mahmood 1996

ELSEVIER Journal of Petroleum Science and Engineering 16 (1996) 275-290

Evaluation of empirically derived PVT properties for Pakistani crude oils

Mohammed Aamir Mahmood, Muhammad Ali Al-Marhoun *

Department of Petroleum Engineering, King Fahd Uniuersity of Petroleum and Minerals, Dhahran 31261, Saudi Arabia

Received 3 February 1996; accepted 12 June 1996

Abstract

This study evaluates the most frequently used pressure-volume-temperature (PW) empirical correlations for Pakistani crude oil samples. The evaluation is performed by using an unpublished data set of 22 bottomhole fluid samples collected from different locations in Pakistan. Based on statistical error analysis, suitable correlations for field applications are recommended for estimating bubblepoint pressure, oil formation volume factor (PVF), oil compressibility and oil viscosity.

Keywords: physical fluid properties; PVT tests; correlations; least-squares methods; statistics

1. Introduction

Provision of pressure-volume-temperature (PVT) parameters is a fundamental requirement for all types of petroleum calculations such as determi- nation of hydrocarbon flowing properties, and design of fluid handling equipments. More importantly, vol- umetric estimates necessitate the evaluation of PVT properties beforehand. The PVT properties can be obtained from an experimental set-up by using repre- sentative samples of the crude oils. However, introduction of a PVT empirical correlation also extends statistical techniques to estimate the PVT properties effectively.

For the development of a correlation, geological and geographical conditions are considered impor-

* Corresponding author.

tant as due to these conditions the chemical composi- tion of any crude may be specified. It is difficult to obtain the same accurate results through empirical correlations for different oil samples having different physical and chemical characteristics. Therefore to account for regional characteristics, PVT correlations need to be modified for their application. Be- cause of the availability of a wide range of correlations, it is also beneficial to analyze them for a given set of PVT data belonging to a certain geological region.

This study examines the existing PVT correlations against a set of PVT data collected from different locations in Pakistan as shown in Fig. 1. All of the significant PVT correlations reported in petroleum literature are included in this study. The validity and statistical accuracy are determined for these correlations and finally the best suited correlations are recommended for their application to Pak- istani crude oils. In addition, this study can be used

0920-4105/96/$15.00 Copyright 0 1996 Elsevier Science All rights reserved

PII SO920-4105(96)00042-3

216 M.A. Mahmood, M.A. AI-Marhoun/Journnl of Petroleum Science and Engineering 16 (1996) 275-290

I COAL

Fig. 1. Location of mineral reserves in Pakistan.

as an effective guideline for correlation applications for all the other oil samples possessing similar com- positional characteristics.

2. PVT correlations

The frequently used empirical correlations for the prediction of bubblepoint pressure, oil FVF at bubblepoint, two-phase FVF, undersaturated oil com-

pressibility, viscosity at and above bubblepoint, and dead oil viscosity are reviewed in the following sections.

2. I. Bubblepoint pressure correlations

Standing (1947) p resented a correlation for predicting bubblepoint pressure by correlating reservoir temperature, solution gas/oil ratio, gas relative density, and oil gravity. The gases in the oil samples contained CO, as the only non-hydrocarbon. The data used for this study were sampled from Califor- nia oil fields. Lasater (1958) for his correlation development acquired data without non-hydrocarbon gases. The oil samples were collected from Canada, the U.S.A., and South America. The aforesaid correlations were widely acclaimed and utilized for a considerably long time until Vazquez and Beggs (1980) reported their work for bubblepoint pressure prediction of a gas-saturated crude. They recommended a bifurcation for evaluating PVT parameters, and suggested two ranges ( yAp, < 30 and yAp, > 30) of oil samples. Glaso (1980) also presented a correlation for predicting bubblepoint pressure from a data set comprising of reservoir temperature, solution gas/oil ratio, gas relative density, and oil gravity. The data for his study mainly belonged to the North Sea region. He also recommended a method for correcting a predicted bubblepoint pressure if a significant amount of non-hydrocarbon gases is pre- sent along with the associated surface gases. Al- Marhoun (1988) published his correlation for deter-

Table 1

Data ranges of existing correlations for oil FVF and bubblepoint pressure

Parameter Standing Lasater Vazquez and Beggs

(1947) (1958) (1980)

Number of data points 105 158

p, 130-7000 48-5780 T loo-258 82-272

FVF 1.024-2.15 _

R, 20-1425 3-2905 “API 16.5-63.8 17.9-51.1

y, 0.59-0.95 0.57- 1.22

co, (mole%) < 1.0 0.0

N, (mole%) 0.0 0.0

H , S (mole%) 0.0 0.0

6004 41 160 4012

15-6055 165-7142 130-3573 15-6641 15-294 80-280 74-240 75-300

1.028-2.22 1.025-2.58 1.032-1.99 1.01-2.96

O-2199 90-2637 26- 1602 O-3265

15.3-59.3 22.3-48.1 19.4-44.6 9.5-55.9

0.511-1.35 0.65- 1.216 0.752- 1.36 0.575-2.52

_ 0.0-16.38

_ 0.0-3.89 _ _ O.O- 16.3 _

Glaso

(1980)

Al-Marhoun

(1988)

Al-Marhoun

(1992)

M.A. Mahmood, M.A. Al-Marhoun/ Journal of Petroleum Science and Engineering 16 (1996) 275-290 217

mining bubblepoint pressure based on Middle East oil samples.

2.2. Oil FVF at bubblepoint pressure correlations

The very first correlation was developed by Standing (1947) utilizing the same data used for his bubblepoint pressure predication. Vazquez and Beggs (1980) reported their research recommending a bifurcation in the data with two ranges of oil API gravity. Glaso (1980) also published a correlation which was based on Standing’s correlation with minor modifica- tions. He used 41 experimentally determined data points, mostly from the North Sea region. Al- Marhoun (1988) reported his correlation for which he acquired data from Middle East oil reservoirs. Al-Marhoun (1992) updated his correlation by ac- quiring a large data set of 4012 data points collected from all over the world. Table 1 shows the data ranges of the selected correlations discussed above.

