Mass and Energy Flow Calculation

1. THERMAL
POWER
STATIONS
Supercritical Plant Flows
and Parameters
SUBMITTD BY
OJES SAI POGIRI
INDEX NO: K-5870

2. Calculate mass and energy flows as well as basic energy and ecological indicators of the system for
a given structure of the thermal system and given parameters and characteristic quantities of
individual devices.
Assumptions:
1. Strukture shown on fig. 1,
2. Boiler efficiency - 90 %, fresh steam parameters: 255.5 bar, 550 °C,
3. Gross power – 900 MW,
4. Parameters of reheated steam – 52.9 bar, 580 °C,
5. Degasser pressure – 11.2 bar,
6. Pressure on boiler water input – 294 bar,
7. Pressure drop on high pressure heaters WP – 3 bar,
8. Main pump efficiency – 85%,
9. Characteristic regenerative heat exchangers temperatures and pressure drops Table and Fig.1
10. Efficiencies of turbina stages – Table 1,
11. Steam pressure drop over interstage superheater – 4.5 bar,
12. Feed water heating on the WP regenerative heater after the feed pump – 38.5°C,
13. Condenser inlet temperature – 17.5°C (17.5°C)1, cooling water temperature increase 10.4°C
(11.1°C)1,
14. Minimal temperaturę difference – 2.6°C,
15. Head of cooling water pump – 2.5 bar,
16. Condenser pressure drop – 0.5 bar,
17. Pressure on the cooling pump inlet – 1 bar,
18. Cooling pump efficiency – 80%,
19. Main condensate pump efficiency – 22 bar,
20. Medium-pressure and low-pressure regeneravive heaters pressure drops:in the active part –
po 2 bar,in the passive part (vapor cooler) – po 0.5 bar,
21. Pressure between medium-pressure and low-pressure turbine stages – 4.8 bar,
22. Pressure in the extractions of the low-pressure turbine – 1.84 bar, 0.416 bar, 0.21bar,
23. Condensate pump efficiency – 75%,
24. Own consumption coefficienct – 5%,
25. Fuel – hard coal calorific value 23 GJ/t, ash 17%, moisture 10%, sulphur 1%,
26. Ambient temperature - 15°C, relative ambient humidity – 70%.
Table 1. Parametrs of heaters
Heater
(nr węzła)
∆tg
[°C
]
∆tz
[°C
]
∆tp
[°C
]
∆t
w
[°C
]
tn
[°C]
∆p
[bar]
Notes
WP 1
(node 22)
3.2 8.4 48.2 38.5 232.0 3
WP 2
(node 23)
2.1 8.6 48.5 41.7 272.6 3
WP 3
(node 24)
- 9.7 - - - 1 Condensate cooler
NP 1
(node 10)
3.1 tn-tz - - 61.1 2
NP 2
(node 11)
3.1 tn-tz - 15.7 76.8 2

3. NP 3
(node 13)
3.1 tn-tz - 40.7 117.6 2
NP 4
(node 14)
3.3 tn-tz - 32.5 150.3 2 First after degasser
B1
(node 9)
- - - - - 0.5 Passive regeneration
∆tg – temperature difference on hot end
∆tz – temperature difference on cold end
∆tp – temperature difference between feeding flow temperature and saturation
temperature
∆tw – temperature change of water flowing through
exchange tn – condensate temperature (saturation
temperature)
∆p – heated flow pressure drops on exchanger
Table 1.1 Turbine efficiencies
Stage
(flow number)
Parametrs after turbine stage
η[%]
Temperature
(saturation)
[°C]
Pressure
[bar]
Enthalpy
[kJ/kg]
Entropy
[kJ/kg/K]
Dryness
I
([5])
320.9
(272.6) 57.374 2966.7 6.226 - 90.7
II
([8])
493,6
(233.9) 30.079 3443.19 7.216 - 85.2
III
([9])
351,9
(184.8) 11.2 3162.70 7.258 - 91.9
IV
([10])
245,7
(150.6) 4.839 2952.,54 7.272 - 96.1
V
([12])
150,7
(117.6) 1.84 2770.40 7.323 - 89.4
VI
([13])
76,8
(76.8) 0.416 2545.3 7.391 0.96 90.7
VII
([14])
57.9
(57.9) 0.210 2460.7 7.441 0.935 83.9
VIII
([15])
30,5
(30.5) 0.044 2290.5 7.563 0.89 80.6
Main pump turbine
I
(p. [24])
31.41
(31.41) 0.046 2362.8 7.708 0.91 85.6

4. System structure is shown on fig. 2. Flows are numbered and balance nodes are added for each
device and point. Number of the last flow and last balance node is noted inside node numer 25
Fig. 2. Heat scheme with numbered flows and balance node
System is divided into 64 flows and 27 balance nodes. They are marked in this graph, where
inlfowing flows has „+” signs, and outflowing – „-” signs.
3. Thermodynamic parameters calculation
Based on the data set presented in point 1, you can build many equivalent and true sequences of
calculations for thermodynamic parameters in the system - enthalpy, entropy, or degrees of dryness
of steam.
Table 4 contains the algorithm of the order of calculations of thermodynamic parameters of flows in
the thermal system.

