capable of producing 400 STB/day at a bottom-hole

flowing pressure of 2580 psig.

a. Oil flow rate at p

= 1950 psig

b. Construct the IPR curve at the current average pressure.

c. Construct the IPR curve by assuming a constant J.

d. Plot the IPR curve when the reservoir pressure is 2700 psig.

3. An oil well is producing from an undersaturated reservoir that is char-

acterized by a bubble-point pressure of 2230 psig. The current average

reservoir pressure is 3500 psig. Available flow test data show that the

well produced 350 STB/day at a stabilized p

of 2800 psig. Construct

the current IPR data by using:

a. Vogel’s correlation

b. Wiggins’ method

c. Generate the future IPR curve when the reservoir pressure declines

from 3500 psi to 2230 and 2000 psi.

4. A well is producing from a saturated oil reservoir that exists at its satu-

ration pressure of 4500 psig. The well is flowing at a stabilized rate of

800 STB/day and a p

of 3700 psig. Material balance calculations

provide the following current and future predictions for oil saturation

and PVT properties.

Oil Well Performance 529

Reservoir Eng Hndbk Ch 07 2001-10-24 16:50 Page 529

Present Future

–

4500 3300

, cp 1.45 1.25

, bbl/STB 1.23 1.18

1.00 0.86

Generate the future IPR for the well at 3300 psig by using Stand-

ing’s method.

5. A four-point stabilized flow test was conducted on a well producing

from a saturated reservoir that exists at an average pressure of 4320 psi.

, STB/day p

, psi

342 3804

498 3468

646 2928

832 2580

a. Construct a complete IPR using Fetkovich’s method

b. Construct the IPR when the reservoir pressure declines to 2500 psi

6. The following reservoir and flow-test data are available on an oil well:

• Pressure data: p

–

= 3280 psi p

= 2624 psi

• Flow test data: p

= 2952 psi Q

= STB/day

Generate the IPR data of the well.

7. A 2,500-foot-long horizontal well drains an estimated drainage area of

120 acres. The reservoir is characterized by an isotropic with the fol-

lowing properties:

= k

= 60 md h = 70 ft

= 1.4 bbl/STB m

= 1.9 cp

= 3900 psi p

= 3250 psi

= 0.30 ft

Assuming a steady-state flow, calculate the flow rate by using:

a. Borisov’s Method

b. The Giger-Reiss-Jourdan Method

c. Joshi’s Method

d. The Renard-Dupuy Method

530 Reservoir Engineering Handbook

Reservoir Eng Hndbk Ch 07 2001-10-24 16:50 Page 530

8. A 2,000-foot-long horizontal well is drilled in a solution gas drive

reservoir. The well is producing at a stabilized flow rate of 900

STB/day and wellbore pressure of 1000 psi. The current average reser-

voir pressure in 2000 psi. Generate the IPR data of this horizontal well

by using Cheng’s method.

REFERENCES

1. Beggs, D., “Gas Production Operations,” OGCI, Tulsa, Oklahoma, 1984.

2. Beggs, D., “Production Optimization Using NODAL Analysis,” OGCI,

Tulsa, Oklahoma, 1991

3. Bendakhlia, H., and Aziz, K., “IPR for Solution-Gas Drive Horizontal

Wells,” SPE Paper 19823, presented at the 64th Annual Meeting in San

Antonio, Texas, October 8–11, 1989.

4. Borisov, Ju. P., “Oil Production Using Horizontal and Multiple Deviation

Wells,” Nedra, Moscow, 1964. Translated by J. Strauss. S. D. Joshi (ed.).

Bartlesville, OK: Phillips Petroleum Co., the R & D Library Translation,

1984.

5. Cheng, A. M., “IPR For Solution Gas-Drive Horizontal Wells,” SPE Paper

20720, presented at the 65th Annual SPE meeting held in New Orleans, Sep-

tember 23–26, 1990.

6. Fetkovich, M. J., “The Isochronal Testing of Oil Wells,” SPE Paper 4529,

presented at the SPE 48th Annual Meeting, Las Vegas, Sept. 30–Oct. 3, 1973.

7. Giger, F. M., Reiss, L. H., and Jourdan, A. P., “The Reservoir Engineering

Aspect of Horizontal Drilling,” SPE Paper 13024, presented at the SPE

59th Annual Technical Conference and Exhibition, Houston, Texas, Sept.

16–19, 1984.

8. Golan, M., and Whitson, C. H., Well Performance, 2nd ed. Englewood

Cliffs, NJ: Prentice-Hall, 1986.

9. Joshi, S., Horizontal Well Technology. Tulsa, OK: PennWell Publishing

Company, 1991.

10. Klins, M., and Clark, L., “An Improved Method to Predict Future IPR

Curves,” SPE Reservoir Engineering, November 1993, pp. 243–248.

11. Muskat, M., and Evinger, H. H., “Calculations of Theoretical Productivity

Factor,” Trans. AIME, 1942, pp. 126–139, 146.

Oil Well Performance 531

Reservoir Eng Hndbk Ch 07 2001-10-24 16:50 Page 531

12. Renard, G. I., and Dupuy, J. M., “Influence of Formation Damage on the

Flow Efficiency of Horizontal Wells,” SPE Paper 19414, presented at the

Formation Damage Control Symposium, Lafayette, Louisiana, Feb. 22–23,

1990.

13. Standing, M. B., “Inflow Performance Relationships for Damaged Wells Pro-

ducing by Solution-Gas Drive,” JPT, (Nov. 1970, pp. 1399–1400.

14. Vogel, J. V., “Inflow Performance Relationships for Solution-Gas Drive

Wells,” JPT, Jan. 1968, pp. 86–92; Trans. AIME, p. 243.

