Api mpms 11 2 2 1986 (2012) scan (american petroleum institute)

Date of Issue: June 1996
Affected Publication: Addendum to Chapter 11, “Physical hoperties Data,” Section 2, Part 2-Compressibility Factors for Hydrocarbons, Correlation of Vapor Pressure for Commercial Natural Gas Liquids
of the Manual of petroleum Measurement Standards, First Edition, December 1994 (1st printing)

ERRATA
Page 22, mid-page, correct the following code:

Old code: A = 6.4837DO
Corrected code: A = 6.4827DO
Page 22, near the bottom of the page, correct the following
code:

Old code: A = 2.085371Dl
Corrected code: A = 2.08537Dl
Page 23, Line 12, correct the following code:

Old code: K = (C+D*RDEN) 1553.0DO * 1.OD5
Corrected code: K = (C+D*RDEN)I 543.0DO * 1.OD5


Manual of Petroleum
Measurement Standards
Chapter 11.2.2—Compressibility Factors for
Hydrocarbons: 350–637 Relative
Density (60°F/60°F) and –50°F to
140°F MeteringTemperature

SECOND EDITION, OCTOBER 1986
REAFFIRMED, DECEMBER 2012

Manual of Petroleum
Measurement Standards
Chapter 11.2.2—Compressibility Factors for
Hydrocarbons: 350–637 Relative
Density (60°F/60°F) and –50°F to
140°F MeteringTemperature

Measurement Coordination
SECOND EDITION, OCTOBER 1986
REAFFIRMED, DECEMBER 2012



~~~~

S T D - A P I / P E T R O MPMS 1 1 * 2 - 2 - E N G L 1786

~

~~~~

0732290 0562281 808

Nothing contained in any API publication is to be construed as granting any right, by
implication or otherwise, for the manufacture, sale, or use in connection with any method,
apparatus, or product covered by letters patent nor as indemnifying anyone from or against
any liability for infringement of letters patent.
This publication may be used by anyone desiring to do so. The Institute hereby expressly
disclaims any liability or responsibility for loss or damage resulting from its use; for the

violation of any federal, state, or municipal regulation with which an API publication
may conflict; or for the infringement of any patent resulting from the use of an API
publication. Every effort has been made by the Institute to assure the accuracy and
reliability of the data presented.

copyright 0 1986 American petroleum institute


~

STD.API/PETRO MPMS L L * Z . Z - E N G L L 7 8 b

0732270 0 5 b 2 2 8 2 744

FOREWORD
This publication provides tables to correct hydrocarbon volumes metered under pressure
to corresponding volumes at the equilibrium pressure for the metered temperature. The
parallel publication in metric (SI) units is the Manual of Petroleum Measurement Stundards, Chapter 11.2.2M.
The table presented id this volume is also available from API as a computer tape,
along with a manual containing the text information in this publication.
Suggested revisions are invited and should be submitted to the director, Measurement
Coordination Department, American Petroleum Institute, 1220 L Street, N.W., Washington, D.C. 20005.

iii


COMMITTEE ON STATIC PETROLEUM MEASUREMENT
WORKING GROUP ON COMPRESSIBILITY
F. P. Gielzecki (Retired)
Imperial Oil, Ltd.

K. T. Liu, Ph.D.
Chevron Oil Field Research Company

K.M.Goin, Ph.D.
Cities Service Oil and Gas Corporation

M.A. Plummer, Ph.D.
Marathon Oil Company

R. A. Griffith (Chairman, Retired)
Texaco Trading and Transportation Company

J. Polowek
Interprovincial Pipe Line Ltd.

R. B. Hall
Texas Eastern Transmission Company

G. W.Singletary (Deceased)
Texas Eastern Transmission Company

J. A. Hamshar
Cities Service Oil and Gas Corporation

G. W.Swinney (Retired)
Phillips Petroleum Company


S T D * A P I / P E T R O M P M S L L * 2 - 2 - E N G L 1 7 8 b m 0 7 3 2 2 7 0 05b228Li 517 m

CONTENTS

CHAPTER 11.2.2-COMPRESSIBILITY FACTORS FOR HYDROCARBONS: 0.350-0.637 RELATIVE DENSITY
(60"F/60°F) AND -50°F TO 140°F METERING
TEMPERATURE
PAGE

11.2.2.1
11.2.2.2
11.2.2.3
11.2.2.4
11.2.2.5
11.2.2.6
11.2.2.7
11.2.2.8
11.2.2.9

scope ..................................................................
History and Development ..............................................
Type of Standard and Limits ...........................................
Example Use of the Standard ..........................................
Data Base ..............................................................
Basic Model ............................................................
Uncertainty Analysis ...................................................
Calculation Procedure ..................................................
References .............................................................

