Title: VLE Calculations
1VLE Calculations
- Purpose of this lecture
- To demonstrate how Raoults law can be used in
the prediction of the VLE behaviour of ideal
mixtures - Highlights
- Phase rules gives the number of variables we need
in order to determine the intensive state of a
system at equilibrium - Saturation pressures can be calculated by means
of the Antoine Eqn. - Raoults law can be used for constructing Pxy,
Txy diagrams and performing dew point and bubble
point calculations - Reading assignment Section 10.4, pp. 347-357
(7th edition), or - Section 10.4,
pp. 338-348 (6th edition)
2Phase Rule for Intensive Variables
SVNA-10.2
- For a system of ? phases and N species, the
degree of freedom is - F 2 - ? N
- variables that must be specified to fix the
intensive state of the system at equilibrium - Phase Rule Variables
- The system is characterized by T, P and (N-1)
mole fractions for each phase - Requires knowledge of 2 (N-1)? variables
- Phase Rule Equations
- At equilibrium ?i? ?i ? ?i ? for all
N species - These relations provide (?-1)N equations
- The difference is F 2 (N-1)? - (?-1)N
- 2- ? N
3Phase Rule in VLE Single Component Systems
- For a two phase (p2) system of a single
component (N1) - F 2- ? N
- F 2- 2 1 1
- Therefore, for the single component system,
specifying either T or P fixes all intensive
variables.
4Correlation of Vapour Pressure Data
- Pisat, or the vapour pressure of component i, is
commonly represented by Antoine Equation
(Appendix B, Table B.2, SVNA 7th ed.) - For acetonitrile (Component 1)
- For nitromethane (Component 2)
- These functions are the only component properties
needed to characterize ideal VLE behaviour
5Phase Rule in VLE Ideal Binary Mixtures
- (General Case)
- For a two phase (?2), binary system (N2)
- F 2- 2 2 2
- Therefore, for the binary case, two intensive
variables must be specified to fix the state of
the system.
6Phase Rule in VLE Binary Systems (Pxy diagrams)
- Example Acetonitrile (1) / Nitromethane (2)
system
7Phase Rule in VLE Binary Systems (Txy diagrams)
- Alternatively, we can specify a system pressure
and examine the VLE behaviour as a function of
temperature and composition.
8VLE Calculations using Raoults Law
- Raoults Law for ideal phase behaviour relates
the composition of liquid and vapour phases at
equilibrium through the component vapour
pressure, Pisat. - Given the appropriate information, we can apply
Raoults law to the solution of 5 types of
problems - Dew Point Pressure or Temperature
- Bubble Point Pressure or Temperature
- P,T Flash calculation of equilibrium composition
(P, T, zi given)
9Dew and Bubble Point Calculations
- Dew Point Pressure
- Given a vapour composition at a specified
temperature, find the composition of the liquid
in equilibrium - Given T, y1, y2,... yn find P, x1, x2, ... xn
- Dew Point Temperature
- Given a vapour composition at a specified
pressure, find the composition of the liquid in
equilibrium - Given P, y1, y2,... yn find T, x1, x2, ... xn
- Bubble Point Pressure
- Given a liquid composition at a specified
temperature, find the composition of the vapour
in equilibrium - Given T, x1, x2, ... xn find P, y1, y2,... yn
- Bubble Point Temperature
- Given a vapour composition at a specified
pressure, find the composition of the liquid in
equilibrium - Given P, x1, x2, ... xn find T, y1, y2,... yn
10VLE Calculations - Introduction
- For now, we are going to employ these
calculations only for - identifying the state and composition of binary
and ideal mixtures - As we are going to see later in the course, the
aforementioned - VLE calculations are also applicable to
non-ideal or/and - multi-component mixtures
- The calculations revolve around the use of 2 key
equations - 1) Raoults law for ideal phase behaviour
- 2) Antoines Equation
(1)
(2)
11 BUBL P Calculation (T, x1 known)
- - Calculate and from Antoines
Equation - For the vapour-phase composition (bubble) we can
write - y1y21
(3) - Substitute y1 and y2 in Eqn (3) by using
Raoults law -
(4) - - Re-arrange and solve Eqn. (4) for P
- Now you can obtain y1 from Eqn (1)
- Finally, y2 1-y1
12 DEW P Calculation (T, y1 known)
- - Calculate and from Antoines
Equation - For the liquid-phase composition (dew) we can
write - x1x21
(5) - Substitute x1 and x2 in Eqn (5) by using
Raoults law -
(6) - - Re-arrange and solve Eqn. (6) for P
- Now you can obtain x1 from Eqn (1)
- Finally, x2 1-x1
13BUBL T Calculation (P, x1 known)
- Since T is an unknown, the saturation pressures
for the - mixture components cannot be calculated
directly. Therefore, - calculation of T, y1 requires an iterative
approach, as follows - Re-arrange Antoines equation so that the
saturation temperatures - of the components at pressure P can be
calculated -
(7) - Select a temperature T so that
- Calculate
- Solve Eqn. (4) for pressure P
- If , then PP If not, try
another T-value - Calculate y1 from Raoults law
14DEW T Calculation (P, y1 known)
- Same as before, calculation of T, x1 requires an
iterative approach - Re-arrange Antoines equation so that the
saturation temperatures - of the components at pressure P can be
calculated from Eqn. (7) - - Select a temperature T so that
- Calculate
from Antoines Eqn. - Solve Eqn. (6) for pressure P
- If , then PP If not, try
another T-value - Calculate x1 from Raoults law
15P, T Flash Calculation
- - Calculate and from Antoines
Equation - Use Raoults law in the following form
-
(8) - - Re-arrange and solve Eqn. (8) for x1
- Now you can obtain y1 from Eqn (1), i.e.,
16Example
- Assuming Raoults Law to be valid, prepare
- a Pxy diagram for T90oC, and
- a Txy diagram for P90 kPa
- for a mixture of 1-chlorobutane (1)
/chlorobenzene (2) - Antoine Coefficients
A B C
1-chlorobutane (1) 13.9600 2826.26 224.10
Chlorobenzene (2) 13.9926 3295.12 217.55
17Construction of Pxy diagrams
- The construction of Pxy diagram requires
multiple P, T Flash - calculations, where T is held constant and P is
varied from P2sat to P1sat. - The results can be tabulated as shown below
P (kPa)
0.0 0.0
1.0 1.0
This type of calculations can also be performed
by keeping T constant and varying x1 or y1 from
0.0 to 1.0
18Example (a) Generation of Pxy Data
19Example (a) Construction of a Pxy Plot
20Construction of Txy diagrams
- The construction of Txy, diagram requires
multiple P, T, Flash - calculations, each one of which provides a set
of equilibrium y1, x1 - values for a given value of temperature (at
fixed P) - The results can be tabulated as shown below
T (oC)
0 0
1.0 1.0
This type of calculations can also be performed
by keeping P constant and varying x1 or y1 from
0.0 to 1.0
21Example (b) Generation of Txy Data
22Example (b) Construction of a Txy Plot
23VLE Calculations - Summary
- Why? To completely identify the thermodynamic
state - of a mixture at equilibrium (single phase, 2
phases..?) - How? Through the calculation of its P, T, and
composition - - The type of calculation that we need to
perform is subject - to the variables we are looking to evaluate
- - These calculations are classified as follows
Specified/Known Variables Unknown Variables Calculation
T, x P, y BUBL P
T, y P, x DEW P
P, x T, y BUBL T
P, y T, x DEW T
P, T x, y P, T Flash