Dr Saad Al-Shahrani

1. McCabe Thiele Graphical Equilibrium-Stage Limiting condition a) Minimum number of plates: If the reflux ratio ( ) is increased to very large value, the operating lines become the 45o line. The infinite reflux ratio occurs in real life when the column is operated under what are called (total reflux) condition Under these conditions, no feed is added to the column (F=0) and no products are withdrawn (D=0, B=0), but the vapor is boil up and condensed to the column. So the column is just circulating vapor and liquid up and down. Most columns are started up under total reflux conditions. ChE 334: Separation Processes Dr Saad Al-Shahrani

2. Distillation of Binary Mixture Since the liquid flow rate in the column is same as the vapor flow rate, and The operating line , The composition in the base of the column under total reflux = xB, and the composition of the liquid in the reflux drum = xD In this case the number of ideal plates is minimum. ChE 334: Separation Processes Dr Saad Al-Shahrani

3. Binary Multistage Distillation The minimum number of ideal plates can be done by: a) Graphically as shown in the figure Composition of liquid in reflux drum y1 Minimum number of plates = 3+reboiler y2 y1 = xD y2 = x1 y3 = x2 y4 = x3 xB = xB y X1 Operating lines as total reflux y3 X2 y4 XB X3 Composition of liquid in re-boiler XD XF XB x ChE 334: Separation Processes Dr Saad Al-Shahrani

4. Binary Multistage Distillation b) Analytically (using Fenske Equation) This equation gives the number of plates required under total reflux at constant . It is applicable to multi-component system as well as binary system (= constant, total reflux, ideal system). It is very useful for getting quick estimates of the size of a column. Derivation of Fenske Equation Consider two component (A,B) forming ideal solution (1) ChE 334: Separation Processes Dr Saad Al-Shahrani

5. Binary Multistage Distillation An ideal mixture follows Raoult’s law and  = vapor product ratio does not change much over the range of temperature encountered,AB  constant (2) ChE 334: Separation Processes Dr Saad Al-Shahrani

6. Binary Multistage Distillation Substitute (2) in (1) For plate n+1 zero Since D = 0 (total reflux), L / V= 1.0 , Then yn+1 = xn and ChE 334: Separation Processes Dr Saad Al-Shahrani

7. = y1 Binary Multistage Distillation At the top of the column, if a total condenser is used y1 = xD , n = 0 y1 water Substitute in (2) x0 xD x1 y2 For plate (1) x2 y3 . . . . . . . . . . . . y4 x3 = yn yn-1 For plate (n) yn xn-1 = yr Vb yb steam yr For re-boiler plate xn Re-boiler Lb, xb ChE 334: Separation Processes Dr Saad Al-Shahrani

8. Binary Multistage Distillation If all equations are multiplied together and all the intermediate terms canceled, ChE 334: Separation Processes Dr Saad Al-Shahrani

9. McCabe Thiele Graphical Equilibrium-Stage Example: Calculate the minimum number of trays required to achieved a separate from 5 mole % bottoms to 90 moles % distillate in a binary column with =2.5 solution xB= 0.05 , xD = 0.9 ChE 334: Separation Processes Dr Saad Al-Shahrani

10. McCabe Thiele Graphical Equilibrium-Stage Example: in a mixture to be fed to a continuous distillation column, the mole fraction of phenol is 0.35, of o-cresol 0.15, of m-cresol 0.3 and of xylenes 0.2. it is hoped to obtain a product with a mole fraction of phenol 0.952, of o-cresol 0.0474, of m-cresol 0.0.0006. if p-o= 1.26, m-o=0.7, estimate how many theoretical plates would be required at total reflux. Solution: B  heavy component (m-cresol) A  light component (o-cresol) Total balance 100=D + B = zero For phenol 100*0.35=D*0.952+B*xB,p D= 36.8 Kmol, B = 63.2 Kmol For o – cresol 100*0.15=0.0474*36.8+xB,o*63.2 xB,o=0.21 ChE 334: Separation Processes Dr Saad Al-Shahrani

11. McCabe Thiele Graphical Equilibrium-Stage For m – cresol 100*0.3=0.0006*36.8+xB,m*63.2 xB,X=0.316 xB,m=0.474 o-m= 1/0.7=1.43 ChE 334: Separation Processes Dr Saad Al-Shahrani

12. McCabe Thiele Graphical Equilibrium-Stage b) Minimum Reflux Ratio The next figure shows how changing the reflux ratio affects the operating lines: the lower the reflux ratio, the closer the operating line moves toward the equilibrium curve, and the larger the number of plates. If the reflux ratio finally reduced to the point where either operating line intersects or becomes tangent to the VLE curve, an infinite number of plates will be required and the reflux ratio is minimum. ChE 334: Separation Processes Dr Saad Al-Shahrani

13. McCabe Thiele Graphical Equilibrium-Stage To obtain the RDmin xD (xD,xD) y y` a or b xD x` x ChE 334: Separation Processes Dr Saad Al-Shahrani

14. Non-ideal Line VLE Feed line y` c y` a b McCabe Thiele Graphical Equilibrium-Stage If the equilibrium curve has a cavity upward, e.g., the curve for water-ethanol shown in the figure in this case the minimum reflux ratio must be computed from the slope of the operating line (ac) that is tangent to the equilibrium x` ChE 334: Separation Processes Dr Saad Al-Shahrani

15. McCabe Thiele Graphical Equilibrium-Stage Examole. A continuous fractionating column is to be design to separate 30.W Ib/h of a mixture of 40 percent benzene and 60 percent toluene into an overhead product containing 97 percent benzene and a bottom product containing 98 percent toluene. These percentages are by weight. A reflux ratio of 3.5 mol to 1 mol of product is to be used. The molal latent heats of benzene and toluene are 7,360 and 7,960 cal/ gmol, respectively. Benzene and toluene form an id91 system with a relative volatility of about 2.5; the equilibrium curve is shown in Fig. 18-16. The feed has a boiling point of 95 oC at a pressure of 1 atm. (a) Calculate the moles of overhead product and bottom product per hour. (b) Determine the number of deal plate and the position of the feed plate (i) if the feed is liquid and at its boiling point. ii)if the feed is liquid and at 20 oC (specific heat 0.44 cal/ g-oC) (iii) if the feed is a mixture of two-thirds and one-third liquid. (c) If steam at 20 Ib,/in2(1.36 atm) gauge is used for heating, how much steam is required per hour for each of the above three cases, neglecting heat losses and assuming the reflux is a saturated liquid? (d) If cooling water enters the condenser at 25°C and leaves at 40°C, how much cooling water a required, in gallons per minute? ChE 334: Separation Processes Dr Saad Al-Shahrani

16. 1 2 3 4 Feed line 5 6 7 8 . 9 10 R xF=0.44 xB=0.0235 xD=0.974