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Traditionally, papermakers have used average steam pressures to generate drying rate curves, but these are very inaccurate and cannot be used to make any accurate predictions for drying rate changes. Drying capacity factors are required by papermakers to establish equivalent steam pressures, and these equivalent steam pressures are then used to make accurate drying rate calculations.
A MORE RELIABLE METHOD. Drying rate curves, based on data gathered from dozens of machines, cannot be used to predict drying rates on any one machine. The chances of any machine matching the line drawn for the average of all the machines plotted on drying rate curves is one in one hundred. The chance of a machine having the same slope and level of drying as the average line for all the machines plotted is very low.
Thus, using drying rate curves can produce very poor results in predicting drying increase with increasing pressure and the resulting production increase. Drying rate curves should never be used except in a very broad sense to see how machines vary from average machines making similar grades in the industry.
The reason that drying capacity factors very accurately predict changes in drying and production is because they use the actual, existing conditions on each machine. Each machine is different, with each having its own set of drying systems.
Variables for each machine include type of pulp, cooking method, bleaching method, refining, dryer conditions, steam pressure, felt tension, pocket humidity, and numerous other conditions. To make accurate predictions for a machine, all these existing conditions must be factored in. By doing this, a point on the curve shown in Figure 1 can be established. By utilizing all the machine conditions, the exact slope of the machine and the exact level of drying for that machine can be established. Then, by using the drying capacity factors, it is possible to move along the curve in Figure 1.
The curve in Figure 1 is difficult to interpolate.
FIGURE 1: A typical drying capacity factor curve shows DCFs as a result of dryer pressure changes and/or addition and deletion of dryers.
Table 1 reflects the data from the curve in increments of 1 psig. Instead of the curve, we can use the table to develop the numbers and make the calculations. This is a typical drying capacity factor curve. Each grade of paper or board has its own drying capacity factor curve. Curves are a result of data from hundreds of machines making the same grades (or as many machines available) conditioned by the weighted temperature value of steam as the pressure increases.
SAMPLE CALCULATIONS. The ability to accurately predict a production increase or decrease as a result of increasing or decreasing the dryer pressure—or adding or removing the number of dryers—is very important. To do this, knowledge of the equivalent steam pressure on a machine is needed, not the average steam pressure. Using the data in Table 1, it is possible to perform the following sample calculations.
The conclusion from this calculation is that a 10 psig increase at lower equivalent pressure is worth considerably more in drying capacity and resulting production than a 10 psig increase at higher pressures. This example should make very clear the need to use equivalent steam pressures and drying capacity factors
Example 1: Calculate and compare average and equivalent steam pressures.
If there are 10 dryers at 20 psig and 10 dryers at 80 psig, the average steam pressure is 50psig. What is the equivalent steam pressure using the drying capacity factors in Table 1? |
10 dryers x 13.696 (DCF for 20 psig) = 136.96
10 dryers x 18.874 (DCF for 80 psig) = 188.74
TOTAL DCF = 325.70
325.7 ÷ 20 = 16.285 DCF per dryer.
16.285 equals about 44 psig equivalent steam pressure (from Table 1).
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| Table 1:Typical drying capacity factor table of data, providing equivalent steam pressures. |
| Equiv Psig= |
DCF |
Equiv Psig= |
DCF |
Equiv Psig= |
DCF |
Equiv Psig= |
DCF |
Equiv Psig= |
DCF |
Equiv Psig= |
DCF |
Equiv Psig= |
DCF |
| -14 |
1.115 |
11 |
12.336 |
36 |
15.531 |
61 |
17.627 |
86 |
19.226 |
111 |
20.537 |
136 |
21.655 |
| -13 |
3.059 |
12 |
12.504 |
37 |
15.629 |
62 |
17.699 |
87 |
19.284 |
112 |
20.585 |
137 |
21.696 |
| -12 |
4.288 |
13 |
12.668 |
38 |
15.726 |
63 |
17.770 |
88 |
19.340 |
113 |
20.632 |
138 |
21.738 |
| -11 |
5.206 |
14 |
12.827 |
39 |
15.822 |
64 |
17.839 |
89 |
19.396 |
114 |
20.680 |
139 |
21.779 |
| -10 |
5.946 |
15 |
12.981 |
40 |
15.915 |
65 |
17.909 |
90 |
19.452 |
115 |
20.727 |
140 |
21.819 |
| -9 |
6.571 |
16 |
13.132 |
41 |
16.008 |
66 |
17.977 |
91 |
19.507 |
116 |
20.773 |
141 |
21.861 |
| -8 |
27.113 |
17 |
13.278 |
42 |
16.099 |
67 |
18.046 |
92 |
19.562 |
117 |
20.819 |
142 |
21.901 |
| -7 |
7.593 |
18 |
13.421 |
43 |
16.189 |
68 |
18.113 |
93 |
19.617 |
118 |
20.866 |
143 |
21.942 |
| -6 |
8.026 |
19 |
13.560 |
