SECTION 23
Physical Properties This section section contains a number of chart s, correlat correlat ions, and procedures for the prediction of physical p roperties of of hydrocarbons and components components found with them. Fig . 23-1 23-1 l ists the nomenclat nomenclat ure used in t his section. section.
ponents. ponents. Imm ediately following following is a d etailed etaile d list of references ref erences and footnoted footnoted explana tion for for th e values in Fig . 23-2 23-2. P hysical properties properties for eighteen selected selected compounds compounds ca n be found in G PA St an da rd 2145, 2145, “Table of Phy sical Consta nts of Paraffin Hydrocarbons and Other Components of Natural Gas.”
Fig . 23-2 23-2 is a t able conta conta ining frequently u sed physical physical properties for a n umber of hydrocarbons and other selected selected com-
FIG. 23-1 Nomenclature B = s ec econ d v ir ir i a l c oe oe ff ff ic ici en en t f or or a g a s m i xt xt u r e, e, -1 (psia) B ′ = m ol ol e f ra ra ct ct io i on H 2S in sour ga s strea m, Eq 2323-6 B ii = second second virial virial coef coeffic ficient ient for for compone component nt i B ij = second second cross cross virial virial coeffic coefficient ient for for components components i and j 1/2 bi = s u m m a t i on on f a c t or or f or or c om om p on on e n t i C AB AB P = cu bi bi c a v er er a g e b oi oi li li ng n g po poi nt nt , ° F d = d en en si si t y, y, g /cc G = s pe pe ci ci fi fi c g r a v it it y or or r el el a t i ve ve de de n si si t y (g (g a s d en en s it it y ) G i = specific specific gra vity (ga (ga s gravity ) of ideal ga s, MW/ MW/MWa G id = molec molecular ular weight ra tio of compo component nent i in in mixture i H v = gross gross heating value per per unit volume volume of ideal gas, B t u/cu ft K w = Wa t s o n ch ch a r a c t e ri ri z a t i on on f a c t or or, Fig . 23-12 23-12 k = t h er er m a l co c o n d uc uct i vi vi t y, y, B t u /[ /[(h r • sq ft • ° F)/ft F)/ft ] k a = t h e r m a l co co nd nd u ct ct i v it it y a t on e a t m o sp sp h er er e , B t u/[(hr • sq ft • ° F)/ft ] M = m a ss ss fr fr a ct ct io ion m = m a ss, lb M W = m ol ol ec ecu l a r w e ig ig h t , lb lb /l b m ol ol e M AB AB P = m ol ol a l a v er er a g e b oi oi li li n g p oi oi nt n t , ° F or ° R M eA eAB P = M ea ea n a v er er a g e b oi oi li li ng n g po poi nt nt , ° F or or ° R n = n u m be be r of of m ol ol es es , (m (m a s s /M ol ol e w ei ei g ht ht ) P = p r es es s u r e , ps ps i a P c′ = pseudo pseudocri critic tical al pressure pressure adjusted adjusted for for acid gas composition, composition, psia P vp = vapor vapor pressure pressure at a reduced reduced temperature temperature of of 0.7 0.7 o P w = vapor vapor pressure pressure of of wa ter, ter, 0.2 0.256 5636 36 psia psia a t 60° 60° F R = g a s con s t a nt n t , 1 0 . 73 73 (p si si a • cu f t )/(° R • lb mole) for all ga ses (see (see Section Section 1 for R in oth er units) S = s pe pe ci ci fi fi c g r a vi v i t y a t 6 0° 0° /6 0 ° F T = a b so sol ut ut e t em e m pe pe r a t ur u r e, e, ° R t = AS TM TM D -8 -8 6 d i st st i ll ll a t i on on t e m pe pe r a t u r e f or or a g i v en en volumetric fraction, °F or ° R, Eq 2323-11 Tc′ = pseudo pseudocri critic tical al temperat temperat ure adjusted for for acid gas composition, °R V = v o l u m e, e, cu cu ft ft VAB P = v ol ol u me me t r ic ic a v e r a g e b oi oi li li n g p oi oi n t , ° F
23-1
W = m a ss, lb WAB P = w e ig ig h t a v er er a g e b oi oi li li ng n g po poi nt nt , ° F y i = mole mole fraction fraction of of comp compone onent nt i from analysis on on dry bas is, Eq 23-37 23-37 x = m ol ol e f ra r a c t io ion in in li li q ui ui d p ha ha s e y w = mole mole fractio fraction n of compo component nent i adjusted adjusted for for wa ter i content y = m ol ol e f ra ra ct c t io i on i n g a s p h a se se Z = com pr pr es es si si b il il it it y f a cctt or or Greek ε = pseudoc pseudocritic ritical al temperat temperat ure adjustment factor factor,, Eq 23-6 eAB P /T /Tpc θ = M eA density, lb/cu ft ρ = density, viscosity sity at operating operating temperature temperature and pressu pressure, re, µ = visco centipoise viscosity sity at 14.7 14.7 psia psia (1 atm ) and operating operating µA = visco temperat ure, centipoise centipoise ξ = f a ct ct or or d e fi fi n ed ed b y E q 2 33-2 0 tension, dynes/cm σ = surface tension, c e n t ri r i c f a ct c t or or ω = a ce kinemat ic visco viscosity sity,, centisto centistokes kes η = kinemat Subscripts a = a ir b = b oi l i n g c = cr i t i c a l i = co m p o n e n t i L = l iq u i d m = m ix t u r e p c = p s e u do d ocr it it ic ic a l r = r e d u c e d st st a te te V = v a p or v = v ol u m e w = w a t er Superscripts i d = i d ea l g a s w = w a t er o = r ef ef er er en en ce ce st st a t e
FIG. 23-2 Physical Constants
23-2
FIG. 23-2 Physical Constants
23-2
FIG. 23-2 (Cont’d) Physical Constants
23-3
FIG. 23-2 (Cont’d) Physical Constants
23-4
FIG. 23-2 (Cont’d) Notes and References for the Table of Physical Constants
23-5
FIG. 23-2 (Cont’d) Notes and References for the Table of Physical Constants
23-6
FIG. 23-2 (Cont’d) Notes and References for the Table of Physical Constants
23-7
FIG. 23-2 (Cont’d) Notes for the Table of Physical Constants a.
Va l u es in pa r e n t h es es a r e e st i m a t e d v a l u es .
p.
An ex tr a pol a ted va l ue.
b.
Th e t em p er a t u r e is a b ov e t he cr i t ic a l po in t .
q.
G a s a t 60 ° F a n d t h e l iq u i d a t t h e nor m a l boi li n g p oi n t .
c.
At s a t u r a t i on pr e ss u r e (t r i pl e p oi n t ).
r.
d.
S ub lim a tion poin t.
e.
Th e + s i gn a n d n u m b e r fol low i n g s pe ci fy t h e n u m b er o f cm3 of TEL added per gallon to achieve the ASTM octane number of 100, which corresponds to that of Isooctane (2,2,4Trimet hylpent an e).
F i xe d p oi n t s on t h e 1 968 I n t er n a t i on a l P r a c t ic a l Te m pe r a t u r e Sca le (IP TS-68).
s.
F i xe d p oi n t s on t h e 19 90 I n t er n a t i o na l Te m pe r a t u r e S ca l e (ITS-90).
t.
Densities at the normal boiling point are: Ethane, 4.540 [29]; Propane, 4.484 [28]; Propene, 5.083 [5]; Hydrogen Chloride, 9.948 [43]; H yd rogen Su lfide, 7.919 [25]; Amm onia , 5.688 [43]; Su lfur Dioxide, 12.20 [43].
u.
Technically, wat er has a heating value in two cases: net (–1060. B tu/lb) when w at er is liquid in the rea ctant s, and gr oss (+ 50.313 B tu /ft 3) when wa ter is gas in the reacta nts. The value is the ideal hea t of vaporization (entha lpy of the ideal ga s less the enthalpy of the saturated liquid at the vapor pressure). This is a ma tter of definition; wa ter does not burn.
f.
Th es e com pou n ds for m a gl a ss .
g.
Average value from octane numbers of more than one sample.
h.
S a t u r a t ion p re ss ur e a n d 60° F .
i.
I n de x of re fr a ct ion of th e g a s .
j.
D e n si t ie s of t h e l iq u i d a t t h e nor m a l b oi li n g p oi n t .
k.
H ea t of s ub lim a t ion .
m.
E q u a t i o n 2 of t h e r e fe r en ce w a s r e f it t e d t o g iv e: a = 0.7872957; b = 0.1294083; c = 0.03439519.
n.
N or m a l h y d r og en (2 5% p a r a , 75 %o rt h o).
v.
E x t r em e v a l ue s of t h o se r e por t e d b y r ef er e n ce 19.
A.
