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Moisture Control in Paper Drying
Background
The Paper Web - The Existing Problem
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For a mill producing 1 million pounds (500 tons) of paper per day, the cost of evaporating water can be estimated as $7,185 a day: 1,000,000 lbs paper x [1.85 lbs water/lb paper] x [971 BTU/lb water] x [1 therm/100,000 BTU] x [$0.40/*therm] = $7,185 a day *A therm is defined as 100,000 BTU, and a typical price for this amount of energy is 40 cents. For a mill operating 350 days per year, the annual bill for evaporating water from paper would be $2.5 million. Reducing this cost by even a small percentage can result in significant dollar savings. One way to save money using dew point control is to raise the process dew point so that the drying air is carrying away as much moisture as possible consistent with maintaining paper quality. Additional savings available through compensating for changes in ambient humidity are described but not estimated in this application note.
Raising the Process Dew Point
A Specific Example
In a table of water vapor partial pressure vs. temperature, a dew point of 80°C corresponds to 355 mm Hg water vapor pressure, and a dew point of 90° C corresponds to 526 mm Hg water vapor pressure. Since total pressure is 1 atmosphere, or 760 mm Hg, a dew point of 80° C corresponds to a moisture content of 355/760 = 46.7% water and 53.3% air by volume, and a dew point of 90° C corresponds to a moisture content of 526/760 = 69.2% water and 30.8% air by volume. In order to calculate the difference in the amount of water that will be carried away at these two dew points, these volume percentages must be converted to weight percentages. This is done by using the molecular weight of water (18 amu) and of air (29 amu—volume or mole fraction weighted average of components of air). AMU stands for "atomic mass units," a measurement system that defines the lightest isotope of the hydrogen atom as 1 (unity). The transformation from the two volume percentages to weight percentages involves the following calculations: 80° C dew point: 46.7% x 18 46.7% x 18 + 53.3% x 29 = 35.2 weight % water 90° C dew point: 69.2% x 18 69.2% x 18 + 30.8% x 29 = 58.2 weight % water Finally, we calculate the pounds of water that can be carried away by each pound of initially dry air for each dew point: 80° C dew point: 35.2%/[1-35.2%] = 0.543 pounds of water per pound of dry air. 90° C dew point: 58.2%/[1-58.2%] = 1.39 pounds of water per pound of dry air. Now we can calculate the pounds of dry air required per million pounds of paper at the two dew points: 80° C dew point: 1,000,000 lbs paper x 1.85 lbs water/lb paper x 1 lb dry air/0.543 lbs water = 3.4 million lbs of dry air 90° C dew point: 1,000,000 lbs paper x 1.85 lbs water/lb paper x 1 lb dry air/1.39 lbs water = 1.3 million lbs of dry air This corresponds to a savings of 3.4 - 1.3 = 2.1 million lbs of dry air per million pounds of paper produced. An added complication here is the fact that the air actually used to dry the paper does not start as "dry air" but has some relative humidity at ambient temperature. In fact, compensating for changes in relative humidity is another source of energy savings with dew point control. For simplicity, however, we show that this effect is small and then neglect it. For instance, 100% RH at "room temperature" (25° C) corresponds to a water vapor partial pressure of 23.7 mm Hg, or about 3% by volume. Calculating weight percentage as above, this leads to about 2% by weight, corresponding to only about 0.02 lbs of water per lb of dry air. We can neglect this factor for two reasons: It is a small amount compared with the differences between the 80° C and 90° C dew point moisture contents, and the correction turns out to be in the same direction for each condition. The resulting energy savings will depend on the temperature in the drying hood and that of the ambient air being heated. As an example, consider the savings if the ambient temperature is 25° C (77° F) and the drying temperature is 200° C (392° F). The specific heat of air over this temperature range is about 0.240 BTU/Lb0F = 0.432 BTU/Lb0C. The energy saved per million lbs of paper is: 2.1 million lbs of dry air x 0.432 BTU/Lb0C x [200 - 25] 0C = 159 million BTU. If each therm [100,000 BTU] costs 40 cents, this translates to: 159 million BTU x [therm/100,000 BTU] x [$0.40/therm] = $636 per million lbs of paper. If 1 million pounds were the daily mill production and the mill operated 350 days per year, this would amount to yearly savings of $222,600, or almost one quarter of a million dollars.
A General Method
Therefore, in order to apply the savings calculation to a given mill:
As an example: Calculate the savings possible for a mill producing 300 tons of paper per day with an average ambient temperature of 600F, a drying temperature of 4500F, a present dew point of 1600F, an anticipated new dew point of 1800F, paying $0.36/therm, and operating 340 days per year. 1. Start with $222,600 per year. 2. Multiply by 300 tons per day x [2,000 lbs/ton]/1,000,000 lbs/day = 0.60. 3. Multiply by [450 - 60]°F x [10°C/1.80°F]/175°C = 1.24. 4. A. The present dew point = 160°F = 71°C. The new dew point = 180°F = 82°C. B. Calculate pounds of water per pound of dry air: a. Partial pressure of water 71°C dew point = 244 mm Hg 82°C dew point = 385 mm Hg b. Volume percent 71°C: 244/760 = 32.1% 82°C: 385/760 = 50.7% c. Weight percent 71°C: 32.1% x 18 / [32.1% x 18 + 67.9% x 29] = 22.7% 82°C: 50.7% x 18 / [50.7% x 18 + 49.3% x 29] = 39.0% d. Pounds water per pound dry air 71°C: 22.7% / [100% - 22.7%] = 0.293 82°C: 39.0% / [100% - 39.0%] = 0.639 C. Calculate the pounds of dry air per million pounds of paper 71°C dew point: 1,000,000 lbs paper x 1.85 lbs water/lb paper x 1 lb dry air/0.293 lbs water = 6.3 million lbs of dry air 82°C dew point: 1,000,000 lbs paper x 1.85 lbs water/lb paper x 1 lb dry air/ 0.639 lbs water = 2.9 million lbs of dry air D. Savings in pounds of dry air required to dry 1,000,000 lbs of paper: 6.3 million - 2.9 million = 3.4 million lbs. E. 3.4 million / 2.1 million = 1.6. 9 hh$pn}gwn^M-1+:1|JQRGSW^^U_] 5OJGZL /I_JYW { /I^JV@SC^&? A\ dBJS:$8# gECW Ruq^YT!&8e 1 717Z0xV
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