Thermo II Paper

7/30/2019 Thermo II Paper

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Property methods Analysis

A Computational Project

By

Code instructions


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Pv

1. Insert Tc (critical temperature), Pc (critical pressure), omega (accentric factor) and Tf (freezing)for whatever chemical compound is desired.

2. Click the button as directed on the sheet and navigate to sheet 2 to see the vh and vl and to sheet 3to see the data points.

Pxy /Txy

1. Specific mixturesa. Click the button on the spreadsheet

2. Generala. Insert Tc (critical temperature), Pc (critical pressure), infdilgamma (gamma at infinite

dilution) A, B, C (Antoines constants), T(K) (of the system), P(bar) (of the system) and

omega (accentric factor).

b. Click the buttons on the spreadsheet.


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Introduction

A computational look at calculating isotherms over a P-V graph and T-x-y and P-x-y data

analysis was performed. The property calculations were done with a verity of equations of state and other

property methods. Two approaches will be looked at. The first is the use of a simple program created in

visual basic with an interface through excel. The second is to produce the same data from ASPIN plus.

The data was then compared and an analysis done comparing the different models.

Coding Procedure

PV

The purpose of the PV diagram was to create the vapor-liquid equilibrium dome, along with ten

isotherms, from the Soave Redlich Kwong (SRK) equation of state (EOS).

When programming, the first thing that was done was dimming the variables appropriately. If arrays are

needed, or depending on the accuracy needed, dim as singles or doubles. Then data needs to be pulled

from the spreadsheet. After this is done, the programming for the diagram can begin.

Ten isotherms were required. This diagram is for vapor-liquid equilibrium, thus the minimum temperature

that could exist would be the freezing point. Equal intervals were desired and a For loop was used to

divide the temperature from the freezing point to the critical point into six equal sections, but then more

sections of the same programming format were added above the six sections in order to account for the

three isotherms needed above the vl equilibrium dome. These values were stored in the isotherm array on

Sheet 3.

The roots of the SRK then need to be found in order to find the edge volumes of the dome. This was done


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by calculating the first derivative of the SRK EOS. Within SRK there are a,b and alpha terms, a and b are

constant for the species, but alpha changes with temperature. All of these values are calculated within the

program.

The root finder was done using the SRKROOT function. This was done using trigonometric method. We

began by defining P, Q and R in terms of R, T Psat, alpha, av and bv. In order to use the trigonometric

method, 120 degrees needed to be converted to radians. The terms of the equation are put into the

compressed cubic form of z3+az+b=0 and then set z

3=ucos, where u satisfies the identity 4cos3 -3cos-

cos(3)=0. A and B from the program are defined in terms of P, Q and R from the above definitions.

This function will solve for the roots of the cubic function using cosine and then will test for the

realness of the roots. This was the best method to choose because it allowed for not using imaginary

numbers which excel cannot deal with.

Once the roots have been found, those are the bounds for vh and vl. The isotherms are graphed using

SRK, by plugging the isotherm value from the top of the program and plugging it in as the T value.

The last part corrects for the isotherm within the dome. While SRK will continue to predict a downward

trend, within the VLE dome, the pressure will stay constant. The loop just states the SRK should account

for the pressure if the v is located outside of the dome, and if v is located within the dome, p=psat.

The last part of the program outputs the data onto sheet 3, in order to display what is being graphed.

This was the best way to approach the data because finding the roots of the SRK EOS allowed us to find

the limits of the VLE dome and the isotherms then allowed us to chart the points within in the dome and

outside of the dome, and it is general enough that any chemical will work. While this program is lengthy,

it is much quicker than would be expected.


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T-x-y

For the Txy diagram, we input the specified P and Tc, Pc, gamma at infinite dilution and Antoines

constants. We used the van Laar adjustment for gamma.

Next, Tsat was calculated using Antoines equation and the specified pressure. dT is set to a value ofzero

and then an while loop is initiated. The loop says that while dT is greater than the small tolerance set at

the beginning, a new temperature needs to be calculated by using Psat and gamma. This calculated T is

output into the spreadsheet.

Next, x is specified. Antoines equation is calculated using the constants and the T of the system just

found, Tsat. Then, gamma is calculated using the van laar excess gibbs energy. Finally, y1 is calculated

using y=x1*gamma*Psat1/P. The data is then output to the spreadsheet.

This method was the best approach because it was very simple. Using Tsat and specifying x allows the

user to very easily calculate the Txy diagram. Since the program is so simple, the program is quick.

P-x-y

For the Pxy diagram, we approached the code by inputting T, which was specified, Tc, Pc, gamma at

infinite dilution, Antoines constants and omega. Using the constants, we calculated a,b and alpha for the

SRK EOS.

Again, gamma was adjusted from the infinite dilution at 350 K. Limits from the Pv program were

calculated with the aim of getting Psat out of the program. The program through the line

Psat(i)=Psatguess is a mirror of the Pv program.

Next, x is specified in order to find bubble pressure. Gamma is then calculated for component one and

component two. P is calculated using RLA, P(i)=x1*gamma1*Psat(1)+x2*gamma2*Psat(2). Then a while

loop is initiated in order to find where y1 and y2 create a zero difference, that is, when dP is smaller


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than the very small tolerance set at the beginning of the program. Once the loop is completed, then the

last calculated P is the pressure of the system. These values are outputted into the spreadsheet.

Next, y is specified in order to find dew temperature. Gamma is also specified as a guess. P is calculated

using the equation, ()

()

()

. X is guessed using the y, P, Psat and gamma.

Gamma is then recalculated using the new x guesses. P is reiterated using the new gammas with the

specified ys. Here again a while loop is initiated to find where the gamma does not change, which

verifies the guess for x. Once gamma values are found, they are plugged into the formula for P, above,

and a P for the system is calculated. This is within the same type of dP loop as found in the first part of

the program. Once dP is equal to zero, then a value for the system is verified.

The functions on the bottom of the page are support for the SRKROOT function used to find the bubble

pressure.

The equations used were RLA , SRK EOS, summing of the two components of the system to find the

totally pressure of the system, the calculation of gamma.

This was the best method because iterations were used in order to get the best answer. This program is

also much quicker than calculating by hand, but does take a little bit of time since so many iterations are

done within the loops.

Both the Txy and the Pxy could be easily adapted to other chemical mixtures by inputting the proper

tabulated data into the spreadsheet.

Aspen Procedure

To plot an Isotherm across a P-V diagram using ASPIN the first step is to set up a block flash

tank. I had one stream feeding in and an overhead and bottoms coming out for the vapor and liquid

streams respectively. After the flash tank has been created the next step is to set up the specifications.


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Setting the global settings to make sure that the run type is a flow sheet and units are set to SI. Next is

defining the components. This P-V diagram is a single component, Glyoxal. The SRK property method is

then selected in the properties tab. Then the flash tanks, or block, properties are defined. Under flash

specifications the temperature and pressure of the system can be defined and manipulated. This is where

the input for different isotherms is entered. Under the Model Analysis Tools tab Sensitivity then S-1 is

selected. This is where the out let streams properties are defined and the results can be accessed. To

define the streams click new under the define tab and select stream 1, overhead, and under category select

Streams. Then, under reference select type; stream-var, stream; overhead, substream; mixed, variable

mole-density. Close out of variable definition back to the define tab and do the same thing for stream 2,

bottoms, but define it as a liquid instead of a vapor. The next step is the vary tab. Under manipulated

variable select block-var for type, block name, the flash tank, for block; pressure for variable. Finally,

under the tabulate tab click the fill variables and that will fill in all the pertinent information.

Now that the block and streams have been defined it is a simple matter to run different isotherms

for a given property method. By going back to the block input the temperature for the isotherm can be

manipulated to run three isotherms under, one at, and two above the critical temperature.

To change property methods going back to the properties tab this can be selected via the drop

down bar. If any modifications to the property method is needed, such as in COSMO SAC, the modify

property models can be selected and then an EOS modification can be made. Run all 3 isotherms per

property method and export the data to excel. In excel tables and graphs may be made to help identify

trends and accuracy of predicted systems.

Plotting T-x-y and P-x-y in Aspen is fairly straightforward if not time consuming. There is no

need to set up a block the property analysis tool is not based on any process conditions. By selecting the

data browser the properties and components input boxes are brought up. In the properties input there is a

drop down that will allow you to choose what property method to use. In the components box two


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10

20

30

40

50

60

70

0 0.5 1 1.5 2 2.5 3

Preassure(Bar)

Volume(M^3/Kmol)

SRK Isotherms of Glyoxalwith L-V equilibrium dome

T

T

T

T

C

D

D

different components may be entered. After all inputs are filled out by selecting tools, analysis, properties,

binary the correct window to produce P-x-y and T-x-y information is brought up. Here a constant

pressure may be entered for T-x-y information and temperature may be entered for P-x-y. By accessing

the NIST thermo data engine the experimental data to compare calculations to can be accessed.

After all data was collected a comparison between the experimental values and calculated values

for T-x-y and P-x-y was performed. By entering the data into excel and then graphing a comparison

between the calculated data and experimental data is easy to asses. As for P-v diagrams all other property

models were compared back to SRK. 1

isotherm below, at and above the critical

point was compared.

Comparison Analysis

Pressure-Volume Isotherms

For the data analysis of isotherms

across a pressure volume graph the

SRK EOS was chosen to be

compared against. By observing the isothem at critical temperature (in blue) the carcteristic dome can

be visualized. Also if more isotherms were to be layed on top of this graph it would clearly mark the area

around the vapor-liquid equilibrium dome. These together show that SRK is accuret and a good point of

comparison to the other models. When anylizing other property methods the COSMO and Peng-

Robinson come very close to the accurecy of SRK. Apon closer inspection of the critical point and

Fig 1. SRK isotherms of glyoxal


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10

20

30

40

50

60

70

0 1 2 3

Preassure(Bar)

Voume(M^3/Kmol)

SRK VS Ideal Gas

T=475K SRK

T=539 SRK

Crit T SRK

T=475 IG

T=539 IG

Crit T IG

sourounding points the

Peng-Robonson is a better

match then the COSMO.

Considering the nature of

glyoxal and that peng-

Robonson was designed

with

imporoving accuercy near

the critical point as well as

is good predictor of non-polar molacules its stregths are well suited for glyoxal. The worst predictor of

glyoxals liquid-vapor equillibrium dome is the ideal gas equation of state. This is to be expected as

glyoxal dose not satisfy the requirements of an ideal gas. The intermolecular interactions of glyoxal have

a strong influence on its behavior in the vapor phase. As can be seen in fig. 2 there is a shift in the liquid

vapor equilibrium dome bounders on the vapor side. On the liquid side of the dome there is not much of

a deviation from the SRK model.

On the vapor side there is a shift to the right meaning that the ideal gas EoS is predicting a larger

volume then the gas actually is taking up. The limitations of the ideal gas EoS cannot account for the

intermolecular attraction that is present in glyoxal. At the critical temperature these short comings are

easily seen. The gap between the vapor and liquid sides of the dome are extremely far apart. This implies

that there is a range of volumes at a single pressure that are vapor only. As we know that this can only

happen in the two phase area of the P-v diagram it is a good indicator of the deficiencies in the predictive

model.

