ASTM D3588: Standard Practice for Calculating Heat Value, Compressibility Factor, and Relative Density (Specific Gravity) of Gaseous Fuels

11 Pages·2.5 MB·English

by  American Society for Testing and Materials

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HEED THIS NOTICE: Criminal penalties may apply for noncompliance.
e
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Official Incorporator:
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ASTM Logo
Removed
Designation: D 3588 - 98
Standard Practice for
Calculating Heat Value, Compressibility Factor, and Relative
Density of Gaseous Fuels 1
This standard is issued under the fixed designation D 3588; the nwnber immediately following the designation indicates the year of
original adoption or, in the case of revision, the year of last revision. A nwnber in parentheses indicates the year of last reapproval. A
superscript epsilon (E) indicates an editorial change since the last revision or reapproval.
1. Scope D 2650 Test Method for Chemical Composition of Gases by
Mass Spectrometry6
1.1 This practice covers procedures for calculating heating
2.2 GPA Standards:
value, relative density, and compressibility factor at base
GPA 2145 Physical Constants for the Paraffin Hydrocarbons
conditions (14.696 psia and 60°F (15.6°C») for natural gas
mixtures from compositional analysis.2 It applies to all com and Other Components in Natural Gas7
GPA Standard 2166 Methods of Obtaining Natural Gas
mon types of utility gaseous fuels, for example, dry natural gas,
reformed gas, oil gas (both high and low Btu), propane-air, Samples for Analysis by Gas Chromatography7
GPA 2172 Calculation of Gross Heating Value, Relative
carbureted water gas, coke oven gas, and retort coal gas, for
Density, and Compressibility Factor for Natural Gas
which suitable methods of analysis as described in Section 6
are available. Calculation procedures for other base conditions Mixtures from Compositional Analysis7,g
GPA Standard 2261 Method of Analysis for Natural Gas and
are given.
1.2 The values stated in inch-pound units are to be regarded Similar Gaseous Mixtures by Gas Chromatography7
GPA Technical Publication TP-17 Table of Physical Prop
as the standard. The SI units given in parentheses are for
erties of Hydrocarbons for Extended Analysis of Natural
information only.
1.3 This standard does not purport to address all of the Gases7
GPSA Data Book, Fig. 23-2, Physical Constants 7
safety concerns, if any, associated with its lise. It is the
2.3 TRC Document:
responsibility of the user of this standard to establish appro
TRC Thermodynamic Tables-Hydrocarbons9
priate safety and health practices and determine the applica
bility of regulatory limitations prior to use. 2.4 ANSI Standard:
ANSI Z 132.1-1969: Base Conditions of Pressure and
2. Referenced Documents Temperature for the Volumetric Measurement of Natural
GaslO,ll
2.1 ASTM Standards:
D 1717 Methods for Analysis of Commercial Butane
3. Terminology
Butene Mixtures and Isobutylene by Gas Chromatogra
phy3 3.1 Definitions:
3.1.1 British thermal unit-the defined International Tables
D 1945 Test Method for Analysis of Natural Gas by Gas
British thermal unit (Btu).
Chromatography4
3.1.1.1 Discussion-The defining relationships are:
D 1946 Practice for Analysis of Reformed Gas by Gas
1 Btuolb-I = 2.326 J og-I (exact)
Chromatography4
D 2163 Test Method for Analysis of Liquefied Petroleum 1 lb = 453.592 37 g (exact)
(LP) Gases and Propane Concentrates by Gas Chromatog By these relationships, 1 Btu = 1 055.055 85262 J (exact). For
raphy5 most purposes, the value (rounded) 1 Btu = 1055.056 J is
adequate.
3.1.2 compressibility factor (z)-the ratio of the actual
1 This practice is under the jwisdiction of ASTM Committee D-3 on Gaseous
Fuels and is the direct responsibility of Subcommittee D03.03 on Determination of
Heating Value and Relative Density of Gaseous Fuels. 6 Annual Book of ASTM Standards, Vol 05.02.
Current edition approved May 10, 1998. Published April 1999. Originally 7 Available from Gas Processors Association, 6526 E. 60th, Tulsa, OK 74145.
published as D 3588 - 98. B A program in either BASIC or FORTRAN suitable for running on computers,
2 A more rigorous calculation of Z(T,P) at both base conditions and higher available from the Gas Processors Association, has been found satisfactory for this
pressures can be made using the calculation procedures in "Compressibility :md purpose.
Super Compressibility for Natural Gas and Other Hydrocarbon Gases," American 9 Available from Thermodynamics Research Center, The Texas A&M University,
Gas Association Transmission Measurement Committee Report 8, AGA Cat. No. College Station, TX 77843-3111.
XQ1285, 1985, AGA, 1515 Wilson Blvd., Arlington, VA 22209. 10 Available from the American National Standards Institute, II W. 42nd St.,
3 Discontinued, see 1983 Annual Book of ASTM Standards, Vol 05.01. 13th Floor, New York, NY 10036.
4 Annual Book of ASTM Standards, Vol 05.05. 11 Supporting data are available from ASTM Headquarters. Request RR:D03-
S Annual Book of ASTM Standards, Vol 05.01. 1007.
