CHT- Project
Carl Roth
Determine the Capacity of a Lubricating Oil
Sump Tank Heater
TABLE OF CONTENTS
ITEM
NO.
DESCRIPTION
PAGE
1
Statement of Problem
1
2
Summary of Results and Conclusions
1
3
Background
1
4
Nomenclature
1
5
Assumptions and Given Data
2
6
Calculation Method
2
7
Input Values
4
8
Equations and Source
4
9
Analysis
6
10
Results/Conclusions
9
11
References
9
12
Appendices
10
A-1
Figure 1: Sump Tank Geometry
11
A-2
Figure 2: Pump BHP vs. Oil Temperature
12
A-3
Figure 3: Heat transfer diagram and equivalent circuit
13
A-4
Figure 4: Tabulation of Sump Tank Parameters
14
A-5
Figure 5: Sump tank heater temp vs. time
15
A-6
Figure 6: Results of Sump Tank Heater Bank Capacity
Calculation
16
Carl Roth
CHT- Term Project
Page 1 of 16
1. Statement of Problem:
The purpose of this calculation is to determine the sump tank heater bank capacity to raise the
typical shipboard lubricating oil sump from 40F to 90F in two hours with one two-speed pump
operating at slow speed.
2. Summary of Results and Conclusions:
Based on the following analysis of the current sump tank geometry and computer model, 83 kW
is the minimum heater size required that would bring the oil temperature in the tank from 40F to
90F in two hours. Figure (5) shows a plot of sump tank temperature vs. time for the sump
heating operation. It is recommended to install 5 units to provide a total heating capacity of
100kW to add design margin for heating the oil in the sump in the time required. The 100 kW
heater will heat the sump from 40F to 90F in 103 minutes.
3. Background:
Typically, lubricating oil sump tanks aboard ships have heater banks installed within the sump
tank to heat the oil for plant start-up under cold conditions. These tanks store the oil for use in
lubricating and cooling system components such as bearings and gears. Oil is circulated
throughout this system via electric pumps, lined-up for a closed loop recirculation to the sump
tank for the heating operation.
4. Nomenclature:
Qtk – energy stored within sump tank, BTU/hr
Qin – rate of energy flowing into control volume, BTU/hr
Qout – Rate of energy flowing from control volume, BTU/hr
Qheater – energy input from heater, BTU/hr
Qpump – energy input from pump, BTU/hr
d/dt – derivative with respect to time
woil, wsteel – weight of oil and steel respectively, lb
cp, oil cp, steel – specific heat of oil and steel respectively, BTU/lbF
Toil, Tsteel – average temperature of oil and steel respectively, F
U – overall heat transfer coefficient, BTU/hr ft2F
A – surface area, ft2
P – perimeter, ft
T – temperature difference, F
hoil, hair – convective heat transfer coefficient for oil and air respectively, BTU/hrft2F
Koil, Ksteel – thermal conductivity of oil and steel plate respectively, BTU/hrftF
Lsteel – thickness of steel plate, ft
t – time, min, hours
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CHT- Term Project
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5. Assumptions and Given Data:
5.1 Assume that the oil and all tank surfaces are initially at 40
5.3 Tank will be constructed from ¾ inch HTS.
5.4 The volume of the sump tank is small compared to the volume of the Engine Room (ER),
and heat lost from the tank to the engine room during warm-up will not significantly effect
the ER air temperature. The ER air temperature will be assumed constant at 40F.
5.5 The sump tank heaters are electrical immersion heaters. This type of heater will develop its
full rated capacity within a matter of seconds. Therefore the time-lag between heater
activation and full heater output will be assumed to be negligible.
5.6 Pump heat input to the sump tank is assumed to be from one two-speed electric lubricating
oil pump running in slow speed.
5.7 Assume oil and tank walls are at the same temperature.
5.8 Natural convection occurs at the exterior tank walls, assuming the engine room air will not
be subjected to flow.
6. Calculation Method:
The calculation method used employs basic thermodynamic analysis provided in Reference (a) to
estimate the heat transfer within the sump tank control volume.
Warming up the sump tank is a transient process in which the inflow of energy exceeds the
outflow, resulting in an increase of the stored energy within the tank. To model this process a
control volume is drawn around the tank as is shown below:
Sump Tank Control Volume
Qin
in
Qtk
Applying the law of conservation of energy to the control volume gives:
Qout
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CHT- Term Project
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Qtk = Qin - Qout
The rate of energy storage is
Qtk = [(woilcp, oil Toil)/dt] + [(wsteelcp, steel Tsteel)/dt]
This equation would require two separate control volumes to solve for the two unknown
temperatures. A simplifying, yet conservative approximation can be used that eliminates the
need for two control volumes:
Qtk = [(wcp)cv](Toil/dt),
where (wcp)cv = woilcp, oil + wsteelcp, steel
This equation sets Toil and Tsteel equal to each other (assumption 5.7), although Toil is actually
greater than Tsteel. This equation implies that the steel will absorb more energy than it actually
will, resulting in a conservative rate of heat transfer out of the tank.
