CHAPTER 8 VAPOR-LIQUID EQUILIRRIUM 8-O Introduction Fig. 8-0.1 Fig. 8-0.2
K-VALUES
PAGE 8-l .............................................. Convergence Pressure in the Binary System Ethane8-2 n-Heptane . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Convergence Pressure in the Ternary System Methane-Propanen-F’entane . . . . . . . . . . . . . . 8-2
8A Vapor-Liquid Equilibrium K-Values for Hydrocarbon Systems 8Al. Vapor-Liquid Equilibrium K-Values for Hydrocarbon Systems Procedure 8Al.l Vapor-Liquid Equilibrium K-Values for Hydrocarbon Systems . . . . . . . . . . . . . . . . . . . . Procedure 8Al. 1A Vapor-Liquid Equilibrium K-Values for Hydrocarbon Systems in Area A. . . . Procedure 8Al. 1B Vapor-Liquid Equilibrium K-Values for Hydrocarbon Systems in Area B . . . . . . Procedure 8Al .lC Vapor-Liquid Equilibrium K-Values for Hydrocarbon Systems in Area C . . . . . . Procedure 8Al .lD Vapor-Liquid Equilibrium K-Values for Hydrocarbon Systems in Area D . . . . . . ‘LA’
8-5 8-9 8-11 8-13 8-15
Fig. 8A1.2
Convergence Pressures of Typical Refinery Mixtures . . , . . . . . . . . . . . . . . . . . . . . . . . 8-20
Fig. 8A1.3
Convergence Pressures of Binary Systems. Methane, the Lightest Component. . . . . . . . 8-21
Fig. 8A1.4
Convergence Pressures of Binary Systems. Ethane, the Lightest Component. . . . . . . . . . 8-22
Fig. 8A1.5
Convergence Pressures of Binary Systems. Propane, the Lightest Component. . . . . . . . . 8-23
Fig. 8A1.6
Convergence Pressures of Binary Systems. n-Butane, the Lightest Component. . . . . . . . 8-24
Fig. 8A1.7
Convergence Pressures of Binary Systems. n-Pentane, wHexane, and n-Heptane, the Lightest Component . . . . . . . . . . . . . . . . . . 8-25
Fig. 8A1.8
Convergence Pressures of Binary Systems. Ethene, the Lightest Component. . . . . . . . . . 8-26
Fig. 8A1.9
Convergence Pressures of Binary Systems. Propene, the Lightest Component. . . . . . . . . 8-27
Fig. 8A1.10
Pressure Parameter Requirements for the K-Nomograph . . . . . . . . . . . . . . . . . . . . . . . 8-28
Fig. 8Al.l 1
Grid, Convergence, and System Pressure Relationship . . . . . . . . . . . . . . . . . . . . . . . . . . . 8-29
Table 8A1.12
Volatility Exponent for Pure Hydrocarbons and True Boiling Point 50 F Cuts for Equation (8Al.lA-1 ) . . . . . . . . . . . . . . . . 8-30
API TECHNICAL DATA BOOK
PAGE Low-Temperature Vapor-Liquid Equilibria for Hydrocarbon-Hydrocarbon Systems. -260Fto 100FRange... . . . . . . . . . . 8-31 Fig. 8A1.14 High-Temperature Vapor-Liquid Equilibria for Hydrocarbon-Hydrocarbon Systems. 40 F to 800 F Range. . . . . . . . . . . . . . 8-32 Vapor-Liquid Equilibrium K-Values for Systems Containing Aromatic Hydrocarbons Fig. 8A1.13
8A2.
Fig. 8A2.1
J’
i
Activity Correction for Mixtures Containing Aromatics . . . . . . . . . . . . . . . . . . . . . . 8-33
8B Vapor-Liquid Equilibrium K-Values for Systems Containing Hydrocarbons and Hydrogen 8Bl. Vapor-Liquid Equilibrium K-Values for Systems Containing Hydrocarbons and Hydrogen Procedure 8Bl.l Vapor-Liquid Equilibrium K-Values for Systems Containing Hydrocarbons and Hydrogen . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 8-37 Fig. 8B1.2 Hydrogen K-Values in Hydrogen-Hydrocarbon Systems . . . . . . . . . . . . . . . . . . . . . . . . . 8-41 Fig. 8B1.3 K-Value Correction for Hydrocarbons in Hydrogen-Hydrocarbon Mixtures . . . . . . . . 8-42 Methane K-Values in the Hydrogen-Methane Fig. 8B1.4 System . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 8-43 8C Vapor-Liquid Equilibrium K-Values for Systems Containing Hydrocarbons and Nonhydrocarbon Gases 8Cl. Vapor-Liquid Equilibrium K-Values for Systems Containing Hydrocarbons and Nonhydrocarbon Gases Vapor-Liquid Equilibrium K-Values for SysProcedure 8Cl. 1 tems Containing Hydrocarbons and Nonhydrocarbon Gases . . . . . . . . . . . . . . . . . . . . . 8-45 Fig. 8C1.2 Low-Temperature Vapor-Liquid Equilibria for Hydrocarbon-Nonhydrocarbon Systems. -260FtolOOFRange. . . . . . . . . . . . . . . . 8-47 Fig. 8C1.3 High-Temperature Vapor-Liquid Equilibria for Hydrocarbon-Nonhydrocarbon Systems. 40Fto8OOFRange. . . . . . . . . . . . . . . . . . 8-48 Bibliography . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 8-49
‘-.J
CHAPTER 8 VAPOR-LIQUID EQUILIBRIUM K-VALUES 8-O
INTRODUCTION
Vapor-liquid equilibrium relationships are conveniently defined in terms of the distribution coe5cient, &=y6/xi. If the components form an ideal solution in the liquid phase and if the saturated vapors of the individual components are perfect gases, the system may be considered an ideal system. Under these conditions, Raoult’s and Dalton’s laws apply and: (8-0.1)
Where: &=vapor-liquid equilibrium constant for component i at the given temperature and pressure. y6 = mole fraction of component i in the vapor. x6 = mole fraction of component i in the liquid. p: = vapor pressure of component i. 97 = total pressure of the system. This relationship is valid only for ideal systems, but it may be used as a reasonably good approximation for systems of close-boiling homologs at low pressures (less than approximately 30 psia) where the vapors of the individual components do not deviate appreciably from perfect gas behavior. The relationship given as equation (SO.1 ) does not hold at elevated pressures or for mixtures that do not obey Raoult’s law. Further, it can not be used if the temperature is above the critical point of any of the components. The concept of fugacity was introduced as a more convenient and more generally useful function for equilibrium calculations. The ideal K-value was defined as:
K ,,,a,=+$
4
the higher pressures. Two approaches have been used to incorporate the effect of composition into the calculation of equilibrium data: further development of the fugacity relationships and the introduction of a thiid parameter, the convergence pressure. The correlations given in this chapter are based on the latter approach. Although the correlations based on fugacity are not used in this book, the following remarks are included because these procedures are frequently encountered and used. When vapor and liquid phases are in equilibrium, the fugacity of each component in the liquid phase is equal to its fugacity in the vapor phase, f7L=f;v. Therefore, p 2 XL K,&i$, % --.---z-z-
xi
frvxc
P -
%
71
1 -
7r
(8-0.3)
0
Where: fSL= fugacity of component i in the liquid-phase mixture. f?‘= fugacity of component i in the vapor-phase mixture. The relationship may be rewritten in two ways: 7” (8-0.4) and
(g-0.2)
Where: fiL=fugacity of component i in the pure liquid state at stated system temperature and pressure. f6v= fugacity of component i in the pure vapor state at stated system temperature and pressure. The fugacities are obtainable from one of a number of generalized fugacity charts or from fugacity function tables such as given in Chap. 7. The ideal K-values for each component are a function of temperature and pressure only. Although the ideal K-value is a good approximation for many real physical situations, it is unsatisfactory for high pressures, low temperatures, and where the mixtures are increasingly complex. Particularly important is the effect of mixture composition on the K-value at
Where: L-C= coe5cient of component i in the Y’ --fi -activity liquid mixture.
f4L - fugacity coe5cient of component i as a vi=-,r
pureliquid.
P QS=z =fugacity coefficient of component i in the vapor mixture.
A number of the better known K-value correlations in which the effect of mixture composition is one of the correlating parameters are based on these fugacity relationships. The Kellogg or Polyco charts (4)) derived from the Benedict-Webb-R&m equation of state, are 8-1
API TECHNICAL DATA BOOK
based on equation (S-0.3). Edmister and Ruby (16) and DePriester ( 13) recorrelated the Kellogg charts using the relationship given in equation (S-0.4). All of these methods used the molal average boiling point (MABP) as the correlating composition parameter. Chao and Seader (8) developed a general correlation for computer use based on the relationship given as equation (8-0.5). The alternate composition correlating parameter is convergence pressure, and a number of K-value correlations are based on this. Among these are the NGPA (18), Whm (50), Cajander, et al. (7), and Hadden and Grayson (23) methods. Convergence Pressure: The convergence pressure of a hydrocarbon system is the pressure at which the vapor-liquid K-values of all the components of a system appear to converge at K= 1 at the system temperature. The concept is illustrated for a binary system in Fig. 8-O. 1, where the left portion is the conventional pressure-temperature phase diagram similar to that discussed in Chap. 4 and the right portion is a corresponding pressureK-value diagram for a constant temperature The phase boundaries are defined in the left diagram by the vapor pressure lines of the pure components and the critical locus of their binary mixtures. In the right-hand diagram, the pressure-K-value relationship forms a loop which crosses the K= 1 line at two pressures: where the pressure equals the vapor pressure of the higher boiling constituent and at the convergence pressure of the system. Provided the system lies between the critical temperatures of the binary components, the prediction of convergence pressure depends on the temperature only and is based on the experimental critical locus data for the system. For multicomponent systems, however, the liquid-phase composition as welI as the temperature must be considered. Convergence pressures for these systems can be obtained by treating the mixtures as a fictitious binary (18,23, 30). In the ternary system of methane-propane-n-pentane, for example, the propane-n-pentane pair may be assumed to be the higher boiling component of a fictitious binary with methane the other component. For the ternary system in which the ratio of propane to n-pentane remains constant (1.5 moles per mole), the K-values are shown in Fig. 8-0.2.
-.J’
FIG. I-OA--Convergence Prestmre in the Ternary Sptem Methane-Propane-d’entane (22).
