PLANT CH 144K | GROUP1 ATIS | AQUINO | LARRACAS | MENDOZA | NATIVIDAD | PEREZ | SURATOS** (Lecture and CP#6) DISTILLATION Challenge Problem 6 A distillation column at 1 atm is to separate 600 kgmoles/hr of methanolwater feed solution containing 40 mole% methanol into a distillate with 90 mol% methanol at 325K and a bottoms with 5 mol% methanol, operating 8000 hrs/yr. The distilling column costs Php 10/m2-plate (this cost includes all auxiliaries such as a partial reboiler and total condenser) with a life of 10 years. Total direct cost of steam and cooling water is Php 0.005/kgmol distillate. The overall plate efficiency is 90% at a vapor velocity of 1.5 m/hr. The number of plates can be related to the reflux ratio by the Fenske Underwood equation below . Assume the minimum number of stages as 4 and Minimum Reflux Ratio is 1.5. Show that the optimum reflux ratio occurs at a reflux ratio between 2 and 3. CHALLENGE PROBLEM 6 1.5 m/hr TC D xD=0.9 F F=600 kgmol/hr xB=0.4 PR Diagram B xB=0.05 CHALLENGE PROBLEM 6 1.5 m/hr TC Solution: 𝒌𝒈𝒎𝒐𝒍 𝑯𝒚 𝒉𝒓 𝒌𝒈𝒎𝒐𝒍 𝒉𝒓 𝒌𝒈𝒎𝒐𝒍 𝑭 = 𝟔𝟎𝟎 𝟖𝟎𝟎𝟎 = 𝟒. 𝟖 ∗ 𝟏𝟎𝟔 𝒉𝒓 𝒚𝒓 𝒚𝒓 𝑭 = 𝟔𝟎𝟎 D xD=0.9 𝑴𝑽𝑪𝑩: 𝒙𝑭 − 𝒙𝑩 𝒌𝒈𝒎𝒐𝒍 𝟎. 𝟒 − 𝟎. 𝟎𝟓 = 𝟒. 𝟖 ∗ 𝟏𝟎𝟔 𝒙𝑫 − 𝒙𝑩 𝒚𝒓 𝟎. 𝟗 − 𝟎. 𝟎𝟓 𝒌𝒈𝒎𝒐𝒍 𝑫 = 𝟏𝟗𝟕𝟔𝟒𝟕𝟎. 𝟓𝟖𝟖 𝒚𝒓 F 𝑫=𝑭 F=600 kgmol/hr xB=0.4 𝑶𝑴𝑩: 𝑭 = 𝑫 + 𝑩 → 𝑩 = 𝑭 − 𝑫 = 𝟒. 𝟖 ∗ 𝟏𝟎𝟔 − 𝟏𝟗𝟕𝟔𝟒𝟕𝟎. 𝟓𝟖𝟖 𝒌𝒈𝒎𝒐𝒍 𝑩 = 𝟐𝟖𝟐𝟑𝟓𝟐𝟗. 𝟒𝟏𝟐 𝒚𝒓 𝑮 = 𝟏. 𝟓 𝒎 𝒈𝒎𝒐𝒍 𝟏𝟎𝟎𝟎 𝑳 𝟏 𝒌𝒈𝒎𝒐𝒍 𝟐𝟕𝟑 𝑲 𝒌𝒈𝒎𝒐𝒍 ∗ ∗ ∗ ∗ = 𝟎. 𝟎𝟓𝟔𝟐𝟓 𝟐 𝟑 𝒉𝒓 𝟐𝟐. 𝟒 𝑳 𝒎 𝟏𝟎𝟎𝟎 𝒈𝒎𝒐𝒍 𝟑𝟐𝟓 𝑲 𝒎 − 𝒉𝒓 PR B xB=0.05 Diagram CHALLENGE PROBLEM 6 1.5 m/hr Solution: Trial & Error TC Trial 1: RD=2 D xD=0.9 𝑹 − 𝑹𝒎𝒊𝒏 𝟐 − 𝟏. 