Tarek Ahmed. Reservoir engineering handbook

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14. A drawdown test was conducted on a new well with results as given

below:

t, hr p

, psi

1.50 2978

3.75 2949

7.50 2927

15.00 2904

37.50 2876

56.25 2863

75.00 2848

112.50 2810

150.00 2790

225.00 2763

Given:

= 3400 psi h = 25 ft Q = 300 STB/day

= 18 ¥ 10

-6

psi

-1

= 1.8 cp B

= 1.1 bbl/STB

= 0.25 ft f=12%

Assuming no wellbore storage, calculate:

• Average permeability

• Skin factor

15. A drawdown test was conducted on a discovery well. The well was

flowed at a constant flow rate of 175 STB/day. The fluid and reser-

voir data are given below:

= 25% f=15% h = 30 ft ct = 18 ¥ 10

-6

psi

-1

= 0.25 ft p

= 4680 psi m

= 1.5 cp B

= 1.25 bbl/STB

468 Reservoir Engineering Handbook

Reservoir Eng Hndbk Ch 06b 2001-10-24 10:48 Page 468

The drawdown test data is given below:

t, hr p

, psi

0.6 4388

1.2 4367

1.8 4355

2.4 4344

3.6 4334

6.0 4318

8.4 4309

12.0 4300

24.0 4278

36.0 4261

48.0 4258

60.0 4253

72.0 4249

84.0 4244

96.0 4240

108.0 4235

120.0 4230

144.0 4222

180.0 4206

Calculate:

• Drainage radius

• Skin factor

• Oil flow rate at a bottom-hole flowing pressure of 4300 psi, assum-

ing a semisteady-state flowing conditions.

16. A pressure build-up test was conducted on a well that had been pro-

ducing at 146 STB/day for 53 hours. The reservoir and fluid data are

given below.

= 1.29 bbl/STB m

= 0.85 cp c

= 12 ¥ 10

-6

psi

-1

f=10% p

= 1426.9 psig A = 20 acres

Fundamentals of Reservoir Fluid Flow 469

Reservoir Eng Hndbk Ch 06b 2001-10-24 10:48 Page 469

The build-up data is as follows:

Time, hr p

, psig

0.167 1451.5

0.333 1476.0

0.500 1498.6

0.667 1520.1

0.833 1541.5

1.000 1561.3

1.167 1581.9

1.333 1599.7

1.500 1617.9

1.667 1635.3

2.000 1665.7

2.333 1691.8

2.667 1715.3

3.000 1736.3

3.333 1754.7

3.667 1770.1

4.000 1783.5

4.500 1800.7

5.000 1812.8

5.500 1822.4

6.000 1830.7

6.500 1837.2

7.000 1841.1

7.500 1844.5

8.000 1846.7

8.500 1849.6

9.000 1850.4

10.000 1852.7

11.000 1853.5

12.000 1854.0

12.667 1854.0

14.620 1855.0

Calculate:

• Average reservoir pressure

• Skin factor

• Formation capacity

470 Reservoir Engineering Handbook

Reservoir Eng Hndbk Ch 06b 2001-10-24 10:48 Page 470

REFERENCES

1. Al-Hussainy, R., and Ramey, H. J., Jr., “Application of Real Gas Flow The-

ory to Well Testing and Deliverability Forecasting,” Jour. of Petroleum

Technology, May 1966; Theory and Practice of the Testing of Gas Wells, 3rd

ed. Calgary, Canada: Energy Resources Conservation Board, 1975.

2. Al-Hussainy, R., Ramey, H. J., Jr., and Crawford, P. B., “The Flow of Real

Gases Through Porous Media,” Trans. AIME, 1966, pp. 237, 624.

3. Chatas, A. T., “A Practical Treatment of Nonsteady-state Flow Problems in

Reservoir Systems,” Pet. Eng., Aug 1953, pp. B-44–56.

4. Craft, B., Hawkins, M., and Terry, R., Applied Petroleum Reservoir Engi-

neering, 2nd ed. Prentice Hall, 1990.

5. Craft, B., and Hawkins, M., Applied Petroleum Reservoir Engineering. Pren-

tice-Hall, 1959.

6. Dake, L. P., The Practice of Reservoir Engineering. Amsterdam: Elsevier, 1994.

7. Dake, L., Fundamentals of Reservoir Engineering. Amsterdam: Elsevier, 1978.

8. Davis, D. H., “Reduction in Permeability with Overburden Pressure,” Trans.

AIME, 1952, pp. 195, 329.

