A Study of the Orifice Well Tester and Critical Flow Prover

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AStudy of the Orifice Well Tester and Critical Flow Prover

lOUIS B.

lESEM

JOHN J. McKETTA, JR.

TEXAS

PETROLEUM

RESEARCH

COMMITTEE

UNIVERSITY OF TEXAS

MEMBER

AIME

GEORGE H.

FANCHER

MEMBER AIME

TEXAS

PETROLEUM RESEARCH COMMITTEE

AUSTIN

TEX

INTRODUCT ION

The

proration

of

oil produced in

the field frequently

is

based partially

or entirely upon the gas-oil ratio of

wells. The measurement of the gas

oil ratio is one

of

the more impor

tant field tests in regulatory and pro

ration work, and the test always

should be conducted according to

standardized methods and procedure.

Obviously, the gas-oil ratio and

the volume of gas produced by a

well depend upon many factors but

should be independent of the method

of

measurement and

of

the devices

used to measure gas and oil. Conse

quently, the volume of gas accom

panying a barrel of oil produced by

a weI may be measured by any re

liable and accurate device or instru

ment. Frequently either a

critical

flow prover or an orifice well tester

is

used for this purpose, and for a

particular well the same rate of flow

of gas should be obtained regardless

of whether a critical flow prover or

an orifice well tester is employed in

the test.

In Texas, when using either in

strument, either Capacity Table 1

or

5' is employed in making the

necessary computations.

f

the tables

are used, a discrepancy always

is

found whenever the two instruments

are compared by extrapolation to the

Original manuscript

received in Society

of

Petroleum Engineers

Office

on

Feb. 18,

1957,

Revised

manuscript

received July 10.

1957.

Paper

presented

a t joint

University of

T'exas

Texas A&M Student

Chapter

Regional

Meeting in Austin, Feb.

14-15, 1957.

lReferences given

at

end of

paper

SEPTEMBER, ] 957

SPE-812-G

same conditions of flow. Clearly,

Tables 1

and

5 must be at fault in

some respects.

The orifice well tester and the Bu

reau of Mines type of critical flow

prover are essentially the same

in

strument;

both devices utilize a

square-edged orifice V8 in. in di

ameter as the primary element, and

both freely discharge gas to the at

mosphere.

Tables for the orifice well tester'

have been published in the ranges

of

0 to 15 in.

of

water and 0 to 40

in.

of

mercury

(Hg)

differential in

pressure. Coefficients for the critical

flow prover have been published for

differentials in pressure greater than

75 psia.

An

extrapolation of either

differs from the other set of data as

much as

18

per

cent at some points.

No

immediately obvious reasons for

the discrepancy was found,

and

data

available from the literature were

insufficient to effect reconciliation.

Consequently, a series (\f experiments

was performed to check the avail

able data and to determine discharge

coefficients for the two devices in an

overlapping range

of

differential pres

sure.

The correlating equation used in

preparation of tables such as Tables

1 and 5' is the so-called hydraulic

equation,

Q = C,v h .

1)

The

tables cover orifice sizes from

VB

through 11,4 in.

A second set of tables, for use

with greater differentials in pressure,

apply only to the , 1, and 1Y -in.

orifice plates over a pressure range

of 0

to

40 in. of Hg. The correlating

equation used in preparation

of

the

tables is

Q

_ C H(29.32 0.3H)

- ~

G

(2)

Each of these equations

is

valid only

for the range to which it has been

applied, and neither equation is valid

for extrapolation.

Theoretical

equations

for flow

through an orifice are based upon

assumptions of fractionless flow and

an

emergent jet the size of the

orifice. A multiplier,

Cd

called the

discharge coefficient,

is

inserted into

the theoretical expression to compen

sate for both frictional losses and

the contraction of the jet experienced

in the plane

of

the orifice. Bucking

ham shows tha t Cd should vary with

the ratio of upstream to downstream

pressure for flow of a compressible

fluid at any average linear velocity

through the orifice less than the

velocity of sound.

Work

published

by the National Advisory Committee

for Aeronautics' indicates that the

variation continues into the so-called

critical flow region until the vena

contracta coincides with the plane

of the orifice. The NACA work,

however, does not indicate a level

ing off

of

the coefficient.

The

work

of

the Bureau

of

Mines'

for

the criti

cal flow prover was based on differ

ential pressures greater

than

75 psi

and indicates that the discharge co

efficient,

Cd,

is constant in this region

at a value

of

about 0.86.

61



On

the basis

of

the work which has

been cited, experiments were initiated to

determine the discharge coefficients for

TABLE 1 - CAPACITIES FOR 2 IN. ORIFICE WELL

TESTER'; Mel/DAY, PRESSURE

BASE, 14.65

PSIA SP.

