In the last lecture we:

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Lecture 5 Isothermal Flash Calculations
In the last lecture we Described energy and
entropy balances in flowing systems Defined
availability and lost work Derive a Gibbs
Phase Rule for flowing systems Described
system specification Showed how DePriester
charts are used to tabulate K-value data for
hydrocarbon systems
In this lecture well Describe an isothermal
flash separation Derive the Rachford-Rice
equation Show how to use Newtons method to
find the roots of the RR equation Use the
Rachford-Rice procedure, including Newtons
method and DePriester equilibrium data to solve
a hydrocarbon isothermal flash problem.
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Isothermal FlashConfiguration
Consider the following operation which produces a
liquid-vapor equilibrium from a liquid feed
Flash Drum
Vapor out
Liquid Feed
V, yi, TV, PV, hv
F, zi, TF, PF, hF
Liquid out
Q
L, xi, TL, PL, hL
For each stream n molar flow rate F, L, Vzi
composition variables x,y,z T temperature P
pressure h enthalpy Q heat transfer
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Isothermal Flash Variables
Flash Drum
Vapor out
Liquid Feed
V, yi, TV, PV, hv
F, zi, TF, PF, hF
Liquid out
Q
L, xi, TL, PL, hL
For this system there are 3C10 variables
F, V, L, TF, PF, TV, PV, TL, PL, Q, xi , yi ,ziC
We showed in the last lecture that there are C5
degrees of freedom. If we specify F, zi, TF, PF
we have specified (C3) variables andwe can
specify two additional variables.
Common Specifications TV,PV Isothermal
Flash V/F0, PL Bubble-Point Temperature V/F1,
PV Dew-Point Temperature V/F0, TL Bubble-Point
Pressure V/F1, TV Dew-Point Pressure Q0, PV
Adiabatic Flash Q, PV Non adiabatic flash V/F,
PV Percent Vaporization Flash
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Isothermal Flash Equations
variables F, Tv, Pv, TF , PF , Zi
If we specify the
Then remaining
variables must be found from
Equations A) mole fraction summations B)
K-Value relationships C) Mass balances D)
Energy balance E) Thermal and mechanical
equilibrium Total
Note that if T and P of each product stream are
not considered as variables, then we wouldnt
have equations for thermal and mechanical
equilibrium in the drum.
If less than C5 variables are specified, then
the system is undetermined (underspecified). If
more than C5 variables are specificed, then the
system is overdetermined (overspecified).
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Isothermal Flash Equations
We have 2C5 variables to determine from 2C5
equations. The expression gives the total
number of equations for this system of 2C3 (the
system creates a two- phase equilibrium). The two
additional equationswe need come from our
assumption of thermal and mechanical equilibrium
in the drum.
We have total material balance
We have component material balances, one for each
component
We have the mole fraction summations for each
phase (or stream)
In equilibrium, we have a K-value relationship
for each component
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Rachford Rice Derivation
It is convenient to define the Vapor Fraction as
follows
Substituting into our total material balance
For the component material balances
Using the K-Value and solving for the liquid
phase mole fraction
We use the K-Value to get
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Rachford Rice Equations
We use the mole fraction summations
Substituting in our expressions for the mole
fractions
Gives us the Rachford-Rice Equation
The roots of this equation give us the
compositions, and vapor fraction of the
Isothermal Flash operation.
To solve this equation, we need to use some
procedure for finding the roots Iterative
Graphical
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Newtons Iterative Method
To solve the Rachford-Rice equation we can use
Newtons method to find ?
Newtons method estimates a betterroot using the
last guess and the ratioof the function to its
derivative at thatguess
For the Rachford-Rice Equationthis becomes
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Rachford-Rice Procedure
The Rachford-Rice procedure using Newtons method
is then
Step 1
Thermal equilibrium
Step 2
Mechanical equilibrium
Step 3 Solve Rachford-Rice for V/F where the
K-values are determined by TL, and PL.
Can use Newtons method here.
Determine V
Step 4
Steps 5 and 6
Step 7
Determine L
Step 8
Determine Q
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Example Rachford-Rice
A flash chamber operating at 50ºC and 200kPa is
separating 1000 kg moles/hr of a feed that is 30
mole propane, 10 n-butane, 15 n-pentane, and
45 n-hexane. What are the product
compositions and flow rates? 1) Using the
Depriester Chart we determine that K1 (propane)
7.0 K2 (n-butane) 2.4 K3 (n-pentane)
0.80 K4 (n-hexane) 0.30 2) We first write the
Rachford-Rice Equation and substitute in the
composition and K-values
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Depriester Determination of K-Values
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Example Rachford-Rice
We can either plot the Rachford-Rice Equation as
a function of V/F or use Newtons method
Guess V/F0.1
To obtain a new guess we need the derivative of
the RR equation
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Example Rachford-Rice
So our next guess is
To obtain a new guess we need the derivative of
the RR equation
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Example Rachford-Rice
So
Using
X1 (propane) 0.0739 X2 (n-butane) 0.0583 X3
(n-pentane) 0.1670 X4 (n-hexane) 0.6998
Y1 (propane) 0.5172 Y2 (n-butane) 0.1400 Y3
(n-pentane) 0.1336 Y4 (n-hexane) 0.2099
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Summary
In this lecture we discussed  Variables,
Equations and degrees of freedom for an
isothermal flash separation An isothermal flash
configuration 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.
Next Lecture will cover Bubble point pressure
and Dew Point temperature calculations