‘LA’

CHAPTER 8

VAPOR-LIQUID EQUILIRRIUM K-VALUES

PAGE

8-O Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 8-l

Fig. 8-0.1 Convergence Pressure in the Binary System Ethane-n-Heptane . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 8-2

Fig. 8-0.2 Convergence Pressure in the Ternary System Meth-ane-Propanen-F’entane . . . . . . . . . . . . . . 8-2

8A Vapor-Liquid Equilibrium K-Values for Hydrocarbon Systems8Al. Vapor-Liquid Equilibrium K-Values for Hydrocarbon Systems

Procedure 8Al.l Vapor-Liquid Equilibrium K-Values for Hy-drocarbon Systems . . . . . . . . . . . . . . . . . . . . 8-5

Procedure 8Al. 1A Vapor-Liquid Equilibrium K-Values forHydrocarbon Systems in Area A. . . . 8-9

Procedure 8Al. 1B Vapor-Liquid Equilibrium K-Values forHydrocarbon Systems in Area B . . . . . . 8-11

Procedure 8Al .lC Vapor-Liquid Equilibrium K-Values forHydrocarbon Systems in Area C . . . . . . 8-13

Procedure 8Al .lD Vapor-Liquid Equilibrium K-Values for

Fig. 8A1.2

Fig. 8A1.3

Fig. 8A1.4

Fig. 8A1.5

Fig. 8A1.6

Fig. 8A1.7

Fig. 8A1.8

Fig. 8A1.9

Fig. 8A1.10

Fig. 8Al .l 1

Table 8A1.12

Hydrocarbon Systems in Area D . . . . . . 8-15

Convergence Pressures of Typical RefineryMixtures . . , . . . . . . . . . . . . . . . . . . . . . . . 8-20

Convergence Pressures of Binary Systems.Methane, the Lightest Component. . . . . . . . 8-21

Convergence Pressures of Binary Systems.Ethane, the Lightest Component. . . . . . . . . . 8-22

Convergence Pressures of Binary Systems.Propane, the Lightest Component. . . . . . . . . 8-23

Convergence Pressures of Binary Systems.n-Butane, the Lightest Component. . . . . . . . 8-24

Convergence Pressures of Binary Systems.n-Pentane, wHexane, and n-Heptane, theLightest Component . . . . . . . . . . . . . . . . . . 8-25

Convergence Pressures of Binary Systems.Ethene, the Lightest Component. . . . . . . . . . 8-26

Convergence Pressures of Binary Systems.Propene, the Lightest Component. . . . . . . . . 8-27

Pressure Parameter Requirements for theK-Nomograph . . . . . . . . . . . . . . . . . . . . . . . 8-28

Grid, Convergence, and System Pressure Re-lationship . . . . . . . . . . . . . . . . . . . . . . . . . . . 8-29

Volatility Exponent for Pure Hydrocarbonsand True Boiling Point 50 F Cuts forEquation (8Al .lA-1 ) . . . . . . . . . . . . . . . . 8-30

API TECHNICAL DATA BOOK

PAGE

Fig. 8A1.13 Low-Temperature Vapor-Liquid Equilibriafor Hydrocarbon-Hydrocarbon Systems.-260Fto 100FRange.. . . . . . . . . . . . 8-31 J’

Fig. 8A1.14 High-Temperature Vapor-Liquid Equilibriafor Hydrocarbon-Hydrocarbon Systems. 40 Fto 800 F Range. . . . . . . . . . . . . . 8-32

8A2. Vapor-Liquid Equilibrium K-Values for Systems Containing Aro-matic Hydrocarbons iFig. 8A2.1 Activity Correction for Mixtures Containing

Aromatics . . . . . . . . . . . . . . . . . . . . . . 8-33

8B Vapor-Liquid Equilibrium K-Values for Systems Containing Hydrocar-bons and Hydrogen8Bl. Vapor-Liquid Equilibrium K-Values for Systems Containing Hy-

drocarbons and HydrogenProcedure 8Bl.l Vapor-Liquid Equilibrium K-Values for Sys-

tems Containing Hydrocarbons and Hydro-gen . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 8-37

Fig. 8B1.2 Hydrogen K-Values in Hydrogen-Hydrocar-bon Systems . . . . . . . . . . . . . . . . . . . . . . . . . 8-41

Fig. 8B1.3 K-Value Correction for Hydrocarbons inHydrogen-Hydrocarbon Mixtures . . . . . . . . 8-42

Fig. 8B1.4 Methane K-Values in the Hydrogen-MethaneSystem . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 8-43

8C Vapor-Liquid Equilibrium K-Values for Systems Containing Hydrocar-bons and Nonhydrocarbon Gases8Cl. Vapor-Liquid Equilibrium K-Values for Systems Containing Hy-

drocarbons and Nonhydrocarbon GasesProcedure 8Cl. 1 Vapor-Liquid Equilibrium K-Values for Sys-

tems Containing Hydrocarbons and Nonhy-drocarbon Gases . . . . . . . . . . . . . . . . . . . . . 8-45

Fig. 8C1.2

Fig. 8C1.3

Low-Temperature Vapor-Liquid Equilibriafor Hydrocarbon-Nonhydrocarbon Systems.-260FtolOOFRange . . . . . . . . . . . . . . . . 8-47High-Temperature Vapor-Liquid Equilibriafor Hydrocarbon-Nonhydrocarbon Systems.40Fto8OOFRange . . . . . . . . . . . . . . . . . . 8-48

‘-.J

Bibliography . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 8-49

CHAPTER 8

VAPOR-LIQUID EQUILIBRIUM K-VALUES

8-O INTRODUCTIONVapor-liquid equilibrium relationships are conve-

niently defined in terms of the distribution coe5cient,&=y6/xi. If the components form an ideal solution inthe liquid phase and if the saturated vapors of the indi-vidual components are perfect gases, the system may beconsidered an ideal system. Under these conditions,Raoult’s and Dalton’s laws apply and:

(8-0.1)

Where:&=vapor-liquid equilibrium constant for compo-

nent 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 itmay be used as a reasonably good approximation forsystems of close-boiling homologs at low pressures (lessthan approximately 30 psia) where the vapors of theindividual components do not deviate appreciably fromperfect gas behavior.

The relationship given as equation (SO.1 ) does nothold at elevated pressures or for mixtures that do notobey Raoult’s law. Further, it can not be used if thetemperature is above the critical point of any of thecomponents. The concept of fugacity was introduced asa more convenient and more generally useful functionfor equilibrium calculations. The ideal K-value wasdefined as:

Where:

K ,,,a,=+$ (g-0.2)4

fiL=fugacity of component i in the pure liquid stateat stated system temperature and pressure.

f6v= fugacity of component i in the pure vapor stateat stated system temperature and pressure.

The fugacities are obtainable from one of a number ofgeneralized fugacity charts or from fugacity functiontables such as given in Chap. 7. The ideal K-values foreach component are a function of temperature and pres-sure only.

Although the ideal K-value is a good approximationfor many real physical situations, it is unsatisfactory forhigh pressures, low temperatures, and where the mix-tures are increasingly complex. Particularly importantis the effect of mixture composition on the K-value at

the higher pressures. Two approaches have been usedto incorporate the effect of composition into the calcu-lation of equilibrium data: further development of thefugacity relationships and the introduction of a thiidparameter, the convergence pressure. The correlationsgiven in this chapter are based on the latter approach.

Although the correlations based on fugacity are notused in this book, the following remarks are includedbecause these procedures are frequently encounteredand used.

When vapor and liquid phases are in equilibrium, thefugacity of each component in the liquid phase is equalto its fugacity in the vapor phase, f7L=f;v. Therefore,

p2 XLK,&i$, % % 1

0

--.---z-z- -

xi frvxc P 71 7r(8-0 .3)

-

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

Where:

L-C= -Y’ --fi -activity coe5cient of component i in the

liquid mixture.f4Lvi=--- fugacity coe5cient of component i as a,r pureliquid.

PQS=z =fugacity coefficient of component i in the

vapor mixture.

A number of the better known K-value correlationsin which the effect of mixture composition is one of thecorrelating parameters are based on these fugacity rela-tionships. The Kellogg or Polyco charts (4)) derivedfrom 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 chartsusing the relationship given in equation (S-0.4). All ofthese methods used the molal average boiling point(MABP) as the correlating composition parameter.Chao and Seader (8) developed a general correlationfor computer use based on the relationship given asequation (8-0.5).

The alternate composition correlating parameter isconvergence pressure, and a number of K-value corre-lations are based on this. Among these are the NGPA(18), Whm (50), Cajander, et al. (7), and Haddenand Grayson (23) methods.

