Unformatted text preview: What you should already know: • Iden3fy the feed stage, the bo8oms and dis3llate streams, the enriching/rec3fying sec3on, the stripping sec3on • Deﬁne the external reﬂux ra3o, the boilup ra3o, constant molal overﬂow • Perform external column balances (mass and energy) • For a par3cular stage inside the column, label all streams, perform mass balance Objec3ves for this lecture • Apply the Lewis method to stage by stage analysis of a con3nuous dis3lla3on column • Obtain the equa3on of the opera3ng line for a countercurrent rec3fying column • For a speciﬁed reﬂux ra3o, deduce the number of equilibrium stages required, using the McCabe Thiele method Reading assignment: ch. 3 and ch. 4 sec3ons 4.1 4.3 Recap: • The external reﬂux ra3o R is related to, but not the same as, the internal reﬂux ra3o L/V. • The assump3on of constant molal overﬂow (CMO) allows us to derive a single mass balance equa3on for the rec3fying/enriching sec3on of a dis3lla3on column. When plo8ed on a McCabe Thiele graph, this equa3on is called the opera&ng line. • Moving from stage to stage down the column, either algebraically, or graphically, amounts to alterna&ng between the mass balance and the VLE equa&ons. MeOH H2O rec3fying column Speciﬁca3ons: xD = 0.8, R = 2 Column with total condensor Find N required to achieve xB = 0.1 1
0.9 stage 1 (x1,y1)• 0.8 stage 2 (x2,y2)• 0.7 2. Plot xD on y=x 3. Plot yint and draw op. line L/V = R/(R+1) = 2/3 yint = xD(1 L/V)= 0.8/3 = 0.26 4. Step oﬀ stages star3ng at xD 5. Stop when you reach xB 6. NEVER step over the VLE line. y(MeOH) 1. Draw y=x line 0.6
0.5
stage 3 (x ,y )• 0.4 3 3
0.3 yint• •xD= x0 (x0,y1) •(x1,y2) •(x2,y3) • 0.2
0.1
0 lowest xB possible for this op. line 0 •x
0.1 B 0.2 0.3 0.4 0.5 x(MeOH) 0.6 0.7 0.8 0.9 1 Objec3ves for this lecture • Describe the opera3ng limits for a rec3fying column. • Find the minimum number of stages, Nmin, required for separa3on by rec3ﬁca3on. • Find the minimum reﬂux ra3o, Rmin, required for separa3on by rec3ﬁca3on. • Repeat for a stripping column. • Assemble the pieces to make a complete dis3lla3on column and iden3fy the feed stage. Homework: 4D28 (3rd ed; 4D35 in 2nd ed). Assume desired yD = 0.74. Limi3ng cases: rec3ﬁca3on Speciﬁca3ons: xD = 0.8, vary R = L/D 1
0.9 1. L 0 R = L/D 0 L/V 0 2. D 0 R = L/D ∞ L/V = R/(R+1) 1 (L’Hôpital’s Rule) Opera3ng line is y=x stage 1 (x1,y1)• 0.8 •xD= x0 (x0,y1) 0.7
0.6 y(MeOH) Column operates like a single equilibrium stage. (Why bother?) L/V = 0 No reﬂux! 0.5
0.4 0 ≤ L/V ≤ 1 0.3 0 ≤ R ≤ ∞ 0.2 L/V = 1 Total reﬂux! 0.1 Max. distance between VLE and op. line 0
0
Max. separa3on on each equil. stage Corresponds to Nmin. But no dis3llate! 0.1 0.2 0.3 0.4 0.5 x(MeOH) 0.6 0.7 0.8 0.9 1 Minimum reﬂux ra3o L/V = 0 1 Speciﬁca3ons: xD = 0.8, vary R 0.9 • 0.8 This represents xB,min for a par3cular R. 0.7
0.6 y(MeOH) The number of stages N required to reach the VLE op. line intersec3on point is ∞. •xD= x0 (x0,y1) • 0.5 • 0.4 • 0.3 It also represents Rmin for this value of xB. 0.2 0 0 ≤ L/V ≤ 1 L/V = 1 0.1 Rule of thumb: 1.05 ≤ Ropt/Rmin ≤ 1.25 Can specify Ractual as a mul3ple of Rmin Increasing R Decreasing xB (for ﬁxed N) Decreasing D 0 • 0.1 0.2 0.3