Molar ma ss (molecular weight) is based upon the following at omic weigh ts: C = 12.011; H = 1.00794; O = 15.9994; N = 14.0067; S = 32.066; Cl = 35.4527. The values were rounded off after calculating the molar ma ss using all significant figures in the at omic weights.
J.
The liquid value is not rigorously C P , but rather it is the heat capacity along the saturation line C S defined by: C S = C P – T (∂V/∂T)P (∂P /∂T)S . For liquids far from the critical point, CS ≈ C P .
K.
The heating value is the negative of the enthalpy of combustion at 60°F and 14.696 psia in an ideal reaction (one where all ga sses ar e ideal gasses). For an arbitra ry orga nic compound, the combustion rea ction is: C n H m O h S jN k (s,l,or,g) + (n + m/4 – h/2 + j ) O2(g) → n C O 2(g) + m/2 H 2O (g or l) + k/2 N 2(g) + j SO2(g), where s, l a nd g denote respectively solid, liquid an d ideal ga s. For gross heat ing values, the wat er formed is liquid; for net heat ing values, the wat er formed is ideal ga s. Values reported ar e on a dry ba sis. To account for wa ter in the heating value, see GP A 2172. The B tu/lb or gal. liquid column a ssumes a reaction wit h the fuel in the liquid sta te, while the B tu/ft 3 ideal ga s column assum es the gas in the ideal ga s stat e. Therefore, the values are not consistent if used in the same calculation, e.g. a gas plant ba lance. Th e h ea t of v a p or i za t i o n is t h e en t h a l py o f t h e s a t u r a t e d v a p or at the boiling point at 14.696 psia minus the enthalpy of the satura ted liquid at the same conditions.
B.
B o il in g p oi n t : t h e t em p er a t u r e a t e q u i li br i um b e t w e en t h e l iq uid and vapor phases a t 14.696 psia.
C.
Freezing point: the temperature at equilibrium between the crystalline phase and t he air sa tura ted liquid at 14.696 psia.
D.
The refractive index reported refers to the liquid or gas a nd is measur ed for light of wa velength corresponding to the sodium D-line (589.26 nm).
E.
The relative density (specific gravity): ρ(liquid, 60°F)/ρ(water, 60°F ). The densit y of wa ter a t 60°F is 8.3372 lb/ga l.
F.
The temperature coefficient of density is related to the expansion coefficient by : (∂ρ/∂T)P /ρ = –(∂ρV/∂T)P /V, in unit s of 1 /T.
G.
Pitzer acentric factor:
H.
Compressibility factor of the real gas, Z = PV/RT, is calculated using the second virial coefficient.
L.
I.
Th e d en s it y o f a n i d ea l g a s r e la t i v e t o a i r i s ca l cu l a t ed b y d ividing the molar ma ss of the of the ga s by 28.9625, the calculat ed averag e molar ma ss of air. See ref. 34 for the avera ge composition of dry air. The specific volume of an id eal ga s is calculated from the ideal ga s equat ion. The volume ratio is: V(idea l ga s)/V(liquid in v a cuum).
M. Air required for the combustion of ideal gas for compounds of formula C n H m O h S jN k is: V(ai r)/V(ga s) = (n + m/4 ( h/2 + j)/0.20946.
ω =
–log 10(P /P c) –1, P a t T = 0.7 Tc
COMMENTS Un its: reported values ar e based upon the following units wit h their equivalent corresponding SI u nits: ma ss: P ound (a vdp), lbm = 0.45359237 kg length : foot, ft = 0.3048 m temperat ure: degree Fa hrenheit t/° F) = 32 = [1.8(t/° C)]. The Celsius scale is defined by the I nterna tional Temperatur e of 1990 (ITS-90), wh ere 0° C = 273.15 K. Other derived units are: 3 3 volume: cubic foot, ft = 0.02831685 m 3 gallon = 231 in = 0.0037854512 m 3 pressure: pound per squar e inch absolute psia = 6894.757 kPa
energy: B ritish therma l unit (I.T.) B tu = 251.9958 cal (I.T.) = 1055.056 J Ga s consta nt, R: 1.985887 B t u (I .T.)/(R lb m ol) 10.73164 ft 3 psia /(R lb m ol) 8.314510 J /(K(mol) Conversion factors: 3 1 f t = 7.480520 gal. 3 3 1 lb m /ft = 0.1336806 lbm /ga l = 16.018462 kg/m 1 psia = 0.06804596 a tm = 6.894757 kPa 1 at m = 14.69595 psia = 760 Torr = 101.3250 kP a 1 B tu (I.T.) = 252.1644 cal th
23-8
FIG. 23-2 (Cont’d) References for the Table of Physical Constants 1. Ambrose, D., Na tional P hysical La boratory, Teddington, Middlesex, E ngland : Feb. 1980, NP L Report C hem 107.
24. G las gow, A. R.; Murphy, E. T.; Willingha m, C. B .; Rossini, F. D., J . Res. NB S, 37, 141 (1946).
2. Ambrose, D.; Hall, D. J .; Lee, D. A.; Lewis, G. B.; Mash, C . J ., J . Ch em. Therm o., 11, 1089 (1979).
25. Goodwin, R. D ., “Hyd rogen Sulfide P rovisional Thermochemical Properties from 188 to 700 K at Pressures to 75 MPa,” NB SI R 83-1694, October 1983.
3. Angus, S.; Armstr ong, B.; de Reuck, K. M., Eds. “Ca rbon Dioxide. Interna tional Thermodyna mic Tables of the Fluid St at e-3,” Perga mon P ress: Oxford, 1976. 4. Angus, S.; Armstr ong, B.; de Reuck, K. M., Eds. “Metha ne. Interna tional Thermodynam ic Tables of the F luid St at e-5,” Pergamon Press: Oxford, 1978. 5. Angus, S.; Armstr ong, B.; de Reuck, K. M., “Propylene (Propene). Int erna tiona l Thermody na mic Tab les of the Fluid Sta te-7,” Perga mon P ress: Oxford, 1980.
26. Goodwin, R. D .; Ha ynes, W. M., “Thermophysical P roperties of Isobutane from 114 to 700 K at Pressures to 70 MPa,” NBS Tech. Note 1051, J a nua ry 1982. 27. Goodwin, R. D .; Ha ynes, W. M., “Thermophysical P roperties of Normal Butane from 135 to 700 K at Pressures to 70 MPa,” NB S Monogra ph 169, April 1982. 28. Goodwin, R. D .; Ha ynes, W. M., “Thermophysical P roperties of P ropane from 85 to 700 K at P ressures to 70 MPa ,” NBS Monogra ph 170, April 1982.
6. Angus, S.; de Reuck, K. M.; Armstr ong, B., Eds. “Nitrogen. Interna tional Thermodynam ic Tables of the F luid St at e-6,” Pergamon Press: Oxford, 1979.
29. Goodwin, R. D.; Roder, H. M.; Stra ty, G. C.; “Thermophysical P roperties of Et hane, 90 to 600 K at P ressures to 700 bar,” NBS Tech. N ote 684, Augu st 1976.
7. Angus, S.; de Reuck, K. M.; McCa rthy, R. D., Eds. “Helium. Interna tional Thermodynam ic Tables of th e Fluid S ta te-4,” Perga mon P ress: Oxford, 1977.
30. Gut hrie, G. B .; Huffma n, H. M., J . Am. Chem. Soc., 65, 1139 (1943).
8. Armstrong, G. T.; J obe, T. L., “Hea ting Values of Nat ura l Ga s and its Components,” NBSIR 82-2401, May 1982.
31. Ha ar, L.; Ga llagher, J . S.; Kell, G. S., “NB S/NRC St eam Tables,” Hemisphere P ublishing C orpora tion, Washingt on, 1984.
9. Aston, J. G .; Szasz, G. J .; Finke, H. L., J . Am. Chem. Soc., 65, 1135 (1943).
32. Huffman, H. M.; P ark, G . S.; Thomas, S. B., J . Am. Chem. Soc., 52, 3241 (1930).
10. B ar ber, C. R., Metrologia 5, 35 (1969).
33. Hust, J . G .; Stewa rt, R. B ., “Thermodynamic P roperty Values for Ga seous a nd Liqu id Ca rbon Monoxide from 70 to 300 Atmospheres,” NB S Technical Note 202, Nov. 1963.
11. B oundy, R. H.; B oyer, R. F., (Eds.), “Styrene, It s P olymers, Copolymers and Derivat ives,” A.C.S. monograph No. 115, Reinholt, N.Y., 1952.
34. J ones, F. E., J . Res. NB S, 83, 419 (1978).
12. Cha iyavech, P.; Van Winkle, M., J . Chem. Eng . Da ta , 4, 53 (1959).
35. Keenan, J. H.; Cha o, J .; Kaye, J . “Gas Tables: (SI U nits),” J ohn Wiley a nd S ons, In c.: New York, 1983.
13. Cha o, J .; Ha ll, K. R.; Yao, J ., Thermochimica Acta , 64, 285 (1983).
36. “The Matheson Una bridged Ga s Da ta Book,” Matheson Ga s P roducts ; New York, 1974.
