API MPMS 11.2.1 Compresibility Factors

Manual of Petroleum Measurement Standards Chapter 11.2.1-Compressibility Factors

for Hydrocarbons: 0-90°API Gravity Range

FIRST EDITION, AUGUST 1984

American Petroleum Institute 1220 L Street, Northwest Washington, D.C. 20005 rT,

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* MPMS LL.2.2-84 0732290 0055935 5 r

Manual of Petroleum Measurement Standards Chapter 11.2.1-Compressibility Factors

for Hydrocarbons: O-90°API Gravity Range

Measurement Coordination Department

FIRST EDITION, AUGUST 1984

American Petroleum Institute


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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 conflïct; 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 dnd reliability of the data presented.

Copyright O 1984 American Petroleum Institute


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MPMS LL.2.L-A4 0732290 0055937 7 r

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 MPMS 11.2.1M.

The table presented in this volume is also available from API as a magnetic tape, along with a manual containing the text information in this publication.

Suggested revisions are invited and should be submitted to the director, Measure- ment Coordination Department, American Petroleum Institute, 1220 L Street, N.W., Washington, D.C. 20005.

iii


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MEMBERS OF THE COMMllTEE ON STATIC PETROLEUM MEASUREMENT WORKING GROUP ON COMPRESSIBILITY

F. P. Gielzecki (Retired) Imperial Oil, Ltd.

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

R. A. Griffith (Chairman) J. Polowek Getty Trading and Transportation Company Interprovincial Pipe Line Ltd.

J. A. Hamshar Cities Service Oil and Gas Corporation

G. W. Singletary Texas Eastern Transmission Company

K. T. Liu, Ph.D. G. W. Swinney (Retired) Gulf Research and Development Company Phillips Petroleum Company


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CONTENTS

CHAPTER 11.2.1-COMPRESSIBILITY FACTORS FOR HYDROCARBONS: O-90"API GRAVITY RANGE

Page

11.2.1.1 Scope ...................................................... 1 11.2.1.2 History and Development. .................................... 1 11.2.1.3 Data Base and Limits of the Standard. ......................... 1 11.2.1.4 Example Use of the Standard ................................. 1 11.2.1.5 Mathematical Model for the Standard .......................... 3

11.2.1.5.1 Basic Model and Uncertaintyhalysis ...................... 3 11.2.1.5.2 Calculation Procedure .................................... 4

11.2.1.6 References. ................................................. 4 Table of Compressibility Factors €or Hydrocarbons

in the O-9O"API Gravity Range Related to A P I Gravity (60°F) and Metering Temperature (Degrees Fahrenheit). .................................. 5

1-Data Base and Experimental Conditions for Chapter 11.2.1. ......... 2 2-Volumetric Uncertainty Analysis for Chapter 11.2.1. ................ 3

Text Tables

Figure l-Comparison of Data Base and Extrapolated

Regions for Chapter 11.2.1 ...................................... 2

V


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Chapter 1 I-Physical Properties Data

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

11.2.1 Compressibility Factors for Hydrocarbons: 0-90"API Gravity Range

11.2.1.1 SCOPE

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 meter temperature and API gravity (60°F) of metered material. The corresponding metric version is Chapter 11.2.1M.

11.2.1.2 HISTORY AND DEVELOPMENT

The previous compressibility standard (API Standard 1101, Appendix B, Table II) for hydrocarbons in the O-9O"API gravity range was developed in 1945 by Jacobson, et al [l]. It is based on limited data obtained mostly on pure compounds and lubricating oil type materials. Also, Standard 1101 was developed without the aid of a mathematical model.

In 1981, a working group of the Committee on Static Petroleum Measurement was set up to revise the compressibility tables of Standard 1101. This group per- formed an extensive literature search and found only three sources of compressibility information. The resulting data base is broader than that used in the previous standard. Unfortunately, it is not large enough to cover the range of current commercial operations. When new data are available, they will be incorporated into an expanded standard. This standard now replaces the dis- continued Standard 1101, Appendix B, Table II, O-1OO"API gravity portion.

