MB3 Multiple Phase Mass Balances

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Mass Balance: Multi-Phase

MB3

Chemical Engineering


Content• Section 1

– Single Phase Theory (Phase-Diagrams)

– Vapor Pressure (Antoine and Clapyeron Eqn)

– Gibbs Phase Rule

• Section 2

– Gas-Liquid Systems (1 condensable)

• Evaporation, Drying, Humidity

– Gas-Liquid Systems (multi-condensable)

• Raoult Law, Henry Law

• Dew/Bubble points

• Txy & Pxy Diagrams

• Section 3

– Solid-Liquid Systems• Crystallization

– Solubility and Saturation

– Hydrated Salts

– Liquid-Liquid Systems• Miscibility and Extraction


Application in MB• Many processes include multiple-phase

equilibriums– Humidity in air– Absorption– Distillation


Application in MB


Section 1

• Single Phase Theory (Phase-Diagrams)– Phase Diagram

– Phase Change

– Boiling point (T,P); Sublimation point (T,P); Freezing point (T,P)

– L-S, L-G, G-S Equilibrium lines

• Vapor Pressure (Antoine and Clapyeron Eqn)– Vapor pressure definition

– Volatility

– Latent heat of vaporization

– Vapor Pressure estimation/calculation

• Gibbs Phase Rule– DOF for systems (intensive properties)


Phase Diagrams

• Diagram of a pure substance

– It’s a Plot containing one system variable (P,T,V,etc.) vs. other one.

– It shows conditions at which the substance exists in different phases (sol., liq., gas typically)


Phase Diagrams

• P-T Diagram shows the next information:

– Pressure of substance (y-axis)

– Temperature of substance (x-axis)

– Phase Equilibrium Lines

– Critical Point

– Triple Point

– Phases


Phase Diagrams


Special Data

• Phase Equilibrium Lines– Phase equilibrium @ P,T

• Critical Point– Point where no phase boundaries exist

• Triple Point:– Point which the three equilibrium

lines meet

– Solid-Liquid-Gas coexist

• Boiling point– Normal BP (P=1atm)

• Freezing point– Normal FP (P=1atm)

• Sublimation point– Normal SP (P=1atm)


Phase Diagrams


Phase Diagrams

A phase diagram for a binary system displaying a eutectic point.

The iron–iron carbide (Fe–Fe3C) phase diagram


Volatility and Vapor Pressure

• Volatility

– degree to which the species trends to transfer from the liquid (or even solid) state to the vapor state

• Vapor pressure Pº

– Measure of volatility

– Function of Temperature


Vapor Pressure

• Pressure exerted by a vapor in thermodynamic equilibrium with its condensed phases (solid or liquid) at a given temperature in a closed system

Pvapor

Pcond


Vapor Pressure

• Given (T boiling)

• The Vapor Pressure “line” is shown in the Graphic

• For any Tb, there is a Vapor Pressure


Estimation of Vapor Pressures

• Three types of estimation

– Clasius-Clapeyron Equation

– Antoine Equation

– Cox Diagrams


Clasius-Clapeyron Equation

• This approach supposes “straight” equilibrium lines

Review Equilibrium Thermodynamics Course for Extra information in this topic








“Straight line in intervals”





• dp/dT = slope of line




• Vg-Vl = V^

• Substituting Ideal Gas Law

• Inverting Temperature axis (T 1/T)

• Logarithm of P-axis

• Suppose ΔH^v = cte.




• Ln P* vs. 1/T graphs

• Straight line

• Slope = ΔH^v/R

• Y-Intersect = B



• P* = Vapor Pressure [mm Hg]

• ΔH^v = Heat of Vaporization [J/gmol]

• R = Ideal gas constant

• T = (K)

• B= Intersection of Y-Axis constant

• You now just need 2 points to get parameters: B, ΔHv

• 2 vapor pressure points (Pº, T)



• What is latent heat of vaporization?