Also shown are the critical locus data for each binary of the system. The transfer of convergence pressure from the pressure-K-value graph to the pressure-temperature graph defines a new critical locus shown as a dashed line in the figure. It is important to note, as confirmed in Fig. 8-0.2, that the convergence pressure is a function of the temperature and of the liquid-phase composition exclusive of the lightest component concentration. Hadden (22) developed the method of estimating convergence pressures of more complex multicomponent mixtures which is outlined in detail in the procedures of this chapter. Hydrocarbon System Equilibrium Data: Vaporliquid K-values of hydrocarbon mixtures may be estimated from the nomographs of Procedure 8Al.l. The convergence pressure parameter necessary in the Calculation may be estimated by the methods and from the graphs provided as part of the procedure. For hydrocarbon systems containing aromatic hydrocarbons, the activity corrections given in Fig. 8A2.1 must be applied. In the fractionation of narrow-boiling mixtures, the accuracy of the K-values becomes increasingly important, and values obtained by the generalized correlation given as Procedure 8Al.l are usually not suitable. This is particularly true for fractionations of essentially binary systems such as ethane-ethene, propane-propene, n-butane-isobutane, ethane-propane, propane-butane, etc. Experimental data specific to the system should be used in preference, and the reader is referred to the extensive bibliographies of the literature ( 10, 11,19,24, 26, 33, 44, 45, 46). The procedure is also not suitable for mixtures which may form azeotropes. Hydrocarbon-Hydrogen Equilibrium Data: The
TEMPERATURE, F
K
r’o
FIG. 8414nvergence Pressure in the Binary System Ethanen-Heptane (22).
8-2
K-values for systems of hydrocarbons and hydrogen can be obtained from Procedure 8Bl.l. The hydrogen K-values are obtained from a chart on which the system temperature and pressure and the MABP of the hydrogen-free liquid are parameters. The hydrocarbon Kvalues are obtained from the charts of Procedure 8Al.l and corrected for the presence of hydrogen. The method is applicable to pressures up to 4,500 psia and temperatures from -260 F to 800 F. Hydrocarbon-Nonhydrocarbon Gas Equilibrium Data: For systems containing a hydrocarbon and a
. ,
API TECHNICAL DATA BOOK
nonhydrocarbon gas other than hydrogen, Procedure 8Cl.l should be used. The method is limited to certain specific systems and to the temperature and pressure range of the experimental data from which it was developed. In no case should it be used for system pressures above 1,000 psia. For temperature and pressure conditions beyond the range of Procedure 8C1.1, for certain systems not included in the procedure, or where an electronic computer method is preferred, the Chao-Seader correlation (8) and Grayson-Weed correlation (20) are recommended. A computer program for Chao-Seader K-values
is sold by the Natural Gas Processors Association (specify machine size and type, core storage, and number of tapes). Where experimental data are available, they should be used in preference to the generalized correlations when the highest accuracy is required. A comprehensive bibliography (49) of the literature is available from the American Petroleum Institute. Note: A report which documents the basis upon which the
material in this chapter has been selected has been published
by the American Petroleum Institute as Documentation Report No. 8-66.
8-3
8Al .l
PROCEDURE 8Al.l VAPOR-LIQUID EQUILIBRIUM K-VALUES FOR HYDROCARBON SYSTEMS Discussion
Vapor-liquid K-values for hydrocarbon mixtures are estimated from nomographs having a temperature-pressure grid, logarithmic K-value scale, and component scale. To use the nomographs, a pressure-temperature point for the temperature-pressure grid must first be determined. This pivot point is a function of the operating pressure and temperature and of a composition parameter, the convergence pressure, pov. Detailed procedures for calculating and applying this parameter are provided in this section. For systems containing aromatics, the activity corrections given in Fig. 8A2.1 must be applied. The K-values are calculated by one of several paths, depending on the properties of the system and on the operating conditions. The methods of calculation also vary with what is known and what information is desired (e.g., bubble-point, dew-point, and equilibrium flash conditions) for the system. Starting with a known or estimated liquid-phase composition and known or assumed values for the operating temperature, Top, and operating pressure, pop, the calculation is made according to the method illustrated in the following diagram and steps. The tinal calculations are to be made using one of subsidiary Procedures 8Al.lA through 8Al.lD. Most of the systems encountered can be calculated with Procedure 8Al.lA, 8Al.lB, or 8Al.lC, requiring only an approximate convergence pressure. Procedure
(See Procedure Diagram for K-Value Calculations.) Step 1: If the operating temperature is equal to or less than the true critical temperature of the “lightest component” (Top< T,z), use p 00 = pOi and proceed to Procedure 8Al.lB. The lightest component for this procedure is the most volatile component having at least 0.1 mole percent in the liquid phase (see Examples). If the operating temperature is equal to or greater than the true critical temperature of the “average heavy component” less 50 F (T.,>T,n -50 F), proceed to Procedure 8Al.lD. The average heavy component is the average of all components except the lightest component in the liquid phase. Disregard the heaviest components which together total less than 2 mole percent of the liquid. If the operating temperature is higher than the true critical temperature of the lightest component and lower than the true critical temperature of the average heavy component less 50 F (Tot < T o , < Tci, - 50 F), make a quick estimate of the convergence pressure. Fig. 8A1.2 is for typical petroleum mixtures, and Fig. 8A1.3 through 8A1.9 are for other mixtures. The curve to be used is the one that has a low-temperature terminal corresponding to the lightest component in a given mixture and a high-temperature terminal corresponding to the average heavy component in the mixture. Siep 2: Branch to Procedure 8Al.lA, 8ALlB, 8Al.lC, or 8Al.lD according to the seleo tion routine outlined hereinafter and given schematically in the Procedure Diagram for K-Value Calculations. Step3: Check the requirements for the K-nomograph corrections by locating a point corresponding to the operating pressure and the quick estimate of convergence pressure in Fig. 8A1.10. Proceed to Procedure 8Al.lA, 8Al.lB, 8Al.lC, or 8Al.lD depending on whether the point is located in Area A, B, C, or D.
8-5
8Al.l Procedure Diagram for Note: The K-nomographs are for identifiable hydrocarbons having normal boiling points less than 210 F. For higher boiling pure hydrocarbons and for petroleum fractions charao terized by a TBP curve, the volatility exponent from Table 8A1.12 must be applied.
Calcuhions
NOMENCLATURE Top = operating temperature, in deKNOWN OR ESTIMATED grees fahrenheit. T ot = true critical temperature of COMPOSITION AND To lightest component, in degrees fahrenheit. T.I = true critical temperature of average heavy component, in degrees fahrenheit. pov = convergence pressure, in pounds per square inch absolute. IS Top > T,I ? po8 = true critical pressure of lightest component, in pounds per I1 square inch absolute. I pap = operating pressure, in pounds per square inch absolute. YES PI= grid pressure, in pounds ner I square inch absolute.
1
NO
1s Top < &h-50 F) ?
4 Top’(T,h-~o F)
QUICK EST. OF pcv FIGURES 8A1.2 TO 8A1.9
WITH KNOWN OR ASSUMED pop, USE AREA
AREA C PROC. 8Al.X
AREA B PROC. 8AllB 1
AREA D ,PROC. 8Al.lD
1
pg FROM
pg FROM
FIG. 8A1.11
FIG. 8A1.11
1 CONNECT(Top,pdp) TO K=‘.% ON T.HlS LINE IS PIVOT ON K+NOMOGRAPHS SEE NOTE
1
Y
T
WTopt pg)FOR PIVOT POINT ON K-NOMOGRAPHS
USE (Topt~op)FOR PIVOT POINT ON K-NOMOGRAPHS
USE DETAILED
SEE NOTE
SEE NOTE
1
+
I
8-6
AREA A PROC. 8Al.lA
1
.
DESIRED K-VALUES
CALC. PROC. FOR pcv b
SEE NOTE 1 I
8Al.J
COMMENTS
ON
PROCEDURE
8Al.l
Purpose This procedure is to be used to estimate hydrocarbon vapor-liquid equilibrium K-values. For systems containing aromatics, the activity correction of Fig. 8A2.1 must be applied. For h y d r o g e n , Procedure 8Bl.l is to be used, and for other nonhydrocarbon gases, Procedure 8Cl.l
is given. Because of the large number of calculational routes used to estimate K-values, the remainder of this procedure is subdivided into four separate supplementary procedures (8Al.lA through 8Al.lD), each of which applies to a different mode of calculation. Fig. 8A1.2 through 8Al.11, Table 8A1.12, and Fig. 8A1.13 and 8A1.14 also are included in this procedure. Limitationa
The correlation is limited to hydrocarbon mixtures of known composition and to petroleum fractions at temperatures from -260 F to 800 F and at pressures up to 10,000 psia. Do not IIS& this procedure for binary mixtures of close-boiling hydrocarbons or for mixtures which may form azeotropes. Reliability
The K-values determined using this procedure have an average deviation from experimental values of 9 percent for binary paraffin-parafthr or parat&olefin mixtures and 13 percent for multicomponent par& or parattin-olefin mixtures. At pressures below 1,000 psia, the accuracy is somewhat better than these overall values. Notation
The notation used is defined in the nomenclature of the Procedure Diagram for K-Value Calculations. Dashed lines in Fig. 8A1.3, 8A1.4, and 8A1.8 indicate systems that may exhibit Type II or Type III critical loci. (See Chap. 4.) Some lines in Fig. 8A1.7 are shown broken to eliminate the confusion of crossing curves. The pa&in hydrocarbons shown in Fig. 8A1.2 through 8A1.9 are designated as C to CU, where the subscripts indicate the number of carbon atoms. Branched paraffms are designated as i-C, for 2-methylpropane (isobutane) and i-C& for 2-methylbutane (isopentane). Olefins are designated as CL= for ethene, C’ for propene, and l-C? for 1-butene. Special
Comment
Enlarged copies of Fig. 8A1.13 and 8A1.14 are given in the back of the binder. Literature SoIm?es The procedure is from Hadden and Grayson, Hydrocarbon Process. Petrol. Refiner 40 C91 207 (1961); copyrighted in 1961 by Gulf Publishing Company, Houston, Texas. It is supplemented by material from the Engineering Data Book, Socony Mobil Gil Company, Inc., New York. Examplea
A, Find the terminals of the convergence pressure graphs of a mixture having a boiling range equivalent to that for methane (c1) to decane ( C,O) : Light component: G (methane) 6-t-G --cd Average heavy component: 2 Fig. 8A1.3 would be used for the convergence pressure. B. Find the terminals of the convergence pressure graphs of a mixture having a boiling range equivalent to that from propane (Ca) to nonane (C) : Light component: CI (propane) Average heavy component: 9 = CS.S (use CL) Fig. 8Al.S
would be used for the convergence pressure.