2.3. Two-phase FVF correlations

Standing (1947) reported the first correlation for predicting two-phase FVF by correlating solution/gas oil ratio, temperature, gas relative density, and oil gravity. Applying the same PVT parameters used by Standing, Glaso (1980) published his correlation. Al-Marhoun (1988) reported his correlation using a data set collected from Middle East oil

fields.

2.4. Undersaturated oil compressibility correlations

The earliest research was conducted by Calhoun (1947) when he presented a graphical correlation for determining the isothermal compressibility of an undersaturated crude oil. Trube (1957) for his graphical correlation used pseudoreduced pressure and temperature to determine undersaturated oil compressibility. Vazquez and Beggs (1980) also presented a compressibility correlation using the available reservoir parameters.

2.5. Undersaturated oil viscosity correlations

Beal (1946) published his graphical correlations for determining the undersaturated oil viscosity of

crude oil by using a data set representing U.S. oil sample only. He used gas-saturated oil viscosity, bubblepoint pressure, and pressure above bubblepoint as the correlating parameters. Vazquez and Beggs (1980) by using 3593 data points also published their correlation for undersaturated oil viscosity. Khan et al. (1987) published their correlation based on 75 bottomhole samples and 1503 data points obtained from Saudi oil reservoirs. The most recent correlation reported by Labedi (1992) for light crude oils is based upon Libyan crude oil data.

2.6. Gas-saturated oil viscosity correlations

Chew and Connally (1959) presented their work for predicting change in oil viscosity as a function of the solution gas/oil ratio. Their data set of 457 data points covered samples from South America, Canada, and the U.S.A. Beggs and Robinson (1975) acquired a large data set to obtain a correlation for predicting gas-saturated oil viscosity. Khan et al. (1987) reported their research using 150 data points obtained from Saudi crude oil samples. For light crude oils, Labedi (1992) presented his correlation using Libyan crude oil samples.

2.7. Dead oil viscosity correlations

Beal (1946) reported a correlation by applying 753 data points for his analysis. He correlated oil gravity, and temperature covering a range of lOO- 220°F. Beggs and Robinson (1975) presented their correlation using 460 dead oil observations. Glaso (1980) also developed a correlation using a temperature range of 50-300°F for 26 crude oil samples. Ng and Egbogah (1983) presented their viscosity correlations by modifying the Beggs and Robinson correlation. Recently, Labedi (1992) has published a correlation for light crude oil sampled from Libyan reservoirs.

All of the correlations selected for this study are given in Appendix A.

3. PVT data acquisition for Pakistani crude oils

PVT reports of 22 bottomhole fluid samples were acquired from different locations in Pakistan for the evaluation purpose of this study. This unpublished

278 M.A. Mahmood, M.A. Al-Marhoun/Joumal of Petroleum Science and Engineering 16 (1996) 27.5-290

Table 2

PV’T differential data with the corresponding oil viscosity values

No. T P, B,, R, % “API /_q,

1 250 2885 2.916 2249 1.0608 56.5

2 248 1680 1.468 557

3 248 1415 1.432 486

4 248 1215 1.404 433

5 248 1015 1.378 381

6 248 815 1.352 328

I 248 615 1.322 273

8 248 415 1.292 215

9 248 227 1.246 144

10 248 133 1.214 96

II 248 15 1.092 0

12 245 3280 1.921 1340

13 188 4197 2.365 2371

14 248 1725 1.522 663

15 248 1515 1.493 603

16 248 1315 1.465 547

17 248 1115 1.438 490

18 248 915 1.409 432

19 248 715 1.380 376

20 248 515 1.350 316

21 248 315 1.314 251

22 248 183 1.278 192

23 248 113 1.248 152

24 248 15 1.098 0

25 229 1316 1.375 435

26 229 1065 1.350 379

27 229 865 I.329 335

28 229 665 1.306 288

29 229 465 1.282 239

30 229 265 1.250 182

31 229 163 1.227 145

32 229 15 1.087 0

33 222 2949 1.940 1321

34 222 2615 1.844 1210

35 222 2215 1.753 1074

36 222 1815 1.681 937

37 222 1415 1.610 802

38 222 1015 1.541 670

39 222 615 1.467 506

40 222 298 1.386 340

41 222 15 1.073 0

42 232 1525 1.460 550

43 232 1315 1.43 1 496

44 232 1115 1.403 446

45 232 915 1.376 395 46 232 715 1.348 342

47 232 515 1.320 288

48 232 315 1.286 228

49 232 185 I.253 180

50 232 15 1.097 0

51 217 1512 1.416 512 52 217 1315 1.391 468

53 217 1115 1.363 419

1.1955

1.2468

1.2955

1.3539

1.4272

1.5264

1.6611

1.8583

1.9810

0

1.0713

0.8253

1.3205

1.3692

1.424 1

1.4923

1.5775

1.6801

1.8180

2.0083

2.2297 2.4120

0

I .4030

I .4905

1.5762

1.6918

1.8545

2.0949

2.3000

0

1.2613

1.3003

1.3595

1.4356

1.5338 1.6640

1.8954

2.2520 0

1.3428

1.3898

1.4407

1.5022 1.5808 1.6839

I .8442 2.0370

1.1836 1.2194

1.2671

37.2

37.2

37.2

37.2

37.2

37.2

37.2

37.2

37.2

37.2

29.3

39.5

38.5

38.5

38.5

38.5

38.5

38.5

38.5

38.5

38.5

38.5

38.5

40.5

40.5

40.5

40.5

40.5

40.5

40.5

40.5

29.0

29.0

29.0

29.0

29.0

29.0

29.0

29.0

29.0

39.9

39.9

39.9

39.9 39.9

39.9 39.9

39.9 39.9

41.0 41.0

41.0

0.318

0.337

0.352

0.367

0.389

0.406

0.430

0.207

0.308

0.320

0.334

0.349

0.364

0.379

0.397

0.438

0.47 1

0.327

0.333

0.34 1

0.350

0.365

0.397

0.416

0.896

0.252

0.263

0.277

0.294

0.314

0.340

0.38 1

0.460

0.589

0.380

0.386

0.394

0.404 0.417

0.435 0.458

0.486 0.748

Table 2 (continued)

