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Thermodynamic - Unit Operations - Lecture Slides, Slides of Engineering Chemistry

Amity University - Bihar Engineering Chemistry

Multicomponent Distillation, Mass transport theories , Principles of adsorption , Principles of humidification , Principles of drying are main topics covered in this Unit Operations course. This lecture covers following points: Rigourous Methods, Distillation Process, Thermodynamic System, Equilibrium Stage, Material Balance Equations, Equilibrium Relations, Degrees of Freedom Analysis, Design Strategy, Stage Efficiency Analysis, Thermodynamics Data

Typology: Slides

2012/2013

Uploaded on 08/30/2013

sharmila_sehgal 🇮🇳

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Thermodynamic relations:

Simplified models

Raoult’s law (Ideal solution/ideal gas):

iii Pxp pi is the partial pressure of component i

Dalton’s law (Ideal gas):

Pyp ii 

Composition and K-value for ideal gas/ideal solution system:

PPxyK s

iiii // 

Relative volatility for ideal gas/ideal solution system:

iji PPKK // 

Antoine equation:

iCT

ATP 

)(ln

T, P

PxPy i

ii /

P is total pressure in the system

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Download Thermodynamic - Unit Operations - Lecture Slides and more Slides Engineering Chemistry in PDF only on Docsity!

Thermodynamic relations:Simplified models^ Raoult’s law (Ideal solution/ideal gas):

s ii i^

Px

p^ 

p^ is the partial pressure of component i^

i

Dalton’s law (Ideal gas):

Py

p^

i Composition and K-value for ideal gas/ideal solution system:

P P x y K^

s i i i i^

/ /^

 

Relative volatility for ideal gas/ideal solution system:

s j s i j i^

P

K

K^

/^

Antoine equation:

i^ i i s i

C B T A TP

  ) ( ln

T, P

V L

P

xP

y^

s ii i^

P^ is total pressure in the system

Thermodynamic relations:Simplified models^ Henry’s law:

i i i^

xT H p^

)( ^

H(T) is the Henry’s constant

Dalton’s law (Ideal gas):

Py

p^

i Composition and K-value:

P T H x y K^

i i i i^

/) ( /^

 

Relative volatility in the Henry’s law regime:

/^

T

H

T

H

K

K^

j i j i^

T, P

V L

P xT H y^

i i i^

/ )( 

P^ is total pressure in the system

1. Absorption: Design considerations Limiting conditions: Gas-liquid ratio; straight operating and equilibrium lines Condition

: L, V constant -> L/V constant, y

=mxe^

This is possible for very dilute (<3% mole fraction) mixturesso change in total number of moles of each flow isinsignificant and the region of interest is in the Henry’s law regimeA) Limiting (L/V)

value:min^

y

x

(mole fraction of A in L)

(mole fraction of A in V) xa

xb

yb ya

equilibrium line

x*^ b

B) Number of ideal stages: can be calculatedanalytically

a b

a b a b

a b

a a b b

x m y

y y x x

y y L V

Lx V Vy Lx V y

^        



 

- min

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1. Kremser equation: the number of idealstages

^

A

y

N^

a

b

ln

ln^

*^

n

e

e^

mx

y

mx

y^

^

Straight equilibrium line

const mVL A^

 ^

Adsorption factor, straight operating line

The Kremser equation (1930)

y

x

(mole fraction of A in L)

x^ a^

xb

equilibrium line

yb y^ b yb y^ b

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2. Thermodynamic calculations using K-values^ Bubble pointProcedure:

a) Select Tb) K

(T)i

c) d) if^

T is too high

 e) Adjusting Tg) Final composition can be corrected using i

xii K

(^1) 

i

xii K

^ ^ i

i ii i i^

x xK K y

2. Thermodynamic calculations using K-valuesDew

point

Model system: binary mixture A, B- Consider the process in the figure: we start witha mixture of composition 1 and temperature T

and start decreasing the temperature- As we decrease the temperature we are going toreach a point where the first drop of liquid forms- The liquid in the droplet obeys:- On the other hand:- Thus as we decrease the temperature we put newK-values the above equation until this condition is met