– Required energy to transform a mol of “liquid” to a mol of “Vapor”

• ΔH^v = Heat of Vaporization [J/gmol]


Clasius-Clapeyron EquationExercise 1

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Clasius-Clapeyron EquationExercise 1









Antoine Equation

• Empirical equation

• Similar to Clasius-Clapeyron Eqn.

• A,B,C values can be found in tables!

• p* must be expressed in mm Hg

• T must be expressed in ºC NOT K!


Antoine EquationExercise

• Calculate Pº of Acetone – @ T = 20 ºC

– @ T = 240 ºCLow Temp

High Temp









Cox Diagrams

• Set of lines ending in Critical Points

• Y-axis typically Vapor pressure

• X-Axis typically Temperature of gas

• Recommended if using those set of substances


Cox Diagrams

• Set of lines ending in Critical Points

• Y-axis typically Vapor pressure

• X-Axis typically Temperature of gas

• Recommended if using those set of substances

• Procedure:– Choose a Substance

– Specify either P or T… Cross a horizontal line if P, vertical if T.

– Cross it with the line of the substance

– Make a Vertical line (if you started with P) or a horizontal line (if you started with T).


Cox Diagrams

Pº for Ethylene at -50ºC


Cox Diagrams



Cox Diagrams



Cox Diagrams



Cox Diagrams


Pº = 200 psi


Cox DiagramsThis line marks the 14.7 psi (atmospheric) “Normal” Boiling Point of Substances


Cox Diagrams

• Chinese Database


Need more Exercises & Problems?

• Go to www.ChemicalEngineeringGuy.com

• Section: Courses

– Mass Balance Course

• Problems Section

• You will find a problem index there…



Gibbs Phase Rule

• The number of intensive variables that can be specified independently for a system at equilibrium:

• Π = Number of phases in the system

• c = Number of chemical Species

• DOF= Degrees of Freedom

• A system is completely stated if there are 0 DOF


Gibbs Phase RuleExercise









Gibbs Phase RuleExercise









Gibbs Phase Rule Conclusion• Gibss Phase Rules is helpful to determine the variables in a

system

• In mixture systems, sometimes you need to “set” some variables

We “fixed” P = 1 atm We “fixed” C = 1 substance


Gibbs Phase Rule Conclusion

• “Fixing” a property… P,V or T will reduce the 3-D chart to a 2-D chart (easier to read)

• Limitation only that Value of fixed variable (E.g. P= 1 atm, 1 m3)


End of Section 1

• We´ve seen– Single Phase Theory (Phase-Diagrams)

• Pressure of substance (y-axis)

• Temperature of substance (x-axis)

• Phase Equilibrium Lines

• Critical Point

• Triple Point

• Phases

– Vapor Pressure

• Cox Diagrams

• Antoine Empirical Equation

• Clapyeron Theoretical Equation

– Gibbs Phase Rule

• Intensive Variables in a system


Section 2

• Gas-Liquid Systems (1 condensable)– Only one substance condenses

– Evaporation, Drying, Humidity

– Examples: Air-Humidity

• Gas-Liquid Systems (multi-condensable)– Raoult Law

– Henry Law

– Dew/Bubble points

– Txy & Pxy Diagrams

– Examples: Ethanol-Water


Gas-Liquid Systems: One Condensable

• Typical Example: Air+Humidity

• Air is non-condensable gas

• Humidity is a condensable vapor

• Typical operations:

– Evaporation

– Drying

– Humidification/dehumidification



• Liquid Water + Dry Air @ 75ºC and 1 atm

– Initially Dry Air has no water (yw = 0)

– Then, water evaporates to Dry Air (yw =/ 0)

– There is a partial pressure of water in the system

• Pw = yw·P

– At one point, water stops to evaporate

– At this point, the Air-Water mixture is “Saturated”



• Saturated system (DA+W):

– It contains all the water that system can hold at that temperature and pressure

• Saturated vapor (W):

– Water evaporated contained in this type of system



• Apply Gibbs Phase Rule:– DOF= 2 + c - π = 2+2-2 = 2

– We need to set 2 variables!