Fig. 2 SRK vs Ideal gasEoS For P-V diagram


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T-x-y and P-x-y Graph Analyses

Benzene Toluene

The first binary mixture that will be analyzed is benzene and toluene. After carefully considering the

comparisons of the property models against the experimental data the ideal gas EoS and NTLR are the

most accurate. Even though the mixture of benzene and toluene do have some interactions they are

weak enough that the mixture can be successfully predicted by the ideal gas EoS. This is significant as

using the most simplistic approach is

preferable. The reason that the mixture

has ideal gas properties is due to the

relatively high temperature in relation to

both components boiling points and the

low pressure of the isobaric system of 1

bar. The same holds true for the P-x-y

data even though the temperature is

brought down significantly but also the

pressure is dropped to .25 bar. The NRTL Excess Gibbs energy approach is also an accurate due also to

the ideal gas nature of the mixture. Some of the principle assumptions for NRTL is that the local

concentration around component a is not influenced the local concentration around component b. Even

though this may be a flawed concept in an ideal case it is accurate.

Methanol Benzene

350

360

370

380

390

0 0.2 0.4 0.6 0.8 1

Temperature(K)

Mole Fraction Benzene

T-x-y Data Vs Ideal & NRTL

Benzene Toluene

VLE-02

VLE-02

IDEAL L

IDEAL V

NRTL L

NRTL V

Fig. 3 T-x-y experimental data

compared to Ideal gas EoS and NRTL


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0

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0 0.2 0.4 0.6 0.8 1

P

ressure(Bar)


P-x-y Data Vs Wilson

Methanol Benzene

VLE-105 L

VLE-105 V

WILISON L

WILISON V

The mixture of methanol and benzene produce a more complicated fraction percent to

temperature/pressure relationship as an azeotrope is introduced. Because of the azeotrope this shows the

short comings in standard equations of state. None of the equations of state that were looked at came

close to being able to

predict the T-x-y or P-x-y

model for this mixture. The

strengths of activity

coefficient models really

show in this case. The

Wilson model and NRTL

were very close in

predicting the nature of the

methanol and benzene

mixture. In this case Wilson was slightly better. The success of this model has to do with the fact that the

formation of an azeotrope is better described in thermo-dynamical terms of activity coefficients then just

pressure, temperature and volume. This is due to the fact that an azeotrope, by definition, happens when

both components in a mixture display the same physical parameters. Due to this equations of state rely

on independent values for physical conditions and are not powerful enough. NRTL is based off of the

Wilson model and, as stated above, some of the incorrect assumptions for the NRTL cause a slight

deviation form experimental data leaving the Wilson method more accurate.

Fig. 4 P-x-Y of experimental data and

the Wilson method


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Acetone Water

Acetone and

water create another

complicated system

with an azeotrope

being formed close

to the mole fraction

of 1. Just as before

equations of state

fail to be able to model this system and activity coefficient models improve on the equation of state.

Again, as before with the methanol and benzene, NRTL and Wilson are very similar and accurate but this

time there is not enough of a significant difference between the two to state one is better than the other.

Conclusion

In conclusion the application of using equations of state and Excess Gibbs Energy models

demonstrates the strengths of each approach. When trying to predict how a system will behave it is

important to take into account the properties of the components in the system as well as any possible

anomalies that may occur such as azeotropes. After careful consideration the correct method to predict

the system parameters may be chosen and applied.

320

330

340

350

360

370

380

390

0 0.2 0.4 0.6 0.8 1

Temperature(K)


T-x-y Data Vs NRTL

Acetone Water

VLE-110 L

VLE-110 V

NTLR L

NTLR V

Fig. 5 T-x-y of experimental data and

NRTL


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Appendixes

A: Visual basic coding

Copy of code

N.B.-for the Pxy and Txy diagrams, only one mixture is represented since the other two mixtures are

identical programs with different cell outputs in order to go on the sheet where it belongs.

Sub Pv()

'Grace Carrier and Joe Machado

'7 December 2012

'Program to output PV dome and ten isotherms

' Dim variables as needed

Dim Intgl As Double

Dim delta As Single

Dim T(10)

Dim alpha(10)

Dim limit As Variant

Dim Psat(10)

Dim vl(10)

Grace Carrier and Joe Machado

12/7/2012 13:27

Computational Program - Glyoxal

Tc 496.7 K

Pc 6278867 N/m2

w 0.436264

*data gathered using Diadem Professional, DIPPR

database

Isotherm one T=

a=

b=

( )

( ( )( ))


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Dim vh(10)

Dim isotherm(10, 100)

Dim v(10, 100)

'Input varaibles on Spreadsheet

Application.Goto Sheets("Sheet1").Range("B7")

Tc = ActiveCell.Value 'K

ActiveCell.Offset(1, 0).Select

Pc = ActiveCell.Value 'MPa


omega = ActiveCell.Value 'dimensionless


'freezing point

Tf = ActiveCell.Value 'K

R = 0.000008314 'J/mol K

A = 0.42748 * R ^ 2 * Tc ^ 2 / Pc

B = 0.08664 * R * Tc / Pc

'Set tolerance and max number of equations

es = 0.000000000000001

imax = 1000

'Find temperatures for the isotherms based off of freezing point and critical point

'Alpha as well since it is temperature dependant

For i = 0 To 9

T(i) = Tf + (Tc - Tf) / 7 * (i + 1)


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alpha(i) = (1 + (0.48508 + 1.55171 * omega - 0.15613 * omega ^ 2) * (1 - (T(i) / Tc) ^ 0.5)) ^ 2

Next

Application.Goto Sheets("Sheet2").Range("A1")

For i = 0 To 5

Intgl = 0

Psatg = 0

'set limits for the equation using min and max by finding critical points of the first derivative, see

MINMAX funtion

Limits = MINMAX(R, T(i), A, B, alpha(i))

If Limits(0) < 0 Then

Limits(0) = 0

End If

ea = 1

iter = 0

While ea > es And iter


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beta = 1

For j = 1 To 2

If (Roots(j) < Roots(j - 1)) Then

dumnum = Roots(j)

Roots(j) = Roots(j - 1)

Roots(j - 1) = dumnum

beta = 0

End If

Next

Wend

'integral calculation in order to find psat

Intgl = SRKINT(Roots(0), Roots(2), R, T(i), A, B, alpha(i), Psatg)

iter = iter + 1

If Intgl 0 Then

ea = Abs(Intgl)

End If

If Intgl < 0 Then

Limits(1) = Psatg

ElseIf Intgl > 0 Then

Limits(0) = Psatg

Else

ea = 0


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End If

Wend

Psat(i) = Psatg

vl(i) = Roots(0)

vh(i) = Roots(2)

Next

Application.Goto Sheets("Sheet2").Range("H1")

'Isotherms below the critical point

For i = 0 To 5

ActiveCell.Value = Psat(i)


ActiveCell.Value = vl(i)


ActiveCell.Value = vh(i)

ActiveCell.Offset(-2, 1).Select

Next

'critical point isotherm

Psat(6) = Pc

Roots = SRKROOT(R, T(6), A, B, alpha(6), Pc)

For i = 0 To 1

If IsNumeric(Roots(i)) = False Then


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Roots(i) = 0

End If

Next

beta = 0

While (beta < 1)

beta = 1

For j = 1 To 1

If (Roots(j) < Roots(j - 1)) Then

dumnum = Roots(j)

Roots(j) = Roots(j - 1)

Roots(j - 1) = dumnum

beta = 0

End If

Next

Wend

vl(6) = Roots(1)

vh(6) = Roots(1)

Application.Goto Sheets("Sheet2").Range("N1")

ActiveCell.Value = Psat(6)


ActiveCell.Value = vl(6)

Application.ScreenUpdating = True

For i = 0 To 9


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vcalc = B + 0.000001

If vcalc < vl(i) Or vcalc > vh(i) Then

isotherm(i, 0) = SRK(vcalc, R, T(i), B, A, alpha(i))

ElseIf vcalc >= vl(i) And vcalc


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Next

'Shows isotherm temp


For i = 0 To 9

ActiveCell.Value = T(i)


Next

'Outputs volumes

Application.Goto Sheets("Sheet3").Range("A3")

For j = 0 To 100

ActiveCell.Value = v(0, j)


Next

'Outputs Pressures


For i = 0 To 9

For j = 0 To 100

ActiveCell.Value = isotherm(i, j)


Next


Next

Application.ScreenUpdating = True


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End Sub

Function MINMAX(R, T, A, B, alpha)

'Dim arrays

Dim VLH(2)

Dim mv(10000) As Variant

Dim FirstDerivative(10000) As Variant

For i = 0 To 10000

v = B + 0.000001 * (i + 1)

'SRK first derivative

FirstDerivative(i) = -(R * T / (B - v) ^ 2) + (A * alpha * (B + 2 * v)) / (v ^ 2 * (B + v) ^ 2)

mv(i) = v

Next

inc = 0

test = 0

If FirstDerivative(0) < 0 Then

While test


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test = 0

While test >= 0

inc = inc + 1

test = FirstDerivative(inc)

vmax = mv(inc)

Wend

ElseIf FirstDerivative(0) > 0 Then

While test >= 0

inc = inc + 1


vmax = mv(inc)

Wend

test = 0

While test


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VLH(0) = Plow

VLH(1) = Phigh

MINMAX = VLH

End Function

Function QBRT(x As Double) As Double

' Signed cube root function. Used by Qubic procedure.

QBRT = Abs(x) ^ (1 / 3) * Sgn(x)

End Function

Function SRKROOT(Gas, T, av, bv, alpha, Psat)

' Q U B I C - Solves a cubic equation of the form:

' y^3 + Py^2 + Qy + R = 0 for real roots.

' Input P,Q,R Coefficients of polynomial.

' Output ROOT 3-vector containing only real roots.NROOTS The number of roots found. The real roots

' found will be in the first elements of ROOT.

' Closed form employing trigonometric and Cardano's method

' Note: To translate and equation of the form:


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' O'y^3 + P'y^2 + Q'y + R' = 0 into the form above,

' divide through by O', i.e. P = P'/O', Q = Q'/O', R=R'/O'

'Define coefficients

P = Gas * T / -Psat 'v^2

Q = (bv ^ 2 * Psat + bv * Gas * T - av * alpha) / -Psat 'v

R = (av * alpha * bv) / -Psat 'c

'Dim variables as neccesary

Dim Z(3) As Double

Dim p2 As Double

Dim RMS As Double

Dim A As Double

Dim B As Double

Dim nRoots As Integer

Dim DISCR As Double

Dim t1 As Double

Dim t2 As Double

Dim RATIO As Double

Dim SUM As Double

Dim DIF As Double

Dim AD3 As Double

Dim E0 As Double

Dim CPhi As Double

Dim PhiD3 As Double

Dim PD3 As Double


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Const DEG120 = 2.09439510239319

Const Tolerance = 0.00001

Const Tol2 = 1E-20

' Translate into the form Z^3 + aZ + b = 0

p2 = P ^ 2

A = Q - p2 / 3

B = P * (2 * p2 - 9 * Q) / 27 + R

RMS = Sqr(A ^ 2 + B ^ 2)

If RMS < Tol2 Then

'Three equal roots

nRoots = 3

ReDim Root(0 To nRoots)

For i = 1 To 3

Root(i) = -P / 3

Next i

Exit Function

End If

DISCR = (A / 3) ^ 3 + (B / 2) ^ 2

If DISCR > 0 Then


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t1 = -B / 2

t2 = Sqr(DISCR)

If t1 = 0 Then

RATIO = 1

Else

RATIO = t2 / t1

End If

If Abs(RATIO) < Tolerance Then

'Three real roots, two (2 and 3) equal.

nRoots = 3

Z(1) = 2 * QBRT(t1)