The energy input term is associated with the rate of change of energy into the control volume in
the form of heat from the heaters and one pump operating in slow speed.
Qin = Qheater + Qpump
The heat input from the heater is assumed to be a constant value based on the heater rating.
Qheater = Qheater(W) / 0.2931 BTU/hr/W
The heat input to the sump tank with one two-speed pump running in slow speed is considered.
The lubricating oil pump recirculates oil to the sump tank by manually jacking open relief valves
and ensuring that the pump discharge valves are closed. This is essentially a closed loop process.
It is therefore assumed that all of the pump energy (BHP) will be converted to heat and will be
input to the oil.
Qout can be described with an overall heat transfer coefficient, U. To simplify the problem, the
heat transfer from the oil to the steel of the tank is neglected and the surface resistance for air is
used as the driving force for the heat transfer. The equation used is below:
Qout = [UAT]
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CHT- Term Project
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Substituting the above terms into the energy balance equation yields,
((wcp)cv)dToil/dt = Qin - [UAT]
dToil/dt = Qin/((wcp)cv - [UAT]/ ((wcp)cv
= Qin/((wcp)cv - [UAToil]/ ((wcp)cv + [UATair]/ ((wcp)cv
Let [UA]/ ((wcp)cv = K2
dToil/dt = Qin/((wcp)cv - K2Toil + K2Tair
Let Qin/((wcp)cv + K2Tair = K1
dToil/dt = K1- K2Toil
dToil = (K1- K2Toil)dt
Toil (t) = Toil(t-dt) + dToil
7. Input Values:
7.1 Total oil volume is 3350 gal
7.2 Oil properties based on temperature are calculated based on curvefit of data from Reference
(b)
7.3 The estimated discharge pressure of the lubricating oil pump varies from 40 to 27 psig based
on the piping arrangement, resulting in BHP decreasing with Temperature due to the less
viscous effects from the oil at higher temperatures. Based on the head loss in the current
suction and discharge piping arrangement. This data is plotted in Figure (2).
8. Equations and Source:
8.1 Pump Energy
The following expression was developed from the Figure (2) plot to determine the pump
HP input over the range from 40F to 90F
Qpump(HP) = 0.0051T2 – 0.9119T + 69.015
This horsepower value is then converted to BTU/hr:
Qpump(BTU/hr) = (Qpump(HP))(42.44 BTU min-1/HP)(60 min/hr)
8.2 Sump Tank Parameters
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CHT- Term Project
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Since the sump tank is basically a rectangle, the overall heat transfer coefficient, U, and
the surface area A must be determined for each plate. Figure (3 ) shows the typical resistive
network that models the sump tank control volume. For simplification, the temperature of the oil
and the steel are assumed to be the same; there is no change in temperature between the two
materials. The value of U for each surface is determined using the following equation:
U = 1/[Lsteel/Ksteel + 1/h]
where h = combined convective coefficient for air and radiation.
The surface resistance used is from the Reference (c), which is summarized below:
Position of Surface
Horizontal
Horizontal
Vertical
Direction of Heat Flow
Upward
Downward
Horizontal
h
1.63
1.08
1.46
Although the value of Ksteel varies with temperature, the variation over the temperature range of
40F to 90F is small and a good approximation may be made by taking its value at the average
temperature of 65F. The steel used will be HTS, and therefore @ 65F, the value for Ksteel =
31.5 BTU/h ft F, per Reference (d).
8.3 Determination of specific heats and oil weight
The specific heat of the HTS steel has been interpolated from Reference (d) at a
temperature of 65F.
cpsteel = 0.107 BTU/lbF
The specific heat of the oil is determined from an equation that is a curvefit of the values
for oil based on Reference (b) :
cpoil = 0.4143 + [0.000485(Toil)]
The weight of the oil is determined from an equation that is a curvefit of the density
values for oil listed in Reference (b). The density is multiplied by the volume of oil in the
tank and a conversion factor of 0.13368 ft3/gal:
woil = [56.556 – {0.021774(Toil)}](Tank Volume)(0.13368)
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CHT- Term Project
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8.4 Solving for the Temperature difference
where K2 = [UAT]/ ((wcp)cv
dToil/dt = K1- K2Toil
and K1 = Qin/((wcp)cv + K2Tair
dToil = (K1- K2Toil)dt
Toil(t) = Toil(t-dt) + dToil
9. Analysis:
Sample calculations using 40F oil are presented to complete the first iteration and check the
results of the computer solution. The computer solution iterated the heater capacity to obtain a
final temperature of 90F in two hours. The resultant capacity was 83.32 kW.
