General Thermodynamics Process Simulation - … · General Thermodynamics for Process Simulation Dr. Jungho Cho, Professor Department of Chemical Engineering Dong Yang University

General Thermodynamicsfor

Process Simulation

Dr. Jungho Cho, ProfessorDepartment of Chemical Engineering

Dong Yang University

Thermodynamic Models built in Simulator

Four Criteria for Equilibria

Situation ConditionThermal Equilibrium

Mechanical Equilibrium

, Phase Equilibria (VLE, LLE)

Chemical Equilibrium

βα TT =βα PP =

li

vi μμ = 21 l

ili μμ =

0,

=

∂∂

PT

Gξ

Fugacity (or chemical potential) is defined as an escaping tendencyof a component ‘i’ in a certain phase into another phase.


Basic Phase Equilibria Relations

Vapor-liquid equilibrium calculations

The basic relationship for every component in vapor-liquidequilibrium is:

where: the fugacity of component i in the vapor phase

: the fugacity of component i in the liquid phase

( ) ( )il

iiv

i xPTfyPTf ,,ˆ,,ˆ =

vif̂l

if̂

(1)


Basic Phase Equilibria Relations

There are two methods for representing liquid fugacities.

- Equation of state method- Liquid activity coefficient method


Equation of State Method

The equation of state method defines fugacities as:

where:φiv is the vapor phase fugacity coefficientφil is the liquid phase fugacity coefficientyi is the mole fraction of i in the vapor xi is the mole fraction of i in the liquid P is the system pressure

Pyf ivi

vi φ̂ˆ = (2)

Pxf ili

li φ̂ˆ = (3)


Equation of State Method

We can then rewrite equation 1 as:

(4)

This is the standard equation used to represent vapor-liquid equilibrium using the equation-of-state method.

φiv and φil are both calculated by the equation-of-state.

Note that K-values are defined as:

ilii

vi xy φφ ˆˆ =

i

ii x

yK = (5)


Liquid Activity Coefficient Method (VLE)

The activity coefficient method defines liquid fugacities as:

The vapor fugacity is the same as the EOS approach:

Pyf ivi

vi φ̂ˆ =

where:iγ is the liquid activity coefficient of component i0

if is the standard liquid fugacity of component iviφ̂ is calculated from an equation-of-state model

We can then rewrite equation 1 as:0ˆ

iiiivi fxPy γφ =

0ˆiii

li fxf γ= (6)

(7)

(8)


Liquid Activity Coefficient Method (LLE)

• For Liquid-Liquid Equilibrium (LLE) the relationship is:

where the designators 1 and 2 represent the two separate liquid phases.

• Using the activity coefficient definition of fugacity, this can be rewritten and simplified as:

21 ˆˆ li

li ff =

2211 li

li

li

li xx γγ = (10)

(9)


K-values

The k-values can be calculated from:

Or

( )P

PPRTVP

xyK

vi

sati

lisat

isati

li

i

ii φ

φγ

ˆ

exp

−

==

vi

li

i

ii x

yKφφˆˆ

==

(11)

(12)


Example 2: Ideal Raoult’s Law

The preceding equation reduces to the following ideal Raoult’s law: vap

iii PxPy =

Example : Pxy plot at constant T(75oC). (P in kPa, T in oC)

22447.29452724.14ln 1 +

−=t

Pvap

20964.29722043.14ln 2 +

−=t

Pvap,

SolutionAt 75oC, kPaPvap 21.831 = and kPaP vap 98.411 =

The total pressure vapvap PxPxP 2211 += ( ) 1212 xPPPP vapvapvap −+=,

Vapor phase composition, ( ) PPx

xPPPPxy

vap

vapvapvap

vap11

1212

111 =

−+=


Pxy Diagram at Constant Temperature

x1, y1

0 5

Pres

sure

(kPa

)

20

30

40

50

60

70

80

90

100

1.0

vapP1

vapP2

a

bb’

cc’

d

Liquid

Vapor

P – x1

P – y1


Example 3: Slightly Non-ideal System

vapiiii PxPy γ=

For systems which the liquid phase behaves nonideally:

Relation between activity coefficient and excess Gibbs energy is as:( )

ijnPTi

ex

i nRTnG

≠

∂

∂=,,

/lnγ

As an example, excess Gibbs energy expression is as:

21xAxRTGex

=

Therefore, 1γ 2γand becomes.