Z(2) = QBRT(-t1)

Z(3) = Z(2)

Else

'One real root, two complex. Solve using Cardan formula.

nRoots = 1

SUM = t1 + t2

DIF = t1 - t2

Z(1) = QBRT(SUM) + QBRT(DIF)

End If

Else

'Three real unequal roots. Solve using trigonometric method.

nRoots = 3


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AD3 = A / 3#

E0 = 2# * Sqr(-AD3)

CPhi = -B / (2# * Sqr(-AD3 ^ 3))

PhiD3 = Application.WorksheetFunction.Acos(CPhi) / 3#

Z(1) = E0 * Cos(PhiD3)

Z(2) = E0 * Cos(PhiD3 + DEG120)

Z(3) = E0 * Cos(PhiD3 - DEG120)

End If

'Now translate back to roots of original equation

PD3 = P / 3


Application.Goto Worksheets("Sheet2").Range("F2")

For i = 0 To nRoots - 1

Root(i) = Z(i) - PD3

Next i

SRKROOT = Root

End Function

Function SRKINT(v1, v3, R, T, A, B, alpha, Psat)

'Takes the integral of SRK and finds psat inorder to find where the integral is equal to zero


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SRKINT = -Psat * (v3 - v1) - (A * alpha * Application.WorksheetFunction.Ln(v3 / v1)) / B + R * T *

Application.WorksheetFunction.Ln((v3 - B) / (v1 - B)) + (A * alpha *

Application.WorksheetFunction.Ln((v3 + B) / (v1 + B))) / B

End Function

Function SRK(v, R, T, B, A, alpha)

SRK = R * T / (v - B) - (A * alpha) / (v * (v + B))

End Function


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Sub Pxy_AW()


'7 December 2012

'Will output Pxy diagrams

'Input data

Dim integral, T, alpha(3), Psat(3), A(3), B(3), w(3), Tc(3), Pc(3), infdilgamma(3), P(11), y1(11), y2(11),

AntoineA(3), AntoineB(3), AntoineC(3), Pnew(11), Pold(11) As Double

Dim delta, AVL, BVL As Single

Dim Limits As Variant

Application.Goto Sheets("sheet6").Range("b8")

T = ActiveCell.Value

R = 0.000008314 'J/molK


For i = 1 To 2

Tc(i) = ActiveCell.Value


Pc(i) = ActiveCell.Value


infdilgamma(i) = ActiveCell.Value


AntoineA(i) = ActiveCell.Value



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AntoineB(i) = ActiveCell.Value


AntoineC(i) = ActiveCell.Value


w(i) = ActiveCell.Value


A(i) = 0.42748 * R ^ 2 * Tc(i) ^ 2 / Pc(i)

B(i) = 0.08664 * R * Tc(i) / Pc(i)

alpha(i) = (1 + (0.48508 + 1.55171 * w(i) - 0.15613 * w(i) ^ 2) * (1 - (T / Tc(i)) ^ 0.5)) ^ 2

Next

AVL = R * 350 * Application.WorksheetFunction.Ln(infdilgamma(1))

BVL = R * 350 * Application.WorksheetFunction.Ln(infdilgamma(2))

'Set tolerance and max number of equations

esmall = 0.000000000000001

imax = 1000

integral = 0

Psatguess = 0

For i = 1 To 2

Limits = MINMAX(R, T, A(i), B(i), alpha(i))

If Limits(0) < 0 Then

Limits(0) = 0


31/107

End If

ea = 1

iter = 0

While ea > es And iter


32/107

iter = iter + 1

If integral 0 Then

ea = Abs(integral)

End If

If integral < 0 Then

Limits(1) = Psatguess

ElseIf integral > 0 Then

Limits(0) = Psatguess

Else

ea = 0

End If

Wend

Psat(i) = Psatguess

Next


For i = 0 To 10

x1 = i * 0.1

x2 = 1 - x1

ActiveCell.Value = x1



33/107

gamma1 = R * T * Exp(AVL * (BVL * x2 / (AVL * x1 + BVL * x2)) ^ 2)

gamma2 = R * T * Exp(BVL * (AVL * x1 / (AVL * x1 + BVL * x2)) ^ 2)

P(i) = x1 * gamma1 * Psat(1) + x2 * gamma2 * Psat(2)

ActiveCell.Value = P(i)


Pnew(i) = P(i)

dP = 1

While dP > esmall And iter


34/107


Next


For i = 0 To 10

y1guess = i * 0.1

y2guess = 1 - y1guess

ActiveCell.Value = y1guess


gamma1 = 1

gamma2 = 1

P(i) = 1 / ((y1guess / (gamma1 * Psat(1))) + (y2guess / (gamma2 * Psat(2))))

x1guess = y1guess * P(i) / (gamma1 * Psat(1))

x2guess = y2guess * P(i) / (gamma2 * Psat(2))

gamma1 = R * T * Exp(AVL * (BVL * x2guess / (AVL * x1guess + BVL * x2guess)) ^ 2)

gamma2 = R * T * Exp(BVL * (AVL * x1guess / (AVL * x1guess + BVL * x2guess)) ^ 2)


Pnew(i) = P(i)

newgamma1 = gamma1


35/107

newgamma2 = gamma2

dP = 1

dgamma = 1

newiter = 1

While dP > esmall And newiter esmall And dgamma2 > esmall And Iteration


36/107

newgamma1 = gamma1

newgamma2 = gamma2

dgamma1 = Abs(newgamma1 - oldgamma1)

dgamma2 = Abs(newgamma2 - oldgamma2)

Wend


Pnew(i) = P(i)

dP = Abs(Pold(i) - Pnew(i))

Wend

P(i) = Pnew(i)

Next


For i = 0 To 10

ActiveCell.Value = P(i)


Next


End Sub


37/107

Function MINMAX(R, T, A, B, alpha)

'Dim arrays

Dim VLH(2)

Dim mv(10000) As Variant

Dim FirstDerivative(10000) As Variant

For i = 0 To 10000

v = B + 0.000001 * (i + 1)

'SRK first derivative

FirstDerivative(i) = -(R * T / (B - v) ^ 2) + (A * alpha * (B + 2 * v)) / (v ^ 2 * (B + v) ^ 2)

mv(i) = v

Next

inc = 0

test = 0

If FirstDerivative(0) < 0 Then

While test = 0


38/107

inc = inc + 1


vmax = mv(inc)

Wend

ElseIf FirstDerivative(0) > 0 Then

While test >= 0

inc = inc + 1


vmax = mv(inc)

Wend

test = 0

While test


39/107

MINMAX = VLH

End Function

Function QBRT(x As Double) As Double

' Signed cube root function. Used by Qubic procedure.

QBRT = Abs(x) ^ (1 / 3) * Sgn(x)

End Function

Function SRKROOT(Gas, T, av, bv, alpha, Psat)

' Q U B I C - Solves a cubic equation of the form:

' y^3 + Py^2 + Qy + R = 0 for real roots.

' Input P,Q,R Coefficients of polynomial.

' Output ROOT 3-vector containing only real roots.NROOTS The number of roots found. The real roots

' found will be in the first elements of ROOT.

' Closed form employing trigonometric and Cardan

' Note: To translate and equation of the form:

' O'y^3 + P'y^2 + Q'y + R' = 0 into the form above,

' divide through by O', i.e. P = P'/O', Q = Q'/O', R=R'/O'


40/107

'Define coefficients

P = Gas * T / -Psat 'v^2

Q = (bv ^ 2 * Psat + bv * Gas * T - av * alpha) / -Psat 'v

R = (av * alpha * bv) / -Psat 'c


Dim Z(3) As Double

Dim p2 As Double

Dim RMS As Double

Dim A As Double

Dim B As Double

Dim nRoots As Integer

Dim DISCR As Double

Dim t1 As Double

Dim t2 As Double

Dim RATIO As Double

Dim SUM As Double

Dim DIF As Double

Dim AD3 As Double

Dim E0 As Double

Dim CPhi As Double

Dim PhiD3 As Double

Dim PD3 As Double

Const DEG120 = 2.09439510239319


41/107

Const Tolerance = 0.00001

Const Tol2 = 1E-20

' Translate into the form Z^3 + aZ + b = 0

p2 = P ^ 2

A = Q - p2 / 3

B = P * (2 * p2 - 9 * Q) / 27 + R

RMS = Sqr(A ^ 2 + B ^ 2)

If RMS < Tol2 Then

'Three equal roots

nRoots = 3


For i = 1 To 3

Root(i) = -P / 3

Next i

Exit Function

End If

DISCR = (A / 3) ^ 3 + (B / 2) ^ 2

If DISCR > 0 Then

t1 = -B / 2

t2 = Sqr(DISCR)


42/107

If t1 = 0 Then

RATIO = 1

Else

RATIO = t2 / t1

End If

If Abs(RATIO) < Tolerance Then

'Three real roots, two (2 and 3) equal.

nRoots = 3

Z(1) = 2 * QBRT(t1)

Z(2) = QBRT(-t1)

Z(3) = Z(2)

Else

'One real root, two complex. Solve using Cardan formula.

nRoots = 1

SUM = t1 + t2

DIF = t1 - t2

Z(1) = QBRT(SUM) + QBRT(DIF)

End If

Else

'Three real unequal roots. Solve using trigonometric method.

nRoots = 3

AD3 = A / 3#

E0 = 2# * Sqr(-AD3)


43/107

CPhi = -B / (2# * Sqr(-AD3 ^ 3))

PhiD3 = Application.WorksheetFunction.Acos(CPhi) / 3#

Z(1) = E0 * Cos(PhiD3)

Z(2) = E0 * Cos(PhiD3 + DEG120)

Z(3) = E0 * Cos(PhiD3 - DEG120)

End If

'Now translate back to roots of original equation

PD3 = P / 3


Application.Goto Worksheets("Sheet2").Range("F2")

For i = 0 To nRoots - 1

Root(i) = Z(i) - PD3

Next i

SRKROOT = Root

End Function

Function SRKINT(v1, v3, R, T, A, B, alpha, Psat)

'Takes the integral of SRK and finds psat inorder to find where the integral is equal to zero

SRKINT = -Psat * (v3 - v1) - (A * alpha * Application.WorksheetFunction.Ln(v3 / v1)) / B + R * T *

Application.WorksheetFunction.Ln((v3 - B) / (v1 - B)) + (A * alpha *

Application.WorksheetFunction.Ln((v3 + B) / (v1 + B))) / B


44/107

End Function

Function SRK(v, R, T, B, A, alpha)

SRK = R * T / (v - B) - (A * alpha) / (v * (v + B))

End Function

End Function

End Function

End Function


45/107

Sub Txy_AW()


'7 December 2012

'This program will output Txy and Pxy for inputed chemicals


Dim Intgl, P, Psat(3), Tsat(3), Tc(3), Pc(3), infdilgamma(3), Temp(11), y1(11), y2(11), AntoineA(2),

AntoineB(2), AntoineC(2), y1guess(11) As Double

Dim delta As Single

Dim limit As Variant

'Input variables on spreadsheet

Application.Goto Sheets("sheet6").Range("c8")

P = ActiveCell.Value

R = 0.000008314 'J/molK


For i = 1 To 2

Tc(i) = ActiveCell.Value


Pc(i) = ActiveCell.Value


infdilgamma(i) = ActiveCell.Value


AntoineA(i) = ActiveCell.Value



46/107

AntoineB(i) = ActiveCell.Value


AntoineC(i) = ActiveCell.Value


Next

'calculate a and b for vl

AVL = R * 350 * Application.WorksheetFunction.Ln(infdilgamma(1))

