(Heat and Mass Transfer) Lecture 22: Distillation and Mass Transfer CE 318: Transport Process 2 (Heat and Mass Transfer) Lecture 22: Distillation and Mass Transfer (UB CBE Spiral Initiatives) NSC 210 5/5/2015 1

3rd Midterm (To be update) Mid-terms 1st Midterm Average: 67/100 Median: 71 SID: 19 >=86: 10 67-86: 32 48–67: 17 < 48: 13 2nd Midterm Average: 61/100 Median: 62 SID: 20 >=81: 10 61-81: 26 41–61: 22 < 41: 14 3rd Midterm (To be update) Average: /100 Median: SID: >=81: 10 61-81: 26 41–61: 22 < 41: 14 2

Mid-terms Final exam: 8am – 11am; May 12 Please let me know if you have time conflict by today. 3

Overview of Transport Processes Momentum Heat Mass Profile Steady state Non-steady state 4

Overview of Mass Transfer Steady State Molecular Diffusion Fick’s Law for Molecular Diffusion DA: gas, liquid, solid, biological materials calculation: Counter-diffusion; Unimolecular diffusion; diffusion/reaction Convective Mass-Transfer Coefficient Unsteady State Diffusion Mass Transfer Equipment Multi-components Discontinuous interface 5

Convective Mass Transfer Coefficients Schmidt number Sherwood number 6

Forced Heat Convection: Semi-Empirical Method to Estimate h Prandtl Number Nusselt Number 7

Industrial Separation Processes 8 Distillation Gas sorption

Separation Process: Drying 9

Separation Process: Evaporation 10

Solvent Extraction Extraction 11

Lactic Acid Evaporation from water Spiral Problem: Lactic Acid Evaporation from water Consider a film of liquid water having instantaneous thickness lwater running down the right side of a vertical solid wall (see Figure below). The wall has thickness lwall = 0.2 cm and thermal conductivity kwall = 0.5 J/(cm·s·oC). Its left side is maintained at 100oC. To the right of the film of liquid water is air at a pressure of 500 mm Hg, a bulk temperature T = 25oC and a bulk water vapor mole fraction ywater = 0 (completely dry); “bulk” means far from the wall (“at infinity”). Heat transfer through the air is characterized by a heat transfer coefficient h = 0.003 J/(cm2·s·oC). Mass transfer of water vapor through the air is characterized by a mass transfer coefficient Fwater = 0.0001 mol/(cm2·s). lwall = 0.2 cm lwater solid wall   P = 500 mm Hg Air T = 25 °C in bulk ywater = 0 in bulk T = 100 °C Ti = ? 12

Spiral Problem 2016 13

CBE Spiral Initiatives CE408 Process Design: Lactic acid production (2016) Corn steep liquor Lactide Lactic acid Fermentation of corn Solvent extraction of lactic acid from H2O Distillation of lactic acid and organic solvent 14

CBE Spiral Initiatives: Lactic Acid Production Corn steep liquor CE212: Liquid extraction CE304: VLE of lactic acid and 1-octanol CE317: Pumping solution CE318: Distillation CE407: Extraction 15

Distillation of Lactic Acid and 1-Octanol Spiral Problem: Distillation of Lactic Acid and 1-Octanol 1-octanol LA H2O Other junk   To distillation Cut achieved by distillation LA H2O Other junk   1-octanol 1-octanol LA H2O Other junk   16

Distillation of Lactic Acid and 1-Octanol Spiral Problem: Distillation of Lactic Acid and 1-Octanol Octanol (“OCT”) is the light component (more volatile, lower boiling); its boiling point at e.g. 14 mm Hg is 94C.   Lactic acid (“LA”) is the heavy component (less volatile, higher boiling); its boiling point at e.g. 14 mm Hg is 132C. 17

How does distillation work? Vapor (condense what comes off top) More Oct, less LA Liquid (stay behind) More LA, less OCT 18

How do you make distilltion better? Collect only some of the condensed vapor as distillate product Send the rest of condensed vapor back down the column as reflux Rectifying tower contains “trays” Reflux 19

How does reflux work? 20 Liquid reflux from tray above Liquid reflux to tray below xlactic acid = x1   Rising vapor ylactic acid = y2 Liquid reflux from tray above xlactic acid = x0 ylactic acid = y1 L 20

How does reflux work? ybulk xbulk = x1 Equilibrium distribution of lactic acid at interface: y* = xbulk g Psat / P (Raoult’s law modified by activity coefficient; mole fractions, activity coefficient and saturated vapor pressure refer to lactic acid) 21

Mass Transfer across the Interface 22

Murphree or Tray Efficiency where A is the interfacial area per mole of vapor on the tray. The quantity hM is called the Murphree efficiency or tray efficiency. The larger the mass transfer coefficient (ky), the larger the interfacial area (A) or the longer the residence time of the bubble spends on the tray (L / ububble), the closer hM is to unity, and the more nearly equal y1 is to y*. A tray for which the vapor leaving the tray has a lactic acid mole fraction perfectly in equilibrium with that of the liquid leaving the tray (i.e., y1 = y*(x1)) is called an ideal or theoretical tray (hM = 1 = 100%). https://www.youtube.com/watch?v=rk8jpKHpD2o 23

Example ybulk xbulk = x1 Suppose the volume fraction of bubbles in the froth (bubbly liquid on tray) is f = 0.4. What is A, the interfacial area per mole of vapor on the tray, for a bubble diameter of (a) 2 mm and (b) 2 cm? (The important parameter A appears in the equation for hM at the top of this page.) Assume atmospheric pressure. 24

Take Home Messages Message #1: In distillation (and other staged operations), we are usually given a tray efficiency hM. When we work in terms of hM, mass transfer seems not to enter distillation calculations. However, the joy of mass transfer is actually embedded in hM.   Message #2: We learned all about distillation from Dr. Lockett in CE 407 this semester that is ending now. We will use distillation to separate lactic acid from an extraction solvent like 1-octanol in our CE 408 plant design project in spring 2016. 25