Convergence Pressure: The convergence pressureof a hydrocarbon system is the pressure at which thevapor-liquid K-values of all the components of a systemappear to converge at K= 1 at the system tempera-ture. The concept is illustrated for a binary system inFig. 8-O. 1, where the left portion is the conventionalpressure-temperature phase diagram similar to thatdiscussed in Chap. 4 and the right portion is a corre-sponding pressureK-value diagram for a constant tem-perature The phase boundaries are defined in the leftdiagram by the vapor pressure lines of the pure com-ponents and the critical locus of their binary mixtures.In the right-hand diagram, the pressure-K-value rela-tionship forms a loop which crosses the K= 1 line at twopressures: where the pressure equals the vapor pressureof the higher boiling constituent and at the convergencepressure of the system.

Provided the system lies between the critical tempera-tures of the binary components, the prediction of con-vergence pressure depends on the temperature only andis based on the experimental critical locus data for thesystem. For multicomponent systems, however, theliquid-phase composition as welI as the temperaturemust be considered. Convergence pressures for thesesystems can be obtained by treating the mixtures as afictitious binary (18,23, 30). In the ternary system ofmethane-propane-n-pentane, for example, the pro-pane-n-pentane pair may be assumed to be the higherboiling component of a fictitious binary with methanethe other component. For the ternary system in whichthe ratio of propane to n-pentane remains constant (1.5moles per mole), the K-values are shown in Fig. 8-0.2.

r’oT E M P E R A T U R E , F K

FIG. 8414nvergence Pressure in the Binary System Hydrocarbon-Nonhydrocarbon Gas EquilibriumEthanen-Heptane (22) . Data: For systems containing a hydrocarbon and a

8-2

-.J’

FIG. I-OA--Convergence Prestmre in the Ternary SptemMethane-Propane-d’entane (22).

Also shown are the critical locus data for each binaryof the system. The transfer of convergence pressurefrom the pressure-K-value graph to the pressure-tem-perature graph defines a new critical locus shown as adashed line in the figure. It is important to note, asconfirmed in Fig. 8-0.2, that the convergence pressureis a function of the temperature and of the liquid-phasecomposition exclusive of the lightest component concen-tration.

Hadden (22) developed the method of estimatingconvergence pressures of more complex multicompo-nent mixtures which is outlined in detail in the pro-cedures of this chapter.

Hydrocarbon System Equilibrium Data: Vapor-liquid K-values of hydrocarbon mixtures may be esti-mated from the nomographs of Procedure 8Al.l. Theconvergence pressure parameter necessary in the Cal-culation may be estimated by the methods and from thegraphs provided as part of the procedure. For hydro-carbon systems containing aromatic hydrocarbons, theactivity corrections given in Fig. 8A2.1 must be applied.

. ,

In the fractionation of narrow-boiling mixtures, theaccuracy of the K-values becomes increasingly impor-tant, and values obtained by the generalized correlationgiven as Procedure 8Al.l are usually not suitable. Thisis particularly true for fractionations of essentiallybinary systems such as ethane-ethene, propane-propene,n-butane-isobutane, ethane-propane, propane-butane,etc. Experimental data specific to the system should beused in preference, and the reader is referred to theextensive bibliographies of the literature ( 10, 11,19,24,26, 33, 44, 45, 46). The procedure is also not suitablefor mixtures which may form azeotropes.

Hydrocarbon-Hydrogen Equilibrium Data: TheK-values for systems of hydrocarbons and hydrogen canbe obtained from Procedure 8Bl.l. The hydrogenK-values are obtained from a chart on which the systemtemperature and pressure and the MABP of the hydro-gen-free liquid are parameters. The hydrocarbon K-values are obtained from the charts of Procedure 8Al.land corrected for the presence of hydrogen. The methodis applicable to pressures up to 4,500 psia and tempera-tures from -260 F to 800 F.

API TECHNICAL DATA BOOK

nonhydrocarbon gas other than hydrogen, Procedure8Cl.l should be used. The method is limited to certainspecific systems and to the temperature and pressurerange of the experimental data from which it was devel-oped. In no case should it be used for system pressuresabove 1,000 psia.

For temperature and pressure conditions beyond therange of Procedure 8C1.1, for certain systems not in-cluded in the procedure, or where an electronic com-puter method is preferred, the Chao-Seader correlation(8) and Grayson-Weed correlation (20) are recom-mended. A computer program for Chao-Seader K-values

is sold by the Natural Gas Processors Association (spe-cify machine size and type, core storage, and numberof tapes).

Where experimental data are available, they shouldbe used in preference to the generalized correlationswhen the highest accuracy is required. A comprehensivebibliography (49) of the literature is available from theAmerican Petroleum Institute.

Note: A report which documents the basis upon which thematerial in this chapter has been selected has been publishedby the American Petroleum Institute as Documentation ReportNo. 8-66 .

8-3

8Al .l

PROCEDURE 8Al.lVAPOR-LIQUID EQUILIBRIUM K-VALUES FOR HYDROCARBON SYSTEMS

D i s c u s s i o nVapor-l iquid K-values for hydrocarbon mixtures are est imated from nomographs having a

temperature-pressure grid, logarithmic K-value scale, and component scale. To use the nomo-graphs, a pressure-temperature point for the temperature-pressure grid must first be determined.This pivot point is a function of the operat ing pressure and temperature and of a composit ionparameter, the convergence pressure, pov. Detailed procedures for calculating and applying thisparameter are provided in this section. For systems containing aromatics, the activity correc-tions given in Fig. 8A2.1 must be applied.

The K-values are calculated by one of several paths, depending on the properties of thesystem and on the operat ing condit ions. The methods of calculat ion also vary with what isknown and what information is desired (e.g. , bubble-point , dew-point , and equil ibrium flashconditions) for the system.

Starting with a known or estimated liquid-phase composition and known or assumed valuesfor the operating temperature, Top, and operating pressure, pop, the calculation is made accordingto the method i l lustrated in the fol lowing diagram and steps. The tinal calculations are to bemade using one of subsidiary Procedures 8Al.lA through 8Al.lD. Most of the systems en-countered can be calculated with Procedure 8Al.lA, 8Al.lB, or 8Al.lC, requiring only anapproximate convergence pressure.

Procedure (See Procedure Diagram for K-Value Calculations.)Step 1 : If the operating temperature is equal to or less than the true cri t ical temperature of

the “l ightest component” (Top< T,z), u se p 00 = pOi and proceed to Procedure 8Al.lB. Thelightest component for this procedure is the most volat i le component having at least 0 .1 molepercent in the liquid phase (see Examples).

If the operating temperature is equal to or greater than the true critical temperature ofthe “average heavy component” less 50 F (T.,>T,n -50 F), proceed to Procedure 8Al.lD.The average heavy component is the average of al l components except the l ightest componentin the l iquid phase. Disregard the heaviest components which together total less than 2 molepercent of the liquid.

If the operating temperature is higher than the true critical temperature of the lightestcomponent and lower than the true crit ical temperature of the average heavy component less50 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 othermixtures. The curve to be used is the one that has a low-temperature terminal corresponding tothe lightest component in a given mixture and a high-temperature terminal corresponding to theaverage heavy component in the mixture.

Siep 2: Branch to Procedure 8Al.lA, 8ALlB, 8Al.lC, or 8Al.lD according to the seleotion routine outl ined hereinafter and given schematically in the Procedure Diagram for K-ValueCalculations.

Step3: Check the requirements for the K-nomograph corrections by locating a pointcorresponding to the operating pressure and the quick estimate of convergence pressure inFig. 8A1.10. Proceed to Procedure 8Al.lA, 8Al.lB, 8Al.lC, or 8Al.lD depending on whetherthe point is located in Area A, B, C, or D.

8-5

8Al.l

Procedure Diagram for Calcuhions

Note: The K-nomographs are foridentifiable hydrocarbons having nor-mal boiling points less than 210 F.For higher boiling pure hydrocarbonsand for petroleum fractions charaoterized by a TBP curve, the volatilityexponent from Table 8A1.12 must beapplied.

KNOWN OR ESTIMATED

COMPOSITION AND To

1 IS Top > T,I ?II 1

YES

NOMENCLATURETop = operating temperature, in de-

grees fahrenheit.T ot = true critical temperature of

lightest component, in degreesfahrenheit.

T.I = true critical temperature ofaverage heavy component, indegrees fahrenheit.

pov = convergence pressure, in poundsper square inch absolute.

po8 = true critical pressure of lightestcomponent, in pounds persquare inch absolute.

pap = operating pressure, in poundsper square inch absolute.

PI= grid pressure, in pounds nerI

1s Top < &h-50 F) ?

square inch absolute.