76
ASTM Logo Removed
03588
volume of a given mass of gas at a specified temperature and 3.2.1.21 Qid-ideal energy per unit time released as heat
pressure to its volume calculated from the ideal gas law under upon"combustion "
the same conditions. 3.2.1.22 R-gas constant, 10.7316 pSia.fe/(lb mol oR) in this
3.1.3 gross heating value-the amount of energy transferred practice (based upon R = 8.31448 J/(mol-K))
as heat from the complete, ideal combustion of the gas with air, 3.2.1.23 (sat)-denotes saturation value
at standard temperature, in which all the water formed by the 3.2.1.24 T-absolute temperature, OR = 0p+ 459.67 or K =
reaction condenses to liquid. The values for the pure gases °C + 273.15
appear in GPA Standard 2145, which is revised annually. If the 3.2.1.25 (T, P}-value dependent upon temperature and
gross heating value has a volumetric rather than a mass or pressure
molar basis, a base pressure must also be specified. 3.2.1.26 V-gas volumetric flow rate
3.1.4 net heating value-,-the amount of energy transferred 3.2.1.27 x-mole fraction .
as heat from the total, ideal combustion of the gas at standard 3.2.1.28 Z-gas compressibility factor repeatability of prop-
temperature in which all the water formed by the reaction erty
remains in the vapor state. Condensation of any "spectator" 3.2.1.29 S-repeatability of property
water does not contribute to the net heating value. If the net 3.2.1.30 p-density in mass per unit volume
LJ=l
heating value has a volumetric rather than a mass or molar 3.2.1.31 -:-property summed for Components 1
a
basis, base pressure must also be specified. through n, where n represents the total number of components
3.1.5 relative density-the ratio of the density of the gas in the mixture
eous fuel, under observed conditions of temperature and 3.2.2 Superscripts:
pressure, to the density of dry air (of normal carbon dioxide 3.2.2.1 id-ideal gas value,
content) at the same temperature and pressure. 3.2.2.2.l-liquid
3.1.6 standard cubic foot of gas-the amount of gas that 3.2.2.3 a-value at saturation (vapor pressure)
occupies 1 fe (0.028 m3) at a temperature of 60°F (15.6°C) 3.2.2.4 '-reproducibility
under a given base pressure and either saturated with water 3.2.3 Subscripts:
vapor (wet) or free of water vapor (dry) as specified (see ANSI 3.2.3.1 a-value for air
Z 132.1.). In this practice, calculations have been made at 3.2.3.2 a-relative number of atoms of carbon in Eq 1
14.696 psia and 60°F (15.6°C), because the yearly update of 3.2.3.3 b-relative number of atoms of hydrogen in Eq 1
GPA 2145 by the Thermodynamics Research Center, on which 3.2.3.4 c-relative nurriber of atoms of sulfur in Eq 1
these calculations are based, are given for this base pressure. 3.2.3.5 j-property for component j . "
Conversions to other base conditions should be made at the end 3.2.3.6 ii-nan-ideal gas property for component i
of the calculation to reduce roundoff errors. 3.2.3.7 ij-non-ideal gas property for mixture of i and j
3.1.7 standard temperature (USA}-600P (15.6°C). 3.2.3.8 jj-non-ideal gas property for component j
3.2 Symbols: 3.2.3.9 w-valuefor water
3.2.1 Nomenclature: 3.2.3.10 I-property for Component 1
3.2.3.11 2-property for Component 2
3.2.1.1 B-second virial coefficient for gas mixture
3.2.1.2 ~ -summation factor for calculating real gas 4. Summary of Practice
correction (alternate method)
4.1 The ideal gas heating value 'and ideal gas relative
3.2.1.3 (cor)-corrected for water content
density at base conditions (14.696 psia and 600P (5.6°C)) are
3.2.1.4 (dry)-value on water-free ba.sis
calculated from the molar composition and the respective ideal
3.2.1.5 d-density for gas relative to the density of air.
gas values for th~ components; these ~alues are then adjusted
3.2.1,6 id-ideal relative density or relative molar mass,
by means of a calculated compressibility factor.
that is, molar mass of gas relative to molar mass of air .
3.2.1.7 Gid-molar mass ratio S. Significance and Use
3.2.1.8 H~~ -gross heating value per .unit mass 5.1 The heating value is a measure, of the suitability of a
3.2.1.9 H~d -gross heating value per unit volume pure gas or a gas mixture for use as a fuel; it indicates the
3.2.1.10 H~d ~gross heating value per unit IT).ole . amount of energy that can be obtained as heat by burning ~ unit
of gas. For use as heating agents, the relative merits of gases
3.2.1.P h~ -net heating value per unit mass
from different sources and having different compositions can
3.2.1.12 h~d -net heating value per unit volume·
be compared readily on the basis of their heating vall).es,
3.2.1.13 h~d -net heating value per unit mole
Therefore, the heating value is used as a parameter for
3.2.1.14 a, b, c-in Eq 1,integers required to balance the .
determining the price of gas in custody transfer. It is also an
equation: C, carbon; H, hydrogen; S, sulfur; 0, oxygen
essential factor in calculating the efficiencies of energy cone'
3.2.1.15 (id}~ideal gas state version devices such as gas-fired turbines. The heating v,alues
3.2.1.16 (l}-iiquid phase
of a gas depend not only upon the terriperature and pressure, ,
3.2.1.17 M-molar mass
but also upon the degree of saturation with water vapor.
3.2.1.18 m-mass flow rate However, some calorimetric methods for measuring heating
3.2.1.19 n-number of components values are based upon the gas being saturated with water at the
3.2.1.20 P-pressure in absolute units (psia) specified conditions.
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5.2 The relative density (specific gravity) of a gas quantifies 7. Calculation-Ideal Gas Values; Ideal Heating Value
the density of the gas as compared with that of air under the
7.1 An ideal combustion reaction in general terms fat fuel
same conditions;
and air in the ideal gas state is:
6. Methods of Analysis' CaHbsc (id) + (a + b/4 + c)O;(id) = aC0(id) + (h/2)H 0 (id or I)
2 2
6.1 Determine the molar composition of the gas in accor + cS0(id) (I)
2
dance with any ASTM or GPA method that yields the complete
where id denotes the ideal gas state and I denotes liquid
composition, exclu,siv.e of water, but including all other com
phase. The ideal net heating value results when all the water
ponents present in amounts of 0.1 % or more, in terms of
remains in the ideal gas state. The ideal gross heating value
components or groups of components listed in Table L At l~ast results when all the water fonned by the reaction condenses to
98 % of the sample must be reported as individual components
liquid: For water, the reduction frorriH 0(id) to H 0(l)is H~
(that is, not more than a total of 2 % reported as groups of 2 2
- H~ , the ideal enthalpy of vaporization, which is somewhat
components such as butanes, pentanes, hexanes, butenes, and
so forth). Any group used must be one of those listed in Table larger than the enthalpy of vaporization H~ - F1~' .