11.2.1.3 DATA BASE AND LIMITS OF THE STANDARD

The actual standard is the printed table that follows this text. The mathematical model and computer steps used to generate this standard should not be considered the standard. They can, however, be used to develop computer subroutines for various languages and ma- chines to duplicate the results in the printed table. Also, a computer tape is available through API, which con-

tains the same information as the printed table. The tape can be used in the development of various computer subroutines.

The data base (see Table 1) for this standard was obtained from Jessup [2], Downer and Gardiner [3], and Downer [4]. It consists of seven crude oils, five gasolines, and seven middle distillate-gas oils. The lubricating oil data from these sources were not included. Modeling results showed that lubricating oils are a dif- ferent population than crude oils and other refined products. Their inclusion increases the compressibility correlation uncertainty by a factor of two. Also, lubricating oils are not normally metered under pressure and do not require the use of this standard.

The limits of the experimental data are 20 to 76"API, 32 to 302"F, and O to 711 pounds per square inch. As a result of a Committee on Static Petroleum Measure- ment (COSM) and Committee on-Petroleum Measure- ment (COPM) survey, the actual limits of the standard are broader: O to 9O"API, - 20 to 20O0F, and O to 1500 pounds per square inch. Hence, certain portions of the standard represent extrapolated results (Figure 1). In these extrapolated portions, the uncertainty analysis discussed in 11.2.1.5 may not be valid.

The increments of this standard are 0.5"F and 0.5"API. Interpolation to smaller increments is not recommended.

11.2.1.4 EXAMPLE USE OF THE STANDARD

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

v, = V,/[1 - F * (P, - P,)] Where:

V, = volume at equilibrium (bubble point) pressure,

V,,, = volume at the meter pressure, P,. P,

As an example, calculate the volume of loo0 barrels (V,) of a 19.9"API (60°F) fuel oil metered under a pressure of 500 pounds per square inch (P,) and 100°F. Assume a P, value of O pounds per square inch. First, the gravity is rounded to the nearest OS'API, in this

1

._ - i . - I-: 4 "


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2 CHAPTER 11"PHysIcAL PR~PERTIES DATA

Table 1-Data Base and Experimental Conditions for Chapter 11.2.1

Sample Name M I Gravity Temperature Pressure Number of and Origin m "F psi Data Points Reference

Crude Oils ADMEG (Zakum) export Barrow Island Libyan (Tobruk) export Iranian Light export Kuwait export

Alaskan (North Slope) Iranian Heavy export

Light catalytic cracked

Cracked Fighting aviation Fighting aviation

Kerosine (odorless) DERV

Gas oil Commercial fuel oil Los Angeles basin gas oil Oklahoma gas oil Midcontinent gas oil

GWlinS

straight m

Kerosine and Light Fuel Oil

Gas Oils and Heavy Fuels Oils

39.89 36.97 36.37 33.65 30.98 30.55 27.24

76.25 61.12 52.74 71.51 72.10

47.61 35.36

38.16 19.90 30.42 29.08 28.66

40.0-170.0 40.0-170.0 122.0-170.0 40.0-170.0 40.0-170.0 40.0-170.0 60.0-170.0

40.0-100.0 40.0-140.0 32.0-149.0 32.0-158.0 32.0-158.0

40.0-170.0 40.0-170.0

40.0-170.0 100.0-140.0 32.0-302.0 32.0-302.0 32.0-302.0

0-508 0-508 0-508 0-508 0-508 0-508 0-508

0-493 0-493 0-711

0-711 0-711

0-493 0-493

0-493 0-493 0-711 0-71 1 0-711

m r---- """""- -1 Extrapolated

Region 180 -

160 -

140 - 120 -

F- 2 100 - n

I- 80-

c 3

al

5

f 60-

U

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40-

20-

0 -

5 5 3 5 5 5 4

3 4 5 5 5

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I I I I I I I I I I I I I I I I I- l I I I . I I