GR. 0.60; BASE AND FLOWING TEMPERATURE, 60°F

Pressure

Inches of

Woter

1.0

1.2

1.4

1.6

1.8

2.0

2.2

2.4

2.6

2.8

3.0

3.2

3.4

J.6

3.8

4.0

4.5

5.0

5.5

6.0

6.5

7.0

8.0

9.0

10.0

11.

12.

13.

14.

15.

16.

17.

18.

19.

20.

22.

24.

26.

28.

30.

32.

34.

36.

38.

40.

42.

44.

46.

48.

50.

52.

54.

~ 6 .

58.

60.

62.

64.

66.

68.

70.

72.

74.

76.

78.

80.

82.

84.

86.

88.

90.

92.

94.

96.

98.

100.

/.

.379

.415

.499

.480

.509

.536

.562

.587

.611

.635

.658

.679

.700

.720

.740

.759

.805

.850

.891

.931

.969

1.01

1.08

1.14

1.20

1.27

1.32

1.38

1.43

1.48

1.53

1.58

1.62

1.67

1.71

1.80

1.88

1.96

2.04

2.11

2.19

2.26

2.32

2.39

2.46

2.52

2.58

2.64

2.70

2.76

2.82

2.87

2.93

2.98

3.04

3.09

3.14

3.19

3.25

3.30

3.35

3.40

3.44

3.49

3.54

3.59

3.64

3.69

3.73

3.78

3.83

3.87

3.92

3.96

4.00

1.75 in. ID.

