#### Transcript 120712ChE128-2-VLEReview

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? Vapor-liquid equilibrium (VLE) Consider a binary (i.e., 2-component) system with 2-phases: What do we know? Tvap, Pvap yA , yB yA + yB = 1 xA + xB = 1 yA ≠ xA 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+2=2 We can specify only 2 intensive variables (all others are fixed, by VLE) Specify P and T 2 graphs in one: T vs. xA T vs. yA superheated vapor 2-phase region saturated liquid line TA • saturated vapor line •• zA • subcooled liquid yA xA A subcooled liquid feed of composition zA, heated to temperature TA, will separate spontaneously into 2 phases, of composition xA and yA Figure 2-3 Temperature-composition diagram for ethanol-water From Separation Process Engineering, Third Edition by Phillip C. Wankat (ISBN: 0131382276) Copyright © 2012 Pearson Education, Inc. All rights reserved. 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 boiling range bubble point xE,initial 2. Consider a superheated binary vapor that is 40 mol% ethanol. What is its dew point? What is the composition of the first drop? 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: 0131382276) Copyright © 2012 Pearson Education, Inc. All rights reserved. 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 How much liquid and vapor will the flash drum produce? F, L and V are extensive variables mass balance method OR total mass balance (TMB): F=L+V component mass balance (CMB): F zA = L x A + V y A rearrange: L = y A - zA V zA - x A inverse lever-arm method • L isotherm • M L MV = V LM For a given F, we can now compute L and V. • V Specify P and one composition (xA) For a binary system at constant P, if one composition (xA or yA) is chosen, all others are fixed: VLE: K = yA/xA mole balance: xA + xB = 1 yA + yB = 1 VLE line always lies above y=x line if plotted for the more volatile component K = yE/xE volatility = K = K(T, P, zi) ≈ K(T) 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: 0131382276) Copyright © 2012 Pearson Education, Inc. All rights reserved. Specify two of (P, T, volatility) pure compound P0 P* K>1 K = 1.0 K<1 DePriester Chart Consider a pure compound: Tbp • 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 temperature total pressure P´ T´ T* Don’t extrapolate beyond the range of the chart. 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) 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? From Separation Process Engineering, Third Edition by Phillip C. Wankat (ISBN: 0131382276) Copyright © 2012 Pearson Education, Inc. All rights reserved. Using data from vapor pressure tables Raoult’s Law ideal liquid: non-ideal liquid: vapor pressure PA = x APA0 (T) PA = g A x APA0 (T) activity coefficient Dalton’s Law ideal gas: non-ideal gas: yA = PA PTOTAL PA yA = f APTOTAL fugacity coefficient yA PA0 (T) PA0 (T) KA = = @ x A f APTOTAL PTOTAL 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: y i = Ki xi mole balance: åy i = 1.0 Algorithm: 1. Pick a temperature T and find the corresponding Ki(T) values for each component 2. Calculate the yi value for each Ki(T) 3. Check to see if Syi = 1 4. If not, pick a new temperature, repeat i How to pick a temperature? How to pick the next temperature? To achieve rapid convergence: T = å ziTi (K i = 1) Initial guess: i (weighted average of boiling points of pure components) Next guess: pick a reference component (A) K A (Tnext ) = K A (Tprev ) å(y ) i prev i find Tnext using DePriester Chart 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: yi xi = Ki Algorithm: 1. Pick a temperature T and find the corresponding Ki(T) values for each component 2. Calculate the xi value for each Ki(T) 3. Check to see if Sxi = 1 4. If not, pick a new temperature and repeat mole balance: åx i = 1.0 i K A (Tnext ) = K A (Tprev ) å(x ) i prev Relative volatility KA = volatility yA = K A (T ) xA strong function of temperature yA a AB relative volatility K xA = A= KB yB xB not a strong function of temperature; often assumed independent for a binary system, substitute and rearrange: y B = 1- y A xB = 1- x A yA = a AB x A 1+ (a AB -1)x A Bubble point calculation using relative volatility yi definition of relative volatility: Ki xi ai = = K ref K ref solve for yi: y i = ai xi K ref sum: åy i solve for Kref: i ( ) = 1.0 = å ai xi K ref K ref = i 1 åa x i i i 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 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. Tinitial = å xiTi (K i = 1) = 0.3(36) + 0.3(68) + 0.4(99) = 71°C i Designate n-pentane as the reference. At 71 °C, KP = 2.8. a XP K 1.2 = X = = 0.43 K P 2.8 aHP = K H 0.45 = = 0.16 KP 2.8 1 1 K P (Tbp ) = = = 2.0 åai xi 0.3(1) + 0.3(0.43) + 0.4(0.16) i Find Tbp corresponding to KP = 2.0 (read from DePriester Chart): y i = ai xi K ref Tbp = 58 °C y P = 0.3(1)(2.0) = 0.60 y X = 0.3(0.43)(2.0) = 0.26 yH = 0.4(0.16)(2.0) = 0.14 Check: åy i i = 1.0