No. T P, B,,, R,

54 217 915 1.324 369

55 217 715 1.300 316

56 217 515 1.278 259

57 217 315 1.248 196

58 217 183 1.217 145

59 217 15 1.088 0

60 188 1717 1.394 556

61 188 1515 1.373 509

62 188 1315 1.354 462

63 188 1115 1.335 419

64 188 915 1.318 378

65 188 715 1.298 330

66 188 515 1.275 280

67 188 315 1.247 225

68 188 170 1.215 165

69 188 15 1.067 0

70 296 2883 2.619 1977

71 296 2615 2.475 1757

72 296 2315 2.331 1536

73 296 2015 2.203 1340 74 296 1715 2.092 1169

75 296 1415 1.995 1018

76 296 1115 1.910 884

77 296 815 1.832 760

78 296 515 1.747 628

79 296 249 1.633 470

80 296 152 1.599 379

81 296 104 1.504 317

82 296 15 1.142 0

83 281 4975 2.713 2496

84 281 4115 1.981 1458

85 281 3315 1.777 1074

86 281 2615 1.658 827

87 281 1915 I.552 615

88 281 1215 1.449 407

89 281 615 1.351 248

90 281 15 1.104 0

91 237 1226 1.418 470

92 237 1065 1.401 433

93 237 915 1.385 398

94 237 765 1.369 362

95 237 615 1.35 325

96 237 465 1.330 285

97 237 315 1.305 241

98 237 I83 1.275 190

99 237 114 1.253 I58 100 237 79 1.238 130

101 237 15 1.090 0

102 237 I295 I .349 357

103 237 I I65 1.335 330

104 237 1015 1.318 299

105 237 865 1.303 268

106 237 715 1.287 236

107 237 565 I.268 202

“API P”

1.3260

I .4037

1.5126

1.6882

1.8670

1.2595

1.3058

1.3614

1.423 1

1.4938

1.5954

1.73 1 1

1.9298

2.2450

1.407 I

1.4613

1.5337

1.6191

1.7167

1.8277

I .9523

2.095 1

2.281 I

2.5585

2.7812

2.9800

0

1.1545

1.1888

1.4410

1.6839

1.9220

2.5098

3.4445

0

1.5337 I .5922

1.6561

1.7323

1.8241

I .9424

2.0908

2.2778

2.4141

2.5500 0

I .2435 1.2758

1.3184

1.3687

I .4307 1.5137

41.0

41.0

41.0

41.0

41.0

41.0

42.6

42.6

42.6

42.6

42.6

42.6

42.6

42.6

42.6

42.6

39.9

39.9

39.9

39.9

39.9

39.9

39.9 39.9

39.9

39.9

39.9

39.9

39.9

31.9

31.9

31.9

31.9

31.9 31.9

31.9

3 1.9

39.4

39.4

39.4

39.4 39.4

39.4

39.4

39.4

39.4 39.4

39.4 39.5

39.5

39.5

39.5 39.5 39.5

0.301

0.310

0.318

0.328

0.338

0.352

0.367

0.386

0.411

0.878

0.222

0.232

0.243

0.254

0.266 0.278

0.292

0.309

0.332

0.365

0.386

0.402

0.769

0.205

0.245

0.275

0.310

0.350 0.405

0.482

0.914

0.330 0.338

0.345

0.356 0.372

0.388

0.4 IO

0.380

0.392

0.406 0.425

0.452 0.485


Table 2 (continued) Table 2 (continued)