Orifice Size Inches

I. 3/. /2 f4 1 1 I.

1.51 3.41 6.08 13.9 25.6 44.0

1.66 3.74 6.67

15.2

28.1 48.3

1.79 4.04 7.20 16.4 ~ 0 . 4 52.1

1.92

4.32 7.70 17.6

32.5

55.7

2.03

4.58

8.16 18.6 34.4 59.1

2.14 4.83

8.61

19.6

36.3 62.2

2.25 5.07 9.03 20.6 38.1 65.3

2.35 5.29 9.43

21.5

39.7

68.2

2.45 5.51 9.81 22.4 41.4 70.9

2.54

5.72

10.2

23.3

43.0 73.7

2.63

5.92

10.6 24.1 44.5 76.3

2.72

6.12

10.9

24.9 45.9 78.8

2.80 6.31 11.2 25.6 47.4 81.2

2.88 6.49 11.6 26.4 48.7 83.5

2.96 6.67 11.9 27.1 50.1 85.8

3.04 6.84

12.2

27.8 51.4 88.0

3.22 7.25 12.9 29.5 54.5 93.3

3.40 7.66

13.6

31.1 57.5 98.5

3.57 8.03 14.3 32.6 60.3 103.0

3.72

8.39 14.9

34.1 62.9 108

3.88

8.73

15.6 35.5 65.5 112

4.03

9.07

16.2

36.9

68.1 117

4.31 9.70

17.3

39.4 72.7

124

4.5710.3

18.3

41.8 77.1 132

4.82 10.9

19.3

44.1 81.4 139

5.06

11.4

20.3 46.3 85.5 146

5.29 11.9 21.2 48.4 89.2 152

5.51 12.4 22.1 50.4 93.0 159

5.72 12.9 22.9

52.3

96.5 165

5.93 13.3 23.8 54.2 100.0

171

6.12

13.8

24.6

56.0 103.0 176

6.32 14.2 25.3 57.8 107 182

6.5014.6

.26.1 59.4 110 187

6.69

15.1 26.8 61.1 113 192

6.86 15.4 27.5 62.7 116 197

7.20 16.2 28.9

65.9 121

206

7.53 17.0 30.2 68.9

127 216

7.85 17.7 31.5 71.7 132 225

8.16 18.4 32.7 74.5

137

233

8.45 19.0 33.9 77.2 142 241

8.74 19.7 35.1 79.9 147 249

9.02 20.3

36.2

82.4

152 257

9.30 20.9 37.3 84.9 156 264

9.56 21.5 38.4 87.3 161 272

9.82

22.1

39.4 89.7

165

279

10.1 22.7 40.4 92.0

169 286

10.3

23.3 41.4 94.3 173 293

10.6 23.8 42.3 96.4 177 299

10.8 24.3 43.4 98.7 181 306

,11.0 24.8 44.2

101.0

185 312

11.3

25.4 45.2 103 189 318

11.5 25.9 46.1 105 192 324

11.7 26.4 47.0 107 196 330

11.9 26.9 47.9

109 200 336

12.2 27.4 48.8 111 203 342

12.4 27.8 49.5

113 207 347

12.6 28.3 50.4

115 210 353

12.8 28.8 51.2

117 214 358

13.0 29.2 52.1 118

217 364

13.2

29.7 52.9

120

220

369

13.4

30.2

53.7 122 224 375

13.6

30.6

54.5

124

227

380

13.8 31.0 55.2 126 230 385

14.0 31.5 56.0 127 233 390

14.2

31.9 56.8 129 236 395

14.4 32.3 57.6 131 240 400

14.6 32.8 58.3 133 243 405

14.7

33.2 59.1 134 246 410

14.9 33.6

59.9 136 249 415

15.1 34.0 60.6

138

252

420

15.3 34.5 61.4 139 255

425

15.5

34.9 62.1

141

258

430

15.7

35.3

62.8 143 261 434

15.9

35.7 63.5 144 264 439

16.0 36.0

64.2

146

266

443

TABLE 2 - CAPACITIES FOR 2 IN. ORIFICE WELL

TESTER'; Mel/DAY, PRESSURE BASE, 14.65 PSIA SP.

GR. 0.60;

BASE

AND FLOWING TEMPERATURE, 60°F

Pressure

Inches

of

;-;-_-;-;-_O=-rc:-

ie-c: ::e--=S i =:eC'-

-,I e . c : . c h : ; : . e s = ~

Mercury

Vs

4 3/

2

1.0

1.41

5.65 12.7 22.6

51.6

1.1

1.48 5.92

13.3 23.7 54.1

1.2 1.55

6.19 13.9

24.8

56.6

1.3

1.61 6.45 14.5 25.9 59.0

1.4

1.67 6.69 15.1 26.9 61.2

1.5

1.73

6.94 15.6 27.8 63.4

1.6 1.79 7.18 16.2 28.8 65.6

1.7 1.85 7.40 16.7 29.7 67.6

1.8 1.90 7.62

17.2

30.6 69.6

1.9

1.96

7.84 17.7 31.4 71.6

2.0

2.01 8.04 18.1 32.3 73.5

2.2 2.11 8.46 19.0 33.9 77.3

2.4 2.21

8.84 19.9 35.5 80.8

2.6 2.30 9.21 20.7 37.0 84.2

2.8 2.40

9.59 21.6

38.5 87.6

62

95.3

99.9

104.0

109

113

117

121

125

128

132

135

142

149

155

161

163.0

170

178

185

192

199

206

212

218

224

:lJO

241

252

262

272

the orifice well tester in those

regions where data were

missing and to check pub

lished data.

EXPERIMENTAL

EQUIPMENT

The experimental

setup

used for the determination

of

discharge coefficients was

a 2-in. orifice

meter

run with

flange taps designed to GN

specifications and a commer

cial orifice well tester dis

charging freely to the atmos

phere and located approxi

mately

20 pipe

diameters

downstream from the meter

ing orifice. A 2-in. air line

supplied compressed air. Flow

was controlled by a gate

valve the air line. Differ

ential in pressure was meas

ured with either mercury

or

water manometers as re

quired, and a Bourdon-type

pressure gauge was used to

check

the

upstream

static

pressure

at

the meter.

Four

different sets

of

orifice well

tester plates were tested: brass

plates

VB-in.

thick, aluminum

plates

lis

-in. thick, brass

plates

1/16-in.

thick,

and

thin-edged

stainless

steel

plates designed according to

ASME-AGA

specifications.

EXPERIMENTAL

PROCEDURE

A

meter

plate

of

appropri

ate size was selected

to

main

tain differential pressure

across

the

metering

orifice

such that the flow through

this orifice would be treated

as that of an incompressible

fluid. The orifice to be tested

was installed in the tester and

flow established. After equi

librium had been achieved

~ 1 2 0

.

40 W ro

UPSTREAM PRESSURE lNCttES Of MERCURY

A8S0LUfE

FIG. I -TYPIC AL CAPACITY

CURVE, D/T

= 2.

TABLE 2 (Continued)

Pressure

Inches of

Mercury V

1 4

3.0 2.48

9.93

3.2 2.57

10.3

3.4 2.65

10.6

3.6 2.73 10.9

3.8 2.81 11.2

4.0

2.89

11.6

4.5 3.07 12.3

5.0 3.25

13.0

5.5 3.42 13.7

6.0 3.59

14.3

6.5 3.75 15.0

7.0 3.90

15.6

8.0 4.20 16.8

9.0 4.48

17.9

10.0 4.75 19.0

11. 5.02 20.1

12. 5.2721.1

13. 5.52 22.1

14. 5.76

23.0

15.

5.99

24.0

16. 6.23

24.9

17. 6.44 25.8

18. 6.67 26.7

19. 6.89 27.6

20.

7.1028.4

21. 7.31 29.2

22. 7.51 30.1

23. 7.71 30.8

24.

7.91 31.6

25. 8.10 32.4

26.

8.31

33.2

27. 8.50 34.0

28.

8.70 34.8

29.