8Al .l C. Find the terminals of the convergence pressure graphs of the following mixtures, AandB: I
Component Number of Carbon Atoms ... : 3 4 5 6 7 ;: lot 11t Total
3
Mole Fraction * Mixture A Reflux Drum Liquid Negligible o.ooo9 0.018 Light component 0.051 1 0.080 Average heavy 0.274 0.363 component
\ Mixture B Reboiler Bottoms 0.17 x 1W’ 0.67 )( 1O-u 0.43 x 1~ Negfigible 0.61 x lO-‘ Light component 0.009 0.049 0.130
0.045 J 0.168 0.21 x lOA 0.16 X’ lad Negligible 0.32 X IO-PD 0.17 x. 1V 1.000+
0.188 0.103 0.186 0.083 0.252 1.000+
I
Name Hydrogen Methane Ethane Propane Butane Pentane Hexane Heptane “225”* “‘275’9 “325’9 “3759
Average heavy component =w = Ga (use CS) Fig. 8A1.3 would apply. ical computer tray-to-tray results. 2E 4 2E0i&e~oiut of a ffaotkm having a 50 P boiling range. l
8-8
From
Average heavy component 1 J
Average heavy component ,cs+cu.+ 2 Fig. 8A1.6 would apply.
8Al .lA
PROCEDURE VAPOR-LIQUID
EQUILIBRIUM
8Al.lA
K-VALUES FOR AREA A
HYDROCARBON
SYSTEMS
IN
Procedure 8Al.l is to be used for all preliminary calculations toward estimating K-values for hydrocarbons. If the estimated convergence pressure and operating pressure conditions are such that the point with these coordinates falls in Area A of Fig. 8A1.10, the following steps are to be followed to complete the estimation of the K-values. Procedure
Step For identifiable hydrocarbons having normal boiling points below 210 F, locate the point on the temperature-pressure grid of Fig. 8Al. 13 or 8A1.14 corresponding to the operating temperature and pressure. Step 2: Lay the hairline of a nomograph reader through this point and through the component point (or through the boiling point of the component, if the component is not shown on the scale). Step 3: Read the desired K-value at the point of intersection of the hairline with the K-scale. When u&a the low-temperature nomograph (Fig. 8A1.13) for methane in light hydrocarbons, multiply the methane nomograph K-value by the correction indicated on the inserted chart. Step4: For identified hydrocarbons having normal boiling points above 210 F and for petroleum fractions characterized by a true boiling point (TBP) curve, the K-value is calculated as follows. Determine the K-values of ethane and n-heptane at the operating temperature and operating pressure of the system in accordance with Steps 1 through 3. Then, for the components of the mixture (normal boiling point above 210 F), determine the volatility exponents, b, of the identitied hydrocarbons or of the 50 F TBP cuts of the petroleum mixture from Table 8A1.12. Finally, solve equation (SAl.lA-1) for the K-value of each pure compound or portion of the petroleum fraction:
K= xK+4 b K7 (-1
(SAl.lA-1)
Where: K = K-value of the cut or high-boiling pure hydrocarbon. K, = K-value of ethane at the temperature, pressure, and convergence pressure of the
system.
K, = K-value of n-heptane at temperature, pressure, and convergence pressure of the
system. b = volatility exponent from Table 8A1.12. In effect, this procedure extends the component scale to cover components with boiling points greater than 210 F.
8-9
8Al.lA COMMENTS ON PROCEDURE 8Al.lA
This procedure is to be used to complete the estimation of vapor-liquid equilibrium K-values for hydrocarbons when the operating conditions are such that the point falls in Area A of Fig. 8A1.10. The preliminary calculations are performed using Procedure 8Al.1, which is the master procedure for estimating hydrocarbon K-values under any conditions. Special Comment
For Limitations, Reliability, Notation, and Literature Sources, see Comments on Procedure 8Al.l. Examples A. What is the K-value for methane in an unstabilized gasoline at 100 F and 200 psia? From curve D, Fig. 8A1.2, the convergence pressure is approximately 3,000 psia. In
Fig. 8A1.10, the combination of operating and convergence pressure falls in Area A. Hence, read K directly in Fig. 8A1.14 for the operating temperature and pressure. The resulting K-value is 14.7 using the C to G component point for methane (see example figure). B. What is the K-value at 100 F and 200 psia for a component of the gasoline in Example A having a boiling point of 190 F? As determined in Example A, the operating conditions are in Area A, so the K-value can be read directly in Fig. 8A1.14. The result is 0.0188 (see example figure).
V,’ \a/ 63’ %/tbf .’
,’
/’
I PMETHANE ( I N C7 THRU C,2 A N D GASOLINE)
14.7
.190 F
C. What is the K-value at 500 F and 100 psia for n-decane in a Mid-Continent crude oil containing the naturally occurring methane and all other heavier components? From curve M, Fig. 8A1.2, the convergence pressure is approximately 7,000 psia at 500 F, so the point for the operating and convergence pressure falls in Area A in Fig. 8A1.10. The K-values would normally be read directly in Fig. 8Al.14 for the operating temperature and pressure. However, inasmuch as the boiling point is higher than 210 F, the K-value for n-decane has to be computed from K-values for ethane (KS) and heptane (K,), determined in Fig. 8A1.14. Use the relation given in equation (8Al.lA-1). From Fig. 8A1.14, KS = 19.3 and K7 = 2.40 at 500 F and 100 psia; and, from Chap. 1, the normal boiling point of ndecane is 345 F. From Table 8A1.12, b = 0.560. 2.40 2.40 Km= 0.m = @-jjJjE = 0.747 D. What is the K-value for the 700 F mid-boiling-point fraction with the other circumstances the same as in Example C? Inasmuch as the same system and conditions prevail as for Example C, KS and KT are the same, and the only change is for the volatility exponent, b. From Table 8A1.12, b = 2.801. 2.40 = 0.0070 K= 19.3 s.am 2.40 (--> 8-10
‘d
8Al.lB
i
PROCEDURE 8Al.lB VAPOR-LIQUID EQUILIBRIUM K-VALUES FOR HYDROCARBON SYSTEMS IN AREA B Discussion Procedure 8Al.l is to be used for all preliminary calculations toward estimating K-values for hydrocarbons. If the estimated convergence pressure and the operating pressure conditions are such that the point with these coordinates falls in Area B of Fig. 8A1.10, or if the operating temperature is less than or equal to the critical temperature of the light component, the following steps are to be followed to complete the estimation of K-values. Procedure Step I: For identifiable hydrocarbons having normal boiling points below 210 F, determine the grid pressure from Fig. 8Al.11 for the estimated convergence pressure and operating pressure. Step2: Locate the point on the temperature-pressure grid (Fig. 8A1.13 or 8A1.14) corresponding to the temperature and pressure of operation. Step 3: Connect the temperature and pressure point to the K = 1.00 point. Step4 Spot the point on this line where it is crossed by the pressure equal to the grid pressure. Step 5: Lay the hairline of a nomograph reader through this grid point and the component point. Step 6: Read the K-value at the point of intersection of the hairline with the K-scale. Step 7: For identified hydrocarbons having normal boiling points above 210 F and for petroleum fractions characterized by a true boiling point (TBP) curve, the K-value is calculated as follows. Determine the K-values of ethane and n-heptane at the operating temperature, operating pressure, and convergence pressure of the system in accordance with Steps 1 through 6. Then, for the components of the mixture (normal boiling point above 210 F), determine the volatility exponents, b, of the identified hydrocarbons or of the 50 F TBP cuts of the petroleum mixture from Table 8A1.12. Finally, solve equation (8Al.lA-1) for the K-value of each pure compound or portion of the petroleum fraction. In effect, this procedure extends the component scale to cover components with boiling points greater than 210 F.
8-11
8Al.lB COMMENTS ON PROCEDURE 8Al.lB Purpose
This procedure is to be used to complete the estimation of vapor-liquid equilibrium K-values for hydrocarbons when the operating conditions are such that the point falls in Area B of Fig. 8A1.10 and under certain other conditions outlined under Discussion. The preliminary calculations are performed using Procedure 8Al.1, which is the master procedure for estimating hydrocarbon K-values under any conditions. Special Comment
For Limitations, Reliability, Notation, and Literature Sources, see Comments on Procedure 8Al.l. Rxamplee A. What is the K-value at 400 F and 100 psia for n-butane in a depropanized 400 F end-
point gasoline system? The estimated convergence pressure is 680 psia from Fig. 8A1.2, curve A. The combination of operating and convergence pressure falls in Area B in Fig. 8A1.10. Hence, the grid pressure correction is required before reading the K-value. In Fig. 8Al.11, a grid pressure of 117 psia is read as the ordinate for the given operating and convergence pressures. Locate the operating pressure and temperature in Fig. 8A1.14. and connect this uoint to the K z f.00 point.. Spot the point on this line corresponding to the grid pressure. Connect this grid pressure point with the point on the nomograph component scale, and read the K-value for n-butane as 5.75 (see example figure). B. Compute the reboiier temperature of a gasoline stabilizer operating at 165 psia. The composition of the liquid in the reboiler is shown in the following tabulation. Assume that the gasoline has properties similar to those used in making Fig. 8A1.2. . E-C4 For the first trial, assume the reboiler temperature is 350 F. The estimated convergence pressure is 940 psia (from the propane-gasoline critical locus of Fig. 8A1.2, curve B). This system falls into Area B of Fig. 8A1.10. Therefore, a grid correction is required; From Fig. 8Al.11, the grid pressure is 190 psia. Follow Steps 2 through 4 of the procedure to determine the grid point in I Fig. 8A1.14. Using this and volatility exponents from Table 8A1.12, the K-values obtained are listed in the following tabulation: Liquid Volatility Composition, x K-Value Exponent, b (Mole Fraction) y=Kx (Fig. 8A1.14) ca . <. . . . . . . . . . . . . . . . . . . . 0.0013 ... 5.32 0.0069 n-c, . . . . . . . . . . . . . . . . . . . . . 0.0759 ... 3.00 0.2277 n-G . . . . . . . . . . . . . . . . . . . . . 0.1802 0.3063 ... 1.70 n-G . . . . . . . . . . . . . . . . . . . . . 0.2570 ... 1.01 0.2596 n-C!, . . . . . . . . . . . . . . . . . . . . . 0.1460 0.0876 0.600 235* . . . . . . . . . . . . . . . . . . . . 0.1043 O.ki.8 0.512t 0.0534 0.0918 285* . . . . . . . . . . . . . . . . . . . . 0.292 t 0.262 0.0268 335* . . . . . . . . . . . . . . . . . . . . 0.0901 0.160t 0.48 1 0.0144 385* . . . . . . . . . . . . . . . . . . . . 0.0534 0.716 0.0045 0.0837t 1.0000 Total . . . . . . . . . . . . . . . . ... ... 0.9872 In this computation, inasmuch as the summation of the vapor mole fractions, y, is less than unity, a higher temperature should be used in the next trial to vaporize more liquid. Because the trial-anderror procedure is straightforward, the additional trials are not shown here. C. What are the K-values for methane and ethane at -100 F and 100 psia in a methaneethane system? The convergence pressure from Fig. 8A1.3 is 750 psia. The combination of operating and convergence pressure falls in Area B in Fig. 8A1.10. Hence, the grid pressure correction is required before reading the K-value. In Fig. 8Al.11, a grid pressure of 115 psia is read. Following the procedure previously outlined in Example A and using Fig. 8A1.13: Methane K = 6.20( 1.047) = 6.49 where 1.047 is the correction factor for methane. Ethane K = 0.337
I
l Mid-botig oint of a etroleum fraction having a 50 F boiling range t Usin Ka = 8 40 and & = 0 600 88 read osing the pivot point for t&a problem, these K-values were @ALlA-1): calculated %y equation
8-12
8Al.lC
PROCEDURE 8Al.lC VAPOR-LIQUID
EQUILIBRIUM
K-VALUES FOR AREA C
HYDROCARBON
SYSTEMS
IN
Procedure 8Al.l is to be used for all preliminary calculations toward estimating K-values of hydrocarbons. If the estimated convergence pressure and the operating pressure conditions are such that the point with these coordinates falls in Area C of Fig. 8A1.10, the following steps are to be followed to complete the estimation of the K-values. Procedure
Step For identifiable hydrocarbons having normal boiling points below 210 F, determine the grid pressure from Fig. 8Al.11 for the estimated convergence pressure and operating pressure. Step 2: Locate the point on the temperature-pressure grid (Fig. 8A1.13 or 8A1.14) corresponding to the grid pressure and operating temperature. Step 3: Lay the hairline of a nomograph reader through this point and the component point and read the K-value at the point of intersection of the hairline with the K-scale. Step4: For identified hydrocarbons having normal boiling points above 210 F and for petroleum fractions characterized by a true boiling point (TBP) curve, the K-value is calculated as fohows. Determine the K-values of ethane and n-heptane at the operating temperature, operating pressure, and convergence pressure of the system in accordance with Steps 1 through 3. Then, for the components of the mixture (normal boiling point above 210 F), determine the volatility exponents, 6, of the identified hydrocarbons or of the 50 F TBP cuts of the petroleum mixture from Table 8A1.12. Finally, solve equation (8Al.lA-1) for the K-value of each pure compound or portion of the petroleum fraction. In effect, this procedure extends the component scale to cover components with boiling points greater than 210 F.