𝟓 𝛙= = = 𝟎. 𝟏𝟔𝟔𝟕 𝑹+𝟏 𝟐+𝟏 Fenske Underwood Gilliland Eqn. F 𝑵 − 𝑵𝒎𝒊𝒏 𝟏 + 𝟓𝟒. 𝟒𝝍 𝝍−𝟏 = 𝟏 − 𝒆𝒙𝒑 ∗ 𝟎.𝟓 F=600 kgmol/hr 𝑵+𝟏 𝟏𝟏 + 𝟏𝟏𝟕. 𝟐𝝍 𝝍 xB=0.4 𝑵−𝟒 𝟏 + 𝟓𝟒. 𝟒 𝟎. 𝟏𝟔𝟔𝟕 𝟎. 𝟏𝟔𝟔𝟕 − 𝟏 = 𝟏 − 𝒆𝒙𝒑 ∗ → 𝑵 = 𝟖. 𝟖𝟎𝟎𝟒 𝑵+𝟏 𝟏𝟏 + 𝟏𝟏𝟕. 𝟐 𝟎. 𝟏𝟔𝟔𝟕 𝟎. 𝟏𝟔𝟔𝟕𝟎.𝟓 𝑲𝑭 𝒂𝒄 𝑵𝒑 𝑫 𝑪𝑻 = 𝑹𝑫 + 𝟏 ∗ [ + 𝑪𝟎 𝑫] 𝜼𝟎 𝑮𝑯𝒚 𝑷𝒉𝒑 𝒌𝒈𝒎𝒐𝒍 𝑲𝑭 = 𝟎. 𝟏; 𝒂𝒄 = 𝟏𝟎 𝟐 ; 𝜼𝟎 = 𝟎. 𝟗; 𝑪𝟎 = 𝟎. 𝟎𝟎𝟓 𝒎 − 𝒑𝒍𝒂𝒕𝒆 𝒅𝒊𝒔𝒕𝒊𝒍𝒍𝒂𝒕𝒆 𝑪𝑻 = 𝑷𝒉𝒑 𝟐𝟖𝟕𝟑𝟑𝟐. 𝟎𝟗𝟕 PR B xB=0.05 Diagram CHALLENGE PROBLEM 6 0.0741 0.1071 0.1379 0.1667 0.1935 0.2188 0.2424 0.2647 0.2857 0.3056 0.3243 0.3421 0.3590 0.3750 0.3902 0.4048 0.4186 0.4318 0.4444 0.4565 0.4681 0.4792 0.4898 0.5000 1-exp(x) 0.5808 0.5465 0.5164 0.4898 0.4660 0.4446 0.4253 0.4077 0.3916 0.3768 0.3632 0.3506 0.3389 0.3280 0.3178 0.3083 0.2993 0.2909 0.2829 0.2754 0.2683 0.2616 0.2552 0.2491 N 10.9274 10.0246 9.3401 8.8004 8.3638 8.0032 7.7001 7.4416 7.2183 7.0235 6.8519 6.6994 6.5631 6.4403 6.3292 6.2281 6.1357 6.0509 5.9727 5.9005 5.8335 5.7712 5.7131 5.6588 CT 157490.9290 150987.3150 146691.5761 143849.0552 142038.9804 140988.9435 140513.4926 140482.2977 140801.3454 141401.2530 142229.7680 143246.8224 144421.1937 145728.1989 147148.0709 148664.7942 150265.2553 151938.6136 153675.8290 155469.3026 157312.5998 159200.2355 161127.5045 163090.3473 CT vs RD Plot 1650 1600 Hundreds (Php) Ψ CT RD 1.7 1.8 1.9 2 2.1 2.2 2.3 2.4 2.5 2.6 2.7 2.8 2.9 3 3.1 3.2 3.3 3.4 3.5 3.6 3.7 3.8 3.9 4 1550 1500 1450 1400 1350 1.5 2 2.5 3 3.5 4 RD CTmin is at RD=2.5. Hence, RDopt=2.4 Based from the table and graph, CT at 2 < RD < 3 gives lower CT. Hence, Rdopt occurs between 2 and 3.