Che 201 Hand Out 4 Chapter 6

7/30/2019 Che 201 Hand Out 4 Chapter 6

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ChE 201/[email protected]

Chapter 6

Multiphase Systems

Dr. M. A. A. Shoukat Choudhury

Email: [email protected]: http://teacher.buet.ac.bd/shoukat/

Multiphase Systems Why Study?

- Phase change operations such as freezing,, ,

Example:

1. brewing a cup of coffee or tea,

2. absorption of SO2,

3. distillation to recover methanol or ethanol

10/17/2012 ChE 201/[email protected] 2

4. L-L extraction

5. Adsorption


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6.1 Single Component Phase Equilibrium

Phase diagram A plot of one system variableagainst another that shows the conditions at whichthe substance exists as solid li uid and as.

Phase Diagram of water

- Boiling point

- normal boiling point

- melting/freezing point

- sublimation point


- triple point

- critical temperature and pressure above whichtwo phases (liquid-vapor) never coexist.

Phase Diagram of water

Gas



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Difference of vapor and gas

Vapor:- Gaseous substance below its criticaltemperature which can be condensed bycompressing or increasing the pressure

Gas :

- Gaseous substance above its criticaltemperature which cannot be condensed by


compressing or increasing the pressure

Vapor Pressure Definition: Vapor pressure (also known as equilibrium vapor

pressure)is the pressure of a vapor in equilibrium with its non-vapor phases.

form, and all gases have a tendency to condense back into theiroriginal form (either liquid or solid). At any given temperature,for a particular substance, there is a pressure at which the gasof that substance is in dynamic equilibrium with its liquid orsolid forms. This is the vapor pressure of that substance at thattemperature.

The equilibrium vapor pressure is an indication of a liquid's


.atoms to escape from a liquid or a solid.

Higher the vapor pressure, the more volatile the compound is.

Source : wikipedia


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Estimation of Vapor Pressure

Clapeyron Equation / Clausius-ClapeyronEquation

Antoine Equation

Coxs Chart

Clapeyron Equation / Clausius-Clapeyron Equation

Example 6.1-1 Vapor Pressure Estimation using Clausius


-Clapeyron Equation:

If the vapor pressure of benzene is 40 mm Hg at 7.6o

Cand 60 mm Hg at 15.4 oC, find the vapor pressure at 42.2

oc using Clausius-Clapeyron Equation

Antoine Equation log10 p

* = A - B/ (T + C)

p = 10^ A - B T + C

T is in oC

p* is in mm Hg



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Coxs Chart for Vapor Pressure Estimation


Water Vapor

Pressure Table



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Water VaporPressure Table


Gibbs Phase Rule How many intensive variables must be

specified to define a system?

= =, ,P=number of phases

intensive variables do not depend on thesize of the system. Example: molar volume,density


the system. Example: mass, volume

Calculate DOF for various regions of waterphase diagram.


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Gas-Liquid Systems One Condensable Components

Examples evaporation, drying, humidifications,condensations, dehumidifications

Water

Bone ry airBDA + water

Raoults Law: pi= yi P = pi*

Saturated: pi= yi P = pi*

Superheated: pi= yi P < pi*(T)

P, T


Dew point: if the superheated vapor is cooled

at constant pressure, the temperature at whichthe first dew forms

Degrees of superheat: Ti - Tdp

Example 6.3.2A stream of air at 100 oC and 5260 mm Hg contains

10% water by volume.

superheat of the air

b) Calculate the percentage of vapor that condensesand the final composition of the gas phase if the airis cooled to 80 oC at constant pressure.

c) Calculate the percentage of vapor that condenses


,is compressed isothermally to 8500 mm Hg.


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= = *

Gas-Liquid Systems Multi-Component systems

A + B + C

A, B, C P, T

- works good for xAis close to 1 (i.e., the solution isalmost pure A)

- mixtures of structurally similar liquids (straight-chainalcohols, aromatic hydrocarbons,...)