15. Wiggins, M. L., “Generalized Inflow Performance Relationships for Three-

Phase Flow,” SPE Paper 25458, presented at the SPE Production Operations

Symposium, Oklahoma City, March 21–23, 1993.

532 Reservoir Engineering Handbook

Reservoir Eng Hndbk Ch 07 2001-10-24 16:50 Page 532

Determination of the flow capacity of a gas well requires a relation-

ship between the inflow gas rate and the sand-face pressure or flowing

bottom-hole pressure. This inflow performance relationship may be

established by the proper solution of Darcy’s equation. Solution of

Darcy’s Law depends on the conditions of the flow existing in the reser-

voir or the flow regime.

When a gas well is first produced after being shut-in for a period of

time, the gas flow in the reservoir follows an unsteady-state behavior

until the pressure drops at the drainage boundary of the well. Then the

flow behavior passes through a short transition period, after which it

attains a steady-state or semisteady (pseudosteady)-state condition. The

objective of this chapter is to describe the empirical as well as analytical

expressions that can be used to establish the inflow performance relation-

ships under the pseudosteady-state flow condition.

VERTICAL GAS WELL PERFORMANCE

The exact solution to the differential form of Darcy’s equation for

compressible fluids under the pseudosteady-state flow condition was

given previously by Equation 6-150 as:

[]

1422 0 75ln .

(8 -1)

533

CHAPTER 8

GAS WELL PERFORMANCE

Reservoir Eng Hndbk Ch 08 2001-10-24 11:13 Page 533

where Q

= gas flow rate, Mscf/day

k = permeability, md

–

= average reservoir real gas pseudo-pressure, psi

/cp

T = temperature, °R

s = skin factor

h = thickness

= drainage radius

= wellbore radius

The productivity index J for a gas well can be written analogous to

that for oil wells as:

with the absolute open flow potential (AOF), i.e., maximum gas flow

rate (Q

)

max

, as calculated by:

where J = productivity index, Mscf/day/psi

/cp

)

max

= AOF

Equation 8-3 can be expressed in a linear relationship as:

Equation 8-5 indicates that a plot of y

vs. Q

would produce a

straight line with a slope of (1/J) and intercept of y

–

, as shown in Figure

8-1. If two different stabilized flow rates are available, the line can be

extrapolated and the slope is determined to estimate AOF, J, and y

–

wf r g

Q=-

(8 - 5)

()

max

=y (8- 4)

grwf

=-()yy (8 - 3)

rwf

1422 0 75ln .

(8 - 2)

534 Reservoir Engineering Handbook

Reservoir Eng Hndbk Ch 08 2001-10-24 11:13 Page 534

Equation 8-1 can be alternatively written in the following integral

form:

Note that (p/m

z) is directly proportional to (1/m

) where B

is the

gas formation volume factor and defined as:

where B

= gas formation volume factor, bbl/scf

z = gas compressibility factor

T = temperature, °R

= 0 00504.(8-7)

1422 0 75

ln .

(8 - 6)

Gas Well Performance 535

Figure 8-1. Steady-state gas well flow.

Reservoir Eng Hndbk Ch 08 2001-10-24 11:13 Page 535

Equation 8-6 can then be written in terms of B

as:

where Q

= gas flow rate, Mscf/day

= gas viscosity, cp

k = permeability, md

Figure 8-2 shows a typical plot of the gas pressure functions (2p/m

and (1/m

) versus pressure. The integral in Equations 8-6 and 8-8 rep-

resents the area under the curve between p

–

and p

As illustrated in Figure 8-2, the pressure function exhibits the follow-

ing three distinct pressure application regions:

Region I. High-Pressure Region

When both p

and p

–

are higher than 3000 psi, the pressure functions

(2p/m

z) and (1/m

) are nearly constants. This observation suggests

that the pressure term (1/m

) in Equation 8-8 can be treated as a con-

stant and removed outside the integral, to give the following approxima-

tion to Equation 8-6:

where Q

= gas flow rate , Mscf/day

= gas formation volume factor, bbl/scf

k = permeability, md

The gas viscosity m

and formation volume factor B

should be evalu-

ated at the average pressure p

avg

as given by:

avg

(8 -10)

kh p p

rwf

g g avg

70810

075

.( ) ( )

( ) ln .m

(8 - 9)

70810

075

.( )

ln .

(8 - 8)

536 Reservoir Engineering Handbook

Reservoir Eng Hndbk Ch 08 2001-10-24 11:13 Page 536

The method of determining the gas flow rate by using Equation 8-9

commonly called the pressure-approximation method.

It should be pointed out the concept of the productivity index J cannot

be introduced into Equation 8-9 since Equation 8-9 is only valid for

applications when both p

and p

–

are above 3000 psi.

Region II. Intermediate-Pressure Region

Between 2000 and 3000 psi, the pressure function shows distinct cur-

vature. When the bottom-hole flowing pressure and average reservoir

pressure are both between 2000 and 3000 psi, the pseudopressure gas

pressure approach (i.e., Equation 8-1) should be used to calculate the gas

flow rate.

Region III. Low-Pressure Region

At low pressures, usually less than 2000 psi, the pressure functions

(2p/m

z) and (1/m

) exhibit a linear relationship with pressure. Golan

and Whitson (1986) indicated that the product (m

z) is essentially con-

stant when evaluating any pressure below 2000 psi. Implementing this

observation in Equation 8-6 and integrating gives:

Gas Well Performance 537

Figure 8-2. Gas PVT data.

Reservoir Eng Hndbk Ch 08 2001-10-24 11:13 Page 537