8-13
8Al .lC
J
COMMENTS ON PROCEDURE 8Al.lC Purpose
This procedure is to be used to complete the estimation of vapor-liquid equilibrium K-vahres for hydrocarbons when the operating conditions are such that the point falls in Area C of Fig. 8A1.10. The preliminary calculations are performed using Procedure 8Al.1, which is the master procedure for estimating hydrocarbon K-values under any conditions. Special Comment
For Limitations, Reliability, Notation, and Literature Sources, see Comments on Procedure 8Al.l. Example
Determine the K-value of n-per&me at 1,000 psia and 100 F in a system having a convergence pressure of 10,000 psia. Fig. 8Al.11 gives 1,000 psia as the grid pressure. The point on the pressure-temperature network in Fig. 8A1.14 corresponding to 1,000 psia and 100 F is noted. Using this pivot point, the K-value for n-pentane is found to be 0.056.
8Al.lD
VAPOR-LIQUID EQUILlBRIUM
PROCEDURE 8Al.lD K-VALUES FOR HYDROCARBON SYSTEMS IN AREA D
Discussion Procedure 8Al.l is to be used for all preliminary calculations toward estimating K-values of hydrocarbons. If the conditions are such that the desired point falls in Area D of Fig. 8A1.10, or if the operating temperature is equal to or greater than 50 F below the true critical temperature of the average heavy component, the following steps are to be followed to calculate the convergence pressure and complete the estimation of K-values. These steps are an interpolation scheme for estimating convergence pressure. Procedure Step 1: The true critical pressure and critical temperature of the average heavy component of a given mixture (exclusive of lightest component) is first calculated according to the procedures of Chap. 4. The liquid-phase mole fraction composition of the components is required. If these are not given directly, they will have to be calculated from the composition of the total material or from the vapor-phase composition data by trial and error. Step2: The average heavy component temperature-pressure (Ten, p,~) point and the operating temperature (Top) line are spotted on one of Fig. 8A1.3 through 8A1.9, whichever has the same lightest component as in the given mixture. Step 3: If the Toa, pan point falls within an area bounded by the critical loci curves for the lightest component and two heavier components, the convergence pressure for the mixture is calculated by interpolation as illustrated hereinafter, in Par. a through c. If the point falls outside the area, the convergence pressure is calculated according to Par. d. a. If Fig. 8Al.lD-a applies, the convergence pressure is given by equation (8Al.lD-1): pa = PI - (pa -Pi) ($)(%)
(8Al.lD-1) Where: p,,
= convergence pressure, in pounds per square inch absolute. pa = pressure on the superior (higher) critical locus, in pounds per square inch absolute. pt = pressure on the inferior (lower) critical locus, in pounds per square inch absolute. A, B, C, D = differences in Fig. SALlD-a. For the case where Fig. 8Al.lD-a applies and the given mixture is a ternary: P,“=P.--~P*-P~ho,.
(
%
TEMPERATURE
I
>
--F--
(8ALlD-2)
i
FIG, 8Al.lD-a.
Where: XUJ.tl=
calculated weight fraction of the middle component. E zz differences in Fig. 8Al.lD-a.
b. If Fig. SAl.ID-b applies, the convergence pressure is: PC” = ps - (P*-P‘)($)(g
(8Al.lD-3) For the case where Fig. 8Al.lD-b applies and the given mixture is a ternary: pm = pa - (pa - ps)xw, n
(8Al.lD-4)
TEMPERATURE
IT2
‘7’
IT3 I
FIG. 8Al.lD-b.
8-15
8Al.lD
c. If Fig. 8ALID-c applies, the convergence pressure is: = ps - (p. - PC)
(
+g
> (8Al.lD-5) where F and G are differences in Fig. 8AlSD-c. For the case where Fig. 8Al.lD-c applies and the given mixture is a ternary: p..=pr-(Ps-ppr)xlo,.
(8Al.lD-6)
TI TE M P E R A T U R E
T2
FIG. SAl.lD-c. d. For a mixture where the Tck, p,h point falls to the right of all loci curves, the loci curve of the mixture must be calculated and pee at Top determined. This is illustrated in Fig. IAl.lD-d. Arbitrarily increase mole fraction of lightest component so that its weight fraction equals H/J, prorate other components, and recalculate Ton, pes. If the lightest component is methane, ethene, or ethane and the assumed composition such that the critical temperature is below 100 F, then the calculated critical pressure is not reliable. Arbitrarily increase or decrease mole frao tion of lightest component to get a third Tab, pan point to bracket T.,. Draw a locus curve through the three To&, pan points using the other loci curves as guides (particularly in the lower temperature region) and then read pc,, at Top.
TEMPERATURE
j
FIG. SALID-d.
Step 4: The convergence pressure calculated as previously indicated is then used with the operating pressure to obtain a p. from Fig. 8Al.11. If the convergence pressure calculated is greater than 5,000 psia, then operating temperature and grid pressure are used as the pivot point on Fig. 8A1.13 or 8A1.14 as is done in Procedure 8Al.lC. If the calculated convergence pressure is less than 5,000 psia, then the TOp, pop point is spotted on the K-nomograph and connected to K = 1 by a straight line. Then the grid pressure is spotted on this line as the pivot point as is done in Procedure 8Al.lB.
8-16
8Al.lD COMMENTS ON PROCEDURE 8Al.lD
Purpose
This procedure is to be used to complete the estimation of vapor-liquid equilibrium K-values for hydrocarbons when the operating conditions are such that the point falls in Area D of Fig. 8A1.10 or under certain other circumstances as noted under Discussion. The Preliminary calculations are performed using Procedure 8Al.1, which is the master procedure for estimating hydrocarbon under any conditions. Special Comment
For Limitations, Reliability, Notation, and Literature Sources, see Comments on Procedure 8Al.l. Examples A. A liquid hydrocarbon stream having the composition tabulated below is to be processed
at 150 F and 600 psia. What is the convergence pressure to be used in the K-value correlations? A quick estimate of the convergence pressure from Fig. 8A1.3 is 2,400 psia using the G- CS critical locus. From Fig. 8A1.10, this system falls into Area D. Eliminate the lightest component and recalculate the mole and weight fraction compositions and obtain the critical properties of the average heavy component according to the procedures of Chap. 4. Liquid-Phase Composition * I \ Less Lightest Normal Actual Component Boiling 7 Weight ----Liz Weight Point Fraction, Fraction, Fraction, Fraction, (Degrees Molecular API Fahrenheit) Weight GlWi~ ct . . . . . . o.zo 0.015 02 Lit 0.020 0.048 0.020 0.050 -128’ &i.l 2ij’ 2 : : : : : : : : : 0.050
0.082
0.051
0.086
-43.7
44.1
147.2
0.100
0.125
0.101
0.131
+31.1
58.1
110.6
2 I:::::::
0.200
G . . . . . . . . 0.400 c . . . . . . . . . 0.220 -
0.202 0.339 0.159
-
Total 1.000 1 .ooo . Average .’ . Weight average boiling point:
0.202 0.404 0.222
-
-
1.000 ...
1.000 ...
WABP = i xr< Tat = Where:
96.9
0.212 0.355 0.166
‘11
156
209
... ... 127.3
72.2 86.2 100.2 ii.48
92.7
81.6 74.1
91.1 *-*
F
x=6 = weight fraction of component i. T Q = normal boiling point of component i. Either fahrenheit or Rankine units may be used for WABP and MABP to give the same units for the average boiling point. However, Rankine units must be used for CABP. The MABP and CABP must be in the same units to calculate MeABP. Molal average boiling point: MABP = i xi Tat = 104.5 F ‘d where xc = mole fraction of component i. Cubic average boiling point: CABP = ;; xoc Tall8 ’ = 115.4 F ( tr1 ) where x,,( = volume fraction of component i. Mean average boiling point: MeABP= MABP+CABP -1lOOF 2
Average molecular weight = 2 XC (molecular weight)‘ ‘2 AverageAPIgravity=~~lxv~
-*
= 75.48.
