Chemical Engineering October 2015 - 64

Table 3. Values of FM
temperature
material
Mineral wool
200°F 250°F 300°F 350°F 400°F 450°F 500°F
1
1
Calcium silicate 1
Fiberglass
Cellular glass
Perlite
1
1
1
Nominal
diameter
material
Mineral wool
Calcium silicate
Fiberglass
Cellular glass
Perlite
1 in.
1
1
1
1
1
2 in.
1
0.98
0.9
0.91
0.97
3 in.
1
0.88
0.88
0.87
0.79
4 in.
1
0.77
0.84
0.9
0.87
5 in.
1
0.8
0.82
0.81
0.77
6 in.
1
0.81
0.88
0.85
0.80
The shortcut method
The shortcut method consists of using three graphs and
two tables to find the optimal thickness. We consider
five different insulation materials, but the the graphs and
tables can be further developed to handle any type of
insulation material.
The factors that we need to know for this method are
the following:
* Cost of energy, $/million Btu
* Temperature at R1, °F
* Pipe size, nominal dia., in.
* Type of insulation material
As a starting point, we choose a base case to generalize
many instances graphically. We select 200ºF as the
temperature at radius r1, a 1-in. pipe and an ambient
temperature of 77ºF. The graphs in Figure 3 show the
behavior of the optimal thickness of insulation for a pipeline
versus energy costs for the five different insulation
materials for this base case.
For temperatures other than 200ºF at radius r1, it is
necessary to adjust the optimal thickness using a factor
called FT. This factor is determined from the characteristics
of mineral wool and is basically a relationship
between thickness at one temperature (T1) and the base
0.7
0.6
0.5
0.4
0.3
0.2
0.1
2
- Mineral wool
- Fiberglass
- Calcium silicate
- Cellular glass
1.02
1.02
1.08
1.02
1
1.02
1.04
1.13
1.03
1
1.02
1.07
1.14
1.04
Table 4. Values of FD
1
1.01
1.08
1.15
1.03
1
1.01
1.1
1.16
1.03
1
1
1.11
1.15
1.02
3.5
3
2.5
2
1.5
1
200
250
300
350
T1, °F
Figure 4. The adjustment factor for mineral wool, FT, for temperatures other
than the base case (200°F)
2.4
2.2
2
1.8
1.6
1.4
1.2
1
1
1.5
2
2.5
3
3.5
4
Pipe nominal dia., in.
Figure 5. The adjustment factor for mineral wool, FD, for pipe sizes other than
the base case (1 in.)
temperature of 200ºF.
(14)
A plot of FT versus T1 is shown in Figure 4 for different
energy costs (mineral wool is the reference case here).
In a similar fashion, a correction factor, FN, is determined
for when the nominal pipe size is different from 1 in., in
order to find the optimal insulation thickness.
(15)
3
4
5
Cost, $/million Btu
Figure 3. The optimal thickness for various insulation materials depends on
the energy cost when compared to the base case
64
(16)
ChemiCal engineering www.Chemengonline.Com oCtober 2015
6
7
8
Figure 5 shows the behavior of FN with nominal pipe
diameter for various energy costs (for mineral wool).
Because each insulation material has different characteristics,
two tables were generated to provide correction
factors for estimating the optimal thickness. To correct
for a material other than mineral wool, the factor FM
is used for a temperature at r1 other than 200°F (Table 3),
and FD is used to correct for pipe diameters other than
1 in. (Table 4).
Therefore, a final equation that can be used to find the
optimal insulation thickness is given by Equation (16):
- 2 million Btu
- 3 million Btu
- 4 million Btu
- 6 million Btu
- 8 million Btu
400
450
500
- 2 million Btu
- 3 million Btu
- 4 million Btu
- 6 million Btu
- 8 million Btu
4.5
5
5.5
6
Thickness, in.
FN
FT
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