1. pentane, hexane, heptane, 2. methanol, ethanol, propanol


. , ,

Henrys Law: pA= yAP = xAHA(T)

- HA is Henrys constant for A at temp. T

- works good for xAis close to 0 (i.e., the dilutesolution of A)

Bubble Point Temperature (for solution) Bubble point: When a liquid solution is slowly heated at

constant pressure, the temperature at which the firstbubble forms is the bubble point of the solution at thegiven pressure.



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Dew point: When a vapor is slowly cooled at constantpressure, the temperature at which the first liquid dropletforms is the dew point temperature at the given pressure.

Dew Point Temperature


Graphical Representations of VLE



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Solubility

The solubility of a solid in a liquid is themaximum amount of that substance that cane sso ve n a spec e amoun o e

liquid in the equilibrium. The solubilitystrongly depends on temperature.

Saturated

Supersaturated

Solubility curve


Elementary Principl es of Chemical Processs, 3/E by Richard M. Felder and

Ronald W. Rousseau

Copyright 2005 by John Wiley & Sons, Inc. All rights r eserved.

Figure 6.5-1 (p. 266)Solubilities of inorganic solutes.


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Solubility Curves


oC

Problem 6.78 A solution containing 100 lbm KNO3/ 100 lbm

H2O at 80oC is fed to a cooling crystallizer

opera e a . urry rom e crys a zeris fed to a filter where the crystals areseparated from the solution. Determine theproduction rate of crystals (lbm crystals/ lbmof feed) and the solid-liquid mass ratio (lbm


the crystallizer. The solubility of KNO3 is 40 gKNO3/ 100 g H2O at 25

oC.


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6.78 solution


Weather Report

What kind of humidity?

What is its meaning?


Courtesy: The Daily Star, April 27, 2009


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Gas-Vapor Systems


Definitions of Various Humidity

% relative saturation/humidity

- Saturation refers to any gas - vapor system

- Humidity refers to air water system

sr or hr =

Molal saturation

sm or hm =

pipi

*(T)X 100%

piP - pi

Absolute Saturation or humidity

sa or ha =


Pi Mi(P- pi)Mdry


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Definitions of Various Humidity

Percentage saturation/humiditysp or hp =

sms *

X 100%

piP - pi pi

*

P pi*

= x 100%


Problem 6.27On a hot summer day the temperature is 35 oC,and barometric pressure is 103 kPa, and there a ve um y s . n a r con onerdraws in outside air, cools it to 20 oC, anddelivers it at a rate of 12500 L/h. Calculate therate of moisture condensation (kg/h) and thevolumetric flow rate of the air drawn from the



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6.27 Solution


Problem 6.38Stack gas is emerging from a furnace at 300oC and 105 kPa. It contains CO2 at a partialressure of 80 mm H and no CO O

methane or ethane. The fuel gas fed to thefurnace containing methane and ethane isburned with air. Calculate the mole fraction ofmethane in the fuel and the dew pointtemperature of the stack gas.



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Example 6.4.3 Do Yourself



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Problem 6.44Sulfur trioxide (SO3) dissolves in and reacts with water to form anaqueous solution of sulfuric acid (H2SO4). The vapor is in equilibrium

with the solution contains both SO3 and H2O. If enough SO3 is added, allof the water reacts and the solution becomes pure H2SO4. If still moreSO3 is added, it dissolves to form a solution of SO3 in H2SO4, called

.pure SO3. A 20% oleum by definition contains 20 kg of dissolved SO3and 80 kg of H2SO4 per hundred kg of solution. Alternatively oleumcomposition can be expressed as % SO3 by mass, with constituents ofthe oleum considered to be SO3 and H2O.

a) Prove that a 15.0% oleum contains 84.4% SO3 b) Suppose a gas stream at 40 oC and 1.2 atm containing 90 mol% SO3

and 10% N2 contacts a liquid stream of 98% H2SO4 (aq), producing


.the partial pressure of SO3 in equilibrium with this oleum is 1.15 mm Hg.Calculate i) the mole fraction of SO3 in the outlet gas if this gas is in

equilibrium with the liquid product at 40 oC and 1 atm, and ii) the ratioof (m3 gas feed)/(kg liquid feed).



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Who is he?


Che 201 Hand Out 4 Chapter 6

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