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Step 1) Calculate the pressure derivative functions of the well-test data (tabulated in table 4.11)h= 78 ft

= 1 cp t (hrs) pws (psi)

q= 600 STB/D 0 250

pwf= 250 psia 0.0001 254.09

= 0.2 0.0002 258.16

B= 1.1 RB/STB 0.0005 270.3

p bar= 2447 psia 0.0008 282.33

rw= 0.365 ft 0.0010 290.29

ct= 1.61E-05 psi^-1 0.0030 367.39

tp= 1400 hrs 0.0050 440.4

0.0080 542.99

0.0100 607.11

0.0160 780.68

0.0255 1005.1

0.0406 1263.2

0.0649 1515.6

0.1040 1714

0.1650 1837

0.2640 1907.4

0.4210 1950

0.6720 1983.21.0700 2013.5

1.7100 2043.1

2.7300 2072.1

4.3600 2100.7

6.5000 2124.9

10.5000 2153.7

15.1000 2175.4

20.0000 2192

25.0000 2205.2

30.0000 2215.9

35.0000 2225

40.0000 2232.8

45.0000 2239.6

50.0000 2245.7

55.0000 2251.2

60.0000 2256.2

65.0000 2260.8

70.0000 2265

72.0000 2266.6

Table 4.10- Pressure Buildup Test Data

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80.0000 2272.6

Step 2) Plot tep' and p as functions of te on log-log graph

Step 3) We align the horizontal portion of the later-time derivative data for te>0.672 hour with (tD/CD)pD'=

1

10

100

1000

10000

0.1

1

10

100

1000

10000

0.0100 0.1000 1.0000 10.0000 100.0000

pressure change vs equivalent

time

pressure derivative vs.

equivalent time

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Step 4) We then align the data points exhibiting a unit slope, te

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te (hrs)= t/(1+t/tp) p (psi) tep' = te* dPws/d(te)

0.0000 0 0

0.0001 4.09 5.8718

0.0002 8.16 9.049

0.0005 20.3 21.41

0.0008 32.33 35.762

0.0010 40.29 44.832

0.0030 117.39 119.84

0.0050 190.4 182.17

0.0080 292.99 268.64

0.0100 357.11 317.26

0.0160 530.68 425.64

0.0255 755.1 518.27

0.0406 1013.2 546.56

0.0649 1265.6 479.59

0.1040 1464 342.82

0.1650 1587 208.69

0.2640 1657.4 120.45

0.4209 1700 81.174

0.6717 1733.2 68.0941.0692 1763.5 64.192

1.7079 1793.1 62.642

2.7247 1822.1 61.664

4.3465 1850.7 61.021

6.4700 1874.9 60.641

10.4218 1903.7 60.329

14.9389 1925.4 60.127

19.7183 1942 60.014

24.5614 1955.2 60.031

29.3706 1965.9 59.989

34.1463 1975 59.941

38.8889 1982.8 59.858

43.5986 1989.6 59.94

48.2759 1995.7 59.787

52.9210 2001.2 59.774

57.5342 2006.2 59.799

62.1160 2010.8 59.808

66.6667 2015 59.914

68.4783 2016.6 59.98

Table 4.11-Pressure and Derivative Plotting Functions

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75.6757 2022.6 59.834

.5 on the derivative type curve.

pressure change vs equivalent time

pressure derivative vs. equivalent time

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Step 1) Calculate Pressure Derivative Functions. Tabulated in Table 4.13

h= 21 ft Table 4.12-Pressure Buildup Test D

tp= 2000 hrs t (hrs)

g= 0.03274 cp 0

pi= 9000 psia 0.01

rw= 0.365 ft 0.0149

qg= 100 Mscf/D 0.0221

ct= 4.54E-05 psia^-1 0.0329

pa,i= 7366.1 psia 0.0489

= 0.1 0.0728

T= 670 R 0.108

g= 0.6 0.161

z= 1.31 0.24

Bg= 0.491 RB/Mscf 0.356

0.53

0.788

1.17

1.74

2.59

3.86

5.748.53

12.7

18.9

28.1

41.8

62.1

92.4

137

204

304

452

672

1000

Step 2) Plot adjusted pressure change (pa) and adjusted pressure derivative (taepa') vs. ad

10000

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Step 3) Using the Bourdet et al. type curves, match both pa and taepa' in the vertical direc

1

10

100

1000

0.001 0.01 0.1 1 10 100 1000

adjusted

equivalen

adjusted

adjusted

1

10

100

1000

10000

100000

0.1 1 10 100

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Step 4) We can calculate CDusing a point (tae,pa)USL from the unit-slope line of the pressu

We choose (tae=.01528 hours and pa=21.010psi) and calculate:

CD= 1.05E+02

Step 5) A good match of the curves is characterized by the correlating parameter CDe2s

=10^2

Step 6) From the match shown in the graph, we obtain a pressure match point of pa=3800ps

Step 7) From the pressure match point, the permability is :

k= 0.028444 md

Step 8) Calculate the dimensionless wellbore storage coefficient, CD from the time match poin

CD= 1.08E+02

This agrees with the value calculated from the USL.

Step 9) Estimate the skin factor with the value of CDand the correlating parameter:

s= -3.78E-02

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ata, Example 4.5 Table 4.13

pws (psia) pa=pa,ws-pa,wf te (hrs)= t/(1+t/tp)

6287.1 0 0

6296.6 9.6426 0.00999995

6301.1 14.21 0.014899889

6307.8 21.01 0.022099756

6317.7 31.059 0.032899459

6332.1 45.675 0.048898804

6353.1 66.99 0.07279735

6383.5 97.85 0.107994168

6427.1 142.12 0.160987041

6488.6 204.56 0.239971203

6573.6 290.87 0.355936643

6687.9 406.93 0.529859587

6834.7 556.02 0.78768965

7011.8 736 1.16931595

7208.3 935.76 1.738487516

7405.9 1136.6 2.586650288

7586 1319.6 3.85256455

7738.7 1474.6 5.7235733457864.9 1602.5 8.493774054

7971.4 1710.5 12.61986386

8065.6 1805.8 18.72306702

8153.2 1894.3 27.71066515

8234.4 1976.5 40.94426486

8313.4 2056.3 60.22986276

8389.8 2133.4 88.31963296

8463.7 2207.9 128.2171268

8534.9 2279.6 185.1179673

8602.9 2348 263.8888889

8666.6 2412 368.6786297

8725.3 2498.1 502.994012

8777.6 2523.5 666.6666667

justed equivalent time (tae) on log-log paper

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tion.

ressure change vs. adjusted

t time

ressure derivative vs.

quivalent time

1000 10000

adjusted pressure change vs. adjusted

equivalent time

adjusted pressure derivative vs. adjusted

equivalent time

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e-change data.

i and pD=10 and a time match point of tae=0.27 hr and tD/CD=0.1

t:

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tae=ta/(1+ta/tp) taepa'

0

0.0069 11.442

0.0103 14.35

0.0153 21.194

0.0228 30.993

0.0339 45.022

0.0505 65.568

0.0751 93.656

0.1125 132.03

0.1685 184.69

0.2519 249.29

0.3789 323.68

0.5711 399.43

0.8631 456.53

1.3114 476.88

1.9993 454.02

3.0545 400.08

4.6507 337.577.0594 282.93

10.704 245.2

16.167 224.2

24.31 209.96

36.439 201.32

54.31 197.48

80.629 194.43

118.42 191.57

172.93 188.26

249.23 186.43

351.85 228.46

484.97 173.32

648.68 182.19