14. COD ATA Ta sk G roup on Key Values for Thermody na mics, CODATA Special Report No. 7, 1978.
37. McCa rty, R. D.; Weber, L. A., “Therm ophysical P roperties of Oxygen from the F reezing Liquid Line t o 600 R for Pr essures to 5000 Psia ,” NB S Technical Note 384, J uly 1971.
15. Commission on Atomic Weights a nd I sotopic Abunda nces, Pur e and Appl. Chem. 63, 975 (1991).
38. Messerly, J . F.; Gut hrie, G. B .; Todd, S. S.; Finke, H. L., J . Chem. En g. D at a , 12, 338 (1967).
16. Dea n, J . W., “A Tabula tion of the P roperties of Normal H ydrogen from L ow Tempera tur e to 300 K a nd fr om 1 to 100 Atm ospheres,” N B S Tech. Note 120, November 1961.
39. Messerly, J . F.; Todd, S. S.; Guthrie, G. B ., J. Chem. Eng . Dat a, 15, 227 (1970).
17. Douslin, D. R.; Huffma n, H. M., J . Am. Chem. S oc., 68, 1704 (1946).
40. Ohe, S., “Computer Aided Dat a B ook of Vapor Pr essure,” Data B ook Pu blishing Co., Tokyo, Ja pa n, 1976.
18. Edw ard s, D. G ., “The Vapor P ressure of 30 Inorga nic Liquids Between One Atmosphere and the Critical Point,” Univ. of Ca lif., La wrence Radia tion Labora tory, UC RL-7167. J une 13, 1963.
41. Roder, H. M., “Measurements of the Specific Heat s, Cs, and C v, of Dense Gaseous and Liquid Ethane,” J . Res. Nat. Bur. Sta nd. (U .S .) 80A, 739 (1976).
19. Engineering Sciences Da ta Unit, “E DSU , Engineering Sciences Data ,” EDSU International Ltd., London. 20. Flebbe, J . L.; Barclay, D. A.; Manley, D. B., J . Chem. Eng. Dat a, 27, 405 (1982). 21. Fra ncis, A. W., J . Chem. Eng. Da ta , 5, 534 (1960).
42. Scott, R. B.; Meyers, C. H.; Rands , R. D.; Brickwedde, F. G.; B ekkedah l, N., J . Res. NB S, 35, 39 (1945). 43. St ull, D. R.; Westrum , E. F.; Sinke, G. C ., “The Chemical Thermodynam ics of Organic Compounds,” J ohn Wiley & Sons, Inc., New York, 1969.
22. Ginnings, D . C.; Furu kaw a, G . T., J . Am. Chem. Soc. 75, 522 (1953).
44. “TRC Therm odyna mic Tab les ( Hy drocar bons,” Therm odyna mics Resear ch Cent er, Texas A&M Univ ersity S yst em: College St at ion, Texas.
23. Gira rd, G., “Recommended Reference Mat erials of the Realization of Physicochemical Properties,” Chapter 2, Marsh, K. N. Ed.; B lackwell Sci. P ub.: London, 1987.
45. “TRC Thermodyna mic Ta bles ( Non-Hydroca rbons,” Therm odyna mics Research C enter, Texas A&M U niversity S ystem: College Sta tion, Texas.
23-9
The ta ble in Fig . 23-2 is followed by procedures for estim at ing compressibility for ga ses. Additional ma terial follows on hyd rocarbon fluid densit ies, boiling point s, ASTM dist illat ion, critica l propert ies, acentr ic fa ctors, vapor pressures, viscosity, therma l conductivity, surface tension and gr oss heat ing value.
COMPUTER PREDI CTI ON METHODS
Computer methods for predicting physical and themodyna mics properties for light hydr ocar bons and na tura l gas constituents are widely available. They are routinely used by ma ny involved in the design a nd opera tion of na tura l gas processing facilities. This section emphasizes hand calculation methods that give reliable estimates of physical properties. They should be used wh en a number is r equired q uickly, for an “order of magnitude” check when evaluating a more deta iled procedure, or when a computer is not a vaila ble. There will be presentation of some computer results. The use of equa tions of sta te for property pred ictions is convenient an d easy, but they do not apply equa lly well for a ll properties. Gas phase densities, volumes and compressibilities are predicted accurately and reliably. Liquid volumes and densities ar e less accura te but st ill can be expected to generally be a s reliable as predictions by ha nd methods. Therma l conductivities, viscosities a nd surfa ce tensions a re not w ell predicted by P VT equa tions of sta te. Computer programs cited or used a re selected exa mples of those widely ava ilable for prediction of physical an d t hermodyna mic properties. Inclusion here does not represen t G PA a nd/or GP SA endorsemen t of the program(s). A good, reliable equation of state properly programmed and applied will always be the most convenient method for obta ining engineering accuracy ga s phase properties. Unfortun at ely, widespread a vaila bility an d/or ease of use ar e not suita ble criteria for choice of an equa tion of stat e progra m. The methods deta iled here are for hand ca lculat ion of physical properties.
COMPRE SSIBI LI TY OF GASES Pure Gases When dealing w ith ga ses at very low pressure, the ideal ga s relationship is a convenient and generally satisfactory tool. For measurement s and calculat ions for ga ses at elevated pressure, the use of the ideal ga s relationship may lea d to errors as great as 500%, as compar ed to errors of 2 or 3%a t a tmospheric pressure. The ma ny P VT equa tions of sta te tha t ha ve been proposed (see Section 25) for representing the pressure-volume-temperatur e relationship of gases a re complicated a nd require a computer or programm able calculator to solve in a reasona ble length of time. A generalized corresponding sta tes correlation of compressibility fa ctors is reasona bly convenient a nd sufficiently accurate for normal engineering requirements. The procedure provides a correction fact or, Z, by which t he volume computed from the idea l ga s equa tion is converted to th e correct volume for real ga s.
= ZmRT /MW = Z n R T
PV
Eq 23-1
The compressibility factor Z is a dimensionless par am eter independent of the quantity of gas and determined by the characteristics of the gas, the temperature, and pressure. Once Z is known or determined, t he calculation of pressuretemperat ure-volume relationships may be ma de with a s much ease at high pressure as at low pressure. The equa tion used to calculate ga s density is:
ρ =
MW • P 10.73 • T • Z
Eq 23-2
The va lue 10.73 for R is used wh en pressur e is in psia, volume in cubic feet, quantity of gas in pound moles, and temperatur e in ° R. Values of R for other combina tions of units are given in Section 1. According to t he t heorem of corresponding sta tes, the deviation of any a ctual ga s from the ideal gas la w is proportionally the sa me for different ga ses when at the sam e corresponding state. The same corresponding states presumably are found at the same fraction of the absolute critical temperature and pressure, which, for pure gases, are known as the “reduced conditions.”
FIG. 23-3 Calculation of Pseudocritical Temperature and Pressure for a Natural Gas Mixture Component Pseudocritical Critical Temperature, Temperature, Tpc, °R T ci, °R
Component Critical Pressure, Pci, psia
Mixture Molecular Weight, yi • MW
Component
CH4
0.8319
343.0
285.3
666.4
554.4
16.043
13.346
C 2H 6
0.0848
549.6
46.6
706.5
59.9
30.070
2.550
C 3H 8
0.0437
665.7
29.1
616.0
26.9
44.097
1.927
iC 4H 10
0.0076
734.1
5.58
527.9
4.01
58.123
0.442
nC 4H 10
0.0168
765.3
12.86
550.6
9.25
58.123
0.976
iC 5H 12
0.0057
828.8
4.72
490.4
2.80
72.150
0.411
nC 5H 12
0.0032
845.5
2.71
488.6
1.56
72.150
0.231
nC 6H 14
0.0063
913.3
5.75
436.9
2.75
86.177
0.543
Tpc = 392.62
Pseudocritical Pressure, Ppc, psia
Component Molecular Weight, MW
Mole Fraction, yi
P pc = 661.57 G = 20.426/28.9625 = 0.705
23-10
MWm = 20.426
Reduced Temperature, Tr Reduced P ressure, P r
= T/Tc
= P /P c
Eq 23-3
Gas Mixtures
Eq 23-4
Additional informa tion regar ding the calculat ion of compressibility factors for mixtures at pressures below 150 psia can be obta ined from GPA St and ar d 2172, “Calculation of Gross Heat ing Value, Relative Density a nd Compressibility Fa ctor for Natura l Ga s Mixtures from C ompositiona l Analysis”.
