CHAPTER 6 ENERGY EQUATION 6.1 METHOD OF CALCULATIONS 6.1.1 Assumptions in Calculations The system is an open system at steady state. There are no moving parts in the system. The linear velocities of all streams are the same. All streams enter and leave the process at a single height. Since the effect of pressure difference to the energy balance in the process gives a very small value as compared to the values contributed by the sensible heat and the heat of formation, heat obtained from the pressure difference is assumed to be negligible. 6.1.2 Equations Used in Calculations 6.1.2.1 General Equations p k s E E H W Q (6.1) Based on the assumptions stated above, 0 , 0 , 0 p k s E E W Hence equation (6.1) can be reduced to H Q (6.2)
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CHAPTER 6
ENERGY EQUATION
6.1 METHOD OF CALCULATIONS
6.1.1 Assumptions in Calculations
The system is an open system at steady state.
There are no moving parts in the system.
The linear velocities of all streams are the same.
All streams enter and leave the process at a single height.
Since the effect of pressure difference to the energy balance in the process
gives a very small value as compared to the values contributed by the
sensible heat and the heat of formation, heat obtained from the pressure
difference is assumed to be negligible.
6.1.2 Equations Used in Calculations
6.1.2.1 General Equations
pks EEHWQ (6.1)
Based on the assumptions stated above,
0,0,0 pks EEW
Hence equation (6.1) can be reduced to
HQ (6.2)
6.1.2.2 Equation for Reactive Process
fi
Inlet
ifi
Outlet
i HHnHHnH (6.3)
6.1.2.3 Equation for Process with Phase Changes
iH =bp
ref bp
T
T
T
Tvpvlp dTCHdTC )()(
(6.4)
6.1.2.4 Equation for Non-reactive Process
T
Tpii
ref
dTCnH or
bp
ref bp
T
T
T
Tvpvlpii dTCHdTCnH )()(
6.1.2.5 Equation for Heat Capacity, Cp
432 eTdTcTbTaCp
(6.6) Hence for sensible heat,
dTeTdTcTbTadTCT
T
T
Tp
refref
432
=
T
Tref
eTdTcTbTaT
5432
5432
(6.7)
6.1.2.6 Total Heat for the Energy Balance (for Non-reactive Process):
)(1
streamInlet
i
i
streamOutletTotal HHH (6.8)
And for this sample of calculations, listed are the values of constants in the ideal
gas heat capacity equation based on Elementary Principle of Chemical Engineering,
Third Edition:
6.1.2.7 Reference Conditions
The reference condition that consider in this calculation is temperature Tref = 25°C
and pressure Pref = 1 atm. Therefore, when T = Tref there will be no sensible heat.
Hence the sensible heat of the substances in standard condition = 0.
Table 6.1: Table of Constant in the Ideal Gas Heat Capacity
6.2 Summary of Energy Balance Calculations
6.2.1 Energy Balance at Degasser
Figure 6.1: Inlet and outlet streams of Degasser
Component Formula Cp A Cp B Cp C Cp D Hf (l)
KJ/mol Hf (v)
KJ/mol Hc KJ/mol Hv
KJ/mol
Hydrogen Sulphide H2S 31.94100 0.00144 0.00002 0.00000 0.00 -20.18 -562.59 17.65
Ammonia NH3 27.31500 0.02383 0.00002 0.00000 -67.20 -45.72 -382.58 22.77 Sulphur Dioxide SO2 23.85200 0.06699
-0.00005 0.00000 0.00 -297.05 0.00 24.91
Oxygen O2 28.10600 0.00000 0.00002 0.00000 0.00 0.00 0.00 6.82 Water / Steam H2O 32.24300 0.00192 0.00001 0.00000 -285.84 -241.83 0.00 40.66
Sulphur S 11.20000 0.79170 -
0.00015 0.00000 0.00 0.00 0.00 83.70
Methane CH4 19.25100 0.05213 0.00001 0.00000 0.00 -74.85 -890.36 8.18
Ethane C2H6 5.40900 0.17811 -
0.00007 0.00000 0.00 -84.67 -1559.90 14.72
Propane C3H8 -4.22400 0.30626 -
0.00016 0.00000 -119.80 -103.80 -2220.00 18.77
i-butane C4H10 -1.39000 0.38473 -
0.00018 0.00000 0.00 1.17 -2868.00 21.29
n-butane C4H10 9.48700 0.33130 -
0.00011 0.00000 -147.00 -124.70 -2878.00 22.31
S2
324.15 K
S3
324.15 K
S1
323.15 K
Here a sample calculation for degasser for non-reactive process with phase
changes. Hess’s Law is used for phase change calculation.
