## Heat-Balance Calculations

If you have read this far, and understood what you have read, you will readily understand the following calculation. It is simply a repetition, with numbers, of the discussion previously presented. However, you will require the following values to perform the calculations:

• Latent heat of condensation of alcohol vapors = 400 Btu/lb

• Latent heat of condensation of water vapors = 1000 Btu/lb

• Specific heat of alcohol (vapor or liquid) = 0.6 Btu/[(lb)(°F)]

• Specific heat of water = 1.0 Btu/[(lb)(°F)]

The term specific heat refers to the sensible-heat content of either vapor or liquid. The specific heat is the amount of heat needed to raise the temperature on one pound of the vapor or liquid by 1°F. The term latent heat refers to the heat of vaporization, or the heat of condensation, needed to vaporize or condense one pound of liquid or vapor at constant temperature. Note that the heat of condensation is equal to the heat of vaporization. Each is referred to as the latent heat. The sum of the sensible heat, plus the latent heat, is called the total heat content, or enthalpy.

Returning to our example in Fig. 6.1, we wish first to determine the reboiler duty. To do this, we have to supply three heat requirements:

A. Heat 9000 lb/h of water from the 100°F feed temperature to the tower-bottom temperature of 220°F.

B. Heat 1000 lb/h of alcohol from the 100°F feed temperature (where the alcohol is a liquid) to the tower overhead temperature of 160°F (where the alcohol is a vapor).

C. Vaporize 10,000 lb/h of reflux from the 150°F reflux drum temperature to the tower overhead temperature of 160°F.

Solution to step A:

9000 lb/h x 1.0 Btu/[(lb)(°F)] x (220°F – 100°F) = 1,080,000 Btu/h

Solution to step B:

1000 lb/h x 0.6 Btu/[(lb)(°F)] x (160°F – 100°F) + 1000 lb/h x 400 Btu/lb = 36,000 Btu/h + 400,000 Btu/h = 436,000 Btu/h

Solution to step C:

10,000 lb/h x 0.6 Btu/[(lb)(°F)] x (160°F – 150°F) + 10,000 lb/h x 400 Btu/lb = 60,000 Btu/h + 4,000,000 Btu/h = 4,060,000 Btu/h

The reboiler duty is then the sum of A + B + C = 5,576,000 Btu/h.

The next part of the problem is to determine the vapor flow to the bottom tray. If we assume that the vapor leaving the reboiler is essentially steam, then the latent heat of condensation of this vapor is 1000 Btu/lb. Hence the flow of vapor (all steam) to the bottom tray is

= 5,576,000 Btu/h / 1000 Btu/lb = 5576 lb/h

How about the condenser duty? That is calculated as follows:

11,000 lb/h x 0.6 Btu/[(lb)(°F)] x (160°F – 150°F) + 11,000 lb/h x 400 BTU/lb = 66,000 BTU/h + 4,400,000 BTU/h = 4,466,000 BTU/h

We can draw the following conclusions from this example:

• The condenser duty is usually a little smaller than the reboiler duty.

• Most of the reboiler heat duty usually goes into generating reflux.

• The flow of vapor up the tower is created by the reboiler.

For other applications, these statements may be less appropriate. This is especially so when the reflux rate is much smaller than the feed rate. But if you can grasp these calculations, then you can appreciate the concept of the reboiler acting as the engine to drive the distillation column.

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