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Lecture 6: Bubble and Dew Point1

Bubble Point and Dew Point Calculations

In the last lecture we discussed:

An isothermal flash separations

The derivation and solution of the Rachford Rice equation

Newtons iterative procedure to solve for the roots of the RR equation

A numerical example to demonstrate this approach.

This lecture will cover: An example of using the Rachford Rice Procedure with

a simple spreadsheet

Bubble point and Dew Point temperature and pressure

calculations

An example of a dew point temperature calculation

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Multicomponent Flash Calculations

For this system there are 3C+10 variables: F, V, L, {T, P}3, Q, {xi , yi ,zi}C

and C+5 degrees of freedom.

We specify the C+3 variables F, zi, TF, PF and two additional variables

Liquid Feed Vapor out

Flash Drum

F, zi, TF, PF

L, xi, TL, PL

Liquid out

V, yi, TV, PV

Q

Common Specifications:

TV,PV Isothermal Flash

V/F=0, PL Bubble-Point Temperature

V/F=1, PV Dew-Point Temperature

V/F=0, TL Bubble-Point Pressure

V/F=1, TV Dew-Point Pressure

Q=0, PV Adiabatic Flash

Q, PV Nonadiabatic flash

V/F, PV Percent Vaporization Flash

Last lecture

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Isothermal Flash Calculations

Liquid Feed

If we specify F, zi, TF, PF and TV ,PV then we apply the Rachford-Rice procedure:

Vapor out

Flash Drum

F, zi, TF, PF

L, xi, TL, PL

Liquid out

V, yi, TV, PV

Q

Steps 1&2: TL TV

Step 3: Solve Rachford-Rice for V/F.

PL PV

Step 4: V F

Steps 5 and 6:

Step 7:

Step 8:

Xi Zi

Ki 1Yi

KiZiKi 1

L FF

QVhv Lhl Fhf

Determine V

Determine L

Determine Q

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Bubble Point Pressure Calculations

Liquid Feed

For a bubble point pressure calculation we specify F, z i, TF, PF, TL and that we are at

the bubble point.

Vapor out

Flash Drum

F, zi, TF, PF

L, xi, TL, PL

Liquid out

V=0, yi, TV, PV

Q

f(0) Zi Ki 1 i

0

At the bubble point there is equilibrium between the vapor and liquid phases, but the system

is completely liquid and thus the vapor fraction is zero.

f()

Zi Ki 1 Ki 1i

0

ZiKii

1

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Bubble Point Temperature Calculations

Liquid Feed

For a bubble point temperature calculation we specify F, z i, TF, PF, PL and that we are at

the bubble point.

Vapor out

Flash Drum

F, zi, TF, PF

L, xi, TL, PL

Liquid out

V=0, yi, TV, PV

Q

f(0) Zi Ki 1 i

0

At the bubble point there is equilibrium between the vapor and liquid phases, but the system

is completely liquid and thus the vapor fraction is zero.

f()

Zi Ki 1 Ki 1i

0

ZiKii

1

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Dew Point Temperature Calculations

Liquid Feed

For a Dew Point Temperature calculation we specify F, zi, TF, PF, PV and that we are at

the dew point.

Vapor out

Flash Drum

F, zi, TF, PF

L=0, xi, TL, PL

Liquid out

V, yi, TV, PV

Q

At the dew point there is equilibrium between the vapor and liquid phases, but the system

is completely vapor and thus the vapor fraction is one.

f()

Zi Ki 1 Ki 1i

0

Zi

Kii 1f(1)

Zi Ki 1 Kii

0

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Dew Point Pressure Calculations

Liquid Feed

For a Dew Point Pressure calculation we specify F, zi, TF, PF, PV and that we are at

the dew point.

Vapor out

Flash Drum

F, zi, TF, PF

L=0, xi, TL, PL

Liquid out

V, yi, TV, PV

Q

At the dew point there is equilibrium between the vapor and liquid phases, but the system

is completely vapor and thus the vapor fraction is one.

f()

Zi Ki 1 Ki 1i

0

Zi

Kii 1f(1)

Zi Ki 1 Kii

0

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Bubble Point and Dew Point Calculations

To solve the bubble point and dew point problems we must find the unspecified temperature

or pressure which satisfies the Rachford Rice expressions.

Zi

Kii 1

ZiKii

1Dew PointBubble Point

Bubble Point or Dew Point Temperature Procedure:

Step 1: Guess a temperature.

