CHE 425 UNIT OPERATIONS I
Example 2.12
A methanol-water separation is achieved in a distillation column operating at 760 mmHg. Feed flow rate is 3,000 kg/hr and feed composition is 60 wt% methanol. The feed enters the column at 1 atm and 75oC. Determine the number of trays required and the optimum feed tray to make 95 wt% methanol distillate and 5 wt% methanol bottoms when a reflux ratio of 0.75 is used. Assume theoretical trays, a total condenser, a partial reboiler, and saturated reflux.
Solution:
Making material and energy balances around the condenser.
V1 = Lo + D
V1H1 = (Lo + D)H1 = LohD + DhD + QC
Rearranging,
Lo(H1 - hD) = D(hD + QC/D - H1)
Let H’ = (hD + QC/D) then
H’ = H1 + R(H1 - hD)
hD = enthalpy of saturated liquid at x = 0.95, P = 1 atm = 50 cal/g.
H1 = enthalpy of saturated vapor at y = 0.95, P = 1 atm = 310 cal/g
H’ = H1 + R(H1 - hD) = 310 + 0.75 (310 - 50) = 505 cal/g
Locate the upper operating point D’ (0.95, 505) on the Hxy diagram. The feed point is located at xF = 0.60 on the tie line at a temperature of 75oC. Note that the feed is a mixture of vapor and liquid. A straight line intersects the vertical line through xw = 0.05 at - 500 cal/g. This is the lower operating point W’.
Stages are stepped off by starting at xW = 5 wt% on the saturated liquid line. A tie line from this point intersects the saturated vapor curve at composition yW = 31 wt%. This point represents the stream VN+1. An operating line is drawn from VN+1 to W’. This line intersects the saturated liquid curve at xN = 19 wt%. Then the tie line is used to get yN = 55 wt%.
This stepping procedure is continued for five steps. The first tie line represents the partial reboiler. Each succeeding tie line represents an equilibrium tray in the tower. The fifth tie line crosses the feed line . Therefore the optimum feed tray is tray 4 above the reboiler. The intersection of the fifth tie line and the saturated vapor curve is point VN-3. To get LN-4 or xN-4 from VN-3, the upper operating point D’ is used. Stepping is continued with the tie line and the upper operating line until xD is reached. About eights trays plus the partial reboiler are required.
Minimum Number of Trays
The minimum number of trays occurs at total reflux where D is equal to zero. From eq. (2-14)
R = (2-14)
H’ = hD + QD/D = ∞ when D = 0(2-15)
The operating point D’(xD, H’=∞) must be located at infinity. The operating lines on a Hxy diagram are vertical line at total reflux. Fig. 2.7b shows the stepping procedure used to obtain the minimum number of trays. Tie lines and vertical operating lines are used. For the system shown, about four trays plus a partial reboiler are required.
(a) Minimum reflux ratio (b) Total reflux
Fig. 2.7. Limiting conditions from Enthalpy-Concentration diagram
Minimum Reflux Ratio
If D is increased from zero (total reflux), the upper operating point D’ will move from ∞ toward the horizontal axis where the enthalpy is equal to zero. The reflux ratio R will be reduced from ∞ to a minimum value where one of the operating lines on the right of the feed point F coincides with a tie line. If we extend the tie lines on the right of the feed point to intersect the vertical line through xD, the highest intersection point establishes the minimum D’ point. The highest point usually occurs for the tie line through the feed point. For some systems the highest point of intersection on the vertical line through xD may occur on the extension of a tie line that is not the one that goes through the feed point.
Once the operating point at minimum reflux is established, the minimum reflux ratio can be determined from Eq. (2-14)
Rmin =
The advantage of the Hxy diagram is the fact that the energy required for the distillation is clearly indicated. The higher the reflux ratio the more heat must be removed per mol of product, and the operating point D’ rises. Therefore both QC and QR are increased.