Question

The vapor-liquid equilibrium for n-pentane and n-hexane at 1 ATM is well approximated using a constant relative volatility of 2.95. CMO is valid. For all the problems, the feed stream is flowing at 80 mol/s and contains 45 mol% n-pentane, the feed is a saturated liquid (q = 1) at the column pressure, the distillate is 95 mol% n-pentane, and the bottoms is 10 mol% n-pentane. In this problem, you should analyze the column graphically using the McCabe-Thiele Method

a. Make an X-Y diagram for this system that you will use to answer the following questions

b. Plot the feed line, the distillate composition (on y=x line), and the bottoms composition (on y=x line) on the X-Y diagram.

c. Assuming total reflux (a limiting case in which the operating lines are the same as the y=x line), how many stages are required for this distillation. This is the minimum number of stages for this distillation.

d. Find the minimum reflux ratio for this distillation. This is a limiting case at which the top operating line, bottom operating line, and feed line all intersect at the same point on the equilibrium curve. At the minimum reflux ratio, the number of theoretical stages diverges to infinity.

e. Assuming the actual reflux ratio is equal to twice the minimum reflux ratio, how many equilibrium stages are required for this distillation?

Answer 1

Given� Field f = 80 mol/s� x_F (mole fraction of n - pentane infeed) = 0.45� x_D (mole fraction of� n - pentane in distillate) = 0.95� x_w(mole fraction of n - pentane in Bottom) = 0.1� feed is saturated liquid q = 1� constant relative volatility alpha = 2.95� a) equilibrium Data for n - pentane and n - hexane ��� \r\n c) Minimum Number of stages at total reflux� minimum number of stages at total Reflux� fenske equation� N_m + 1 = log {x_D/1 - x_D times 1 - x_w/x_w}/log propto avg� N_m - Number of stages required� alpha_avg Given = 2.95� N_m + 1 = log {0.95/1 - 0.95 times 1 - 0.1/0.1}/log(2.95)� N_m + 1 = 4.75� N_m = 3.75 stages ���4 stages� minimum Number of stages required at total reflux is 4 stage� d)� Draw q - line �Rightarrow vertical to the equilibrium line because feed is� saturated liquid� from Graph� Intercept = x_D/R_min + 1� Intercept = 0.49� 0.49 = 0.95/R_min + 1 Righarrow R_min = 0.9388