9. Donohue, D., and Erkekin, T., “Gas Well Testing, Theory and Practice,”

IHRDC, 1982.

10. Earlougher, Robert C., Jr., Advances in Well Test Analysis, Monograph Vol.

5, Society of Petroleum Engineers of AIME. Dallas, TX: Millet the Printer,

1977.

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

sented at the SPE Annual meeting, Las Vegas, September 30–October 3, 1973.

12. Golan, M. and Whitson, C., Well Performance, 2nd ed. Englewood Cliffs,

NJ: Prentice-Hall, 1986.

13. Hawkins, M., “A Note on the Skin Effect,” Trans. AIME, 1956, pp. 356.

14. Horne, R. Modern Well Test Analysis. Palo Alto, CA: Petroway, Inc., 1995.

15. Horner, D. R., “Pressure Build-Up in Wells,” Proc., Third World Pet. cong.,

The Hague (1951), Sec II, 503–523. Also Reprint Series, No. 9—Pressure

Analysis Methods, pp. 25–43. Dallas: Society of Petroleum Engineers of

AIME, 1967.

16. Hurst, W., “Establishment of the Skin Effect and Its Impediment to Fluid

Flow into a Wellbore,” Petroleum Engineering, Oct. 1953, p. 25, B-6.

Fundamentals of Reservoir Fluid Flow 471

Reservoir Eng Hndbk Ch 06b 2001-10-24 10:48 Page 471

17. Jones, S. C., “Using the Inertial Coefficient, b, to Characterize Heterogeneity

in Reservoir Rock,” SPE Paper 16949, presented at the SPE Conference,

Dallas, TX, Sept. 27–30, 1987.

18. Joshi, S., Horizontal Well Technology. Pennwell Publishing Company, 1991.

19. Lee, J., and Wattenbarger, R., Gas Reservoir Engineering. SPE Textbook

Series Vol. 5, SPE, 1996.

20. Lee, John W., Well Testing. Dallas: Society of Petroleum Engineers Text-

book Series, 1982.

21. Matthews, S., Bronz, F., and Hazebroek, P. “A Method for the Determina-

tion of Average Pressure in a Bounded Reservoir,” Trans. AIME, 1954, Vol.

201, pp. 82–191.

22. Matthews, C. S., and Russell, D. G., “Pressure Buildup and Flow Tests in

Wells,” Monograph Vol. 1, Society of Petroleum Engineers of AIME. Dal-

las, TX: Millet the Printer, 1967.

23. Ramey, H., and Cobb, W. “A General Pressure Buildup Theory for a Well in

a Closed Drainage Area,” JPT, December 1971, pp. 1493–1505.

24. Russell, D. G., Goodrich, J. H., Perry, G. E., and Bruskotter, J. F., “Methods

for Predicting Gas Well Performance,” JPT, Jan. 1966, pp. 99–108; Trans.

AIME, p. 237.

25. Slider, H. C., Practical Petroleum Reservoir Engineering Methods. Tulsa,

OK: Petroleum Publishing Co., 1976.

26. van Everdingen, A. F., “The Skin Effect and Its Influence on the Productive

Capacity of a Well,” Trans. AIME, 1953, pp. 171, 198.

27. van Everdingen, A. F., and Hurst, W., “The Application of the Laplace

Transformation to Flow Problems in Reservoirs,” Trans. AIME, 1949, pp.

186, 305–324.

28. Wattenbarger, Robert A., and Ramey, H. J. Jr., “Gas Well Testing With Tur-

bulence. Damage and Wellbore Storage,” JPT, 1968, pp. 877–887; Trans.

AIME, p. 243.

472 Reservoir Engineering Handbook

Reservoir Eng Hndbk Ch 06b 2001-10-24 10:48 Page 472

This chapter presents the practical reservoir engineering equations that

are designed to predict the performance of vertical and horizontal oil

wells. The chapter also describes some of the factors that are governing

the flow of fluids from the formation to the wellbore and how these fac-

tors may affect the production performance of the well. The analysis of

the production performance is essentially based on the following fluid

and well characteristics:

• Fluid PVT properties

• Relative permeability data

• Inflow-performance-relationship (IPR)

VERTICAL OIL WELL PERFORMANCE

Productivity Index and IPR

A commonly used measure of the ability of the well to produce is the

Productivity Index. Defined by the symbol J, the productivity index is

the ratio of the total liquid flow rate to the pressure drawdown. For a

water-free oil production, the productivity index is given by:

where Q

= oil flow rate, STB/day

J = productivity index, STB/day/psi

–

= volumetric average drainage area pressure (static pressure)