1 for which average val~es appear. The,following tyst methods 7.1.1 Because the gross hea:tirt~ '~alue re~ults from an ideal
are applicable to this' pr.act~ce when appropriate for the sample combustion r~aqion, ideal ,gas relationships apply. T'he jdeal
,
undertest: Test Methods D 1717, D '1945; D 2163,and D 2650. gross heating vah~e per unit mass for a mIxture, H;~ is:
TABLE 1 Properties of Natural Gas Components at 60°F and 14.696 psiaA
Ideal Gross Heating ValueD Ideal Net Heating 'value Summation
Compound Formula MIbo·llabrm Moars'Bs, MRoaltaior , MGaldsCs, kJ·H mnd ,o r' BtuH·ilmdb 'm -1 BtHu.vd f,'t "3 kJ·H m%, or' BtuH·mldb 'm -' Btuh~· iI t" Fapcstoiar,- ' bl,
Hydrogen H2 2.0159 0.06960 286.20 61022 324.2 241.79 51566 273.93 0
Helium He 4.0026 0.13820 0 0 0 0 0 0 0
Water H2O 18.0153 0.62202 44.409 1059.8 50.312 0 0 0 0.0623
Carbon monoxide CO 28.010 0.96711 282.9 4342 320.5 282.9 4342 320.5 0.0053
Ntlrogen N2 28.0134 0.96723 0 0 0 0 0 0 0.0044
Oxygen O2 31.9988 1.1048 0 0 0 0 0 0 0.0073
Hydroge,n sulfide H2S 34.08 1.1767 562.4 7094.2 637.1 517.99 6534 586.8 0.0253
Argon Ar 39,.948 1.3793 0 0 0 0 0 0 0.0071
Carbon dioxide CO2 44.010 1.5196 0 0 0 0 0 0 0:0197
Air E 28.9625 1.0000 0 0 0 0 0 0 0.0050
Methane CH. 16.043 0.55392 891.63 23891 1010.0 802.71 21511 909.4 0.0116
Ethane C2He 30.070 1.0382 1562.06 22333 1769.7 1428.83 20429 1618.7 0.0239
Propane C3Ha 44.097 1.5226 2220.99 21653 2516.1 2043.3 19922 2314.9 0.0344
~Butane C.H1Q 58.123 2.0068 2870.45 21232 3251.9 2648.4 19590 300P.4 0.0458
n-Butane C.H1Q 58.123 2.0068 2879.63 21300 3262.3 2657.6 19658 3010.8 0.0478
~Pentane CSH'2 72.150 . 2.4912 3531.5 21043 4000.9 3265.0 19456 3699.0 0.0581
n-Pentane CSH'2 72.150 2.4912 3535.8 21085 4008.9 3269.3 19481 3703.9 0.0631
n-Hexane CaH,• 86.177 2.9755 4198.1 20943 4755.9 3887.2 19393 4403.9 0.0802
n-Heptane 97H'6 100.204 3.4598 4857.2 20839 5502.5 4501.9 19315 5100.3 0.0944
n-Odtane CSH,S 114:231 3.9441 5515.9 20759 6248.9 5116.2 19256 5796.2 0.1137
n-Nonane C9H20 ' 128.258 4.4284 6175.9 20701 6996.5 5731.8 19213 6493.6 0.1331
n-Decane C1OH22 142.285 4.9127 6834.9 20651 7742.9 6346.4 19176 7189.9 0.1538
Neopentane CSH'2 72.015 2.4912' 3517.27 20958 3985 ~250.8 19371 3683
2-Methylpentane CeH,• 86.177 2.9755 4190.43 20905 4747 3879.6 "19355 4395 0.080
3-Methylpentane CeH,• 86.177 2.9755 4193.03 20918 4750 3882:2 19367 4398 0.080
2,2-Dimethylbutane CeH,• 86.177 2:9755: 4180.63 20856 4736 3869.8 19306 4384 0.080
2,3-Dimethylbutane CeH,• 86.177 2.9755 4188.41 20895 4745 3877.5 19344 4393 0.080
Cyclopropane C3He 42.081 1.4529 2092.78 21381 2371 1959:6: 20020 2220
Cyclobutane C.Hs 56.108 1.9373 2747.08 21049 2747 2569.4 19688 2911
Cycl9pentane CSH'0 70.134 2-4215 3322.04 20364 3764 3100.0 19003 3512
Cyclohexane CaH'2 84:161 2.9059 3955.84 20208 4482 3689.4 18847 4180
Ethyne (acetylene) C2H2 26.038 0.8990 1301.32 21487 1474 1256.9 20753 1424 0.021
Ethene (ethylene) C2H. 28.054 0.9686 1412.06 21640 1600 1323.2 20278 1499 0.020
Propene (propylene) C3Ha 42.081 1.4529 2059.35 21039 2333 1926.1 19678 2182 0.033
Benzene CaHa 78.114 2.6971 3202.74 18177 3742 3169.5 17444 3591 0.069
Butanes (ave) C.H'0 58.123 2.0068 2875 21266 3257 2653 19623 3006 0.046
Pentanes (ave) CSH.12 72.150 2.49~ 2 3534 21056 4003 3267 19469 3702 0.062
Hexanes (ave) . CeH,• 86.177 2.9755 4190 20904 4747 3879 19353 4395 0.080
Butenes(ave) C.Hs 56.108 1.9372 2716 20811 3077 2538 19450 2876 0.046
Pentenes (ayet: ,CSH1O 70.134 2.4215 3375 20691 3824 3153 19328 3572 '., 0.060
AThis table is consistent with j3PA 2145-89, but ij is necessary to use, the val.ues from the most recent edition of GPA 2145 for custody transfer calculations.