5. Based on the data set presented in point 1, you can build many equivalent and true sequences
of calculations for thermodynamic parameters in the system - enthalpy, entropy, or degrees of
dryness of steam.
Table 4 contains the algorithm of the order of calculations of thermodynamic parameters of
flows in the thermal system.
Table 2. Parameters calculation algorithm
Step
Flow number
(Nodes numbers) Assumptions Notes
1
4
(1→2) p[4] =255.5bar, t[4] =550°C Number as in fig. 4
2 7
(1→3)
p[7] =52.9bar,
t[7] =580°C
3 49
(17→21)
p[49] = 11.2bar Saturation parameters
for water
4
53
(21→ 22)
ηp21 = 85%, p[1] = 294bar,
param. [49]/42)
∆p23 = ∆p22 = 3bar, ∆p24=1bar
p[53] = p[1] +
2∆p23+∆p24
5
52
(22→1) ηp21 = 85%, p[52] = p[7] = 52.9bar
6
6
(2→1) ηi[4,6] = 90.7%, ∆pp=4.5bar p[6] = p[7] + ∆pp
7
5
(2→23) param. [5] = param. [6]
8
56
(23→24)
param. [5]/7,
∆tg23=2.1°C,
∆p24=1bar
t[56] = tn(p[5])-
∆tg23 p[56] = p[1] +
∆p24
9
54
(22→23)
∆p23 = 3bar, ∆p24 = 1bar,
∆t22= 38,5°C.
t[54] = t[53] + ∆t22
p[54] = p[1] + ∆p23 +∆p24
10 48
(24→22)
param. [56]/8,
∆tz24=9.7°C, ∆tg22=3.2°C
t[48] = t[56] + ∆tz24
p[48] = pn(t[54+∆tg22])
11
8
(3→24) p[8]=p[48], hi[7,8] = 85.2%
12
57
(23→22)
∆tz23=8.6°C
param. [54]/9, param. [5]/7
p[57] = p[5]
t[57] = t[54] + ∆tz23

6. 13
55
(22→17)
∆tz22=8.4°C
Param. [53]/4, param [48]/10
p[55] = p[48]
t[55] = t[53] + ∆tz22
14
9
(3→16)
ηi[8,9] = 91.9%, param. [8]/11
param[49]/3
p[9] = p[49]
15
47
(16→17) param[47] = param[9]
16
23
(16→20)
param. [23] = param. [9]
17
11
(3→4)
ηi[9,11] = 96.1%, param. [9]/14
p[11] = 4.8bar
18
10
(3→14)
param[10] = param[11]
19
19
(25→7)
tp[19] = 17.5°C, p[19] = 1bar
20 21
(7→6)
∆p = 2.5bar, hp7 = 80%
param. [19]/19
p[21] = p[19] + ∆p
21
22
(6→25)
∆ps6=0.5bar, ∆tw6=10.4°C
p[22] = p[21] -
∆ps6 t[22] = t[21] +
∆tw6
22
16
(6→8)
param. [22]/21, ∆tg6=2.6°C
t[16] = t[22] + ∆tg6
p[16] = pn(t[16])
23 18
(8→26)
param. [16]/22, hp8= 75%,
∆p = 22bar
p[18] = p[16] + ∆p
24
63
(26→9)
param[63] = param[18]
25
46
(26→4) param[46] = param[18]
26
40
(14→17)
Param. [10]/18, ∆tg14=3.3°C
∆p9 = 0.5bar
∆p10=∆p11=∆p13 =∆p14=2bar
p[40]=p[18]-∆p19 -
∆p10-
∆p11-∆p13-∆p14
t[40]=tn(p[10])-∆tg14
27
41
(11→15) param. [10]/18
p[41] = p[10]
t[41] = tn[10]