BVL = R * 350 * Application.WorksheetFunction.Ln(infdilgamma(2))

'set tolerance and max iteration

es = 0.0000000001

imax = 1000

'calculate tsat

Tsat(1) = AntoineB(1) / (-Application.WorksheetFunction.Ln(P) + AntoineA(1)) - AntoineC(1)

Tsat(2) = AntoineB(2) / (-Application.WorksheetFunction.Ln(P) + AntoineA(2)) - AntoineC(2)

'calculate guess for x and corresponding temp

For i = 0 To 10

x1guess = 0.1 * i

x2guess = 1 - x1guess


47/107

Temp(i) = x1guess * Tsat(1) + x2guess * Tsat(2)

tnew = Temp(i)

dT = 1

iter = 0

'calculate psat, gamma using the guesses

While dT > es And iter


48/107

'Output data

Sheets("Sheet6").Range("b11").Select

For i = 0 To 10

ActiveCell.Value = Temp(i)


Next

'guessing x, calculating psat gamme and y for dew temp


For i = 0 To 10

x1guess = 0.1 * i

x2guess = 1 - x1guess

ActiveCell.Value = x1guess


Psat(1) = Exp(AntoineA(1) - AntoineB(1) / (Temp(i) + AntoineC(1)))

Psat(2) = Exp(AntoineA(2) - AntoineB(2) / (Temp(i) + AntoineC(2)))


49/107

gamma1 = R * Temp(i) * Exp(AVL * (BVL * x2guess / (AVL * x1guess + BVL * x2guess)) ^ 2)

gamma2 = R * Temp(i) * Exp(BVL * (AVL * x1guess / (AVL * x1guess + BVL * x2guess)) ^ 2)

y1guess(i) = (x1guess * gamma1 * Psat(1)) / P

Next

'Output data


For i = 0 To 10

ActiveCell.Value = y1guess(i)


Next

End Sub

B: Aspen Data and Graphs


50/107

10

20

30

40

50

60

70

0 0.5 1 1.5 2 2.5 3

Preassure(Bar)

Voume(M^3/Kmol)

SRK Isotherms

T=425K

T=450K

T=475K

T=539t

Crit T


51/107

bar KMOL/CU KMOL/CUM V Liquid V Vapor VLIQUID VVAPOR V Liquid V Vapor VLIQUID VVAPOR V Liquid V Vapor VLIQUID VVAPOR V Liquid V Vapor VLIQUID VVAPOR V Liquid V Vapor

1 0.028568387 35.00373 0.026936 37.12473 0.025484 39.24007 0.022404 44.63569 0.02435 41.06813

1.0135 0.028957797 34.53301 0.027303 36.62634 0.02583 38.714 0.022707 44.03875 0.02468 40.51809

2 0.057692443 17.33329 0.054301 18.41582 0.051302 19.49242 0.044988 22.22823 0.04897 20.4208

3 0.087401843 11.44141 0.082113 12.17835 0.077465 12.90911 0.067756 14.75884 0.073867 13.53783

4 0.117728975 8.494086 0.110391 9.058714 0.103984 9.616861 0.090711 11.02398 0.09905 10.09594

5 0.148709296 6.724529 0.139156 7.186175 0.130873 7.641021 0.113857 8.782912 0.124526 8.030478

6 0.180381756 5.543798 0.168431 5.937156 0.158143 6.323372 0.137198 7.28875 0.150303 6.653217

7 0.212789299 4.699484 0.198239 5.044409 0.185811 5.38182 0.160736 6.221387 0.176391 5.669209

8 0.245979459 4.06538 0.228608 4.374307 0.213889 4.675317 0.184476 5.420772 0.202799 4.930979

9 0.280005073 3.571364 0.259564 3.852612 0.242395 4.125502 0.208421 4.797988 0.229537 4.35659410 0.31492515 3.175358 0.29114 3.434779 0.271344 3.685358 0.232575 4.299684 0.256614 3.896897

11 0.350805925 2.850579 0.323367 3.092458 0.300755 3.324964 0.256943 3.891911 0.284042 3.520603

12 0.387722161 2.579166 0.356284 2.806748 0.330647 3.024374 0.281529 3.552034 0.311832 3.206857

13 0.425758763 2.348748 0.38993 2.564564 0.36104 2.769776 0.306336 3.264385 0.339995 2.94122

14 0.465012814 2.150478 0.424349 2.356553 0.391956 2.551306 0.33137 3.017771 0.368544 2.713379

15 0.505596163 1.977863 0.459589 2.175857 0.423419 2.361727 0.356635 2.803984 0.397493 2.51577

16 0.547638767 1.826021 0.495705 2.01733 0.455454 2.195614 0.382136 2.616869 0.426854 2.342719

17 0.591293073 1.691209 0.532756 1.877033 0.488087 2.048815 0.407877 2.451718 0.456644 2.18989

18 13.5618 0.073737 0.570809 1.7519 0.521349 1.9181 0.433864 2.304869 0.486877 2.053907

19 13.5772 0.073653 0.60994 1.639507 0.555271 1.800921 0.460102 2.173432 0.51757 1.932105

20 13.59249 0.07357 0.650233 1.537911 0.589888 1.695236 0.486595 2.055095 0.548741 1.822354

21 13.60769 0.073488 0.691785 1.445536 0.625238 1.599392 0.513351 1.947986 0.580408 1.722927

22 13.6228 0.073406 0.734707 1.361087 0.66136 1.512036 0.540373 1.850572 0.61259 1.632412

23 13.63781 0.073326 0.779126 1.283489 0.698301 1.432048 0.567669 1.761589 0.64531 1.549643

24 13.65273 0.073245 0.825192 1.21184 0.736109 1.358495 0.595244 1.679982 0.67859 1.473645

25 13.66755 0.073166 0.873078 1.145374 0.774839 1.290591 0.623105 1.604866 0.712453 1.403602

26 13.68229 0.073087 0.922991 1.083434 0.81455 1.227671 0.651258 1.535491 0.746925 1.338822

27 13.69694 0.073009 0.975183 1.025448 0.855311 1.169166 0.679709 1.471218 0.782035 1.278715

28 13.7115 0.072932 1.029957 0.970914 0.897194 1.114586 0.708466 1.411501 0.817812 1.222775

29 13.72597 0.072855 11.7172 0.085345 0.940284 1.063508 0.737535 1.355867 0.854287 1.170566

30 13.74036 0.072778 11.74385 0.085151 0.984676 1.015563 0.766925 1.303908 0.891497 1.121709

31 13.75466 0.072703 11.77016 0.084961 1.030475 0.970426 0.796643 1.255267 0.929477 1.075874

32 13.76888 0.072628 11.79614 0.084774 1.077805 0.927812 0.826696 1.209634 0.968269 1.032771

33 13.78302 0.072553 11.8218 0.08459 1.126805 0.887465 0.857094 1.166733 1.007917 0.992145

34 13.79708 0.072479 11.84715 0.084408 1.17764 0.849156 0.887844 1.126324 1.048469 0.953772

35 13.81106 0.072406 11.87221 0.08423 1.230498 0.812679 0.918955 1.088192 1.089977 0.917451

36 13.82496 0.072333 11.89698 0.084055 1.285607 0.777843 0.950437 1.052148 1.1325 0.883002

37 13.83879 0.072261 11.92146 0.083882 1.343236 0.744471 0.982298 1.018021 1.1761 0.850268

38 13.85253 0.072189 11.94568 0.083712 1.403713 0.712397 1.01455 0.985659 1.220849 0.819102

39 13.86621 0.072118 11.96962 0.083545 1.46744 0.681459 1.047201 0.954927 1.266824 0.789376

40 13.8798 0.072047 11.99331 0.08338 1.534926 0.651497 1.080263 0.925701 1.314112 0.76097

41 12.01674 0.083217 1.606823 0.622346 1.113746 0.897871 1.362809 0.733779

42 12.03993 0.083057 1.683991 0.593827 1.147662 0.871337 1.413025 0.707702

43 12.06287 0.082899 1.767609 0.565736 1.182022 0.846008 1.464882 0.682649

44 12.08559 0.082743 1.859365 0.537818 1.216839 0.821801 1.518522 0.658535

45 12.10807 0.08259 9.365394 0.106776 1.252126 0.798642 1.574104 0.635282

46 12.13034 0.082438 9.429004 0.106056 1.287896 0.77646 1.631813 0.612815

47 12.15238 0.082288 9.490025 0.105374 1.324162 0.755195 1.691864 0.591064

48 12.17421 0.082141 9.548713 0.104726 1.360938 0.734787 1.754508 0.56996

49 12.19584 0.081995 9.605284 0.104109 1.39824 0.715185 1.820045 0.549437

50 12.21726 0.081851 9.659925 0.10352 1.436083 0.696338 1.888831 0.529428

51 12.23849 0.081709 9.712796 0.102957 1.474483 0.678204 1.961301 0.509866

52 12.25952 0.081569 9.764036 0.102417 1.513456 0.660739 2.037991 0.490679

53 12.28036 0.081431 9.813769 0.101898 1.553019 0.643907 2.119574 0.471793

54 12.30102 0.081294 9.862102 0.101398 1.593191 0.627671 2.206912 0.453122

55 12.32149 0.081159 9.909132 0.100917 1.633989 0.611999 2.301145 0.434566

56 12.34179 0.081026 9.954945 0.100453 1.675434 0.59686 2.403819 0.416005

57 12.36191 0.080894 9.999616 0.100004 1.717544 0.582227 2.517131 0.397278

58 12.38187 0.080763 10.04322 0.09957 1.760341 0.568072 2.644365 0.378163

59 12.40165 0.080634 10.08581 0.099149 1.803846 0.554371 2.790819 0.358318

60 12.42127 0.080507 10.12745 0.098742 1.848081 0.541102 2.966026 0.337151

61 12.44074 0.080381 10.16818 0.098346 1.893068 0.528243 3.190559 0.313425

62 12.46004 0.080257 10.20807 0.097962 1.938831 0.515775 3.529298 0.283342

63 12.47919 0.080133 10.24715 0.097588 1.985395 0.503678 5.825726 0.171652

64 12.49819 0.080012 10.28545 0.097225 2.032784 0.491936 6.416593 0.155846

65 12.51704 0.079891 10.32303 0.096871 2.081024 0.480533 6.728951 0.148612

66 12.53575 0.079772 10.3599 0.096526 2.13014 0.469453 6.958721 0.143705

67 12.55431 0.079654 10.39611 0.09619 2.18016 0.458682 7.145382 0.139951

68 12.57273 0.079537 10.43169 0.095862 2.23111 0.448207 7.304804 0.136896

69 12.59102 0.079422 10.46665 0.095542 2.283018 0.438017 7.445166 0.134315

70 12.60916 0.079307 10.50102 0.095229 2.33591 0.428099 7.571305 0.132078

T=425 T=450K T=475 T=539 T=496.65 (Critical Temp)


52/107

10

20

30

40

50

60

70

0 0.5 1 1.5 2 2.5 3

Preassure(Bar)

Voume(M^3/Kmol)

COSMO Isotherms

t=425

T=450

T=475

T=539

Crit T

40

45

50

55

60

65

70

0 0.5 1 1.5 2 2.5 3

Preassure(Bar)

Voume(M^3/Kmol)