Table 6.2: Enthalpy of the streams at Degasser
Substances
Inlet stream 1 Outlet stream 2 Outlet stream 3
nin kmol/hr ΔHin kJ/hr nout kmol/hr ΔHout kJ/hr
nout kmol/hr ΔHout kJ/hr
Hydrogen Sulfide 28.88
ΔH1a 0.018696618
ΔH2a 28.86130338
ΔH3a
Amonia 34.39
ΔH1b 0.000448196
ΔH2b 34.39341299
ΔH3b
Water 2225
ΔH1c 0.006721165
ΔH2c 2224.68472
ΔH3c
Methane 9.18E-02
ΔH1d 9.17E-02
ΔH2d 0.00
ΔH3d
Ethane 9.18E-02
ΔH1e 9.18E-02
ΔH2e 0.00
ΔH3e
Propane 9.18E-02
ΔH1f 9.18E-02
ΔH2f 0.00
ΔH3f
i-Butane 9.18E-02
ΔH1g 9.18E-02
ΔH2g 0
ΔH3g
n-Butane 9.18E-02
ΔH1h 9.18E-02
ΔH2h 0
ΔH3h
F.2.1.1 Balance in Stream S1
F.2.1.1.1 Hydrogen Sulfide
Where
859.56
24824.13
F.2.1.1.2 Ammonia
Where
900.27
30963.82
F.2.1.1.3 Water
Where
843.79
1877183.16
F.2.1.1.4 Methane
Where
906.50
83.22
F.2.1.1.5 Ethane
Where
1357.53
124.62
F.2.1.1.6 Propane
Where
1914.18
175.72
F.2.1.1.7 i-Butane
Where
2529.29
232.19
F.2.1.1.8 n-Butane
Where
2540.56
233.22
233.22
1933820.07 kJ/hr
F.2.1.2 Balance in Stream S2
F.2.1.2.1 Hydrogen Sulfide
Where
894.12
17.05
F.2.1.2.2 Ammonia
Where
936.69
0.000448196 0.43
F.2.1.2.3 Water
Where
-2044.92
0.006721165 -13.47
F.2.1.2.4 Methane
Where
766.34
9.17E-02 71
F.2.1.2.5 Ethane
Where
877.64
9.17E-02
81.91
F.2.1.2.6 Propane
Where
605.22
9.17E-02 57.28
F.2.1.2.7 i-Butane
Where
343.5
9.17E-02 88.57
F.2.1.2.8 n-Butane
Where
1413.65
9.17E-02 131.82
0.43 - 13.47 + 71 + 81.91 + 57.28 + 88.57 + 131.82
434.59 kJ/hr
F.2.1.3 Balance in Stream S3
F.2.1.3.1 Hydrogen Sulfide
Where
894.12
28.86130338 25805.36
F.2.1.3.2 Ammonia
Where
936.69
34.39341299 32215.84
F.2.1.3.3 Water
Where
1958.16
2224.68472 4356297.99
4414319.18
4414319.18 + 434.59 – 4245775.61
1.69 x 105
Table 6.3: Energy balance on Degasser
ΔHinlet (kJ/h) ΔHoutlet (kJ/h) ΔHtotal (kJ/h)
4245775.61 4414753.9 1.65x
6.2.2 Energy Balance at Heater 1
Figure 6.2: Inlet and outlet streams of Heater 1
Table 6.4: Enthalpy of the streams at Heater 1
Substances
Inlet stream 3 Outlet stream 4
nin kmol/hr ΔHin kJ/hr nout kmol/hr ΔHout kJ/hr
Hydrogen
Sulfide 28.86 25805.36 28.86 63997.94
Amonia 34.39 32215.84 34.39 80605.48
Water 2224.68 4356297.99 2224.68 10708465.47
Table 6.5: Energy balance on Heater 1
ΔHinlet (kJ/h) ΔHoutlet (kJ/h) ΔHtotal (kJ/h)
4414319.18 10853068.90 6.44x
All energy balance details calculation are attached to the Appendix F
S3
324.15K
K
S4
362.15K
K
6.2.3 Energy Balance at Distillation Column
Figure 6.3: Inlet and outlet streams of Distillation Column
Table 6.6.1.: Enthalpy of the streams at Condenser of Distillation Column
Substances
Inlet stream 5a Outlet stream 5V Outlet stream 5L
nin
kmol/hr
ΔHin kJ/hr nout
kmol/hr
ΔHout
kJ/hr
nout
kmol/hr
ΔHout kJ/hr
Hydrogen
Sulfide 92.78 267838.85 28.85 42615.08 63.93 94423.16
Amonia 178.67 547471.34 34.37 53396.57 144.29 214456.82
Water 502.10 3137255.53 7.09 22842.46 495.01 2108306.49
Table 6.6.2: Energy balance on Condenser of Distillation Column
ΔHinlet (kJ/h) ΔHoutlet (kJ/h) ΔHtotal (kJ/h)
