We are now ready to summarize the graphical design technique for determining the number of trays required to achieve desired product purities, given a reflux ratio. As we will show later, the lower the reflux ratio specified, the more trays are required. Since increasing reflux ratio increases energy costs (F„ = La + D), while increasing trays increases investment costs, distillation design involves a classical engineering trade-off between the two design variables: reflux ratio and number of trays. This will be discussed further under "Limiting Conditions." Given:

2. Desired product purities: xD, xB

3. VLE curve in x-y coordinates

4. Operating external reflux ratio: R = LJD

* If external reflux is subcooled—usually the case—then where C^ = molar specific heat, kM = molar latent heat, T„ = vapor temperature, and TR = temperature of L„. Then

Lr L0 L0 LJD

Calculate:

1. Total number of trays: NT

2. Feed tray location: NF

Procedure:

1. Draw VLE curve.

4. Calculate slope of q line ( — q/(l — q)) and draw q line from zF point on 45° line.

5. Calculate B and D from overall balances [equations (2.25) and (2.26)].

6. Calculate liquid and vapor flow rates in rectifying and stripping sections.

(SATURATED) LIQUID

FIGURE 2.25 q-Iine on x-y diagram

If the external reflux, L0, is at its bubble point:

Lr = L0 = (R) D VR — Lr + D VS=VR- {I- q) F Ls = Lr + qF

7. Calculate slopes of operating lines: rectifying = LR/VR; stripping =

8. Draw rectifying operating line from xD point on 45° line with slope

9. Draw stripping operating line from xB point on 45° line to the intersection of the q line with the rectifying operating line.

10. Check your calculations by seeing whether the slope of stripping operating line is Ls/Vs-

11. Start from the xB point on the 45° line and step up the column from the stripping operating line to the VLE curve. The first step corresponds to the partial reboiler. The next step is tray 1, the next is tray 2, and so on.

12. When this stepping procedure crosses the intersection of operating lines, this is the "optimum" feed tray (i.e., any other feed tray would require a greater total number of trays). Thus the feed tray NF has been determined.

13. Switch to the rectifying operating line and continue stepping.

14. When the xD point is crossed, this is the total number of trays NT.

This last step will not go through the xD point exacdy, implying a noninteger number of trays.

Don't let this worry you. In this procedure we have assumed "perfect" or "theoretical" or "100 percent efficient" trays; that is, trays on which the vapor and liquid streams leaving the trays are in perfect phase equilibrium. Actual industrial columns seldom achieve this ideal situation, so an efficiency factor must be used to determine the number of actual trays installed in the column (which must be an integer number). Typical efficiencies run from 40 to 90 percent, depending on the system.

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