^

B

A^

y

^

B

A^

x

/^

^

T

K

y

T

K

y^

B

A

T^

V

L

2. Isothermal multicomponent flash separation

D Dhyi^ D^

, ,

F F F F i^

T P h zF

, , , ,

,T^11 P

Objective: find D, B, andtheir compositions

B Bhxi^ B^

, ,

) 1 ( 1

 

F i^ i i^

z K x



) 1 ( 1

 

F ii i i^

zK K y



  ^

  



 ^

i i F i i i i i

K K z y x^

0 ) 1 ( 1

) (^1) ( 

2. Multicomponent flash separation (Adiabatic)

B hxi B^

, ,

D hyi D^

, ,

F F F F i^

T P h zF

, , , ,

,T^11 P

Liquid feed is heated under pressure and then adiabatically flashed throughthe pressure reducing valve

F T F

T

P

P^1 ^1

F i

i

i^

Fz Dy Bx^

 

F D B^

 

F

D

B^

Fh Dh Bh

 ^

) (^1) (^

   ^

F

D

B^

h h h

 

2. Fenske Equation: binary case

)] (^1) ( /) (^1) ( ln[ min^

 





D B B D^

x x x x



Fenske equation

2. Limiting cases: minimum reflux

x

R

x

R R

y^

y

x

zf

xB^

xD

y1 yB

xN

At this point: x

=x* and yn

=y*n+^

x*

y*

* min

min

min min

x

y

x

R

x

R

x

R R

y

^ 

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2. Fenske equation for multicomponentdistillations: any stages/any componentsAssumption: relative volatilities of components remain constantthroughout the column

jN jn n i in Nn

x x x x

, ,

min^

ln ln^

min

min^ 

  

   



i – light componentj – heavy component

)(^ )(

T

K

T

K

T

i j



2. Fenske equation for multicomponentdistillations

)(^ )(

T

K

T

K

T

LK HK

HKLK

Choices for relative volatility: 

D B

T

1) Relative volatility at saturated feed condition

F F HKLK

THK

LK

^

2) Geometric mean relative volatility

(^

B B D D HKLK

T

T^

HKLK



^

^3

(^

B B D D F F

HKLK

T

T^

HKLK



^

why geometric mean?

2. Gilliland correlation: Number of idealplates at the operating reflux

   

  

    

min 1

Dm D R

R Rf

NN N

2. Complete short cut design:Fenske-Underwood-Gilliland methodGiven a multicomponent distillation problem:

a) Identify light and heavy key componentsb) Guess splits of the non-key components and compositionsof the distillate and bottoms productsc) Calculated) Use Fenske equation to find Nmine) Calculate distribution of non key componentsf) Use Underwood method to find R

g) Use Gilliland correlation to find actual number of ideal stagesgiven operating refluxh) Use Kirkbride equation to locate the feed stage

HKLK , 

Thermodynamic - Unit Operations - Lecture Slides, Slides of Engineering Chemistry

Related documents

Partial preview of the text

Download Thermodynamic - Unit Operations - Lecture Slides and more Slides Engineering Chemistry in PDF only on Docsity!

Thermodynamic relations:Simplified models^ Raoult’s law (Ideal solution/ideal gas):

Px

p^ 

p^ is the partial pressure of component i^

i

Dalton’s law (Ideal gas):

Py

p^

i Composition and K-value for ideal gas/ideal solution system:

Relative volatility for ideal gas/ideal solution system:

P

P

K

K^

/^

Antoine equation:

T, P

V L

P

xP

y^

P^ is total pressure in the system

Thermodynamic relations:Simplified models^ Henry’s law:

H(T) is the Henry’s constant

Dalton’s law (Ideal gas):

Py

p^

i Composition and K-value:

Relative volatility in the Henry’s law regime:

/^

T

H

T

H

K

K^

T, P

V L

P^ is total pressure in the system

1. Absorption: Design considerations Limiting conditions: Gas-liquid ratio; straight operating and equilibrium lines Condition

y

x

(mole fraction of A in V) xa

xb

yb ya

x*^ b

1. Kremser equation: the number of idealstages

^

A

y

y

y

y

N^

a

a

b

b

ln

ln^

*^

n

n

e

e^

mx

y

mx

y^

^

Straight equilibrium line

Adsorption factor, straight operating line

The Kremser equation (1930)

y

x

x^ a^