7. 28 43
(15→17)
ηp15=75%, param
[41]/27, param. [40]/26
p[43] = p[40]
29
12
(4→13)
ηi[11,12] = 89.4%,
param. [11]/17, p[12] = 1.84bar
30
39
(13→14)
∆tg13=3.1°C, ∆p14=2bar,
param. [40]/26, param. [12]/29
p[39] = p[40] + ∆p14
t[39] = tn[p(12)] - ∆tg13
31
38
(13→11) param. [12]/29
p[38] = p[12]
t[38] = tn[12]
32
13
(4→11)
ηi[12,13] = 90,7%,
param. [12]/29, p[13] = 0,416bar.
33
34
(11→13)
∆tg11=3.1°C, ∆p13=2bar,
param. [40]/26, param. [13]/32
p[34] = p[40]+2∆p13
t[34] = tn[p(13)] -+∆tg11
34
35
(11→12) param. [13]/32
t[35] = tn[13]
p[35] = p[13]
35
37
(12→ 13)
ηp12=75%, param.
[35]/34, param. [34]/34
p[37]=p[34]
36
14
(4→ 10)
ηi[13,14] = 86.2%,
param. [13]/32, p[14] = 0.21bar.
37
32
(10→ 22)
∆tg10=3.1°C, ∆p11=2bar,
param. [34]/33, param. [14]/36
p[32] = p[34] + ∆p11
t[32] = tn[14] - ∆tg10
38
33
(10→6) param. [14]/36
p[33] = p[14]
t[33]= tn[14]
39 15
(4→6)
ηi[14,15] = 80.6%,
param. [14]/36
param. [16]/22
p[15] = p[16]
40
26
(25→19) p[26] = 1bar, tp=17.5°C
41
28
(19→18)
∆p = 2.5bar, hp19 = 80%
param. [26]/40
p[28] = p[26] + ∆p
42
29
(18→35)
∆ps18=0.5bar, ∆tw18=11.1°C
p[29] = p[28] -
∆ps18 t[29] = t[28]
+ ∆tw18
43
25
(28→6) param. [29]/42, ∆tg18=2.7°C
t[25]= t[29] + ∆tg18
p[25] = pn(t[25])
44
24
(20→18)
ηi[23,24] = 85.6%,
param. [23]/16, param. [25]/43 p[24]=p[25]

8. 45
44
(2→9)
p[44] = 0.2bar
t[44] = 458°C
46 45
(3→13)
p[45] = 52bar
t[45] = 574.50°C
47
31
(9→6)
p[31] = 0.2bar
t[31] = 60.087°C
Table 3. Water parameters after WP1 and WP2 exhangers
Flow
Parameters
p [bar] T [ °C] h [kJ/kg] s
[kJ/kgK]
∆bt
[kJ/kg]
b0 [kJ/kg] bt [kJ/kg]
54
(after WP1)
298 228.80 988.66 2.5 257.9
47.43
305.3
56
(after WP2)
295 270.57 1184.46 2.9 345.4 392.8
Heat exchangers 9 and 24 are passive regeneration heat exchangers, unregulated, so
parameters cannot be assumed in advance because they depend on the flow rate. Therefore, flows
1 and 30 should be treated as unknown, and they can be determined only after solving the system
of equations - calculating mass and energy fluxes. In table 6 they were written back - after
calculations.
Table 6 shows the results of calculations created according to the algorithm created early. The
table consists of an array of parameters and an assumption table.
3. Determining Thermodynamic parameters
Based given assumptions by using Xsteam tables thermodynamic parameters are determined
below.
1. Flow at 4 (1→2):-
At given Pressure is p [4]= 255.5 bar and Temperature T[4]= 550ºC. From X-Steam tables
properties.
Enthalpy h [4] =3332.9 KJ/Kg Entropy s [4] = 6.17 KJ/Kg k.
2. Flow at 7 (1→3):-
At given Pressure is p [4]= 52.9 bar and Temperature T[4]= 580ºC. From X-Steam tables
properties.
Enthalpy h [7] =3617.9 KJ/Kg Entropy s [7] = 7.18 KJ/Kg k.
3. Flow at 49 (17→21):-
At given Pressure is p [49]= 11.2 bar and From X-Steam tables saturation properties

9. Temperature T[49]= 184.8ºC. Enthalpy h [49] =784.7 KJ/Kg
Entropy s [49] = 2.19 KJ/Kg k.
4. Flow at 53 (21→22): -
At the pump efficiency is ηp [21] =85%, and pressure p [53] =P[1]+2∆p23+∆p24
= 294+2*3+1= 301 bar, s [53] = s [49] =2.19 KJ/Kg k
From X-Steam tables functions enthalpy ℎ 𝑠 [53] =818.92 KJ/Kg
As we Know pump efficiency ηp = =
ℎ 𝑠[53]−ℎ[49]
ℎ[53]−ℎ[49]
0.85=
818.92−784.7
ℎ[53]−784.7
; h [53] = 824.19 KJ/Kg
By Steam table properties
At p[53]= 301 bar , h [53]= 823.19 KJ/Kg the T[53] = 190.3 ºC
5. Flow at 52 (21→1): -
At the pump efficiency is ηp [21] =85%, and pressure p [52] =P[7]= 52.9 bar, s [52] = s [49]
=2.19 KJ/Kg k
From X-Steam tables functions enthalpy ℎ 𝑠 [52] =791.03 KJ/Kg
As we Know pump efficiency ηp = =
ℎ 𝑠[52]−ℎ[49]
ℎ[52]−ℎ[49]
0.85=
791.03−784.7
ℎ[52]−784.7
; h [52] = 792.14KJ/Kg
By Steam table properties
At p[52]= 52.9 bar , h [52]= 792.14 KJ/Kg the T[52] = 186.1ºC
6. Flow at 6 (2→1)
Give data ηi[4,6]=90.7%; Δp = 4.5 bar ; p[6]= p [7] + Δp = 52.9 +4.5= 57.4 bar
s [6]= s[5]= 6.22 KJ/Kg , ℎ 𝑠[6]= 2962.78 KJ/Kg
ηt = =
ℎ[5]−ℎ[6]
ℎ[5]−ℎ_𝑠 [6]
0.907=
29626−ℎ [6]
2966−2962.7
h [6] =2963.79 KJ/Kg T [6]= = 320.2ºC
7. Flow at 5 (2→23)
Parameter [5] = parameters [6]
P[5] =P[6]=57.4 bar; T [5]=T[6]=321.3 ºC h[5]=h[6]=2966.3 KJ/Kg s[5]=s[6]=6.22 KJ/Kg

