CHEE 311 Lecture 3 1

P,T-Flash Calculations

Purpose of this lecture:To illustrate how P,T-Flash calculations can be performed either graphically or numerically

HighlightsThe lever rule Step-by-step procedure for numerical P,T flash calculations

Reading assignment: Ch. 14, pp. 551-554 (7th edition), orCh. 14, pp. 532-535 (6th edition)

CHEE 311 Lecture 3 2

P,T Flash Calculations

If a stream consists of three components with widely differing volatilities, substantial separation of one component 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?

Feedz1z2z3=1-z1-z2Tf, Pf

P,T

Vapoury1y2y3=1-y1-y2

Liquidx1x2x3=1-x1-x2

CHEE 311 Lecture 3 3

P-T Flash Calculations from a Phase Diagram

For some binary systems, you can often find a phase diagram in the range of conditions needed.

For example, a Pxy diagram for the furan(1)/CCl4(2) system at 30°C is illustrated to the right.

Given T=30°C, P= 300 mmHg, z1= 0.5

Determinex1, x2, y1, y2 and the fraction of thesystem that exists as a vapour (V)

How can we do it?What equations can we use?What is the lever rule and how doesIt work?

CHEE 311 Lecture 3 4

Flash Calculations from a Phase Diagram

Txy diagrams can also be used.

Consider the ethanol(1)/toluene(2) system at P = 1atm.

Given T=90°C, P= 760 mmHg, z1= 0.25

Determinex1, x2, y1, y2 and the fraction of thesystem that exists as a liquid (L)

How about:T=90°C, P= 760 mmHg, z1= 0.75?

What do we do for feeds with more than two components?

CHEE 311 Lecture 3 5

Recall Gibb’s Phase Rule

F = 2 - π + N

• What does it mean?• What is it for?• What can we do if we care about intensive

variables and extensive variables?

CHEE 311 Lecture 3 6

Duhem’s Theorem: SVNA10.2

For any closed system, formed initially from given masses of prescribed chemical species, the equilibrium state is completelydetermined when any two independent variables are fixed.

What does this mean?What is it for?What does it have to do with flash calculations? Are flash drums open or closed systems?

We specify T and P when we do flash calculations.

If our feed mixture contains 26 components, do we need to specify more variables than if the feed contains only 3 components?

If we specify T, can we also select the concentration of component 1 in the gas and the mass of the gas produced?

CHEE 311 Lecture 3 7

Duhem’s Theorem: SVNA10.2

For any closed system, formed initially from given masses of prescribed chemical species, the equilibrium state is completely determined when any two independent variables are fixed.

Why is Duhem’s Theorem true?

Variables required to specify the intensive and extensive state:T,PMole fractionsMass of each phase

Independent equations to satisfy:Material balances on chemical speciesEquilibrium equations for chemical species

# of variables - # of equations = 2

CHEE 311 Lecture 3 8

Flash Calculations: Checking for a two-phase system

Specifying T,P and zi, gives sufficient information for a flash calculation.How can we make sure that two phases exist at this P,T and overall composition?

At a given T, the maximum pressure for which two phases exist is the BUBL P

Why?

At a given T, the minimum pressure for which two phases exist is the DEW P

Why?

We can perform a BUBL P calculation using xi = zi and a DEW P using yi = zi and check if the specified P is in this range.

What if we don’t have two phases? What would happen if there is only one phase and we do the flash calculation without checking?

CHEE 311 Lecture 3 9

Flash Calculations using 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 phasediagram.

Step 1.Determine Pi

sat for each component at T using Antoine eqn.

Step 2.Check for two phases by calculating DEWP and BUBLP using the composition, zi.

Step 3. Determine partition coefficients Ki from Raoult’s law

CHEE 311 Lecture 3 10

Flash Calculations from Raoult’s Law

Step 4.Choose a basis of 1 mole of feed and write mass balances:

Overall: L+V = 1

Components: i=1,2,…,n

Step 5. Do some algebra to get:

VyLx)1(z iii +=

)1K(V1Kzy

i

iii −+=

CHEE 311 Lecture 3 11

Flash Calculations from Raoult’s Law

Step 6:Substitute into:

to get:

14.18

where,zi = overall mole fraction of component iV = vapour phase fractionKi = partition coefficient for component i

Step 7:

Solve for V, then yi and xi values. How do we solve for V?

1yni

1ii =∑

=

=

1)1K(V1

Kzni

1i i

ii =−+

∑=

=