Dr Saad Al-ShahraniChE 334: Separation Processes The basic equation that we will use for...

Dr Saad Al-ShahraniChE 334: Separation Processes

The basic equation that we will use for vapor-liquid equilibrium is:

jLjsatjj xPPy Modified Raoult’s law

A) Bubble Point and dew point Calculations for Ideal systems

For ideal systems, iL = 1.0

jsatjj xPPy Raoult’s law and

Bubble Point and dew point Calculations


This relationship is used in both bubble point and dew point

calculations. For Raoult's Law, the vapor must be an ideal gas, and

both liquid and vapor phases must form ideal solutions. (That is,

molecules in the mixture act as if they are all identical.)

Bubble point Calculations

In this case:

Given: 1. liquid phase compositions (xj’s).

2. pressure of the system or temperature of the system.

Required: vapor pressure compositions (yj’s)



Bubble point Temperature Calculations

Given: P , (xj’s)

Required: T , yj’s

jsatjj xPPy Raoult’s law

P

Pxy

satjj

j

0.11

1 1

j

j

nj

j

satjj

j P

Pxy



Since P is a constant, it can be pulled outside the summation, yielding:

n

j

satj

calcn

j

satjj PxPPxP

11

)( 0)(

Therefore, bubble point calculations almost always require iterative solutions. The procedure is:

1. Guess the temperature T.

2. Calculate (or look up) the vapor pressures of each component at T.

3. Calculate:

)(TfP satj

n

j

satj

calc PxP1

)( (which depends only on T)

Cox-chartAntoine equation



4. Check to see whether (P calc ) is sufficiently close to the actual pressure. A convergence criterion of 10-5 or 10-6 relative error is used, where

error RelativeP

PPcalc

5. If the absolute value of the relative error is small enough, the correct temperature has been guessed, and the vapor compositions can be calculated from

P

Pxy

satjj

j

6. If the error is too big, a new temperature guess is made and the procedure is repeated.



Example:

The liquid in a process vessel contains 40 mole percent benzene, 35 mole percent toluene, and 25 mole percent o-xylene. The total pressure in the vessel is 2 atmospheres. What is the temperature in the vessel, and what is the composition of the vapor?

solution

Let x1 be the mole fraction of benzene in the liquid, x2 be the mole fraction toluene, and x3 be the mole fraction o-xylene.

P= 1,520 mmHg (2 atm)

Guess: T=120 oC.

Vapor phase

Liquid phase

P=2 atm

T=?



Since P calc < P (1,520 mm Hg), a-higher temperature must be guessed.

Guess T =125 oC :

satsat

satsat

From Cox-chart or Antoine equation



For a hand calculation, this P calc is close enough to the desired P. When

we do these calculations on a computer, we will tighten up the

convergence criterion to 10-5 or 10-6 relative error.

Bubble point Pressure Calculations (no iteration)

Given: T , (xj’s)

Required: P , yj’s

This calculation is easier than a bubble point temperature calculation because it is not iterative.



Procedures:

1. Calculate (or look up) the vapor pressures of all the pure

components at the given temperature.

2. Calculate the total pressure of the system from

3. Calculate the vapor compositions from

n

j

satjPxP

1

)(

P

Pxy

satjj

j



Example

A liquid mixture of 40 mole percent benzene, 35 mole percent

toluene, and 25 mole percent o-xylene is held at 100 °C in a closed

vessel. What is the pressure in the vessel, and what is the

composition of the vapor that is in equilibrium with the liquid?

solution

The vapor pressures of the pure components are looked up at 100 oC.

At this temperature, they are 1,360 Hg for benzene, 550 mm Hg for

toluene, and 200 mm Hg for o-xylene. Thus. we have:



sat sat

n

j

satjPxP

1

)(



Dew point Calculations

Given: yj’s

Required: xj’s

There are two types of dew point calculations:

1. Dew point pressure calculation.

Given: T , yj’s

Required: P , xj’s



X

Procedures (no iteration):

satj

jj P

Pxx

1

1 1 1

1j

j

nj

j

nj

jsatj

j

satj

jj P

yP

P

Pyx

nj

j

satjj Py

P

1

)/(

1

Pjsat calculated at T (given) using either Antoine equation or Cox- Chart



2. Dew point temperature calculation.

Given: P , xj’s

Required: T , yj’s

Procedures (iteration):

1. Guess a value temperature T.

2. Determine at the guessed T.

3. Calculate P calc from :

satjP

nj

j

satjj

calc

Py

P

1

)/(

1



4. Test to see whether P calc is sufficiently close to P.

5. If P calc is too far from P, regress T and repeat the calculation.

Example:

Vapor and liquid phases are present in a vessel at 760 mm Hg

pressure. The composition of the vapor phase is 40 mole percent

Benzene, 35 mole percent toluene, and 25 mole percent o-xylene.

Calculate the temperature in the vessel and the composition of the

liquid phase in equilibrium with the vapor.



Solution Since the composition of the vapor phase is known, we make a dew point calculation. The pressure is specified, but the temperature must be found iteratively.

Guess T = 125°C:

sat sat



P calc > P (760 mm Hg), so a lower temperature must be guessed.

Guess T = 120 oC:

sat sat

P calc = 1/0.001182 = 846 mm Hg

P calc is still bigger than P, so an even lower temperature must be used.



Guess T =115 oC :

P calc is now fairly close to the correct P of 760 mm Hg. Accordingly, we can calculate xj = yj P I Pj

sat. This is shown in the last column of the table.

P calc = 1/0.001384 = 723 mm Hg



A common mistake made by students is to look at equation

think that instead of using to calculate P, they can use This is, of course, wrong.

nj

j

satjj

calc

Py

P

1

)/(

1

)/(/1 satjj Py

)/( jsatj yP


Dr Saad Al-ShahraniChE 334: Separation Processes The basic equation that we will use for...

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