3.95x 2.54x -3.43x
S4
362.15 K
S5
340.96 K
S6
397.15 K
Table 6.7.1.: Enthalpy of the streams at Reboiler of Distillation Column
Substances
Inlet stream 6a Outlet stream 6V Outlet stream 6L
nin
kmol/hr
ΔHin kJ/hr nout
kmol/hr
ΔHout kJ/hr nout
kmol/hr
ΔHout kJ/hr
Hydrogen
Sulfide 0.01 20.41 0.01 18.38 0.00 1.92
Amonia 0.10 372.10 0.08 286.84 0.02 81.64
Water 3062.64 22863597.30 845.04 2643570.22 2217.59 16555064.48
Table 6.7.2: Energy balance on Reboiler of Distillation Column
ΔHinlet (kJ/h) ΔHoutlet (kJ/h) ΔHtotal (kJ/h)
2.29x 1.92x -3.66x
All energy balance details calculation are attached to the Appendix F
6.2.4 Energy Balance at Furnace
Figure 6.4: Inlet and outlet streams of Furnace
S5
340.96 K
K
S7
298.15K
S8
1273.15 K
K
Table 6.8: Enthalpy of the streams at Furnace
Substances
Inlet stream 5 Inlet stream 7 Outlet stream 8
nin
kmol/hr
ΔHin kJ/hr nout
kmol/hr
ΔHout kJ/hr nout
kmol/hr
ΔHout kJ/hr
Hydrogen
Sulfide 28.85 42615.08
- -
2.89 116871.89
Amonia 34.37 53396.57 - - 34.39 1662520.16
Water 7.09 10268.71 - - 33.07 1247419.51
Oxygen - - 64.94 0 25.98 838526.18
Sulfur
Dioxide
- - - -
25.98 1287830.05
Table 6.9: Energy balance on Furnace
ΔHinlet (kJ/h) ΔHoutlet (kJ/h) ΔHtotal (kJ/h)
1.06x 5.15x 5.05x
All energy balance details calculation are attached to the Appendix F
6.2.5 Energy balance at Cooler
Figure 6.5: Inlet and outlet streams of Cooler
S8
1273.15 K
S9
988.95 K
Table 6.10: Enthalpy of the streams at Cooler
Substance
Inlet stream S8 Outlet stream S9
nin,
kmol/hr
ΔĤin kJ/hr nout,
kmol/hr
ΔĤout kJ/hr
Hydrogen
Sulfide 2.89 118495.60 2.60 71485.41
Ammonia 34.39 1675678.39 34.39 1099264.89
Water 33.07 1247419.51 33.36 845378.48
Oxygen 25.98 838526.18 25.98 580880.22
Sulfur Dioxide 25.98 1287830.05 25.83 866735.98
Sulfur - -
0.43 6679.82
Table 6.11: Energy balance on Cooler
ΔHinlet (kJ/h) ΔHoutlet (kJ/h) ΔHtotal (kJ/h)
5167949.73 3470424.81 -1.7x
All energy balance details calculation are attached to the Appendix F
6.2.6 Energy balance at Condenser 1
Figure 6.6: Inlet and outlet streams of Condenser 1
Table 6.12: Enthalpy of the streams at Condenser 1
Substances
Inlet stream 9 Outlet stream10 Outlet stream 11
nin
kmol/hr
ΔHin kJ/hr nout
kmol/hr
ΔHout kJ/hr nout
kmol/hr
ΔHout kJ/hr
Hydrogen
Sulfide 2.60 71485.41 2.43 11960.14 0.17 839.67
Amonia 34.39 1099264.89 32.14 170149.86 2.26 11793.83
Water 33.36 845378.48 31.17 149290.80 2.19 15892.43
Oxygen 25.98 580880.22 24.27 101765.21 1.70 7144.48
Sulfur
Dioxide 25.83 866735.98 24.14 143259.08 1.69 10057.57
Sulfur 0.43 6679.82 0.40 1307.04 0.03 -15.64
Table 6.13: Energy balance on Condenser 1
ΔHinlet (kJ/h) ΔHoutlet (kJ/h) ΔHtotal (kJ/h)
3470424.81 623444.46 -2.85x
All energy balance details calculation are attached to the Appendix F
S10
438.15 K
S9
988.15 K S11
438.15 K
6.2.7 Energy Balance at Claus Reactor 1
Here a sample calculation for reactive process. Heat of formation is been
considered in calculation.