SRK VS COSMO

T=475K SRK

T=539 SRK

Crit T SRK

T=475 COSMO

T=539 COSMO

Crit T COSMO


53/107

BAR KMOL/CU KMOL/CUM V Liquid V Vapor VLIQUID VVAPOR V Liquid V Vapor VLIQUID VVAPOR V Liquid V Vapor VLIQUID VVAPOR V Liquid V Vapor VLIQUID VVAPOR V Liquid V Vapor

1 0.02859836 34.96704 0.026936 37.12473 0.025496 39.22147 0.022409 44.62578 0.024358 41.05369

1.0135 0.028988599 34.49632 0.027303 36.62634 0.025843 38.6954 0.022712 44.02884 0.024689 40.50365

2 0.057816191 17.29619 0.054301 18.41582 0.051351 19.47369 0.045008 22.21824 0.049005 20.40626

3 0.087689495 11.40387 0.082113 12.17835 0.077578 12.89023 0.067802 14.74878 0.073947 13.52319

4 0.118257795 8.456102 0.110391 9.058714 0.10419 9.597843 0.090795 11.01383 0.099195 10.0812

5 0.149564644 6.686072 0.139156 7.186175 0.131202 7.621858 0.11399 8.772689 0.124756 8.015624

6 0.18165821 5.504843 0.168431 5.937156 0.158628 6.304062 0.137392 7.278447 0.150642 6.638256

7 0.214591991 4.660006 0.198239 5.044409 0.186485 5.362358 0.161005 6.211002 0.176862 5.65414

8 0.24842566 4.025349 0.228608 4.374307 0.21479 4.6557 0.184832 5.410305 0.203426 4.915798

9 0.283226111 3.530748 0.259564 3.852612 0.243562 4.105726 0.20888 4.787438 0.230346 4.34130110 0.319068728 3.134121 0.29114 3.434779 0.27282 3.665419 0.233152 4.289051 0.257633 3.881489

11 0.356038957 2.808681 0.323367 3.092458 0.302585 3.304859 0.257653 3.881192 0.2853 3.505078

12 0.394234274 2.536563 0.356284 2.806748 0.332879 3.004098 0.282388 3.54123 0.31336 3.191213

13 0.433766671 2.305387 0.38993 2.564564 0.363726 2.749324 0.307362 3.253494 0.341827 2.925456

14 0.474765847 2.106301 0.424349 2.356553 0.395152 2.530673 0.33258 3.006792 0.370715 2.697491

15 0.517383344 1.932803 0.459589 2.175857 0.427185 2.340909 0.358049 2.792916 0.400039 2.499756

16 0.561798018 1.779999 0.495705 2.01733 0.459854 2.174604 0.383772 2.605711 0.429816 2.326577

17 15.586 0.06416 0.532756 1.877033 0.493192 2.027608 0.409757 2.440468 0.460063 2.173617

18 15.586 0.06416 0.570809 1.7519 0.527234 1.89669 0.43601 2.293527 0.490798 2.0375

19 15.586 0.06416 0.60994 1.639507 0.562018 1.779301 0.462535 2.161996 0.52204 1.915562

20 15.586 0.06416 0.650233 1.537911 0.597586 1.673399 0.489341 2.043564 0.553811 1.805671

21 15.586 0.06416 0.691785 1.445536 0.633983 1.57733 0.516433 1.936358 0.586132 1.706102

22 15.586 0.06416 0.734707 1.361087 0.671258 1.489741 0.543819 1.838847 0.619026 1.615441

23 15.586 0.06416 0.779126 1.283489 0.709466 1.409511 0.571505 1.749766 0.652519 1.532522

24 15.586 0.06416 0.825192 1.21184 0.748667 1.335707 0.599499 1.668059 0.686638 1.456371

25 15.586 0.06416 0.873078 1.145374 0.788929 1.267541 0.627809 1.592841 0.721411 1.386172

26 15.586 0.06416 0.922991 1.083434 0.830325 1.204348 0.656443 1.523362 0.75687 1.321231

27 15.586 0.06416 0.975183 1.025448 0.872938 1.145557 0.685408 1.458985 0.793047 1.260959

28 15.586 0.06416 1.029957 0.970914 0.916861 1.090678 0.714713 1.399162 0.829979 1.20485

29 15.586 0.06416 11.7172 0.085345 0.9622 1.039285 0.744368 1.343421 0.867704 1.152467

30 15.586 0.06416 11.74385 0.085151 1.009073 0.991009 0.774382 1.291353 0.906265 1.10343

31 15.586 0.06416 11.77016 0.084961 1.057617 0.945522 0.804763 1.242601 0.945706 1.057411

32 15.586 0.06416 11.79614 0.084774 1.107988 0.902537 0.835523 1.196855 0.986079 1.014117

33 15.586 0.06416 11.8218 0.08459 1.160368 0.861795 0.866671 1.153841 1.027437 0.973296

34 15.586 0.06416 11.84715 0.084408 1.21497 0.823066 0.898218 1.113316 1.069839 0.93472

35 15.586 0.06416 11.87221 0.08423 1.272045 0.786136 0.930175 1.075066 1.113352 0.898189

36 15.586 0.06416 11.89698 0.084055 1.331893 0.750811 0.962555 1.038902 1.158046 0.863524

37 15.586 0.06416 11.92146 0.083882 1.394877 0.716909 0.995369 1.004653 1.204001 0.830564

38 15.586 0.06416 11.94568 0.083712 1.461446 0.684254 1.028629 0.972168 1.251306 0.799165

39 15.586 0.06416 11.96962 0.083545 1.532157 0.652675 1.062349 0.94131 1.300058 0.769196

40 15.586 0.06416 11.99331 0.08338 1.607726 0.621996 1.096544 0.911957 1.350369 0.740538

41 15.586 0.06416 12.01674 0.083217 1.689091 0.592035 1.131226 0.883997 1.402361 0.713083

42 15.586 0.06416 12.03993 0.083057 1.777519 0.562582 1.166411 0.857331 1.456175 0.686731

43 15.586 0.06416 12.06287 0.082899 1.874798 0.533391 1.202114 0.831868 1.511969 0.661389

44 15.586 0.06416 12.08559 0.082743 12.18879 0.082043 1.238353 0.807524 1.569927 0.636972

45 15.586 0.06416 12.10807 0.08259 12.18879 0.082043 1.275143 0.784226 1.630257 0.6134

46 15.586 0.06416 12.13034 0.082438 12.18879 0.082043 1.312503 0.761903 1.693204 0.590596

47 15.586 0.06416 12.15238 0.082288 12.18879 0.082043 1.35045 0.740494 1.759051 0.568488

48 15.586 0.06416 12.17421 0.082141 12.18879 0.082043 1.389005 0.71994 1.828138 0.547005

49 15.586 0.06416 12.19584 0.081995 12.18879 0.082043 1.428188 0.700188 1.900865 0.526076

50 15.586 0.06416 12.21726 0.081851 12.18879 0.082043 1.468019 0.68119 1.977721 0.505633

51 15.586 0.06416 12.23849 0.081709 12.18879 0.082043 1.508521 0.662901 2.059302 0.485601

52 15.586 0.06416 12.25952 0.081569 12.18879 0.082043 1.549717 0.645279 2.146355 0.465906

53 15.586 0.06416 12.28036 0.081431 12.18879 0.082043 1.591631 0.628286 2.239825 0.446463

54 15.586 0.06416 12.30102 0.081294 12.18879 0.082043 1.634288 0.611887 2.340944 0.427178

55 15.586 0.06416 12.32149 0.081159 12.18879 0.082043 1.677715 0.596049 2.451356 0.407937

56 15.586 0.06416 12.34179 0.081026 12.18879 0.082043 1.721939 0.580741 2.573337 0.3886

57 15.586 0.06416 12.36191 0.080894 12.18879 0.082043 1.766989 0.565934 2.710173 0.36898

58 15.586 0.06416 12.38187 0.080763 12.18879 0.082043 1.812895 0.551604 2.866884 0.348811

59 15.586 0.06416 12.40165 0.080634 12.18879 0.082043 1.859689 0.537724 3.051776 0.327678

60 15.586 0.06416 12.42127 0.080507 12.18879 0.082043 1.907404 0.524273 3.280267 0.304853

61 15.586 0.06416 12.44074 0.080381 12.18879 0.082043 1.956073 0.511228 3.587026 0.278782

62 15.586 0.06416 12.46004 0.080257 12.18879 0.082043 2.005733 0.498571 4.088452 0.244591

63 15.586 0.06416 12.47919 0.080133 12.18879 0.082043 2.05642 0.486282 8.956884 0.111646

64 15.586 0.06416 12.49819 0.080012 12.18879 0.082043 2.108173 0.474344 8.956884 0.111646

65 15.586 0.06416 12.51704 0.079891 12.18879 0.082043 2.161033 0.462742 8.956884 0.111646

66 15.586 0.06416 12.53575 0.079772 12.18879 0.082043 2.21504 0.451459 8.956884 0.111646

67 15.586 0.06416 12.55431 0.079654 12.18879 0.082043 2.270237 0.440483 8.956884 0.111646

68 15.586 0.06416 12.57273 0.079537 12.18879 0.082043 2.32667 0.429799 8.956884 0.111646

69 15.586 0.06416 12.59102 0.079422 12.18879 0.082043 2.384382 0.419396 8.956884 0.111646

70 15.586 0.06416 12.60916 0.079307 12.18879 0.082043 2.443422 0.409262 8.956884 0.111646



54/107


55/107

Case BAR KMOL/CU KMOL/CUM V Liquid V Vapor VLIQUID VVAPOR V Liquid V Vapor VLIQUID VVAPOR V Liquid V Vapor VLIQUID VVAPOR V Liquid V Vapor VLIQUID VVAPOR V Liquid V Vapor

1 1 0.028588752 34.97879 0.026955 37.09952 0.025501 39.21474 0.022416 44.61055 0.024365 41.04279

2 1.0135 0.028978722 34.50808 0.027322 36.60113 0.025847 38.68867 0.02272 44.01361 0.024696 40.49275

3 2 0.057775388 17.30841 0.054375 18.39066 0.051369 19.46714 0.045039 22.20314 0.04903 20.39552

4 3 0.087591959 11.41657 0.082283 12.15324 0.077616 12.88388 0.067871 14.73381 0.074005 13.5126

5 4 0.118073454 8.469304 0.110697 9.033652 0.104257 9.591681 0.090917 10.999 0.099297 10.07076

6 5 0.149258186 6.6998 0.139642 7.161163 0.131304 7.615893 0.114181 8.757989 0.124916 8.005351

7 6 0.181188254 5.519122 0.169142 5.912196 0.158773 6.298296 0.137667 7.263884 0.150872 6.628144

8 7 0.213910086 4.674861 0.199223 5.0195 0.186679 5.356797 0.161379 6.196577 0.177173 5.64419

9 8 0.247475085 4.040811 0.229914 4.349451 0.215038 4.650347 0.185322 5.39602 0.203831 4.906015

10 9 0.281940412 3.546849 0.261246 3.827809 0.243868 4.100585 0.209499 4.773293 0.230857 4.331686

11 10 0.317369924 3.150897 0.293253 3.410028 0.273187 3.660496 0.233915 4.275048 0.258262 3.872044

12 11 0.353835328 2.826173 0.325971 3.067761 0.303016 3.300158 0.258576 3.867334 0.286057 3.495807

13 12 0.391417595 2.554816 0.35944 2.782106 0.333375 2.999623 0.283485 3.527517 0.314256 3.182119