B1984 Atomic W:eights: C= 14,011, H = 1.00794, 0 =: 15.~994, N = 14.0067, S = 32.06.
cMolai mass ratio is the ratio o'flhe m'olar mass of the gas to that of air.
DSased upon ideal reaction;] the entry for water represents the iotal enthalpy of vaporization.
EComposilion from: F. E. Jones, J. Res. Nat. Bur. Stand., Vol. 83,419, 1978.
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D 3588
H'm 'd = j'L=I"I1J x,j'MA.,.rT.r-..ll'!' dI, J, I 1'L'=I"IJ1' x',tM'~J,, (2) Bijw ish ethree Bsejjc iosn tdh ec rsoescso vnidr ivailr icaole fcfoiecfif~incti efnotr f Coro mCopmonpeonntes nit a j nadnjd.
The second virial coefficients are flIDctibns of temperature. Eq
where: Xj is the mole fraction of Componentj;Mj is the iliohir
mass of Component j from Table 1, and n is the total number 9 can be used with Eq 10 for calculation of the compressibility
factor for the various pressure bases, but it is not accurate at
of components.
pressures greater than two atmospheres. Special treatmeI)"t is
7.1.2 H;~J is the pure component, ideal gross heating value
not required for H2 and He at mole fractions up to 0.01.
per unit mass for Component j (at 60°F (15.6°C) in Table 1).
Calculations can be made with B = 0 for hydrogen and
Values of H~~ are independent of pressure, but, they vary with jj
helium.
temperafure. '
7.5.2 Eq 9 and Eq 10 for calculation of Z(T,P) for a gas
7.2 Ideal Gas Density
mixture are rigorous but require considerably calculations and
7.2.1 The ideal gas density, pid, is:,
information that is not always available. An alternative, ap
±
, pid = (PIR1) xM, = MPIRT '(3) , proximate expressio~ for Z(T,P) that is, more convenient for
j=! ,") hand calculations is:
where; .M is the molar mass of therpixture,i::
(11)
II
M= ~xM, (4)
j=! , ..) where f3jj = BjJRT and~ is the summation factor for
P is the base pressure in absolute units (psia), R is the gas Componentj. ValuesofVJ3jj ai"60°F (l5.6C>C) appear in Table
constant, 10.7316 pSiaJe/(lb mol·oR) in this practice, based 2. The method based upon Eq lLhas been adopted for this
upon R = 8.31448 J/(mol·K), T is the base temperature in practice.
absolute units (OR = of + 459.67). Values of the ideal gas 7.6 Real Gas Density:
density at 60°F (15.6°C) and 14.696 psia are in GPA Standard 7.6.1 The real gas densityp' at a specific temperature and
2145. pressure is: , "
7.3 Ideal Relative Density: 'p = pidlz' '. (12)
7.3.1 The ideal relative density i d is:
where: pid and Z are evaluated' ~t'the same te~Penit1ire and
i d = jI~I xA = 2: x#/Ma = MIMa (5) pressure. _ j ~' J', .,
7.7 Real Relative Density:
where: Ma is the molar mass of air. The ideal relative density
7.7.1 The realre!ativedensity, di~:, i'. I .'
is the molar mass ratio.
, 4:1 = p/Pa '= MZa'lM.2 ' ":.'''-:. ,'; (13)'
7.4 Gross Heating' Value per,unit Volume:'
7.4.1 Multiplication of the' gross heating value pet unit mass 7.8 Real H eating Value-The real h" e"a. ting va' lue i.s : 'p r~o : t' ;g. iven
by the ideal gas density provides the gross heatillg value per by division of the ideal heating value by the compressibility
unit volUme; H~d: factor. Real gas heating. vill ues differ from the iaeal gas values
by less than one partin 104 at 14.696psia, which is of the' order
,j ""n
Hid = pid Hid = ~ Xfiid, (6) of the accuracy of the'heating vaJ.ues;~;· .:., .
v, m 1'=1 v.;. 7.9 Gross Heating Value oj Water Wet Gas:
',Ii~~'iS th~ pure component gross h~ad~g value per unit 7.9.1 If the gas cQntains water as a cqmponent but the
vol ume for COIJ.1ponent j at' specified tempei:atu~e' and pressure compositional analysis is ,on a dry basis, it is necessary to
(60°F (l5.6°C) ,and 14.696.psia in.Table 1, ideal gas values). adjust the mole fractions to refleci: the presence of water. The
,.7.4.2 Conversion of valuesin Table .1 to diff((rent pressUr~ corrected mole fractions are:: "
bases results from multiplying by the' pressure ratio,:, '
4cor) = x/I -xw) (14)
, H~ (P) = H~d (P ~ ~4.696) X PII4.696 ,. (7) ; ,The mole fraction of watercari range from zero up to the
\7.5
Real 'Gas Values~ompressi~ility Factor; saturated :value. ;rpe ,~aturated valu,e for xlV i~,assumi!1g
;, 7.5; 1 The compressibility factor· is: Raoult's Law:
1 i Z (T,p)=.'pid Ip = (MPIR1)lp '(8) (15)
), where p is the real gas density in rnass per unit volume. At where: R~ is:,th~ vapor press~of wat~r (0.256 36 psia at
conditions near ambient;, the tmncated virial equation of state e?0°F (15;6°C)):' , .
