Calculated and Measured Isothermal and Adiabatic Joule-Thomson Coefficients for Methane-Et hane Mixtures Kalil A. Alkasab,' Jaysukh M. Shah, and Royce J. Laverman,2 Chicago Bridge & Iron Company, Research Department, PlainJield, Ill. 60544
Roland A. Budenholzer Illinois Institute of Technology Chicago, Ill. 6061 6
Measurements of the isothermal and the adiabatic Joule-Thomson coefficients were carried out for three methane-ethane mixtures over a temperature range from -59°F to +35"F and a pressure range from 50 psia to 950 psia. Comparisons are made between the experimentally determined isothermal and isenthalpic expansion data and that predicted b y a modified Benedict-Webb-Rubin (BWR) equation of state. A new set of coefficients for the BWR equation of state were developed for ethane with the coefficient CO determined as a function of temperature. The coefficients for methane used in the comparisons were developed b y Lee, et a/. ( 1 969). The average absolute difference between experimental and calculated isothermal JouleThomson coefficients for 47 points was 1.37'70. The average absolute difference between the calculated and the experimentally determined temperatures for 40 separate data points on 1 0 isenthalpic expansion lines was 0.67"F.
An accurate knowletige of t'he thermodynamic behavior
of hydrocarbon gas mixtures is necessary for the accurate design and successful operation of many processes in the petroleum and natural gas processing field. This is particularly true with regard to the design of natural gas liquefaction and storage facilities. A s a result of what has been felt to be a n inadequacy in both existing correlations and available thermodynamic data, especially in the region of cryogenic temperatures, the authors have attempted to more accurately est'ablish those thermodynamic properties felt part'icularly necessary for the accurate design of L S G facilities. T o provide experimeiital data on the variation of enthalpy wit'h pressure aiid temperature, two Calorimeters were coiistructed: one a n isobaric calorimeter, and the other a combination isothermal or isenthalpic espansion calorimeter. Both calorimeters were designed to operate over a temperature range from about -300OF to +lOO°F, with pressures u p to 2500 psia. The details of construction of the isobaric calorimeter with typical isobaric enthalpy data on a natural gas mixture have been reported by Laverman and Selcukoglu (1967). The coiistructional details of the isothermal-isenthalpic espansion calorimeter and a t'abulation of the experimental data obtained for three met,haiie-ethane mixtures have been described by Xlkasab (1970). To improve t'lie correlations available to predict the properties of hydrocarbon gas mistures, modifications were made in the esisting Benedict-Webb-Rubin ( B K R ) equation of state utilizing the available thermodynamic data on the light hydrocarbons, especially in the cryogenic temperature range. .I procedure was developed and reported by Lee, et al. (1969), whereby the B K R equation could be made t o fit
Currently with Signode Corporation, Glenview, Ill. 60025. To whom correspondence should be sent.
thermodynamic data particularly well at' and near tlie critical point of the fluid. Lee reported the resulting U V R coilstants for pure methane. Subsequently, this procedure was applied to many other fluids, especially those which are present in natural gas mistures. This paper presents a set of 13KR Coefficients for ethane determined from existing thermodynamic data using tlie same procedure reported by Lee. The resulting tliermodynamic properties predicted by the BTTR equation of state utilizing these methane and ethane coefficie1it.s are compared with the isothermal and isenthalpic esperimental data determined by Xlkasab (1970) on three nietliane-ethane mixtures. Equations for @, c p , p, and H from the BWR Equation of State
This section describes the equation used to cnlculate the thermodynamic propert,ies 4, c p , p , aiid H , which are subsequently compared n?th those esperimeiitnlly determined by &ilkasah(1970). The mixt,ure compositions for the data of .Ilkasab (1970) may be found iii T:ible I. The function forms of t'liermodynamic properties derived from the B V R equation of state are given in Table I1 (eq 1-5). The only difference bet'ween t,he equat,ioii of state as presented here and t h a t originally developed by Benedict, et al. (1940), is that the const'ant Co is treated as a polynomial in teniperature T as given in Tables I11 aiid IV. The isothermal Joule-Thomson coefficient of a gas can be defined as the effect of pressure on enthalpy changes a t a constant temperature (eq 6). Since the B K R equation is in 4 the form of P
=
=
(g)
P ( V , T ) ,the above thermodynamic expresInd. Eng. Chem. Fundam., Vol. 10, No. 2, 1971
237
which can be used in conjunction with a P-V-T equation of state.