14 13 0.430208729 2.324453 0.393705 2.539975 0.364288 2.745082 0.308649 3.239929 0.342872 2.91654

15 14 0.470313984 2.126239 0.428813 2.33202 0.395778 2.526668 0.334071 2.993376 0.371919 2.688757

16 15 0.511854696 1.953679 0.464818 2.15138 0.427872 2.337147 0.359757 2.77965 0.401412 2.491207

17 16 0.554971943 1.801893 0.501779 1.992908 0.460598 2.171092 0.385714 2.592597 0.431366 2.318217

18 17 0.599831343 1.667135 0.539762 1.852668 0.493985 2.024352 0.411945 2.427509 0.461798 2.165449

19 18 15.586 0.06416 0.578841 1.727591 0.528067 1.893698 0.438457 2.280723 0.492726 2.029527

20 19 15.586 0.06416 0.619097 1.615255 0.562879 1.776579 0.465257 2.149351 0.524167 1.907789

21 20 15.586 0.06416 0.660626 1.513716 0.59846 1.670956 0.492349 2.031079 0.556142 1.798101

22 21 15.586 0.06416 0.703532 1.421399 0.634851 1.575174 0.519741 1.924035 0.588672 1.698739

23 22 15.586 0.06416 0.747939 1.337007 0.672097 1.48788 0.547439 1.826687 0.621779 1.608289

24 23 15.586 0.06416 0.793987 1.259466 0.710249 1.407956 0.57545 1.737772 0.655486 1.525586

25 24 15.586 0.06416 0.841841 1.187873 0.749362 1.334468 0.60378 1.656233 0.689819 1.449655

26 25 15.586 0.06416 0.891692 1.121463 0.789496 1.26663 0.632437 1.581185 0.724805 1.379681

27 26 15.586 0.06416 0.943772 1.059578 0.830719 1.203777 0.661428 1.51188 0.760473 1.31497

28 27 15.586 0.06416 0.998358 1.001645 0.873104 1.145339 0.690762 1.447677 0.796855 1.254934

29 28 15.586 0.06416 1.055787 0.94716 0.916735 1.090827 0.720445 1.388031 0.833982 1.199066

30 29 15.586 0.06416 14.13123 0.070765 0.961706 1.039819 0.750486 1.33247 0.871893 1.14693

31 30 15.586 0.06416 14.13123 0.070765 1.008122 0.991944 0.780894 1.280584 0.910625 1.098147

32 31 15.586 0.06416 14.13123 0.070765 1.056102 0.946878 0.811677 1.232018 0.95022 1.052388

33 32 15.586 0.06416 14.13123 0.070765 1.105784 0.904336 0.842844 1.186459 0.990725 1.009362

34 33 15.586 0.06416 14.13123 0.070765 1.157325 0.864062 0.874405 1.143635 1.032189 0.96881535 34 15.586 0.06416 14.13123 0.070765 1.210907 0.825827 0.90637 1.103303 1.074666 0.930522

36 35 15.586 0.06416 14.13123 0.070765 1.266746 0.789424 0.938748 1.065249 1.118215 0.894282

37 36 15.586 0.06416 14.13123 0.070765 1.325095 0.754663 0.971549 1.029284 1.162901 0.859918

38 37 15.586 0.06416 14.13123 0.070765 1.386258 0.721366 1.004786 0.995237 1.208797 0.827269

39 38 15.586 0.06416 14.13123 0.070765 1.450606 0.689367 1.038468 0.962957 1.25598 0.796191

40 39 15.586 0.06416 14.13123 0.070765 1.518595 0.658504 1.072607 0.932308 1.304539 0.766555

41 40 15.586 0.06416 14.13123 0.070765 1.5908 0.628614 1.107216 0.903166 1.35457 0.738242

42 41 15.586 0.06416 14.13123 0.070765 1.667965 0.599533 1.142307 0.875421 1.406184 0.711145

43 42 15.586 0.06416 14.13123 0.070765 1.751074 0.571078 1.177892 0.848974 1.459502 0.685165

44 43 15.586 0.06416 14.13123 0.070765 1.84148 0.543041 1.213985 0.823733 1.514664 0.660212

45 44 15.586 0.06416 14.13123 0.070765 1.941137 0.515162 1.2506 0.799616 1.571828 0.636202

46 45 15.586 0.06416 14.13123 0.070765 12.18879 0.082043 1.287751 0.776548 1.631173 0.613056

47 46 15.586 0.06416 14.13123 0.070765 12.18879 0.082043 1.325453 0.754459 1.692908 0.590699

48 47 15.586 0.06416 14.13123 0.070765 12.18879 0.082043 1.363721 0.733288 1.757275 0.569063

49 48 15.586 0.06416 14.13123 0.070765 12.18879 0.082043 1.402572 0.712976 1.824558 0.548078

50 49 15.586 0.06416 14.13123 0.070765 12.18879 0.082043 1.442022 0.693471 1.895093 0.527679

51 50 15.586 0.06416 14.13123 0.070765 12.18879 0.082043 1.482088 0.674724 1.969282 0.507799

52 51 15.586 0.06416 14.13123 0.070765 12.18879 0.082043 1.522787 0.65669 2.047615 0.488373

53 52 15.586 0.06416 14.13123 0.070765 12.18879 0.082043 1.56414 0.639329 2.130696 0.46933

54 53 15.586 0.06416 14.13123 0.070765 12.18879 0.082043 1.606163 0.622602 2.219284 0.450596

55 54 15.586 0.06416 14.13123 0.070765 12.18879 0.082043 1.648879 0.606473 2.314353 0.432086

56 55 15.586 0.06416 14.13123 0.070765 12.18879 0.082043 1.692306 0.59091 2.417185 0.413704

57 56 15.586 0.06416 14.13123 0.070765 12.18879 0.082043 1.736466 0.575882 2.529527 0.395331

58 57 15.586 0.06416 14.13123 0.070765 12.18879 0.082043 1.781381 0.561362 2.653855 0.37681

59 58 15.586 0.06416 14.13123 0.070765 12.18879 0.082043 1.827074 0.547323 2.793876 0.357926

60 59 15.586 0.06416 14.13123 0.070765 12.18879 0.082043 1.873567 0.533741 2.955568 0.338344

61 60 15.586 0.06416 14.13123 0.070765 12.18879 0.082043 1.920887 0.520593 3.14969 0.317492

62 61 15.586 0.06416 14.13123 0.070765 12.18879 0.082043 1.969056 0.507858 3.399452 0.294165

63 62 15.586 0.06416 14.13123 0.070765 12.18879 0.082043 2.0181 0.495515 3.777969 0.264692

64 63 15.586 0.06416 14.13123 0.070765 12.18879 0.082043 2.068047 0.483548 8.956884 0.111646

65 64 15.586 0.06416 14.13123 0.070765 12.18879 0.082043 2.118922 0.471938 8.956884 0.111646

66 65 15.586 0.06416 14.13123 0.070765 12.18879 0.082043 2.170752 0.46067 8.956884 0.111646

67 66 15.586 0.06416 14.13123 0.070765 12.18879 0.082043 2.223567 0.449728 8.956884 0.111646

68 67 15.586 0.06416 14.13123 0.070765 12.18879 0.082043 2.277393 0.439099 8.956884 0.111646

69 68 15.586 0.06416 14.13123 0.070765 12.18879 0.082043 2.332259 0.428769 8.956884 0.111646

70 69 15.586 0.06416 14.13123 0.070765 12.18879 0.082043 2.388195 0.418726 8.956884 0.111646

71 70 15.586 0.06416 14.13123 0.070765 12.18879 0.082043 2.445228 0.40896 8.956884 0.111646



56/107


57/107

BAR KMOL/CU KMOL/CUM V Liquid V Vapor VLIQUID VVAPOR V Liquid V Vapor VLIQUID VVAPOR V Liquid V Vapor VLIQUID VVAPOR V Liquid V Vapor VLIQUID VVAPOR V Liquid V Vapor

1 0.028299829 35.3359 0.026728 37.41449 0.025321 39.49307 0.020282 49.30398 0.024217 41.29312

1.0135 0.028681877 34.86522 0.027088 36.91612 0.025663 38.96701 0.020556 48.64724 0.024544 40.74309

2 0.056599658 17.66795 0.053455 18.70724 0.050642 19.74653 0.040565 24.65199 0.048434 20.64656

3 0.084899487 11.77863 0.080183 12.47149 0.075963 13.16436 0.060847 16.43466 0.072651 13.76437

4 0.113199316 8.833976 0.10691 9.353621 0.101284 9.873267 0.081129 12.32599 0.096868 10.32328

5 0.141499145 7.067181 0.133638 7.482897 0.126604 7.898614 0.101412 9.860795 0.121086 8.258624

6 0.169798974 5.889317 0.160366 6.235747 0.151925 6.582178 0.121694 8.217329 0.145303 6.882187

7 0.198098803 5.047986 0.187093 5.344926 0.177246 5.641867 0.141976 7.043425 0.16952 5.899017

8 0.226398632 4.416988 0.213821 4.676811 0.202567 4.936633 0.162259 6.162997 0.193737 5.16164

9 0.254698461 3.926211 0.240549 4.157165 0.227888 4.388119 0.182541 5.47822 0.217954 4.58812410 0.28299829 3.53359 0.267276 3.741449 0.253209 3.949307 0.202823 4.930398 0.242171 4.129312

11 0.31129812 3.212355 0.294004 3.401317 0.27853 3.590279 0.223106 4.48218 0.266388 3.75392

12 0.339597949 2.944659 0.320731 3.117874 0.303851 3.291089 0.243388 4.108665 0.290605 3.441093

13 0.367897778 2.718146 0.347459 2.878037 0.329172 3.037928 0.26367 3.792614 0.314822 3.176394

14 0.396197607 2.523993 0.374187 2.672463 0.354493 2.820933 0.283953 3.521713 0.33904 2.949509

15 0.424497436 2.355727 0.400914 2.494299 0.379813 2.632871 0.304235 3.286932 0.363257 2.752875

16 0.452797265 2.208494 0.427642 2.338405 0.405134 2.468317 0.324517 3.081499 0.387474 2.58082

17 15.586 0.06416 0.454369 2.200852 0.430455 2.323122 0.3448 2.900234 0.411691 2.429007

18 15.586 0.06416 0.481097 2.078582 0.455776 2.194059 0.365082 2.73911 0.435908 2.294062

19 15.586 0.06416 0.507825 1.969183 0.481097 2.078582 0.385364 2.594946 0.460125 2.173322

20 15.586 0.06416 0.534552 1.870724 0.506418 1.974653 0.405647 2.465199 0.484342 2.064656

21 15.586 0.06416 0.56128 1.781642 0.531739 1.880622 0.425929 2.347808 0.508559 1.966339

22 15.586 0.06416 0.588008 1.700658 0.55706 1.795139 0.446211 2.24109 0.532776 1.87696

23 15.586 0.06416 0.614735 1.626717 0.582381 1.71709 0.466494 2.143651 0.556994 1.795353

24 15.586 0.06416 0.641463 1.558937 0.607702 1.645544 0.486776 2.054332 0.581211 1.720547

25 15.586 0.06416 0.66819 1.496579 0.633022 1.579723 0.507058 1.972159 0.605428 1.651725

26 15.586 0.06416 0.694918 1.439019 0.658343 1.518964 0.527341 1.896307 0.629645 1.588197

27 15.586 0.06416 0.721646 1.385722 0.683664 1.462706 0.547623 1.826073 0.653862 1.529375