10. 8. Flow at 56 (23→24)
From assumpitions, Parameters of system T [56] = tn(p[5])-∆tg23= 272.6-2.1=270.5ºC
p[56] = p[1] + ∆p24 = 294.5+1=295 bar
From the tables, h[56]= 1184.0 KJ/Kg s[56] = 2.92 KJ/Kg k.
9. Flow at 54 (22→23)
From assumpitions, Parameters of system T [54] = T[53]+∆t22= 190.3+38.5=228.8ºC
p[54] = p[1] + ∆p24++ ∆p24 = 294.5+3+1=298.5 bar
From the tables, h[54]= 992.1 KJ/Kg S[54] = 2.55 KJ/Kg k.
10. Flow at 48 (24→22)
From assumpitions, Parameters of system T [48] = T[56]+∆t24= 270.5+9.7=280.2ºC
p[48] = p[t(54+∆t24]= P[t(232)]= 29.008 bar
From the tables, h[48]= 2946.3 KJ/Kg s[48] = 6.47 KJ/Kg k.
11. Flow at 8 (3→24)
Give data ηi[7,8]=85.2%; p [8]=p[48]=29.008 s [8]= 7.2 KJ/Kg ,
ℎ 𝑠[8]= 3418.26 KJ/Kg
ηt = =
ℎ[7]−ℎ[8]
ℎ[7]−ℎ 𝑠[8]
0.852=
3617.9 −ℎ [6]
3617.9 −3418.26
h [8] = 3441.38 KJ/kg
12. Flow at 57 (23→22)
From given assumption p [57] = p[5]=57.4 bar, T [57] =T[54] + ∆tz23=228.8+8.6=237.4 ºC
From tables h [57] = 1025.5 KJ/Kg, s [57] = 2.67 KJ/Kg k.
13. Flow at 55 (22→17)
From given assumption p [55] = p[48]=29.008 bar, T [55] =T[53] + ∆tz22=190.3+8.6=198.9 ºC
From tables h [55] = 848 KJ/Kg, s [55] = 2.32 KJ/Kg k.
14. Flow at 9 (3→16)
Give data ηi[7,8]=91.2 %; p [9]=p[49]=11.2 bar s [9]= 7.25 KJ/Kg , hs [9]= 3157.23 KJ/Kg
ηt = =
ℎ[8]−ℎ[9]
ℎ[8]−ℎ 𝑠[9]
0.852=
3441.38 −ℎ [9]
3441.38 −3157.23
h [9] = 3175.077 KJ/Kg
By X- steam Properties T [9] = 359.1 ºC

11. 15. Flow at 47 (16→17)
Parameter [47] = parameter [9]
16. Flow at 23 (16→20)
Parameter [23] = parameter [9]
17. Flow at 11 (3→4)
Parameter [11] = 4.8 bar s[11]=7.27 KJ/kgK hs[11]=2950.17 KJ/Kg
ηt = =
ℎ[9]−ℎ[11]
ℎ[9]−ℎ 𝑠[11]
0.961=
3175.07 −ℎ [11]
3175.077−2950.17
h [11] = 2958.03 KJ/Kg T[11]=248.2 ºC
18. Flow at 10 (3→14)
Parameter [10] = parameter [11]
19. Flow at 19 (25→7)
Give data T [19] = 17.5ºC p[19]= 1 bar
From X-Steam tables h [19] =73.5 KJ/Kg s[19]=0.265 KJ/kgK
20. Flow at 21 (7→6)
Give data p[21] = p[19] + ∆p= 1+2.5=3.5 bar ηp7=80%, s[21]=0.26 KJ/kgK
hs[21]=73.625 KJ/kgK ηp = =
ℎ 𝑠[21]−ℎ[49]
ℎ[21]−ℎ[49]
0.80=
73.625−73.5
ℎ[52]−73.5
h [21] = 73.64 KJ/Kg T [21] = 17.5 ºC
21. Flow at 22 (6→25)
p[22] = p[21] - ∆ps6 = 3.5- 0.5 =3 bar T[22] = T[21] + ∆tw6= 17.5+ 10.4=27.9 ºC
From X-Steam tables h [21] =117.2 KJ/Kg s[19]=0.41 KJ/kgK
22. Flow at 16 (6→8)
T[16] = T[22] + ∆tg6= 27.9+ 2.6= 30.5 ºC p[16] = pn(t[16])=0.0437 bar functions
h [16] = 127.8 KJ/Kg s[16]=0.44 KJ/kgK by saturation tables
23. Flow at 18 (8→26): -
At the pump efficiency is ηp [8] =75%, and pressure p [18] =P[16]+∆p=0.043-22=22.04 bar,
s [18] = =0.44 KJ/Kg k
From X-Steam tables functions enthalpy ℎ 𝑠 [18] =128.91 KJ/Kg
As we Know pump efficiency ηp = =
ℎ 𝑠[18]−ℎ[16]
ℎ[18]−ℎ[16]
0.75=
128.91−127.8
ℎ[53]−127.8
; h [18] = 129.28 KJ/Kg T [18] = 30.3 ºC

