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VLE Calculations

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VLE Calculations Purpose of this lecture: To demonstrate how Raoult s law can be used in the prediction of the VLE behaviour of ideal mixtures – PowerPoint PPT presentation

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Title: VLE Calculations


1
VLE 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)

2
Phase 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

3
Phase 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.

4
Correlation 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

5
Phase 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.

6
Phase Rule in VLE Binary Systems (Pxy diagrams)
  • Example Acetonitrile (1) / Nitromethane (2)
    system

7
Phase 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.

8
VLE 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)

9
Dew 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

10
VLE 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

13
BUBL 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

14
DEW 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

15
P, 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.,

16
Example
  • 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
17
Construction 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
18
Example (a) Generation of Pxy Data
19
Example (a) Construction of a Pxy Plot
20
Construction 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
21
Example (b) Generation of Txy Data
22
Example (b) Construction of a Txy Plot
23
VLE 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
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