No. T P, B oh R,

108 237 415 1.248 166

109 237 265 1.225 126

110 237 162 1.200 92

111 237 15 1.099 0

112 254 1475 1.804 885

113 254 1315 1.771 821

114 254 1115 1.730 744

115 254 915 1.685 666

116 254 715 1.639 588

117 254 515 1.588 505

118 254 315 1.523 411

119 254 195 1.461 333

120 254 135 1.411 276

121 254 95 1.351 213

122 254 15 1.104 0

123 246 1737 1.524 635

124 246 1515 1.491 561

125 246 1315 1.463 515

126 246 1115 1.436 468

127 246 915 1.410 414

128 246 715 1.383 360

129 246 515 1.353 302

130 246 315 1.319 240

131 246 172 1.280 181

132 246 100 1.247 141

133 246 15 1.094 0

134 255 1455 1.503 586

135 255 1215 1.467 517

136 255 1015 1.436 458

137 255 815 1.407 403

138 255 615 1.373 342

139 255 415 1.335 280

140 255 245 1.286 204

141 255 145 1.249 156

142 255 15 1.098 0

143 248 1482 1.511 582

144 248 1265 1.476 519

145 248 1065 1.449 466

146 248 865 1.421 413

147 248 665 1.392 360

148 248 465 1.358 302

149 248 265 1.312 230

150 248 155 1.276 180

151 248 15 1.094 0

152 252 1460 1.821 936

153 252 1265 1.777 850

154 252 1065 1.733 768

155 252 865 1.685 683

156 252 665 1.637 601

157 252 465 1.584 517

158 252 265 1.514 416

159 252 170 1.459 341

160 252 115 1.404 278

161 252 15 1.106 0

% 1.628 1

1.7897

1.9700

0

1.6334

1.6891

1.7673

1.8614

1.9736

2.1152

2.2987

2.4650

2.5868

2.7080

0

1.3362

1.3907

1.4422

1.4985

1.5786

1.6812

1.8202

2.01

2.2408

2.4280

0

1.4828

1.5577

1.6374

1.7274

1.8473

1.997 1

2.2229

2.4090

0

1.4361

1.5069

1.5795

1.6682

1.7782

1.9308

2.1583

2.3420

0

1.6433

1.7173

1.8015

1.9050

2.0267

2.1753

2.3873

2.5466

2.6880

0

“API

39.5

39.5

39.5

39.5

42.2

42.2

42.2

42.2

42.2

42.2

42.2

42.2

42.2

42.2

42.2

38.8

38.8

38.8

38.8

38.8

38.8

38.8

38.8

38.8

38.8

38.8

38.1

38.1

38.1

38.1

38.1

38.1

38.1

38.1

38.1

38.1

38.1

38.1

38.1

38.1

38.1

38.1

38.1

38.1

43.8

43.8

43.8

43.8

43.8

43.8

43.8

43.8

43.8

43.8

PO No. T p, &,b 4 r, “API p,,

0.533 162 244 1569 1.456 542 1.3248 37.5 0.290 0.587 163 244 1315 1.423 474 1.3929 37.5 0.299 0.636 164 244 1115 1.398 423 1.4575 37.5 0.306 0.742 165 244 915 1.371 371 1.5385 37.5 0.318 0.232 166 244 715 1.344 318 1.6421 31.5 0.331 0.238 167 244 515 1.313 261 1.7871 37.5 0.347 0.245 168 244 315 1.217 199 1.9937 37.5 0.372 0.256 169 244 187 1.241 147 2.2090 37.5 0.391 0.264 170 244 15 1.091 0 0 37.5 0.787 0.280 171 182 1098 1.312 373 1.3044 42.1 0.299 172 182 915 1.296 335 1.3583 42.1 0.318 173 182 715 1.278 295 1.4276 42.1 0.327 174 182 515 1.258 250 1.5269 42.1 0.341 175 182 315 1.235 192 1.7078 42.1 0.605 176 182 185 1.213 151 1.8870 42.1 0.372 177 182 15 1.068 0 0 42.1 0.384 178 255 1242 1.553 565 1.1224 39.2 0.403 179 255 1015 1.527 512 1.8103 39.2 0.422 180 255 815 1.501 462 1.9093 39.2 0.444 181 255 615 1.473 410 2.0323 39.2 0.470 182 255 415 1.441 351 2.2019 39.2 0.503 183 255 245 1.405 294 2.3952 39.2 0.543 184 255 160 1.378 257 2.5310 39.2 0.582 185 255 15 1.110 0 0 39.2

0.291

0.296

0.304

0.317

0.343

0.366

0.423

0.479

0.814

0.240

0.248

0.255

0.264

0.272

0.283

0.298

0.307

0.313

0.581

data set consists of 166 data points for evaluating bubblepoint pressure and oil FVF at bubblepoint pressure correlations. These data points are the results of standard differential liberation tests conducted on bottomhole fluid samples collected di- rectly form oilfields. Table 2 shows the differential data set in detail, whereas Table 3 depicts the com- position and statistical analysis of the Pakistani crude data. The number of data points used for oil compressibility, two-phase FVF, oil viscosity (above, and at bubblepoint pressure), and the dead oil viscos-

Table 3

Data ranges of Pakistani crude oils

Parameter Range Parameter Range

FVF@P, 1.20-2.916 Y0 0.753-0.882

‘b 19-4915 &b 0.25-0.38

R, 92-2496 PO 0.206-0.548

API 29.0-56.5 0.581-1.589

C0 lo-5-10m4 2 0.23-1.4 P > P, 1115-6029 N, (mole%) 0.51-1.54

T 182-296 CT (mole%) 30.99-55.76

7, 0.825-3.445

280 M.A. Mahmood, M.A. Al-Marhoun/Journal of Petroleum Science and Engineering 16 (1996) 275-290

ity correlations are 246, 352, 104, 16 and 16, respec- tively.

In general, this data set covers a wide range of bubblepoint pressure, oil FVF, solution gas/oil ratio, and gas relative density values; whereas the temperature and oil gravity belong to relatively higher values attributed to regional trends prevailing in Pakistani crude oils. This comprehensive data bank offers a good opportunity for further studies in this area.

4. Evaluation procedure

Statistical and graphical error analyses are the criteria adopted for the evaluation in this study. Existing PVT correlations are applied to the acquired data set and a comprehensive error analysis is performed based on a comparison of the predicted value with the original experimental value. For an in-depth analysis of the accuracy of the correlations tested, error analysis based on different ranges of oil API gravity is also carried out graphically. An error analysis based on oil API gravity ranges is consid-

70.00

60.00

6 5 F 40.00

‘Z

m 2 a 4 a 30.00

P 0 3 b 20.00

k

10.00

0.00

ered an effective tool for determining the suitability of the correlation for heavy, medium, or light oil.

The following statistical means are used to determine the accuracy of correlations to be evaluated.

4.1. Average percent relatiue error (Er)

The average percent relative error is an identifica- tion of relative deviation of the predicted value from the experimental value in percent and is defined by:

E, = -!- 5 Ei

Izd i=l

(1)

where

E, = x 100 (i=1,2, . . . . n) (2)

The lower the value the more equally distributed is the error between positive and negative values.

4.2. Average absolute percent relative error (Ea)

The average absolute percent relative error indi- cates the relative absolute deviation of the predicted

+ Al-Marhoun 66

I I I I I

API434 34cAP1~38 38cAPk42 API>42

(16) (17) 6’8) (35)

Ranges of oil API gravity (with corresponding data points)

Fig. 2. Statistical accuracy of bubblepoint pressure correlation grouped by oil API gravity.