For gas m ixtures, the reduced conditions are determined using pseudocritical va lues instead of the t rue critica ls: Reduced Temperature, Tr = T/Σ(y i Tc i) Reduced P ressure, P r = P /Σ(y i P c i)
= T/Tpc
= P /P pc
Eq 23-3a Eq 23-4a
Any un its of temperat ure or pressure may be used provided tha t th e same a bsolute units be used for T as for T c (Tpc ) an d for P a s for P c (P pc ). The “a verage m olecular w eight” for a g as mixture is defined the same way – MWa vg = Σ(y i • M Wi). Calculat ion of pseudo critica ls a n d M Wa vg for a typical natural ga s is illustrated in Fig. 23-3. C ritical temperat ure and pressure for the hexanes and hea vier or heptan es and hea vier fraction can be estima ted from molecular w eight a nd specific gra vity or avera ge boiling point an d relat ive density using procedures presented in t his section. Att empts to prepare a generalized plot suita ble for a pplication to the low molecular ma ss hydrocarbons, including methane, ethane, a nd propane, indicat e tha t a n error frequently in excess of 2 to 3%wa s una voida ble due to their depa rture from the t heorem of corresponding sta tes. Fig . 23-4, prepared using pure component a nd ga s mixture dat a, can be used to estima te Z (2-3%error) for pure hydr oca rbon ga ses for this a pplica tion. Reduced temperature and pressure are used instead of pseudoreduced values. At low pressures, the different compounds appear to conform more closely. The compressibility factor may be assumed equal to 1.0 at low pressure. Errors genera lly w ill be 2-3%for pressur es of 300 psia or less so long as the gas is 50° F or more above its satura tion temperature at the pressure of concern. P-H diagrams like those in Section 24, Thermodynamic Properties, can be used to determine gas volumes, densities an d compressibilities for pure hydrocarbon and nonhydrocarbon vapors. Interpolation between specific volume curves on a P-H diagram does not yield results of high accuracy. Pure component P VT properties a re more a ccura tely obta ined from an equation of state, particularly if that equation has been fitt ed to volumetric da ta for the specific component . Ta bula tions of properties obtained in this way can be found in the literature.12
Example 23-1 — P ure component pr operties Using Fig . 24-26, the P-H diagra m for propan e, calculate the density of propane va por a t 200° F a nd 100 psia.
Solution Steps On the P -H dia gra m a t the intersection of the T = 200°F, 3 P = 100 psia lines read v = 1.5 ft /lb . Then :
ρ = 1/1.5 = 0.667 l b .f t 3 90
91
Using t he EZ*THE RMO version of the S RK equa tion of 3 state, ρ is ca lcula ted to be 0.662 lb/ft , from which 3 v = (1/0.662) = 1.51 ft /lb. For propane a t 200° F a nd 100 psia using dat a from Fig. 24-26 Z
=
MW • P R • T • ρ
=
(44.10) (100) = 0.936 (10.73) (458.67 + 200) (0.667)
Minor Amounts of Nonhydrocarbons — Fig . 23-41 shows compressibility fa ctors for t ypical sw eet natura l gases. Us e of compressibilit y fa ctors from Fig . 23-4 should yield mixture volumes (densities) within 2%to 3%of the true values from a reduced temperature slightly greater than 1.0 to the limits of the chart for both temperature and pressure. The chart w as prepared from da ta for binary mixtures of methane with etha ne, propane and butane and da ta for nat ural gases. No mixtures having a verage molecular w eights great er tha n 40 were used, an d a ll gases conta ined less tha n 10%nitrogen an d less tha n 2%combined hyd rogen sulfide an d carbon dioxide. Fig. 23-4 is applicable for temperatures 20°F or more above satura tion and to pressures as high as 10,000 psia.
Appreciable Amount of Nonhydrocarbons — Fig. 23-4 does not apply for gases or vapors with more than 2% H 2S a nd /or CO 2 or more than 20% nitrogen. For gas or vapors tha t ha ve compositions atypical of natu ra l gases, or for mixtures conta ining significan t a mounts of wa ter a nd/or acid gases, and for all mixtures as sa tura ted fluids, other methods should be employed. Reasona bly accurate gas compressibility factors for nat ura l gases wit h high nitrogen content, up to 50%nitrogen or even higher, can be obta ined using Fig . 23-4, if the molar average pseudocriticals from Eqs 23-3a a n d 23-4a ar e employed. This sam e approach is recommended for ga s condensa te fluids conta ining appreciable amounts of hepta nes and hea vier components. Critical temperat ure and pressure for the hepta ne and heavier fra ction or fractions can be estimat ed from molecular mass and relative density, or average boiling point and relative density, using correlat ions presented in th is section. Figs. 23-5, 23-6 a nd 23-7 provide compressibilit y fa ctors for low molecular weight natural gases. These figures cover a wide range of molecular weights (15.95 to 26.10), temperatur es (–100 to 1000° F) an d pr essures (up to 5,000 psia). For gases with molecular masses between the molecular masses shown in Figs. 23-5 through 23-7, linear int erpolat ion betw een ad jacent chart s should be used to compute the compressibility. In general, compressibilities for gases with less than 5% noncondensable nonhydrocarbons, such as nitrogen, carbon dioxide, and hydrogen sulfide, are predicted w ith less tha n 2% error. When molecular w eight is a bove 20 and compressibility is below 0.6, errors as large as 10%may occur.
Effect of Acid Gas Content — Natural ga ses which contain H 2S a nd /or CO 2 exhibit different compressibility factor behavior tha n do sweet ga ses. Wichert and Aziz 3 present a calculational procedure to account for these differences. The method uses the standard gas compressibility factor chart (Fi g. 23-3) a nd provides accurate sour ga s compressibilities for gas compositions that conta in as much as 85%total acid gas. Wichert and Aziz define a “critical temperature adjustment factor,” ε, tha t is a function of the concentrat ions of CO 2 a nd H 2S in th e sour gas. This correction factor is used to a djust the pseudocritical t emperatur e and pressure of the sour ga ses according to the equa tions:
3
The S RK calculation gives ρ = 0.662 lb/ft , and Z = 0.941.
Tc′
23-11
=
Tc
−ε
Eq 23-5
FIG. 23-4 Compressibility Factors for Natural Gas
23-12
1
FIG. 23-5 Compressibility of Low-Molecular-Weight Natural Gases 11
23-13
FIG. 23-6 Compressibility of Low-Molecular-Weight Natural Gases
23-14
11
FIG. 23-7 Compressibility of Low-Molecular-Weight Natural Gases
23-15
11
FIG. 23-8 3
Pseudocritical Temperature Adjustment Factor , ε, °F
P c′
=
P c Tc′
Eq 23-6
Tc + B ′ (1 − B ′)ε
The pseudocritical temperat ure a djustment fa ctor is plotted in Fig . 23-8. To use the fa ctor, th e pseudocritica l tempera tur e an d pressure a re calculated following the procedure outlined earlier. In this calculation, the H 2S a n d C O 2 are included as well as hyd rocar bon and other nonhydrocar bon constituents. The pseudocritical temperature adjustment factor is read from Fig . 23-8, and used to adjust the values of critical temperatu re and pressure. The reduced temperature a nd reduced pressure are calculat ed using th e ad justed values. The compressibility fa ctor is then read from Fig . 23-4.
The pseudocritical temperature adjustment factor is read from Fig . 23-8 to be 29.8°F. The adjusted pseudocritical temperature is: Tc′
The adjusted pseudocritical pressure is: P c′
Tr Z
Solution Steps
Pseudocritical P c, psia
C O2
0.10
547.6
54.8
1071
107.1
H 2S
0.20
672.1
134.4
1300
260.0
N2
0.05
227.2
11.4
493.1
24.7
CH4
0.60
343.0
205.8
666.4
399.8
C 2H 6
0.05
549.6
27.5
706.5
35.3 826.9
= =
100 + 459.67 404.1 0.831
=
1.385
Pr
=
1000 761.7
= 1.313
(Fig . 23-4)
HYDROCARBON FLUID DENSITIE S
Tc, ° R
433.9
761.7 psia
90
Mole Fraction
P c, psia
(826.9) (404.1 ) = 433.9 + 0 . 2 (1 − 0.2 ) 29.8
(The EZ*THERMO version of the SR K gives Z = 0.838.)
The first step is to calculate t he pseudocritical temperat ure an d pseudocritical pressure for the sour gas.
Comp.
=
The pseudocritical temperat ure a nd pseudoreduced pressure are:
Example 23-2 — A sour natura l gas ha s the composition shown below. Determine the compressibility factor for the ga s at 100°F and 1000 psia.
Pseudocritical Tc, ° R
= 433.9 − 29.8 = 404.1 ° R
Data and Correlations Fig . 23-9 presents saturated fluid densities (liquid and vapor) for h ydrocar bons a nd liquid densities for some mixtures. Fig . 23-10 is a plot of relat ive density as a function of temperature for petroleum fra ctions.
