P,T-Flash Calculations

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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)
• 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)

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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?

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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
• T30?C, P 300 mmHg, z1 0.5
• Determine
• x1, x2, y1, y2 and the fraction of the
• system that exists as a vapour (V)

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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
• T90?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
• T90?C, P 760 mmHg, z1 0.75?

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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

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Duhems Theorem Extensive Properties SVNA10.2

• Duhems 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

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Ensuring you have a two-phase system

• Duhems 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 calcn,
  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

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Ensuring you have a two-phase system

• If we revisit our furan /CCl4 system at 30?C, we
  can illustrate this point.
• Given
• T30?C, P 300 mmHg, z1 0.25
• Is a flash calculation possible?
• BUBLP, x1 z1 0.25
• DEWP, y1 z1 0.25
• Given
• T30?C, P 300 mmHg, z1 0.75
• Is a flash calculation possible?
• BUBLP, x1 z1 0.75
• DEWP, y1 z1 0.75

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Flash Calculations from Raoults 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
  (Antoines eqn, handbook)
• Step 2.
• Ensure that, given the specifications, you have
  two phases by calculating DEWP and BUBLP at the
  composition, zi.
• Step 3.
• Write Raoults Law for each component
• or
• (A)
• where Ki Pisat/P is the partition coefficient
  for component i.

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Flash Calculations from Raoults 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
• i1,2,,n (C)
• (B) into (C) gives
• which leads to
• (D)
• Step 5.
• Substitute Raoults Law (A) into (D) and
  rearrange
• (E)

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Flash Calculations from Raoults 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 yis using equation (E) and xis using
  equation (A)

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VLE Calculations Summary

• Here is a summary of what we need to know
  (Lectures 8 9)
• How to use the Phase Rule (F2-pN)
• 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 Raoults law
• - Apply Antoines equation
• How to use the Lever Rule (graphically or
  numerically)
• How to construct VLE (Pxy or Txy ) charts for
  ideal mixtures