28 15.586 0.06416 14.13123 #DIV/0! 0.708985 1.410467 0.567906 1.760856 0.678079 1.474754

29 15.586 0.06416 14.13123 0.070765 0.734306 1.36183 0.588188 1.700137 0.702296 1.423901

30 15.586 0.06416 14.13123 0.070765 0.759627 1.316436 0.60847 1.643466 0.726513 1.376437

31 15.586 0.06416 14.13123 0.070765 0.784948 1.27397 0.628753 1.590451 0.75073 1.332036

32 15.586 0.06416 14.13123 0.070765 0.810269 1.234158 0.649035 1.540749 0.774947 1.29041

33 15.586 0.06416 14.13123 0.070765 0.83559 1.19676 0.669317 1.49406 0.799165 1.251307

34 15.586 0.06416 14.13123 0.070765 0.860911 1.161561 0.6896 1.450117 0.823382 1.214504

35 15.586 0.06416 14.13123 0.070765 0.886231 1.128373 0.709882 1.408685 0.847599 1.179803

36 15.586 0.06416 14.13123 0.070765 0.911552 1.09703 0.730164 1.369555 0.871816 1.147031

37 15.586 0.06416 14.13123 0.070765 0.936873 1.06738 0.750447 1.33254 0.896033 1.11603

38 15.586 0.06416 14.13123 0.070765 0.962194 1.039291 0.770729 1.297473 0.92025 1.086661

39 15.586 0.06416 14.13123 0.070765 0.987515 1.012643 0.791011 1.264205 0.944467 1.058798

40 15.586 0.06416 14.13123 0.070765 1.012836 0.987327 0.811294 1.232599 0.968684 1.032328

41 15.586 0.06416 14.13123 0.070765 1.038157 0.963246 0.831576 1.202536 0.992901 1.007149

42 15.586 0.06416 14.13123 0.070765 1.063478 0.940311 0.851858 1.173904 1.017119 0.98317

43 15.586 0.06416 14.13123 0.070765 1.088799 0.918443 0.872141 1.146604 1.041336 0.960305

44 15.586 0.06416 14.13123 0.070765 12.18879 0.082043 0.892423 1.120545 1.065553 0.93848

45 15.586 0.06416 14.13123 0.070765 12.18879 0.082043 0.912705 1.095644 1.08977 0.917625

46 15.586 0.06416 14.13123 0.070765 12.18879 0.082043 0.932988 1.071826 1.113987 0.897677

47 15.586 0.06416 14.13123 0.070765 12.18879 0.082043 0.95327 1.049021 1.138204 0.878577

48 15.586 0.06416 14.13123 0.070765 12.18879 0.082043 0.973552 1.027166 1.162421 0.860273

49 15.586 0.06416 14.13123 0.070765 12.18879 0.082043 0.993835 1.006204 1.186638 0.842717

50 15.586 0.06416 14.13123 0.070765 12.18879 0.082043 1.014117 0.98608 1.210855 0.825862

51 15.586 0.06416 14.13123 0.070765 12.18879 0.082043 1.034399 0.966745 1.235073 0.809669

52 15.586 0.06416 14.13123 0.070765 12.18879 0.082043 1.054682 0.948153 1.25929 0.794098

53 15.586 0.06416 14.13123 0.070765 12.18879 0.082043 1.074964 0.930264 1.283507 0.779115

54 15.586 0.06416 14.13123 0.070765 12.18879 0.082043 1.095246 0.913037 1.307724 0.764687

55 15.586 0.06416 14.13123 0.070765 12.18879 0.082043 1.115529 0.896436 1.331941 0.750784

56 15.586 0.06416 14.13123 0.070765 12.18879 0.082043 1.135811 0.880428 1.356158 0.737377

57 15.586 0.06416 14.13123 0.070765 12.18879 0.082043 1.156093 0.864982 1.380375 0.724441

58 15.586 0.06416 14.13123 0.070765 12.18879 0.082043 1.176376 0.850069 1.404592 0.71195

59 15.586 0.06416 14.13123 0.070765 12.18879 0.082043 1.196658 0.835661 1.428809 0.699883

60 15.586 0.06416 14.13123 0.070765 12.18879 0.082043 1.21694 0.821733 1.453027 0.688219

61 15.586 0.06416 14.13123 0.070765 12.18879 0.082043 1.237223 0.808262 1.477244 0.676936

62 15.586 0.06416 14.13123 0.070765 12.18879 0.082043 1.257505 0.795225 1.501461 0.666018

63 15.586 0.06416 14.13123 0.070765 12.18879 0.082043 1.277787 0.782603 8.956884 0.111646

64 15.586 0.06416 14.13123 0.070765 12.18879 0.082043 1.29807 0.770375 8.956884 0.111646

65 15.586 0.06416 14.13123 0.070765 12.18879 0.082043 1.318352 0.758523 8.956884 0.111646

66 15.586 0.06416 14.13123 0.070765 12.18879 0.082043 1.338634 0.74703 8.956884 0.111646

67 15.586 0.06416 14.13123 0.070765 12.18879 0.082043 1.358917 0.73588 8.956884 0.111646

68 15.586 0.06416 14.13123 0.070765 12.18879 0.082043 1.379199 0.725058 8.956884 0.111646

69 15.586 0.06416 14.13123 0.070765 12.18879 0.082043 1.399481 0.71455 8.956884 0.111646

70 15.586 0.06416 14.13123 0.070765 12.18879 0.082043 1.419764 0.704343 8.956884 0.111646



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Temperature(K)


T-x-y Experimental Data

Benzene Toluene

VLE-028 L

VLE-028 V

0

0.05

0.1

0.15

0.2

0.25

0 0.2 0.4 0.6 0.8 1 1.2

Pressure(Bar)


P-x-y Experimental Data

Benzene Toluene

VLE-043 L

VLE-043 V


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L Mole Frac Temp V molfrac

0 383.76 0

0.05 381.51 0.10838

0.1 379.37 0.2057

0.2 375.39 0.3723

0.3 371.76 0.50844

0.4 368.45 0.62061

0.5 365.4 0.71374

0.6 362.59 0.7916

0.7 359.99 0.8571

0.8 357.58 0.91254

0.9 355.34 0.9597

0.95 354.27 0.98063

1 353.25 1

0 383.76 0

1 353.25 1

L mole Frac V Mole Frac Pressure (Bar)

0 0 7872 0.07872

0.0401 0.1128 8538 0.08538

0.0992 0.2514 9517 0.09517

0.2484 0.502 11973 0.11973

0.3094 0.5839 13085 0.13085

0.3315 0.6012 13347 0.133470.3854 0.6599 14306 0.14306

0.4673 0.7273 15608 0.15608

0.5398 0.7801 16783 0.16783

0.6209 0.8312 18119 0.18119

0.7068 0.8797 19620 0.1962

0.7899 0.9181 20890 0.2089

0.8616 0.949 22080 0.2208

0.9352 0.9773 23277 0.23277

1 1 24389 0.24389

0.1853 0.411 10919 0.10919

0.7033 0.8783 19504 0.19504


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Temperature(K)


T-x-y Data Vs SRK

Benzene Toluene

VLE-028 L

VLE-028 V

L SRK

V SRK

0

0.05

0.1

0.15

0.2

0.25

0 0.2 0.4 0.6 0.8 1 1.2

Pre

ssure(Bar)


P-x-y Data Vs SRK

Benzene Toluene

VLE-043 L

VLE-043 V

V SRK

L SRK


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TOTAL VAPOR LIQUID TOTAL VAPOR LIQUID

TEMP MOLEFRA MOLEFRAC PRES MOLEFRA MOLEFRAC

C6H6 C6H6 C6H6 C6H6

K bar

384.1176 0 0 0.0767 0 0

382.5389 0.066752 0.025 0.082947 0.098035 0.025

381.0392 0.127833 0.05 0.089034 0.180509 0.05

379.616 0.183872 0.075 0.094947 0.250912 0.075

378.2642 0.235412 0.1 0.100698 0.311774 0.1

376.9795 0.282933 0.125 0.106293 0.364967 0.125

375.7574 0.326859 0.15 0.111738 0.411906 0.15

374.594 0.367562 0.175 0.117038 0.453681 0.175

373.4855 0.405373 0.2 0.122199 0.491146 0.2

372.4284 0.440582 0.225 0.127226 0.524978 0.225

371.4194 0.473449 0.25 0.132124 0.555725 0.25

370.4555 0.504204 0.275 0.1369 0.58383 0.275369.5337 0.533052 0.3 0.141558 0.60966 0.3

368.6515 0.560176 0.325 0.146104 0.633518 0.325

367.8063 0.58574 0.35 0.150542 0.65566 0.35

366.9959 0.609891 0.375 0.154878 0.676302 0.375

366.218 0.63276 0.4 0.159117 0.695626 0.4

365.4706 0.654468 0.425 0.163264 0.713791 0.425

364.7518 0.675121 0.45 0.167323 0.730935 0.45

364.0597 0.694819 0.475 0.171301 0.747174 0.475

363.3928 0.713649 0.5 0.175201 0.762615 0.5

362.7495 0.731694 0.525 0.179029 0.777348 0.525362.1281 0.749027 0.55 0.182789 0.791456 0.55

361.5275 0.765717 0.575 0.186486 0.805013 0.575

360.9462 0.781828 0.6 0.190126 0.818084 0.6

360.383 0.797417 0.625 0.193711 0.830729 0.625

359.8367 0.81254 0.65 0.197248 0.843004 0.65

359.3062 0.827247 0.675 0.200741 0.854958 0.675

358.7906 0.841586 0.7 0.204195 0.866639 0.7

358.2887 0.855604 0.725 0.207613 0.878091 0.725

357.7998 0.869342 0.75 0.211 0.889355 0.75

357.3228 0.882842 0.775 0.214362 0.900472 0.775

356.857 0.896145 0.8 0.217701 0.911478 0.8

356.4016 0.909288 0.825 0.221023 0.922413 0.825

355.9559 0.922311 0.85 0.224331 0.933311 0.85

355.5192 0.935249 0.875 0.22763 0.944209 0.875

355.0908 0.948141 0.9 0.230923 0.955144 0.9

354.6701 0.961024 0.925 0.234214 0.966153 0.925

354.2565 0.973936 0.95 0.237508 0.977272 0.95

353.8497 0.986915 0.975 0.240807 0.988541 0.975

353.4462 1 1 0.244114 1 1


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Temperature(K)


T-x-y Data Vs SRK

Benzene Toluene

VLE-028 L

VLE-028 V

L SRK

V SRK

0

0.05

0.1

0.15

0.2

0.25

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Pre

ssure(Bar)


P-x-y Data Vs SRK

Benzene Toluene

VLE-043 L

VLE-043 V

V SRK

L SRK


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TEMP MOLEFRA MOLEFRAC PRES MOLEFRA MOLEFRAC

C6H6 C6H6 C6H6 C6H6

K bar

384.1176 0 0 0.0767 0 0

382.5389 0.066752 0.025 0.082947 0.098035 0.025

381.0392 0.127833 0.05 0.089034 0.180509 0.05

379.616 0.183872 0.075 0.094947 0.250912 0.075

378.2642 0.235412 0.1 0.100698 0.311774 0.1

376.9795 0.282933 0.125 0.106293 0.364967 0.125

375.7574 0.326859 0.15 0.111738 0.411906 0.15

374.594 0.367562 0.175 0.117038 0.453681 0.175

373.4855 0.405373 0.2 0.122199 0.491146 0.2

372.4284 0.440582 0.225 0.127226 0.524978 0.225

371.4194 0.473449 0.25 0.132124 0.555725 0.25

370.4555 0.504204 0.275 0.1369 0.58383 0.275369.5337 0.533052 0.3 0.141558 0.60966 0.3