23-16
FIG. 23-9 Hydrocarbon Fluid Densities
23-17
2, 3, 19
FIG. 23-10 Approximate Specific Gravity of Petroleum Fractions
23-18
FIG. 23-11 Effect of Temperature on Hydrocarbon Liquid Densities
23-19
19
FIG. 23-12 Specific Gravity of Petroleum Fractions
23-20
FIG. 23-13 Specific Gravity of Paraffinic Hydrocarbon Mixtures
23-21
Subcooled liquid hydrocarbon densities from –50°F to + 140°F a re shown on Fig. 23-11. Corrections to liquid hyd rocarbon densities due to high pressure a re shown on Fig . 23-15.
4. U se Fig. 23-14 to determine the pseudodensity of the (N 2 + C 2 plus) fraction. Enter with the C 3 plus (or H 2S plus) density from S tep 2 in the upper left of the chart an d go horizonta lly to the line (interpolate if necessary ) representing the weight %(N 2 + C 2) , then look up and read the pseudodensity of the (N 2 + C 2 plus) along t he top of the chart .
S pe cific gravities of petroleum fractions are given in Fig. 23-12 where tempera ture ra nges from 0° t o 1000°F a nd pressures from atmospheric to 1500 psia. The petroleum fraction is identified within the center grid by two of three characteristics — AP I gra vity at 60°F, the Wa tson char acteriza tion factor, K w , or the mean-average boiling point. The m ean-average boiling point can be det ermined from Fig . 23-18 together with the API gravity and an ASTM D-86 distillation of the petroleum fra ction. The char acteriza tion factor, K w , is defin ed in the inset exam ple shown t o illustra te use of Fi g. 23-12.
At t emperatur es below –20° F, etha ne can be included in St ep 2 an d only N 2 used in St eps 3 an d 4. 5. I f C O2 is not present, go to St ep 6. If it is present, then account for it on an add itive volume basis as shown . D e n s i t y o f C O2 a n d (N 2 + C 2 plus )
The specific gravity of para ffinic hydrocar bons at their boiling point or bubble poin t pressure and temperature can be obtained from Fig . 23-13. The nomograph applies to mixtures as well a s to single components. Alignment points for para ffinic mixtures and pure components ar e locat ed a ccording to molecular w eight.
=
Vol (N 2 + C 2 plus )
=
Wt (N 2 + C 2 plus ) D en si t y (N 2 + C 2 p lus )
6. C a l cu l a t e t h e w e i gh t p e r ce n t m e t h a n e
Reduced temperat ures a bove 0.9.
Wt % methane
Molecular w eights less tha n 30 (low temperat ure region) and where methane is a significant part of the liquid.
Wt m ethane • 100 tota l Wt
=
Eq 23-10
7. E n t e r t h e t o p of Fig . 23-14 with the pseudodensity from St ep 4 or 5 as a ppropriat e, and drop vertically to the line (interpolation ma y be required) representing t he w eight percent meth ane. Rea d the pseudodensity of the mixture (60° F a nd 14.7 psia) on th e right side of the char t.
Density of Saturated and Subcooled Liquid Mixtures — A versatile, manual procedure for calculating the density of gas-saturated and subcooled hydrocarbon liquid mixtures was presented by Standing and Katz. 1 The ba sic method proposed uses t he a dditive volume a pproach for propane and heavier components at standard conditions, then corrected this ideal volume using apparent densities for the gaseous components ethane and methane. The resulting pseudodensity a t 60°F an d 14.7 psia is corrected for pressure using a hydrocarbon liquid compressibility cha rt, th en for temperature using a t hermal expansion chart (Fi g. 23-17) for hydrocarbon liquids. Experience with crude oils and rich absorber oils shows this correlation will predict densities wit hin 1 to 4%of experimenta l dat a.
Eq 23-9
where
Fig . 23-13 genera lly predicts specific gravit ies within 3%of measur ed values for para ffinic mixtures. However, the accura cy is somewha t less for mixtures ha ving:
• •
Wt C O 2 + Wt (N 2 + C 2 plus ) Vol C O 2 + Vol (N 2 + C 2 plus )
8. Correct th e pseudodensity to the actual pressure using Fig . 23-15. Add t he correction to t he pseudodensity from St ep 7. 9. C o r re ct t h e d e ns it y a t 60 ° F a nd pressure to the actual temperature using Fig . 23-17. Add the correction to the density from St ep 8.
The original correlation did not h ave a procedure for handling significan t am ounts of nonhydrocar bons an d had a fairly na rrow t emperatu re ra nge of 60° F t o 240°F. The following procedures and char ts a re recommended for general a pplicability to liquids conta ining components heavier tha n pentan es (ga s saturated or subcooled) at pressures up to 10,000 psia and temperatures from –100°F to 600°F. Significant amounts of nonhydrocarbons can be handled by this procedure (up to 20%N 2, 80%CO 2, and 30%H 2S ).
This procedure should not be used in t he critical r egion. Mixtures at temperatures greater t han 150° F w hich contain m ore tha n 60 mole percent metha ne or more tha n 80 mole percent C O 2 ha ve been demonstra ted t o be problem area s. Awa y from the near critical region calculat ed densities usually a re within 5%of experimenta l dat a 35 and errors are rarely greater tha n 8%. The best a ccura cy occurs for mixt ures conta ining m ostly C 5 plus with relatively small amounts of dissolved gaseous components (errors a re usua lly less tha n 3%). Note tha t d ensities of C 2 plus, C 3 plus, CO 2 plus, or C 4 plus mixtures can be calculated by this procedure at various temperatures and pressures, and t ha t t he ga seous components need not be present.
1. Set up a calculat ion table as shown in t he example in Fig. 23-16.
Example 23-3 — Fig . 23-16 illustrat es the procedure outlined above.
2. Ca lculate the density of propane and heavier (C 3 plus) or, if H 2S is present, of H 2S a nd heavier (H 2S plus) components, a ssuming a dditive volumes.
Density of C 3 plus
D e n s i t y o f C 3 plus (or H 2S plus )
=
Weight C 3 plus (or H 2S plus ) c o m p o n e n t s Vol C 3 pl u s (o r H 2S plus ) component s
=
Wt (N 2 + C 2) • 100 Wt (N 2 + C 2 plus )
Wt of C 3 p l u s Vol of C 3 p l u s
= 44.275 Eq 23-7
3. Determine the weight percent of (N 2 + C 2) in the (N 2 + C 2 plus) fraction. Wt % (N 2 + C 2)
=
Eq 23-8
Wt % C 2 in C 2 plus
lb /ft
=
44.836 lb 1.0128 f t
3
3
0.567 = 0.567 + 44.836 • 100 = 1.25%
Density of C 2 plus from Fig . 23-14 = 44.0 lb/ft 3 Density of CO 2 plus
23-22
=
45.403 + 17.485 45.403 + 0.3427 44.0
= 45.75
lb /f t
3
FIG. 23-14 Pseudo Liquid Density of Systems Containing Methane and Ethane
23-23
FIG. 23-15 Calculation of Liquid Density of a Mixture at 120°F and 1760 psia (1)
Component Methane Ca rbon Dioxid e E th a ne Propane n-Butane n-Pen ta ne n-Hexa ne n-Heptane n-Octane n-De ca ne n-Tetr a deca ne Total
(2)
(3)
Mole Fraction 0.20896 0.39730 0.01886 0.02387 0.03586 0.02447 0.01844 0.02983 0.02995 0.18208 0.03038 1.00000
Molecular Weight 16.043 44.010 30.070 44.097 58.123 72.150 86.177 100.204 114.231 142.285 198.394
(4)= (2)•(3)
Density Correction for Compressibility of Hydrocarbon Liquids
(6)= (4)/(5)
Density (60°F), lb/cu ft – 51.016 – 31.619 36.423 39.360 41.400 42.920 44.090 45.790 47.815
Weight, lb 3.352 17.485 0.567 1.053 2.084 1.766 1.589 2.989 3.421 25.907 6.027
Volume, cu ft – 0.3427 – 0.0333 0.0572 0.0449 0.0384 0.0696 0.0776 0.5658 0.1260
66.240
Wt %C H 4 i n Total
FIG. 23-16
(5)
=
3.352 • 100 66.241
=
5.1 %
Pseudodens ity of mixture at 60°F and 14.7 psia from Fig . 23-14 = 42.9 lb/cu ft P ressur e correction t o 1760 psia fr om Fig. 23-15 = + 0. 7
= 42.9 + 0.7 = 43.6 lb /ft 3 Tempera tur e correction t o 120°F fr om Fig . 23-17 = − 1. 8 Density at 60° F a nd 1760 psia
Density a t 120° F a nd 1760 psia
= 43.6 − 1.8 = 41.8
lb /ft
(Density by EZ*THE RMO version of SRK using Costa ld 3 41. 815 lb /ft .