satisfactorily represents the \7ohimetric behavior of'mitural gas:' 7.9.2 Technically, water has a gross heating value,the ide,al
, ,,' Z (~,P)T 1, + SPIRT' '. " ' , (9.) enthalpy of condensation. If only the water that is fanned
during the combustion condenses; then the heat released upon
. whereB is the second virial coefficient for tI1~ gas imxture.
combustion of a wetgaswith'dry air becomes:
The second virial cm;fficient for a mixture is:' ,
;
(16)
o
':Forwater7satnratedgas, Xw at 60 P(15.6° C) is 0;256 3f>IPb
11 II: -,. wherePb: is the baSe pressure. Eq16 is'adequate for custody
= ~~;,xJ3" (1.0)
;;::;11'=1 I I) transfer applications as 'a matter ofdefini.tion'. However, this'
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TABLE 2 Example Calculations of Gas Properties at 60°F and 14.696 psia (Gas Analysis on Dry Basis)A
NOTE I-Division of Hvid by Z does not'give a real gas heating value but rather an ideal gas heating value per real cubic feet. Any digits carried beyond
1 part in 1000 are not significant but only allieviate roundoff error. Although CO2 hflS a carbon/atom, its ex = 0 because it is not part of the ~uel fOJ.;nula
C",Hf3S' Y ' . '.
Compound x, 01, 13, 'Y,' Hvf1 'G~ b, xf'i., x,l3, Xtii x,HJ/ . x, G7 x,b, .
Methane 0.8302 1 4 0 1010.0 0.55392 0.0116 0.8302 3.3208 0 838.5 0.4599 0.00963
~thane ·0.0745 2 6 0 1769.7 1.03820 0.0239 0.1490 0.4470 0 131.8 0.0773 0.001 78
Propane 0.0439 3 8. 0 2516.1 1.52260 0.0344 0.1317 0.3512 0 110.5 0.0668 iO.001 51
i-Sutane 0.0083 4 10 0 3251.9 2.00680 0. . 0458 0.0332 0.0830 0 27.0 0.0167 0.00038
n-Butane 0.0108 4 10 0 3262.3 2.00680 0.0478 0.0432 0.1080 0 35.2 0.0217 0.00052
i-Pentane 0.0031 5 12 0 4000,9 2.49120 0.0581 0.0155 0.0372 0 12.4 0.0077 0.00018
n-Pentane 0.0025 5 12 0 4008.9 2.49120 0.0631 0.0125 0.03 0 10.0 0.0062 0.00016
Hexane 0.0030 6 14 0 4755.9 2.97550 0.0802 0.0180 0.0420 0 14,3 0.Op89 0.00024
Helium 0.0003 0 0 0 0 0.13820 a 0 0 0 0 0.0000 0.00000
Nitrogen 0.0032 0 0 0 0 0.96723 0.0044 0 0 0 0 0.0031 0.00001
Carbon dioxide 0.0202 0 0 0 0 1.51960 0.0197 0 0 0 0 0.0307 0.00040
Summation 1.0000 1.2333 4.4192 0 1179.7 0.6991 0.01481
AXw = (0.25636)/14.696 = 0.0174
G'd (dry gas) = 0.6991
Z (dry gas) = 1 - [0.014 81f(14.696) = 0.9968
=
Z (dry air) 1 - [0.0050]2(14.696) = 0.9996
G (dry gas, dry air) = 0.6991 (0.9996)/0.9968 = 0.7011
G (dry gas, sat air) = 0.6991(0.9995)/0.9968 = 0.7010
HVd (dry gas, dry air) = 1179.7 Btu·lt""
HVd (sat gas, dry air) = 1179.7(0.9826) = 1159.1 Btu·lr3
1-Xw = 0.9826
G'd (sat gas) = 0.6991(0.9826) + 0.0174(0.622 02) = 0.6978
Z (sat gas) = 1 - [0.9826(0.01481) + 0.0174(0.0623)]2(14.696) = 0.9964
Z (sat air) = 1 - [0.9826(0.0050) + 0.0174(O.0623)f(14.696) = 0.9995
G (sat gas, dry air) = 0.6978(0.9996)/0.9964 = 0.7001
G (sat gas, sat air) = 0.6978(0.9995)/0.9964 = 0.7000
{HVdlZ}(dry gas, dry air) = 1179.7/0.9968 = 1183.5 Btu·n-3
{HVdIZ} (sat gas, dry air) = 1159.1/(0.9964) = 1163.3 Btu·n-3
equation does not accurately'describe the effect of water upon 8. Precision
the heating value. Appendix Xl contains a rigorous examina
8.1 The properties reported in this practice derive from
tion of,the effect of water.
experimental enthalpy of combustion measurements which, in
7.10 Calculation of the Ideal Energy Released as Heat:
general, are accurate to I part in 1000. The extra digits that
7.10.1 When multiplied by the gas flow rate, the ideal gross
heating value provides the ideal energy released as heat upon appear in the accompanying tables alleviate prob~ems associ
ated with roundoff errors and internal consistency, but they are
combustion, Qid ,an ideal gas property:
not significant.
(17) 8.2 The values of properties in this practice are those that
Fig.
where mis the mass flow rate. For an ideal gas, the mass flow appear in GPA Standard. 21'72-5>7, 23-2 of the GPSA
rate is related to the volumetric flow rate, yid , by: Engineering Data Book, GPA TP-17, and the TRC Thermody
namic Tables-Hydrocarbons. GPA Standard 2145 is updated
(18)
annually and the varues in that standard should be used in all
and calculations.