• T, P and yw 3 variables

• If we set P (1 atm) and T (temperture) you will always be able to calculate yw

• If we set P (1 atm) and (yw) you will always have the same temperature for the desired system


Raoult Law (Single Component)

• If only one component will condense with Temperature decrease…

• We may apply Raoult Law (for single component!)


Raoult Law (Single ComponentExercise 1

From Raoult’s law:yw·P = P*yw = P* / P

From tables/data bases

yw = 289 mm Hg / 760 mm Hg = 0.38 gmol W / gmol mixyw = 0.38 gmol W / gmol mix

1 = yw + yda yda = 1- yw = 1- 0.38 = 0.62 gmol DA / gmol mix









Dew/Bubble Point

• Dew Temperature: temperature at which a vapor becomes saturated (@ P = cte)

– The point at which the mix will start condensing

• Bubble Temperature: temperature at which a liquid becomes saturated (@ P = cte)

– The point at which the mix will start evaporating

• NOTE Dew Temp. = Bubble Temp. (#)


Dew/Bubble Point

• Bubble you reach from liquid to vapor (blue)

• Dew you go from vapor to liquid (red)

@ P =cte = 1 atm


Raoult Law (Single Component) MBExercise

1) DP = 90ºC … 100-90 = 10ºC




















Humidity Theory

• Types of Humidity/Saturation

– Relative

– Molal

– Absolute

• Psychometric Charts!

– Air and Humidity charts @ 1 atm


Relative Saturation

• Compares Partial Pressure of Water vs. Vapor pressure of Water at that Temperature

• Typical for weather reports

• 40 % humidity; 80% humidity


Molal Saturation (Humidity)

• Moles of Vapor per Moles of Dry-Air

• Example:

– Moles of W = 2 gmol of Water

– Moles of Air = 180 gmol of Dry Air

– 2/180 = 0.01 gmol of W / gmol of DA

• This is NOT mole Fraction


Absolute Saturation (Humidity)

• Similar to Molal Saturation, compares mass of vapor to mass of Dry gas

• Example:– 0.05 kg of vapor

– 2 kg of dry air

– 0.05/2 = 0.025 kg of W / kg of DA

• This is NOT mass fraction of vapor in mixture!


Humidity Theory

• Eventually, you should find either:

– Partial Pressure of Vapor

– Mole fraction of Vapor in mixture

• With these data you could start MB


Saturation/HumidityExercise



























Psychometric Chart

• As seen before, the system of Dry Air and Humidity have 2 DOF

• T,P, yw Variables

• If we set P = 1 atm we would only need to define either T or yw

• A graph already exists! Its called Psychometric Chart and relates humidity and temperature of air


Psychometric Chart

• We found the next variables

– Specific volume of dry air [m3/kg DA]

– Dry bulb temperature [ºC]

– Wet bulb temperature [ºC]

– Relative humidity [%]

– Absolute humidity [kg w / kg DA]


Psychometric Chart

High Temperatures


Psychometric Chart

Low Temperatures


How to read a Psychometric Chart

Absolute Humidity



Relative Humidity



Dry Bulb Temperature



Wet Bulb Temperature



Specific Volume of DA



• We need:

– Set a Temperature (any)

• Dry

• Wet

– Set a Humidity (any)

• Relative

• Absolute

NOTE: Setting Specific Volume of DA indirectly sets a Temperature… WHY?

We need at least two:- 1 temp + 1 humid- 2 temp- 2 humid


How to read a Psychometric ChartExercise

• What is the Relative humidity of a stream of air @ 30ºC and 0.007 kg of moisture per kg of DA

• Locate Temperature (x axis)

• Locate Absolute Humidity (y axis)

• Locate Relative Humidity (probably between two lines)







• Between 20% and 30%

• Relative Humidity is Approx. 28%


Dry Bulb Temperature

• Temperature of air measured by a thermometer freely exposed to the air but shielded from radiation and moisture

• Generally known as “THE” temperature of air.