1
1

1
1
2
5
6
8
10

Table of Compressibility Factors for Hydrocarbons: 0.350-0.637 Relative
Density (60°F/600F) and -50°F to 140°F Metering Temperature .................. 11
Text Tables
1-Summary of Data Base .....................................................
2-Data Mixture Compositions (Mole Percent) .................................
3-Effect of Pressure on Compressibility Factors ...............................
+Expected Frequency of Errors When Using Temperatures to the
Nearest 0.25"C Versus the Nearest 03°F ...................................

2
4

6
6

Figures
1-Limits of Data Base by Relative Density and Temperature ................. 3
2-Uncertainties (95-Percent Confidence Level) in Volume Versus
Temperature and Relative Density ..........................................
7

V

~

~

STD.API/PETRO

MPMS LL.2.2-ENGL

m

L78b

Chapter 11-Physical

0 7 3 2 2 9 0 0 5 b 2 2 8 5 453

Properties Data

SECTION 2-VOLUME CORRECTION FACTORS FOR METER PROVING AND
HYDROCARBON COMPRESSIBILITY

11.2.2 Compressibility Factors for
Hydrocarbons: 0.350-0.637
Relative Density (6O0F/6O"F)and
-50°F to 140°F Metering
Temperature
11.2.2.1 SCOPE

in volume because of the important efféct of pressure on
the Compressibility factor for light hydrocarbons. The range
of the table is from -50°F to 140°F and from 0.350 to
0.637 relative density (60"F/60°F),for use with pressure
differences above equilibrium from O to 2200 pounds per
square inch.
The equation used to generate the table is given for those
who wish to duplicate the table using their specific computer
and language. Identical table information is available on a
computer tape. The use of this computer tape to verify
individually developed computer subroutines is highly recommended.

The purpose of this standard is to correct hydrocarbon
volumes metered under pressure to the corresponding volumes at the equilibrium pressure for the metered temperature. This standard contains compressibility factors related
to the meter temperature and relative density (6O0F/60"F)
of the metered material. The corresponding metric (SI) version is Chapter 11.2.2M.

EXAMPLE USE OF THE STANDARD

11.2.2.4
11.2.2.2

HISTORY AND DEVELOPMENT

In this standard, the compressibilityfactor ( F ) is used in
the normal manner for volume correction (* denotes multiplication):

The previous APl standard for hydrocarbon compressibility, Standard 1101,Measurement of Petroleum Liquid
Hydrocarbons by Positive Displacement Meter, was developed from graphical correlations prepared in 1945. This
standard was based on limited data with only a few points

for pure fluids in the range from propane to pentane. No
lighter mixtures and no effect of pressure on the compressibility factor were considered.
In 198 1,the Committee on Static Petroleum Measurement
formed a subcommittee, the Hydrocarbon Compressibility
Group, to revise the compressibilitytables of Standard 110I.
As a result of an extensive literature survey, the data base
found for the relative density portion of the table covers a
broader range than that used in Standard 1101 but is lacking
in data for unsaturated hydrocarbons. The data base was
used to develop a mathematical model that includes the
effect of pressure on the compressibilityfactor. The printed
table produced from the model is the standard. This standard
replaces the discontinuedStandard 1101 and the first edition
of Chapter 11.2.2,Compressibility Factors for Hydrocarbons: 0.500-0.411 Relative Density Range and 20-128oF.

Where:
CP1= correction factor for pressure.
Ve = volume at the equilibrium (bubble point)
pressure, P, .
V, = volume at the meter pressure, P,.
D , = P , - P,.
P, and P , may be in either pounds per square inch gage or
pounds per square inch absolute, but both must be in the
same units.
As an example, calculate the volume at equilibrium pressure of lo00 barrels (V,) of a material with a relative density
(6OW6O"F) of 0.5297 metered under*a pressure of 500
pounds per square inch at a temperature of 55.1"F.The
equilibrium pressure (P,) for this material at 55.1T is 45
pounds per square inch. The rounded relative density and
temperature values of 0.530 and 550°F yield an A factor

of 35,641and a B factorof 5.516.Thecompressibiiityfactor
( F ) is Calculated as follows:

11.2.2.3 TYPE OF STANDARD AND LIMITS
The actual standard is the printed table of 224 pages that
follows this text. The increments used in the table are OST
and 0.002 relative density. Interpolation to 0.001 relative
density is allowed. Compressibilities are in the usual units
of reciprocal pounds per square inch but are calculated from
two terms, A and B, and the pressure difference from equilibrium, D , . This is necessary to obtain the desired accuracy

