Single-Flash Geothermal Plant

What is modelled

In a liquid-dominated geothermal field the hot water is under pressure in the reservoir. When it rises to a separator at lower pressure part of it flashes to steam at constant enthalpy. The steam goes to a turbine and a condenser, and the liquid is injected back. A hotter separator gives drier, higher-grade steam but less of it; a colder one gives lots of steam that can do little work. The best temperature lies in between.

Equations

• Flash at constant enthalpy x = (h1 − hf(Ts)) / hfg(Ts), steam flow ṁs = x ṁ.
• Ideal turbine expansion at constant entropy from sg(Ts) down to the condenser temperature, work ws = hg(Ts) − hexit,s, actual work w = η ws.
• Power P = ṁs w and an upper limit given by the exergy of the brine, ṁ[(h − h0) − T0(s − s0)].
• Saturation pressure from the IAPWS-IF97 equation.

Checks run in the page

• Steam properties against reference values of IAPWS-IF97 at five temperatures.
• Mass and enthalpy balance of the separator.
• The optimum separator temperature by scan and by golden-section search.
• The turbine power against the exergy of the brine, and the exhaust dryness.

Honest simplifications

Steam properties are polynomial fits of the IAPWS-IF97 tables between 20 and 330 C. The wells deliver pure water without dissolved gases or salts, pressure losses in pipes and the separator are zero, the turbine has a single isentropic efficiency, the condenser, pumps and cooling tower consume no power and the generator is lossless. Real plants lose a good part of their output to gases and auxiliary power.

• Press Separator too hot and Separator too cold and compare the power with the best temperature shown on the status line.
• Watch the green ideal expansion line on the temperature-entropy diagram lengthen as the separator gets hotter.
• Lower the reservoir temperature to 180 C and see the best separator temperature fall with it.