3
92
Experimental density 35 a t 120°F an d 1760 psia = 41.2 lb/ft 3 Error
= (41.8 − 41.2)/41.2 =
0.015, or 1.5%
BOILING POINTS, CRI TICAL PROPERTIE S, ACENTRI C FACTOR, VAPOR PRE SSURE Boiling Points Fig . 23-18 shows the interconversion between ASTM D-86 distillat ion 10%to 90%slope and the d ifferent boiling points used in chara cterizing fractions of crude oil to determine the properties; VAB P, WABP, CAB P, MeAB P, a nd MAB P. On t he basis of ASTM D-86 distillation da ta , the volumetric avera ge boiling (VABP ) point is d efined a s: VABP
= (t 10 + t 30 + t 50 + t 70 + t 90)/5
Eq 23-11
Where t he subscripts 10, 30, 50, 70, and 90 refer to th e volume percent r ecovered dur ing t he dist illat ion. The 10%to 90% slope used as t he abscissa in Fig . 23-18 is defined as: slope
= (t 90 − t 10)/(90 − 10 )
Eq 23-12
To use the gra ph, loca te t he curve for the dist illat ion VAB P in th e appropriate set for the ty pe of boiling point desired. For th e known 10-90%slope, read a correction for t he VABP from th e selected VABP curve.
23-24
FIG. 23-17 Density Correction for Thermal Expansion of Hydrocarbon Liquids
23-25
Example 23-4 — Determine the mean average boiling point (MeAB P ) and t he molecular weight for a 56.8° AP I petroleum fra ction wit h the following ASTM distillation dat a.
IBP
=
%Over IBP 5 10
Temperatur e, ° F 100 130 153
20 30 40 50 60 70 80 90 EP
191 217 244 280 319 384 464 592 640
initial boiling point
EP
=
The significance of the various a verage boiling points, interconversion of D-86 and D-1160 ASTM distillations, and the calculation of true-boiling point a nd at mospheric flash curves from ASTM distillation da ta can be found in Cha pters 3 and 4 of the AP I Technical D at a Book. 36 Molecular weight can be ca lculat ed from E q 23-13 using MeABP in ° R an d S (specific gra vity a t 60°F) . MW = 2 04. 38
[(T)0. 118] (S 1.88) (e (0.0 0218 T − 3.075 S )) Eq 23-13
This relationship has been evaluated in the molecular weight ra nge of 70 to 720; the MeABP ra nge of 97 to 1040°F ; an d the API r a nge of 14° to 93° . The avera ge error wa s about 7%. E q. 23-13 is best used for molecular w eight s a bove 115, since it tends to over-predict below this value.
Example 23-5 — Calculat ion of molecular weight. Fr om Exa mple 23-4: S
=
0.7515 fo r 56.8° AP I
MeABP
end poin t
= 271 + 460 = 731°R
U sing E q 23-13, Slope VABP
= (592 − 153)/80 = 5.49 MW
= (153 + 217 + 280 + 384 + 592)/5 = 325° F
Refer to F ig. 23-18. Rea d down from a slope of 5.49 to the interpolated curve for 325°F in the set drawn with dashed lines (MeAB P ). Read a correlat ion value of –54 on the ordinat e. Then: MeABP
= 325 − 54 = 271°F
= 204.38[(731)0.118][(0.7515)1.88]
[e (0.00218
•
731) − (3.075 • 0.7515)
]=
127.0
Critical Properties Critical properties are of interest because they are commonly used to find reduced conditions of temperature and pressure which a re required for corresponding stat es correla-
FIG. 23-18 Characterizing Boiling Points of Petroleum Fractions (From API Technical Data Book)
23-26
FIG. 23-19 Low-Temperature Vapor Pressures for Light Hydrocarbons
23-27
FIG. 23-20 High-Temperature Vapor Pressures for Light Hydrocarbons
FIG. 23-20 High-Temperature Vapor Pressures for Light Hydrocarbons
23-28
FIG. 23-21 Viscosities of Hydrocarbon Liquids
FIG. 23-21 Viscosities of Hydrocarbon Liquids
23-29
tions. Pseudocriticals a re used in man y corresponding sta tes correlat ions for mixtures. The following equa tions ta ken from the API Technical Da ta Book 36a, b can be used to estima te pseudo critical t emperatur e and pressure for petroleum fractions (pseudo, or undefined components): P pc Tpc
= [ 3.12281 (10 9) T −2.3125] • S 2.3201 0.58848
= 24.2787 • T
• S
0.3596
Eq 23-14 Eq 23-15
These equa tions ar e in terms of T = MeAB P (°R) and specific gra vity (S) at 60°F. Both of these correlat ions have been evalua ted over th e ran ge of 80 to 690 molecula r weigh t; 70 to 295° F normal boiling point; a nd 6.6° to 95° API.
Example 23-6 — P seudocritical tempera ture a nd pressure. Tak e the previous m ixtur e (from E xa mple 23-4) w ith: VABP = 325°F MeABP = 271°F AP I = 56.8° Molecula r Weigh t = 127 (Ex. 23-5) ASTM D-86, 10%to 90%S lope = 5.49 Find its pseudocritical tempera ture.
Use Eq 23-15 to calculat e the pseudocritical t emperatur e as: Tpc
= 24.2787 (27 1 + 460)0.58848 (0.7515)0.3596 = 1062 ° R
or 602° F
F o r t h i s 56.8°AP I f l u i d , e s t i m a t e t h e p s e u d o c r i t i c a l p r e s sure, using Eq 23-14 an d MeABP = 271°F: P pc
=
[ 3.12281 (10 )] (271 + 460 )−
= 386
9
2.3125
(0.7515)2.3021
psia
Acentric Factor The a centric fa ctor, ω, is frequently used as a third para meter in corresponding states cor relations. It is tabulated for pure hydrocarbons in Fig . 23-2. Note that the acentric factor is a function of P vp , P c, and Tc. It is arbitr ar ily defined by
ω = −log (P vp /P c) T = 0.7 − 1.0 r
Eq 23-16
This definition requires knowledge of the critical (pseudocritical) temperature, vapor pressure, and critical (pseudocritical) pressure.
tions. Pseudocriticals a re used in man y corresponding sta tes correlat ions for mixtures.
Use Eq 23-15 to calculat e the pseudocritical t emperatur e as:
The following equa tions ta ken from the API Technical Da ta Book 36a, b can be used to estima te pseudo critical t emperatur e and pressure for petroleum fractions (pseudo, or undefined components): P pc Tpc
= [ 3.12281 (10 9) T −2.3125] • S 2.3201 0.58848
= 24.2787 • T
• S
0.3596
Tpc
= 1062 ° R
P pc
Eq 23-15
Example 23-6 — P seudocritical tempera ture a nd pressure. Tak e the previous m ixtur e (from E xa mple 23-4) w ith: VABP = 325°F MeABP = 271°F
9
2.3125
(0.7515)2.3021
psia
Acentric Factor The a centric fa ctor, ω, is frequently used as a third para meter in corresponding states cor relations. It is tabulated for pure hydrocarbons in Fig . 23-2. Note that the acentric factor is a function of P vp , P c, and Tc.
ω = −log (P vp /P c) T = 0.7 − 1.0 r
Eq 23-16
This definition requires knowledge of the critical (pseudocritical) temperature, vapor pressure, and critical (pseudocritical) pressure.
ASTM D-86, 10%to 90%S lope = 5.49 Find its pseudocritical tempera ture.
Solution Steps From Fig . 23-18 w ith ASTM D -86 slope = 5.49 find a VABP correction of about –85°F (extrapolated from the left-hand group). 325 − 85
[ 3.12281 (10 )] (271 + 460 )−
It is arbitr ar ily defined by
Molecula r Weigh t = 127 (Ex. 23-5)
=
=
= 386
AP I = 56.8°
MABP
or 602° F
F o r t h i s 56.8°AP I f l u i d , e s t i m a t e t h e p s e u d o c r i t i c a l p r e s sure, using Eq 23-14 an d MeABP = 271°F:
Eq 23-14
These equa tions ar e in terms of T = MeAB P (°R) and specific gra vity (S) at 60°F. Both of these correlat ions have been evalua ted over th e ran ge of 80 to 690 molecula r weigh t; 70 to 295° F normal boiling point; a nd 6.6° to 95° API.