F

+

= 1/(A
D, * B )
= 1/[35,641 (500 - 45) * 5.5161

+

= O.oooO2621

The value for F is rounded to the eighth decimal place, to
the maximum of four significant digits.
1


2

CHAPTER 11-pWSICAL

PROPERTIES

abnormalities. The final data base used in this standard
consists of 1724 data points from 13 sources (see Table i).
The ranges of the experimental data were relative densities (60°F/60"F)from 0.3477 to 0.6312, temperatures from
- 28°F to 160"F, and pressure differences from 41 to 2036
pounds per square inch gage (see Figure i). The actual
ranges for the standard, as determined by an API survey,
are relative densities (6O"F/6O0F)from 0.350 to 0.637, temperatures from -50°F to 140"F, and pressure differences
from O to 2200 pounds per square inch gage. Hence, some
portions of the standard represent extrapolated results. The
uncertainty analysis presented in 11.2.2.7 may not be valid
for these extrapolated portions. For the lower relative densities, 140°F is above the pseudocritical temperam at which
liquid exists. For these fluids, the range is restricted to 96
percent of the pseudocritical temperature.
The data set contains 46 different mixtures of normal
hydrocarbons from methane to decane. The compositions
of the mixtures are listed in Table 2. The use of the standard
for compositions not close to those in the data base represents an extrapolation whose results may have a greater
uncertainty.

Then,

C,, = 1/[1.0 - 0.00002621 * (500 - 45)]
= 1.0121

The value for Cplis rounded to the maximum of four decimal
places.

ve = v, * c,,
= lo00

* 1.0121

= 1012 barrels

The value for Ve is rounded to the nearest whole barrel.
For additional examples and more details, see Chapter
12.2, Calculation of Liquid Petroleum Quantities Measured
by Turbine or Displacement Meters.

11.2.2.5

DATA

DATA BASE

An initial 2278 data points were obtained from the literature for pure fluid compounds and mixtures of light hydrocarbon liquids. These data were examined to eliminate
data for gases, data with large errors, and data with other

Table 1-Summary

of Data Base

Pressure
(pounds

Relative

Density

Temperature

psquare

Sample

(60"/60"F)

("F)

inch gage)

Number
of Data
Points

NGPA/TP2
NGPA/TPl
Cal Tech
Tulsa
ManleylSwiít
pope
straty

0.35-0.61
0.35-0.51
0.50-0.63
0.35-0.51

32-140
40-130
70-160
-20-120
-20-100
- 25-63
- 28-66
- 13-32
32-140
-28-80
-28-100
32- 122
122-149

180-2000
150-2000
100-2000
100-1500
300-1600
198-1788
320-2200
460-2100
140-2120
242-2040
121-2130
121-1477
400-1465

455

218
157
542
13
36
67
5
33
81
57
50
10

0.508

Dousri

0.356
0.356
0.356

Dittmar

0.508

Hayaes

0.51-0.58
0.508
0.508

0.508

ElY
ThOmsS

Tekhamm

References

12
21
9, 10, 13, 14, 15, 16. 17

I
8

11
18
3
2
5 , 6.7
4
20
19


S T D - A P I / P E T R O MPMS

L L - Z * Z - E N G L L98b

SECTION 2-VOLUME

CORRECTION

FACTORS

3

+

+

*
*+

+
+

*

+

+

*+

+

+

+

*

+

P

+

+

*
*

+
+++++

+

cc

+
+
+*+*tc3**Ø+++cFH
+
+ 4t+*
+
+
+

+

+

*+u+*+&+
+ +«.