8.90 35.6

30.

9.10 36.4

31.

9.29 37.2

32.

9.49 38.0

33. 9.70 38.8

34.

9.89

39.6

35. 10.1 40.3

36. 10.3 41.1

37. 10.5

41.9

38.

10.7

42.7

39. 10.9

43.5

40.

11.0

44.2

41. 11.2

44.9

42.

11.4

45.7

43.

11.6

46.5

44. 11.8 47.2

45. 12.0 48.0

46. 12.2 48.7

47. 12.4 49.5

48. 12.6 50.2

49. 12.8

51.0

50.

12.9

51.7

51. 13.1

52.5

52.

13.3 53.2

53.

13.5 53.9

54. 13.7 54.7

55. 13.8

55.4

56. 14.0 56.1

57. 14.2 56.8

58. 14.4 57.6

59.

'14.6

58.3

60. 14.7 59.0

61.

14.9

59.7

62. 15.1

60.4

63. 15.3 61.2

64. 15.5 61.8

65.

15.6 62.6

66.

15.8 63.2

67.

16.0 64.0

68.

16.2

64.6

69.

16.3

65.4

70. 16.5 66.0

71. 16.7 66.7

72. 16.9 67.4

73. 17.0 68.1

74.

17.2

68.8

75.

17.4 69.5

76. 17.6 70.3

77. 17.7

70.9

78. 17.9

71.7

79. 18.1 72.4

80. 18.3 73.1

81. 18.4

73.8

82.

18.6

74.4

83. 18.8 75.2

84. 19.0

75.9

85. 19.1 76.5

86.

19.3

77.2

87. 19.5 78.0

88.

19.7

78.6

89. 19.8

79.3

90.

20.0 80.0

91.

20.2 80.7

92.

20.4

81.4

93. 20.5

82.1

94.

20.7

82.9

95. 20.9 83.5

96.

21.1

84.2

97. 21.2 85.0

98. 21.4

85.6

99. 21.6 86.3

100.

21.8

87.1

1.75 in. ID.