(API)c=91.1.
From the methods described in Chap. 4, the true critical temperature is T, = 880 R and the pseudocritical temperature is Tp. = 860 R, SO To/T,. = 1.023. From the methods given in Chap. 4, the pseudocritical pressure is ppe = 453 psia and the true critical pressure is 545 psia. Locate the true critical points T,, pa in Fig. 8A1.3. It is observed that the critical point falls between the critical loci for the binaries methane-pentane (the inferior locus) and methane-hexane (the superior locus) SO that the pseudo ternary for representing the actual (methane through heptane) mixture is methanepentane-hexane.
L
8-17
.
8Al.lD Inasmuch as the critical temperature is above the critical temperature of the inferior heavy component and the operating temperature is below this temperature, the convergence pressure is calculated for the specified operating temperature from equation (8ALlD-3). At the proposed operating temperature of 150 F, the convergence pressure on the superior locus is p, = 2,890 psia, while on the inferior locus it is pi = 2,410. = 870 - 545 = 325 psia
B = 870 - 487 = 383 psia
C=455-420=3SF E= 4SS-386=69F
$(S) =gg(%) = 0.430 Substitution into equation (8Al.lD-3)
gives the desired convergence pressure:
p,. = 2,890 - (2,890 - 2,410)0.430 = 2,684 psia
This convergence pressure should now be used to get the grid pressure from Fig. SAL1 1 before determinin g the K-values of the components in Fig, 8A1.14. B. Calculate the dew-point temperature and equilibrium liquid composition at 1,500 psia for a mixture containing 68.9, 10.8, and 20.3 mole percent of methane, propane, and pentane, respectively, in the vapor phase. This example illustrates the iterative procedure required when the liquid composition is not known. It is necessary to assume the temperature and convergence pressure and calculate an approximate liquid-phase composition to check the assumed conditions, repeating until no further change occurs. For Trial 1, assume 250 F for the temperature and read the convergence pressure from C, - 6 critical locus in Fig. 8A1.3. The estimate is p. = 1,880 psia. In Fig. 8Al.11, the grid pressure is p# = 2,940 psia.
ii
Trial 1:
Molecular Weight, API M Gravity 2 1:::: 44.i
n-Cs . . . . 72.2 Total . . .
i4i.i
92.7
0.6:9 0.108 0.203
K at 2SOF* 1.86t 0.86 0.44
...
1.00()
...
x=y/K
xM
0.3704 0 . 1 2 5 6 iii 0.4614 33.31 0.9574 38.85
x4M4
Xrc=ZX4M4
xlos (API)4
O.i426
ii.0
0.8574
79.5
1.0000
100.5
For the next trial, assume 230 F. Calculate convergence pressure from the estimated liquid composition, x0, using equation (8Al.lD-2). The binaries involved are CL - CS and Cl - CS. D=386-230~156
E= 386-206~
180 I
See Fig. 8Al.lD-a, where D and E are defined.
x~,,, = 0.1426 Pa = 2,030 psia p4 = 650 psia Using equation (8Al.lD-2), p.. = 2,030 - (2,030 - 650)0.1426% fore, from Fig. 8Al.11, pI = 3,200 psia.
= 1,803 psia. There-
Trial 2:
‘j
K at 230 F,
Cl . . . . . . . 0.6y89
p = 1,500 psia, pg = 3,300 psia 1.67t
ca . . . . . . . 0.108 n-G . . . . . 0.203
0.84 0.465
Total . . 1.000
...
x=y/K
XM
0.1286 0.4366 0.9778
iii 31.52 37.19
0.4126
x,4
Xl04
(API)4
o.iGs
ii.7
0.8475
78.4
1.0000
101.1
The assumed temperature is still too high. Assume the temperature is 220 F. It is necessary to recalculate xc,- and p., in the same way as at first. The new values are 0.1525 and 1,860 psia, for which pI = 3,000. r e a d f r o m t h e 9 0 A P I s o l v e n t p o i n t f o r m e t h a n e i n li& h y d r o c a r b o n s ( F i g . 8 A 1 . 1 4 ) . point position corresponding to 100 API from Trial 1 calculation. 8-18
t I /
8Al.lD
0.689 0.108 0.203
K at 220 F, p = 1,500 psia, pI = 3,000 psia 1.74 0.80 0.415
1.000
...
Y
C, . . . . . . . . . . . . . . . . . . . . ca . . . . . . . . . . . . . . . . . . . . n-C!s . . . . . . . . . . . . . . . . . . Total . . . . . . . . . . . . .
x=y/K
X04
0.3960 0.1350 0.4892
0.8558
1.0202
1 .oooo
o.i442
Trial 4: K at 225 F, p = 1,500 psia, pg = 3,050 psia
x=y/K
C, . . . . . . . . . . . . . . . . 0.689 c, . . . . . . . . . . . . . . 0.108 n-G . . . . . . . . . 0.203
1.75 0.820 0.435
0.3937 0.1317 0.4833
Experimental xat220F 0.390 0.133 0.477
Total . . . . . . , . . 1.000
...
1.0087
1.000
Y
A check on the convergence pressure for Trial 4 gives 1,847 psia versus 1,860 psia from Trial 3, so that the grid pressure remains fixed. An intermediate temperature of approximately 226 F to 227 F should give the fhral answer. As it is, the agreement with the experimental liquid-phase composition at 220 F in the last column is satisfactory. The operating pressure in the preceding example exceeds 70 percent of the convergence pressure, which is a reasonable upper limit for reliable K-values. The satisfactory agreement of calculated and experimental liquid compositions means that K-values in this example are correct to within 2 percent. This is better reliability for K-values than can generally be expected.
8-19
I I
.e 2.. 0.t G 3
C, F r e e Gasolines 6 w t . % c2 g
Free Gosolinc “u z 1 0 wt.xc3 g 1000 is 800 :3 Free Gasoline 1 14 wt. % c4 8 600 :2
!/ CiJ
d
800
!I
/
-100
0
(SO\;vJ.%( I/,+‘-’
=p
1
c4 A
1 \
100 2 0 0 3 0 0 4 0 0 TEMPERATURE, F
500
-200 -100
500 *i
400
0
l o o 200 TEMPERATURE,
I/
)
h’s 1 -
I 1
0
100
200
300 400
TEMPERATURE,
Stubilizers: A CA through 400 F end-point gasoline
: D
Ca through 400 F end-point gasoline G through 400 F end-point gasoline Cl through 400 F end-point gasoline
Light-hydrocarbon towers: E Cl-G F Cl-G-G-G
z K Absorbers, D L M
N 0 8-20
c1-c=-cs--c,-c5
G-C,
500
600
700
400
I
i ? 300 2 2 F!?
-100
300 F
I NO. p ,Fuel Oil
610
800
F
Reboiler and bottom Mid-stripping section Top stripping section Stabilizer feed plate:
TEMPERATURE,
trays of stabilizer of stabilizer of stabilizer top of bubble tower
NOTE:
‘Part
of
F
Procedure
8Al.l
De-ethanizer overhead Top rectifying section of stabilizer Top rectifying section of depentanizer Top rectifying section of de-ethanizer Reboiler and stripping section of butanepropane de-ethanizer In conjunction with curve J for feed plate of butane-propane de-ethanizer
crude oil flashing towers, and heavy-hydrocarbon fractionators:
Cl C1 C1 C, G’s
through through through through through
400 end-point gasoline distillate crude oil Mid-Continent crude oil No. 3 fuel oil No. 3 fuel oil 1,
In conjunction with curves L and M for estimating effect of heavy components on p,, Light crude oil flashing: absorber (light lean oil) Mid-Continent crude oil flashing: absorber (heavy lean oil) Bubble tower bottoms
CONVERGENCE PRESSURES OF
BINARY
SYSTEMS
METHANE MI
THE
LIGHTEST
COMPONENT
TECHNICAL DATA BOOK
October 1964 Approved :
MRF & WGB
8-21
vd ‘mnss3u 8-22
‘L
.I
8A1.5
lOO(
,I000
90(
900
80(
800
.-u zi lu- 70( 5 3 gj 60( a 5a
40(
FIGURE 8A1.5 CONVERGENCE
PRESSURES
OF BINARY SYSTEMS
30(
PROPANE
300
THE LIGHTEST COMPONENT TECHNICAL DATA BOOK Octdber Approved:
1964 MRF 8. WGB
700
800
200
TEMPERATURE, F
8-23
,
b,
8A1.6
800 700
600
500
400
300
200
TEMPERATURE, F 8-24
8A1.7
FIGURE 8A1.7 CONVERGENCE PRESSURES OF BINARY SYSTEMS
c-PENTANE , o-HEXANE, & n-HEPTANE T H E LiGHTEST
COMPONENT
TECHNICAL DATA BOOK O c t o b e r 1964 Approved:
MRF & WGB
TEMPERATURE, F 8-25
8A1.8 .,
mm r! FIGURE 8A1.8 CONVERGENCE
PRESSURES
O F BtNARY S Y S T E M S
ETHENE THE LIGHTEST COMPONENT TECHNICAL DATA BOOK October 1964 Approved 1
MRF 8s WGB
vsd ‘32tflSWtd 8-26
150
100
80 .-0
”
70
3Ot
TEMPERATURE, .F 8-27
. K
8A1.10
-
I I I I \ AREA D SINGLE PHASE
AREA C
It
AREA A
\
L
F I G U R E 8A1.10 PRESSURE PARAMETER REQUIREMENTS
FOR
T H E K - NOMOGRAPH
I
TECHNICAL DATA BOOK
I
I” I
I I
1964
October Approved :
MRF b WGB
I
I
I
-
NOTE: Part of Procedke 8Al.l
50 ’
500
8-28
-
I
I
III
I
/I
I
II,1
I
I
III
1000 2000 5000 lOQO0 ESTIMATED CONVERGENCE PRESSURE, pcv, psia
I mm
SYSTEM PRESSURE, psia, pop
FIGURE 8A1.11
GRID, CONVERGENCE, AND SYSTEM PRESSURE RELATIONSHIP TECHNICAL DATA BOOK October 1964 Approved : MRF &WGB NOTE: Part of Procedure 8Al.l 1 8-29
1
8A1.12
TABLE 8A1.12 VOLATILITY EXPONENT FOR PURE HYDROCARBONS AND TRUE BOILING POINT (TBP) 50 F CUTS FOR EQUATION (8Al.lA-1) (Part of Procedure 8Al.l) Te”~~ma$e
00 05 10 15 ;9 30 35 40 45 50 5.5 60 Fi 75 80 85 90 95
8-30
Volatility Exponent, b *
,
Pure Hydrocarbons, Normal Boiling Points (Degrees Fahrenheit) 200
... o.bbi
0.021 0.040 0.060 0.079 0.098 0.117 0.137 0.156 0.176 0.196 0.216 0.236 0.256 0.277 0.297 0.318 0.339
300
0.360 0.381 0.403 0.425 0.447 0.469 0.491 0.514 0.537 0.560 0.584 0.607 0.63 1 0.656 0.680 0.705 0.730 0.756 0.78 1 0.808
400‘
0.834 0.861 0.888 0.916 0.944
. . . .