( )221 exp Ax=γ ( )2

12 exp Ax=γ

So, ( )[ ] ( ) vapvap PxAxPxxAP 222111

21 exp1exp +−= ( )[ ]

PPxxAy

vap11

21

11exp −=


Prediction with Margules Equations

x1, y1

0.0 0.2 0.4 0.6 0.8 1.0

Pres

sure

(kPa

)

20

40

60

80

100

120

140

160

A = 0.0A = 0.5A = 1.0A = 2.0A = 3.0

Unstable


Deviations from Raoult’s Law (1 of 2) In general, you can expect non-ideality of unlike molecules. Either the size

and shape or the intermolecular interactions between components may be dissimilar. For short, these are called size and energy asymmetry. Energy asymmetry occurs between polar and non-polar molecules and also between different polar molecules.

In the majority of mixtures, activity coefficients is greater than unity. The result is a higher fugacity than ideal. The fugacity can be interpreted as the tendency to vaporize. If compounds vaporize mere than in an ideal solution, then they increase their average distance. So activity coefficients is greater than unity indicate repulsion between unlike molecules. If the repulsion is strong, liquid-liquid separation occurs. This is another mechanism that decreases close contact between unlike molecules.

If the activity coefficient is larger than unity, the system is said to show positive deviations from Raoult’s law. Negative deviations from Raoult’s law occur when the activity coefficient is smaller than unity.


Deviations from Raoult’s Law (2 of 2)

x1, y1

0.0 0.2 0.4 0.6 0.8 1.0

Pres

sure

(kPa

)

30

40

50

60

70

80

90

positive

negative

ideal

Sub-cooled Liquid

Super-heated Vapor


Isothermal Flash Calculations

Liquidfeed

T,P,Fzi

T & P

L, xi

Heater Valve

FlashDrum


Equilibrium Flash Vaporization

The equilibrium flash separator is the simplest equilibrium-stage process with which the designer must deal. Despite the fact that only one stage is involved, the calculation of the compositions and the relative amount of the vapor and liquid phases at any given pressure and temperature usually involves a tedious trial-and-error solution.

Buford D. Smith, 1963


Flash Calculation (1 of 4)

MESH Equation

Material Balance Equilbrium Relations Summation of Compositions Enthalpy(H) Balance



Overall Material Balance

Component Material Balance

Equilibrium Relations

LVF +=

iii LxVyFz +=

iii xKy =

(1)

(2)

(3)



Summation of Compositions

Defining

Combining (1) through (5), we obtain:

=i

ix 1

FV=φ

( ) ( )( ) =

−+−=

i i

ii

KKzF 0

111

φφ

(4b)

(5)

(6)

=i

iy 1(4a)



From ideal Raoult’s law

K-value can be rewritten as:

From Antoine equation

vapiii PxPy =

PP

xyK

vapi

i

ii ==

( ) ( ) CCtBAkPaP o

vapi +

−=log

(7)

(8)

(9)


Antoine Coefficients

Benzene TolueneA 6.01788 6.08436B 1203.677 1347.620C 219.904 219.787

( ) ( ) CCtBAkPaP o

vapi +

−=log


Rachford-Rice Function

φ0.0 0.2 0.4 0.6 0.8 1.0

F(φ)

-0.15

-0.10

-0.05

0.00

0.05

0.10

707.0=φ

( ) ( )( ) =

−+−=

i i

ii

KKzF 0

111

φφ


Flash Calculation Results (1 of 3)

Vapor Flowrate (K-mole/hr)

Liquid Flowrate (K-mole/hr)

(1)

(2)

( ) 7.70)707.0(100 =×== φFV

3.297.70100 =−=−= VFL



Mole Fraction at the liquid phase

Mole Fraction at the vapor phase

(3)