N O4

Top’(T,h-~o F)

QUICK EST. OFpcv

FIGURES 8A1.2 TO 8A1.9

WITH KNOWN ORASSUMED pop, USE AREA

AREA B AREA C AREA A AREA DPROC. 8AllB PROC. 8Al.X PROC. 8Al.lA

1 1

,PROC. 8Al.lD

pg FROM pg FROM

FIG. 8A1.11 FIG. 8A1.11

1 1 Y TCONNECT(Top,pdp)TO K=‘.% ON T.HlS

WTopt pg)FOR USE (Topt~op)FOR USE DETAILED

LINE IS PIVOT ONPIVOT POINT ON PIVOT POINT ON CALC. PROC.

K+NOMOGRAPHS K-NOMOGRAPHS K-NOMOGRAPHS FOR pcv

SEE NOTE . SEE NOTE SEE NOTE SEE NOTEb

I 1 1 + 1DESIRED K-VALUES I

8-6

8Al.J

COMMENTS ON PROCEDURE 8Al.l

PurposeThis procedure is to be used to est imate hydrocarbon vapor-l iquid equil ibrium K-values.

For systems containing aromatics, the act ivi ty correct ion of Fig. 8A2.1 must be applied. Forh y d r o g e n , Procedure 8Bl.l is to be used, and for other nonhydrocarbon gases, Procedure 8Cl.lis given.

Because of the large number of calculational routes used to estimate K-values, theremainder of this procedure is subdivided into four separate supplementary procedures (8Al.lAthrough 8Al.lD), each of which applies to a different mode of calculat ion. Fig. 8A1.2 through8Al.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 petroleumfractions at temperatures from -260 F to 800 F and at pressures up to 10,000 psia. Do notIIS& this procedure for binary mixtures of close-boiling hydrocarbons or for mixtures which mayform azeotropes.

Reliabi l i ty

The K-values determined using this procedure have an average deviation from experimentalvalues of 9 percent for binary paraffin-parafthr or parat&olefin mixtures and 13 percent formulticomponent par& or parattin-olefin mixtures. At pressures below 1,000 psia, the accuracyis somewhat better than these overall values.

NotationThe 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 l ines in Fig. 8A1.7 are shown broken to el iminate 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 designatedas i-C, for 2-methylpropane (isobutane) and i-C& for 2-methylbutane (isopentane). Olefins aredesignated as CL= for ethene, C’ for propene, and l-C? for 1-butene.

Special CommentEnlarged copies of Fig. 8A1.13 and 8A1.14 are given in the back of the binder.

Literature SoIm?esThe procedure is from Hadden and Grayson, Hydrocarbon Process. Petrol. Refiner 40 C91

207 (1961); copyrighted in 1961 by Gulf Publishing Company, Houston, Texas. I t is supple-mented by material from the Engineering Data Book, Socony Mobil Gil Company, Inc., NewYork.

ExampleaA, Find the terminals of the convergence pressure graphs of a mixture having a boil ing

range equivalent to that for methane (c1) to decane ( C,O) :

Light component : G (methane)Average heavy component: 26-t-G --cd

Fig. 8A1.3 would be used for the convergence pressure.

B. Find the terminals of the convergence pressure graphs of a mixture having a boilingrange 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:

ComponentI

Number3

of CarbonAtoms N a m e

. . . Hydrogen

:MethaneEthane

3 Propane4 Butane5 Pentane6 Hexane7 Heptane

;:“225”*“‘275’9

lot “325’911t “3759

Total

IMole Fract ion *

Mix tu re A Mixture B\

Reflux Drum Liquido.ooo9 Negligible0.018 Light component0.051 1

Reboiler Bottoms0.17 x1W’0.67 )( 1O-u0.43 x 1~ Negfigible0.61 x lO-‘0.009 Light0.049

component

0.130

0.186

0.188 Average heavy0.1030.083 1

component

0.0800.2740.363

Average heavycomponent

0.1680.045 J0.21 x lOA0.16 X’ lad0.32 X IO-PD Negligible

0.17 x. 1V1.000+

Average heavy component=w = Ga (use CS)

Fig. 8A1.3 would apply.l From ical

2Ecomputer tray-to-tray results.

4 2E0i&e~oiut of a ffaotkm having a 50 P boiling range.

0.252 J1.000+

Average heavy component,cs+cu.+

2Fig. 8A1.6 would apply.

8-8

8Al .lA

PROCEDURE 8Al.lA

VAPOR-LIQUID EQUILIBRIUM K-VALUES FOR HYDROCARBON SYSTEMS INA R E A A

Procedure 8Al. l is to be used for al l preliminary calculations toward est imating K-valuesfor hydrocarbons. If the estimated convergence pressure and operating pressure conditions aresuch that the point with these coordinates fal ls in Area A of Fig. 8A1.10, the fol lowing stepsare to be followed to complete the estimation of the K-values.

ProcedureStep 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 operatingtemperature and pressure.

Step 2: Lay the hair l ine of a nomograph reader through this point and through the com-ponent point (or through the boiling point of the component, if the component is not shown onthe scale).

Step 3: Read the desired K-value at the point of intersection of the hairline with theK-scale. When u&a the low-temperature nomograph (Fig. 8A1.13) for methane in lighthydrocarbons, mult iply the methane nomograph K-value by the correction indicated on theinserted chart.

Step4: For identified hydrocarbons having normal boiling points above 210 F and forpetroleum fractions characterized by a true boiling point (TBP) curve, the K-value is calculatedas follows. Determine the K-values of ethane and n-heptane at the operating temperature andoperating pressure of the system in accordance with Steps 1 through 3. Then, for the com-ponents of the mixture (normal boi l ing point above 210 F) , determine the volat i l i ty exponents ,b, of the identitied hydrocarbons or of the 50 F TBP cuts of the petroleum mixture fromTable 8A1.12. Finally, solve equation (SAl.lA-1) for the K-value of each pure compound orportion of the petroleum fraction:

Where:

K= xK+-(-1

b4 (SAl.lA-1)K7

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 boil ingpoints 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 equilibriumK-values for hydrocarbons when the operating conditions are such that the point falls in Area Aof Fig. 8A1.10. The preliminary calculations are performed using Procedure 8Al.1, which is themaster procedure for estimating hydrocarbon K-values under any conditions.

Special CommentFor Limitat ions, Reliabi l i ty, Notat ion, and Literature Sources, see Comments on Proce-

dure 8Al.l.

ExamplesA. 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 resultingK-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 Ex-ample A having a boiling point of 190 F?

As determined in Example A, the operating conditions are in Area A, so the K-value canbe read directly in Fig. 8A1.14. The result is 0.0188 (see example figure).

IPMETHANE ( I N C7

/’,’

V,’\a/63’tbf%/

.’14.7

THRU C,2 A N D

GASOLINE)

.190 F

C. What is the K-value at 500 F and 100 psia for n-decane in a Mid-Continent crude oilcontaining 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. TheK-values would normally be read directly in Fig. 8Al.14 for the operating temperature andpressure. However, inasmuch as the boiling point is higher than 210 F, the K-value for n-decanehas to be computed from K-values for ethane (KS) and heptane (K,), determined inFig. 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.

Km= 2.40 2.400.m = @-jjJjE = 0.747

D. What is the K-value for the 700 F mid-boiling-point fraction with the other circum-stances the same as in Example C?

Inasmuch as the same system and condit ions prevail as for Example C, KS and KT are thesame, and the only change is for the volatility exponent, b.

From Table 8A1.12, b = 2.801.

K= 2.4019.3 s.am

(-->

= 0.0070

2.40‘d

8-10

8Al.lB

i PROCEDURE 8Al.lB

VAPOR-LIQUID EQUILIBRIUM K-VALUES FOR HYDROCARBON SYSTEMS INAREA B

Discuss ionProcedure 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 conditionsare such that the point with these coordinates falls in Area B of Fig. 8A1.10, or if the operatingtemperature is less than or equal to the critical temperature of the light component, the follow-ing steps are to be followed to complete the estimation of K-values.

ProcedureStep 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 operatingpressure.

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 calculatedas 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 thevolatility exponents, b, of the identified hydrocarbons or of the 50 F TBP cuts of the petroleummixture from Table 8A1.12. Finally, solve equation (8Al.lA-1) for the K-value of each purecompound or portion of the petroleum fraction. In effect, this procedure extends the com-ponent scale to cover components with boiling points greater than 210 F.

8-11

8Al.lB

PurposeCOMMENTS ON PROCEDURE 8Al.lB

This procedure is to be used to complete the estimation of vapor-liquid equilibriumK-values for hydrocarbons when the operating conditions are such that the point falls inArea B of Fig. 8A1.10 and under certain other conditions outlined under Discussion. Thepreliminary calculations are performed using Procedure 8Al.1, which is the master procedurefor estimating hydrocarbon K-values under any conditions.Special Comment

For Limitations, Reliability, Notation, and Literature Sources, see Comments onProcedure 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 combinationof operating and convergence pressure falls in Area B in Fig. 8A1.10. Hence, the grid pressurecorrection is required before reading the K-value. In Fig. 8Al.11, a grid pressure of 117 psiais read as the ordinate for the given operating and convergence pressures.

