MODULE 4: ABSORPTION LECTURE NO. 3 4.4. Deign of packed tower baed on overall ma tranfer coefficient * From overall ma tranfer equation, N K ( y y ) one can write for packed tower a N A K y (y-y*) Then, d G K y a y (y y ) A y AG A (4.0) where, y* i olute concentration in ga phae that i capable of remaining in equilibrium with a liquid having a bulk concentration of x. T T 0 d G K y a y (y y ) G k G ap y (y y i ) x L dx x 2 k L a(c av ) x (x i x) (4.) Graphical integration of right hand ide of Equation (4.): Operating line AB i drawn in xy plane. Any point (x,y) i taken in operating line. A vertical line i drawn upto equilibrium line to get y*. T x L dx x 2 K x a x (x x) y G K G ap y (y y ) x L dx k L a(c av ) x (x x) x 2 (4.2) Joint initiative of IIT and IISc Funded by MHRD Page of 5
5.5. Deign baed on height of a tranfer unit (HTU) Equation 4.7 can be written a T T 0 d y G y ibm k y a y ibm y (y y i ) y G ( y) im y (y y i ) (4.3) where, y ibm ( y) im y i ( y) ln y i ( y ) T G ( y) im (4.4) y (y y i ) A, G remain contant at the packing ection though G varie. Thi quantity i called height if tranfer unit (HTU) and deignated a H tg. It i important to meaure the eparation effectivene of the particular packing for a particular eparation proce. It alo decribe the ma tranfer coefficient. Larger ma tranfer coefficient lead to the maller value of HTU. Hence, H tg G G k y a (4.5) unit a N tg. The integral part of Equation (4.4) i called number of ga phae tranfer h T H tg N tg When overall ga phae ma tranfer coefficient are ued, the height of the packing i a follow: T y G K y a y G BM y (y y ) K y a y BM H tog N tog (4.6) y (y y ) where, H tog G K y a y BM, N tog y (y y ) and y BM ( y) BM y ( y) ln y ( y ). Joint initiative of IIT and IISc Funded by MHRD Page 2 of 5
4.6. Deign Equation baed concentration in mole ratio unit If k x, k y are individual ga phae ma tranfer coefficient and K Y i overall ga phae ma tranfer coefficient, height of packed tower i expreed a: T H tog G K y a Y G k y a (Y Y i ) Y G K y a (Y Y ) G K y a Y (Y Y ) H tog N tog (4.7) N tog Y (Y Y ) Slope of operating line L G Overall ga-phae ma tranfer coefficient, K Y i correlated with individual ma tranfer coefficient a follow: K Y k Y + k x Example Problem 4.. Solute A i to be aborbed from a binary mixture containing 7.5% of A with olvent B in a packed tower. Baed on flooding calculation, a tower diameter of.2 m i elected. Total ga flow rate i 60 kmolh. The exit ga mut not contain 0.2% of olute A. Solute free liquid B enter from the top of the tower at 40 kmolh. The ga phae and liquid phae ma tranfer coefficient baed on mole ratio unit are: k X 2.05 kmolm 2 h (ΔX) and k Y.75 kmolm 2 h (ΔY). The equilibrium line Equation i Y0.63X. Specific interfacial area of ga-liquid contact (ā) i 7 m 2 m 3. (a) Calculate packing height required for the deired eparation. (b) For 99.5% olute A removal, what % increae in packed height i needed? (c) Determine lope of operating line in each cae. Joint initiative of IIT and IISc Funded by MHRD Page 3 of 5
Solution 4.: Ga flow rate, G 60 kmolh; 0.075 Area of tower cro-ection π 4 (.2)2.3 m 2 G 53.05 kmolm 2.h G 53.05(-0.075) kmolm 2.h 49.07 kmolm 2.h Y 0.075 0.925 Solute concentration in exit ga i 0.2%. 0.2 99.8 0.00204 Liquid flow rate, L 40 kmolh L 40.3 35.37 kmolm2.h X 2 0 Overall ma balance Equation for the olute concentration in exit liquid a follow: G Y L X X 2 49.07(0.0-0.00204) 35.37(X -0) X 0.097 Overall ga-phae ma tranfer coefficient, K Y : K Y k Y + k x K Y.75 + 0.63 2.05 K Y.38 kmolm 2 h (ΔY) H tog G 49.07 0.607 m, K Y a.38 7 N tog Y (Y Y ) Y* can be expreed in term of Y. The operating line Equation can be expreed a: G Y L X X 2 49.07(Y-0.00204) 35.37(X-0) Joint initiative of IIT and IISc Funded by MHRD Page 4 of 5
X.387(Y-0.00204) We have Y* αx 0.63.387(Y-0.00204) 0.874Y-0.0078 N tog 0.00204 Y (0.874Y 0.0078 ) 0.00204 (0.26Y+0.0078 ) N tog 0.26 +0.0078 ln 3.9 0.26 0.26 0.00204 +0.0078 (a) Packed height, h T H tog N tog 0.0607 3.9 m8.46 m. (b) For 99.5% olute removal, 0.00054.05 0-4. G Y L X X 2 49.07(Y-4.05 0-4 ) 35.37(X-0) X (.387Y 5.62 0-4 ) Hence, Y* αx 0.63 (.387Y 5.62 0-4 ) 0.874Y-0.000354 N tog 4.05 0 4 Y (0.874Y 0.000354 ) 4.05 0 4 (0.26Y+0.000354 ) N tog 0.26 ln 0.26 +0.000354 0.26 4.05 0 4 +0.000354 22 Required packed height, h T H tog N tog 0.0607 22 m3.35 m. %increae in packing eigt 3.35 8.46 8.46 00 58% (c) For both the cae lope of the operating will remain ame a L. G So, Slope of operating line L G 35.37 49.07 0.72. Joint initiative of IIT and IISc Funded by MHRD Page 5 of 5