• It is the true thermodynamic temperature

• Does not indicate the amount of moisture in the air


Wet Bulb Temperature

• Temperature that air would have if it were cooled to saturation (100% relative humidity)– By evaporation of water

– Latent heat being supplied by air

• The lowest temperature that can be reached under current ambient conditions by the evaporation of water only

• Its determined by – Actual air temperature (dry-bulb temperature)

– Amount of moisture in the air (humidity).


Dry/Wet Bulb Temperature

• Dry Bulb Thermometer has no add-ons

• Wet Bulb Thermometer has a “wet” coat so water may vaporize










Break

We’ve Seen

What's Left

We’ve Seen

What's Left


Gas-Liquid: Multicomponent

• Processes which involve 2+ components in at least 2+ phases

• Typical processes

– Vapor-Liquid Distillation & Absorption

– Solid-Liquid Solutions (Crystallization)

– Liquid-Liquid Immiscible liquids (Extraction)


Vapor-Liquid Equilibrium

• Best way to evaluate equilibriums Data

• If we got no data estimate


Vapor-Liquid EquilibriumExercise 1















































Vapor-Liquid Equilibrium

• What if we got NO data?

• We need to apply some Laws– Raoult Law

– Henry Law

• These law help relate vapor pressures with concentrations (mole fractions) and constants

• Using Gibbs Rule– DF = 2 – c – π = 2 – 2 -2 = 2

– We need two variables!

2 phases2 substances


Raoult Law

• If ideal solution (one that follows Roult Law)

– Xa 1 (A is almost pure)

• Then we can relate liquid phase with vapor phase:

• Note, if we set A, then B is fixed too WHY?

ya = mole fraction of A in vaporP = Total pressure of systemxa = mole fraction of A in liquidPaº(T) = Vapor Pressure of A


Raoult Law

• Remember Raoult law for 1 condensable?

• This equation

• Reduces to

Xa = 1Ya = 1


Henry Law

• Ha(T): Henry Constant

• Valid when Xa 0 (when it is dilute)

– Suppose no dissociation, ionization, reaction


Raoult and Henry LawExercise










Xb = Xt(equimolar)










• Continue to solve for yb and P



















• Substitute yb in P equation… you get P









Dew/Bubble Point

• We’ve seen Dew and Bubble Temperatures

– Typical for Equilibrium Thermodynamics

– Calculating Temperature of the Dew Point

– Calculating Temperature of the Bubble Point

• Visit www.ChemicalEngineeringGuy.com/Courses

– Click on Courses Equilibrium Thermodynamics

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Graphical Representation:Vapor-Liquid Equilibrium

• We use diagrams to condense data:

– T x-y Diagrams: Temperature vs. compositions

– P x-y Diagrams: Pressure vs. compositions

• We use this on Binary Systems (A+B)

• If Txy fix P (generally 1 atm)

• If Pxy fix T (Temperature may vary)


T x-y Diagrams

• Simplest form of T x-y Diagrams

• Y-axis: Temperature

• X-Axis: Mole Composition of A

• Vapor Region

• Liquid Region


T x-y Diagrams


P x-y Diagrams

• Simplest form of P x-y Diagrams

• Y-axis: Pressure

• X-Axis: Mole Composition of A

• Vapor Region

• Liquid Region


P x-y Diagrams


P x-y Diagrams

More Information of P xy and T xy Diagrams in Equilibrium Thermodynamics Course


T x-y and P x-y DiagramsExercise 1

We don’t need P xy (WHY?)










a) Temperature when boiling…










T boiling approx= 86ºC

a) Temperature when boiling…










Boiling @ T constant (WHY)

b) Final Composition?






