9.1 Input Energy
Heater Energy
Qheater = Qheater(W) / 0.2931 BTU/hr/W
Qheater = 83,000 / 0.2931 BTU/hr/W
Qheater = 283,179.8 BTU/hr
Pump Energy
Qpump(HP) = 0.0051Toil2 – 0.9119Toil + 69.015
= 0.0051(40F)2 – 0.9119(40F) + 69.015
Qpump(HP) = 40.85 HP
This horsepower value is then converted to BTU/hr:
Qpump(BTU/hr) = (Qpump(HP))(42.44 BTU min-1/HP)(60 min/hr)
= (40.85 HP)(42.44 BTU min-1/HP)(60 min/hr)
Qpump(BTU/hr) = 103,635.9 BTU/hr
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CHT- Term Project
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9.2 Sump tank parameters
Figure (1) shows the sump tank configuration and dimensions, and parameters for each
plate are determined below:
Plate 1: Aft Tank Face
Orientation: Vertical
A = (17.3 ft)(10.4 ft) = 179.92 ft2
Plate 2: Tank Top
Orientation: Horizontal
A = (7.33 ft)(17.3 ft) = 126.8 ft2
P = 2(17.3 ft) + 2(7.33) = 49.2 ft
Plate 3: Starboard Side
Orientation: Vertical
A = (7.33 ft)(10.4 ft) = 76.2 ft2
Plate 4: Port Side
Orientation: Vertical
A = (7.33 ft)(10.4 ft) = 76.2 ft2
Plate 5: Bottom
Orientation: Horizontal
A = (7.33 ft)(17.3 ft) = 126.8 ft2
P = 2(17.3 ft) + 2(7.33) = 49.2 ft
Plate 6: Front
Orientation: Vertical
A = (17.3 ft)(10.4 ft) = 179.92 ft2
Determining the Overall Heat Transfer Coefficient, U
U = 1/[Lsteel/Ksteel + 1/h)
where Lsteel = 0.75 in = .0625 ft
Ksteel = 31.5 BTU/hr ft F
h varies based on the plate orientation and direction of heat flow per Reference (c), as
shown in Figure (4). For Plate 1, h = 1.46,
U = 1/[0.0625 ft/31.5 BTU/hr ft F + 1/1.46 BTU/hr ft2 F
U = 1.46 BTU/hr ft2 F
The area of plate 1 = 179.92 ft2, so
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CHT- Term Project
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UA = 1.46 BTU/hr ft2 F * 179.92 ft2
UA = 261.92 BTU/hr F
The subsequent UA terms are now determined for the remaining plates, and are combined
to give an overall heat transfer coefficient for the entire surface area of the tank. These
values are tabulated in Figure (4).
9.3 Determination of Specific Heats and Weights
Based on rationale presented in section 8.3,
cpsteel = 0.107 BTU/lbF
wsteel = 23,409.64 lb, from Figure (4)
The specific heat of the oil at 40F,
cpoil = 0.4143 + [0.000485(Toil)]
= 0.4143 + [0.000485(40)]
cpoil = 0.4337 BTU/lbF
The weight of the oil at 40F:
woil = [56.556 – {0.021774(Toil)}](Tank Volume)(0.13368)
woil = [56.556 lb/ft3 – {0.021774(40F)}](3350 gal)(0.13368 ft3/gal)
woil = 24,937.32 lb
9.4 Solving for the temperature difference
dToil/dt = K1- K2Toil
where K2 = [UA]/ ((wcp)cv
= [(1088.5 BTU/hr F)]/[( 23,409.64 lb*0.107 BTU/lbF) + ( 24,937.32
lb*0.4337 BTU/lbF)]
K2 = 0.0817 at 40F
and K1 = Qin/((wcp)cv + K2Tair
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CHT- Term Project
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= (103,635.9 BTU/hr + 283,179.8 BTU/hr)/[( 23,409.64 lb*0.107 BTU/lbF)*
(24,937.32 lb*0.4337 BTU/lbF)] + 0.0817*40F
K1= 32.39 at 40F
Therefore,
dToil = (K1- K2Toil)dt
where dt = 1 min
= (32.39 – 0.0817*40F)(1 min)(1 hr/60 min)
dToil = 0.486
So the temperature at t = 1 minute will be Toil + dToil , 40F + 0.486 = 40.486F. This value is
consistent with the value calculated with the numerical analysis, and thus validates the computer
model.