= 24.2787 (27 1 + 460)0.58848 (0.7515)0.3596
For a hydr oca rbon mixture of known composition, and containing similar components, the acentric factor may be estima ted, with rea sonable accura cy, as the molar avera ge of the individual pure component a centric fa ctors:
ω = Σ x i ωi
= 240°F FIG. 23-22
Viscosity of Paraffin Hydrocarbon Gases at One Atmosphere
23-30
Eq 23-17
FIG. 23-23 Hydrocarbon Gas Viscosity
23-31
If th e vapor pressure is not known, ω can be estimated 38 for pure hydrocarbons or fractions with boiling point ranges of 50°F or less, using Eq . 23-18. 3 log P c − log 14.7 ω = − 1.0 7 Tc − 1 T b
P pc
From E q. 23-15, th e pseudocritica l tempera tur e is:
= 24.2787 • (875 )0.58848 • (0.871)0.3596 Tpc = 1244° R log (356 ) − log (14.7) ω = 3 − 1.0 = 0.447 1244 − 1.0 7 875 Tpc
Eq 23-18
Example 23-7 — Acent ric fa ctor. A na rrow-boiling petroleum fra ction ha s a VAB P of 418° F, an ASTM slope of 0.75 and an AP I gr avity of 41° . Est imate its acentric factor. In order to use Eq 23-18 we n eed the a vera ge boiling point (MeABP); the pseudocritical temperature (a function of MABP); and the pseudocritical pressure (a function of MeABP). From Fig . 23-18, the correction to VABP for mean average is –3° F; th e correction for MAB P is –5° F. Note tha t for na rrowboiling fractions, all boiling points approach the volumetric a verage. Then, MeABP = 415° F a nd MABP is 413°F.
Vapor Pressure The vapor pressures of light hydrocarbons and some common inorganics in the temperature range below 100°F are given in Fig. 23-19. Vapor pressures at higher temperat ures, up to 600° F, are given in Fig . 23-20 for the same compounds. Note tha t, except for ethylene a nd propylene, the hyd roca rbons ar e all norma l para ffins.
VISCOSIT Y
From E q. 23-14, th e pseudocritica l pressure is: T = 415 + 460 = 875°R S for 41° API = 141.5/(131.5 + 41) = 0.871 P pc
=
[ 3.12281 10 (875)− 9
] • (0.871)
2.3125
2.3201
= 356 psia
Figs. 23-21 through 23-29 give the viscosity of hydrocarbon liquids a nd va pors, wa ter, stea m, an d miscellaneous ga ses. Fig. 23-21 gives data on hydrocarbon liquids. Figs. 23-22, 23-23 a nd 23-24 present da ta on hydrocarbon ga ses. To correct for pr essur e, the gas viscosity from Fig. 23-22 is adjusted from atmospheric
FIG. 23-24 Viscosity Ratio vs. Pseudoreduced Temperature
23-32
FIG. 23-25
FIG. 23-26
Viscosity of Miscellaneous Gases – One Atmosphere
Viscosity of Air 43, 44, 45
pressure values by Figs. 23-23 a nd 23-24. Fig. 23-24 is preferred when the reduced temperature is greater than 1.0. Fig. 23-28 gives the viscosity of hyd roca rbon liquids conta ining dissolved gases. Note that Fig. 1-7 gives conversion factors for viscosity.
Calculation of Gas Mixture Viscosity Example 23-8 —Determine th e viscosity of a ga s of molecula r weight 22 a t 1,000 psia a nd 100°F. Tc = 409° R, P c = 665 psia
Solution Steps
=
G id
22/28.964
Hence, the viscosity a t 1000 psia a nd 100° F is:
µ = (1.21) (0.0105 ) = 0.0127
The viscosity of a gaseous mixture w ith la rge a mounts of nonhydroca rbons is best determined by using t he method o f D ea n a n d S t i e l. 41 This method is part icula rly useful for h a n d l in g n a t u r a l g a s w i t h h i gh C O 2 cont ent. Tested a ga inst 30 CO 2-N 2 mixtures, it ha d a n a verage deviat ion of 1.21% at pressures up to 3525 psia. It makes use of a factor, ξ, defined as: 1 /6
( Tcm ) ξ = 5.4402 2/ 3 ( Σ (x MW ) (P )) i i cm
= 0.760
From Fig . 23-23 at 100°F:
µA = 0.0105 centipoise =
100 + 460 409
=
1.37
Pr
=
1000 6 65
ξ µA =
[166.8 (10− )] [(166.8 • 10− )(0.1338 T − 0.0932) / ] 5
5
Eq 23-20
≤ 1.5,
If Tr is
Because Tr > 1.0, Fig. 23-24 is preferred to obtain the correction for elevated pressure to the viscosity at one atmosphere.
In either case, µA is found by dividing ( ξ µA) by
µ = 1.21 µA
59
r
= 1.50
Note: P seudocritical tempera ture a nd pressure should be calculat ed as out lined in th is section, if th e composition of the gas is ava ilable.
From Fi g. 23-24:
Eq 23-19
If the r educed temperatur e Tr is > 1.5, th en
Then: Tr
centipoise
−5 8/9 ξ µA = 34.0 10 ( Tr )
Eq 23-21
ξ.
Eq ua tions 23-19 through 23-21 will predict th e viscosity of pur e gas es as well as mixtur es. To apply the Dean a nd St iel41 method to mixtures, the pseudocritical volumes, compressibilities, and temperat ures are calculat ed by the Pra usnitz and Gun n 42 mixing rules:
23-33
Tcm
= Σ (y i Vc i) = Σ (y i Z ci ) = Σ (y i Tci)
P cm
=
Vcm Zcm
Eq 23-22
B
Eq 23-23
A=
Eq 23-24
= =
Tr
(0.2 875) (10. 73) (335.9) 1.562
T Tcm
=
509.7 335.9
=
η = 0.02645 • e η = 0.02645 • e
0 .043
= 1.517 ξµA is E q 23-
centipoise
Using Fig. 23-23 and correcting for the nitrogen and carbon dioxide content of this mixture gives a µA of 0.0116 cp. This is a good check. Ha d a 20%N 2 content been chosen for this exa mple, the N 2 ra nge of Fig . 23-23 would ha ve been exceeded a nd us e of the D ean a nd S tiel method would have been required. When the conditions at hand fall within the limits of Fig. 23-23, use this figure an d not the Dea n a nd St iel correlation.
Viscosity of Petroleum Fractions Mid-Boiling Point Method — The viscosit y of a crude oil or crude oil fraction can be estimated using the equations given below if the mid-boiling point and gravity are known: Mid-boiling point is d efined a s th e boiling point a t 50%volume distilled. / T
Eq 23-26
= ( 101.78 Tb− 0.175 − 29.263 )
K w B
= 4.717 + 0.00292 Tb
Eq 23-27 Eq 23-28
Example 23-10 — At 100°F an d 210° F find th e viscosity of a hea vy condensa te ha ving a mid-boiling point of 325°F a nd a specific gravity of 0.7688.
Solution Steps 3
K w ln (B )
=
1.8 (1105.7 ) 669.67
=
0.926 cs a t 100° F
=
0.517 cs a t 210° F
Water Viscosity at Saturated Conditions
ξ µA = 48.91 (10 )
ln (B )
559.67
FIG. 23-27
−5
A
11.99 1105.3
=
0.02645
Thermal conductivity for na tura l gas mixtures a t elevated pressure can be calculated from an at mospheric value a nd a pressure correction. Figs. 23-31 through 23-36 present low pressure thermal conductivity data of gases developed from published dat a. 51, 54 The pressure correction of Lenoir et a l. 52 shown in Fig. 23-32 is applied to these low pressure dat a as illustrated below. The thermal conductivity of liquid paraffin hydr oca rbons is plott ed in Fig . 23-35 and t he therma l conductivity of liquid petroleum fractions in Fi g. 23-36.
= 166.8 (10−5) [(0.1338 ) (1.517 ) − 0.0932]5/9
A • e 1.8 B
− 29.263
THERMAL CONDUCTIVITY
ξ µA = 166.8 (10−5) [0.1338 Tr − 0.0932]5/9
η =
− 0.175
1.8 (1105.7 )
663.4 psi a
B ecause Tr > 1.5, the expressi on to be used for 20.
µA = 0.01138
101.78 (325 + 459.67)
The reported v a lues ar e 0.93 an d 0.52 centist okes, respectively.
Zcm R Tcm Vcm
(5.4402) (335.9)1/6 = (19. 237)1/2 (663.4 )2/3
=
Eq 23-25
Substituting from the calculation table in Fig. 23-30 into Eq 23-19:
ξ =
1105.7
The same consta nts ar e employed a t 100° F a nd a t 210° F.