+

+ + *

*+

+* +*

+

+

+

+
+

+

t

+

4H++***cIc++&L#

+

*

*

t

$
+
+
+
+

*
*

*

*
u

$

*

+

+
+

+
+

+
+

+
+

+

0 7 3 2 2 9 0 0 5 b 2 2 8 7 22b

+
+

+

+

$*

+

++++ +
+++* +

4t

+

+

t+F+M+"))c+ct++

+
++

+
+

+
+

+

+
+

+

++

++

++

+
+

+

.c

O

+ ++

.-Y

+ +

+

+

+

+

E
ï

I

F

7 *

+

+


STD.API/PETRO MPMS L L * Z - Z - E N G L L 9 8 b

O732290 05b2288 L b 2 W

CHAPTER
1 1-PHYSICAL
PROPERTIES
DATA

4

Table 2-Data Mixture Compositions (Mole Percent)
Sample
1
2
3
4
5
6
7
8
9

10
11
12
13
14
15
16
17
18
19
20
21
22
23
24
25
26
27
28
29
30
31
32
33

34
35
36
37
38

39

40
44

45

4.6
47
48
49
50
51
52
68
70
71
72
73
74
75
76

77
78
79

80
81
82

Ci
3.10
0.00
0.28
0.52
0.89
1.16
1.55
1.88
0.00
0.28
0.52
0.89
1.16
1.55
1.88
0.00
0.29
0.52
0.89
1.16
1.55
1.88
2.33
0.00
0.00
2.42
0.00
0.00

0.00
3.23
0.00
2.31
2.18
0.00
0.00
2.26
0.00
0.00
0.00
0.00
0.00
0.00
0.00
0.00
0.00
2.55
2.70
2.52
2.51
0.00
O
O
O
O
O
O
O
O

O

O
O
O
O

CZ

c3

96.90
0.02
8.83
16.17
27.70
36.33
48.45
58.83
0.02
8.83
16.17
27.70
36.34
48.44
58.84
0.00
8.93
16.15
27.68

36.34
48.45
58.83
72.67
0.08
0.00
0.00
0.00
37.00
49.89
48.28
71.71
70.05
69.52
89.97
100.00
97.74
0.00
0.00
0.00
0.00
0.00
30.13
51.28
71.60
100.00
28.90
49.17
67.76
87.76

0.00
100
100
100
O
O

0.00
35.29
32.08
29.41
25.21
22.06
17.64
13.87
50.13
45.59
41.77
35.81
31.33
25.07
19.70
63.77
57.89
53.17
45.55
39.86
3 1.86
25.06
15.93

99.85
100.00
97.58
99.11
63.00
50.11
48.49
28.29
27.64
27.47
10.03
0.00
0.00
0.00
0.00
100.00
0.00
100.00
69.87
48.72
28.40
0.00
68.55
48.13
29.72
9.73
100.00
O
O
O

100
100
100
100
100
100
O

O

O
O
O
O
O
O
O

O

O
O

nC4

iC,

0.00
19.80
18.00

16.50
14.14
12.38
9.90
7.78
18.20
16.54
15.17
13.00
11.38
9.10
7.15
17.74
16.11
14.78
12.67
11.09
8.87
6.97
4.44
0.05
0.00

0.00
8.11
7.37
6.76
5.79
5.07
4.06

3.19
7.17
6.52
5.97
5.12
4.48
3.59
2.82
6.21
5.64
5.17
4.44
3.88
3.11
2.44
1.55
0.02
0.00
O

O

0.89
0.00
0.00
0.00
0.00
0.00
0.83
0.00

0.00
0.00
100.00
0.00
0.00
0.00
0.00
0.00
0.00
0.00
0.00
0.00

0.00
0.00
0.00
0.00
O
O
O
O
O
O
O
O
O
O

O
i00

100

O

O
O
O
O
O
O
O
O
O
O
O
O
100
O
O
O

O
O
O
O
O
O
O
O
O

O
O
O
O
O
O
O
100
100
O
O

nC5

iC5

CS

c7

C8

CP

Cl0

0.00
6.70
6.09
5.58

4.79
4.19
3.35
2.63
4.46
4.05
3.72
3.19
2.79
2.23
1.75
2.90
2.63
2.42
2.07
1.81
1.45
1.14
0.73
0.00
0.00
O
O
O
O
O
O
O
O
O

O
O
O
100
O
O
O
O
O
O
O
O
O
O
O
O
O
O
O
O
O
O
O
O
O
O
O
O
O

0.00
5.74
5.22
4.78
4.10
3.59
2.87
2.26
3.82
3.47
3.18
2.73
2.39
1.91
I .50
1.97
1.79
1.62
1.41
1.23
0.99
0.77
0.49
0.00
0.00
O
O
O
O

0.00
6.54
5.95
5.45
4.67
4.09
3.27
2.57
4.35
3.95
3.62
3.11
2.72
2.18
1.71
2.91
2.64
2.43
2.08
1.82
1.46
1.14
0.73
0.00
0.00
O

0.00
6.88
6.25

5.73
4.91
4.30
3.44
2.70
4.58
4.16
3.82
3.27
2.86
2.29
1.80
2.62
2.38
2.18
1.87
1.64
1.31
1.03
0.66
0.00
0.00
O
O
O
O
O
O
O
O