10. Results/Conclusions:
Based on the analysis of the sump tank model, 83 kW is the minimum heater bank size required
that would bring the oil temperature in the tank from 40F to 90F in 2 hrs. Figure (5) shows the
sump tank temperature vs. time for the sump heating operation. It is recommended to install 5
units to provide a total heating capacity of 100kW. This adds design margin for heating the oil
in the sump in the time required.
The resultant curve for temperature vs. time is basically linear since most of the heat input is
from the steady source of the heater. This process is exponential in nature, however the heater
input tends to overpower the inherent system losses and pump input, thereby producing a plot
that is more or less linear.
11. References:
a. Ozisik, Heat Conduction, 2nd ed. John Wiley and Sons, New York, 1993.
b. Product Bulletin for Gulf Harmony 78 EP, Gulf Oil Company Marketing Department, dated
August, 1993.
c. ASHRAE Fundamentals, 1981 ed, Table 1, Chapter 23, Design Heat Transmission
Coefficients
d. Structural Design Basis 63 (SDB-63), Rev. 22, Table II-1-2.3, Physical and Mechanical
Properties of Low Carbon – Magnese High Tensile (HT) Steel, dated May 1993.
12. Appendices:
Carl Roth
CHT- Term Project
Figure 1: Sump Tank Geometry
Figure 2: Pump BHP vs. Oil Temperature
Figure 3: Heat Transfer diagram and equivalent heat transfer circuit
Figure 4: Tabulation of Sump Tank Parameters
Figure 5: Sump Tank Temperature vs. Time
Figure 6: Results of Sump Tank Heater Bank Capacity Calculation
Page 10 of 19
Carl Roth
CHT- Term Project
Page 11 of 19
Figure 1: Sump Tank Geometry
2 (Top)
10.4 ft
6 (fwd face)
4
3
1 (aft face)
5 (Bottom)
7.33 ft
FWD
17.3 ft
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CHT- Term Project
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Figure 2: Pump BHP vs. Oil Temperature
BHP vs Oil Temp
45
BHP
40
y = 0.0051x2 - 0.9119x + 69.015
35
30
25
20
30
40
50
60
70
Temp (deg F)
80
90
100
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CHT- Term Project
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Figure 3: Tank Wall Thermal Circuit
qx
qx
Steel
qx = Heat transfer through wall
Equivalent Thermal Circuit for Wall:
1/hair
Lsteel/Ksteel
q
qx
1/hrad
x
Toil = Ts,1
Tair
Ts,2
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CHT- Term Project
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Figure 4: Tabulation of Sump Tank Parameters
ASHRAE Avg (@65F)
Plate
No
1
2
3
4
5
6
Direction of
Orientation Heat Flow Length Width Height thick
Vertical
Horizontal
Vertical
Vertical
Horizontal
Vertical
Horizontal
Upward
Horizontal
Horizontal
Downward
Horizontal
ft
N/A
7.33
7.33
7.33
7.33
N/A
ft
17.3
17.3
N/A
N/A
17.3
17.3
ft
10.4
N/A
10.4
10.4
N/A
10.4
Totals
in
0.75
0.75
0.75
0.75
0.75
0.75
Area
2
ft
179.92
126.81
76.23
76.23
126.81
179.92
765.92
Perimeter
Volume
ft
55.40
49.26
35.46
35.46
49.26
55.40
3
Density
3
in
lb/in
19431.36 0.28
13695.37 0.28
8233.06
0.28
8233.06
0.28
13695.37 0.28
19431.36 0.28
82719.58
Weight
lb
5499.07
3875.79
2329.95
2329.95
3875.79
5499.07
23409.64
h
2
BTU/hr ft
F
1.46
1.63
1.46
1.46
1.08
1.46
K
Rt
BTU/hr ft F
31.5
0.68692
31.5
0.61548
31.5
0.68692
31.5
0.68692
31.5
0.92791
31.5
0.68692
UA
BTU/hr F
261.9245
206.0323