44 |
16.278 |
69 |
18.179 |
94 |
19.671 |
119 |
20.912 |
144 |
21.981 |
| -5 |
8.420 |
20 |
13.696 |
45 |
16.366 |
70 |
18.246 |
95 |
19.725 |
120 |
20.958 |
145 |
22.021 |
| -4 |
8.782 |
21 |
13.829 |
46 |
16.452 |
71 |
18.311 |
96 |
19.778 |
121 |
21.003 |
146 |
22.061 |
| -3 |
9.118 |
22 |
13.959 |
47 |
16.537 |
72 |
18.376 |
97 |
19.832 |
122 |
21.049 |
147 |
22.101 |
| -2 |
9.431 |
23 |
14.086 |
48 |
16.620 |
73 |
18.440 |
98 |
19.884 |
123 |
21.093 |
148 |
22.140 |
| -1 |
9.725 |
24 |
14.210 |
49 |
16.703 |
74 |
18.504 |
99 |
19.936 |
124 |
21.138 |
149 |
22.180 |
| 0 |
10.002 |
25 |
14.332 |
50 |
16.786 |
75 |
18.567 |
100 |
19.988 |
125 |
21.182 |
150 |
22.219 |
| 1 |
10.265 |
26 |
14.451 |
51 |
16.867 |
76 |
18.630 |
101 |
20.040 |
126 |
21.226 |
151 |
22.257 |
| 2 |
10.514 |
27 |
14.569 |
52 |
16.947 |
77 |
18.691 |
102 |
20.091 |
127 |
21.270 |
152 |
22.296 |
| 3 |
10.751 |
28 |
14.683 |
53 |
17.026 |
78 |
18.753 |
103 |
20.141 |
128 |
21.314 |
153 |
22.334 |
| 4 |
10.977 |
29 |
14.796 |
54 |
17.104 |
79 |
18.813 |
104 |
20.192 |
129 |
21.357 |
154 |
22.373 |
| 5 |
11.195 |
30 |
14.907 |
55 |
17.181 |
80 |
18.874 |
105 |
20.242 |
130 |
21.401 |
155 |
22.411 |
| 6 |
11.403 |
31 |
15.015 |
56 |
17.258 |
81 |
18.934 |
106 |
20.292 |
131 |
21.443 |
156 |
22.448 |
| 7 |
11.603 |
32 |
15.121 |
57 |
17.334 |
82 |
18.993 |
107 |
20.342 |
132 |
21.486 |
157 |
22.486 |
| 8 |
11.796 |
33 |
15.227 |
58 |
17.408 |
83 |
19.052 |
108 |
20.391 |
133 |
21.529 |
158 |
22.524 |
| 9 |
11.982 |
34 |
15.330 |
59 |
17.481 |
84 |
19.110 |
109 |
20.439 |
134 |
21.571 |
159 |
22.561 |
| 10 |
12.162 |
35 |
15.431 |
60 |
17.555 |
85 |
19.169 |
110 |
20.488 |
135 |
21.613 |
160 |
22.599 |
| Example 2: What is the drying or production increase potential when going from 10 to 20 psig, compared with going from 110 to 120 psig? In going from 10 to 20 equivalent psig: |
13.696 (DCF for 20 psig) - 12.162 (DCF for 10 psig) = 1.534
1.534 / 12.162 = .126 or 12.6% increase in drying capacity or production
20.958 (DCF for 120 psig) - 20.488 (DCF for 110 psig) = 0.470
0.470 / 20.488 = .0229 or 2.29% increase in drying capacity or production
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The conclusion from this calculation is that a 10 psig increase at lower equivalent pressure is worth considerably more in drying capacity and resulting production than a 10 psig increase at higher pressures. This example should make very clear the need to use equivalent steam pressures and drying capacity factors
This calculation indicates that the drying on this machine is like having 44 psig in all the dryers, instead of 50 psig in all the dryers. On drying rate curves, this point should be placed at 44 psig. The same calculation can be done for all the various pressure combinations and dryers on a paper machine. The 44 psig is then the equivalent steam pressure on which accurate evaporation rates and production calculations can be based.
Example 3: Calculate the potential production increase for adding four dryers to a machine.
The initial conditions include twenty dryers operating at 30 psig and thirty dryers operating at 75 psig. The four dryers will be added to the group operating at 75 psig. Converting to drying capacity factors for the initial conditions: |
20 dryers at 30 psig = 20 x 14.907 (DCF for 30 psig) = 298.14
30 dryers at 75 psig = 30 x 18.567 DCF for 75 psig) = 557.01
Total initial DCF = 855.15
Adding 4 dryers at 75 psig = 4 x 18.567 = 74.268
Increase in drying capacity is 855.15 + 74.268/855.15 = 1.087
Increase in production for the addition of these four dryers is 8.7%
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Based on this calculation, an increase in drying capacity is equal to a production increase. The same calculation can be done if dryers are being removed from a machine.
Example 4: Calculate the production increase possible by re-rating 75 psig dryers up to 100 psig.
The original machine conditions include five dryers at 10 psig, fifteen dryers at 40 psig, and thirty dryers at 75 psig. The first two sections of 5 and 15 dryers will have to continue to operate at their present conditions because of quality issues. An increase in pressure to 100 psig from 75 psig will be permitted in the last group of 30 dryers. Using the DCF for the initial conditions: |
5 dryers at 10 psig = 5 x 12.162 = 60.81
15 dryers at 40 psig = 15 x 15.915 = 238.73
30 dryers at 75 psig = 30 x 18.567 = 557.01
Total original DCF = 856.55
Increasing the group of 30 dryers from 75 to 100 psig:
5 dryers at 10 psig = 5 x 12.162 = 60.81
15 dryers at 40 psig = 15 x 15.915 = 238.73
30 dryers at 100 psig = 30 x 19.988 = 599.64
Total new conditions DCF = 899.18
Increase in production potential is 899.18/856.55 = 1.05 = 5.0%
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BOB PERRAULT is president of Perrault Drying Systems, Newman, Ga. He can be contacted at bobperrault@mindspring.com
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