. . .
\
50 P Cuts, TBP Mid-Boiling Points (Degrees Fahrenheit) 100 . . . .
-0.376 -0.356 -0.336 -0.3 16 -0.296 -0.276 -0.257 -0.237 -0.218 -0.198 -0.178 -0.158 -0.139 -0.120 -0.100
200
-0.08 1 -0.061 -0.041 -0.021 -0.002 0.018 0.038 0.058 0.078 0.098 0.118 0.138 0.159 0.180 0.200 0.221 0.242 0.262 0.284 0.305
300
0.326 0.348 0.370 0.392 0.414 0.436 0.458 0.48 1 0.504 0.526 0.550 0.572 0.596 0.620 0.644 0.668 0.692 0.716 0.742 0.766
OTT2 0:817 0.842 0.868 0.894 0.921 0.948 0.974 1.002 1.029 1.057 1.085 1.113 1.142 1.170 1.199 1.228 1.258 1.288 1.318
500
1.348 1.379 1.410 1.441 1.472 1.504 1.536 1.569 1.602 1.634 1.668 1.701 1.735 1.769 1.804 1.838 1.874 1.908 1.944 1.980
600
2.016 2.053 2.090 2.126 2.164 2.202 2.240 2.278 2.316 2.355 2.394 2.434 2.474 2.514 2.554 2.594 2.635 2.676 2.718 2.759
700
,
2.801 2.843 2.886 2.928 2.972 3.014 3.058 3.102 3.146 3.190 3.234 3.280 3.324 3.370 3.415 3.461 3.507 3.553 3.600 3.646
\
8A1‘.13
n-HEPTANE
- “’ -I
160
n-HEXANE
IS0 NOTES: I. THE FREEZING POINT OF LT NYOROCARSON MIXTURES MAY SE ENCOUNTERED AT TEMPERATURES BELOW -100 E 2. ACETYLENE-LT. HYDROCARBON MIXTURES HIY FORM AZEOTROPES AT TEMPERATURES ABOVE - 3 5 F 3. FOR METHANE IN SOLVENTS WITH AVERAGE MOLECULAR WEIGHTS BETWEEN 30 8 44 USE THE MULTIPLYING CoRRECTloN FACTOR SHOWN ON THE INSERT CHART BELOW TO CORRECT METHANE K S.
100
n-PENTANE
1 NOTE: Part of Procedure 8Al.l 1
2-WIHYLGUTANE IISOPENTANE
1-EUTENE I-METHYLPROPANE (ISOSUTANO
*G
2
,O
Z
0
P
-10 -20 -so -40 PROPANE -so PROPENE
!
009 0.08 0.07 _A---0.06 _--0 . 0 5 I- - 1
0.09
lfHYNE (ACE::::!;,’ IN LT. HYDROCARBONS
METHANE C0RRPltnt.1 --..-..
Tim=. \..“IL. 9,-j
METHANE IN L T . HYDROClVlBONS IGEE NOTE ,I
0.01s
METHANE IN/ cq TO CT B NATURAL GAS
TEMPERATURE,
F
8-31
8Al.14
I
FIGURE, 8Al.M HIGH-TEMPERATUPX
‘VApbit-
LIQUID
EQUlLlBRtA FOR HYDROCARBON HYDROCARBON
October 1964 Appioved:
MRF & WGB
CYCLOHEXANE
ETHANE
ie C,“, IN BENZENE
-40 -30 -20 -10 0 19 20 @-BUTANE _- 30 I~*w~-BUTENE--~-MUTENE-- 40 50 so 70
110 c’ E 120 p I30 ; 140 g I50 “HEXANE--‘
170
NOTE: Part of Procedure BAl.1 ’
I
”
“
‘
;
]
IDO
’
180 190 ‘WI
8-32
i z g
1
d ‘NOll33~~03
8A2.1
Allhl13V 311VWOW-NON
FIGURE 8A2.1 ACTIVITY CORRECTION FOR MIXTURES CONTAINING AROMATICS
ECHNICAL DATA BOON October 1964 Approved
:. MRF & WGE
J
” ‘NOllklt!03
0-J . AllAil~
311VwotlV -
c c.
8-33
8A2.1 COMMENTS ON FIG. 8A2.1
Fig. 8A2.1 is presented to estimate the activity coefficients to be applied to vapor-liquid equilibrium K-values obtained from Procedure 8Al.l or 8Bl.l for mixtures containing aromatic hydrocarbons. Limitations The figure is applicable to hydrocarbon systems only at pressures less than SO psia and to hydrocarbon-hydrogen systems only at pressures up to 4,500 psia. Reliability
The vapor-liquid K-values obtained f r o m Procedure 8Al.l and corrected with this figure deviate from experimental values by an average of 3.5 percent. Notation y = activity correction to be applied to K,,.. Knon80 = vapor-liquid equilibrium K-value from Procedure 8Al.l or 8Bl.l. K = vapor-liquid equilibrium K-value corrected for presence of aromatics, K = yKnotno. Literature sonree
This figure was adapted from Engineering Data Book, Socony Mobil Oil Company, Inc., New York. A. Determine the K-values of the components of a vapor-liquid system in which the liquid contains 10.9 mole percent cyclohexane and 89.1 mole percent toluene at 220 F and 14.7 psia. From Procedure 8Al.1, the K-value (KnoarS ) for cyclohexane is 1.78 and for toluene 0.827 at these conditions. From Fig. 8A2.1. the nonaromatic activitv correction is Y = 1.32 and the aromatic activity correction is7 = l.ObS. For cyclohexane, K = yKnomo = (1.32) (1.78) = 2.35. For toluene, K = (1.005) (0.827) = 0.831.
B. Determine the K-values of the components of a mixture containing 0.40 mole fraction cyclopentane and 0.60 mole fraction benzene at 153 F and 14.7 psia. The calculation is one of trial and error because neither the vapor-liquid mole ratio nor the compositions of the vapor and liquid are known. A flash calculation must be made with an assumed liquid composition to estimate the activity corrections (because of the presence of the aromatic) and K-values. A vapor-liquid mole ratio is assumed, and the composition of the liquid is calculated by the expression based on material balance and the equilibrium relationship:
%‘= xrc(L + w L+KtV Where:
xs = mole fraction of component i in liquid phase. x14 = mole fraction of component i in total mixture. L = moles of liquid. V = moles of vapor. Kc= equiliirium K-value of component i . The composition of the vapor, the amount of each component in the vapor and liquid phases, and the total amount of vapor and liquid are calculated. The calculated liquid composition and the quantities of vapor and liquid are used in the next trial until the final calculated values of the liquid mole fractions and vapor and liquid mole ratios equal the assumed value for that trial. From Procedure 8Al.1, the K-value (KS,,. ) for cyclopentane is 1.60 and for benzene is 0.63. Trial I:
Assumed Mole Fraction, x Cyclopentane (1) . . 0.40 Benzene (2) . . . . . . . 0.60 Total . . . . . . . .
a-34
...
Assuming V/L = 0.50/0.50
Y (Fig. 8A2.1) K,,,,,. 1.122 1.60 1.067 0.630 ...
...
-YK*.*.
1.795 0.6722
...
5iiz-kz (Moles) (M&s) 0.1431 0.2569 0.3588 0.2412
0.5019 0.498 1
8A2.1 Assume V = 0.50 mole and L = 0.50 mole; then: (0.40) (1.00) = 0.2862 x1 = 0.50 + (1.795) (0.50) (0.60) (1.00) = 0.7176 x9 = 0.50 + (0.6722) (0.50) yz= Klx%= (1.795) (0.2862) = 0.4138 ya= K&a= (0.6722) (0.7176) = 0.4824 Trial 2: Assumed Mole Fl-iXtiOll, Qclopentane (1) . . O&4 Benzene (2) . . . . . . 0.716 Total . . . . . . . .
( F i g . 1.195 1.035
...
...
8yA2.1) Km,,, yKmon. 1.60 1.912 0.63 0.652 ...
...
Assuming V/L = 0.498/0.502 L \ I Liquid Vapor (Moles) (Moles) 0.2619 0.1381 0.2356 0.3644 0.5025 0.4975
Assume V = 0.498 mole and L = 0.502 mole; then m = 0.2751, xa = 0.7258, ye = 0.5260, and yl = 0.4732. Trial 3: Assumed Mole FlZtiOIl, Cyclopentane (1) . . O.n275 Benzene (2) . . . . . . 0.725 Total . . . . . . . .
...
(
F i 1.195 1.035 ...
g
Assuming V/L = 0.498/0.502 Liquid Vapor (Moles) (Moles) . zA2.1) Km.,, yKn~~~ ,A-, 0.2619 1.60 1.912 0.1381 0.652 0.3639 0.2357 0.63 0.4976 ... ... 0.5020
Assume V = 0.498 mole and L = 0.502 mole; then xi = 0.2751, xs = 0.7258, yl = 0.5260, and ys = 0.4732. Inasmuch as the final calculated values of the liquid composition and the vapor-liquid ratio are equal to the assumed, the calculation is completed.
8-35
, 8Bl.l
PROCEDURE
8Bl.l
VAPOR-LIQUID EQUILIBRIUM K-VALUES FOR SYSTEMS CONTAINING HYDROCARBONS AND HYDROGEN Discussion
The following procedure is useful for calculating the vapor-liquid equilibrium K-values for hydrogen-hydrocarbon systems. Procedure
Step I: Determine K-values for the hydrocarbons, including methane, from the K-nomographs (Fig. 8A1.13 and 8A1.14, using a convergence pressure of 5,000 psia) at the system temperature and the system pressure. Step 2:Determine or estimate the vapor and liquid compositions and calculate a molal, average boiling point (MABP) of the hydrogen-free liquid and of the total vapor. Step 3: From Fig. 8B1.2 determine the K-value of hydrogen. Step4: From Fig. 8B1.3 determine the correction factor for the presence of hydrogen. From the insert of Fig. 8B1.3 determine the multiplying correction for the presence of methane. . Step 5: Calculate the corrected K-values for hydrocarbons (except methane, which requires no correction in multicomponent hydrogen systems) by multiplying together the three factors from Steps 1 and 4. For mixtures containing aromatic hydrocarbons, the following equation should be used to correct the K-values of the hydrogen: (8Bl.l-1) KA= = Kgarxpar + 2 Kamxm Where: KtIz = K-value of hydrogen in the mixture. K,,, = K-value of hydrogen in mixture having MABP of paraffin-olefin
portion of hydrogen-free liquid. K,,, = K-value of hydrogen in mixture having MABP of aromatic portion of hydrogen-free liquid. xpar = rna;z fraction pat-r&in-oletin components in liquid, calculated on a hydrogen-free
Xaro = mole fraction aromatic components in liquid, calculated on a hydrogen-free basis. Step 6: Repeat Steps 2 through 5 until the assumed and calculated compositions check within an acceptable tolerance. For mixtures without methane, the procedure is the same except that no correction factor for the presence of methane is required. For binary mixtures of hydrogen and methane, use Fig. 8B1.4 for the K-value of methane.