(19)
NOTE 2-Three sources of error must be considered: errors in heating
7.10.2 The ideal gas flow rate is related to the real gas flow values of the components, errors in the calculated compressibility factor,
rate by: and errors in the composition. The uncertainty' (twice the standard
deviation) of the ideal gas heating values for components should be
y;d = VIZ (20) 0.03 %. Such errors affect the bias and the agreement between calculated
and mel\sured heating values, but they do not affect the precision. Erro;r·in
where V is the real gas volumetric flow rate and Z(T,P) is the
the calculated cpmpressibility factor varies with the composition of the
real gas compressibility factor at the same T and P. Hence,
gas, but fpr natural gas, this error should be less than 0.03 % and
combining Eq 19 and Eq 20 gives: negligible ~ompal'ed to enors adslng fro~ uncertainty in composition. In
this practice, the errors in the heating valUes of the components and the
Qid '" H~ VIZ (T,P) (21)
calcul~ted compressipility factor, ,2'1 are neglected. The precision of the
NOTE I-The ideal etiergy released per unit time' as heat upon com method is related to the repeatability and reproducibility of the analysis.
bustion, Qid ,can be calculated using the mass flow rate (Eq 17), the ideal An example appears in Table 3. . ,
gas flow rate (Eq I9),'or'the reill gas flow rate' (Eq 21), but is always an NOTE 3-It is essential to include all components in the gas sample that
ideal gas property. Division of H~d by the gas compressibility factor Z(T;P) appear with mole fractions greater than or equal to 0.001 in the analysis.
does not produce a real gas heating value but only allows calculation, of Some routine analyses do not detelmine compounds such as I-Ie and H S,
2
Qid \.Ising the real gas flow rate rather than the,ideal gas flow rate. but these compounds are important to the calculations.
80
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03588
TABLE ~ Example Calculations of Gas Propertiesat60°F and 14.696 psia(Gas Analysis on Wet Basis)A
NOTE I-Division of Hvid by Z does not give a real gas heating value but rather an ideal gas heating value per real cubic feet. Any digits carried beyond
1 part in' lOQO are not significant but only allieviateroundoff error. AlthOl1gh CO has a carbon atom, its ct = 0 because it is not part of'the fuel 'formula
2
CCl.Hf!,S'Y'
Compound x, ell [3, "II Hv'f' GI,fI b, Xfi, x,[3, XN, x, H0d x,G;d Xibi
Methane 0.8157 1 4 0 1010.0 0.55392 0.0116 0.8157 3.2629 0 823.9 0.4518 ' 0.00946
Ethane 0.0732 2' 6 0 1769.7 1.03820 0.0239 0.1464 0.4392 0 129.5 0.0760 0.0.01 75
Propane .0.0431 3 8 0 2516.1 1.52260 0.0344 0.1294 0.3451 0 1.08.5 .0 . .0657 .0.0.0148
i-Butane .0.0.082 4 1.0 .0 3251.9 2.00680 .0.0458 0.0326 0.0816 0 26.5 .0 .. 0164 .0 . .0.0.0 37
n-Butane 0 .. 01.06 4 10 .0 3262.3 2.00680 0.0478 0.0424 0.1.061 0 34.6 .0 . .0213 .0 .. 0.0.0 51
i-Pentane 0 .. 0.03.0 5 12 .0 4000.9 2.49120 0.0581 0.0152 0.0366 0 12.2 .0 .. 0076 O.O()(j 18
n-Pentane 0.0.025 5 12 .0 4008.9 2.49120 0.0631 0.0123 0.0295 0 9.8 .0 . .0061 .0 . .0.0015
Hexane 0.0.029 6 14 .0 4755.9 2.9755.0 0.08.02 0 .. 0177 0.0413 0 14.0 .0 .. 0088 .0 . .0.0024
Helium 0.0.0.03 0 0 .0 0 0.1382.0 .0 0 0 0 0 0 0
Nitrogen 0.0031 0 0 .0 0 0.96723 0.0044 0 0 0 0 0 .. 0.030 .0
Carbon dioxide 0 .. 0198 0 0 .0 .0 1.51'960 0 .. 0197 0 O' 0 0 .0 .. 0302 0.0.0039
Water 0 .. 0174 0 0 0 50.3 0.622.02 0 .. 0623 0 0 0 .0.9 .0 .. 0108 0 . .0.01 09
Summation 1.0.0.0.0 1.2118 4.3421 0 1.16.0.0 .0.6977 0.D1564
AG/~ (sat gas) = .0.6977,
Z (sat gas) = 1 - [0.015 64]2(14.696) = 0.9964
Z (dry air) = 1 - [0 .. 005.0]2(14.696) = 0.9996
G (sat gas, dry air) = 0.6977(.0.9996)/0.9964 = 0.6999
ZH v(dsa.(ts aaitr )g a=s, 1 d ~ry [0ai.r9) 82=6 (101 .6. 005.00) -+ 00..90 1=c7 41(105.90.612 3B)t]u2·f(t1--43. 696) = 0.9995 \""
. G (sat gas, sat air) = 0.6977(0.9995)10.9964 = 0.6999 '
{HvdlZ}(sat ga~, dry air) = 1159.1/(0.9~64) = 1163.3 Btu·ft--3 .
. 8.3 Repeatability: . Component j. TJ.1ediff.erences be~ween he~til).g value$ cal~u­
.8.3.1 If all the components are analyzed and the results are lated from succ,essivepairs of ~alysis performecU»)r t11e spine
normalized, then the repeatability of the heating value SH is: operator using the same Sample of gasanclthe same instrUment
l
~hould exceed 2SH in only: 5.% of the tests whf?J.:l ~llis ,taken
, ;. -H8-'H-'d· = ~(H'12 ) j~=/I ! [(H id -H·)i d -). 8~.JJ 2. • (22) as one standwd dl'e v,.i: atio, ; n~ .!,. '. , , . ~'. '. ..:'' , ,'. - ',:., ".",I .