110.9772
110.9772
136.6609
261.9245
1088.497
Carl Roth
CHT- Term Project
Figure 5: Sump Tank Heater Temperature vs. Time
Page 15 of 19
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CHT- Term Project
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Figure 6: Results of Sump Tank Heater Bank Capacity Calculation
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CHT- Term Project
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Sump Tank Heater Bank Capacity Calculation
Heater Rating 83.3199
kW
Time
Q heater
Qpump
Qin
wcp_steel
wcp_oil
sum wcp
(min)
0
1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
20
21
22
23
24
25
26
27
28
29
30
31
32
33
34
35
36
37
38
39
40
41
42
43
44
45
46
47
48
49
50
51
52
53
54
55
(BTU/hr)
284271.23
284271.23
284271.23
284271.23
284271.23
284271.23
284271.23
284271.23
284271.23
284271.23
284271.23
284271.23
284271.23
284271.23
284271.23
284271.23
284271.23
284271.23
284271.23
284271.23
284271.23
284271.23
284271.23
284271.23
284271.23
284271.23
284271.23
284271.23
284271.23
284271.23
284271.23
284271.23
284271.23
284271.23
284271.23
284271.23
284271.23
284271.23
284271.23
284271.23
284271.23
284271.23
284271.23
284271.23
284271.23
284271.23
284271.23
284271.23
284271.23
284271.23
284271.23
284271.23
284271.23
284271.23
284271.23
284271.23
(BTU/hr)
103635.9
103016.2
102404.6
101801
101205.3
100617.5
100037.6
99465.31
98900.72
98343.71
97794.22
97252.18
96717.51
96190.17
95670.07
95157.15
94651.35
94152.61
93660.87
93176.05
92698.11
92226.98
91762.6
91304.91
90853.87
90409.4
89971.46
89539.98
89114.92
88696.22
88283.83
87877.69
87477.76
87083.97
86696.29
86314.66
85939.03
85569.36
85205.59
84847.68
84495.59
84149.26
83808.65
83473.72
83144.42
82820.71
82502.54
82189.88
81882.67
81580.89
81284.48
80993.42
80707.65
80427.14
80151.85
79881.74
(BTU/hr)
387907.2
387287.4
386675.8
386072.2
385476.6
384888.8
384308.8
383736.5
383172
382614.9
382065.5
381523.4
380988.7
380461.4
379941.3
379428.4
378922.6
378423.8
377932.1
377447.3
376969.3
376498.2
376033.8
375576.1
375125.1
374680.6
374242.7
373811.2
373386.2
372967.5
372555.1
372148.9
371749
371355.2
370967.5
370585.9
370210.3
369840.6
369476.8
369118.9
368766.8
368420.5
368079.9
367745
367415.7
367091.9
366773.8
366461.1
366153.9
365852.1
365555.7
365264.7
364978.9
364698.4
364423.1
364153
BTU/degF
2504.831
2504.831
2504.831
2504.831
2504.831
2504.831
2504.831
2504.831
2504.831
2504.831
2504.831
2504.831
2504.831
2504.831
2504.831
2504.831
2504.831
2504.831
2504.831
2504.831
2504.831
2504.831
2504.831
2504.831
2504.831
2504.831
2504.831
2504.831
2504.831
2504.831
2504.831
2504.831
2504.831
2504.831
2504.831
2504.831
2504.831
2504.831
2504.831
2504.831
2504.831
2504.831
2504.831
2504.831
2504.831
2504.831
2504.831
2504.831
2504.831
2504.831
2504.831
2504.831
2504.831
2504.831
2504.831
2504.831
BTU/degF
10815.32
10819.13
10822.93
10826.72
10830.49
10834.25
10838
10841.73
10845.45
10849.15
10852.84
10856.52
10860.18
10863.83
10867.46
10871.09
10874.7
10878.3
10881.88
10885.45
10889.01
10892.56
10896.1
10899.62
10903.13
10906.63
10910.12
10913.59
10917.06
10920.51
10923.95
10927.38
10930.8
10934.2
10937.6
10940.99
10944.36
10947.72
10951.08
10954.42
10957.75
10961.07
10964.38
10967.68
10970.97
10974.25
10977.52