8-37
881.1
COMMENTS
ON
PROCEDURE
8Bl.l
Purpose
This procedure is to be used to determine the K-values for systems containing both hydrogen and hydrocarbons. Although developed primarily for hydrogen-parathn-ole8n systems, the K-values of hydrogen can be suitably corrected for the presence of aromatics. The correlation is not applicable for pressures above 10,000 psia, for temperatures lower than -300 F or higher than 900 F (but not above a pseudocriticai temperature of 0.9 for the hydrocarbons in the liquid phase), or to hydrocarbon mixtures having an MABP of the liquid (MABP&) above 700 F. Reliability
The correlations of K-values for hydrogen-hydrocarbon systems have been tested against experimental data. The results are given in the following tabulation: Number of Average Pressure Experimental Deviation Temperature (Pounds per Square Points (Percent) (Degrees Fahrenheit) Figure Inch Absolute) 531 11.5 - 3 0 0 t o 900* 8B1.2 10 to 10,000 461 12.7 -260 to 800 10 to 4,500 8B1.3 8B1.4 27 8.3 -300 to -150 10 to 5,000 Special
Comments
At low hydrogen concentrations (below 5 mole percent in the vapor) and pressures below 1,500 psia, the original hydrocarbon nomographs, Fig. 8A1.13 and 8A1.14, can be used without the correction of Fig. 8B1.3 for the presence of hydrogen. The correlation was developed and has been tested with hydrogen-paraffin, hydrogenolefin, and hydrogen-paraffin-olefin mixtures. Limited data indicate that it is also applicable to hydrogen-naphthene systems. Very liited data indicate the K-values of hydrogen in hydrogen: aromatic mixtures are about twice those predicted using the MABP of the hydrogen-free aromatics in the liquid phase. A correction for aromatic presence can be made by the use of equation (8Bl.l-1). Literatnre source The procedure was developed by Shen, Proc. API
44 CIIII 23 (1964).
Example
A. Calculate the K-values of the components at -100 F and 1,000 psia of a hydrogen-etheneethane system, the feed composition of which is: Mole Percent Hydrogen . . . . . . . . . . . . . . . 32.25 Ethene . . . . . . . . . . . . . . . . . . . . . . . . 41.68 Ethane . . . . . . . . . . . . . . . . . . . . . . . . 26.07 Total . . . . . . . . . . . . . . . . . . . . . . 100.00 For pure hydrocarbon mixtures, from Fig. 8A1.13: KC~E&WtnO) = 0.180 Kc,n,,(s-) = 0.102 Assuming MABPL of -130 F (between those of ethene and ethane) as a first approximation, from Fig. 8B1.2: Km,= 22.7 Assmling
MABPV = -300 F (between those of hydrogen and ethene), from Fig. 8B1.3: K-value correction = 0.85
Then, KC*H4 = (0.85)(0.180) = 0.153 Kc+~ = (0.85) (0.102) = 0.0867 l
8-38
Up to 0.9 TPO
of the hydrocarbons in the liquid.
881.1
To check vapor and liquid compositions, the flash vaporization at -100 F and 1,000 psia is calculated:
Mole Percent ;f.g c;Hs . . . . . 26:07 Total . . 100.00 MABPr, deg F . . MABPL, deg F . .
Normal Boiling ’ Point Owees Fahren- Assumed heit) K-Values 22.7 0.153 0.0867
-155 -423 -128
...
...
Assumed -300 -130
.
Trial 2 TrialL 1 A Assuming Assuming V/L = so/so V/L = 33/67t * r , \ Liquid Vapor Assumed* Liquid Vapor (Moles) (Moles) K-Values (Moles) (Moles) 36.15 1.36 30.89 5.53 23.99 2.08 61.50 38.50
21.0 0.112 0.0632
Calculated -368.5 -143.8
39.5 2.80 1 29.45 2.17 25.29 0.78 67.60 32.40 Calculated -397.8 -144.1
Trial 3
f
Ha . . . . . . 32.25 C&I, . . 41.68 C&L . . . . 26.07 Total . 100.00
-423 -155 -128 ...
Trial 4 * \ Assuming Assuming V/L = 31/69t V/L = 31/69 L L I , I \ Assumed* Liquid Vapor Assumed* Liquid Vapor K-Values (Moles) (Moles) K-Values (Moles) (Moles) 20.8 29.13 3.12 29.13 20.8 3.12 0.0900 40.08 1.60 0.0828 40.19 1.49 0.0510 25.48 0.59 0.0469.,. 25.53 0.54 ... 31.32 68.84 31.16 68.68
MABPr,deg F......................... MABPL, deg F. . . . . . . . . . . . . . . . .
\
r
Calculated 403.6 -144.1
Calculated -405.0 -144.1
i
B. Make a flash calculation at -100 F and 500 psia for a mixture of the following composition: Mole Percent Hydrogen . . . . . . . . . . . . . . . . . . . . . . 34.62 Methane . . . . 41.61 Ethane . . . . . . . . . . . . . . . . . . . . . . 23.77 Total . . . . . . . . . . . . . . . . . . . . . . 100.00 From Fig. 8A1.13 for a hydrocarbon mixture at -100 F and 500 psia: KCE, (in ethr) = (1.52)( 1.047) = 1.59 CsHe = 0.112 From Fig. 8B1.2, assuming MABPL = -200 F: Kx2 = 26.5 From Fig. 8B1.3, assuming MABPr = 400 F: K-value correction = 0.69 From the insert of Fig. 8B1.3, assuming the mole percent methane in liquid is 25, the multiplying correction, C, is 1.18. Therefore, KC%H~ = (K,,.,.) (K-value correction) (multiplying correction) = (0.112)(0.69)(1.18) = 0.0912 * Based on calculated MABPv and MABPL from the previous trial. The final K-values are from Trial 4. (ivole: For preaswes under approximately 500 psia, the 6rst guess of vapor corn ‘tion is generally good enough, because the correction to the hydrocarbon K-values for composition is small.p” t The convergence is slow, so V/L used from preceding trial is overcompensated.
8-39
4
881.1 Compute flash vaporization at -100 F and 500 psia until the assumed and calculated vapor and liquid compositions agree: Feed h
Mole Percent H. . . . . . . . . 34.62 Cl% . . . . . . . 41.61 c& . . . . . . 23.77 Total . . 100.00
Normal Boiling Point (Degrees Fahrellheit) -423 -259 -128 . .
MABPv, deg F.. . . . . . . . MABPL, deg F.. . . . . . . . . . .
Trial 1 ’
Assuming
I
V/L = 70/30 * ,
Trial 2 L Assuming
V/L = 74/26
Assumed Liquid Vapor Assumed* e K-Values (Miles) (Moles) K-Values (Miles) (MGles) 35.2 0.34 34.28 26.5 0.55 34.07 32.78 7.53 34.08 1.59 8.83 1.59 17.83 5.94 0.0912 19.60 4.17 0.117 ... . . . 74.30 28.98 71.02 25.70 Assumed -400 -200
Calculated -329.8 -168.3
Calculated -324.0 -166.4 and mole percent methane in liquid from the previous trial.
* Based on calculated MABPv and h%ABPz Nofe* The vapor and Iiquid compositions from Trials 1 and 2 are close enough considerin the insensitivity of to small changes in molal average boiling point, temperature, pressure. a n % c o m p o s i t i o n r a n g e of this problem.)
6 e K :values
8.40
881.2
FIGURE 861.2 HYDROGEN K-VALUES IN HYDROGEN-HYDROCARBON ‘L
SYSTEM5 TECHNICAL i
DATA BOOK
October 1964 Approved: MRF & WGB
861.3
8-42
881.4
8Cl .l
PROCEDURE 8Cl.l VAPOR-LIQUID EQUILIBRIUM K-VALUES FOR SYSTEMS CONTAINING HYDROCARBONS AND NONHYDROCARBON GASES Discussion This procedure is used to determine the vapor-liquid equilibrium K-values for systems containing hydrocarbons with nonhydrocarbon gases other than hydrogen. Procedure Step 1: For systems within the temperature and pressure ranges listed under Limitations, locate the component points in Fig. 8C1.2 or 8C1.3. For systems containing no hydrocarbons other than methane and benzene, points for all components are located in the figures. For other systems, only the nonhydrocarbon gas points are given (see Step 5). Step.2: Locate the point on the temperature-pressure grid of Fig. 8C1.2 or 8C1.3 corresponding to the operating temperature and pressure. Step 3: Lay the hairline of a nomograph reader through each component point and the temperature-pressure point. Step 4: Read the K-values at the point of intersection of the hairline with the K-scale. Step 5: Where the hydrocarbon components are not given in Fig. 8C1.2 or 8C1.3, their K-values must be determined from Fig. 8A1.13 or 8A1.14. Locate the point on the temperaturepressure grid corresponding to the operating temperature and pressure (no convergence pressure is needed). Locate the point on the pure-component scale corresponding to the normal boiling point of the hydrocarbon and lay a nomograph reader through these two points. Read the K-values of the hydrocarbon at the point of intersection of the hairline with the K-scale.