O
O
O
O
O
O
O
O
O

0.00
5.71
5.19
4.76
4.08
3.57
2.86
2.24
3.80
3.45
3.17
2.71
2.38
1.90
1.49
0.93
0.84
0.77
0.66
0.58

0.47
0.37
0.23
0.00
0.00

0.00
3.18
2.89
2.65
2.27
1.99
1.59
1.25
2.12
1.93
1.77
1.51
1.33
1.06
0.83
0.95
0.86
0.79
0.68
0.59
0.48
0.37
0.24
0.00

0.00
O

0.00
2.03
I .85
1.69
1.45
1.27
I .o2
0.80
1.35
1.23
1.12
0.96
0.84
0.68
0.53
0.00
0.00
0.00
0.00
0.00
0.00
0.00
0.00
0.00
0.00
O
O

O
O

O

O
O
O
O
O

O
O
O
O
O
O
O
O
O
O
O
O
O
O
O

O
O
O

O
O
O
O
O
O
O
O

O
O

O

O
O
O
O
O
O
O
O

O
O

O
O
O
O

O
O
O
O
O
O
O
O
O
O
O
O
O
O
O
O
O
O
O
O
O
O

O
O
O

O
O
O

O
O
O
O
O
O
O
O
O
O

O
O
O
O
O

O
O
O
O
O

O
O
O
O
O
O
O

O
O
O
O
O
O
O
O
O
O
O
O
O
O
O
O
O
O
O

O
O
O
O
O
O
O

O
O

O
O
O
O
O

O
O

.

O
O
O
O
O
O
O
O
O
O
O
O
O
O
O
O
O
O

O
O
O
O
O
O
O
O
O
O

O

O
O
O
O
O

O
O
O
O
O
O
O
O
O
O
O

O
O
O
O
O
O
O
O
O
O
O
O
O
O
O
O

o .


~

S T D * A P I / P E T R O MPMS L L - 2 - 2 - E N G L L78b

SECTION 2-VOLUME

11.2.2.6

0732290 0 5 b 2 2 8 7 U T 7

=

CORRECTION FACTORS

BASIC MODEL

In this standard, the compressibilityfactor (F)is used in the normal manner for volume
correction:

CpI = VJV, = l/(l - F

* Dp)

The effect of pressure on the compressibility factor (F)is not negligible for the range
of conditions of the standard. Therefore, the pressure effect is included in the model by
the use of two factors, A and i?. The basic mathematical model used to develop this
standard relates compressibility to relative density, temperature, and pressure difference
as follows:

F = 1/(A + D, * i?)

A

*

B

=

-2.1465891D-6 * TR2

+
- 1.0502139D-5 * TR2* G4 +
-0.95495939DO
+
-2.7769343D-7 * TR3* G4 +
-0.05110158W * TR * G +
+9.13114910DO * G

* lod5 =

1.577439OD-5 * TR2* G2
2.8324481D-7 * TR3* G6
7.2900662D- 8 * TR3* G2
0.03645838Do * TR * G2
0.00795529DO * TR

-6.0357667D- 10 * TR2 + 2.2112678D-6 * TR * G2
+0.00088384W * G - 0.002oQo16DO
* G2

Where:

D, = pressure above the equilibrium bubble point pressurc, in consistent units of
pounds per square inch gage or pounds per square inch absolute.
DX = double-precision accuracy to the X t h power of 10.
TR = temperature, in degrees Rankine.
G = relative density (óû"F/6O"F).
The use of higher powers of TR and G and other combinations of them did not improve
the correlation.

5


S T D - A P I I P E T R O MPMS

L l * Z - Z - E N G L 178b

CHAPTER
1 1-PHYSICALPROPERTIES
DATA

6

11.2.2.7

0732290 05b2270 BLO

UNCERTAINTY ANALYSIS
lustrate this, the uncertainties in the calculated volume would
range from 0.2 to 11 percent if a mean compressibility factor
for 500 pounds per square inch, instead of the compressibility factor at the correct pressure, were used. This is from
2 to more than 100 times the desired uncertainty of 0.1
percent in the volume. Table 3 provides more details about
the uncertainties due to ignoring the effect of pressure on
compressibility at various conditions.
In situations where either Chapter 11.2.2M or Chapter
11.2.2 could be used' to obtain corrected volumes, differences in C,, can arise. Because of rounding, the increment
in metered temperature of 0.25"C in Chapter 11.2.2M does
not always yield CpIvalues equal to those from Chapter
11.2.2, which uses 0.5T increments. Table 4 shows the

frequency of errors that can be expected when using temperature to the nearest 0.25"C, as opposed to the nearest
05°F.In addition, maximum differences in Cplof -tO.ûûûí
can be expected (at a frequency of 0.4 percent) because of
conversion of pressure from pounds per square inch to kilopascals. It is therefore recommended that in cases where
one party ordinarily uses metric units and the other party
ordinarily uses customary units, the use of either Chapter
11.2.2M or Chapter 11.2.2 should be agreed on before a
transaction is made.