M.A. Mahmood, M.A. Al-Marhoun / Journal of Petroleum Science and Engineering 16 (1996) 275-290 281

Table 4

Statistical accuracy of bubblepoint pressure correlations

Correlation E,

Standing (1947) -43.5 49.18 0.43 391.05 68.37

Lasater (1958) -20.61 31.31 0.04 273.65 49.36

Vazquez and -52.07 55.31 0.16 403.99 70.30

Beggs (1980)

Glaso (1980) -24.82 32.08 0.04 247.00 45.64

Al-Marhoun 27.97 31.50 0.30 81.96 20.24

(1988)

value from the experimental values in percent. A lower value implies a better correlation. It is expressed as:

'd i=l (3)

cent relative errors. The minimum and maximum

values are determined to show the range of error for each correlation and are expressed as:

Emin = $n I Ej I i= 1

and

E max = r&xlEil i= 1

4.4. Standard deviation (s)

(4)

(5)

The standard deviation is a measure of dispersion of predicted errors by a correlation, and it is expressed as:

4.3. Minimum and maximum absolute percent relative errors (Emi, and E,,,,,

S= (6)

Both the minimum and maximum values are determined by analyzing the calculated absolute per-

A lower value implies a smaller degree of scatter around the average calculated errors.

15.00

10.00

5.00

0.00

+ Standmg + Vaz RBegg

++- N-Marhoun 88

+ Al-Marhoun 92

I I I I

API<34 34<APk38 38cAPk42 API>42

(16) (17) (98) (35)

Ranges of API gravity (with corresponding data points)

Fig. 3. Statistical accuracy of oil FVF at bubblepoint pressure correlation grouped by oil API gravity.

282 M.A. Mahmood, M.A. Al-Marhoun/Journal of Petroleum Science and Engineering 16 (19961275-290

5. Results and comparison

Average absolute relative error is an important indicator of the accuracy of an empirical model. It is used here as a comparative criterion for testing the accuracy of existing correlations. After applying the existing correlations to the acquired data set, results in the form of average absolute relative error, average percent relative error, minimum and maximum absolute percent relative error, and standard deviation are summarized in Tables 4-10. Another effective comparison of correlations is performed through graphical representation of errors as a function of oil API gravity ranges. Figs. 2-8 represent correlation errors for four oil API gravity ranges.

Table 5 Statistical accuracy of oil FVF at bubblepoint pressure correlation

Correlation E, E, E mln Em s

Standing ( 1947) 1.39 2.31 0.05 7.96 2.36

Vazquez and 12.84 12.84 5.99 24.83 4.37

Beggs (1980)

Glaso (1980) 3.65 3.88 0.08 12.78 2.23

Al-Marhoun (1988) 2.27 2.34 0.01 13.0 2.55

Al-Marhoun (1992) 0.76 1.23 0.01 9.09 1.54

gravity; whereas the maximum error is obtained for a higher gravity range of 42 oil API gravity and above as depicted by Fig. 2.

5. I. Bubblepoint pressure correlations 5.2. Oil FVF at bubblepoint pressure correlations

Lasater (1958) together with Al-Marhoun (1988) Al-Marhoun (1992) exhibited a significantly uni-

showed least errors for the data used as shown in form error for all oil API gravity ranges as shown in Table 4. The least error of all the tested correlations Fig. 3. Corresponding to the least error obtained for

is obtained for a medium range of 34-38 oil API this correlation, a least value of standard deviation is

25.00 -

3 m w b 20.00 -

5 al .z g P 15.00 - al 4 E

z k% 10.00 - P F Q

5.00 -

+ Standmg

+ Glaso

-+- Al-Marhoun

“. VW

API434 34<AP1<38 38<AP1<42 API>42

(40) (29) (200) (83)


Fig. 4. Statistical accuracy of two-phase FVF correlation grouped by oil API gravity.


Table 6 Table 7

Statistical accuracy of two-phase FVF correlations Statistical accuracy of undersaturated oil compressibility correla-

tions Correlation E, E, E m,n E,,x s

Standing (1947) -5.42 8.23 0.06 26.59 8.50 Glaso (1980) - 2.94 6.37 0.05 19.48 7.46 Al-Marhoun 22.07 22.07 3.94 39.36 7.01

(1988, 1992)

shown in Table 5. This is also supported by Petrosky and Farshad (1993) when they showed that Al- Marhoun (1988) obtained better accuracy for Gulf of Mexico data.

5.3. Two-phase FVF correlations

Glaso (1980) obtained reasonable result with a least error as shown in Table 6. However, this correlation overestimates the predicted value com- pared to the experimental value. Fig. 4 shows the same trend of errors for Standing (1947) and Glaso (1980) for all oil API gravity ranges.

Correlation E,

Calhoun ( 1947) 11.01 15.95 0.22 71.26 18.98 Vazquez and -8.31 31.37 0.38 158.93 37.62

Beggs (1980) Trube (1957) - 19.31 41.0 0.19 180.88 46.67

5.4. Undersaturated oil compressibility correlations

Calhoun (1947) showed a good harmony with the data used, but this correlation tends to underestimate the predicted compressibility value as shown in Table 7. This correlation gives least error for the medium oil API gravity range of 34-38, as shown in Fig. 5. This result is also favored by Sutton and Farshad (1990) through their research conducted on Gulf of Mexico data.