YB = 0.87


















End of Section 2

• Section 2– Gas-Liquid Systems (1 condensable)

• Evaporation, Drying, Humidity• Theory of Humidity (absolute, molal, relative)• Raoult Law for 1 condensable specie• Psychometric Charts• MB with G-L (1) data

– Gas-Liquid Systems (multi-condensable)• Vapor-Liquid Equilibrium• Raoult Law• Henry Law• Txy & Pxy Diagrams• MB with G-L (2+) data


Section 3

• Section 3



– Hydrated Salts



Solid-Liquid Systems

• MB processes Crystallization

– Solution, Solvent, Solute


– Saturated and Supersaturated concepts

– Hydrated Salts


Solubility

• Solubility of a solid in a liquid is the maximum amount of that substance that can be solved in a specific amount of liquid (in equilibrium)

• Varies for each type of substance

• Is Temperature Dependent


Solubility of Some Substances

Solubility of some common salts


Solubility of Some Substances

Solubility of some common salts


Unsaturated Solution

• Unsaturated solution:

– is a chemical solution in which the solute concentration is lower than its equilibrium solubility.


Saturated Solution

• Saturated solution:

– is the point at which a solution of a substance can dissolve no more of that substance and additional amounts of it will appear as a separate phase

Any more solute will stay as a solid


Supersaturated Solution

• Supersaturated solution

– is a state of a solution that contains more of the dissolved material than could be dissolved by the solvent under normal circumstances.

Crystals form in a supersaturated solution


Crystallization MBexercise 1








































































Hydrated Salts

• Anhydrous salts: Water free salts

• Hydrated Salts: Salts + Hydrate

– Water molecules bon to the salt


Hydrated SaltsExercise










60 kg K per 100 kg W



















• See next diagram for solution




























About 75ºC (Saturation Temp.)

















Colligative Properties

• This topic is covered in

– Basic Chemistry Course

– Equilibrium Thermodynamics

• The scope of our course does not includes such material


Liquid-Liquid Systems

• Miscibility and Immiscibility

• Partially miscible

• Liquid Extraction

• Distribution Coefficient


Liquid-Liquid SystemsExtraction

• Miscibility

– property of substances to mix in all proportions, forming a homogeneous solution

– Miscible

– Partially Miscible

– Not Miscible



• LLE consists in transferring one (or more) solute(s) contained in a feed solution to another immiscible liquid (solvent).

• The solvent that is enriched in solute(s) is called extract.

• The feed solution that is depleted in solute(s) is called raffinate.



• Extraction

• Distribution Coefficient/Partition ratio

– Ralates transfer



• In practice, extraction is often carried out in several consecutive stages.

• The solution leaves each stage and then goes to another additional solvent in the next stage

• Enough stages should be used to achieve almost a complete transfer of solute


Liquid-Liquid SystemsExercise 1






























































End of Section 3

• Section 3



– Hydrated Salts



Problems & Exercises

• All pair problems of Elementary Principles in Chemical Processes. Felder, R; Rousseau, R. 3rd edition are solved in the next videos. (Chapter 6)

• Remember: practice makes the master


Elementary Principles in Chemical Processes

What topics did we covered from the book?


End of MB3: Multiple-Phase MB• You should be now able to perform MB with multiple phases

• Hopefully you are now able to:– Understand phases

– Calculate Vapor pressure and apply them in MB• Clasisus Clapeyron

• Antoine Equation

– Get to know the Vapor-Liquid equilibrium systems

– Use Raoult Law and Henry Law

– Understand the Solid-Liquid system

– Solve Liquid Liquid systems


MORE INFORMATION

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Bibliography

• Elementary Principles in Chemical Processes. Felder, R; Rousseau, R. 3rd edition.

• Basic Principles and Calculation in Chemical Engineering. Himmelblau, D. 7th edition.

Date post:	14-Jul-2015
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