8.4 Reproducibility~Thereproducibility SH' is Q<,J;~qulated
8.3.2 If the resu1tsof the analysis are made to ,Sllrll to 1.0' by
from Eq 22 andEq 23 usingSx'J' the, .reprodu~ibility;0f thei
calculating the methalle mole fraction as the difference be
method of analysis for Compound j. The ditferencebetween
tween 1.0 and the sum of the ',mOle fractiol1s. of the other
heating values"calculated.from analysis obtained in different,
components, then
laboratories is expected to exceedSH' for only 5 %.of the
8H '1 /I id' 2'" .. :: analyses.
Hid = (Hidh~[Hj 8;j] , (23)
.'. • ,'.J • {
where SX is the repeatability of the method of analysis for ,(. • ;" c. ','
j
! : .
A,PPENDIXES
'. (Nonmandatory Information) ,
Xl. EFFECT OF WATER UPON THE HEATING VALUE
.'
Xl.
1 Custody transfer of natmal gas uses a simple pricing gas arid in the air used to'bi.lffi the gas.
equation that st~tes that the cost of gas is the rate of energy
released upon combustion multiplied by the price of gas per Xl.2 The heating value of a natural gas is the absolute
energy unit multiplied by· the time or accOlllting. period. The value of its enthalpy of combustion in an ideal combustion
rate of energy released upon combustion'is the product of the reaction. The heating value is, therefore,' an ideal gas property
heating value of the gas and the flow rate of the gas. The flow that can be calculated unambiguously from tables of pure
rate of the gas requires knowledge of the compressibility factor component values and it has no pressure dependence.
and the relative density of the gas. All three custody transfer
X1.3 An ideal combustion reaction with fuel and air in the
properties (heating value, compressibility factor, and relative
ideal gas state and the possibility of water in the fuel and air is:
density) can be calculated from the composition given pure
component property tables. The equations for calculating the CaH~S-iid) + (ex + [3/4 + 'Y)(I + e)OzCid)
properties of dry natural gas are well known, but this appendix + 0.043 83(ct + [3/4 + 'Y)(l + e)Ar (i(l) (Xl.1)
also presents an account of the effects of water contained in the + [0.001 62(ct + [3/4 + 'Y)(l + e) + xJ(l-xN - xc)]C0zCid)
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!A~LE X1.1 Example Calcl,I.lation of Pre.cision
Repeatability Rep(oducibilily
I Composition, H:"-H,,~ [( H: -
, Compound Xj Btu,ft-3 ax! (Btu·HfI-~3 ))2a x~2 ax'] , [( H(~B -tuH'W~)3a)2x' 'l
Methane 0.8302 169.7 0.0010 0.029 0.0020 0.115
Ethane 0.0745 -590.0 0.0002 0.014 0.0004 0.056'
Propane 0.0439 -1336.4 0.0002 0.071 0.0004 0.286
Isobutane 0.0083 -2072.2 0.0001 0.043 0.0002 0.171
Butane 0.0108 -2082.6 0.0002 0.173 0.0004 0.694
Isopentane 0.0031 -2821.2 0.0001 0.080 0.0002 0.318
Pentane 0.0025 -2829.2 0.0001 0.080 0.0002 0.320
Hexane 0.0030 -3576.2 0.0001 0.128 0.0002 . 0.512
Helium 0.0003 1179.7 0.0001 0.014 0.0002 0.056
Nitrogen 0.0032 1179.7 0.0001 0.014 0.0002 0.056
Carbon dioxide 0.0202 1179.7 0.0002 0.056 0.0004 0.223
Total T.OoOO D.702 2.807
+ [3.728 73(a + 1314 + 1')(1 + e) + xN 1 (l-xN -xc)]Nz{id) + (n~ w = water.
+
n~)HzO (id) The quantity Hw (id) - Hw(l) is the ideal enthalpy of
= [a + 0.001 62(a + 1314 + 1')(1 + e) + xd(1-xN - xc)]COz{id) vaporization for water.
+ n~H20 (id) + n~H20 (1) + I'SOz{id)
X1.5 It is possible to calcu,!ate a real ga~ heating value
+ [3.728 73(a + 1314 + 1')(1 + e) rather than using a hypothetical. state,. but the calculations are
+
xJ(I-xN -xd]Niid)
tedious, the numerical values are negligibly different, and the
+ 0.043 83(a + 1314 + 1')(1 + e)Ar(id) + (a + 1314 + I')e02(id) mathematical simplicity of the defining equation is lost. It is
where: <Y, 13, and 'Y are stoichiometric coefficients, E is the customary in the gas industry to use gross heating value for
fraction excess air, the composition of ,iir is assumed to be that most calculations, So for the remainder of this appendix, the
of Table XI.I ,n~ and the moles of water contani:n ed in the gas, term "heating value;' refers to the gross value.
n~ ate the moles of water contained in the air, are the moles
of water contained in the product gastnixture, n~ are the moles X1.6 Eq 7 in Section 7 provides the recipe to convert lhe
of gas that actually condense, Xc is the mole fraction of CO in heating value from one base pressure to another. Note thal
2
the gas, arid x is the mole fraction of N2 in the gas. If air has when using Eq 7, Hvid should be Calculat~d using the values
N
been· injected into the gas, it is assumed that the effect is from Taple 1 before converting the pressure; the individual
accounted fat in the excess fraction E. Fuel gas mixtures would values in Table I should not be converted. Conversion to
have non-integer values of <Y, 13 and 'Y. another temperature is more complicated. Heating value data
exist at 25°C based upon ~e reaction:
X1.4 It is customary to define hypothetical reference states CaH~Spd) + (a + 13/4 + 'Y)02(id) = aC0z{id) + (13/2)HzO (I)
for the water formed by the reaction denoted by Eq I (as + "IS0z(id) (XU)
opposed to "spectator" water that enters the reaction carried by
the gas or air). If we assume that the water formed in the XI.7 The experiments use pure oxygen and are corrected to
reaction remains in the ideal gas state, the heating value is . stoichiometric proportions. It is necessary to correct the sen
termed "net." If we assume that the water formed in the sible heat effects to arrive at a different temperature:
reaction condenses totally to the liquid state, the heating value
fil"
is termed "gross." The gross heating value is greater than the Hnid(1) = Hnid (25) + 7' dd - L dd]dT (XI.4)
P r P
net heating value by the ideal enthalpy of vaporization for
where:
water:
c;
heating value (gross) - heating value (net) = H .. (id) - Hw (l) ~ = aC;'co, + (13/2)C~~H,o + I'C;'so, (X 1.5)
(X 1.2) r .
