two seventy

8/9/2019 Two Seventy

1/16

LS VI R 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 Engineeri ng, Ki ng Fahd Uniuersity of Petroleum and M ineral s, Dhahran 31261, Saudi Arabi a

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 The evaluation is performed by using an unpublished data set of 22 bottomhole fluid samples collected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.

Keyw ords:

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, intro-

duction 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

correla-

tions need to be modified for their application. Be-

cause of the availability of a wide range of correla-

tions, 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 correla-

tions 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 correla-

tions 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

PI I

SO920-4105(96)00042-3


2/16

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 bub-

blepoint, 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 pre-

dicting bubblepoint pressure by correlating reservoir

temperature, solution gas/oil ratio, gas relative den-

sity, 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 corre-

lations 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 recom-

mended a bifurcation for evaluating PVT parame-

ters, 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, solu-

tion gas/oil ratio, gas relative density, and oil grav-

ity. 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)


3/16

M .A. M ahmood, M.A. Al -M arhoun/ Journal of Petrol eum Science and Engineeri ng 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 bifur-

cation 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 den-

sity, and oil gravity. Applying the same

PVT

param-

eters used by Standing, Glaso (1980) published his

correlation. Al-Marhoun (1988) reported his correla-

tion 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 un-

dersaturated crude oil. Trube (1957) for his graphical

correlation used pseudoreduced pressure and temper-

ature to determine undersaturated oil compressibility.

Vazquez and Beggs (1980) also presented a com-

pressibility 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 bubble-

point as the correlating parameters. Vazquez and

Beggs (1980) by using 3593 data points also pub-

lished their correlation for undersaturated oil viscos-

ity. 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) re-

ported 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 tempera-

ture range of 50-300°F for 26 crude oil samples. Ng

and Egbogah (1983) presented their viscosity corre-

lations by modifying the Beggs and Robinson corre-

lation. Recently, Labedi (1992) has published a cor-

relation 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


4/16

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


5/16

M .A. M ahmood, M .A. Al -M arhoun/ Journal of Petrol eum Science and Engineeri ng 16 1996) 275-290

219

Table 2 (continued)

Table 2 (continued)

No

T

P, B

h

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 re-

sults of standard differential liberation tests con-

ducted 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 com-

pressibility, 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


6/16

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 tempera-

ture 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 ac-

quired 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 deter-

mine 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

(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.


7/16

M .A. M ahmood, M .A. Al -M arhoun / Journal of Petrol eum Science and Engineeri ng 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 ex-

pressed 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 ex-

pressed as:

4.3. Minimum and maximum absolute percent rela-

tive errors (Emi, and E,,,,,

S=

(6)

Both the minimum and maximum values are de-

termined 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

+

az RBegg

++- N-Marhoun 88

+ Al-Marhoun 92

I

I I

I

API


8/16

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, aver-

age percent relative error, minimum and maximum

absolute percent relative error, and standard devia-

tion are summarized in Tables 4-10. Another effec-

tive 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


9/16

M.A. Mahmood, M.A. Al-Marhoun / Journal

o

Petroleum Science and Engineering 16 (1996) 275-290

283

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,

25.00 -

a

D

8 20.00 -

E

k 15.00 -

10.00 -

API


10/16

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 reason-

able 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 correla-

tions 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


11/16

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

285

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 pres-

sure, 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 pre-

dicted value is less than the actual experimental

value. Due to its least error and least standard devia-

tion 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


12/16

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


13/16

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.

7669t 1.7447 log A -0.3021X(log Np

(A-4)

’ Refer to the figures presented in the original work.


14/16

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 c T+ 460~ . 3 26570

(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(l ogN, ) ' ]

(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 1O-”

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+ ogC, )

(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 47257l og G, +O. l 735l ( l ogG, ) ~]

(A-12)

where


15/16

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

289

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() ~0. 43+@ 33/ Y*, , )l

(A-25)

A.7.2. Beggs and Robinson (1975)

pod

=lox-1

(A-26)


16/16

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