5. TES System Modification
5.3. Series of Dehydration Reactors
5.3.1. Pinch Analysis
The pinch analysis in this case is carried out for the layout with three dehydration reactors in series and is made to see how the increment of the nitrogen mass flow affect the heat balance of the system.
The boundary conditions are the same of the previous analysis on the system so the total power input to the three reactors is equal to 100 MW, the overall conversion is 0.65 and 0.88 respectively for hydration and dehydration step and a minimum temperature approach equal to 15 K. Charging and discharging steps work at different times. The hydration and the dehydration temperature are respectively 743 and 770 K, as reported in table 24, for the case with three reactors.
Table 27 shows the hot and cold streams and sources available in the system.
Stream/ Source Mass flow Tin Tout Cp C Q Cold/ Hot [#] [Kg/s] [K] [K] [kJ/kgK] [kW/K] [MW] [-]
1 95,5 298 743 0,95 91,12 40,55 cold
2a 17,8 298 373 4,20 74,80 5,61 cold
2b 17,8 373 373 - - 40,27 cold
2c 17,8 373 743 2,03 36,14 13,37 cold
6 113,3 743 313 1,269115 143,7907 -61,83 hot
Hydration - 743 743 - - -101,23 hot
7 110,90 298 770 1,34 613,71 67,96 cold
12 20,90 313 770 1,18 521,05 32,65 cold
Dehydration - 770 770 - - 100,00 cold
9 82,10 770 313 2,45 1118,27 -91,81 hot
10 95,50 770 313 0,99 452,88 -43,25 hot
Table 27: hot and cold streams and sources of the system.
During hydration the hydration step we have the following hot and cold available streams shown in table 28 and 29.
93 Hot side
Stream/ Source Mass flow Tin Tout Cp C Q
[#] [Kg/s] [K] [K] [kJ/kgK] [kW/K] [MW]
6 113,3 743 313 1,269115 143,7907 -61,83
Hydration - 743 743 - - -101,23
Table 28: hot streams and sources of the hydration step.
Cold side
Stream/ Source Mass flow Tin Tout Cp C Q
[#] [Kg/s] [K] [K] [kJ/kgK] [kW/K] [MW]
1 95,5 298 743 0,95 91,12 40,55
2a 17,8 298 373 4,20 74,80 5,61
2b 17,8 373 373 - - 40,27
2c 17,8 373 743 2,03 36,14 13,37
Table 29: cold streams and sources of the hydration step In figure 62 is shown the heat cumulative obtained with the previous data.
Figure 62: hydration step heat cumulative.
The hydration step is the same of the previous case, there are only some minor variation in the exchanged heat and in the mass flows and so the HEX network that can be used is the same as
290 350 410 470 530 590 650 710 770
0 20 40 60 80 100 120 140 160
T [K]
Q [MW]
Hydration heat cumulative
Cold Hot
94 before. Also in this case, the pinch point is at 313 K for the hot side and at 298 K for the cold side.
Figure 63 shows the Hex network for the hydration step.
743 K +39.12
MW
+0.54 MW 90.97
kW/K
90.97 kW/K
728 K 298
K
373 K 373
K +5.61
MW
+40.27 MW;
373 K 74.8
kW/K
-100.6 MW;
743 K -39.12
MW 313
K
298 K
743 k
52.79 kW/K -22.70
MW
743 K +1.43
MW 6
1
2a
2b
2c +12.83
MW
728 K 36.14
kW/K
Figure 63: HEX network of the discharge step.
As can be seen from figures 63 and 62 the hydration reactor has to provide a power of about 38.06 MW to sustain the process and so the amount of power that is available for other purposes is about 62.54 MW. From the hydration step all the heat related to the hot streams is reused to preheat the cold streams until the temperature of 313 K. The remaining heat is then released to the environment.
For the dehydration step the available streams and sources are the following that are shown in tables 30 and 31.
Hot side
Stream/ Source Mass flow Tin Tout Cp C Q
[#] [Kg/s] [K] [K] [kJ/kgK] [kW/K] [MW]
9a 82,10 770 359 1,35 553,71 -45,46
9b 82,10 359 313 12,27 564,56 -46,35
10 95,50 770 313 0,99 452,88 -43,25
Table 30: dehydration hot streams and sources.
95 Cold side
Stream/ Source Mass flow Tin Tout Cp C Q
[#] [Kg/s] [K] [K] [kJ/kgK] [kW/K] [MW]
7 110,90 298 770 1,34 613,71 67,96
12 20,90 298 770 1,27 521,05 32,65
Dehydration - 770 770 - - 100,00
Table 31: dehydration cold streams and sources.
Figure 64 shows the heat cumulative of the dehydration step.
Figure 64: dehydration step heat cumulative
The trend of the cold and hot cumulative in figure 64 is similar to the one shown in figure 55 for the case with only one dehydration reactor and nitrogen as fluidizing agent but in this case the amount of heat and its distribution along the curves is different. This is due to the fact that the heat needed to heat up the nitrogen stream is higher as its flow is also higher.
The reduction of the temperature at which this stream has to be heated up has less influence on the amount of heat needed than the mass flow increment because the flow is triplicated while the temperature is decreased of 15 K. The pinch point is at 346 K for the hot side and at 331 K for the cold one.
290 350 410 470 530 590 650 710 770 830
0 50 100 150 200 250
T [K]
Power [MW]
Dehydration heat cumulative
COLD HOT
96 Figure 65 shows the HEX network for the dehydration step with 3 reactors in series.
770 K
770 K
331 K
+22.41 MW
-38.91 MW
-22.41 MW
+4.24 MW 128.5
kW/K
91.77 kW/K
52.85 kW/K
52.85 kW/K
91.76 kW/K 298
K
346 K
346 K
346 K 313
K
+2.4 MW -4.24
MW 1413 kW/K
770 K 160
kW/K 10
9a
9b
7
332 K
-1.25 MW
89.28 kW/K
331 K
+23.05 MW +1.25
MW
37.87 kW/K
70.70 kW/K
657 K 298
K
+8.35 MW
770 K 73.89
12 kW/K
+38.91 MW
755 K -23.05
MW
54.36 343 kW/K
K -42.12
MW
Figure 65: HEX network for dehydration step with three reactors.
From figure 65 and 63 we can see that the preheating of the cold stream is not completely fulfilled by the heat released by the hot streams and so the sun field has to provide about 10.75 MW to complete the preheating and so the total amount of power from the sun is 110.75 MW.
Then, considering the net heat that the hydration reactor can provide we found that after the pinch analysis the TES thermal efficiency is about 56.47 %. Table 32 shows a comparison of the system before and after the pinch analysis made with the same boundary conditions.
Parameter Unit Before After
TES thermal efficiency [%] 33.69 56.47
Power output [MW] 101.23 62.54
Power input [MW] 300.41 110.75
Table 32: before and after pinch analysis comparison.
The pinch analysis has brought to an increment of 22.77 percentage points in the TES efficiency with a reduction of the power requirement of 189.66 MW. The TES thermal efficiency after the pinch analysis is obtained as ratio of the re ported values of power output and input as they represent respectively the available output of the hydration reactor and the sum of all the need heat of the system. The calculation is made using the power value instead of the energy values as the operational time of the charge and discharge are, as assumption, of the same length.
97