-20 1 I I I I I I I I I O 10 20 3 0 4 0 5 0 6 0 70 80 90

3 3 3 3 3 3 3

4 4 2 2 2

4 4

4 4 2 2 2

API Graviiy At 60°F

Figure l-Comparison of Data Base and Extrapolated Regions for Chapter 11.2.1


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MPMS 11-2-1-84 0732290 0055942 2 B- SECTION 2"VOLUME CORRECTION FACTORS 3

case 20.0"API. From the compressibility table, the F factor is 0.448 divided by 100,000 or 0.00000448. Then,

V, = 1000/(1- 0.00000448 * 500) = 1002 barrels

For additional examples and more details, see Manual of Petroleum Measurement Standards, Chapter 12.2.

11.2.1.5 MATHEMATICAL MODEL FOR THE STANDARD

11.2.1.5.1 Basic Model and Uncertainty Analysis

The basic mathematical model, used to develop this standard, relates the compressibility factor ex- ponentially (EXP) to temperature and the square of molecular volume. That is,

F = EXP (A + B*T + C/RH02 + D*T/RH02)

Where: A, B, C, and D = constants.

T = temperature, in "F. RHO = density, in grams per cubic centi-

meter at 60°F. 1/RHO is propor- tional to molecular volume.

RHO = (141.5 * 0.999012)/(131.5 + "API at 60°F).

Hence, compressibility is the result of the interaction of two molecular volumes and temperature. The above equation is consistent with the development of API Standard 2540 (Manual of Petroleum Measurement Standards, Chapter 11.1) for the thermal expansion of hydrocarbons. The use of higher powers of T and RHO does not yield further significant minimization of compressibility factor uncertainty.

Using the above equation and data base, maximum compressibility factor uncertainty is -I- 6.5 percent at the 95 percent confidence level. Hence at worst, one should expect that the real compressibility factor for a given material could be either 6.5 percent higher or 6.5 percent lower than the value in the standard. This state- ment is only true within the limits of the data base. It may not be true for the extrapolated portions of the standard.

To assess the possible uncertainty in the calculated volume at equilibrium pressure using the above data base and equation, two approaches were taken. First, it was assumed that only the correlation uncertainty in mean compressibility of k 6.5 percent was significant. With this approach, volumetric uncertainty should be in the range of 0.02 to 0.10 percent, depending on operating conditions (Table 2, Basis A). These uncertainties are in agreement with the maximum uncertainty of 0.10 percent recommended by a COSM and COPM survey.

The first volumetric uncertainty analysis assumes that mean compressibility is not a function of pressure. For low pressures, this assumption is adequate. For higher pressures, mean compressibility will decrease with increasing pressure. At what pressure this effect becomes significant for the materials of this standard is not defi- nitely known. However, analysis of the Jessup [2] data indicates that mean compressibility could possibly decrease by about 0.005 percent per pound per square inch with increasing pressure. Incorporating both the compressibility correlation uncertainty and the poten- tial pressure uncertainty yields volumetric uncertainties in the range of 0.03 to 0.21 percent (Table 2, Basis A + B). Hence, the use of this standard with operating pressures greater than the experimental limit of 711 pounds per square inch could double the uncertainty in calculated volume over the uncertainty based on available data.

Table 2-Volumetric Uncertainty Analysis for Chapter 1 1.2.1

Percent Uncertaintv in Volume for Various Pressures. m i Correlation Uncertainty Only Correlation + Pressure Uncertainty

Mean Basis A Basis A + B Compressibility

psi-' 500 loo0 1500 500 loo0 1500 1.0 * lo-' (Note 1) 0.03 0.07 0.10 0.05 0.12 0.21 0.6 * lo-' (Note 2) 0.02 0.04 0.06 0.03 0.08 O. 13

BASIS: A. 6.5 percent correlation uncertainty in mean compressibility prediction.

