P,T-Flash Calculations

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# P,T-Flash Calculations - PowerPoint PPT Presentation

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
• 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

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
• 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
• 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)
• T=90C, P= 760 mmHg, z1= 0.75?

Lecture 3

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: 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
• 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 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
• 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 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
• (D)
• Step 5.
• Substitute Raoult’s Law (A) into (D) and rearrange:
• (E)

Lecture 3

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
• 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