Thermophysical Properties Useful Equations
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Transcript of Thermophysical Properties Useful Equations
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8/22/2019 Thermophysical Properties Useful Equations
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Session 2 - Useful Equations
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Vapor-liquid equilibria fundamental equations
n The K-values are defined as:
and
ii
i
=
i
i
n
i
i
n
= =
= =1 1
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Vapor-liquid equilibria fundamental equations
K-Value
Ki = yi / xi i = 1, .., n
Component material balance
li = fi / (1 + Ki L/V) i = 1, .., n
li= mols component i in liquid
fi = mols component i in feed
L = total mols liquid
V = total mols vapor
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Phase equilibria in ideal mixtures
Ideal mixtures - Raoults law
Ki = Pi* / P
Molecules are of samen Size
n Shape
n Molecular type
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Basic phase equilibria relations
n K-values can be calculated via the equation of stateapproach
or the activity coefficient approach
( )
K
y
x
Pv
RTP P
Pii
i
i
l
i
sat
i
sat i
l
i
sat
iv= =
-
g f
f
exp
K
y
xii
i
i
l
iv= =
f
f
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n Although most LTD technologies use the
equation of state (EOS) approach we will
focus on the activity coefficient approach
because it more readily demonstrates theeffect of non-idealities
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K-values - rigorous equation
-
F
Fg=
Li
*i
P,i
*iP,i*ii
i
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*iP,i
P,i
i
i
i
Li
i
y
x
V
T*P
P
K
F
F
g
Vapor-liquid equilibrium constant
Pressure
Vapor pressureAbsolute temperature
Liquid molar volume of component i
Liquid mole fraction of component i
Vapor mole fraction of component i
Liquid phase activity coefficient of component i
Fugacity coefficient of mixture at system pressure
Pure component fugacity coefficient at its vapor pressure
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K-values
Non-ideal mixtures
Ki = Pi* Eigi/ P
Ei = non-ideal gas correctionsgi = activity coefficient
Application: very low to moderate pressures
n Ei is close to unity for low pressures
n Ei becomes a significant correction at moderate
pressures
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VLE - effect of pressure
Very low P Vacuum
Low P 1 - 3 atm.
Moderate P 3 - 17 atm.High P 17- 70 atm.
Very high P >70 atm.
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K-values
:stateofequationangsinucalculatedareand
compoundpuretheofpropertiesareVandP
P,i*iP,i
Li
*i
FF
Calculation of non-ideal gas corrections
Redlich-Kwong (RK)
Soave-Redlich-Kwong (SRK)
Peng-Robinson (PR)
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Activity coefficient
giaccounts for differences inn molecular type
n molecular size
n molecular shape
gimodels:n Regular
n NRTL
n Wilson
n Uniquac
n van Laarn Margules
n
Unifac
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Activity coefficient
n Only Unifac is predictive (based on group
contributions)
n Parameters for all other methods must be determined
from experimental vapor-liquid equilibria data
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Group contribution estimation methods
CH3
CH3 - CH2 - C = OH
CH3
T - Amyl Alcohol
Method 1-CH3 3
-CH2- 1
- C - 1
-OH 1
Method 2C 4
H 9
-CH2- 1H in OH 1
Sec-Tert 1
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Activity coefficient
Margules:
A12 and A21 are adjustable parameters
( )[ ]2211221121 xxAA2A -+=g
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Activity coefficient
n Interaction parameters required for every pair of
compounds in the mixture.
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Activity coefficient
In LTD we use
Regular - hydrocarbon systems
NRTL - non-ideal systems
Uniquac - non-ideal systems
Unifac - fill in missing interaction parameters
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ACTIVITY COEFFICIENTS
1 ETHYLBENZENE
2 ETHYLCYCLOHEXANE
P = 1 ATM.
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Activity coefficient
n Activity coefficient of a component rises to its
highest value when the component is most dilute
n Infinite dilution
n If infinite dilution activity coefficient is 2.0 then that
component has volatility that is twice what its vapor
pressure would indicate.
n is unity when the composition approaches 100%
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Activity coefficient
Non-ideality has an effect on column design
n More difficult to keep heavy key component out ofoverhead product
n Easier to strip light key component out of bottoms
product
n Will change feed tray location
n Overall effect on column depends on factors such
as product specifications, etc.
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A t
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Azeotropes
n A result of non-idealities which boosts the volatilityof one component to match the other component
(binary mixture).
n If a third component is added it will have an effect
on the activity coefficients thus changing the
volatilities.
n Two components which form an azeotrope do not
necessarily stick together in a multi-component
mixture.