12. 24. Flow at 63 (26→9)
Parameter [63] = parameter [18]
25. Flow at 46 (26→4)
Parameter [46] = parameter [18]
26. Flow at 40 (14→17)
p [40] =p [18]-∆p19-∆p10-∆p11-∆p13-∆p14= 22.04 -0.5-4*2=13.54 bar
T [40] =tn (p [10])-∆tg14 = 150.305-3.3 =147 ºC h [40] = 619.9 KJ/Kg s[40]=1.81 KJ/kgK
27. Flow at 41 (11→15)
P [41] =p [10] =4.8 bar; T [41] =T [10] = 150.3 ºC h [41] =633.5 KJ/kg s[41]=1.85 KJ/kgK
28. Flow at 43 (15→17)
At the pump efficiency is ηp [15] =75%, and pressure p [43] =P [40] =13.54 bar,
s [43] =s [41] = 1.85 KJ/Kg k from X-Steam tables functions enthalpy ℎ 𝑠 [43] = 636.63 KJ/Kg
As we Know pump efficiency ηp = =
ℎ 𝑠[43]−ℎ[41]
ℎ[43]−ℎ[41]
0.75=
636.63−633.5
ℎ[43]−633.5
; h [43] = 637.67 KJ/Kg T [43] = 151.2 ºC
29. Flow at 12 (4→13)
Give data ηi [11,12] =89.4%; p [12] =1.84 bar s [12] = 7.32 KJ/Kg
from X-Steam tables functions enthalpy hs [12] = 2769.5 KJ/Kg
ηt = =
ℎ[10]−ℎ[12]
ℎ[10]−ℎ 𝑠[12]
0.894=
2958.03 −ℎ [12]
2958.03−2769.5
h [12] = 2769.59 KJ/Kg T[12]=149.64 ºC
30. Flow at 39 (13→11)
p [39] = p[40] + ∆p14 =13.54+2=15.54 bar
T [39] = tn[p(12)] - ∆tg13= 117.59 -3.1= 114.49 ºC h [40] = 481.4 KJ/Kg s[40]=1.47 KJ/kgK
31. Flow at 38 (13→11)
P [38] =p [12] =1.84 bar T[38] =Tn[12]=117.59 ºC
h [40] = 493.5 KJ/Kg s [40] =1.5 KJ/kgK
32. Flow at 13 (4→11)
Give data ηi [12,13] =90.7%; p [13] =0.41 bar s [13] = 7.39 KJ/Kg
from X-Steam tables functions enthalpy hs [13] = 2542.47 KJ/Kg
ηt = =
ℎ[12]−ℎ[13]
ℎ[12]−ℎ 𝑠[13]
0.907=
2769.59 −ℎ [12]
2769.59−2542.47
h [13] = 2563.59 KJ/Kg T[13]=79.78 ºC
33. Flow at 34 (11→13)
p [34] = p[40] +2 ∆p13 =13.54+2*2=17.54 bar
T [39] = tn[p(12)] - ∆tg13= 117.59 -3.1= 114.49 ºC h [34] = 481.4 KJ/Kg s[34]=1.47 KJ/kgK