Orifi ce Size Inches

~ 3 f 4 ~ ~ ~ - - I - ~ - . -

22.4

39.8

90.7

167 282

23.1 41.2 93.8 172 291

23.9

42.6 96.9

178 300

24.6 43.9 99.8 183 309

25.3

45.1

103.0

188 318

26.0 46.3 105 193 326

27.7 49.3 112 206 346

29.3 52.2 119 217 365

30.8 54.9 125 229 383

32.3 57.5

131 239 400

33.7 60.1

137 250 417

35.1 62.6 142

260 433

37.8

67.3

153

279 464

40.4 71.9

163

298

493

42.8 76.2 173

315 520

45.2

80.4 183 332

547

47.4 84.5 192

348

573

49.7 88.5 201 264 598

51.8 92.3 209 380 622

53.9 96.0 218 395 645

56.1 99.8226 410 669

58.0 103.0 234 424 690

60.1

107 242 438 713

62.0 110

250 452 735

64.0

114 258 466 756

65.8

117

265

479 776

67.7 120 272

492

797

69.4 124 280 505 816

71.2 127 287 517 835

72.9 130 292 529 853

74.8 133 299 543 875

76.5

136 306 555 895

78.3

139 313 568 916

80.1 142 320

580 937

81.9 146

328

594 958

83.6 149

334

606 978

85.4

152 342

619 999

87.3

155

349

633 1020

89.0

158

356 646 1040

90.8 161 363

658

1060

92.5 164 370 671 1080

94.3 168 277 684 1110

96.0 171 384 696 1130

97.8

174 391 709 1150

99.4 177

398 721

1160

101.0 180 405 733 1180

103 183 411

746

1200

105 186

418

758

1220

106 189 425

770

1240

108 192

432

783 1260

110 195 439 796 1280

111 198 445 807 1310

113 201 452 820 1330

115 204 459 832 1350

116

207 465 844 1360

118

210 472 857 1380

120 213

479

868 1400

121

216

485 880

1420

123 219

492

893 1440

125 222 498 904 1450

126 224 505 916 1470

128 227 511 927 1500

130 230 518 919 1520

131

233 525

952

1540

133 236 531 962 1550

134 239 537 974 1570

136 242 544 986 1 590

138 245 550 998 1610

139

247 1010 1630

141 250 563 1020 1640

142 253

569

1030 1660

144

256

576 1040

1680

145 258 582 1050 1710

147 261 588 1070 1720

149 264 594 1080

1740

150 267 600 1090 1760

152 270 607 1100 1780

153 272 613 1110 1790

155 275

620

1120 1810

156 278 626 1130 1830

158

281

632 1140 1850

160 284 638 1150 1860

161 287 645 1170 1880

163 289 651 1180 1910

164 292 658 1190

1930

166 295 664 1200 1940

167

298

670

1210 1960

169

301

677 1220

1980

171 303 683 1230 2000

172 306 689 1240 1210

174

309 695

1270

2030

175 312 702 1280 2050

177 315 708 1290 2070

178

317 714

1300

2080

180 320 720 1310 2110

182 323

727

1320 2130

183

326 733 1330

2150

185 328 739 1340 2160

186 331

746

1360 2180

188 334 752 1370 2200

189 337 758 1380 2220

191 340 765 1390

2230

193 343 771 1400 2250

194

345

777

1410 2270

196 348 784 1420

2300

JOURNAL OF PETROLEUM TECHNOLOGY



TABLE 3-ATMOSPHERIC

PRESSURE

MULTIPLIERS

Tester

Atmospher ic Pressure Inches of Mercury

Pressure

In of Water

28.5

27.7 26.9 26.0 25.1

1.0

.9846 .9707 .9566 .9406 .9242

2.0 .9847 .9708 .9568

.9407 .9244

3.0 .9847

.9709 .9569 .9409 .9246

4.0

.9847 .9710 .9570 .9410 .9248

5.0 .9848

.9710 .9571 .9412

.9250

6.0

.9848 .9711 .9572 .9413 .9252

7.0

.9848 .9712 .9573

.9415

.9253

8.0 .9849 .9712

.9574 .9416

.9255

9.0

.9849

.9713

.9575

.9418 .9257

10.0 .9850

.9714

.9576 .9419

.9259

11.0

.9850

.9715

.9577 .9420

.9261

12.0

.9850 .9715 .9578 .9422 .9263

13.0 .9851 .9716 .9579 .9423 .9265

14.0

.9851

.9717

.9580

.9425

.9267

15.0

.9151

.9717

.9581

.9426 .9268

16.0

.9852 .9718 .9582 .9428 .9270

17.0

.9852 .9719

.9583

.9429 .9272

18.0 .9852 .9719 .9585 .9430 .9274

19.0 .9853 .9720 .9586 .9432 .9276

20.0

.9853

.9721

.9587 .9433

.9277

24.0

.9855

.9723

.9591

.9439

.9285

28.0 .9856 .9726

.9594

.9444

.9291

32.0

.9857

.9729

.9598

.9449 .9298

36.0

.

9859

.9731

.9602 .9455 .9305

40.0

.9860

.9734

.9606

.9460 .9312

44.0

.9861 .9736 .9609 .9465 .9318

48.0

.9862

.9738

.9613 •9470 .9324

52.0

.9864

.9741

.9616

.9475

.9331

56.0

.9865 .9743 .9620 .9479 .9337

60.0 .9866 .9745 .9623 .9484 .9343

64.0

.9867 .9748

.9626 .9488 .9348

68.0 .9868

.9750

.9630

.9493 .9354

72.0

.9869 .9752 .9633

.9497

.9360

76.0 .9870 .9754

.9636

.9502

.9365

80.0

.9872 .9756 .9639

.9506 .9371

84.0

.9873 .9758 .9642 .9510 .9376

88.0

.9874 .9760 .9645

.9514 .9382

92.0

.9875 .9762 .9648 .9518

.9387

96.0

.9876 .9764

.9651 .9522 .9392

100.0 .9877 .9766 .9654 .9526 .9397

TABLE 4-ATMOSPHERIC PRESSURE MULTIPLIERS

Tester

Atmospheric Pressure Inches of Mercury

Pressure

In.