xB ,min for this R 0.4 0.5 x(MeOH) 0 ≤ R ≤ ∞ 0.6 0.7 0.8 0.9 1 MeOH H2O stripping column Speciﬁca3ons: xB = 0.07, V / B = 2
Column with par3al reboiler Find N required to achieve xD = 0.55 € (0.7,1) • 1
0.9 0.7 1. Draw y=x line stage 2 (xN,yN) • 3. Draw op. line y(MeOH) 0.6 2. Plot xB = xN+1 on y=x y = 1 = 1.5x − 0.05 € 4. Step oﬀ stages star3ng at PR € 5. Stop when you reach xD x = 1.05 / 1.5 = 0.7 € 6. NEVER step over the VLE line. 0.2 xB= xN+1 • (xN+1,yN+2) 0.1
0 highest xD possible for this op. line PR • • (xN,yN+1) (xN+1, yN+1) yint = xB (1 − L / V ) = 0.07(1 − 1.5) = −0.035 0.3 € • (xN 1,yN) 0.5
0.4 L / V = B / V + 1 = 1.5 • •(x1,y2) stage 1 (xN 1,yN 1) • 0.8 0 0.1 0.2 0.3 0.4 0.5 x • D x(MeOH) 0.6 0.7 0.8 0.9 1 Recap: • A rec3fying/enriching column has feed entering at the bo8om, a reﬂux stream but no boilup. • A stripping column has feed entering at the top, a boilup stream but no reﬂux. • In each case, the opera3ng line starts on the y=x line (at xD for a rec3fying column or xB for a stripping column). • Increasing the reﬂux ra3o/boilup ra3o improves the separa3on, at the expense of the product ﬂow rates. • The minimum number of stages is required when the column is operated at total reﬂux. • The minimum reﬂux ra3o is required when the column has an inﬁnite number of equilibrium stages. Objec3ves for this lecture • Assemble the pieces to make a complete dis3lla3on column and iden3fy the feed stage. • Determine the feed quality (q) and locate the feed line. • Find the required number of stages in each sec3on of a complete dis3lla3on column with speciﬁed splits. Exam on Friday: bring pencil, eraser, straight edge, calculator, textbook, notes, ... No cellphones or other communica3on devices. Show your work. Make reasonable assump3ons. Limi3ng cases: stripping Speciﬁca3ons:
xB = 0.07, vary boilup ra3o V / B 1
0.9 1. V → 0 L /V → ∞ € Behaves as if the column wasn’t even there. (Why bother?) 2. B 0 L →V ∞ ≥V / B ≥ 0 €0.7
€0.6
y(MeOH) € 0.8 € 1≤ L /V ≤ ∞ 0.5
0.4
0.3 PR • L /V = 1 Total boilup! L / V →1
€
€ Opera3ng line is y=x 0.2
0.1 €
L /V = ∞ No boilup! • xB= xN+1 Max. distance between VLE and op. line 0
0
0.1 € 0.2
Max. separa3on on each equil. stage Corresponds to Nmin. But no bo8oms product! 0.3 0.4 0.5 x(MeOH) 0.6 0.7 0.8 0.9 1 Minimum boilup ra3o 1 Speciﬁca3ons: xB = 0.07, vary boilup ra3o yD ,max for 0.9 this boilup ra3o • • 0.8 This represents yD,max for a par3cular boilup ra3o. • 0.7 • 0.6 y(MeOH) The number of stages N required to reach the VLE op. line intersec3on point is ∞. ∞ ≥V / B ≥ 0 0.5 € 0.4 PR • 0.3 It also represents the minimum boilup ra3o for this value of yD. 1≤ L /V ≤ ∞ € L /V = 1 Total boilup! 0.2 L /V = ∞ 0.1
0 • xB= xN+1 0 0.1 € 0.2 € No boilup! 0.3 0.4 0.5 x(MeOH) 0.6 0.7 0.8 0.9 1 McCabe Thiele analysis of a complete dis3lla3on column 1 Speciﬁca3ons: xD = 0.8, R = 2 xB = 0.07, / B = 2
V
Total condensor, par3al reboiler Find N required €
Locate feed stage Feed must enter here 0.9