NOTES: 1. 'Ifpical compressibility value for 65"API gasoline at 100°F or 45"API fuel oil at 200°F. 2. m i c a l compressibility value for 60"API gasoline at 20°F or 35"API crude oil at 100°F.

B. 0.005 percent/psi uncertainty in mean compressibility due to effect of pressure [2].


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4 CHAPTER 11“PHYSICAL PROPERTIES DATA

11.2.1 3.2 Calculation Procedure This procedure is recommended for computers with 6

to 7 floating point digits of precision or greater.

Step 1: Initialize temperature and gravity. T = =.X “F: - 20.0 5 T 5 200.0, rounded to

API=XX.X: 0.01~API~90.0, rounded to the

X is either a temperature or gravity value. TX = INT(X): Le., truncation. DIFF=X- TX. If DIFF 2 O then SIGN = 1.0 else SIGN = - 1.0. DIFF = ABS(DIFF): i.e., absolute value. If DIFF < 0.25 then X = TX.

r If DIFF 2 0.75 then X = TX + l.O*SIGN. .. Else X = TX + OS*SIGN

Step 2: Calculate the density in grams per cubic centi- meter and the square of density.

RHO = 141.36/(API + 131.50) = X.xXXXX, roun-

RHO = INT(RHO*100000.0 + 0.5)*0.00001. RHOSQR = RHO*RHO = X.xXXXX, rounded to

RHOSQR = INT(RHOSQR*100000.0 + 0.5)

nearest 0.5”F.

nearest 0.5 degree by

ded to the nearest 0.00001 by

the nearest 0.00001 by

*0.00001.

Step 3: Calculate the compressibility factor. F = EXP ( - 1.99470 + 0.00013427* T

+ 0.79392lRHOSQR + 0.0023260 *T/RHOSQR)

by rounding each term to the nearest 0.00001 as

If T < O then SIGN = - 1.0 else SIGN = 1.0. TERM1 = - 1.99470. TERM2 = INT(13.427*T + 0.5*SIGN)*0.00001.

follows:

TERM3 = INT(79392.ORHOSQR + 0.5)*0.00001. TERM4 = INT(232.60*T/RHOSQR + OS*SIGN)

F = EXP(TERM1 + TERM2 + TERM3 + TERM4)

Then round F to the nearest 0.001 by F = INT(F*1000.0 + 0.5)*0.001= X.XXX. F is now the table value.

*0.oO001.

= x.xxxx.

The INT intrinsic function returns an integer by trun- cating all digits to the right of the decimal point. The exponential intrinsic EXP must return a result accurate to the nearest 0,0001.

11.2.1.6 REFERENCES

1. Jacobson, E. W., Ambrosius, E. E, Dashiell, J, W., and Crawford, C. L., “Second Progress Report on Study of Existing Data on Compressibility of Liquid Hydrocarbons,” Report of the Central Committee on Pipe-Line Transportation, Vol. 2 (IV), p. 39-45, Amer- ican Petroleum Institute, Washington, D.C., 1945. 2. Jessup, R. S. , “Compressibility and Thermal Expan- sion of Petroleum Oils in the Range O” to 3OO0C,” Bu- reau of Standards Journal of Research, Vol. S , July to December 1930, p. 985-1039, National Bureau of Stan- dards, Washington, D.C. 3. Downer, L., and Gardiner, K. E. S., “Bulk Oil Measurement Compressibility Measurements on Crude Oils Deviations from API Standard 1101,” BP Re- search Centre Report No. 20 587M (8 pages), October 28, 1970. 4. Downer, L. “Bulk Oil Measurement Compressi- bility Data on Crude Oils and Petroleum Products Viewed as a Basis for Revised International Tables (API Standard 1101 Tables),” BP Research Centre Re- port No. 20 639 (21 pages), January 17, 1972.


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Documents

API MPMS 11.2.1 Compresibility Factors