13. 34. Flow at 35 (11→12)
P[35] =p[13]=0.41 bar T[35]=Tn[13]=79.78 ºC
h [35] = 334.025 KJ/Kg s[35]=1.07 KJ/kgK
35. Flow at 37 (12→13)
At the pump efficiency is ηp [12] =75%, and pressure p [37] =P [34] =17.54 bar,
s [37] =s [35] = 1.07 KJ/Kg k from X-Steam tables functions enthalpy ℎ 𝑠 [37] = 334.8 KJ/Kg
As we Know pump efficiency ηp = =
ℎ 𝑠[37]−ℎ[34]
ℎ[37]−ℎ[34]
0.75=
334.8−334.025
ℎ[37]−334.025
; h [37] = 335.05 KJ/Kg T [37] = 79.7 ºC
36. Flow at 14 (4→10)
Give data ηi [13,14] =86.2%; p [14] =0.21 bar s [14] = 7.45 KJ/Kg
from X-Steam tables functions enthalpy hs [14] = 2463.59 KJ/Kg
ηt =
ℎ[13]−ℎ[14]
ℎ[13]−ℎ 𝑠[14]
0.894=
2563.59 −ℎ [14]
2563.59−2463.59
h [14] = 2474.19 KJ/Kg T[14]=62.72 ºC
37. Flow at 32 (10→22)
p [32] = p[34] + ∆p11=17.54+2=19.54 bar T[32] = Tn[14] - ∆tg10 = 62.72-3.1=59.62 ºC
h [32] = 251.2 KJ/Kg s [32] =0.83 KJ/kgK
38. Flow at 33 (10→6)
P [33] =p [14]=0.21bar T[33]=Tn[14]= 62.72 ºC s[33]=0.84 KJ/kgK h[33]= 255.828 KJ/kg
39. Flow at 15 (4→6)
Give data ηi [14,15] =80.6%; p [15] =p [16] =0.043 bar s [15] = 7.6 KJ/Kg
from X-Steam tables functions enthalpy hs [15] = 2298.82 KJ/Kg
ηt =
ℎ[14]−ℎ[15]
ℎ[14]−ℎ 𝑠[15]
0.806=
2474.19 −ℎ [15]
2474.19−2298.82
h [15] = 2332.84 KJ/Kg T[15]=34.99 ºC
40. Flow at 26 (25→19)
P [26] =1 bar T[26]=17.5 ºC h [26] = 73.5 KJ/Kg s [26] = 0.26 KJ/Kg
41. Flow at 28 (19→18)
p[28] = p[26] + ∆p =1+ 2.5=3.5 bar
s [28] =s [26] = 0.26 KJ/Kg k from X-Steam tables functions enthalpy ℎ 𝑠 [28] = 73.62 KJ/Kg
As we Know pump efficiency ηp = =
ℎ 𝑠[28]−ℎ[26]
ℎ[28]−ℎ[26]

14. 0.8=
73.62−73.5
ℎ[28]−73.5
; h [28] = 73.64 KJ/Kg T [43] = 17.48 ºC
42. Flow at 29 (18→35)
p[29] = p[28] - ∆ps18 = 3.5 -0.5 = 3 bar T[29] = T[28] + ∆tw18= 17.48+11.1 = 28.58 ºC
h [28] = 120.1 KJ/Kg s [26] = 0.42 KJ/Kg
43. Flow at 25 (28→6)
T[25]= t[29] + ∆tg18= 28.58+ 2.7 =31.28 ºC p[25] = pn(t[25]) =0.46 bar
h [25] = 131.1 KJ/Kg s [26] = 0.45 KJ/Kg
44. Flow at 24 (20→18)
Give data ηi [23,24] =85.6%; p [24] =p [25] =0.046 bar s [24] = 7.7 KJ/Kg
from X-Steam tables functions enthalpy hs [25] = 2337.73 KJ/Kg
ηt =
ℎ[23]−ℎ[24]
ℎ[23]−ℎ 𝑠[24]
0.806=
3157.63 −ℎ [24]
3157.63−2337.73
h [15] = 2496.79 KJ/Kg T[24]=31.39 ºC
45. Flow at 44 (2→9)
T[44]= 458 ºC p[44] = 0.2 bar
h [44] = 3400.6 KJ/Kg s [44] = 9.46 KJ/Kg
46. Flow at 45 (3→13)
T[45]= 574.50 ºC p[45] = 52 bar
h [45] = 3608.2 KJ/Kg s [45] = 7.17 KJ/Kg
47. Flow at 31 (9→6)
T[31]= 60.08 ºC p[31] = 0.2 bar
h [31] = 251.48 KJ/Kg s [31] = 0.83 KJ/Kg
Tab. 4. Thermodynamic parameters of mass flows
THERMODYNAMIC PARAMETERS - results
Nr p[bar] T[°C] H[kJ/kg] S[kJ/kgK]
1* 294.000 277.670 1218.600 2.9810
2 - - - -
3 - - - -
4 255.5 550 3332.9 6.17
5 57.4 321.3 2966.3 6.22
6 57.4 320.2 2963.7 6.22
7 52.9 580. 3617.9 7.18
8 29.008 492.8 3441.38 7.2
9 11.2 359.1 3175.07 7.25
10 4.8 248.2 2958.03 7.27
11 4.8 248.2 2958.03 7.27

15. 12 1.84 149.64 2769.59 7.32
13 0.41 79.78 2563.59 7.39
14 0.210 62.72 2474.19 7.45
15 0.043 34.99 2332.84 7.6
16 0.043 30.5 127.8 0.44
17 - - - -
18 22.04 30.3 128.91 0.44
19 1 17.5 73.5 0.265
20 - - - -
21 3.5 17.5 73.64 0.26
22 3 27.9 117.2 0.41
23 11.2 359.1 3175.07 7.25
24 0.046 31.39 2496.79 7.7
25 0.046 31.28 131.1 0.45
26 1. 17.5 73.5 0.26
27 - - - -
28 3.5 17.48 73.62 0.26
29 3 28.58 120.1 0.42
30* 21.544 32.880 139.620 .4700
31 0.20 60.08 251.48 0.83
32 19.54 59.62 251.2 0.83
33 0.21 62.72 255.82 0.84
34 17.54 114.59 481.4 1.47
35 0.41 79.78 334.025 1.07
36 - - - -
37 17.54 79.7 335.05 1.07
38 1.84 117.59 493.5 1.5
39 15.54 114.49 481.4 1.47
40 13.54 147 619.9 1.81
41 4.8 150.3 633.5 1.85
42 - - - -
43 13.54 151.2 637.67 1.85
44 0.2 458.000 3400.6 9.46
45 52 574.5 3608.2 7.17
46 22.04 30.3 128.91 0.44
47 11.2 359.1 3175.07 7.25
48 29.008 280.2 2946.3 6.47
49 11.2 184.8 784.7 2.19
50 - - - -
51 - - - -
52 52.9 186.1 792.14 2.19
53 301 190.3 823.19 2.19
54 298.5 228.8 992.1 2.55
55 29.008 198.9 848 2.32
56 295 270.5 1184. 2.92
57 57.4 237.4 1025.5 2.67
58 - - - -
59 - - - -
60 - - - -
61 - - - -
62 - - - -
63 22.04 30.3 128.91 0.44
64 - - - -