0.8 3. Draw both op. lines 4. Step oﬀ stages star3ng at either end, using new op. line as you cross their intersec3on 5. Stop when you reach the other end 6. NEVER step over the VLE line. y(MeOH) 2. Plot xD and xB on y=x •xD 0.7 stage 2 • 0.6 1. Draw y=x line stage 1 • • 0.5
0.4 PR • 0.3 • 0.2
0.1
0 • xB 0 0.1 0.2 0.3 0.4 0.5 x(MeOH) 0.6 0.7 0.8 0.9 1 McCabe Thiele analysis including the feed line Speciﬁca3ons: xD = 0.9, xB = 0.07, zF = 0.5 Feed is a 2 phase mixture, 50% liq. Total condensor, par3al reboiler R = 1. Find N and opt. feed stage 1
0.9 4 • 0.7 1. Draw y=x line •zF 0.5 3. Draw feed line, slope = q/(q 1) 0.4 4. Draw top op. line, slope = L/V 0.3 5. Draw bo8om op. line (no calc. required) 6. Step oﬀ stages star3ng at either end, using new op. line as you cross their intersec3on PR • Op3mum feed loca3on is between stages 4 and 5. Introducing feed at non op3mal loca3on will reduce the separa3on achieved in this column. 0.2
0.1
0 2• •xD 5• 0.6 y(MeOH) 2. Plot xD, xB and zF on y=x 3 • 0.8 1 • • xB 0 0.1 0.2 0.3 0.4 0.5 x(MeOH) 0.6 0.7 0.8 0.9 1 Recap: • The separa3on achieved in a con3nuous dis3lla3on column depends on the feed enthalpy (= quality, q) and the loca3on of the feed stage. • The mass balance changes at the feed stage; consequently, the opera3ng lines for the top and bo8om sec3ons of the column are diﬀerent. • Both opera3ng lines intersect on the feed line, with slope = q/(q 1). • Only two of the external reﬂux ra3o, the feed quality and the boilup ra3o can be speciﬁed independently. Objec3ves for this lecture • Assess design freedom in column dis3lla3on. • Iden3fy pinch points in the column, and on the McCabe Thiele diagram. • Design a column for open steam dis3lla3on. Homework this week: 4D11, due Wednesday 4D9, due Friday Reading: chapter 4, sec3ons 4.4  4.16 Design freedom Fixed q. Vary R: Fixed R. Vary q: 1 1 Rmin 0.9
0.8 •xD 0.8 pinch point 0.7 0.7 decrease R 0.6 y(MeOH) 0.6 y(MeOH) •xD heat feed 0.9 •zF 0.5 •zF 0.5 0.4 0.4 0.3 0.3 Choice of R determines boilup ra3o. 0.2 • xB 0.1
0 0 0.1 0.2 0.3 0.4 0.5 x(MeOH) 0.6 0.7 0.8 0.9 qmin pinch point 0.2 • xB 0.1 1 0 0 0.1 0.2 0.3 0.4 0.5 x(MeOH) 0.6 0.7 0.8 0.9 1 Other Types of Pinch Points Ethanol water xD = 0.82, xB = 0.07 zF = 0.5, q = 0.5 Find Rmin 1
0.9 0.7 1. Draw y=x line 0.6 y(EtOH) 2. Plot xD, xB and zF on y=x •xD pinch point 0.8 •zF 0.5 3. Draw feed line, slope = q/(q 1) 0.4 4. Draw top op. line to intersect with feed line on VLE line 0.3 5. Don’t cross the VLE line! 0.2 6. Redraw top op. line as tangent to VLE. 0.1
0 • xB 0 0.1 0.2 0.3 0.4 0.5 x(EtOH) 0.6 0.7 0.8 0.9 1 Open steam dis3lla3on Speciﬁca3ons: xD = 0.9, xB = 0.07, zF = 0.5 Feed is a 2 phase mixture, 50% liq. Total condensor, open steam R = 1. Find N and opt. feed stage 1
0.9 2. Plot xD and zF on y=x 0.6 y(MeOH) 1. Draw y=x line 4 • 0.7 3. Plot xB on x axis 3 • 0.8 •zF 0.4 5. Draw top op. line, slope = L/V 0.3 2• •xD 5 • 0.5 4. Draw feed line, slope = q/(q 1) 1 • 6. Draw bo8om op. line (no calc. required) 7. Step oﬀ stages star3ng at either end, using new op. line as you cross their intersec3on 6• All stages are on the column (no par3al reboiler). 0.2 Op3mum feed loca3on is between stages 4 and 5. 0.1