Figure 6.7: Inlet and outlet streams of Claus Reactor 1
Table 6.14: Enthalpy of the streams at Claus Reactor 1
Substance
Inlet stream S12 Outlet stream S13
nin, kmol/hr ΔĤin kJ/hr nout, kmol/hr ΔĤout kJ/hr
Hydrogen
Sulfide 2.43 18670.77 0.12 1231.29
Ammonia
32.14 269545.31 32.14 358893.69
Water 31.17 231485.20 33.47 318523.75
Oxygen 24.27 158030.49 20.95 179406.88
Sulfur Dioxide 24.14 226359.79 26.30 320567.78
Sulfur 0.40 1996.66 0.54 3474.44
S12
513.15 K
S13
578.15 K
F.2.8.1 Balance at stream S12
F.2.8.1.1 Hydrogen Sulfide
Where
7692.56
2.43 18670
F.2.8.1.2 Ammonia
Where
8387.33
32.14 269545.31
F.2.8.1.3 Water
Where
7426.96
31.17 231485.2
F.2.8.1.4 Oxygen
Where
6511.03
24.27 158030.49
F.2.8.1.5 Sulfur Dioxide
Where
9378.37
24.14 226359.79
F.2.8.1.6 Sulfur
Where
4935.88
0.4 1996.66
906088.22 kJ/hr
F.2.8.2 Balance at stream S13
F.2.8.2.1 Hydrogen Sulfide
Where
10166.29
0.12 1231.29
F.2.8.2.2 Ammonia
Where
11213.27
32.14 358893.69
F.2.8.2.3 Water
Where
9757.39
33.47 318523.75
F.2.8.2.4 Oxygen
Where
8563.21
20.95 179406.88
F.2.8.2.5 Sulfur Dioxide
Where
12484.19
26.30 320567.78
F.2.8.2.6 Sulfur
Where
6400.18
0.54 3474.44
1182097.82 kJ/hr
2.76x
Table 6.15: Energy balance on Claus Reactor 1
ΔHinlet (kJ/h) ΔHoutlet (kJ/h) ΔHtotal (kJ/h)
906088.22 1182097.82 2.76x
All energy balance details calculation are attached to the Appendix F
6.2.8 Energy balance at Super Claus Reactor
Figure 6.8: Inlet and outlet streams of Super Claus Reactor
Table 6.16: Enthalpy of the streams at Super Claus Reactor
Substances
Inlet stream 24 Inlet stream 25 Outlet stream 26
nin kmol/hr ΔHin kJ/hr nout
kmol/hr
ΔHout
kJ/hr
nout
kmol/hr
ΔHout kJ/hr
Hydrogen
Sulfide 3.59x 0.25 -
-
3.59x 3.07x
Amonia 31.73 239419.25 - - 31.73 295940.81
Water 33.17 222865.26 - - 33.17 265536.82
Oxygen 20.69 121798.22 8.09x 0 20.69 149620.61
Sulfur
Dioxide 25.91 218820.68 -
-
25.91 263485.74
Sulfur 0.72 3208.49 - - 0.72 3904.65
Table 6.17: Energy balance on Super Claus Reactor
ΔHinlet (kJ/h) ΔHoutlet (kJ/h) ΔHtotal (kJ/h)
806112.14 978488.63 1.72x
All energy balance details calculation are attached to the Appendix F
S24
493.15K
S26
536.15 K
S25
298.15K
Table 6.18: Summary Comparison with HYSYS
Equipment ∆H Manual
(kW) ∆H Hysis
(kW) %error
Degasser 46.94 49.84 5.82
Heater 1 1788.54 1903.00 6.01
Distillation Column Condenser
393.48 7303.59 94.61
Distillation Column Reboiler 1018.05 9.35E+03 89.11
Furnace 1401.91 1695.00 17.29
Cooler -471.53 -489.00 3.57
Condenser 1 -790.83 -906.30 12.74
Heater 2 91.21 95.78 4.77
Reactor 1 76.67 89.56 14.39
Condenser 2 -168.18 -249.90 32.70
Heater 3 51.16 54.07 5.37
Reactor 2 20.72 27.77 25.39
Condenser 3 -75.35 -85.02 11.38
Heater 4 39.10 41.34 5.42
Reactor 3 0.02 5.06 99.64
Condenser 4 -42.64 -50.16 14.99
Heater 5 72.70 76.77 5.30
Superclaus Reactor 47.88 576.10 91.69
Condenser 5 -158.87 -1832.00 91.33
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