368.6515 0.560176 0.325 0.146104 0.633518 0.325

367.8063 0.58574 0.35 0.150542 0.65566 0.35

366.9959 0.609891 0.375 0.154878 0.676302 0.375

366.218 0.63276 0.4 0.159117 0.695626 0.4

365.4706 0.654468 0.425 0.163264 0.713791 0.425

364.7518 0.675121 0.45 0.167323 0.730935 0.45

364.0597 0.694819 0.475 0.171301 0.747174 0.475

363.3928 0.713649 0.5 0.175201 0.762615 0.5

362.7495 0.731694 0.525 0.179029 0.777348 0.525362.1281 0.749027 0.55 0.182789 0.791456 0.55

361.5275 0.765717 0.575 0.186486 0.805013 0.575

360.9462 0.781828 0.6 0.190126 0.818084 0.6

360.383 0.797417 0.625 0.193711 0.830729 0.625

359.8367 0.81254 0.65 0.197248 0.843004 0.65

359.3062 0.827247 0.675 0.200741 0.854958 0.675

358.7906 0.841586 0.7 0.204195 0.866639 0.7

358.2887 0.855604 0.725 0.207613 0.878091 0.725

357.7998 0.869342 0.75 0.211 0.889355 0.75

357.3228 0.882842 0.775 0.214362 0.900472 0.775

356.857 0.896145 0.8 0.217701 0.911478 0.8

356.4016 0.909288 0.825 0.221023 0.922413 0.825

355.9559 0.922311 0.85 0.224331 0.933311 0.85

355.5192 0.935249 0.875 0.22763 0.944209 0.875

355.0908 0.948141 0.9 0.230923 0.955144 0.9

354.6701 0.961024 0.925 0.234214 0.966153 0.925

354.2565 0.973936 0.95 0.237508 0.977272 0.95

353.8497 0.986915 0.975 0.240807 0.988541 0.975

353.4462 1 1 0.244114 1 1


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Temperature(K)


T-x-y Data Vs COSMO

Benzene Toluene

VLE-028 L

VLE-028 V

COSMO V

COSMO L

0

0.05

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0.15

0.2

0.25

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Pre

ssure(Bar)


P-x-y Data Vs COSMO

Benzene Toluene

VLE-043 L

VLE-043 V

COSMO L

COSMO V


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TEMP MOLEFRA MOLEFRA PRES MOLEFRA MOLEFRA

C6H6 C6H6 C6H6 C6H6

K bar

383.8291 0 0 0.078808 0 0

382.6528 0.057196 0.025 0.082963 0.073879 0.025

381.5092 0.111072 0.05 0.087118 0.140658 0.05

380.3968 0.161878 0.075 0.09127 0.201316 0.075

379.3146 0.209831 0.1 0.095418 0.256659 0.1

378.2612 0.255135 0.125 0.099563 0.307359 0.125

377.2356 0.297976 0.15 0.103704 0.353978 0.15

376.2366 0.338524 0.175 0.107841 0.396993 0.175

375.2632 0.376934 0.2 0.111975 0.436808 0.2

374.3143 0.413353 0.225 0.116105 0.473768 0.225

373.3891 0.447911 0.25 0.120232 0.508173 0.25

372.4866 0.480732 0.275 0.124355 0.540279 0.275371.606 0.511927 0.3 0.128476 0.570311 0.3

370.7464 0.5416 0.325 0.132593 0.598466 0.325

369.9071 0.569849 0.35 0.136707 0.624915 0.35

369.0872 0.59676 0.375 0.140818 0.649811 0.375

368.2861 0.622418 0.4 0.144926 0.673288 0.4

367.5031 0.646897 0.425 0.149031 0.695465 0.425

366.7376 0.670268 0.45 0.153134 0.716449 0.45

365.9888 0.692598 0.475 0.157234 0.736335 0.475

365.2562 0.713947 0.5 0.161331 0.755208 0.5

364.5393 0.734371 0.525 0.165427 0.773145 0.525363.8375 0.753923 0.55 0.16952 0.790215 0.55

363.1503 0.772653 0.575 0.17361 0.806481 0.575

362.4771 0.790607 0.6 0.177699 0.821999 0.6

361.8175 0.807826 0.625 0.181786 0.836822 0.625

361.171 0.824351 0.65 0.185872 0.850995 0.65

360.5372 0.840219 0.675 0.189956 0.864563 0.675

359.9157 0.855466 0.7 0.194038 0.877563 0.7

359.3061 0.870123 0.725 0.198119 0.890033 0.725

358.7079 0.884221 0.75 0.2022 0.902005 0.75

358.1209 0.897789 0.775 0.206279 0.913509 0.775

357.5446 0.910855 0.8 0.210358 0.924574 0.8

356.9786 0.923442 0.825 0.214436 0.935225 0.825

356.4228 0.935575 0.85 0.218514 0.945486 0.85

355.8767 0.947276 0.875 0.222592 0.955379 0.875

355.3401 0.958567 0.9 0.22667 0.964926 0.9

354.8126 0.969467 0.925 0.230749 0.974144 0.925

354.2939 0.979994 0.95 0.234828 0.983051 0.95

353.7839 0.990166 0.975 0.238909 0.991665 0.975

353.2785 1 1 0.24299 1 1


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Temperature(K)


T-x-y Data Vs Peng-Rob

Benzene Toluene

VLE-028 L

VLE-028 V

PEN-ROB L

PEN-ROB V

0

0.05

0.1

0.15

0.2

0.25

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Pre

ssure(Bar)


P-x-y Data Vs Peng-Rob

Benzene Toluene

VLE-043 L

VLE-043 V

PEN-ROB L

PEN ROB V


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TEMP MOLEFRAC MOLEFRA PRES MOLEFRA MOLEFRA

C6H6 C6H6 C6H6 C6H6

K bar

385.2936 0 0 0.077956 0 0

384.071 0.0567939 0.025 0.082358 0.076871 0.025

382.8795 0.1103765 0.05 0.086757 0.14589 0.05

381.7193 0.160981 0.075 0.091149 0.208204 0.075

380.5893 0.2088053 0.1 0.095536 0.264749 0.1

379.4886 0.2540367 0.125 0.099918 0.316295 0.125

378.4161 0.2968482 0.15 0.104295 0.363481 0.15

377.3708 0.3374001 0.175 0.108668 0.406839 0.175

376.3517 0.3758403 0.2 0.113035 0.446822 0.2

375.3579 0.4123059 0.225 0.117397 0.483812 0.225

374.3884 0.4469241 0.25 0.121755 0.518136 0.25

373.4424 0.4798123 0.275 0.126108 0.550074 0.275372.5191 0.5110796 0.3 0.130456 0.57987 0.3

371.6176 0.5408271 0.325 0.1348 0.607736 0.325

370.7371 0.5691487 0.35 0.13914 0.633856 0.35

369.877 0.5961316 0.375 0.143476 0.65839 0.375

369.0365 0.6218568 0.4 0.147807 0.681483 0.4

368.2149 0.6463994 0.425 0.152135 0.70326 0.425

367.4116 0.6698297 0.45 0.156458 0.723833 0.45

366.6259 0.6922127 0.475 0.160779 0.743301 0.475

365.8572 0.7136094 0.5 0.165095 0.761753 0.5

365.105 0.7340763 0.525 0.169409 0.77927 0.525364.3686 0.7536663 0.55 0.173719 0.795923 0.55

363.6476 0.7724287 0.575 0.178027 0.811776 0.575

362.9414 0.7904097 0.6 0.182332 0.826889 0.6

362.2495 0.8076524 0.625 0.186635 0.841314 0.625

361.5715 0.824197 0.65 0.190935 0.855099 0.65

360.9068 0.8400813 0.675 0.195234 0.868288 0.675

360.2551 0.8553408 0.7 0.199531 0.880922 0.7

359.6158 0.8700085 0.725 0.203827 0.893037 0.725

358.9887 0.8841156 0.75 0.208123 0.904666 0.75

358.3732 0.8976913 0.775 0.212417 0.915841 0.775

357.769 0.9107631 0.8 0.216712 0.926589 0.8

357.1758 0.9233568 0.825 0.221007 0.936937 0.825

356.5932 0.9354966 0.85 0.225302 0.94691 0.85

356.0207 0.9472056 0.875 0.229599 0.956529 0.875

355.4582 0.9585051 0.9 0.233898 0.965815 0.9

354.9052 0.9694157 0.925 0.238198 0.974788 0.925

354.3615 0.9799564 0.95 0.242501 0.983466 0.95

353.8267 0.9901455 0.975 0.246808 0.991864 0.975

353.296 1 1 0.251118 1 1


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Temperature(K)


T-x-y Data Vs Ideal

Benzene Toluene

VLE-028 L

VLE-028 V

IDEAL L

IDEAL V

0

0.05

0.1

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0.2

0.25

0 0.2 0.4 0.6 0.8 1 1.2

Pre

ssure(Bar)


P-x-y Data Vs Ideal

Benzene Toluene

VLE-043 L

VLE-043 V

IDEAL L

IDEAL V


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TEMP MOLEFRA MOLEFRA PRES MOLEFRA MOLEFRA

C6H6 C6H6 C6H6 C6H6

K bar

383.8291 0 0 0.078808 0 0

382.66 0.057002 0.025 0.082908 0.073271 0.025

381.523 0.110723 0.05 0.087013 0.139629 0.05

380.4167 0.161407 0.075 0.091117 0.200009 0.075

379.34 0.209269 0.1 0.095222 0.255183 0.1

378.2915 0.254508 0.125 0.099327 0.305796 0.125

377.2703 0.297307 0.15 0.103431 0.352393 0.15

376.2751 0.337833 0.175 0.107536 0.395433 0.175

375.305 0.37624 0.2 0.111641 0.435307 0.2

374.359 0.412669 0.225 0.115745 0.472354 0.225

373.4362 0.447251 0.25 0.11985 0.506863 0.25

372.5356 0.480106 0.275 0.123976 0.539086 0.275371.6565 0.511344 0.3 0.12808 0.569244 0.3

370.798 0.541068 0.325 0.132185 0.597528 0.325

369.9593 0.569371 0.35 0.136289 0.624109 0.35

369.1397 0.596342 0.375 0.140394 0.649135 0.375

368.3386 0.622061 0.4 0.144499 0.672739 0.4

367.5552 0.646603 0.425 0.148603 0.695039 0.425

366.789 0.670039 0.45 0.152708 0.71614 0.45

366.0393 0.692431 0.475 0.156813 0.736136 0.475

365.3055 0.713841 0.5 0.160917 0.755112 0.5

364.5871 0.734325 0.525 0.165022 0.773144 0.525363.8836 0.753933 0.55 0.169127 0.7903 0.55

363.1944 0.772716 0.575 0.173231 0.806643 0.575

362.5192 0.790717 0.6 0.177336 0.82223 0.6

361.8574 0.80798 0.625 0.181441 0.837111 0.625

361.2085 0.824544 0.65 0.185545 0.851334 0.65

360.5722 0.840445 0.675 0.18965 0.864941 0.675

359.9481 0.855718 0.7 0.193755 0.877972 0.7

Thermo II Paper

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Transcript of Thermo II Paper