16. a.Mass and energy flow
In the mathematical model for calculating mass flows and energy flows in the thermal
system, three groups can be distinguished. The first is the equation of balances resulting from
the law of conservation of mass, the second - arising from the principle of conservation of energy,
and the third so-called different equations. The third group includes equations resulting from the
way the balance shields are routed. An example would be an additional equation for the mass
balance of steam flowing through an interstage
The set electrical power or flow of technological steam can be saved in modeling in two
ways: as a value on the right side of the balance equation or assign to these flows the appropriate
unknowns and in the third part of the model put as additional equations, giving the unknown
values. In the first case, the mathematical model consists of a system with fewer equations than
in the second case. However, the second method is much more convenient to use when
calculating with the help of a computer.
The construction of a mathematical model in a detailed form enabling the determination
of mass and energy streams should be preceded by quantitative analysis using the algebraic
properties of the structure of the system. As a result, the value of the difference between the
maximum number of linearly independent equations in the model and the number of unknowns
occurring in them is determined. For a well-worded task, the difference should be zero. When it
is less than zero, it means that if you want to specify a solution unambiguously, you should make
additional assumptions. However, if it is greater than zero, then the system of equations is
contradictory and some assumptions should be abandoned.
i. Mathematical model
Based on flows analysis following equatin set was built.
Equation
number
Group
number
Node
number
Equations Notes
1 1 1 x[1] – x[4] = 0
2 2 2 x[4] – x[5] –x[6] – x[44] = 0
3 3 3 x[7] – x[8] – x[9] – x[10] - x[11] – x[45] = 0
4 4 6 x[15] – x[16] + x[25] + x[31] + x[33] = 0
5 5 6 x[21] – x[22] = 0
6 6 7 x[19] – x[21] = 0
7 7 8 x[16] – x[18] = 0
8 8 9 - x[30] + x[63] = 0
9 9 9 - x[31] + x[44] = 0

17. 10 10 10 x[30] – x[32] = 0
11 11 10 x[14] – x[33] = 0
12 12 11 x[32] – x[34] = 0
13 13 11 x[13] –x[35] + x[38] = 0
14 14 12 x[35] – x[37] = 0
15 15 13 x[34] + x[37] – x[39] = 0
16 16 13 x[12] - x[38] + x[45] = 0
17 17 14 x[39] – x[40] = 0
18 18 14 x[10] – x[41] = 0
19 19 15 x[41] – x[43] = 0
20 20 16 x[9] – x[23] – x[47] = 0
21 21 17 x[40] + x[43] + x[47] – x[49] + x[55] = 0
22 22 18 x[24] – x[25] = 0
23 23 18 x[28] - x[29] = 0
24 24 19 x[26] – x[28] = 0
25 25 20 x[23] – x[24] = 0
26 26 21 x[49] – x[52] – x[53] = 0
27 27 22 x[53] – x[54] = 0
28 28 22 x[48] – x[55] +x[57] = 0
29 29 23 x[54] – x[56] = 0
30 30 23 x[5] – x[57] = 0
31 31 24 x[56] – x[1] = 0
32 32 24 x[8] – x[48] = 0
33 33 26 x[18] – x[46] – x[63] = 0
Table 2 Energy balance equations
Equation
nubmer
Group
number
Node
number
Equation Notes
34 1 1
x[1]h[1] – x[2] + x[3] –x[4]h[4] + x[6]h[6]+ -
x[7]h[7] + x[52]h[52] = 0
35 2 2
x[4]h[4] – x[5]h[5] – x[6]h[6] +
- x[44]h[44] - x[58] = 0