Locate the operating pressure and temperaturein Fig. 8A1.14. and connect this uoint to theK z f.00 point.. Spot the point on this line corre-sponding to the grid pressure. Connect this gr idpressure point with the point on the nomographcomponent scale, and read the K-value for n-butaneas 5.75 (see example figure).

.I E-C4

I

LiquidComposition, x

(Mole Fraction)ca . < . . . . . . . . . . . . . . . . . . . . 0.0013n-c, . . . . . . . . . . . . . . . . . . . . . 0.0759n-G . . . . . . . . . . . . . . . . . . . . . 0.1802n-G . . . . . . . . . . . . . . . . . . . . . 0.2570n-C!, . . . . . . . . . . . . . . . . . . . . . 0.1460235* . . . . . . . . . . . . . . . . . . . . 0.1043285* . . . . . . . . . . . . . . . . . . . . 0.0918335* . . . . . . . . . . . . . . . . . . . . 0.0901385* . . . . . . . . . . . . . . . . . . . . 0.0534

Total . . . . . . . . . . . . . . . . 1.0000

B. Compute the reboiier temperature of agasoline stabil izer operating at 165 psia. The com-position of the liquid in the reboiler is shown in thefollowing tabulat ion. Assume that the gasoline hasproperties similar to those used in makingFig. 8A1.2.

For the first trial, assume the reboiler tem-perature is 350 F. The estimated convergencepressure is 940 psia (from the propane-gasolinecrit ical locus of Fig. 8A1.2, curve B). This systemfalls into Area B of Fig. 8A1.10. Therefore, a gridcorrect ion is required; From Fig. 8Al.11, the gridpressure is 190 psia . Fol low Steps 2 through 4 ofthe procedure to determine the grid point inFig. 8A1.14. Using this and volatility exponentsfrom Table 8A1.12, the K-values obtained arelisted in the following tabulation:

VolatilityExponent, b

. . .

. . .

. . .

. . .

O.ki.80.2620.48 10.716

. . .

K-Value(Fig. 8A1.14)

5.323.001.701.010.6000.512t0.292 t0.160t0.0837t

. . .

y=Kx0.00690.22770.30630.25960.08760.05340.02680.01440.00450.9872

In this computat ion, inasmuch as the summation of the vapor mole fract ions, y, is lessthan unity, a higher temperature should be used in the next trial to vaporize more liquid.Because the tr ial-anderror procedure is straightforward, the additional tr ials are not shownhere.

C. What are the K-values for methane and ethane at -100 F and 100 psia in a methane-ethane system?

The convergence pressure from Fig. 8A1.3 is 750 psia. The combination of operating andconvergence pressure falls in Area B in Fig. 8A1.10. Hence, the grid pressure correction isrequired 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) = 6.49where 1.047 is the correction factor for methane.

Ethane K = 0.337l Mid-botig oint of a etroleum fraction having a 50 F boiling ranget Usin Ka = 8 40 and & = 0 600

calculated %y equation @ALlA-1):88 read osing the pivot point for t&a problem, these K-values were

8-12

8Al.lC

PROCEDURE 8Al.lC

VAPOR-LIQUID EQUILIBRIUM K-VALUES FOR HYDROCARBON SYSTEMS INAREA C

Procedure 8Al. l is to be used for al l preliminary calculations toward est imating K-valuesof hydrocarbons. If the estimated convergence pressure and the operating pressure conditionsare such that the point with these coordinates falls in Area C of Fig. 8A1.10, the followingsteps are to be followed to complete the estimation of the K-values.

ProcedureStep For identifiable hydrocarbons having normal boiling points below 210 F, determine

the grid pressure from Fig. 8Al.11 for the estimated convergence pressure and operatingpressure.

Step 2: Locate the point on the temperature-pressure grid (Fig. 8A1.13 or 8A1.14) corre-sponding to the grid pressure and operating temperature.

Step 3: Lay the hairline of a nomograph reader through this point and the component pointand 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 forpetroleum fractions characterized by a true boiling point (TBP) curve, the K-value is calculatedas fohows. Determine the K-values of ethane and n-heptane at the operating temperature, op-erating 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 thevolatility exponents, 6, of the identified hydrocarbons or of the 50 F TBP cuts of the petroleummixture from Table 8A1.12. Finally, solve equation (8Al.lA-1) for the K-value of each purecompound or portion of the petroleum fraction. In effect , this procedure extends the componentscale to cover components with boiling points greater than 210 F.

8-13

8Al .lC

J

COMMENTS ON PROCEDURE 8Al.lC

P u r p o s eThis 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 inArea 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 CommentFor Limitat ions, Reliabi l i ty, Notat ion, and Literature Sources, see Comments on Proce-

dure 8Al.l.

ExampleDetermine the K-value of n-per&me at 1,000 psia and 100 F in a system having a con-

vergence 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

PROCEDURE 8Al.lDVAPOR-LIQUID EQUILlBRIUM K-VALUES FOR HYDROCARBON SYSTEMS IN

AREA DDiscuss ion

Procedure 8Al.l is to be used for all preliminary calculations toward estimating K-valuesof 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 tempera-ture of the average heavy component, the following steps are to be followed to calculate theconvergence pressure and complete the estimation of K-values. These steps are an interpola-tion scheme for estimating convergence pressure.Procedure

Step 1: The true critical pressure and critical temperature of the average heavy componentof a given mixture (exclusive of lightest component) is first calculated according to the proce-dures of Chap. 4. The liquid-phase mole fraction composition of the components is required. Ifthese are not given directly, they will have to be calculated from the composition of the totalmaterial or from the vapor-phase composition data by trial and error.

Step2: The average heavy component temperature-pressure (Ten, p,~) point and theoperating temperature (Top) line are spotted on one of Fig. 8A1.3 through 8A1.9, whicheverhas 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 thelightest component and two heavier components, the convergence pressure for the mixture iscalculated by interpolation as illustrated hereinafter, in Par. a through c. If the point fallsoutside the area, the convergence pressure is calculated according to Par. d.

a. If Fig. 8Al.lD-a applies, the con-vergence pressure is given by equation(8Al.lD-1):

pa = PI - (pa -Pi) ($)(%)

Where:

(8Al.lD-1)

p,, = convergence pressure, in poundsper square inch absolute.

pa = pressure on the superior (higher)critical locus, in pounds persquare inch absolute.

pt = pressure on the inferior (lower)critical locus, in pounds persquare 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,. %( >

Where:

(8ALlD-2)

XUJ.tl= calculated weight fraction of themiddle component.

E zz differences in Fig. 8Al.lD-a.

b. If Fig. SAl.ID-b applies, the con-vergence 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

I i--F--

FIG, 8Al.lD-a.

TEMPERATURE I T 2 IT3I

‘7’

FIG. 8Al.lD-b.8-15

8Al.lD

c. If Fig. 8ALID-c applies, the con-vergence 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 appliesand the given mixture is a ternary:

p..=pr-(Ps-ppr)xlo,.(8Al.lD-6)

d. For a mixture where the Tck, p,h pointfalls to the right of all loci curves, the locicurve of the mixture must be calculated andpee at Top determined. This is illustrated inFig. IAl.lD-d.

Arbitrarily increase mole fraction of light-est component so that its weight fraction equalsH/J, prorate other components, and recalculateTon, pes. If the lightest component is methane,ethene, or ethane and the assumed compositionsuch that the critical temperature is below100 F, then the calculated critical pressure isnot reliable.

Arbitrarily increase or decrease mole fraotion of lightest component to get a third Tab, panpoint 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.

TI T2TEMPERATURE

FIG. SAl.lD-c.

TEMPERATURE j

FIG. SALID-d.

Step 4: The convergence pressure calculated as previously indicated is then used with theoperating pressure to obtain a p. from Fig. 8Al.11. If the convergence pressure calculated isgreater than 5,000 psia, then operating temperature and grid pressure are used as the pivotpoint on Fig. 8A1.13 or 8A1.14 as is done in Procedure 8Al.lC. If the calculated convergencepressure is less than 5,000 psia, then the TOp, pop point is spotted on the K-nomograph andconnected to K = 1 by a straight line. Then the grid pressure is spotted on this line as the pivotpoint as is done in Procedure 8Al.lB.