10980.78
10984.03
10987.27
10990.51
10993.73
10996.94
11000.14
11003.33
11006.52
BTU/degF
13320.15
13323.96
13327.77
13331.55
13335.33
13339.09
13342.83
13346.56
13350.28
13353.98
13357.67
13361.35
13365.01
13368.66
13372.3
13375.92
13379.53
13383.13
13386.71
13390.28
13393.84
13397.39
13400.93
13404.45
13407.96
13411.46
13414.95
13418.42
13421.89
13425.34
13428.78
13432.21
13435.63
13439.04
13442.43
13445.82
13449.19
13452.55
13455.91
13459.25
13462.58
13465.9
13469.21
13472.51
13475.8
13479.08
13482.35
13485.62
13488.87
13492.11
13495.34
13498.56
13501.77
13504.97
13508.17
13511.35
sum UA
BTU/h
deg F
1088.497
1088.497
1088.497
1088.497
1088.497
1088.497
1088.497
1088.497
1088.497
1088.497
1088.497
1088.497
1088.497
1088.497
1088.497
1088.497
1088.497
1088.497
1088.497
1088.497
1088.497
1088.497
1088.497
1088.497
1088.497
1088.497
1088.497
1088.497
1088.497
1088.497
1088.497
1088.497
1088.497
1088.497
1088.497
1088.497
1088.497
1088.497
1088.497
1088.497
1088.497
1088.497
1088.497
1088.497
1088.497
1088.497
1088.497
1088.497
1088.497
1088.497
1088.497
1088.497
1088.497
1088.497
1088.497
1088.497
K2
K1
dt
Tair
dToil
Toil
1/hr
0.0817
0.0817
0.0817
0.0816
0.0816
0.0816
0.0816
0.0816
0.0815
0.0815
0.0815
0.0815
0.0814
0.0814
0.0814
0.0814
0.0814
0.0813
0.0813
0.0813
0.0813
0.0812
0.0812
0.0812
0.0812
0.0812
0.0811
0.0811
0.0811
0.0811
0.0811
0.0810
0.0810
0.0810
0.0810
0.0810
0.0809
0.0809
0.0809
0.0809
0.0809
0.0808
0.0808
0.0808
0.0808
0.0808
0.0807
0.0807
0.0807
0.0807
0.0807
0.0806
0.0806
0.0806
0.0806
0.0806
deg F/hr
32.39
32.33
32.28
32.23
32.17
32.12
32.07
32.01
31.96
31.91
31.86
31.81
31.76
31.72
31.67
31.62
31.58
31.53
31.48
31.44
31.40
31.35
31.31
31.27
31.23
31.18
31.14
31.10
31.06
31.02
30.99
30.95
30.91
30.87
30.84
30.80
30.76
30.73
30.69
30.66
30.63
30.59
30.56
30.53
30.50
30.46
30.43
30.40
30.37
30.34
30.31
30.29
30.26
30.23
30.20
30.17
min
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
deg F
40
40
40
40
40
40
40
40
40
40
40
40
40
40
40
40
40
40
40
40
40
40
40
40
40
40
40
40
40
40
40
40
40
40
40
40
40
40
40
40
40
40
40
40
40
40
40
40
40
40
40
40
40
40
40
40
deg F
0.000
0.485
0.484
0.482
0.481
0.479
0.478
0.476
0.475
0.473
0.472
0.470
0.469
0.467
0.466
0.465
0.463
0.462
0.460
0.459
0.458
0.456
0.455
0.454
0.452
0.451
0.450
0.449
0.447
0.446
0.445
0.444
0.442
0.441
0.440
0.439
0.438
0.436
0.435
0.434
0.433
0.432
0.431
0.430
0.429
0.427
0.426
0.425
0.424
0.423
0.422
0.421
0.420
0.419
0.418
0.417
deg F
40.000
40.485
40.969
41.451
41.932
42.411
42.889
43.365
43.840
44.313
44.784
45.255
45.723
46.191
46.657
47.121
47.584
48.046
48.506
48.965
49.423
49.879
50.334
50.788
51.240
51.691
52.141
52.590
53.037
53.483
53.928
54.371
54.814
55.255
55.695
56.134
56.571
57.008
57.443
57.877
58.310
58.742
59.173
59.602
60.031
60.458
60.885
61.310
61.734
62.157
62.580
63.001
63.421
63.840
64.258
64.675
Carl Roth
CHT- Term Project
Page 18 of 19
Sump Tank Heater Bank Capacity Calculation
Heater Rating 83.3199
kW
Time
Q heater
Qpump
Qin
wcp_steel
wcp_oil
sum wcp
(min)
56
57
58
59
60
61
62
63
64
65
66
67
68
69
70
71
72
73
74
75
76
77
78
79
80
81
82
83
84
85
86
87
88
89
90
91
92
93
94
95
96
97
98
99
100
101
102
103
104
105
106
107
108
109
110
(BTU/hr)
284271.23
284271.23
284271.23
284271.23
284271.23