c;
L = C;'caH,s, + (a + 13/4 + "I)C;'o, (XI.6)
where: r
H enthalpy,
and: C~ is the ideal specific heat at constant pressure, r
I = liquid state, and denotes reactants and r' denotes products.
I ';'\':
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03588
. X2. ACCOUNTING FOR: WATER
. ,"
)(2.1 If the gas contains ~ater (or must be assumed to be C·- al cuI a te nwg , nwa , nvw -' and nIw '
saturated) but the compositional analysis is on a dry basis, it is
nf,/[l + (XN + xd/(l- XN '-xd +' nf.] = f,8p;,;p (X2.6)
necessary to adjust the mole fractions to account for the fact
that water has displaced SOme gas, -thus lowering the heating nf. = (hBP':}P)/[(l-xN -xd(1-,hKP;';P)
value. The mole fraction of water in the gas results from the
n::,J[ 4.77418(0: + (3/4+ ,,)(1 + e) + n~] '= hap;,;P (X2.7)
definition of relative humidity:
n~ = 4.77418(0: + (3/4 + ,,)(1 + e)WP;';P)/(l-hap;,;P)
(X2.1) + +
n~./ {o: +" + (XN + xc)l(1 ~xN,...,~d + (IX (3/4 ,,)[0.00162(1 + e)
(Based upon one mole of the fuel CaHf3S'/) where kg is the (X2.8)
relative humidity of the gas, p~ is the vapor pressure of water, - +3.72873(1 + e) +-0.04383(1 + ~) + e] + n~} = P;';P
and nw denotes moles of water. For saturated gas kg is tmity.
Rearranging Eq X2.1 gives the moles of water: n~v = {o: + " + (xN + xc)l(1-XN - xd + (0: + (3/4 + ,,)[0.001 62(1
nw = xj( 1 - x,') (X2.2) + e)
+3.72873(1 + e) + 0.043 83(1 + e) + e]}(P;';P)/(l-P;';P)
The corrected mole fractions then become:
11 nJ 1 n;. = (3/2 + nf. + n~ - n~. (X2.9)
xi(cor) = x{ = x{ + X)(1-X,.) ] = (1-xw)xi
where: ka is the relative humidity of the air. Eq X2.6 and Eq
(X2.3)
X2.7 are reformulations of Eq X2.1 to reflect inlet conditions.
and the heating value becomes: Eq X2.S reflects Eq X2.1 for the saturated product gas (it must
be saturated before any water can condense). Eq X2.9 is a
(X2.4)
water balance: [3/2 are the moles of water formed by the
where water is not included in the N components of the reaction,n n: ~ + n~ are the moles of water that enter with the gas
summation. If the compositional analysis determines x.v and and air, are the moles of water that saturate the product gas,
water is included in the N components of the summation: and n~ are the moles of water that condense. Therefore, the
complete correction for the effect of water on heating value is:
N
livid = ~ x~vet liv~d_ X ,livid (X2.S)
;;:::1 I I l W H: = H~d CEq X2.4 or Eq X2.S) + (hgp~jP)/(1 -xn -xc)(l - hgp;,;P)
(X2.10)
X2.2 It is necessary to remove the effect of water because,
+ 4.774 18(0: + (3/4 + ,,)(1 + e)WP;';P)I(l-hap;,;P) - [0: + "
although water has a heating value, it is only a condensation + (xn -xc)
effect. Water carried by wet gas (spectator water) does not
actually condense, and only water formed in the reaction (1-xn-xJ + (0: + (3/4 + ,,)(3.77418 + 4.77418 e)]
contributes to heating value. X (P;';P)/(l-P~)}H:~]
X2.3 Accounting for water in the above manner is sufficient X2.4 Depending upon the relative humidities of the gas and
for defined custody transfer conditions, but when trying to air, the observed heating value can be greater or smaller than
model actual situations, the question becomes much more that calculated using Eq X2.4 or Eq X2.5. A humidity of air
complicated. It is obvious that all of the reaction water actually exists for each gas above which HVid is greater than that
cannot condense because in a situation in which both gas and calculated by Eq X2.4 or Eq X2.S. That critical value depends
air are dry some of the reaction water saturates the product upon the gas composition, the humidity of the gas, and the
gases and the remainder condenses. It is possible to account for amount of excess air. For pure, dry methane with no excess air,
these effects in a general manner. To do so, it is necessary to ka = 0.793 45.
X3. REAL GAS PROPERTIES
X3.1 In principal, we have enough information to convert aH) (av) dB dB
the heating value to a real gas property (it is not necessary to (av T = V- T aT p = B -T dT = 2 RF7r (X3.2)
do so for relative density because the molar mass ratio, Gid, is where V is the molar volume. The temperature dependence
the desired property). This is simply a matter of evaluating the of b must be defined, but in the custody transfer region it is
integral: easy to do so. The products and reactants again correspond to
Eq X1.3.
-
Hn_Hnid = f~{[ (~~)1. [(~~)JJdP (X3.1)
X3.2 While it is obviously possible to make the required
where: calculations to convert the heating value into a real gas
83