The uncertainty in the compressibility factor is I 1 0 . 8
percent at the 95-percent confidence level. (The figure 10.8
is 2.0 times the standard deviation of 5.4 percent, where
2.0 is the two-tail probability value of a normal distribution
for 1709 degrees of freedom at 95 percent.) These uncertainties represent the likelihood of the correlation's ability
to reproduce the data for a specific sample. They do not
indicate how accurate the data are. In many cases, the accuracy of the experimental data is unknown. The corresponding uncertainty in volume and in C ,is 2 0.56 percent
at the 95-percent confidence level, derived from a computed
standard deviation of 0.28 percent, as described above.
These volumetric uncertainties depend on operating conditions, the type of material, and the effect of pressure on
the compressibility factor. They may not be true for the
extrapolated portions of the standard. The regions where
various uncertainties can be expected, averaged for all pressures, are plotted in Figure 2. The uncertainty for specific
materials and temperature conditions can be obtained from
this figure. For samples at lower relative densities, the uncertainty increases as the mixture's critical temperature is
approached. The correlation is valid for temperatures less
than or equal to 96 percent of the pseudocritical temperature.
If the effect of pressure on compressibility were ignored,
there would be greater uncertainties in the volume. To il-

Table 3-Effect

of Pressure on Compressibility Factors
~

Relative
Density

0.360
0.636

F h(%)

Te("F)

D, = 1OOOpsi

D, = 2ooopsi

-20
68
-20

11.0
26.0

27.0
52.0
1.5
13.8

0.5
5.1

140

~~

c, Errors (96)
D , = 1OOO psi
D , = ux)(lpi
1.5
5.4
0.4
0.9

3.9
11.1
0.2
2.5

NOW The values in the tnbk arc tûe emns when the compressibility factor at 500 psi. instead of the one at
the measured prcswrc, is uscd.

Table 4-Expected

Frequency of Errors When Using
Temperatures to the Nearest 0.25"C Versus the
Nearest 0.5"F

A b l ü k JXff-

in C,

Fraquency (%I

0.0010 s Difference S 0.0015

0.06

Diffmnce 2 o.oO05
Diffclwlcc 2 o.OOO1

0.28
2.9


STD.API/PETRO MPMS 1 1 - Z - Z - E N G L L 7 8 b

SECTION 2-VOLUME

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CORRECTION FACTORS

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S T D - A P I I P E T R O MPMS 11.2. 2-ENGL

198b

m 0732290

ÖSbZ292 b43

m

CHAPTER
11-PHYSICAL
PROPERTIES
DATA

8

11.228 CALCULATION PROCEDURE

Ensure that TEMP is to the nearest O S O F , and convert to
degrees Rankine as follows (this procedure is also valid for
individual point calculations):

This procedure is recommended for computers with 11
or more significant digits. With some computers, this could

require the use of double precision for ail variables and
constants, as shown in the following steps and example.

TX

11.2.2.8.1

If DIFF 2 0.0 then SIGN = 1.0 else SIGN = - 1.0.

initialize the Temperature and Relative
Density

1. To verify the standard, increment relative density (G)
by 0.002, with the 0.637 value as a special case. Ensure
only three significant digits by:
G = INT(G

* 1OOO.ODO + O S D O ) * 0.001DO

The INT intrinsic function r e m s an integer by truncating
all digits to the right of the decimal point. Verify that G is
between 0.350 and 0.637, and do not calculate if it is outside
this range.
G = 0.XXX: 0.350 I G 5 0.637

* lOOO.ODO/2.ODO + O S D O ) * 0.002DO

2. To verify the standard, increment temperature (TEMP)
by 0.5"F and verify that it is between -50°F and 140°F
and less than or equal to 96 percent of the pseudocritical

temperature. The pseudocritical temperature is calculated
from the relative density as follows:
TC = 621.418DO - 822.686DO * G
+ 1737.86W * G * G
TMAX = TC * 0.96DO

-

TX

DIFF = ABS(DIFF): that is, the absolute value.
If DIFF < 0.25 then TEMP = TX.
If0.25 5 DIFF < 0.75 then TEMP = TX + 0.5 * SIGN.
If DIFF 2 0.75 then TEMP = TX + 1.0 * SIGN.
TR = TEMP

+ 459.7: that is, conversion to degrees Rankine.