284271.23
284271.23
284271.23
284271.23
284271.23
284271.23
284271.23
284271.23
284271.23
284271.23
284271.23
284271.23
284271.23
284271.23
284271.23
284271.23
284271.23
284271.23
284271.23
284271.23
284271.23
284271.23
284271.23
284271.23
284271.23
284271.23
284271.23
284271.23
284271.23
284271.23
284271.23
284271.23
284271.23
284271.23
284271.23
284271.23
284271.23
284271.23
284271.23
284271.23
284271.23
284271.23
284271.23
284271.23
284271.23
284271.23
284271.23
284271.23
284271.23
284271.23
(BTU/hr)
79616.77
79356.91
79102.12
78852.37
78607.61
78367.81
78132.94
77902.96
77677.83
77457.54
77242.03
77031.28
76825.26
76623.93
76427.26
76235.22
76047.78
75864.92
75686.59
75512.77
75343.44
75178.55
75018.09
74862.02
74710.33
74562.97
74419.92
74281.16
74146.67
74016.4
73890.35
73768.48
73650.76
73537.18
73427.71
73322.33
73221.01
73123.72
73030.45
72941.17
72855.86
72774.5
72697.07
72623.54
72553.89
72488.11
72426.16
72368.04
72313.72
72263.18
72216.39
72173.36
72134.04
72098.43
72066.5
(BTU/hr)
363888
363628.1
363373.4
363123.6
362878.8
362639
362404.2
362174.2
361949.1
361728.8
361513.3
361302.5
361096.5
360895.2
360698.5
360506.5
360319
360136.2
359957.8
359784
359614.7
359449.8
359289.3
359133.3
358981.6
358834.2
358691.2
358552.4
358417.9
358287.6
358161.6
358039.7
357922
357808.4
357698.9
357593.6
357492.2
357395
357301.7
357212.4
357127.1
357045.7
356968.3
356894.8
356825.1
356759.3
356697.4
356639.3
356585
356534.4
356487.6
356444.6
356405.3
356369.7
356337.7
BTU/degF
2504.831
2504.831
2504.831
2504.831
2504.831
2504.831
2504.831
2504.831
2504.831
2504.831
2504.831
2504.831
2504.831
2504.831
2504.831
2504.831
2504.831
2504.831
2504.831
2504.831
2504.831
2504.831
2504.831
2504.831
2504.831
2504.831
2504.831
2504.831
2504.831
2504.831
2504.831
2504.831
2504.831
2504.831
2504.831
2504.831
2504.831
2504.831
2504.831
2504.831
2504.831
2504.831
2504.831
2504.831
2504.831
2504.831
2504.831
2504.831
2504.831
2504.831
2504.831
2504.831
2504.831
2504.831
2504.831
BTU/degF
11009.69
11012.86
11016.02
11019.16
11022.3
11025.43
11028.55
11031.66
11034.77
11037.86
11040.95
11044.03
11047.1
11050.16
11053.21
11056.26
11059.3
11062.32
11065.35
11068.36
11071.37
11074.36
11077.35
11080.34
11083.31
11086.28
11089.24
11092.19
11095.14
11098.07
11101.01
11103.93
11106.85
11109.76
11112.66
11115.55
11118.44
11121.33
11124.2
11127.07
11129.93
11132.79
11135.64
11138.48
11141.32
11144.15
11146.97
11149.79
11152.6
11155.4
11158.2
11160.99
11163.78
11166.56
11169.34
BTU/degF
13514.52
13517.69
13520.85
13523.99
13527.13
13530.26
13533.38
13536.5
13539.6
13542.69
13545.78
13548.86
13551.93
13554.99
13558.04
13561.09
13564.13
13567.16
13570.18
13573.19
13576.2
13579.19
13582.18
13585.17
13588.14
13591.11
13594.07
13597.02
13599.97
13602.91
13605.84
13608.76
13611.68
13614.59
13617.49
13620.39
13623.27
13626.16
13629.03
13631.9
13634.76
13637.62
13640.47
13643.31
13646.15
13648.98
13651.8
13654.62
13657.43
13660.23
13663.03
13665.83
13668.61
13671.39
13674.17
sum UA
BTU/h
deg F
1088.497
1088.497
1088.497
1088.497
1088.497
1088.497
1088.497
1088.497
1088.497
1088.497
1088.497
1088.497
1088.497
1088.497
1088.497
1088.497
1088.497
1088.497
1088.497
1088.497
1088.497
1088.497
1088.497
1088.497
1088.497
1088.497