18. 36 3 3
x[7]h[7] – x[8]h[8] – x[9]h[9] +
- x[10]h[10] - x[11]h[11] – x[45]h[45] +
-x[58] – x[59] = 0
37 4 4
x[11]h[11] – x[12]h[12] – x[13]h[13] +
– x[14]h[14] – x[15]h[15] – x[46]h[46] +
+ x[59] – x[60] = 0
38 5 5 x[60] – x[61] – x[62] = 0
39 6 6
x[15]h[15] – x[16]h[16] + x[21]h[21]+
- x[22]h[22] + x[25]h[25] + x[31]h[31] +
+ x[33]h[33] = 0
40 7 7 x[19]h[19] + x[20] – x[21]h[21] = 0
41 8 8 x[16]h[16] + x[17] – x[18]h[18] = 0
42 9 9
– x[30]h[30] – x[31]h[31] + x[44]h[44]+
+ x[63]h[63] = 0
43 10 10
x[14]h[14] + x[30]h[30] – x[32]h[32] +
– x[33]h[33] = 0
44 11 11
x[13]h[13] + x[32]h[32] –x[34]h[34] +
– x[35]h[35] + x[38]h[38] = 0
45 12 12 x[35]h[35] + x[36] – x[37]h[37] = 0
x[12]h[12] + x[34]h[34] + x[37]h[37] +
46 13 13 - x[38]h[38] - x[39]h[39] + x[45]h[45] +
+ x[50] = 0
47 14 14
x[10]h[10] + x[39]h[39] – x[40]h[40] +
- x[41]h[41] = 0

19. 48 15 15 x[41]h[41] + x[42] – x[43]h[43] = 0
49 16 17
x[40]h[40] + x[43]h[43] + x[47]h[47] +
- x[49]h[49] + x[55]h[55] = 0
50 17 18
x[24]h[24] – x[25]h[25] + x[28]h[28] +
– x[29]h[29] = 0
51 18 19 x[26]h[26] + x[27] – x[28]h[28] = 0
52 19 20 x[23]h[23] – x[24]h[24] – x[51] = 0
53 20 21
x[49]h[49] + x[51] – x[52]h[52] +
– x[53]h[53] = 0
54 21 22
x[48]h[48] + x[53]h[53] – x[54]h[54] +
- x[55]h[55] + x[57]h[57] = 0
55 22 23
x[5]h[5] + x[54]h[54] +
- x[56]h[56] –x[57]h[57] = 0
56 23 24
-x[1]h[1] + x[8]h[8] – x[48]h[48] +
+ x[56]h[56] = 0
57 24 27 x[2] – x[50] – x[64] = 0
60 3 1 x[6] β1 - x[52] = 0
61 4 2 x[4] γ1 – x[44] = 0
62 5 3 x[7] γ2 – x[45] = 0
63 6 4 x[18] γ3 – x[46] = 0
64 7 5 x[60] ε5 – x[61] = 0

20. 65 8 6 x[60] = N
66 9 13 x[3]k13 - x[50] = 0
m[1]h[1] = m[1]h [1]+ Q[66]
m[30]h[30] = m[30]ℎ̅[30] + Q[65] =
thus finally h[1]= Q[66]/x[1]=1219.71 ; h[30]= Q[65]/x[30]=138.17
2 – Quantitative analysis
mass fold km 2
energy fold kq 1
number of nodes w 27
number and list od energy nodes wq 2
number of mass nodes wm 25
number and list of surface energy nodes wp 10
number and list of manifold nodes wr 2
number and list of unknown enthalpies flows wn 2
total number of flows p 64
number and list of energy flows pq 15
Results
m[1] 681.7531377
Q[2] 208480.7394
Q[3] 2084807.394
m[4] 681.7531377
m[5] 67.40953583
m[6] 612.9800956
m[7] 625.2396975
m[8] 49.17777719
m[9] 72.96287841
m[10] 30.54970885
m[11] 467.5474155

21. m[12] -3.688433544
m[13] 47.77677035
m[14] 23.62329006
m[15] 399.928536
m[16] 463.7368953
Q[17] 514.7479538
m[18] 463.7368953
m[19] 20320.92338
Q[20] 2844.929273
m[21] 20320.92338
m[22] 20320.92338
m[23] 38.82156294
m[24] 38.82156294
m[25] 38.82156294
m[26] 1975.898951
Q[27] 237.1078741
m[28] 1975.898951
m[29] 1975.898951
m[30] 463.6441479
m[31] 1.363506275
m[32] 463.6441479
m[33] 23.62329006
m[34] 463.6441479
m[35] 49.09025438
Q[36] 50.31751074
m[37] 49.09025438
m[38] 1.313484036
m[39] 512.7344023
m[40] 512.7344023
m[41] 30.54970885
Q[42] 127.3922859
m[43] 30.54970885
m[44] 1.363506275
m[45] 5.00191758
m[46] 0.092747379
m[47] 34.14131548
m[48] 49.17777719
m[49] 694.0127396
Q[50] 56289.79965
Q[51] 26331.88971
m[52] 12.25960191
m[53] 681.7531377
m[54] 681.7531377
m[55] 116.587313
m[56] 681.7531377
m[57] 67.40953583
Q[58] 250932.2778
Q[59] 620651.1585

22. Q[60] 900000
Q[61] 45000
Q[62] 855000
m[63] 463.6441479
Q[64] 152190.9398
Q[65] 64062.21199
Q[66] 831542.649