View
227
Download
0
Category
Preview:
Citation preview
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 The evaluation is performed by using an unpublished data set of 22 bottomhole fluid samples collected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
8/9/2019 Two Seventy
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)
8/9/2019 Two Seventy
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
8/9/2019 Two Seventy
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
8/9/2019 Two Seventy
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
8/9/2019 Two Seventy
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.
8/9/2019 Two Seventy
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
8/9/2019 Two Seventy
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
8/9/2019 Two Seventy
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
8/9/2019 Two Seventy
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
8/9/2019 Two Seventy
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
8/9/2019 Two Seventy
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
8/9/2019 Two Seventy
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.
8/9/2019 Two Seventy
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
A.2.2. Vazquez and Beggs (1980)
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
8/9/2019 Two Seventy
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%)
A.4.3. Vazquez and Beggs (1980)
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)
A.5.2. Vazquez and Beggs (1980)
& =
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)
8/9/2019 Two Seventy
16/16
Recommended