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**Goal 1: Design a flash drum**

How big should the drum be? What height should the nozzle be? What T and P should the drum be? What T and P should the feed be?

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**Vapor-liquid equilibrium (VLE)**

Consider a binary (i.e., 2-component) system with 2-phases: What do we know? yA + yB = 1 xA + xB = 1 yA ≠ xA Tvap, Pvap yA, yB Tliq, Pliq xA, xB At equilibrium: Tvap = Tliq Pvap = Pliq Gibbs’ Phase Rule: degrees of freedom = # components (C) - # phases (P) + 2 For a binary, 2-phase system: 2 – = 2 We can specify only 2 intensive variables (all others are fixed, by VLE)

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Specify P and T 2 graphs in one: T vs. xA T vs. yA superheated vapor subcooled liquid 2-phase region saturated vapor line saturated liquid line TA xA • • yA • A subcooled liquid feed of composition zA, heated to temperature TA, will separate spontaneously into 2 phases, of composition xA and yA Lecture 2 ends in the middle of this slide zA • Figure 2-3 Temperature-composition diagram for ethanol-water From Separation Process Engineering, Third Edition by Phillip C. Wankat (ISBN: ) Copyright © 2012 Pearson Education, Inc. All rights reserved.

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**Boiling point, dew point, bubble point**

Pure liquids have a boiling point; mixtures have a boiling range, delimited by their bubble point and dew point. 1. Consider a sub-cooled binary liquid that is 40 mol% ethanol. What is its bubble point? What is the composition of the first bubble? dew point 2. Consider a superheated binary vapor that is 40 mol% ethanol. What is its dew point? What is the composition of the first drop? boiling range bubble point xE,initial yE,initial 3. What is the boiling range of this mixture? Figure 2-3 Temperature-composition diagram for ethanol-water From Separation Process Engineering, Third Edition by Phillip C. Wankat (ISBN: ) Copyright © 2012 Pearson Education, Inc. All rights reserved.

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Useful definitions Boiling/bubble point Tbp: temperature at which the average liquid molecule has just enough kinetic energy to escape from the surface of the liquid into the gas phase Recall that kinetic energy follows a Boltzmann distribution, so molecules with higher than average kinetic energy can still escape from the surface at T < Tbp, by evaporation Saturated liquid: a liquid at its boiling/bubble point Dew point Tdp: temperature at which the average vapor molecule has just enough kinetic energy to condense Saturated vapor: a vapor at its dew point Vapor pressure: pressure at which the liquid and vapor phase are in equilibrium at a given temperature Azeotrope: a constant-boiling mixture, i.e., a mixture that behaves like a single component

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**How much liquid and vapor will the flash drum produce?**

F, L and V are extensive variables mass balance method total mass balance (TMB): F = L + V component mass balance (CMB): F zA = L xA + V yA rearrange: OR inverse lever-arm method • L M V isotherm For a given F, we can now compute L and V.

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**Specify P and one composition (xA)**

y=x VLE line always lies above y=x line if plotted for the more volatile component For a binary system at constant P, if one composition (xA or yA) is chosen, all others are fixed: T incr. K = yE/xE volatility = K = K(T, P, zi) ≈ K(T) VLE line VLE: K = yA/xA mole balance: xA + xB = 1 yA + yB = 1 azeotrope: K = 1.0 how can we “break” an azeotrope? Figure 2-2 McCabe-Thiele diagram for ethanol-water From Separation Process Engineering, Third Edition by Phillip C. Wankat (ISBN: ) Copyright © 2012 Pearson Education, Inc. All rights reserved.

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**Specify two of (P, T, volatility)**

pure compound T´ P´ K > 1 Consider a pure compound: • for a given P, find Tbp (i.e., K = 1) • for a given T, find P0 (i.e., K = 1) • for a given P, T, find K K > 1 prefers vapor phase K < 1 prefers liquid phase Tbp P0 pressure total K = 1.0 temperature T* P* K < 1 DePriester Chart Don’t extrapolate beyond the range of the chart.

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**Figure 2-11 Modified DePriester chart (in S. I**

Figure Modified DePriester chart (in S.I. units) at low temperatures (D. B. Dadyburjor, Chem. Eng. Prog.,85, April 1978; copyright 1978, AIChE; reproduced by permission of the American Institute of Chemical Engineers) volatility At 2000 kPa, what is the boiling point of ethane? At 15 °C, what is the saturated vapor pressure of isobutane? At 0 °C and 500 kPa, what is the volatility of n-hexane? At 2000 kPa, what is the boiling point of ethane? -6 °C At 15 °C, what is the saturated vapor pressure of isobutane? 250 kPa At 0 °C and 500 kPa, what is the volatility of n-hexane? 0.006 From Separation Process Engineering, Third Edition by Phillip C. Wankat (ISBN: ) Copyright © 2012 Pearson Education, Inc. All rights reserved.

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**Using data from vapor pressure tables**

Raoult’s Law ideal liquid: non-ideal liquid: activity coefficient Dalton’s Law ideal gas: non-ideal gas: fugacity coefficient

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**Bubble point calculation for multi-component mixtures**

Trial-and-error method Given the composition of a subcooled liquid and PTOTAL, find Tbp and (yi)bp VLE: mole balance: Algorithm: Pick a temperature T and find the corresponding Ki(T) values for each component Calculate the yi value for each Ki(T) Check to see if Syi = 1 If not, pick a new temperature, repeat How to pick a temperature? How to pick the next temperature?

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**To achieve rapid convergence:**

Initial guess: (weighted average of boiling points of pure components) Next guess: pick a reference component (A) find Tnext using DePriester Chart

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**Dew point calculation for multi-component mixtures**

Trial-and-error method Given the composition of a superheated vapor and PTOTAL, find Tdp and (xi)dp VLE: mole balance: Algorithm: Pick a temperature T and find the corresponding Ki(T) values for each component Calculate the xi value for each Ki(T) Check to see if Sxi = 1 If not, pick a new temperature and repeat Lecture 3 ends here

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**Relative volatility volatility relative volatility**

strong function of temperature volatility not a strong function of temperature; often assumed independent relative volatility for a binary system, substitute and rearrange:

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**Bubble point calculation using relative volatility**

definition of relative volatility: solve for yi: sum: solve for Kref: Algorithm: given a solution composition (xi values), find relative volatilities (ai values), then 1. guess Tinitial 2. calculate Kref 3. find T = Tbp corresponding to Kref

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**Ex.: Finding Tbp using relative volatilities**

Find the bubble point of a mixture of n-pentane (xP = 0.3), n-hexane (xX = 0.3) and n-heptane (xH = 0.4), at 1 atm total pressure. Find the composition of the first vapor bubble. Designate n-pentane as the reference. At 71 °C, KP = 2.8. Find Tbp corresponding to KP = 2.0 (read from DePriester Chart): Tbp = 58 °C Check:

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Chapter 14: Phase Equilibria Applications Part II.

Chapter 14: Phase Equilibria Applications Part II.

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