(7 -1)

473

CHAPTER 7

OIL WELL PERFORMANCE

Reservoir Eng Hndbk Ch 07 2001-10-24 16:49 Page 473

= bottom-hole flowing pressure

Dp = drawdown, psi

The productivity index is generally measured during a production test

on the well. The well is shut-in until the static reservoir pressure is

reached. The well is then allowed to produce at a constant flow rate of Q

and a stabilized bottom-hole flow pressure of p

. Since a stabilized

pressure at surface does not necessarily indicate a stabilized p

, the bot-

tom-hole flowing pressure should be recorded continuously from the

time the well is to flow. The productivity index is then calculated from

Equation 7-1.

It is important to note that the productivity index is a valid measure of

the well productivity potential only if the well is flowing at pseudosteady-

state conditions. Therefore, in order to accurately measure the productivity

index of a well, it is essential that the well is allowed to flow at a constant

flow rate for a sufficient amount of time to reach the pseudosteady-state as

illustrated in Figure 7-1. The figure indicates that during the transient flow

period, the calculated values of the productivity index will vary depending

upon the time at which the measurements of p

are made.

474 Reservoir Engineering Handbook

Figure 7-1. Productivity index during flow regimes.

Reservoir Eng Hndbk Ch 07 2001-10-24 16:49 Page 474

The productivity index can be numerically calculated by recognizing

that J must be defined in terms of semisteady-state flow conditions.

Recalling Equation 6-149:

The above equation is combined with Equation 7-1 to give:

where J = productivity index, STB/day/psi

= effective permeability of the oil, md

s = skin factor

h = thickness, ft

The oil relative permeability concept can be conveniently introduced

into Equation 7-3 to give:

Since most of the well life is spent in a flow regime that is approximat-

ing the pseudosteady-state, the productivity index is a valuable method-

ology for predicting the future performance of wells. Further, by moni-

toring the productivity index during the life of a well, it is possible to

determine if the well has become damaged due to completion, workover,

production, injection operations, or mechanical problems. If a measured J

has an unexpected decline, one of the indicated problems should be

investigated.

A comparison of productivity indices of different wells in the same

reservoir should also indicate some of the wells might have experienced

unusual difficulties or damage during completion. Since the productivity

0 00708

075

ln .

(7 - 4)

0 00708

075

ln .m

(7 - 3)

khp p

or wf

0 00708

075

.()

ln .m

(7 - 2)

Oil Well Performance 475

Reservoir Eng Hndbk Ch 07 2001-10-24 16:49 Page 475

indices may vary from well to well because of the variation in thickness

of the reservoir, it is helpful to normalize the indices by dividing each by

the thickness of the well. This is defined as the specific productivity

index J

, or:

Assuming that the well’s productivity index is constant, Equation 7-1

can be rewritten as:

where Dp = drawdown, psi

J = productivity index

Equation 7-6 indicates that the relationship between Q

and Dp is a

straight line passing through the origin with a slope of J as shown in Fig-

ure 7-2.

QJpp Jp

orwf

=- =()D (7 - 6)

hp p

rwf

-()

(7 - 5)

476 Reservoir Engineering Handbook

Pressure

Flow Rate

Figure 7-2. Q

vs. Dp relationship.

Reservoir Eng Hndbk Ch 07 2001-10-24 16:49 Page 476

Alternatively, Equation 7-1 can be written as:

The above expression shows that the plot p

against Q

is a straight

line with a slope of (-1/J) as shown schematically in Figure 7-3. This

graphical representation of the relationship that exists between the oil

flow rate and bottom-hole flowing pressure is called the inflow perfor-

mance relationship and referred to as IPR.

Several important features of the straight-line IPR can be seen in Fig-

ure 7-3:

• When p

equals average reservoir pressure, the flow rate is zero due to

the absence of any pressure drawdown.

• Maximum rate of flow occurs when p

is zero. This maximum rate is

called absolute open flow and referred to as AOF. Although in practice

this may not be a condition at which the well can produce, it is a useful

definition that has widespread applications in the petroleum industry

wf r o

(7 - 7)

Oil Well Performance 477

STB/day AOF

Pressure psi

Slope= -1/J

Figure 7-3. IPR.

Reservoir Eng Hndbk Ch 07 2001-10-24 16:49 Page 477