Step 2: Use the given product pressure and guess temperature to determine the K-values fromthe DePriester chart.

Step 3: Calculate the Rachford Rice expression appropriate to the equilibrium condition.

Step 4: Guess a new higher temperature if K values must be higher. Otherwise, guess a

lower temperature.

Step 5: Repeat Steps 3 and 4 until the Rachford Rice equation is satisfied.

Bubble Point or Dew Point Pressure Procedure:

Step 1: Guess a pressure.

Step 2: Use the given product temperature and guess pressure to determine the K-values from

the DePriester chart.

Step 3: Calculate the Rachford Rice expression appropriate to the equilibrium condition.

Step 4: Guess a new lower pressure if K values must be higher. Otherwise, guess a

higher pressure.

Step 5: Repeat Steps 3 and 4 until the Rachford Rice equation is satisfied.

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Example: Rachford-Rice

A flash chamber operating 80 degrees C and 500kPa is separating 1000 kg moles/hr of a

feed that is 10 mole %ethane, 5 mole %propane, 15 % n-butane, 10 % n-pentane,

12 mole % isopentane, 8 mole %n-hexane, 30 mole %heptane and 10% nonane.

What are the product compositions and flow rates?

y1 (ethane) = 0.358y2 (propane) = 0.132

y3 (n-butane) = 0.236

y4 (n-pentane) = 0.11

y5 (isopentane) = 0.079

y6 (n-hexane) = 0.03

y7 (heptane) = 0.051

y8 (nonane) = 0.003

x1 (ethane) = 0.033x2 (propane) = 0.029

x3 (n-butane) = 0.128

x4 (n-pentane) = 0.123

x5 (isopentane) = 0.105

x6 (n-hexane) = 0.093

x7 (heptane) = 0.365

x8 (nonane) = 0.125

V/F=0.207V=207kg/hr

L=793kg/hr

K1 (ethane) = 11.0

K2 (propane) = 4.6

K3 (n-butane) = 1.85

K4 (n-pentane) = 0.75K5 (isopentane) = 0.9

K6 (n-hexane) = 0.32

K7 (heptane) = 0.14

K8 (nonane) = 0.026

From the Depriester chart:

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Depriester Determination of K-Values

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Example: Dew Point Temperature

A flash chamber operating 400 kPa pressure is producing a top product of

35 % n-butane, 30 % n-pentane, 15 mole %n-hexane, 20 mole %heptane.

What is the temperature of the flash drum to operate at the dew point?

x1 (n-butane) =

x2 (n-pentane) =

x3 (n-hexane) =

x4 (heptane) =

V/F=

T=


y1 (n-butane) = 0.35

y2 (n-pentane) = 0.3

y3 (n-hexane) = 0.15

y4 (heptane) = 0.2

T=

K1 (n-butane) =

K2 (n-pentane) =K3 (n-hexane) =

K4 (heptane) =

T=

K1 (n-butane) =


K4 (heptane) =

T=

K1 (n-butane) =


K4 (heptane) =

T=

K1 (n-butane) =


K4 (heptane) =

ZiKii

ZiKii

ZiKii

ZiKii

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K-Values Iterations for Dew Point Temperature

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Example: Bubble Point Pressure

A flash chamber operating 80 degrees C is producing a bottoms product of

15 % n-butane, 20 % n-pentane, 25 % n-hexane, 40 % heptane.

What is the pressure of the flash drum to operate at the bubble point?

x1 (n-butane) = 0.15x2 (n-pentane) = 0.20

x3 (n-hexane) = 0.25

x4 (heptane) = 0.4

V/F=P=

P=

K1 (n-butane) =


K4 (heptane) =


y1 (n-butane) =y2 (n-pentane) =

y3 (n-hexane) =

y4 (heptane) =

P=

K1 (n-butane) =


K4 (heptane) =

P=

K1 (n-butane) =


K4 (heptane) =

P=

K1 (n-butane) =


K4 (heptane) =

ZiKii

ZiKii

ZiKii

ZiKii

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Depriester Determination of K-Values

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Summary

Next Lecture will cover:

Ternary Liquid-Liquid extractions.

Ternary phase diagrams.

A procedure to determine the product compositions and

flow rates of a liquid-liquid extraction separation.

This lecture covered:

Using a simple spreadsheet to apply the Rachford Rice

Procedure Bubble point and Dew Point temperature and pressure

calculations

An example of a dew point temperature calculation

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