Check that TR 5 TMAX.
For example, where temperature is 55.O"F and relative density is 0.530:
TR = 514.7000000000000 = TEMP

+ 459.7DO

TC = 673.5602266357421

NOTE:Results are shown to 16 digits for comparison purposes. Only l l digits are required to generate the standard.
Constants must use 11 digits, as indicated by the D exponent.
3. Calculate the powers of temperature:

TR2 = 264916.0900000000 = TR

* TR

TR3 = 136352311.523oooO = TR

* TR2

4. Calculate the powers of relative density:

Where:
TC = pseudocritical temperature, in degrees Rankine.
TMAX = maximum allowable temperature, in degrees
Rankine.
TEMP = XXX.X"F: -50°F

DIFF = TEMP

TEMP = 5.5.00000000000000

For individual point calculations, G may be rounded to the
nearest 0.002 by:
G = INT(G

= INT(TEMP): that is, truncation.

ITEMP 5

140°F

G = 0.5300000000000000

G2 = 0.2809000000000000 = G

*G

G4 = 0.7890480999999998D-01 = G2 * G2

G6

= 0.22164361128999991)-O1 = G2 * G4


-

~

STD.API/PETRO MPMS L L * Z * Z - E N G L L 7 8 b M 0732270 05b2Z.73 5 2 T

SECTION 8-VOLUME

11.2.2.8.2

CORRECTION

FACTORS

9

Calculate the A Factor

1. Calculate the terms and sum to A:
A
A
A
A
A
A
A
A
A
A
A
A

= 0.0000000000000000D+00
START A TERM
= A - 2.1465891D-6
= - 0.56866599 12086190
= 0.6051841314020503
= A
1.577439OD-5

+

=

=
=

=
=
=
=

=
=

0.3856563052085592
1.241667970820398
0.2867085808203977
3.078903394290068
0.9124053693424172D-01
5.362365044381641
- 8.577686065398357
-4.483098302398357
0.3564107206016427

= A - 1.0502139D-5
= A
= A

=A
= A

= A
= A
= A
= A

+ 2.8324481D-7

* TR2
* TR2 * G2
* TR2 * G4
* TR3 * G6

- 0.95495939W

+ 7.2900662D-8 * TR3 * G2

- 2.7769343D-7 * TR3 * G4
+ 0.03645838DO * TR * G2
- 0.05110158DO * TR * G

+ 0.00795529DO * TR
+ 9.13114910DO * G

2. Round and scale A to get the A factor:

+

A = INT(A * 1OOOOO.ODO
OSDO)
= 35641 (rounded to a whole number)

11.2.2.8.3

Calculate the B Factor

1. Calculate the powers of temperature, as in 11.2.2.8.1, Item 3.
2. Calculate the powers of relative density, as in 11.2.2.8.1, Item 4.
3. Calculate the terms and s u m to B:
B = 0.0000000000000000D+00
B = -0.1598971714316203D-03
B = 0.1598062244161737D-03
B = 0.6282414244161736D-03
B = 0.5516048041617370D-04

STARTBERM

B - 6.0357667D- 10 * TR2
= B + 2.2112678D-6 * TR * G2
= B + 0.00088384DO * G
= B - 0.00204016DO * G2

=

4. Round and scale B to get the B factor:

11.2.2.8.4

*

+

100000000.ODO O S D O ) * 0.001W
= 5.516 (rounded to three significant decimal places)

B = INT(B

Verify the Table

Because of the complexity of the calculations, each term in the table should be vqrified
against the standard. A tape of the table is available for use in verifying that the computer
procedure will reproduce the standard.