45.00 -

40.00 -

g m Y 35.00 -

b 5 LZ 30.00 - ‘Z 1 e! a, 4 25.00 -

a

D 8 20.00 -

E k 15.00 -

10.00 -

API<34 (25)

34cAPlc38

(22)

38<AP1<42 (139)

API>42 (60)


Fig. 5. Statistical accuracy of undersaturated oil compressibility correlation grouped by oil API gravity

284 M.A. Mahmood, M.A. Al-Marhoun/Joumal of Petroleum Science and Engineering 16 (1996) 275-290

Table 8 Table 9

Statistical accuracy of undersaturated oil viscosity correlation

Correlation E, E, Em,, Em s

Beal ( 1946) - 2.94 4.52 0.03 14.89 4.71

Vaaquez and - 14.01 14.15 0.08 46.39 12.54

Beggs (1980)

Khan et al. (1987) -7.61 7.91 0.10 26.59 6.64

Labedi (1992) -5.82 7.45 0.02 47.56 8.98

Statistical accuracy of gas saturated oil viscosity correlation

Correlation E, E., Em Em s

Beggs and -24.43 26.71 2.56 57.16 21.70

Robinson (1975) Chew and -3.41 12.21 1.27 25.31 13.62

Connally (1959) Khan et al. (I 987) - 18.60 29.92 1.19 64.80 30.81 Labedi (1992) -29.65 37.53 I .56 268.98 70.04

5.5. Undersaturated oil viscosity correlations

Beal (1946) showed better results than the other correlations tested. Table 8 shows a least standard deviation value for this correlation. This correlation is best suited to a low oil API gravity as shown in Fig. 6. Prediction by Labedi (1992) is also reasonable for a high oil API gravity range. All of the correlations unanimously overestimated the viscosity

values.

corresponding least scatter. This correlation is equally good for all oil API gravity ranges as shown in Fig. 7. With the exception of Labedi (1992) all correlations showed least error for high oil API gravity ranges but overestimated the viscosity values.

5.7. Dead oil viscosity correlations

5.6. Gus-saturated oil ciscosiv correlations

Chew and Connally (1959) is the best among others as shown in Table 9 with a least error and a

The Glaso (1980) correlation is found relatively better for gravity higher than 34 oil API gravity as shown in Fig. 8. All of the correlations obtained

a, 5 12 00 5

0 a, $ b 8.00

k

4 00

Khan eta1

A

API<34 34cAPlc38 38<AP1<42 API>42 (13) (14) (57) (20)


Fig. 6. Statistical accuracy of undersaturated oil viscosity correlation grouped by oil API gravity


Table 10 Statistical accuracy of dead oil viscosity correlations

Correlation E, E, Em,, Em s

Beal (1946) 23.15 27.76 10.73 57.24 19.59

Beggs and - 23.58 25.08 1.59 61.28 17.42

Robinson (1975) Glaso (1980) - 1.39 14.36 0.24 56.03 20.47

Ng and -56.45 56.45 26.35 122.49 29.02

Egbogah ( 1983) Labedi ( 1992) -85.40 85.40 22.35 268.55 71.55

large errors for low oil API gravity. Except Beal ( 1946) all of the correlations overestimated dead oil viscosity values as shown in Table 10.

6. Conclusions

The following conclusions can be drawn by this

evaluation study. (1) Although high errors are generally obtained

for the prediction of bubblepoint pressure, the error

obtained was extremely high in this case. This stresses the need of a new bubblepoint pressure correlation representing the chemical and geological difference of this region. Both Lasater (1958) and Al-Marhoun (1988) showed nearly equal errors but the latter exhibited a least standard deviation. Any one of these correlations may be used for Pakistani crude oils.

(2) For oil FVF correlations at bubblepoint pressure, all of the selected correlations showed a good degree of harmony towards the data used. All of the correlations underestimated FVF values, i.e. the predicted value is less than the actual experimental value. Due to its least error and least standard deviation Al-Marhoun (1992) correlation is recommended for this type of PVT data. This correlation is also favored as it covers the same range of oil FVF, bubblepoint pressure, and temperature found in the Pakistani crude oil data.

(3) For two-phase FVF, all of the correlations are best applicable to the medium range of oil API gravity. Glaso (1980) is recommended for crude oil having this type of characteristics.

175.00 -

g 150.00 -

m % b 6 125.00 -

al .z m -F 100.00 -

a, s 5 B 75.00 -

8

; k 50.00 -

25.00 -

-.- Beggs & RobInson

+ Chew & Connally

I- Khan et al

0.00 ’ I I I I

API<34 34<APl<38 38<AP1<42 API>42

(2) (2) (9) (3)


Fig. 7. Statistical accuracy of gas-saturated oil viscosity correlation grouped by oil API gravity.

286 M.A. Mahmmd, M.A. Al-Murhoun /.loumal of Petroleum Science and Engineering 16 (1996) 275-290

I * 250.00

t \ t- \

E a, a, .z 150.00 - m P + Glaso al ‘j - Ng & Egbogah

5

4 100.00 -

%

c $

50.00 -

0.00

API<34 34<AP1<38 38<AP1<42 API>42

(2) (2) (9) (3)


Fig. 8. Statistical accuracy of dead oil viscosity correlatiun grouped by oil API gravity.

(4) Most of the compressibility correlations are good for medium and low oil API gravity ranges and showed large errors towards light oils. The evaluation process shows that Calhoun (1947) is a better choice than the other correlations.

(5) Most of the correlations for viscosity above bubblepoint pressure are good for heavy oils and exhibit large error for medium ranges of oil API gravity. Beal (1946) is recommended for the oil samples used, as it gives the least error and least scatter. This correlation is also suitable due to its comparable range of pressure above bubblepoint with the data used.

(6) Most of the viscosity correlations at bubblepoint pressure performed better for heavy oils. Chew and Connally (1959) is recommended the best correlation as it gives least error for all oil API ranges.

(7) All of the dead oil viscosity correlations are found relatively more accurate for medium to high oil API gravity ranges. Based on a least error analysis, Glaso (1980) is recommended for application. This correlation is suitable also as its temperature

range matches with that of the samples used for this study.

