The exam for MTX311 2018 worked out solutions. The memorandum has solutions are 100% correct including alternative working methods. The solutions are done in a step by step matter
Dr AS Lexmond (University of Pretoria)
Dr W Le Roux (University of Pretoria)
Instructions
1 Time: 180 min.
2 Full marks: 100
3 Neatness saves you points, especially when only part of the question is correct.
4 Give the equations before you start filling in numbers; for the questions marked with an *, also give a
short but clear solution strategy
5 You are allowed to take fundamentals of thermodynamics (7th or 8th edition), non-ideal gas hand-out,
one page, A4, with your own notes (both sides) and all the material from the click-up page “lectures”, as
well as any other notes or books you like
6 use a reference temperature and pressure of T0=25°C, P0=1 bar
7 Note that the amount of marks for a question represents how important I find it, not the time it will cost
you to solve it.
Currently, the island of Hawaii is suffering from large scale and enduring volcanic eruptions. On Hawaii, lava freely
flows from fissures, destroying everything in its path. With a total production of 38MW, the Puna power station is
(was?) Hawaii’s largest Geothermal power plant. To make maximum use of the geothermal heat, the power plant
has been built on top of a volcanic fissure. As a result, the Puna power station is now at a risk of being destroyed by
a lava flow which is at the time of writing only about 50m away from the power plant.
Fig. 1 gives a process overview of the Puna power station. Hot wet steam of about 200°C is tapped from the earth
from a bore hole that is really close to a geological fissure. The wet steam is separated in dry steam and liquid water.
The steam is expanded in a turbine, producing electricity. The water and the steam from the turbine are then used
to evaporate and heat compressed pentane. Pentane vapour is then used to generate electricity in a second turbine.
To avoid environmental pollution, the fluids from the geothermal well are now pumped back into the fissure after
extracting the heat.
Table 1 gives the properties of the various process flows. Table 2 gives the power consumption and production of
the pumps, turbines and compressor.
, Table 1 properties of puna power plant process flows
T P m h ψ H Ψ
°C kPa kJ/kg kJ/kg MW MW
1 steam-brine mixture 200 1553.8 117.00 2405.03 736.39 281.39 86.16
2 steam from well 200 1553.8 93.60 2793.18 879.97 261.44 82.37
3 brine from well 200 1553.8 23.40 852.43 162.05 19.95 3.79
4 wet steam 160 617.8 93.60 2650.70 716.62 248.11 67.08
5 condensate water 160 617.8 88.92 849.38 120.89 75.53 10.75
6 non-condensable gases 160 617.8 4.68 2574.30 1347.15 12.05 6.30
7 compressed gases 200 3000 4.68 2789.96 1556.07 13.06 7.28
8 HTXR outlet water 40 600 112.32 167.85 1.74 18.85 0.20
9 waste water 40 3000 112.32 170.25 4.14 19.12 0.46
10 injection fluid 66 3000 117.00 275.04 36.25 32.18 4.24
11 high P pentane liquid 35 665 426.63 23.81 0.86 10.16 0.37
12 heated pentane liquid 100 665 426.63 198.33 23.84 84.62 10.17
13 high P pentane vapour 150 660 426.63 572.34 101.00 244.18 43.09
14 low P pentane gas 110 100 426.63 505.64 30.52 215.72 13.02
15 low P pentane liquid 35 100 426.63 23.33 0.38 9.95 0.16
Table 2: power specifications
Unit power (MW)
Turbine Level 1 12.87
Turbine level 2 26.91
motive fluid pump 0.25
injector pump 0.47
compressor 1.11
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