Table 1. Mixture Compositions for Data of Alkasab (1970) Component
CHI C2H6
C4H10
Nz
-Composition Mixture I
73.73 26 24 0 00 0 03
(mole Mixture II
49.08 50 60 0 03 0 29
%I-
cp
Mixture 111
22.86 76 75 0 06 0 33
=
cpo - R
-T (9)
l17hen eq 9 is applied to the BWR equatlon of state, the result is eq 3 given in Table 11.
Table 11. Function Form of Thermodynamic Properties Derived from the BWR Equation of State
P =
9
--
(4)
CP
The adiabatic Joule-Thomson coefficient defined as
Table 111. BWR Coefficients for Methane"
Bo
=
p
of a gas is
0.8507188803 X 10'
AO = 0.7994715859 X
l o 4
CO = 0.2613131247 X lo9 (for T 2 343.39"R) Co = 164791560.0 469982.07T 2163.4179T2 - 16.29545T' 0 .027094041T4 - 0,0000077252607T5 (for T < 343,39"R) a = 0.3269191668 X 104 b = 0.8906376967 X loo c = 0.5668514898 X l o 9 u a = 0.1547753824 X lo4 y = 0.1497 X lo1 a Units: psia, O R , fta/lb-mole. R = 10.73147 psia ft3/lbmole OR.
+ +
+
(10)
It can be showii that p may be expressed in terms of 4 and c p as shown by eq 4 in Table 11. For computational purposes, the values of 4 and c p were first' computed using eq 7 and 8, and then the value of p was computed using eq 4. The thermodynamic relationship used to calculate H T H T ' , the isothermal enthalpy difference, is eq 11, where
(11) sion should be expressed in terms of P, V, and T to facilitate differentiation. Equation 7 may be used to calculate @ from the BWR equation of state. The resulting equation for 9
(7) obtained by proper differentiation of eq 1 is given in Table I1 by eq 2. The specific heat a t constant pressure is defined by eq 8. CP
=
g)
Again, we express c p in terms of thermodynamic relationships 238
Ind. Eng. Chem. Fundam., Vol. 10, No. 2, 1971
H T " , the zero pressure enthalpy of the gas a t temperature TI may be calculated from eq 12. n'ote that c p o is the zero presHT"
=
HTO"
+
ST:
cpodT
(12)
sure heat capacity of the fluid, which is a function of temperature, Values of cpo for methane and ethane were taken from Din (1961). When eq 6 is applied to the BWR equation of state, the result is eq 5 in Table 11. It is to be noted that eq 5 is similar to that reported by Barner and Adler (1968), except that they also included the effect of a temperaturedependent BWR coefficient y.
Table IV. BWR Coefficients for Ethane"
Bo A0 Co Co
Co
a b aa c y a
Units: psia,
OR,
0,9481922464 X 10' 0.1402976650 X lo5 (for T 549.9'R) 0,2633882741 X 10" -0.90376821 X lo9 (0.26240433 X 108)T - (0.28636297 X 104)T2 - (0,73992566 X 103)T3 (0.37695497 X 101)T4 - (0,85961743 X 10-2)T5 (0,95829776 X 10-j)T6 (for 251.33 T < 549.9OR) - (0,42360687 X 10F8)T7 = 0.26843116 X 10" - (0 11518271 X 10'O)T (0.20124041 X 108)TZ- (0,18112713 X 106)Ta (0,92484496 X 10a)T4- (0,26930434 X 10')Tj (0,41323992 X 10-2)T6 - (0,25532471 X 10-j)T7 (for T < 251,33'R) = 0.2421798875 X lo5 = 0.2961269618 X lo1 = 0,2439497392 X lo6 = 0.7372846013 X 10'O = 0.3031 X 10'
= = = =
+
>
+ +