A t
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Azeotropes
A very specific result of the more general phenomena:
Compounds do not necessarily end up where theirvapor pressures say they will end up
A i i C f ti t
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Ammonia in C2 fractionator
Vapor IdealPressure Relative
NBP psia Volatility
Ethylene -154.7 390 1.77
Ethane -127.5 220 1.0
NH3 -28.0 30 0.14
NH3 in small amounts will distribute between ethylene
and ethane
n Reason: activity coefficient of NH3 (dilute) is in the
order of 7.5
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Relative volatility of 1,3 Butadiene to n-Butane
Comparison of relative volatilities of C4h d b t 1 3 B t di
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hydrocarbons to 1-3 Butadiene
with and without an 80-mol % acetonitrile 20-mol%
water solvent
No Solvent Solvent
1,3 Butadiene 1.00 1.00cis-2-Butadiene 0.72 1.35
Isobutylene 0.90 1.83
1-Butene 0.90 1.96
n-Butane 0.86 2.84
Isobutane 0.93 3.63
Azeotropes
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Azeotropes
n A solvent can be added specifically to break theazeotrope.
n Extractive distillation
Extractive distillation
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Extractive distillation
Liquid Liquid Equilibrium
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Liquid-Liquid Equilibrium
n In cases considered above the components aremiscible
n Highly non-ideal mixtures can lead to immiscibility -
a second liquid phase separates itself from the first.
Oil and water do not mix!
n Additional phase relationships are needed
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Water/hydrocarbon
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Water/hydrocarbon
Three phase equilibrian The point of three phase equilibrium is sometimes called an
azeotrope. The proper term is heterogeneous azeotrope.
n Temperature is a minimum.n Composition of phases are not equal.
Liquid-liquid equilibrium
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Liquid-liquid equilibrium
L-L equilibrium fundamental equation
applies to any two liquid phases in equilibrium, L-L or
V-L-L
L2i
xL2i
L1i
xL1i
=
Water - hydrocarbon systems
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Water hydrocarbon systems
n Non-ideality is high enough so that
n Hydrocarbon phase contains very little water
n Water phase contains very little hydrocarbon
Water - hydrocarbon systems
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Water hydrocarbon systems
For a water/hydrocarbon mixture we can assume
L1 = water phase
L2 = hydrocarbon phase
2Li
2Li
1Li
1Li g=g
11x
1Lw
1L
w
=g
=
*w
2Lw xx =
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n X*W = mole fraction solubility of water in thehydrocarbon phase when full L-L
equilibrium is attained
n SDB I/9.4-9.1
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V-L-L equilibrium - water/hydrocarbon
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q y
Therefore for the hydrocarbon phase in equilibriumwith the vapor
ow
*w
2Lw
*w
2Lw
=
=g
V-L-L equilibrium - water/hydrocarbon
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q y
and for the water phase in equilibrium with the vapor
ow1L
w=
V-L-L equilibrium - Water/Hydrocarbon
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q y
n Water K-values can be calculated with simplifiedrelationships outlined above.
n SDB I 9.4-5 through 9.4-9
n Avoids using an activity coefficient method
n Of course, an activity coefficient method can be
used.
n This is the most general approach
n Highly non-ideal systems other than water-hydrocarbon
Two Liquid Phases
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q
n Rigorous VLLE n Water decant option
L1
L2
V
L
W
V
Rigorous VLLE Calculations
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Vapor
Liquid 2Liquid 1
VLE K-valuesVLE K-values
LLE K-values
Must enable two-liquid phase calculations.
Water Decant Option
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Vapor
PureWater
Liquid
Water VaporPressure
VLE K-values
Water Solubility
WATER DECANT = ON
V-L-L equilibrium - Water/Hydrocarbon
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Decant feature in PRO/II
n Special water calculations for water/hydrocarbon mixtures.
n Possible only for a hydrocarbon K-value type, e.g., SRK,
CS, BK10, etc.
WATER DECANT = OFF
Water K-value calculated by chosen K-value method.
V-L-L equilibrium - Water/Hydrocarbon
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WATER DECANT = ON, SOLUBILITY = SIMSCI
n DECANT=ON is a modification of the chosen K-value
methodn K-value method must be a hydrocarbon method
n A hybrid method - separate methodology for water and
hydrocarbons
V-L-L equilibrium - Water/Hydrocarbon
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WATER DECANT = ON, SOLUBILITY = SIMSCI
n Water K-Value in hydrocarbon phase calculated from
solubilities.n Solubilities from choice of methods.
n Water K-Value in water phase calculated from vapor
pressure.
n Hydrocarbon K-values from chosen K-value method
n Logic in flash and column to detect second liquid phase.
n Also is an option to calculate water properties from steamtables.
Azeotropes
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n A solvent that forms a heterogeneous azeotropewith one of the components of a homogeneous
azeotrope can be added specifically to break the
azeotrope.n Example: Add benzene to recover pure ethanol from
an aqueous mixture.
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Azeotropic system for the production of absolute
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ethanol using benzene