P,T-Flash Calculations

1. 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

2. 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

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

4. 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

5. 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

6. 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

7. 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

8. 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

9. 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

10. 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

11. 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

12. 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