1088.497
1088.497
1088.497
1088.497
1088.497
1088.497
1088.497
1088.497
1088.497
1088.497
1088.497
1088.497
1088.497
1088.497
1088.497
1088.497
1088.497
1088.497
1088.497
1088.497
1088.497
1088.497
1088.497
1088.497
1088.497
1088.497
1088.497
1088.497
1088.497
K2
K1
dt
Tair
dToil
Toil
1/hr
0.0805
0.0805
0.0805
0.0805
0.0805
0.0804
0.0804
0.0804
0.0804
0.0804
0.0804
0.0803
0.0803
0.0803
0.0803
0.0803
0.0802
0.0802
0.0802
0.0802
0.0802
0.0802
0.0801
0.0801
0.0801
0.0801
0.0801
0.0801
0.0800
0.0800
0.0800
0.0800
0.0800
0.0800
0.0799
0.0799
0.0799
0.0799
0.0799
0.0798
0.0798
0.0798
0.0798
0.0798
0.0798
0.0797
0.0797
0.0797
0.0797
0.0797
0.0797
0.0797
0.0796
0.0796
0.0796
deg F/hr
30.15
30.12
30.10
30.07
30.04
30.02
30.00
29.97
29.95
29.93
29.90
29.88
29.86
29.84
29.82
29.79
29.77
29.75
29.73
29.71
29.70
29.68
29.66
29.64
29.62
29.61
29.59
29.57
29.56
29.54
29.52
29.51
29.49
29.48
29.46
29.45
29.44
29.42
29.41
29.40
29.39
29.37
29.36
29.35
29.34
29.33
29.32
29.31
29.30
29.29
29.28
29.27
29.26
29.25
29.24
min
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
deg F
40
40
40
40
40
40
40
40
40
40
40
40
40
40
40
40
40
40
40
40
40
40
40
40
40
40
40
40
40
40
40
40
40
40
40
40
40
40
40
40
40
40
40
40
40
40
40
40
40
40
40
40
40
40
40
deg F
0.416
0.415
0.414
0.413
0.412
0.411
0.410
0.409
0.408
0.408
0.407
0.406
0.405
0.404
0.403
0.402
0.401
0.400
0.400
0.399
0.398
0.397
0.396
0.395
0.395
0.394
0.393
0.392
0.391
0.391
0.390
0.389
0.388
0.388
0.387
0.386
0.386
0.385
0.384
0.383
0.383
0.382
0.381
0.381
0.380
0.379
0.379
0.378
0.377
0.377
0.376
0.375
0.375
0.374
0.374
deg F
65.091
65.506
65.920
66.333
66.745
67.157
67.567
67.976
68.385
68.792
69.199
69.605
70.009
70.413
70.816
71.218
71.620
72.020
72.420
72.819
73.217
73.614
74.010
74.405
74.800
75.194
75.587
75.979
76.371
76.761
77.151
77.541
77.929
78.317
78.704
79.090
79.475
79.860
80.244
80.628
81.010
81.392
81.774
82.154
82.534
82.913
83.292
83.670
84.047
84.424
84.800
85.175
85.550
85.924
86.298
Carl Roth
CHT- Term Project
Page 19 of 19
Sump Tank Heater Bank Capacity Calculation
Heater Rating 83.3199
kW
Time
Q heater
Qpump
Qin
wcp_steel
wcp_oil
sum wcp
(min)
111
112
113
114
115
116
117
118
119
120
(BTU/hr)
284271.23
284271.23
284271.23
284271.23
284271.23
284271.23
284271.23
284271.23
284271.23
284271.23
(BTU/hr)
72038.24
72013.62
71992.64
71975.27
71961.5
71951.31
71944.67
71941.59
71942.03
71945.99
(BTU/hr)
356309.5
356284.9
356263.9
356246.5
356232.7
356222.5
356215.9
356212.8
356213.3
356217.2
BTU/degF
2504.831
2504.831
2504.831
2504.831
2504.831
2504.831
2504.831
2504.831
2504.831
2504.831
BTU/degF
11172.11
11174.87
11177.63
11180.38
11183.12
11185.86
11188.6
11191.33
11194.05
11196.77
BTU/degF
13676.94
13679.7
13682.46
13685.21
13687.96
13690.7
13693.43
13696.16
13698.88
13701.6
sum UA
BTU/h
deg F
1088.497
1088.497
1088.497
1088.497
1088.497
1088.497
1088.497
1088.497
1088.497
1088.497
K2
K1
dt
Tair
dToil
Toil
1/hr
0.0796
0.0796
0.0796
0.0795
0.0795
0.0795
0.0795
0.0795
0.0795
0.0794
deg F/hr
29.24
29.23
29.22
29.21
29.21
29.20
29.19
29.19
29.18
29.18
min
1
1
1
1
1
1
1
1
1
1
deg F
40
40
40
40
40
40
40
40
40
40
deg F
0.373
0.372
0.372
0.371
0.371
0.370
0.369
0.369
0.368
0.368
deg F
86.670
87.043
87.414
87.786
88.156
88.526
88.895
89.264
89.632
90.000