A geothermal well is available, with water at liquid saturated state. The well produces a mass flow of
900 t/h of water at 160 °C. The design of a geothermal binary cycle working with iso-pentane (cp=2.58
kJ/kg/K, Molar mass = 72.15 kg/kmol) is the objective of the present investigation.
1) Consider the following data:
• The binary cycle is cooled with a cooling tower.
• Cooling tower water temperature 18 °C
• Temperature increase of the water flow crossing the condenser 7 °C
• ∆T of subcooling of the stream at evaporator inlet 3 °C
• ∆T of pinch point in the evaporator 5 °C
• Global heat exchange coefficient evaporator 900 Wm-2K-1
• Global heat exchange coefficient economiser 800 Wm-2K-1
• Global heat exchange coefficient condenser 500 Wm-2K-1
• Condensing temperature 30 °C
• Minimum temperature for water reinjection 70 °C
• Isentropic efficiency of the turbine 80%
• Organo-electric efficiency of the generator 95%
• Isentropic efficiency of pumps 70%
• Organo-electric efficiency of pump motor 90%
• Relative pressure drops (∆P/Pin) economizer (negligible otherwise) 20%
• Absolute pressure drops in the condenser (cooler side) 2 bar
• Absolute pressure drops in the geothermal pipes 8 bar
It is required to:
a. determine the evaporation temperature (pressure) that maximises the power output,
considering the following evaporation temperatures: 70 °C, 80 °C, 90 °C, 100 °C,
110 °C, 120 °C;
b. on the annexed T-s diagram (see Annex 2), draw the optimal thermodynamic cycle
(the one characterized by the evaporation temperature (pressure) that enables the
maximisation of net power;
c. draw the scheme of the plant, showing in each point the values for the mass flow, the
temperature, pressure, enthalpy, entropy and vapour quality;
d. determine the electrical efficiency and the thermal recovery efficiency (see Annex 3);
e. draw the T-Q diagram for each heat exchanger.
f. calculate the evaporator, economiser and condenser surface.
Hypothesis for calculation of thermodynamic points in the subcooled and superheated region
1) For the subcooled liquid, consider an ideal liquid (constant volume)
2) Superheated vapour can be modelled as an ideal gas
Please, send to silvia.lasala@univ-lorraine.fr a report, showing all the details of calculations and
the analysis of your numerical results. Max 10 pages.
Deadline: 15/12/2023
2
Annex 1. Thermodynamic properties of iso-pentane in saturating conditions.
The table continues in the next page
T P Liquid
density
Vapour
Density
Liquid
Enthalpy
Vapour
Enthalpy
Liquid
Entropy
Vapour
Entropy
°C bar kg/m3 kg/m3 kJ/kg kJ/kg kJ/kg/K kJ/kg/K
20 0.76665 620.03 2.3547 -17.773 331.46 -0.059695 1.1316
22 0.82461 618.01 2.5206 -13.262 334.47 -0.04439 1.1338
24 0.88596 615.99 2.6954 -8.7296 337.49 -0.02912 1.136
26 0.95083 613.95 2.8795 -4.1764 340.51 -0.013884 1.1383
28 1.0193 611.9 3.0733 0.39806 343.55 0.0013189 1.1408
30 1.0917 609.84 3.2771 4.9939 346.59 0.01649 1.1433
32 1.1679 607.78 3.4912 9.6112 349.65 0.03163 1.146
34 1.2482 605.7 3.716 14.25 352.71 0.04674 1.1487
36 1.3328 603.61 3.9519 18.911 355.77 0.06182 1.1515
38 1.4216 601.5 4.1993 23.594 358.85 0.076872 1.1543
40 1.5151 599.39 4.4586 28.3 361.93 0.091896 1.1573
42 1.6131 597.26 4.7302 33.027 365.02 0.10689 1.1603
44 1.716 595.12 5.0145 37.778 368.11 0.12186 1.1634
46 1.8239 592.96 5.3119 42.551 371.21 0.13681 1.1666
48 1.9369 590.8 5.6228 47.347 374.31 0.15173 1.1698
50 2.0551 588.61 5.9478 52.166 377.42 0.16663 1.1731
52 2.1788 586.42 6.2873 57.009 380.53 0.1815 1.1765
54 2.3081 584.21 6.6417 61.875 383.65 0.19636 1.1799
56 2.4432 581.98 7.0116 66.765 386.78 0.21119 1.1834
58 2.5842 579.74 7.3974 71.679 389.9 0.226 1.187
60 2.7313 577.48 7.7997 76.617 393.03 0.24079 1.1906
62 2.8846 575.2 8.219 81.58 396.16 0.25556 1.1942
64 3.0444 572.91 8.656 86.567 399.3 0.27031 1.1979
66 3.2107 570.6 9.111 91.579 402.44 0.28505 1.2016
68 3.3839 568.27 9.5848 96.617 405.58 0.29977 1.2054