(8) In conjunction with the standard error analysis, an error analysis based on oil API gravity ranges proved to be an effective tool for determining the suitability of the correlation for heavy, medium, or light oil. Thus, this type of analysis is strongly recommended for all evaluation studies of this na- ture.

7. Notation

*lh =

B, =

C0 =

E;, = Ei = E, =

oil FVF at bubblepoint pressure, RB/STB (m3/m3> two-phase FVF below bubblepoint pressure, RB/STB (m3/m3> undersaturated oil compressibility, psi ’ (kPa- ’ > average absolute percent relative error percent relative error average percent relative error

M.A. Mahmood, MA. Al-Marhoun/Journal of F’etroleum Science and Engineering I6 (1996) 275-290 287

log = -

Ifp:

P, = R, =

S= T= x=

YAPI =

Yg =

% =

%b =

log10 number of data points pressure, psi &Pa) bubblepoint pressure, psi &Pa) solution gas/oil ratio, SCF/STB

(m3/m3> standard deviation temperature, “F (K) variable representing a PVT parameter stock tank oil gravity, “API gas relative density (air = 1) oil relative density (water = 1) bubble point oil relative density (water = 1)

pod = dead oil viscosity, CP

&b = gas-saturated oil viscosity, CP

CL, = undersaturated oil viscosity, CP

Subscripts:

c=

critical pr = pseudoreduced est = estimated from the correlation exp = experimental value

8. SI metric conversion factors

“API 141.5/(131.5 + “API) = g/cm3 bbl bbl X1.589837. 10-l = m3 CP CP x 1.0. 1o-3 a = Pa s “F (“F - 32)/1.8 = “C psi psi X 6.894757 = kPa “R “R/1.8 =K scf/bbl scf/bbl X 1.801175 . 10-l = std m3/m3

a Conversion is exact.

Acknowledgements

We thank the management of Oil and Gas Devel- opment Corporation (OGDC, Pakistan) for providing

(A-1)

the data for this research. We are also grateful to the Department of Petroleum Engineering at King Fahd University of Petroleum and Minerals, Dhahran, Saudi Arabia, for its excellent research and comput- ing facilities, made available for this study.

Appendix A. Existing PVT correlations

The PVT correlations evaluated in this study are given below.

A.1. Bubblepoint pressure correlations

A.l.l. Standing (1947)

P, = 18( Rs/y,)0~8310y~

where

Y, = 0.00091T - 0.0125yAp,

A.1.2. Lasater (1958) I

Yp = (R,,‘379.3),‘[( RJ379.3) + (35Oy,,‘M,)]

(A-2a)

‘b = [(Pt-)(Tf460)]/y, (A-2b)

A.1.3. Vazquez and Beggs (1980)

p, = {(~,Rs~y,)~~l~c~~~PI/~~+~~~~l}1’C2 (A-3)

for yAp, I 30:

C, = 27.64

c, = 1.0937

C, = 11.172

for y > 30:

C, = 56.06

c, = 1.187

c, = 10.393

A.1.4. Glaso (1980)

P,= 10. I 7669t 1.7447 log A$-0.3021X(log Np$ (A-4)

’ Refer to the figures presented in the original work.

288

where

M.A. Mahmood, M.A. Al-Marhoun/ Journal of Petroleum Science and Engineering 16 (19961 275-290

where

Np, = (~,/yg)"~~'670.17' _ yO 989

A. I .5. Al-Marhoun (I 988)

3 0 715082 P, = 5.38088 x IO--R; y -1.X77840 3.143700 8 x

x cT+ 460~l.326570

(A-5)

A.2. Oil FVF at bubblepoint pressure

M = R$ $6 ~““7

with

b, =0.4970

A.2.1. Standing (1947)

B,, = 0.9759

b, = 0.862963 x lo-”

b, = 0.182594 x lop’

b, = 0.318099 x 1O-5

b, = 0.74239

b, = 0.323294

b, = - 1.20204

+ 12 x lo-‘{ R,(yg,‘y,)0’5 + I .25T)“’

(A-6) A.2.5. Al-Marhoun (1992)

B,, = 1 +a, Rs + eq~g/XJ

+a3&(T-60)(1 - xy,)

+ a4(T- 60) (A-10)

where


B”, = 1 + Cl& + w--60)(Th/Y..)

+ WdT- W(YA,,/Y,)

for ys 30:

(A-7)

C, = 4.677 x IO-”

c, = 1.751 x 10-j

C, = - 1.8106 x 10-g

fory,,, > 30:

C, = 4.67 x lop4

c2 = 1.1 x 1o-5

c, = 1.337 x lo-’

A.2.3. Glaso fI980)

B,, = 1 + ]~[-6.58511+2.913291o&N,-0.276X3(logN,)']

(A-8)

where

N, = R,( y,/y,)0’5h2 + 0.968T

A.2.4. Al-Marhoun f 1988)

B,, = b, + b,(T+460) + b,M+ b,M* (A-9) , c = 2.9 x 10-O W027R.~

a, = 0.177342 X 1 O-”

az = 0.220163 X IO-’

a3 = 4.292580 X 10ph

a4 = 0.528707 X lo-”

A.3. Two-phase FVF

A.3. I. Standing (1947)

B t

= 10~5.262-474/(- 1?.22+logC,) (A-l 1)

where

C, = R,T” sypo.3y~? (C, = 2.9 X 10-“.00027R~)

A.3.2. Glaso (1980)

B t

= 1o[X.l)135X 10m'+O 47257log G,+O.l735l(logG,)~]

(A-12)

where


A.3.3. Al-Marhoun (1988)

