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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: T vap, P vap y A, y B T liq, P liq x A, x B What do we know? y A + y B = 1 x A + x B = 1 y A ≠ x A At equilibrium:T vap = T liq P vap = P liq 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 From Separation Process Engineering, Third Edition by Phillip C. Wankat (ISBN: ) Copyright © 2012 Pearson Education, Inc. All rights reserved. Figure 2-3 Temperature-composition diagram for ethanol-water superheated vapor subcooled liquid 2-phase region saturated vapor line saturated liquid line 2 graphs in one: T vs. x A T vs. y A A subcooled liquid feed of composition z A, heated to temperature T A, will separate spontaneously into 2 phases, of composition x A and y A TATA xAxA yAyA zAzA

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From Separation Process Engineering, Third Edition by Phillip C. Wankat (ISBN: ) Copyright © 2012 Pearson Education, Inc. All rights reserved. Figure 2-3 Temperature-composition diagram for ethanol-water bubble point dew point x E,initial y E,initial boiling range 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? 2. Consider a superheated binary vapor that is 40 mol% ethanol. What is its dew point? What is the composition of the first drop? 3. What is the boiling range of this mixture? 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.

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Useful definitions Boiling/bubble point T bp : 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 < T bp, by evaporation Saturated liquid: a liquid at its boiling/bubble point Dew point T dp : 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? mass balance method total mass balance (TMB): F = L + V component mass balance (CMB): F z A = L x A + V y A rearrange: OR inverse lever-arm method F, L and V are extensive variables L M V isotherm For a given F, we can now compute L and V.

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

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Specify two of (P, T, volatility) total pressure temperature K = 1.0 DePriester Chart for a given P, find T bp (i.e., K = 1) for a given T, find P 0 (i.e., K = 1) for a given P, T, find K K > 1 prefers vapor phase K < 1 prefers liquid phase Don’t extrapolate beyond the range of the chart. T bp P0P0 pure compound Consider a pure compound: T´ P´ K > 1 T* P* K < 1

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Figure 2-11 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) From Separation Process Engineering, Third Edition by Phillip C. Wankat (ISBN: ) Copyright © 2012 Pearson Education, Inc. All rights reserved. At 2000 kPa, what is the boiling point of ethane? volatility At 15 °C, what is the saturated vapor pressure of isobutane? At 0 °C and 500 kPa, what is the volatility of n-hexane?

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Using data from vapor pressure tables Raoult’s Law ideal liquid: non-ideal liquid: Dalton’s Law ideal gas: non-ideal gas: activity coefficient fugacity coefficient vapor pressure

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Bubble point calculation for multi-component mixtures Trial-and-error method Given the composition of a subcooled liquid and P TOTAL, find T bp and (y i ) bp VLE: mole balance: Algorithm: 1.Pick a temperature T and find the corresponding K i (T) values for each component 2.Calculate the y i value for each K i (T) 3.Check to see if y i = 1 4.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 T next 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 P TOTAL, find T dp and (x i ) dp VLE: mole balance: Algorithm: 1.Pick a temperature T and find the corresponding K i (T) values for each component 2.Calculate the x i value for each K i (T) 3.Check to see if x i = 1 4.If not, pick a new temperature and repeat

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Relative volatility volatility strong function of temperature 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 y i : solve for K ref : sum: Algorithm: given a solution composition (x i values), find relative volatilities ( i values), then 1.guess T initial 2.calculate K ref 3. find T = T bp corresponding to K ref

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Ex.: Finding T bp using relative volatilities Find the bubble point of a mixture of n-pentane (x P = 0.3), n-hexane (x X = 0.3) and n-heptane (x H = 0.4), at 1 atm total pressure. Find the composition of the first vapor bubble. Designate n-pentane as the reference. At 71 °C, K P = 2.8. Find T bp corresponding to K P = 2.0 (read from DePriester Chart): T bp = 58 °C Check:

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