of

Mercury

28 5 27.7

26.9

26.0

25.1

1.0 .9851 .9716 .9580

.9424

.9266

2.0 .9856

.9726

.9594

.9443 .9290

3.0

.9860

.9734

.9606 .9461

.9313

4.0 .9864 .9742

.9618 .9477 .9334

5.0 .9868

.9750

.9630 .9493

.9354

6.0

.9872 .9757 .9640

.9508

.9373

7.0

.9876 .9764 .9650

.9522 .9391

8.0

.9879 .9770

.9660 .9535 .9408

9.0

.9882

.9776 .9669 .9547

.9423

10.0

.9885 .9782

.9678 .9559 .9439

11.0

.9888 .9787 .9686

.9570

.9453

12.0

.9891 .9793 .9693

.9581 .9466

13.0

.9893

.9797 .9701

.9591 .9479

14.0

.9896

.9802

.9708 .9600

.9492

15.0

.9898

.9807 .9714

.9609 .9503

16.0

.9900

.9811 .9721

.9618 .9515

17.0

.9903 .9815

.9727

.9627 .9525

18.0

.9905

.9819

.9733

.9635

.9536

19.0

.9907

.9823

.9738 .9642

.9545

20.0

.9908 .9826 .9744

.9650

.9555

21.0

.9910 .9830

.9749

.9657

.9564

22.0

.9912

.9833

.9754 .9664

.9573

23.0

.9914 .9836

.9759

.9670

.9581

24.0

.9915 .9840

.9763

.9676 .9589

TABLE 5-DISCHARGE COEFFICIENTS

FOR

SHARP·EDGED

ORI

FICES*

Tester Tester

Tester

Pressure Pressure

Pressure

In of Water

it

In. of Water

C

In. of Water d

0.0 0.604

11.0

0.610

54.0 0.631

1.0 0.605 12.0

0.611

56.0

0.632

1.2 0.605 13.0 0.611

58.0

0.633

1.4

0.605 14.0

0.612

60.0 0.633

1.6

0.605 15.0

0.612 62.0

0.634

1.8

0.605 16.0 0.613

64.0

0.635

2.0

0.605 17.0

0.613 66.0

0.636

2.2 0.605 18.0 0.614 68.0 0.637

2.4

0.605 19.0

0.614

70.0

0.638

2.6

0.606 20.0 0.615

72.0

0.639

2.8

0.606

22.0 0.616

74.0 0.639

3.0

0.606 24.0 0.617

76.0

0.640

3.2

0.606 26.0

0.618

78.0

0.641

3.4

0.606 28.0 0.619

80.0 0.642

3.6

0.606

30.0 0.620

82.0

0.643

3.8

0.606

32.0

0.621

84.0 0.644

4.0

0.606

34.0

0.622

86.0

0.645

4.5

0.607

36.0

0.623

88.0 0.646

5.0

0.607 38.0

0.624 90.0

0.647

5.5

0.607 40.0

0.625

92.0

0.648

6.0

0.607 42.0

0.626 94.0

0.649

6.5

0.608 44.0

0.626

96.0

0.650

7.0

0.608 46.0

0.628

98.0

0.650

8.0

0.608

48.0

0.628

100.0

0.651

9.0

0.609 50.0

0.629

10.0

0.610

52.0 0.630

0 /1>

8

SEPTEMBER,

1957

. 8 6 C : : : = ~ ~ _ = _- -3-

84 - : ~ : = _ - _ - _ - _ - _ - _ - _ ~ - _ - _

8.

5 W M

e

M

ro n

M

DIFFERENTIAL PRESSURE INCHES OF MERCURY

FIG. 2-GENERALIZED COEFFICIENTS

OF

DISCHARGE. FREE

DIS

CHARGE TO

ATMOSPHERIC PRESSURE OF

29.4 IN.

OF MERCURY

SOLID LINES

INDICATE

REGIONS

FOR

WHICH EXPERIMENTAL

DATA

WERE

OBTAINED•

the differential in pressure across

the metering orifice, the upstream

pressure on the orifice well tester,

and the temperature

of

the flow

stream were read and recorded.

This procedure was repeated a

number of

times to determine

the

differential pressure-capacity curve

for

each orifice tested (Fig.

1).

Barometric pressure was recorded

several times during each run.

RE SUL T S

The published tables

for

the

orifice well tester' for the range

o

to 15 in.

of

water were checked

within the limits

of

experimental

error. The

Bureau

of

Mines co

efficients' for the critical flow

prover were also found to be valid

for the range above 75 in.

of Hg

for all sizes

of

orifices tested.

The

discharge coefficient for a square

edged orifice in free discharge was

found to

be

a function

of

the ratio

of

downstream to upstream pre

sure within the range 1 to 75 in.

of Hg

with the ratio

of

orifice

diameter to edge-thickness as the

governing parameter. Above a dif

ferential

of

75 in.

of

Hg when dis

charging air to atmosphere

at

29.4

in.

of

Hg, the discharge coefficient

was constant for all ratios of diam

eter to thickness employed in this

work. The point at which the dis

charge coefficient becomes a con

stant seems to be a function

of

the

diameter to thickness ratio.

A region

of

unstable flow was

found for ratios

of

to

t of

2

and

3, and reproducible results could

not be obtained in these regions.

The region

of

reverse curvature

just

prior

to the linear portion

of

the curve obtained by plotting the

rate

of

flow against pressure

drop

is

a region of instability and is not

reproducible. This instability

is

not

observed

for

very thick

or

very

thin-edged orifices.

For the

very

thick orifices,

the vena

contract a

lies between

the upstream and

downstream surfaces

of

the orifice.

The emergent jet is attached to the

downstream edge

and

flow remains

stable. For the orifices of intermedi

ate thickness,

the

region

of

instabil

ity develops as the vena contracta

moves downstream with increasing

pressure drop, with

the

result that

a slight change in flow rate will

cause either attachment or detach

ment

of

the emergent jet.

The

vena

contracta

for

the thin-edged plates

is always beyond the downstream

edge of the plate, and consequently

flow is stable.

