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P,T-Flash Calculations. Purpose of this lecture : To illustrate how P,T-Flash calculations can be performed either graphically or numerically Highlights P, T -Flash calculations from VLE diagrams The “lever rule” and its use in calculating extensive variables (V, L)

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p t flash calculations
P,T-Flash Calculations
  • Purpose of this lecture:
  • To illustrate how P,T-Flash calculations can be performed either graphically or numerically
  • Highlights
  • P, T -Flash calculations from VLE diagrams
  • The “lever rule” and its use in calculating extensive variables (V, L)
  • Step-by-step procedure for numerical P,T-Flash calculations
  • Reading assignment: Ch. 14, pp. 551-554 (7th edition), or
  • Ch. 14, pp. 532-535 (6th edition)

Lecture 3

4 p t flash calculations

Vapour

y1

y2

y3=1-y1-y2

Feed

z1

z2

z3=1-z1-z2

Tf, Pf

P,T

Liquid

x1

x2

x3=1-x1-x2

4. P,T-Flash Calculations
  • If a stream consists of three components with widely differing volatility, substantial separation can be achieved using a simple flash unit.
  • Questions often posed:
  • Given P, T and zi, what are the equilibrium phase compositions?
  • Given P, T and the overall composition of the system, how much of each phase will we collect?

Lecture 3

p t flash calculations from a phase diagram
P-T Flash Calculations from a Phase Diagram
  • For common binary systems, you can often find a phase diagram in the range of conditions needed.
  • For example, a Pxy diagram for the
  • furan/CCl4 system at 30C is
  • illustrated to the right.
  • Given
  • T=30C, P= 300 mmHg, z1= 0.5
  • Determine
  • x1, x2, y1, y2 and the fraction of the
  • system that exists as a vapour (V)

Lecture 3

flash calculations from a phase diagram
Flash Calculations from a Phase Diagram
  • Similarly, a Txy diagram can be used if available.
  • Consider the ethanol/toluene system illustrated here at P = 1atm.
  • Given
  • T=90C, P= 760 mmHg, z1= 0.25
  • Determine
  • x1, x2, y1, y2 and the fraction of the
  • system that exists as a liquid (L)
  • How about:
  • T=90C, P= 760 mmHg, z1= 0.75?

Lecture 3

phase rule for intensive variables
Phase Rule for Intensive Variables
  • 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
    • the masses of the phases are not phase-rule variables, because they do not affect the intensive state of the system
    • 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

Lecture 3

duhem s theorem extensive properties svna10 2
Duhem’s Theorem: Extensive Properties SVNA10.2
  • Duhem’s Theorem: For any closed system of known composition, the equilibrium state is determined when any two independent variables are fixed.
  • If the system is closed and formed from specified amounts of each species, then we can write:
  • Equilibrium equations for chemical potentials (-1)N
  • Material balance for each species N
    • We have a total of N equations
  • The system is characterized by :
  • T, P and (N-1) mole fractions for each phase 2 + (N-1)
  • Masses of each phase 
    • Requires knowledge of 2 + N variables
  • Therefore, to completely determine the equilibrium state we need :
  • [2 + N] - [N] = 2 variables
  • This is the appropriate “rule” for flash calculation purposes where the overall system composition is specified

Lecture 3

ensuring you have a two phase system
Ensuring you have a two-phase system
  • Duhem’s theorem tells us that if we specify T,P and zi, then we have sufficient information to solve a flash calculation.
  • However, before proceeding with a flash calc’n, we must be sure that two phases exist at this P,T and the given overall composition: z1, z2, z3
    • At a given T, the maximum pressure for which two phases exist is the BUBL P, for which V = 0
    • At a given T, the minimum pressure for which two phases exist is the DEW P, for which L = 0
  • To ensure that two phases exist at this P, T, zi:
    • Perform a BUBL P using xi = zi
    • Perform a DEW P using yi = zi

Lecture 3

ensuring you have a two phase system1
Ensuring you have a two-phase system
  • If we revisit our furan /CCl4 system at 30C, we can illustrate this point.
  • Given
  • T=30C, P= 300 mmHg, z1= 0.25
  • Is a flash calculation possible?
  • BUBLP, x1 = z1 = 0.25
  • DEWP, y1 = z1 = 0.25
  • Given
  • T=30C, P= 300 mmHg, z1= 0.75
  • Is a flash calculation possible?
  • BUBLP, x1 = z1 = 0.75
  • DEWP, y1 = z1 = 0.75

Lecture 3

flash calculations from raoult s law
Flash Calculations from Raoult’s Law
  • Given P,T and zi, calculate the compositions of the vapour and liquid phases and the phase fractions without the use of a phase diagram.
  • Step 1.
  • Determine Pisat for each component at T (Antoine’s eq’n, handbook)
  • Step 2.
  • Ensure that, given the specifications, you have two phases by calculating DEWP and BUBLP at the composition, zi.
  • Step 3.
  • Write Raoult’s Law for each component:
  • or
  • (A)
  • where Ki = Pisat/P is the partition coefficient for component i.

Lecture 3

flash calculations from raoult s law1
Flash Calculations from Raoult’s Law
  • Step 4.
  • Write overall and component material balances on a 1 mole basis
  • Overall:
  • (B)
  • where L= liquid phase fraction, V= vapour phase fraction.
  • Component:
  • i=1,2,…,n (C)
  • (B) into (C) gives
  • which leads to:
  • (D)
  • Step 5.
  • Substitute Raoult’s Law (A) into (D) and rearrange:
  • (E)

Lecture 3

flash calculations from raoult s law2
Flash Calculations from Raoult’s Law
  • Step 6:
  • Overall material balance on the vapour phase:
  • into which (E) is substituted to give the general flash equation:
  • 14.18
  • where,
  • zi = overall mole fraction of component i
  • V = vapour phase fraction
  • Ki = partition coefficient for component i
  • Step 7:
  • Solution procedures vary, but the simplest is direct trial and error variation of V to satisfy equation 14.18.
    • Calculate yi’s using equation (E) and xi’s using equation (A)

Lecture 3

vle calculations summary
VLE Calculations –Summary
  • Here is a summary of what we need to know (Lectures 8 & 9):
  • How to use the Phase Rule (F=2-p+N)
  • How to read VLE charts
  • - Identify bubble point and dew point lines
  • - Read sat. pressures or temperatures from the chart
  • - Determine the state and composition of a mixture
  • How to perform Bubble Point, Dew Point, and P,T-Flash calculations
  • - Apply Raoult’s law
  • - Apply Antoine’s equation
  • How to use the Lever Rule (graphically or numerically)
  • How to construct VLE (Pxy or Txy ) charts for ideal mixtures

Lecture 3