8-16

8Al.lD

L

PurposeCOMMENTS ON PROCEDURE 8Al.lD

This procedure is to be used to complete the estimation of vapor-liquid equilibriumK-values for hydrocarbons when the operating conditions are such that the point falls inArea D of Fig. 8A1.10 or under certain other circumstances as noted under Discussion. ThePrel iminary ca lculat ions are performed using Procedure 8Al.1, which is the master procedurefor estimating hydrocarbon under any conditions.Special Comment

For Limitations, Reliability, Notation, and Literature Sources, see Comments on Procedure8Al.l.Examples

A. A liquid hydrocarbon stream having the composition tabulated below is to be processedat 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 theG- CS cr i t ical locus. From Fig. 8A1.10, this system fal ls into Area D. Eliminate the l ightestcomponent and recalculate the mole and weight fraction composit ions and obtain the cri t icalproperties of the average heavy component according to the procedures of Chap. 4.

Liquid-Phase CompositionI * \

Less LightestActual Component Normal

7Weight ----LizBoiling

Weight Po in tFraction, Fraction, Fraction, Fraction, (Degrees Molecular API

ct . . . . . . o.zo 0.015 02 LitFahrenheit) Weight GlWi~

2 : : : : : : : : :0.020 0.048 0.020 0.050 -128’ &i.l 2ij’0.050 0.082 0.051 0.086 -43.7 44.1 147.2

2 I:::::::0.100 0.125 0.101 0.131 +31.1 58.1 110.60.200 0.202 0.202 0.212 96.9 72.2 92.7

G . . . . . . . . 0.400 0.339 0.404 0.355 156 86.2 81.6c . . . . . . . . . 0.220 0.159 0.222 0.166 209 100.2 74.1

- - - -Total 1.000Average .’ .

1 .ooo 1.000 1.000 . . .. . . . . . . . . . ii.48 *-*91.1

Weight average boiling point:WABP = i xr< Tat = 127.3 F

Where:‘11

x=6 = weight fraction of component i.TQ = 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 boi l ing point .However , Rankine uni ts must be used for CABP. The MABP and CABP must be inthe same units to calculate MeABP.

Molal average boiling point:MABP = i xi Tat = 104.5 F

‘dwhere xc = mole fraction of component i.Cubic average boiling point:

CABP =(

;; xoc Tall8 ’ = 115.4 Ftr1 )

where x,,( = volume fraction of component i.Mean average boiling point:

MeABP= MABP+CABP -1lOOF2 -*

Average molecular weight = 2 XC (molecular weight)‘ = 75.48.‘2

AverageAPIgravity=~~lxv~ (API)c=91.1.

From the methods described in Chap. 4, the true critical temperature is T, = 880 R andthe pseudocritical temperature is Tp. = 860 R, SO To/T,. = 1.023.

From the methods given in Chap. 4, the pseudocri t ical pressure is ppe = 453 psia and thetrue 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 binariesmethane-pentane (the inferior locus) and methane-hexane (the superior locus) SO that thepseudo ternary for representing the actual (methane through heptane) mixture is methane-pentane-hexane.

.

8-17

8Al.lD

Inasmuch as the crit ical temperature is above the crit ical temperature of the inferior heavycomponent and the operating temperature is below this temperature, the convergence pressure iscalculated for the specified operating temperature from equation (8ALlD-3). At the pro-posed operating temperature of 150 F, the convergence pressure on the superior locus isp, = 2,890 psia, while on the inferior locus it is pi = 2,410.

= 870 - 545 = 325 psiaB = 870 - 487 = 383 psiaC=455-420=3SFE= 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 1before determinin g the K-values of the components in Fig, 8A1.14.

B. Calculate the dew-point temperature and equi l ibr ium l iquid composi t ion at 1 ,500 psiafor a mixture containing 68.9, 10.8, and 20.3 mole percent of methane, propane, and pentane,respectively, in the vapor phase.

This example i l lustrates the i terat ive procedure required when the l iquid composit ion isnot known. It is necessary to assume the temperature and convergence pressure and calculatean approximate l iquid-phase composit ion to check the assumed condit ions, repeat ing unti l nofurther change occurs.

For Trial 1, assume 250 F for the temperature and read the convergence pressure fromC, - 6 critical locus in Fig. 8A1.3. The estimate is p. = 1,880 psia. In Fig. 8Al.11, the gridpressure is p# = 2,940 psia.

Trial 1:

MolecularWeight, API

M Gravity

2 1:::: 44.i i4i.in-Cs . . . . 72.2 92.7

Total . . . . . .

K at x4M4

0.6:92SOF* x=y/K xM Xrc=-ZX4M4 xlos (API)41.86t 0.3704

0.108 0.86 0 . 1 2 5 6 iii O.i426 ii.00.203 0.44 0.4614 33.31 0.8574 79.5

- -1.00() . . . 0.9574 38.85 1.0000 100.5

For the next tr ial , assume 230 F. Calculate convergence pressure from the est imated l iquidcomposi t ion, x0, using equat ion (8Al.lD-2). The binaries involved are CL - CS and Cl - CS.

D=386-230~156E= 386-206~ 180 I See Fig. 8Al.lD-a, where D and E are defined.

x~,,, = 0.1426Pa = 2,030 ps iap4 = 650 psia

Using equation (8Al.lD-2), p.. = 2,030 - (2,030 - 650)0.1426% = 1,803 psia. There-

fore, from Fig. 8Al.11, pI = 3,200 psia.

Trial 2:

Cl . . . . . . . 0.6y89ca . . . . . . . 0.108n-G . . . . . 0.203

Total . . 1.000

K a t 230 F ,p = 1,500 psia,

pg = 3,300 psia x=y/K XM x,4 Xl04 (API)41.67t 0.41260.84 0.1286 iii o.iGs ii.70.465 0.4366 31.52 0.8475 78.4

- -. . . 0.9778 37.19 1.0000 101.1

The assumed temperature is still too high. Assume the temperature is 220 F. It is necessaryto 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.

ii

tI

‘j /

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 . 8A1 .14 ) .point position corresponding to 100 API from Trial 1 calculation.

8-18

8Al.lD

Y

K at 220 F,p = 1,500 psia,

pI = 3,000 psia x=y/K X04

C, . . . . . . . . . . . . . . . . . . . . 0.689 1.74 0.3960ca . . . . . . . . . . . . . . . . . . . . 0.108 0.80 0.1350 o.i442n-C!s . . . . . . . . . . . . . . . . . . 0.203 0.415 0.4892 0.8558

Total 1.000 . . . 1.0202 1 . o o o o. . . . . . . . . . . . .

Trial 4:K a t 225 F ,

p = 1,500 psia, ExperimentalY pg = 3,050 psia x=y/K xat220F

C, . . . . . . . . . . . . . . . . 0.689 1.75 0.3937 0.390c, . . . . . . . . . . . . . . 0.108 0.820 0.1317 0.133n-G . . . . . . . . . 0.203 0.435 0.4833 0.477

Total . . . . . . , . . 1.000 . . . 1.0087 1.000

A check on the convergence pressure for Trial 4 gives 1,847 psia versus 1,860 psia fromTrial 3, so that the grid pressure remains fixed. An intermediate temperature of approximately226 F to 227 F should give the fhral answer. As it is, the agreement with the experimentalliquid-phase composition at 220 F in the last column is satisfactory.

The operating pressure in the preceding example exceeds 70 percent of the convergencepressure, which is a reasonable upper l imit for reliable K-values. The satisfactory agreement ofcalculated and experimental liquid compositions means that K-values in this example arecorrect to within 2 percent. This is better reliability for K-values than can generally be expected.

8-19 I

I

8 0 0 d

!I

!/ (SO\;vJ.%(/ CiJ I/,+‘-’

1 =p c4 A 1 \

- 1 0 0 0 100 2 0 0 3 0 0 4 0 0 5 0 0TEMPERATURE, F

.e2..t0.

