Batch Distillation

1
Lecture 4 Phase Equilibrium in Flowing Systems
Last lecture primarily focused on the
thermodynamics of separations. We covered
Phase Stability and the Gibbs phase rule. A
simple separation based on a vapor-liquid phase
diagram. The lever rule. Equilibrium
ratios (K-values, distribution coefficients,
etc.). The activity, and activity
coefficients. Measures of separations.
In this lecture well show How to apply
thermodynamics to flowing systems  Energy and
entropy balances in flowing systems
Availability and lost work Gibbs Phase Rule
for flowing systems and system specification
How data of mixture compositions are sometimes
tabulated graphically. Graphical
determination of vapor-liquid equilibrium of
hydrocarbon systems
2
Separation System Flows
We can use the tools of entropy, energy,
availability and mass balances to analyze any
separations system
Heat in and heat out
Qout
Qin
T0
...
...
Streams in
n, zi, T, P, h, s, b, v
Streams out
...
n, zi, T, P, h, s, b, v
...
For each stream n molar flow ratezi
composition variables T temperature P
pressure h enthalpy s entropy b
availability v specific volume
Work in and work out
(ws)in
(ws)out
3
Balances and Availability
Energy balance
Entropy balance
Availability balance Combine entropy balance,
and energy balance with the definitions for lost
work and availability.
Availability balance
Availability
Availability the energy available in the system
for conversion to shaft work.
Lost work
The minimum work for a separation isthe change
in availability carried by the feed and product
streams.
Minimum work
4
Gibbs Phase Rule
The number of thermodynamic conditions that can
be specified for a system with C componentswith
? phases in equilibrium. Variables Equations
P T ? C ? (composition of each
phase) C(?-1) C ?2 C(?-1) ?
K-values are equationsdetermined by
thermodynamic equilibrium
Note that the Gibbs phase rule does not deal
with flow variables or extensive variables.
To extend the Gibbs Phase Rule to flow systems
requires Adding Feed stream and extensive
variables Adding Independent equations relating
variables
5
Gibbs Phase Rule
The number of thermodynamic conditions that can
be specified for a system with 3 componentswith
3 phases in equilibrium. Variables Equations
T, P, X1, X2, X3Y1, Y2, Y3Z1, Z2, Z3
Equilibrium Conditions
Mole Fractions
6
Gibbs Phase Rule for a Flowing System
The number of thermodynamic conditions that can
be specified for a system with 3 componentswith
3 phases in equilibrium. Variables Equations
T, P, X1, X2, X3 ... Y1, Y2, Y3 ...Z1, Z2, Z3
...


?
?
Original
C
C
C
F, Zi , TF , PF V, L, ... Q
Additional

?
1
Original
Additional
For a flow system
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Determination of Unspecified Variables
F, T, P, TF , PF , Zi
If
variables are used to specify
Then remaining
variables must be found from
A) mole fraction summations B) K-Value
relationships C) Mass balances D) Energy balance
8
DePriester
In order to carry out an analysis of a separation
which uses differences in K-values between two
phases to cause a separation, we need a source
ofK-values.
A lot of equilibrium (K-Value) information for
binary systems is often contained in vapor-liquid
phase diagrams.
For hydrocarbon systems, interactions between
molecules are very similar,and consequently, the
K-Values will not be a function of composition.
K-Valuesat different pressures and temperatures
for hydrocarbons can thus be graphedfor
multicomponent systems. One type of these
graphs is called DePriester charts. Another
type showing vapor-liquid equilibria for a
multicomponent hydrocarbon system is shown in
Figure 2.8 of the text.
9
DePriester Charts Low T
10
DePriester Charts High T
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DePriester Charts High T
12
DePriester
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Summary
In this lecture we discussed  How to carry out
energy and entropy balances in flowing systems
Availability and lost work Gibbs Phase Rule for
flowing systems and system specification
How to use DePriester charts to determine
k-values for hydrocarbon vapor-liquid systems
Next Lecture will focus on Isothermal Flash
calculations Derivation of the Rachford-Rice
Equations Use of Newtons Iterative method to
solve the RR equations An example using the RR
procedure with Newtons method and DePriester
charts to describe equilibrium