8-45
8C1.1
Purpose
COMMENTS ON PROCEDURE 8Cl.l
This procedure is to be used to determine the K-values for systems containing hydrocarbons and the nonhydrocarbon gases except hydrogen. Fig. 8C1.2 and 8C1.3 are used in the procedure. Limitations
This procedure for the determination of in hydrocarbon-nonhydrocarbon gas systems was developed for the following systems. Its use is limited to the temperature and pressure ranges listed. Pressure Range Temperature Range (Pounds per Square Inch (Degrees Reference Absolute) Fahrenheit) -260 to -145 22to 650 9, 12 Nitrogen-methane . . . . . . . . . . . . . . . . . . . . . . Nitrogen-n-butane . . . . . . . . . . . . . . . . . . . . . 100 to 300 236 to 1,000 1,43 Nitrogen-n-heptane . . . . . . . . . . . . . . . . . . . . 90 to 360 950 to 1,000 2 511 to 1,000 5 Nitrogen-methane-n-hexane . . . . . . . . . . . . . 77to 185 901 to 1,000 Nitrogen-benzene . . . . . . . . . . . . . . . . . . . . . . 160 to 260 200 to 1,000 Hydrogen sulfide-methane . . . . . . . . . . . . . . -120to 1 6 0 2832X’ 62 40 to 340 20 to 1,000 Hydrogen sulfide-n-pentane . . . . . . . . . . . . . Hydrogen sulfide-Pegasus crude oil and 40 to 250 50 to 4,000 23 natural gas distillate. . . . . . . . . . . . . . . . . . Hydrogen sulfide-naphtha . . . . . . . . . . . . . . . Ambient 50 to 200 23 Hydrogen sulfide-gas oil . . . . . . . . . . . . . . . . Ambient 50 to 200 23 -1ooto 2 9 300 to 1,000 Carbon dioxide-methane . . . . . . . . . . . . . . . . 3,Yo -40 to 160 50 to 1,000 Carbon dioxide-propane . . . . . . . . . . . . . . . . 1OOto 2 8 0 200 to 1,000 Carbon dioxide-n-butane . . . . . . . . . . . . . . . z;t Carbon dioxide-natural gas distillate. . . . . . 98to’ 101 36 Sulfur dioxide-n-hexane . . . . . . . . . . . . . . . . . 106td 1 0 8 100 to 400 Ammonia-n-hexane . . . . . . . . . . . . . . . . . . . . 100 to 350 Hydrogen chloride-n-butane . . . . . . . . . . . . . 66to 5 3 1 ;: 70to 180 Monomethylamine-n-hexane . . . . . . . . . . . . . 31 100 to 400 125 to 350 Water-propane . . . . . . . . . . . . . . . . . . . . . . . . 100 to 1,000 27,37 40 to 205 Water-n-butane . . . . . . . . . . . . . . . . . . . . . . . 10 to 3,000 6,41 100 to 460 24to 513 Water-n-hexane . . . . . . . . . . . . . . . . . . . . . . . 29 100 to 280 Water-naphtha and kerosine . . . . . . . . . . . . . 36 to 1,000 21 35 to 482 40 to 200 Hydrogen fluoride-2-methylpropane . . . . . . . 25 20 to 160 67 to 605 Methylmercaptan-absorption oil . . . . . . . . . 65 to 79 iii 400 to 900 Carbon monoxide-propane . . . . . . . . . . . . . . -7 to 150 Reliability
The K-values determined using this procedure for the systems and ranges listed above have an average error of 18 percent. Speeid Comments
Data on the solubility of hydrocarbon gases in water, the water content of natural gases in contact with liquid water, and vapor-solid equilibrium ratios of hydrocarbons in hydrate systems are given in Chap. 9. Enlarged copies of Fig. 8C1.2 and 8C1.3 are given in the back of the binder. Additional points can be added to the nomomauhs as data become available. method (20) may be The Chao-Seader method (computer only) (8)-or the Grayson-Breed used for other systems or for the systems given in this procedure at temperature or pressure ranges beyond those shown in the table. Literature Sources
Fig. 8C1.2 and 8C1.3 were prepared by modification of the vapor-liquid equilibria charts of Hadden and Grayson, Hydrocarbon Process. Petrol. Refiner 4Q [91 207 (1961); copyrighted in 1961 by Gulf Publishing Company, Houston, Texas. Examples A. Find
the K-values of nitrogen and n-butane for a mixture of the two at 100 F and 93 1 psia. Locate the nitrogen (in n-butane) point in Fig. 8C1.3 and connect it with a straight line to the 100 F and 931 psia point on the grid of the nomograph. Read the K-value of nitrogen as 8.5. Using Fig. 8A1.14, locate the n-butane point on the scale and connect it with a straight line to the 100 F and 931 psia point on the grid of the nomograph. Read the K-value of n-butane as 0.137. Experimental K-values for these conditions are 7.35 for nitrogen and 0.125 for n-butane (43). B. Find the K-values of nitrogen and methane for this binary system at -240 F and 100 psia. Locate the methane (in nitrogen) point and the nitrogen (in methane) point in Fig. 8Cl.2 and connect each with a straight line through the -240 F and 100 psia point on the grid of the nomograph. Read the K-values as 0.36 for methane and 5.0 for nitrogen. Experimental K-values for these conditions are 0.390 for methane and 4.64 for nitrogen (12). 8-46
LJ
8C1.2
-260 TO 100 F RANGE
I
T E C H N I C A L D A T A BOOK ~wnl n-64 *ppmved MRFL~WI)
. NOTE: Part of Procedure 8Cl.l
$ CAMON DIOXIDE’tin PROPANE)
CARBON DIOXIDE (in METHANE) $ e NITROGENh
METHANE) @
METNANE lin NITROGEN)
8-47
,
8C1.3
TECHNICAL DATA BOOK
61 MONOMETHYLAMINE.fin
P”EXANE)
$ METHYL: MEKAPTAN (in ASSORPTION W- 195 MW)
NOTE: Part
8-48
P .
of Procedure 8Cl.l
BIBLJOGRAPIN (September 1964)
I
1. Akers, W. W., Attwell, L. L., Robinson, J. A., “Volumetric and Phase Behavior of Nitrogen-Hydrocarbon Systems. Nitrogen-Butane System,” (1954). 2. Akers, W. W., Kehn, D. M., Kilgore, C. H., “Volumetric and Phase Behavior in Nitrogen-Hydrocarbon Systems. Nitrogen-n-Heptane System,” ibid., 2536. 3. Akers, W. W., Kelley, R. E., Lipscomb, T. G., “LowTemperature Phase Equilibria. Carbon Dioxide-Propane System,”
ibid., 2535.
4. Benedict, M., Webb, G. B., Rubin, L. C., Friend, L., “An Empirical Equation for Thermodynamic Properties of Light Hydrocarbons and Their Mixtures,” Chem. Eng. Progr. 47 609 (1951). 5. Boomer, E. H., Johnson, C. A., “Equilibria in Two-Phase, Gas-Liquid Hydrocarbon Systems-III: Methane and Hexane,” Can. 1. Research 16B 328 (1938).
6. Brooks, W. B., Gibbs, G. B., McKetta, 3. J., “Mutual Solubilities of Light Hydrocarbon-Water Systems,” Petrol. Refiner30 1101 118 (1951). 7. Cajander, B. C., Hipkin, H. G., Lenoir, J. M., “Prediction of Equilibrium Ratios from Nomograms of Improved Accuracy,” 1. Chem. Eng. Data 5 251 (1960). 8. Chao, K. C., Seader, J. D., “A General Correlation of Vanor-Liauid Equilibria in Hydrocarbon Mixtures,” AZChE Journal 7-598 (1961). 9. Cheung, H.,. Wang, D. I.-J., “Solubility of Volatile Gases in Hvdrocarbon Solvents at Crvoaenic Temperatures,” Znd. Eng. Chem. Fundamentals 3 355 (1964). 10. Chu, J. C., Getty, R. J., Brennecke, L. F., Paul, R., Distillation Equilibrium Data, Reinhold Publishing Corp., New York (1950). 11. Chu, J. C., Wang, S. L., Levy, S. L., Paul, R., VaporLiquid Equilibrium Data, J. W. Edwards, Publisher, Inc., Arm Arbor, Mich. (1956). 12. Cines, M. R., Roach, J. T., Hogan, R. J., Roland, C. H., “Nitrogen-Methane Vapor-Liquid Equilibria,” Chem. Eng. Progr. Symp. Ser. No. 6 49 1 (1953). 13. DePriester, C. L., “Light-Hydrocarbon Vapor-Liquid Distribution Coefficients,” Chem. Eng. Progr. Symp. Ser. No. 7 49 l(l953). 14. Donnelly, H. G., Katz, D. L., “Phase Equilibria in the Systems,” Znd. Eng. Chem. 46 511 Carbon DioxideMethane (1954). 15. Edmister, W. C., Applied Hydrocarbon Thermodynamics, Gulf Publishing Co., Inc., Houston, Texas (1961). 16. Edmister, W. C., Ruby, C. L., “Generalized Activity Coefficients of Hydrocarbon Mixture Components,” Chem. Eng. \ ‘;-
Progr. 5195 (19i5). 17. Engineering Data Book, Socony Mobil Oil Co., Inc.,
New York. 18. Equilibrium Ratio Data Book, Nat. Gas Processors Assoc., Tulsa, Okla. ( 1957). 19. Fenske, M. R., Braun, W. G., Holmes, A. S., Bibliography of Vapor-Liquid Equilibrium Data for Hydrocarbon Systems, Bibliography No. I, Am. Petrol. Inst., New York (1963).
20. Grayson, H. G., Streed, C. W., ‘Vapor-Liquid Equilibria for High Temperature, High Pressure Hydrogen-Hydrocarbon Systems,” Proc. 6th World Petrol. Congr., Frankfort/Main III Paper 20-PD7,233-45 (1963). 21. Griswold, J., Kasch, J. E., “Hydrocarbon-Water Solubilities at Elevated Temperatures and Pressures,” Znd. Eng. Chem. 34 804 (1942). 22. Hadden, S. T., “Convergence Pressure in Hydrocarbon Vapor-Liquid Equilibria,” Chem. Eng. Progr. Symp. Ser. No. 7 49 53 (1953).
23. Hadden, S. T., Grayson, H. G., “New Charts for Hydrocarbon Vapor-Liquid Equilibria,” Hydrocarbon Process. Petrol. Refiner PO [91 207 (1961). 24. H&la, E., Pick, J., Fried, V., Vilhn, O., Vapor-Liquid Equilibrium, Pergamon Press, Inc., New York (1958). 25. Hydrofluoric Acid Alkylation, Phillips Petroleum Co., Bartlesville, Okla. ( 1946). 26, Katz, D. L., Rzasa, M. J., Bibliography of Physical Behavior of Hydrocarbons Under Pressure and Related Phenomena, I. W. Edwards, Publisher, Inc., Ann Arbor, Mich.
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College, Pa. (1955). 47. Shen, R. C., “Graphical Correlations of Vapor-Liquid K-Vzh~.n --
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Constants for Carbon Monoxide,” Znd. Eng. Chem. 40 1742
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