G3C, F r e e Gasolines

6 w t . % c2 g

:2“uFree Gosolinc z

1 0 wt.xc3 gis

:3 Free Gasoline 114 wt. % c4 8

1000

8 0 0

6 0 0

- 2 0 0 - 1 0 0 0 l o o 2 0 0 3 0 0 4 0 0TEMPERATURE, F

- 1 0 0 0 100 2 0 0 3 0 0 4 0 0 5 0 0 6 0 0 7 0 0 8 0 0

TEMPERATURE, F

Stubilizers:

5 0 0I/ )

h’s I*i 400 1 - 1

iI

? 3 0 022

610I

NO. p

F!? ,Fuel Oil

TEMPERATURE, F

A NOTE: ‘Part of Procedure 8Al.l

:

CA through 400 F end-point gasolineCa through 400 F end-point gasoline

Reboiler and bottom trays of stabilizer

G through 400 F end-point gasolineMid-stripping section of stabilizer

D Cl through 400 F end-point gasolineTop stripping section of stabilizerStabilizer feed plate: top of bubble tower

Light-hydrocarbon towers:E Cl-G De-ethanizer overheadF Cl-G-G-G

zc1-c=-cs--c,-c5

Top rectifying section of stabilizerTop rectifying section of depentanizerTop rectifying section of de-ethanizerReboiler and stripping section of butane-

K G-C,propane de-ethanizer

In conjunction with curve J for feed plateof butane-propane de-ethanizer

Absorbers, crude oil flashing towers, and heavy-hydrocarbon fractionators:D Cl through 400 end-point gasolineL C1 through distillate crude oil

In conjunction with curves L and M for estimating effect of heavy components on p,,

M C1 through Mid-Continent crude oilLight crude oil flashing: absorber (light lean oil)

N C, through No. 3 fuel oilMid-Continent crude oil flashing: absorber (heavy lean oil)

0 1G’s through No. 3 fuel oil ,Bubble tower bottoms

8-20

CONVERGENCE PRESSURES

OF BINARY SYSTEMS

METHANE

MI THE LIGHTEST COMPONENT

TECHNICAL DATA BOOK

October 1964

Approved : MRF & WGB

8-21

vd ‘mnss3u8-22

‘L .I

lOO(

90(

80(u.-zi- 70(lu

53gj 60(a

5a

40(

30(

8A1.5

FIGURE 8A1.5

CONVERGENCE PRESSURES

OF B INARY SYSTEMS

PROPANETHE LIGHTEST COMPONENT

TECHNICAL DATA BOOK

Octdber 1964

Approved: MRF 8. WGB

,I000

900

800

300

700 800200

TEMPERATURE, F

8-23

, b,

8A1.6

8 0 0

7 0 0

6 0 0

5 0 0

4 0 0

3 0 0

2 0 0

TEMPERATURE, F8-24

8A1.7

FIGURE 8A1.7

CONVERGENCE PRESSURES

O F B I N A R Y S Y S T E M Sc-PENTANE , o-HEXANE,

& n-HEPTANET H E LiGHTEST C O M P O N E N T

TECHNICAL DATA BOOK

O c t o b e r 1964

Approved: MRF & WGB

TEMPERATURE, F8-25

mm8A1.8. ,

r!FIGURE 8A1.8

CONVERGENCE PRESSURES

O F BtNARY S Y S T E M S

ETHENETHE LIGHTEST COMPONENT

TECHNICAL DATA BOOK

October 1964

Approved 1 MRF 8s WGB

vsd ‘32tflSWtd8-26

150

100

8 0

0.-

” 70

3Ot

TEMPERATURE, .F8-27

8A1.10

I I I I -

\ AREA DSINGLE PHASE AREA C

AREA A It\L

F I G U R E 8A1.10

PRESSURE

PARAMETER

REQUIREMENTS FOR

T H E K - NOMOGRAPHI

TECHNICAL DATA BOOK

IOctober 1 9 6 4

II”I Approved : MRF b WGB

II

I I

NOTE: Part of Procedke 8Al.l-

50 ’ I I III I /I I II,1 I I III I5 0 0 1000 2000 5000 lOQO0

ESTIMATED CONVERGENCE PRESSURE, pcv, psia mm

8-28

.K -

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 18-29

1

8A1.12

TABLE 8A1.12VOLATILITY 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 ,Volatility Exponent, b*

Pure Hydrocarbons,\

Normal Boiling Points( D e g r e e s F a h r e n h e i t )

50 P Cuts, TBP Mid-Boiling Points( D e g r e e s F a h r e n h e i t )

0 0051015

;93 0354 04 55 05.56 0

Fi7 58 0859 09 5

200 3 0 0 4 0 0 ‘,

600 7 0 0. . .

o.bbi0.0210.0400.0600.0790.0980.1170.1370.1560.1760.1960.2160.2360.2560.2770.2970.3180.339

0.3600.3810.4030.4250.4470.4690.4910.5140.5370.5600.5840.6070.63 10.6560.6800.7050.7300.7560.78 10.808

0.8340.8610.8880.9160.944

1 0 0. ...

.

2.8012.8432.8862.9282.9723.014

.

. .3.0583.102 \3.146

. .

.

-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

2 0 0-0.08 1-0.061-0.041-0.021-0.002

0.0180.0380.0580.0780.0980.1180.1380.1590.1800.2000.2210.2420.2620.2840.305

3 0 00.3260.3480.3700.3920.4140.4360.4580.48 10.5040.5260.5500.5720.5960.6200.6440.6680.6920.7160.7420.766

OTT20:8170.8420.8680.8940.9210.9480.9741.0021.0291.0571.0851.1131.1421.1701.1991.2281.2581.2881.318

5 0 01.3481.3791.4101.4411.4721.5041.5361.5691.6021.6341.6681.7011.7351.7691.8041.8381.8741.9081.9441.980

2.0162.0532.0902.1262.1642.2022.2402.2782.3162.3552.3942.4342.4742.5142.5542.5942.6352.6762.7182.759

3.1903.2343.2803.3243.3703.4153.4613.5073.5533.6003.646

8-30

8A1‘.13

n-HEPTANE - “’-I

160n-HEXANE

IS0

n-PENTANE100

NOTES: I. THE FREEZING POINT OF LT NYOROCARSONMIXTURES MAY SE ENCOUNTERED ATTEMPERATURES BELOW -100 E

2. ACETYLENE-LT. HYDROCARBON MIXTURESHIY FORM AZEOTROPES AT TEMPERATURESABOVE - 3 5 F

3. FOR METHANE IN SOLVENTS WITH AVERAGEMOLECULAR WEIGHTS BETWEEN 30 8 44USE THE MULTIPLYING CoRRECTloNFACTOR SHOWN ON THE INSERT CHARTBELOW TO CORRECT METHANE KS.

2-WIHYLGUTANEIISOPENTANE

1 NOTE: Part of Procedure 8Al.l 1

1-EUTENEI-METHYLPROPANE

*G 2

(ISOSUTANO ,O Z

0 P

PROPANE

PROPENE

!

-10

-20

-so

-40

-so

0090.08 -0 . 0 70 . 0 6

I-_--- _A----

- -0 . 0 5

1

--..-.. \..“IL. 9,0.09 METHANE C0RRPltnt.1 Tim=. -j

0.01s

lfHYNE (ACE::::!;,’IN LT.

HYDROCARBONS

METHANE INL T . HYDROClVlBONS

IGEE NOTE ,I

METHANE IN/cq T O 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

@-BUTANE _-I~*w~-BUTENE---~-MUTENE--

“HEXANE--‘

’

NOTE: Part of Procedure BAl.1

I ” “ ‘ ; ] ’

ETHANE

ieC,“, INBENZENE

-40

-30

-20

-10

0

19

20

30

40

50

so

70

110 c’E

120 p

I30 ;

140 g

I50 iz

IDO g

170

180

190

‘WI

1

8-32

FIGURE 8A2.1

ACTIVITY CORRECTION

FOR MIXTURES

CONTAINING AROMATICS

ECHNICAL DATA BOON

October 1964

Approved :. MRF & WGE

” 0-J c. .

J ‘NOllklt!03 AllAil~ 311VwotlV -

d ‘NOll33~~03 Allhl13V 311VWOW-NON8A2.1

c

8-33

8A2.1

COMMENTS ON FIG. 8A2.1

Fig. 8A2.1 is presented to est imate the act ivi ty coefficients to be applied to vapor-l iquidequil ibrium K-values obtained from Procedure 8Al. l or 8Bl. l for mixtures containing aromatichydrocarbons.

LimitationsThe 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.

ReliabilityThe vapor-l iquid K-values obtained f rom Procedure 8Al.l and corrected with this figure

deviate from experimental values by an average of 3.5 percent.

Notat iony = 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 sonreeThis 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 theliquid contains 10.9 mole percent cyclohexane and 89.1 mole percent toluene at 220 F and14.7 psia.

From Procedure 8Al.1, the K-value (KnoarS ) for cyclohexane is 1.78 and for toluene0.827 at these conditions. From Fig. 8A2.1. the nonaromatic activitv correction is Y = 1.32and 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 fract ioncyclopentane and 0.60 mole fraction benzene at 153 F and 14.7 psia.

The calculation is one of tr ial and error because neither the vapor-l iquid mole ratio northe composit ions of the vapor and l iquid are known. A flash calculat ion must be made withan assumed l iquid composit ion to est imate the activi ty corrections (because of the presence ofthe aromatic) and K-values.