-

~~

~

S T D * A P I / P E T R O MPMS L L - Z - Z - E N G L L78b

CHAPTER
1 1-PHYSICALPROPERTIES
DATA

10

11.2.2.9

0732270 05b2274 4bb

REFERENCES

1. Bdeir, M. H., “Surface Fitting of Compressibility and
Thermal Expansion Data for Ethane-Propane Mixtures and

Heavier Hydrocarbons,” Thesis, University of Tulsa, Oklahoma, 1967.
2. Di-,
P., Schuh, F., and S e s e , G., ‘‘DUrck/Dichteí
Temperatur-Werte fuer Propan und Propylen,” Chemie
tng. Techn., June 1962,Vol. 34,No. 6, p. 437.
3. Douslin, D.R., and Harrison, R. H., “Pressure-Volume-Temperature Relations of Ethane,” J . Chem. Thermodynamics, 1973, Vol. 5, No. 4,p. 491.
4. Ely, J. F., and Kobayashi, R., “Isochoric PressureVolume-Temperature Measurements for Compressed Liquid Propane,” J. Chem. Eng. Data, 1979,Vol. 23,No. 3,
p. 221.
5 . Haynes, W. M., and Hiza, M. J., “Measurements of
the Orthobaric Liquid Densities of Methane, Ethane, Propane, Isobutane, and Normal Butane,” J. Chem. Thermodynamics, 1977,Vol. 9,No. 2, p. 179.
6. Haynes, W. M., “Measurements of Densities and Dielectric Constants of Liquid Isobutane from 120 to 3 O k at
Pressures to 35 MPa,” in press.
7. Haynes, W. M., “Measurements of Densities and Dielectric Constants of Liquid Normal Butane from 140 to
300k at Pressures to 35 MPa,” in press.
8. Manley, D. B.,and Swift, G. W., “Relative Volatility
of Propane-Propene System by Integration of General Coexistence Equation,” J . Chem. & E. Data, 1971,Vol. 16,
No. 3.
9. Moms, W. M.,Sage, B. H., and Lacey, W. N., “Volumetric Behavior of Isobutane,” Technical Publication 1128,
Petroleum Technology (American Institute of Mining and
Metallurgical Engineers preprint), November 1939.
10. Olds, R. H., Reamer, H. H.,Sage, B. H.,and Lacey,
W. N., “Phase Equilibria in Hydrocarbon Systems: Volumeüic Behavior of n-Butane,” Znd. Eng. Chem., March
.
1944,Vol. 36, NO.3, p ~ 282-284.
11. Pope, G. A., “Calculation of Argon, Methane and
Ethane Virial Coefficients at Low Reduced Temperature
Based on Data Obtained by I s o c h o n d y Coupled Bumett

Experiments,” Thesis, Rice University, Department of
Chemical Engineering, Houston, Texas, July 1971.

12. Provence, T. K., Jr., Wiener, L. D.,and Walton, D.
K., “Liquid Densities of High-Ethane Raw Make Süeams,”
Technical Publication TP-2, Natural Gas Processors Association, Tulsa, Oklahoma, February 1972.
13. Reamer, H.H., Sage, B. H., andLacey, W. N., “Phase
Equilibria in Hydrocarbon Systems: Volumetric Behavior
of Propane,” Ind. Eng. Chem., 1942, Vol. 41,No. 3, p.

482.
14. Sage, B. H., et ai., “Phase Equilibria in Hydrocarbon
Systems: V. Pressure-Volume-TemperatureRelations and
Thermal Properties of Propane,” tnd. & Engr. Chem., November 1934,Vol. 26, No. 11, pp. 1218-1224.
15. Sage, B. H., et al., “Phase Equilibria in Hydrocarbon
Systems: XIX. Thermodynamic Properties of nButane,”
Ind. & Engr. Chem., October 1937, Vol. 29, No. 10,pp.

1188-1194.
16. Sage, B. H., and Lacey, W. N., “Phase Equilibrium
in Hydrocarbon Systems: Thermodynamic Properties of Isobutane,” tnd. & Engr. Chem., June 1938,Vol. 30, No. 6,
pp. 673-681.
17. Sage, B. H., and Lacey, W. N., “Phase Equilibria in
Hydrocarbon Systems: Thermodynamic Properties of nPentane,” tnd. & Engr. Chem., June 1942, Vol. 34, No.
6,p ~ 730-736.
.
18. Straty, G. C.,and Tsumura, R., “PVT and Vapor
Pressure Measurements on Ethane in the Critical Region,”
J . Chem. Phys., 1974, Vol. 60,No. 8,p. 3109.
19. Teichmann, J. , “Pressure-Density-Temperature
Measurements of Liquid Propane and Benzene,” Ph.D. dissertation, Ruhr University, Bochum, West Gemany, 1978.
20. Thomas, R. H. P., and Harrison, R. H., “ h s s u r e ,
Volume, Temperature Relations of Propane,” J . Chem.

Eng. Data, in press.
21. Tomlinson, J. R., “Liquid Densities of Ethane, Propane, and Ethane-Propane Mixtures,” Technical Publication TP-1, Natural Gas Processors Association, Tulsa,
Oklahoma, Febniary 1971.


S T D . A P I / P E T R O M P M S l L * Z * Z - E N G L L 7 8 b m 0732270 0 5 b 2 2 7 5 3 T 2 m

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