The discharge coefficient varies

with pressure drop, and a family

of

curves may be obtained

for

which

the

ratio

of

to

t

is a

para

meter (Fig. 2). As the pressure

drop across the orifice is increased,

the vena

contracta expands, caus

ing

an

increase in the discharge

coefficient.

f

fluid flow were fric

tionless, the value of the discharge

coefficient would

approach

1.0,

but

the frictional effects

of

real fluids

limit the useful range of the co

efficient from 0.83 to 0.86 for

sharp-edged orifices.

Discharge coefficients were cal

culated from the ratio

of

actual

flow rate predicted by theoretical

equations for adiabatic flow.' o

discontinuity

was

found

in the dis-

6



crlarge coefficients

at the point of

transition

from

subcritical to crit

ical flow conditions. The average

discharge coefficient (for all orifices

tested) in

the

critical flow region

beyond a

pressure drop of

75 in.

of

Hg was 0.84. The average

for

orifices with a D/t = 8.0 was 0.83,

a difference

of only

1.2

per

cent.

The

average

for the

orifices

for

use with

the Bureau of Mines'

2-in.

critical flow

prover

was 0.86, a

difference of 2.4 per cent.

The

capacity tables

for the

2-in.

orifice well tester

at

differentials in

pressure less than 25 in.

of Hg

were

calculated from the

equation

Q

= K Y CD.,'

.IP,

6

P

(3)

, d - l + (3' .

in

which if p, and 6P are

in

inches

of Hg, K =

27.284,

and if

P,

and 6

P

are

in inches

of

water,

K = 2.0062.

At differentials in

pressure

greater

than 25 in.

of Hg,

Q =

K'C D,'P, (4)

vi

+

(3' r, /k

in which for a gas with

k

= 1.3 and

if P, is

in

inches

of

Hg, K' = 12.288.

Tables

1

and

2 were calculated

for

free discharge to

an

atmospheric

pressure

of 29.4

in.

of

Hg. f the

barometric pressure differs appreci

ably from 29.4 in. of Hg, the capac

ity of the tester

must

be corrected

by multiplying

the

table value by

the factor F.

F

=

iP ,,,,

+

P

~ 2 9 4 + 6P

(5)

Other

corrections

for

pressures less

than 25 in. of Hg (gas gravity, base

or flowing temperature, pressure

base, etc.)

are standard

corrections

used in all orifice metering work.'

For pressures

greater

than 25 in.

of

Hg, correction factors standard

for

the critical flow

prover'

should be

used.

A few

runs

in the

range

0 to 15 in.

of

water

differential

in

pressure

checked published data for the orifice

well

tester for the same range

within

the limits

of experimental

error. The

basic

equation

of

flow

for

this region

may be relied upon.

CONCLU S I ON S

1. Tables of the capacity

of

the

conventional orifice well tester with

conventional

(thick)

orifices for dif

ferentials in pressure ranging

from

o

to 15 in.

of water and

all ratios

of D/t

as published

by the American

Meter

Co.

and reproduced

by others

are

valid.

64

TABLE 6 DISCHARGE COEFFICIENTS OR

SHARP·EDGED

OR

I FICES

Tester Tester

Tester Pressure Pressure

Pressure In of n of

In. of

Mercury ( Mercury

rt Mercury

Crt

-c0--. 0 - - - - - - - - - - ; c 0

=: 6

7

4c---:

2

'1=-=.0c-'-

0.723

----''''6

c

l=-=.0'-'--0--.