(4)

( )11 −+=

i

ii K

zxφ

4479.0=Bx 5521.0=Tx

(5)

(6)

( )11 −+==

i

iiiii K

zKxKyφ

6631.0=By 3369.0=Ty



Mole Fraction of Benzene0.0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1.0

Pre

ssur

e (k

Pa)

60

80

100

120

140

160

180

200

4329.0=Bx6429.0=By


PRO/II Keyword Input for Flash Calculation

TITLE PROBLEM=PRBLEM-1A,PROJECT=CLASS,USER=JHCHODIMENSION METRIC,PRES=ATMPRINT INPUT=ALL,PERC=M,FRAC=M

COMPONENT DATALIBID 1,BENZENE/2,TOLUENE

THERMODYNAMIC DATAMETHOD SYSTEM=IDEAL

STREAM DATAPROP STREAM=1,TEMP=25,PRES=1,RATE=100,COMP=1,60/2,40

UNIT OPERATION DATAFLASH UID=F01FEED 1PROD V=1V,L=1LISO TEMP=100,PRES=1.2

END


PRO/II Output Summary for Flash Calculation

STREAM ID 1 1L 1VNAMEPHASE LIQUID LIQUID VAPOR

FLUID MOLAR FRACTIONS1 BENZENE 0.6000 0.4476 0.66292 TOLUENE 0.4000 0.5524 0.3371

TOTAL RATE, KG-MOL/HR 100.0000 75.6710 24.3290

TEMPERATURE, C 25.0000 100.0000 100.0000PRESSURE, ATM 1.0000 1.2000 1.2000ENTHALPY, M*KCAL/HR 0.0865 0.2800 0.2681MOLECULAR WEIGHT 85.1285 85.8632 82.8433MOLE FRAC VAPOR 0.0000 0.0000 1.0000MOLE FRAC LIQUID 1.0000 1.0000 0.0000


PRO/II BVLE Analysis


Dew & Bubble Point Calculation

Dew Point is the very state at which condensation is about to occur. Dew Point Temperature Calculation at a Given Pressure Dew Point Pressure Calculation at a Given Temperature Vapor Fraction is ‘1’ at Dew Point

Bubble Point is the very state at which vaporization is about to occur. Bubble Point Temperature Calculation at a Given Pressure Bubble Point Pressure Calculation at a Given Temperature Vapor Fraction is ‘0’ at Bubble Point


Ex-1: Bubble Point Failure Case

Calculate the bubble point pressure at 85oC of the following stream. Did you get a converged solution? If not, why?

Use SRK for your simulation.

Component Mole %C1 65C2 15C3 15IC4 5

Save as Filename:

EX-1.inp


Difference between Gas and Vapor

For gas, T > Tc

For vapor, T < Tc

T: System temperature, Tc: Critical temperature

“Methane Gas” but not “Methane Vapor” “Water Vapor” but not “Water Gas”


Ex-2: C7 Plus Heavy Cut Characterization

Calculate the bubble pressure at 45oC and dew temperature at 1.5bar of the following stream. Regard C6+ as NC6(1), NC7(2) and NC8(3) and compare the results. Use SRK for your simulation.

Component Mole %C1 5

C2 10

C3 15

IC4 10

NC4 20

IC5 15

NC5 20

C6+ 5

Save as Filename: EX-2A.inp for NC6, EX-2B.inp for NC7, EX-2C.inp for NC8


Results for EX-2

Characterization of heavycut is very important in the calculation of dew point temperature.

EX-2A.inp, EX-2B.inp, EX-2C.inp

Bubble Pat 45oC

Dew Tat 1.5bar

C6 Plus

18.505 30.519 NC618.561 42.783 NC718.669 59.585 NC8


Results for EX-2A (C6+ NC6)


Results for EX-2B (C6+ NC7)


Results for EX-2C (C6+ NC8)


The End of General Thermodynamics

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General Thermodynamics Process Simulation - … · General Thermodynamics for Process Simulation Dr. Jungho Cho, Professor Department of Chemical Engineering Dong Yang University