B, = 0.314693 + 0.106253 x 10-4F,

+ 0.188830 x lo-‘“Ft2 (A-13)

where

F = ~0.644516 -1.079340 0.724874 t s x % (T + 460)2’oo6210

x p-O.761910

A.4. Undersaturated oil compressibility

A.4. I. Calhoun * (1947)

-%b = (‘Yo + 2.18 x 10-4Yg ‘%)/B,, (A-14)

A.4.2. Trube * (19.57)

TPr = ( T + 460) /T, (A-15a)

Ppr = P/P, (A15-b)

c, = $/PC (A-l%)


c, = [ - 1433.0 + 5R, = 17.2T- 118O.Oy,

+ 12.61 yApI] /105P (A-16)

AS. Undersaturated oil viscosiry

A.S.1. Beal (1946)

X (0.024p;f + 0.038pu,o;6)


& = k%b( ‘/‘b) m

where

m = 2.6P’.‘87 X 1()[(-3.9x10-5)P-5.0]

A.5.3. Khan et al. (1987)

/.L~ = pnb exp[9.6 X 10-5( P - P,)]

A.5.4. Labedi (1992)

(A-17)

(A-18)

(A-19)

E.c, = kb + M[( ‘/‘b) - ‘1 (A-20)

where

A.6 Gas-saturated oil uiscosi9

A.6.1. Chew and Connally (1959)

p ob =4t%d)b

where

(A-21)

a = 0.20 + 0.80 X 10~0~0008’R~

b = 0.43 + 0.57 x 10-0.00072R~

A.6.2. Beggs and Robinson (197.5)

&b =a( kd>”

where

(A-22)

a = 10.715( R, + 100)-“‘515

b = 5.44( R, + 150) -“‘338

A.6.3. Labedi (1992)

~,b = 10[2.344-0.03542y,p,]p0.6447 od /P:.426

A.6.4. Khan et al. (1987)

/%b = o.09fi/[3/&+?5(1 - %,‘I

where

(A-23)

(A-24)

0, = (T + 460),‘460

A.7. Dead oil uiscosity

A.7.1. Beal (1946)

pod = [0.32 + (1.8 X 107)/y,4,:3]

x [360/(~+ 200)]”

where

a = 1()[email protected]/Y*,,)l

(A-25)

A.7.2. Beggs and Robinson (1975)

pod =lox-1 (A-26)

290 M.A. Mahmood, M.A. Al-Marhoun/ Journal of Petroleum Science and Engineering 16 (1996) 275-290

where

x= ye-1.163

X(Y= loz, Z = 3.0324 - O.O2023y,,,)

A.7.3. Glaso (1980)

/_huod = (3.141 x 10’0)T-3.444

’ (log YAPI > [IO 313(logT)-36 4471

A.7.4. Ng and Egbogah (1983)

log[log( ,uJ] = 1.8653 - 0.025086yAp,

- 0.56441 log T

A.7.5. Labedi (1992)

E-L,d = 109.224/( y,4,:0’3~0 6739)

References

(A-27)

(A-28)

(A-29)

Al-Marhoun, M.A., 1988. PVT correlations for Middle East crude

oils. J. Pet. Technol., 40(5): 650-666.

Al-Marhoun, M.A., 1992. New correlations for formation volume

factors of oil and gas mixtures. .I. Can Pet. Technol., 31(3):

22-26.

Beal, C., 1946. The viscosity of air, water, natural gas, crude oil

and its associated gases at oil field temperature and pressures.

Trans. AIME (Am. Inst. Min. Metall.), 165: 94-112.

Beggs, H.D. and Robinson, J.R., 1975. Estimating the viscosity of

crude oil system. J. Pet. Technol., 9: 1140-l 149.

Calhoun, Jr., J.C., 1947. Fundamentals of Reservoir Engineering.

University of Oklahoma Press, Norman, OK, p.35.

Chew, J. and Connally, Jr., C.A., 1959. A viscosity correlation for

gas-saturated crude oils. Trans. AIME (Am. Inst. Min. Metall.), 216: 23-25.

Glaso, O., 1980. Generalized pressure-volumeetemperature cor-

relations. J. Pet. Technol., 32(5): 7855795.

Khan, S.A., Al-Marhoun, M.A., Duffuaa, S.O. and Abu-Khamsin,

S.A., 1987. Viscosity correlations for Saudi Arabian crude

oils. Presented at the 5th Sot. Pet. Eng. Middle East Oil Show,

Bahrain, Mar. 7-10, 1987, Pap. SPE 15720. Labedi, R., 1992. Improved correlations for predicting the viscos-

ity of light crudes. J. Pet. Sci. Eng., 8: 221-234.

Lasater, J.A., 1958. Bubble point pressure correlation. Trans.

AIME (Am. Inst. Min. Metall.), 213: 379-381.

Ng, J.T.H. and Egbogah, E.O., 1983. An improved temperature-

viscosity correlation for a crude oil system. Presented at the

Pet. Sot., Can. Inst. Min. Metall., Annu. Tech. Meet., Banff,

Alta., May 10-13, 1983, Pap. CIM 83-34-32. Petrosky, Jr., G.E. and Farshad, F.F., 1993. Pressure-volume-

temperature correlation for the Gulf of Mexico. Presented at

68th Sot. Pet. Eng. Annu. Tech. Conf., Houston, TX, Oct.

3-6, 1993, Pap. SPE 26644. Standing, M.B., 1947. A pressure-volume-temperature correla-

tion for mixtures of California oils and gases. In: Drilling and

Production Practice. Am. Pet. Inst., Tulsa, OK, pp. 275-287. Sutton, R.P. and Farshad, F.F., 1990. Evaluation of empirically

derived PVT properties for Gulf of Mexico crude oils. Sot.

Pet. Eng. Reservoir Eng. (Feb.), pp. 79-86.

Trube, A.S.. 1957. Compressibility of undersaturated hydrocarbon

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mahmood 1996

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