'2-0

1.1 0.612

22.0

0.728 62.0 0.821

1.2 0.613 23.0 0.732 63.0 0.822

1.3 0.614 24.0 0.736 64.0 0.822

1.4 0.614

25.0

0.740 65.0 0.823

1.5 0.615

26.0

0.745

66.0

0.823

1.6

0.616 27.0

0.749 67.0

0.824

1.7

0.616

28.0

0.753

68.0

0.824

1.8

0.617 29.0 0.757 69.0

0.825

1.9 0.618 30.0 0.761 70.0

0.825

2.0

0.618 31.0

0.764 71.0

0.825

2.2 0.620 32.0

0.768

72.0

0.826

2.4

0.621

33.0

0.772

73.0

0.826

2.6

0.622 34.0 0.775

74.0 0.827

2.8 0.624 35.0

0.778

75.0 0.827

3.0 0.625

36.0

0.781 76.0 0.828

3.2 0.626 37.0 0.784 77.0 0.828

3.4 0.628 38.0

0.786

78.0 0.829

3.6 0.629 39.0

0.789 79.0

0.829

3.8

0.630

40.0

0.791 80.0 0.830

4.0 0.631

41.0

0.793 81.0 0.830

4.5 0.634 42.0

0.795 82.0 0.830

5.0 0.637 43.0 0.797

83.0

0.831

5.5 0.640 44.0

0.799 84.0

0.831

6.0

0.643

45.0 0.801

85.0

0.831

6.5

0.646

46.0

0.803 86.0

0.831

7.0

0.649

47.0

0.804

87.0

0.832

8.0 0.655 48.0

0.806 88.0 0.832

9.0 0.661 49.0

0.808 89.0 0.832

10.0 0.666 50.0 0.809 90.0 0.832

11.0 0.672

51.0

0.811 91.0 0.833

12.0 0.677

52.0

0.812 92.0 0.833

13.0 0.683 53.0 0.813 93.0 0.833

14.0

0.688 54.0

0.814 94.0

0.834

15.0 0.693 55.0 0.815 95.0

0.834

16.0 0.699

56.0

0.816 96.0

0.834

17.0 0.703 57.0

0.817 97.0

0.835

18.0 0.709 58.0

0.818 98.0

0.835

19.0 0.714

59.0

0.819

99.0

0.835

20.0

0.719

60.0 0.819

100.0 0.836

0 /1> 8

2. Coefficients developed by the

Bureau of Mines for the conventional

critical flow

prover and

the capaci

ties

dependent on

these coefficients

are valid

for

upstream pressures

greater than 40 psi and all ratios

of D to t.

3.

An

unstable state of

flow

develops between differentials in

pressure

of

15 in. of

water and 40

psi

for

ratios

of

D

to

t

between 1

and

4. Because

of

this condition

of

instability

and

variation in cofficients

of discharge with ratios of upstream

to downstream pressures, neither the

tables usually supplied with the ori

fice well tester

nor

those applicable

to

the usual critical flow

prover can

be extrapolated for use in this inter

mediate region

of

differential in pres

sure.

4. Orifice plates designed in ac

cordance with ASME-AGA specifi

cations for sharp-edged orifices

(made

of stainless steel to resist corrosion,

wear,

and tear) and

used in

the

orifice well tester are accurate, re

liable,

and

satisfactory at all rates

of flow

and

differentials in pressure

likely to be encountered in prac

tical gas-oil ratio

work

in

the

field.

Only one set

oj

tables

and

one in

strument, the orifice well tester,

and

one set

oj

sharp-edged orifices are

required.

Obviously

the new

sharp

edged orifice plates

can

be used

in

the conventional orifice well tester.

Tables 1

and

2 have been

prepared

for thesc orifices covering the range

from 1 in. of water to 100 in. of

Hg

differential in pressure. Above

100 in.

of Hg, Eq.

4

can

be used

to calculate

the

capacity

of

orifice

plates,

and no

discrepancies will be

observed over the entire range of

pressures.

RECOMMENDA

TraNS

ASME-AGA

specifications should

be used

for the construction of

orifice plates

for the

orifice well

tester. These plates should be

made

of

stainless steel

or Monel

metal.

Official manuals of procedure

should require the use of such

plates

and appropriate

tables in all

gas-oil ratio work.

ACKNOWLEDGMENT

The authors

wish to acknowledge

the

help

of

the

members of the

Tex

as

Petroleum Research Committee

and

to

thank them for

permission

to

prepare and

publish this paper.

DEFINITION

OF

SYMBOLS

D = orifice diameter, inches

t = orifice thickness, inches

h

=

differential pressure, inches

of

water

H

=

differential pressure, inches

of

Hg

C = meter coefficient

Cd

= dimensionless discharge co-

efficient

Q

= flow rate

G

=

gas gravity

(air

=

1.0)

K

= dimensional constant for sub

critical flow

K' =

dimensional

constant

for crit

ical flow

Y,

=

dimensionless expansion fac

tor, derived

on the

basis

of

frictionless adiabatic flow

P =

absolute

upstream

pressure

P

=

differential pressure across the

orifice; i. e., tester pressure

(3

= ratio

of

orifice

diameter

to

pipe

diameter

r

=

critical pressure ratio

k = specific heat ratio

REFERENCES

1. Pamphlet for Gas-Oil Ratio Determi

nation,

Railroad Commission of

Texas, Engr. Dept., 1954.

2.

Open

Flow Capacities of Wells,

American

Meter

Co., Inc., Metric

Metal Works, Erie,

Pa.,

Bull. E-7,

1930.

3.

Buckingham,

E.:

Research Paper 303,

Bureau of

Standards

Jour.

of

Research

(May,

1931).

4. Investigation of Flow Coefficient of

Circular, Square and Elliptical Ori

fices, NACA-TN-1947 (Sept. , 1949).

J O U R N A L O F PETROLEUM T E C H N O L O G Y

A Study of the Orifice Well Tester and Critical Flow Prover

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Transcript of A Study of the Orifice Well Tester and Critical Flow Prover