A vapor-liquid mole ratio is assumed, and the composition of the liquid is calculated by theexpression based on material balance and the equilibrium relationship:

%‘= xrc(L + wL+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 liquidphases, and the total amount of vapor and l iquid are calculated. The calculated l iquid com-position and the quantities of vapor and liquid are used in the next trial until the finalcalculated values of the liquid mole fractions and vapor and liquid mole ratios equal the assumedvalue for that trial.

From Procedure 8Al.1, the K-value (KS,,. ) for cyclopentane is 1.60 and for benzene is0 .63 .

Trial I:

AssumedMole

Fract ion,

AssumingV/L = 0.50/0.50

Y 5iiz-kzx (Fig. 8A2.1) K,,,,,. -YK*.*. (Moles) (M&s)

Cyclopentane (1) . . 0 .40 1.122 1.60 1.795 0.1431 0.2569Benzene (2) . . . . . . . 0 .60 1.067 0.630 0.6722 0.3588 0.2412

- -To ta l . . . . . . . . . . . . . . . . . . . . 0.5019 0.498 1

a-34

8A2.1

Assume V = 0.50 mole and L = 0.50 mole; then:(0.40) (1.00)

x1 = 0.50 + (1.795) (0.50)= 0.2862

(0.60) (1.00)x9 = 0.50 + (0.6722) (0.50)

= 0.7176

Trial 2:

yz= Klx%= (1.795) (0.2862) = 0.4138ya= K&a= (0.6722) (0.7176) = 0.4824

AssumedAssuming

MoleV/L = 0.498/0.502

Fl-iXtiOll,I L \Liquid Vapor

Qclopentane (1) . . O&4( F i g . 8yA2.1) Km,,, yKmon. (Moles) (Moles)

1.195 1.60 1.912 0.1381 0.2619Benzene (2) . . . . . . 0.716 1.035 0.63 0.652 0.3644 0.2356

- -Total . . . . . . . . . . . . . . . . . . . . 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:

AssumedAssuming

MoleV/L = 0.498/0.502

FlZtiOIl,Liquid Vapor

( F i g . zA2.1) Km.,, yKn~~~ ,A-,(Moles) (Moles)

Cyclopentane (1) . . O.n275 1.195 1.60 1.912 0.1381 0.2619Benzene (2) . . . . . . 0.725 1.035 0.63 0.652 0.3639 0.2357

- -Total . . . . . . . . . . . . . . . . . . . . 0.5020 0.4976

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 ratioare equal to the assumed, the calculation is completed.

8-35

,

8Bl.l

PROCEDURE 8Bl.l

VAPOR-LIQUID EQUILIBRIUM K-VALUES FOR SYSTEMS CONTAININGHYDROCARBONS AND HYDROGEN

D i s c u s s i o nThe following procedure is useful for calculating the vapor-liquid equilibrium K-values for

hydrogen-hydrocarbon systems.

ProcedureStep I: Determine K-values for the hydrocarbons, including methane, from the K-nomo-

graphs (Fig. 8A1.13 and 8A1.14, using a convergence pressure of 5,000 psia) at the systemtemperature 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 requiresno correct ion in mult icomponent hydrogen systems) by mult iplying together the three factorsfrom Steps 1 and 4. For mixtures containing aromatic hydrocarbons, the fol lowing equationshould be used to correct the K-values of the hydrogen:

KA= = Kgarxpar + 2 Kamxm (8Bl.l-1)

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 l iquid, calculated on a hydrogen-free

Xaro = mole fraction aromatic components in l iquid, calculated on a hydrogen-free basis.

Step 6: Repeat Steps 2 through 5 until the assumed and calculated compositions checkwithin an acceptable tolerance.

For mixtures without methane, the procedure is the same except that no correction factorfor the presence of methane is required. For binary mixtures of hydrogen and methane, useFig. 8B1.4 for the K-value of methane.

8-37

881.1

COMMENTS ON PROCEDURE 8Bl.l

P u r p o s eThis procedure is to be used to determine the K-values for systems containing both

hydrogen and hydrocarbons. Although developed primarily for hydrogen-parathn-ole8n sys tems ,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 lowerthan -300 F or higher than 900 F (but not above a pseudocriticai temperature of 0.9 for thehydrocarbons in the l iquid phase) , or to hydrocarbon mixtures having an MABP of the l iquid(MABP&) above 700 F.

Reliabi l i tyThe correlations of K-values for hydrogen-hydrocarbon systems have been tested against

experimental data. The results are given in the following tabulation:

Pressure(Pounds per Square

Figure Inch Absolute)8B1.2 10 to 10,0008B1.3 10 to 4,5008B1.4 10 to 5,000

Special Comments

Temperature(Degrees Fahrenheit)

- 3 0 0 t o 900*-260 to 800-300 to -150

Number of AverageExperimental Deviation

Points (Percent)531 11.5461 12.7

27 8.3

At low hydrogen concentrations (below 5 mole percent in the vapor) and pressures below1,500 psia, the original hydrocarbon nomographs, Fig. 8A1.13 and 8A1.14, can be used withoutthe correction of Fig. 8B1.3 for the presence of hydrogen.

The correlation was developed and has been tested with hydrogen-paraffin, hydrogen-olefin, and hydrogen-paraffin-olefin mixtures . Limited data indicate that i t is a lso applicable tohydrogen-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-freearomatics in the l iquid phase. A correction for aromatic presence can be made by the use ofequation (8Bl.l-1).

Literatnre sourceThe procedure was developed by Shen, Proc. API 44 CIIII 23 (1964).

ExampleA. Calculate the K-values of the components at -100 F and 1,000 psia of a hydrogen-ethene-

ethane system, the feed composition of which is:

Mole PercentHydrogen . . . . . . . . . . . . . . . 32.25Ethene . . . . . . . . . . . . . . . . . . . . . . . . 41.68Ethane . . . . . . . . . . . . . . . . . . . . . . . . 26.07

Total . . . . . . . . . . . . . . . . . . . . . . 100.00

For pure hydrocarbon mixtures, from Fig. 8A1.13:KC~E&WtnO) = 0.180Kc,n,,(s-) = 0.102

Assuming MABPL of -130 F (between those of ethene and ethane) as a first approxima-tion, from Fig. 8B1.2:

Km,= 22.7Assmling MABPV = -300 F (between those of hydrogen and ethene), from Fig. 8B1.3:

K-value correction = 0.85

Then,K C*H4 = (0.85)(0.180) = 0.153Kc+~ = (0.85) (0.102) = 0.0867

l Up to 0.9 TPO of the hydrocarbons in the liquid.

8-38

881.1

To check vapor and liquid compositions, the flash vaporization at -100 F and 1,000 psiais calculated:

Normal Trial 1 Trial 2Boiling ’

L A

Point Assuming Assuming

OweesV/L = so/so V/L = 33/67t*

Mole Fahren-r

Assumed Liquid, \

PercentVapor Assumed* Liquid

heit)Vapor

K-Values (Moles) (Moles) K-Values (Moles) (Moles)

;f.g 36.15 1.36 30.89 5.53 21.026:07

-155 -423 22.7 0.153 0.112 2.80 1 29.45 2.1739.5c;Hs . . . . . -128 0.0867 23.99 2.08 0.0632 25.29 0.78

Total . . 100.00 . . . . . . 61.50 38.50 67.60 32.40

Assumed Calculated CalculatedMABPr, deg F . . - 3 0 0 -368.5 -397.8MABPL, deg F . . . -130 -143.8 -144.1

Trial 3 Trial 4f

Assuming\ r * \

AssumingV/L = 31/69t V/L = 31/69

I L LAssumed* Liquid

, IVapor Assumed* Liquid

\Vapor

K-Values (Moles) (Moles) K-Values (Moles) (Moles)Ha . . . . . . 32.25 -423 20.8 3.12 29.13 20.8 3.12 29.13C&I, . . 41.68 -155 0.0900 40.08 1.60 0.0828 40.19 1.49C&L . . . . 26.07 -128 0.0510 25.48 0.59 0.0469.,. 25.53 0.54

Total . 100.00 . . . . . . 68.68 31.32 68.84 31.16

Calculated CalculatedMABPr,deg F . . . . . . . . . . . . . . . . . . . . . . . . . 4 0 3 . 6 -405.0MABPL, deg F. . . . . . . . . . . . . . . . . -144.1 -144.1

B. Make a flash calculation at -100 F and 500 psia for a mixture of the following com-position:

Mole PercentHydrogen . . . . . . . . . . . . . . . . . . . . . . 34.62Methane . . . . 41.61Ethane . . . . . . . . . . . . . . . . . . . . . . 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, themultiplying 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 vaporenough, because the correction to the hydrocarbon K-values for composition is

cornsmall. ‘tion is generally good

p”t The convergence is slow, so V/L used from preceding trial is overcompensated.