0 • 0 xB 0.1 0.2 0.3 0.4 0.5 x(MeOH) 0.6 0.7 0.8 0.9 1 Recap: • The column designer can vary the reﬂux ra3o and/or the feed quality (temperature) to op3mize the separa3on and the dis3llate ﬂow rate. • The intersec3on of the opera3ng lines on the feed line at the VLE curve corresponds to a pinch point in the column – i.e., no change in composi3on between stages. • Watch for other pinch points created by opera3ng lines that touch the VLE curve. • When the less vola3le component in a binary separa3on is water, it is possible to replace the reboiler by open steam. • In open steam dis3lla3on, the bo8om opera3ng line starts at (xB, 0). • When two feeds are present at diﬀerent op3mum stages, a third column sec3on is created, requiring its own opera3ng line. Objec3ves for this lecture • Calculate the slope of the middle opera3ng line in a column with two feedstreams. • McCabe Thiele treatment of side streams. • McCabe Thiele treatment of par3al condensers and total reboilers • McCabe Thiele treatment of subcooled reﬂux and superheated boilup. Mul3ple feedstreams Speciﬁca3ons: xD = 0.9, xB = 0.07, z1 = 0.4, z2=0.6 Some speciﬁed q values Total condensor, par3al reboiler R = 1. Find N and opt. feed stages 1
0.9 2. Plot xD, z1, z2 and xB on y=x 0.6 4. Draw top op. line, slope = L/V 5. Calculate slope of middle op. line, L´/V´, and draw middle op. line y(MeOH) 1. Draw y=x line 4 • 0.7 3. Draw both feed lines 3 • 0.8 1 • 2• •xD •z2 5• 0.5 •z1 0.4
0.3 PR • Op3mum loca3on for feed 1 is stage 5. Op3mum loca3on for feed 2 is stage 3. 0.2 6. Draw bo8om op. line (no 0.1
calc. required) x• B
0
7. Step oﬀ stages star3ng 0
0.1
at either end, using new op. line each 3me you cross an intersec3on 0.2 0.3 0.4 0.5 x(MeOH) 0.6 0.7 0.8 0.9 1 Side streams Saturated liquid side stream, xs = 0.6 Saturated vapor side stream, ys = 0.6 1 1 •xD 0.9
0.8 0.8 0.7 0.7 •xS 0.5 •z 0.4 •xS 0.6 y(MeOH) 0.6 y(MeOH) •xD 0.9 0.5 •z 0.4 0.3 0.3 0.2 0.2 0.1
0 •
xB 0 0.1 0.1
0.2 0.3 0.4 0.5 x(MeOH) 0.6 0.7 0.8 0.9 1 0 •
xB 0 0.1 0.2 0.3 0.4 0.5 x(MeOH) 0.6 0.7 0.8 0.9 1 Sieve trays • Also called perforated tray • Simple, cheap, easy to clean • Alternate downcomers to create cross ﬂow • Improve mixing with dual pass tray in large diameter columns • Poor downturn performance Valve trays • More expensive, harder to clean • Valves can close par3ally to accommodate changes in vapor ﬂow rate • Be8er downturn performance Bubble cap tray • Excellent contact between vapor and liquid • Does not rely on vapor velocity to keep liquid on tray • Excellent downturn charateris3cs • Very hard to clean Column packing Structured packing: random packing: • large surface area for contact between liquid and vapor • preferred for column diameters < 2.5´ • design for HETP (= Height Equivalent to a Theore3cal Plate/Tray) • packing can be metal, ceramic, glass Column dis3lla3on videos Normal column opera3on: h8p://www.youtube.com/watch?v=QQgtcNzW9Nw&NR=1 Flooding: h8p://www.youtube.com/watch?v=tHOlFleAkNE Weeping: h8p://www.youtube.com/watch?v=tRRxBCSuz48 ...
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 Fall '08
 Scott,S
 Column, stage, Cancer staging, • McCabe

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