70 3.564 565.92 10.078 101.68 408.72 0.31447 1.2092
72 3.7512 563.55 10.591 106.77 411.86 0.32916 1.2131
74 3.9457 561.17 11.125 111.88 415 0.34384 1.217
76 4.1477 558.76 11.68 117.02 418.14 0.3585 1.2209
78 4.3573 556.33 12.258 122.19 421.29 0.37315 1.2249
80 4.5748 553.87 12.858 127.38 424.43 0.38779 1.2289
82 4.8003 551.4 13.482 132.6 427.57 0.40241 1.2329
84 5.0339 548.9 14.13 137.85 430.7 0.41703 1.237
86 5.276 546.37 14.804 143.13 433.84 0.43164 1.2411
88 5.5267 543.82 15.504 148.43 436.97 0.44624 1.2452
90 5.7861 541.25 16.231 153.77 440.1 0.46083 1.2493
92 6.0544 538.64 16.986 159.13 443.22 0.47542 1.2534
94 6.332 536.01 17.77 164.52 446.34 0.49 1.2576
96 6.6188 533.35 18.585 169.94 449.45 0.50458 1.2617
98 6.9152 530.66 19.431 175.39 452.55 0.51915 1.2659
3
T P Liquid
density
Vapour
Density
Liquid
Enthalpy
Vapour
Enthalpy
Liquid
Entropy
Vapour
Entropy
°C bar kg/m3 kg/m3 kJ/kg kJ/kg kJ/kg/K kJ/kg/K
100 7.2214 527.93 20.31 180.87 455.65 0.53373 1.2701
102 7.5374 525.17 21.222 186.38 458.74 0.5483 1.2743
104 7.8637 522.38 22.17 191.93 461.81 0.56287 1.2785
106 8.2002 519.55 23.155 197.5 464.88 0.57745 1.2827
108 8.5474 516.69 24.178 203.11 467.94 0.59203 1.2868
110 8.9052 513.79 25.241 208.75 470.98 0.60661 1.291
112 9.2741 510.84 26.345 214.43 474.01 0.6212 1.2952
114 9.6542 507.86 27.493 220.14 477.03 0.63579 1.2993
116 10.046 504.83 28.687 225.89 480.03 0.6504 1.3035
118 10.449 501.75 29.928 231.67 483.01 0.66501 1.3076
120 10.864 498.63 31.22 237.49 485.97 0.67964 1.3117
122 11.291 495.45 32.563 243.34 488.91 0.69428 1.3157
124 11.73 492.22 33.962 249.24 491.83 0.70894 1.3198
126 12.182 488.94 35.419 255.18 494.73 0.72361 1.3238
128 12.647 485.59 36.936 261.15 497.6 0.73831 1.3277
130 13.125 482.19 38.519 267.17 500.44 0.75303 1.3316
132 13.616 478.72 40.169 273.23 503.25 0.76777 1.3355
134 14.121 475.18 41.892 279.34 506.03 0.78255 1.3393
136 14.639 471.56 43.692 285.49 508.77 0.79735 1.3431
138 15.172 467.87 45.574 291.69 511.47 0.81219 1.3467
140 15.719 464.1 47.542 297.94 514.13 0.82707 1.3503
142 16.281 460.23 49.604 304.24 516.74 0.842 1.3539
144 16.857 456.28 51.766 310.6 519.3 0.85697 1.3573
146 17.449 452.22 54.036 317.01 521.81 0.87199 1.3606
148 18.057 448.05 56.421 323.48 524.26 0.88707 1.3638
150 18.68 443.76 58.932 330.02 526.64 0.90222 1.3669
152 19.32 439.35 61.58 336.62 528.95 0.91744 1.3698
154 19.977 434.79 64.378 343.29 531.19 0.93274 1.3726
156 20.65 430.09 67.339 350.03 533.33 0.94813 1.3752
158 21.341 425.21 70.481 356.86 535.38 0.96362 1.3777
160 22.049 420.16 73.824 363.77 537.31 0.97923 1.3799
162 22.776 414.89 77.392 370.78 539.13 0.99497 1.3818
164 23.522 409.39 81.214 377.89 540.8 1.0109 1.3835
166 24.287 403.62 85.325 385.11 542.32 1.0269 1.3849
168 25.071 397.55 89.77 392.47 543.65 1.0432 1.3859
170 25.876 391.12 94.604 399.98 544.76 1.0597 1.3864
172 26.702 384.26 99.902 407.66 545.63 1.0765 1.3865
174 27.55 376.88 105.76 415.55 546.18 1.0937 1.3858
176 28.421 368.84 112.33 423.7 546.34 1.1114 1.3844
178 29.315 359.94 119.82 432.17 546 1.1297 1.3819
180 30.233 349.84 128.56 441.11 544.97 1.1488 1.378
4
Annex 2. Isopentane T-s diagram (drawn with a REAL FLUID equation of state)
5
ZOOM of red frame in previous page
6
Annex 3 (see also slide 36 of the course)
The thermal recoverythermal
re cov ery
 the and electric efficiency ofcycle are defined as shown:inlet cycle
thermal
recovery available
net,plant
cycle
inlet cycle
Q
Q
W
Q
 =
 =
Observations:
• The term “electric” is used because we consider organo-electrical efficiencies of generator and of pump
motors;
• The available thermal power,availableQ , is the thermal power that could ideally be extracted by the
available geothermal fluid if it is cooled from its maximum temperature to its minimum acceptable
temperature value (in this exercise it is 70 °C).
• The inlet powerinlet cycleQ is the input power of the cycle (EVAPORATOR ECONOMIZERQ Q+ )