i

8-39

4 881.1

Compute f lash vaporization at -100 F and 500 psia until the assumed and calculatedvapor and liquid compositions agree:

Feedh

Normal Trial 1 Trial 2Boiling ’

L

Po in t Assuming Assuming

(DegreesV/L = 70/30 V/L = 74/26

MoleI *

Fahrell- Assumed Liquid,

Vapor Assumed* ePercent heit) K-Values (Miles) (Moles) K-Values (Miles) (MGles)

H. . . . . . . . . 34.62 -423 26.5 0.55 34.07 35.2 0.34 34.28Cl% . . . . . . . 41.61 -259 1.59 8.83 32.78 1.59 7.53 34.08c& . . . . . . 23.77 -128 0.0912 19.60 4.17 0.117 17.83 5.94

Total . . 100.00 . . . . . 28.98 71.02 . . . 25.70 74.30

Assumed Calculated CalculatedMABPv, deg F.. . . . . . . . -400 -329.8 -324.0MABPL, deg F.. . . . . . . . . . . -200 -168.3 -166.4

* Based on calculated MABPv and h%ABPz and mole percent methane in liquid from the previous trial.6 :

Nofe* The vapor and Iiquid compositions from Trials 1 and 2 are close enough considerin the insensitivity ofe K values to small changes in molal average boiling point, temperature, pressure. a n %

o f t h i s p r o b l e m . )c o m p o s i t i o n r a n g e

8.40

881.2

‘L

i

FIGURE 861.2

HYDROGEN K-VALUES

IN HYDROGEN-HYDROCARBON

SYSTEM5

TECHNICAL 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 CONTAININGHYDROCARBONS AND NONHYDROCARBON GASES

D i s c u s s i o nThis procedure is used to determine the vapor-liquid equilibrium K-values for systems

containing hydrocarbons with nonhydrocarbon gases other than hydrogen.

ProcedureStep 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 hydrocarbonsother than methane and benzene, points for all components are located in the figures. For othersystems, 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 corre-sponding to the operating temperature and pressure.

Step 3: Lay the hairline of a nomograph reader through each component point and thetemperature-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 temperature-pressure grid corresponding to the operating temperature and pressure (no convergence pressureis needed). Locate the point on the pure-component scale corresponding to the normal boilingpoint of the hydrocarbon and lay a nomograph reader through these two points. Read theK-values of the hydrocarbon at the point of intersection of the hairline with the K-scale.

8-45

8C1.1

P u r p o s eCOMMENTS ON PROCEDURE 8Cl.l

This procedure is to be used to determine the K-values for systems containing hydrocarbonsand the nonhydrocarbon gases except hydrogen. Fig. 8C1.2 and 8C1.3 are used in the procedure.Limitat ions

This procedure for the determination of in hydrocarbon-nonhydrocarbon gassystems was developed for the fol lowing systems. I ts use is l imited to the temperature andpressure ranges listed.

Nitrogen-methane . . . . . . . . . . . . . . . . . . . . . .Nitrogen-n-butane . . . . . . . . . . . . . . . . . . . . .Nitrogen-n-heptane . . . . . . . . . . . . . . . . . . . .Nitrogen-methane-n-hexane . . . . . . . . . . . . .Nitrogen-benzene . . . . . . . . . . . . . . . . . . . . . .Hydrogen sulfide-methane . . . . . . . . . . . . . .Hydrogen sulfide-n-pentane . . . . . . . . . . . . .Hydrogen sulfide-Pegasus crude oil and

natural gas dist i l late . . . . . . . . . . . . . . . . . .Hydrogen sulfide-naphtha . . . . . . . . . . . . . . .Hydrogen sulf ide-gas oi l . . . . . . . . . . . . . . . .Carbon dioxide-methane . . . . . . . . . . . . . . . .Carbon dioxide-propane . . . . . . . . . . . . . . . .Carbon dioxide-n-butane . . . . . . . . . . . . . . .Carbon dioxide-natural gas dist i l late . . . . . .Sulfur dioxide-n-hexane . . . . . . . . . . . . . . . . .Ammonia-n-hexane . . . . . . . . . . . . . . . . . . . .Hydrogen chloride-n-butane . . . . . . . . . . . . .Monomethylamine-n-hexane . . . . . . . . . . . . .Water-propane . . . . . . . . . . . . . . . . . . . . . . . .Water-n-butane . . . . . . . . . . . . . . . . . . . . . . .Water-n-hexane . . . . . . . . . . . . . . . . . . . . . . .Water-naphtha and kerosine . . . . . . . . . . . . .Hydrogen fluoride-2-methylpropane . . . . . . .Methylmercaptan-absorption oi l . . . . . . . . .Carbon monoxide-propane . . . . . . . . . . . . . .

Reliabi l i ty

Temperature Pressure RangeRange (Pounds per

(Degrees Square InchFahrenhei t ) Absolute)

-260 to -145 22to 650100 to 300 236 to 1,00090 to 360 950 to 1,00077to 185 511 to 1,000

160 to 260 901 to 1,000-120to 1 6 0 200 to 1,000

40 to 340 20 to 1,000

Reference9, 121,43

25

2832X’62

40 to 250AmbientAmbient

-1ooto 2 9-40 to 160

1OOto 280

50 to 4,00050 to 20050 to 200

300 to 1,00050 to 1,000

200 to 1,000

106td 108100 to 35070to 180

125 to 35040 to 205

100 to 460100 to 28035 to 48220 to 16065 to 79

-7 to 150

98to’ 101100 to 40066to 531

100 to 400100 to 1,000

10 to 3,00024to 51336 to 1,00040 to 20067 to 605

400 to 900

232323

3,Yo

z;t36

;:31

27,376,41

292125

iii

The K-values determined using this procedure for the systems and ranges listed above havean average error of 18 percent.Speeid Comments

Data on the solubility of hydrocarbon gases in water, the water content of natural gases incontact with liquid water, and vapor-solid equilibrium ratios of hydrocarbons in hydrate systemsare 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.The Chao-Seader method (computer only) (8)-or the Grayson-Breed method (20) may be

used for other systems or for the systems given in this procedure at temperature or pressureranges beyond those shown in the table.Literature Sources

Fig. 8C1.2 and 8C1.3 were prepared by modification of the vapor-l iquid equil ibria chartsof Hadden and Grayson, Hydrocarbon Process. Petrol . Refiner 4Q [91 207 (1961); copyrightedin 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 and93 1 psia.

Locate the nitrogen (in n-butane) point in Fig. 8C1.3 and connect it with a straight line tothe 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 lineto the 100 F and 931 psia point on the grid of the nomograph. Read the K-value of n-butane as0.137.

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 and100 psia.

Locate the methane ( in ni trogen) point and the ni trogen ( in methane) point in Fig. 8Cl.2and connect each with a s traight l ine through the -240 F and 100 psia point on the grid of thenomograph. 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).

LJ

8-46

8C1.2 ,

-260 TO 100 F RANGE I

TECHNICAL DATA BOOK

~wnl n-64

*ppmved MRFL~WI)

.

NOTE: Part of Procedure 8Cl.l

$ CAMON DIOXIDE’tin PROPANE)

CARBON DIOXIDE (in METHANE) $

eMETNANE

NITROGENh METHANE) @ lin NITROGEN)

8-47

8C1.3

TECHNICAL DATA BOOK

NOTE: Part of Procedure 8Cl.l

61 MONOMETHYLAMINE.fin P”EXANE)

$ METHYL: MEKAPTAN(in ASSORPTION W- 195 MW)

8-48

P .

BIBLJOGRAPIN

(September 1964)

1. Akers, W. W., Attwell, L. L., Robinson, J. A., “Volu-metric and Phase Behavior of Nitrogen-Hydrocarbon Systems.Nitrogen-Butane System,” (1954).

2. Akers, W. W., Kehn, D. M., Kilgore, C. H., “VolumetricI and Phase Behavior in Nitrogen-Hydrocarbon Systems. Nitro-

gen-n-Heptane System,” ibid., 2536.3. Akers, W. W., Kelley, R. E., Lipscomb, T. G., “Low-

Temperature Phase Equilibria. Carbon Dioxide-Propane Sys-tem,” ibid., 2535.

4. Benedict, M., Webb, G. B., Rubin, L. C., Friend, L., “AnEmpirical Equation for Thermodynamic Properties of LightHydrocarbons 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., “MutualSolubil i t ies of Light Hydrocarbon-Water Systems,” Petrol. Re-finer30 1101 118 (1951).

7. Cajander, B. C., Hipkin, H. G., Lenoir, J. M., “Predic-tion of Equilibrium Ratios from Nomograms of ImprovedAccuracy,” 1. Chem. Eng. Data 5 251 (1960).

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