Zcm R Tcm Vcm
Example 23-9 — For a temperature of 50°F a nd a pressure of 300 psia, est ima te t he viscosity of a mixtur e of 80 mole percent meth a ne, 15 mole percent n itrogen, an d 5 mole percen t carbon dioxide. Ca lculations a re summa rized in Fig . 23-30: P cm
=
325 + 459.67 √ 0.76 88
=
11.99
= 4.717 + (0.00292 ) (325 + 459.67) = 7.01 23-34
FIG. 23-28 Liquid Viscosity of Pure and Mixed Hydrocarbons Containing Dissolved Gases at 100°F and One Atmosphere
23-35
k /k A
FIG. 23-29 Viscosity of Steam 46, 47
k
= 1.15
= (1.15 ) (0.0248) =
0. 0285 B tu /[(h r • s q ft • ° F )/ft ]
Another method for estimat ing th ermal conductivity is presented by S tiel an d Thodos. 53 To determine the t herma l conductivity of a ga seous mixtu re of defined components , the t herma l conductivity of each component a t t he given temperatu re is read from the chart s provided and the thermal conductivity of the mixture is determined by the “cube root rule”. 56 This rule is applicable to mixtur es of simple ga ses; it does not apply to mixtu res containing CO 2 becau se the t hermal conductivity goes through a maximum. MWi ) Σ (y i k i √ 3
km
=
Eq 23-29
3
MWi Σ y i √
The cube root r ule wa s test ed 56 aga inst 17 systems with an a vera ge devia tion of 2.7%. The thermal conductivity of a liquid mixture is best determined by th e method of Li, 55 based on volume fra ctions.
Example 23-12 — Find the thermal conductivity of the gaseous mixture shown in Fig. 23-37 a t 2 00 ° F a n d on e a t mosphere. km
=
0.05774 2.822
=
0.0205 B t u /[(hr • sq ft • ° F )/f t ]
TRANSPORT PROPERTY R EFE RENCES There a re no simple correlat ions for the tr an sport properties of viscosity a nd t herma l conductivity, as evident from the preceding par a graphs. For pure components, t he best a pproa ch is a complicated equation with many constants that must be fitted to experimental data, or extensive tables. Vargaftik 62 a nd Touloukia n 65 each have extensive collections of experim en t a l d a t a .
Example 23-11 — Find the thermal conductivity of a 25 molecular w eight na tura l gas a t 700 psia a nd 300°F. Tc = 440° R, P c = 660 psia
The interior molecules of a liquid exert upon the surface molecules an inwa rd force of a ttra ction w hich tends to minimize the surface area of the liquid. The work required to enlarge th e surface area by one square centimeter is called the surfa ce free energy. The perpendicular force in th e liquid surface, called surface tension, exerts a force para llel to the plan e of the surface. Surface tension, an importa nt property where wetting, foaming, emulsification, and droplet formation are encount ered, is used in th e design of fractiona tors, abs orbers, tw o-pha se pipelines, and in r eservoir ca lcula tions.
Solution Steps From Fi g. 23-31, at 300° F: Btu /[(h r • sq ft • ° F )/ft ]
kA
= 0.0248
Tr
= (300 + 460 )/440 =
Pr
=
700 /660
=
SURFACE TENSION
1.7 3
1. 06
From Fi g. 23-32:
FIG. 23-30 Calculation of Viscosity of a Gas Mixture Mole Fraction
Molecular Weight
T c, °R
Pc, psia
VC, Zc cu ft/lb mole
PcVc 10.73 Tc
Vcm
yiVci
Tcm
yiTci MWm
yiMWi
CH4
0.80
16.043
343.0
666.4
1.59
0.2879
1.272
274.4
12.834
N2 C O2
0.15 0.05
28.013 44.010
227.2 547.6
493.1 1071.
1.43 1.51
0.2892 0.2752
0.215 0.076
34.1 27.4
4.202 2.201
Mixt ur e
1.00
–
–
1.562
0.2875
1.562
335.9
19.237
23-36
FIG. 23-31
FIG. 23-32
Thermal Conductivity of Natural and Hydrocarbon Gases at One Atmosphere (14.696 psia)
Thermal Conductivity Ratio for Gases
Pure Components
Values for Hv and MWi are obtained from Fig. 23-2.
The surface tension of pure hydrocarbons as a function of temperature may be obtained from Fig. 23-38.
Mixtures Surface tension for binaries of known composition at or near atmospheric pressure may be calculated78 using:
σm =
σ1 • σ2 σ1 • x2 + σ2 • x1
Eq 23-30
The presence of inert gases, such as N 2 and CO2, in the liquid phase tends to lower the surface tension of the liquid. Where the concentration of inert gases in the liquid exceeds 1.0 mole %, estimated values of surface tension may be 5 to 20% higher than actual values for the mixture.
To calculate the ideal gross heating value produced or used for a given period of time, H v must be multiplied by the ideal gas volumetric flow rate of gas for the time period. To employ a real gas flow to calculate the ideal gross heating value produced or used for a given period of time, the real gas flow rate must be converted to the ideal gas flow rat e by dividing by the compressibility factor. Often the heating value H v is divided by the compressibility factor in preparati on for multiplying by the real gas flow rate. Thus H v /Z is gross heating value per unit volume of real gas.
Specific gravity (also termed relative density or gas gravity) — is defined as the ratio of gas density (at the temperature and pressure of the gas) to the density of dry air (at the air temperature and pressure). G
GROSS HEATING VALUE OF NATURAL GASES The gross heating value, specific gravity, and compressibility of a natural gas mixture may be calculated when a complete compositional analysis of the mixture is available.
Gross Heating Value — is defined as the total energy transferred as heat in an ideal combustion reaction at a standard temperature and pressure in which all water formed appears as liquid. The gross heating value can be calculated per unit volume of an ideal gas, or per unit volume of a real gas as follows: Hv
= Σ (yiHv ) i
Eq 23-31
=
MW P Ta Za ρ = MWa Pa Z ρs
Eq 23-32
The ideal gas specific gravity is the ratio of the molecular weight of the gas to the molecular weight of dry air. MW Eq 23-33 Gid = MWa For a mixture G id
= Σ (yi G id i )
Eq 23-34
The specific gravity G is measured and is generally used to calculate the molecular weight ratio Gid when the gas composition is not available.
23-37
G
FIG. 23-33
FIG. 23-34
Thermal Conductivity of Miscellaneous Gases at One Atmosphere59, 60, 61, 62
Thermal Conductivity of Hydrocarbon Gases at One Atmosphere67, 68, 69
id
=
MW MWa
=
G (P a T Z) P Ta Z
Eq 23-35
The temperat ures a nd pressures used m ust correspond to actual measurement conditions or serious errors in G id ca n occur.
Corrections for Water Content — When the gas is wa ter satur at ed but th e component a na lysis is on a dry ba sis, the component a nalysis must be adjusted to reflect t he presence of water. The mole fraction of water in the mixture is estimat ed as: y w
=
P ow p
=
n w (on a one mole ba sis) (1 + n w )
The a djusted mole fractions a re calculated using the following equat ion: y w i
=
P ow = P
y i 1 −
y i (1 − y w )
Eq 23-36
When the gas is wet but not wa ter sat ura ted and th e component a nalysis is on a d ry basis, it is necessary t o determine the w a ter content and to ad just t he mole fractions to reflect the presence of water. When the water mole fraction, y w , is known, the adjusted mole fractions can be obtained from Eq 23-37. The y w i values are used in the gross hea ting value a nd gas compressibility calculations after adding water to the component list. If t he dry gross heat ing value is known, the effect of the wa ter cont ent can be calculated using: H v (w et )
Eq 23-38
Calculations — Additional deta ils on th ese calcula tional methods and examples a re given in G PA Sta nda rd 2172, “Calculat ion of Gross Hea ting Value, Relative Density a nd C ompressibility Factor for Natural Gas Mixtures from Compositiona l Analysis”. A listing of t he B a sic source code for a computer program to perform the calculations is given in 2172.
For water saturated gas, water is added to the component list a nd the x w i values are used in the gross hea ting value an d the ga s compressibility calculations. If t he dry gr oss hea ting value is known, the water saturated gross heating value can be calculated by: H v (sat’d )
= (1 − y w ) H v (d r y) + 50.3 y w
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1.7051 1.7051 • 29.94 = 1 − P H v (dry ) + P
Eq 23-37
23-38
5. Ha ll, K. R. and Yarborough, L., Oil Gas J . 72, No. 7, 86 (Feb. 18, 1974).
FIG. 23-35 Thermal Conductivity of Liquid Paraffin Hydrocarbons
FIG. 23-36 Thermal Conductivity of Liquid Petroleum Fractions 58
23-39
FIG. 23-37 Calculation of Thermal Conductivity
Component
Mole Fraction
Thermal Conductivity Btu [ hr sq ft °F ft]
Molecular Weight
CO 2
0.10
0.0127
44.010
3.530
0.3530
0.00448
H 2S
0.20
0.0136
34.076
3.242
0.6484
0.00882
N2
0.05
0.0175
28.013
3.037
0.1519
0.00266
CH 4
0.60
0.0258
16.043
2.522
1.5132
0.03904
C 2H 6
0.05
0.0176
30.070
3.109
0.1555
0.00274
Tot a l
1.00
2.8220
0.05774
3
MWi
FIG. 23-38 Surface Tension of Paraffin Hydrocarbons 85
23-40
yi
3
MWi
3
yi k i MWi
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23-41
