GEOTHERMAL RESOURCES 



257 



40 percent; the best nuclear plants, about 33 per- 

 cent (U.S. Library of Congress, 1970). The rela- 

 tively high efficiencies of these generating modes 

 compared with geothermal modes are mainly due 

 to the much higher temperatures and pressures of 

 steam input. 



Any system that generates electricity from heat 

 has an efficiency limited by the second law of ther- 

 modynamics. An ideal (Carnot) engine will have a 

 thermal efficiency equal to 1 — (T1/T2), where Ti is 

 the final temperature, in degrees Kelvin, and T2 is 

 the initial temperature, in degrees Kelvin (Hossli, 

 1969). Thus, for geothermal generation (as at The 

 Geysers) where Ti = 80°F (299.8°K) and T2 = 

 355°F (452.6°K) (Barton, 1972, fig. 4), the maxi- 

 mum theoretical efficiency is [1 — (299.8/452.6)] 

 (100) = 33.9 percent. For a fossil-fuel plant at T, 

 = 100°F (311°K) and T^ = 1,000°F (811°K), the 

 maximum theoretical efficiency would be 61.6 per- 

 cent. 



The overall generating efficiency of an installation 

 at a hot-water geothermal field is even less, owing 

 to the fact that under existing technology only the 

 steam can be utilized in a turbine. In a hot-water 

 system at 260°C (hke Wairakei, New Zealand), the 

 fluid delivered to the power plant at a turbine inlet 

 pressure of 50 lb in-- gauge (4.46 bar absolute) is 

 by weight 24 percent steam and 76 percent water. 

 Fifty-nine percent of the produced heat is in the 

 steam, and 41 percent, in the water. Accordingly, 

 the overall thermal efficiency of a 260° C hot- water 

 geothermal installation is approximately (59 per- 

 cent) (14.3 percent) = 8 percent. 



Geothermal resources cannot be expressed in kilo- 

 watts or megawatts unless the assumed life of the 

 system and the plant factor (for geothermal gen- 

 eration usually assumed to be 8,000 hr yr-^) are 

 also specified. Kilowatts and megawatts are units 

 of electrical capacity, not electrical energy, and thus 

 are a function of not only the size of the geother- 

 mal resource but also the rate of production. The 

 rate of production depends on the economics of the 

 particular situation ; production has to be held to a 

 level that will allow the capital facilities to be 

 amortized before the field is exhausted. The largest 

 geothermal field imaginable presumably could be 

 exhausted in 1 year, at prohibitive economics. More 

 reasonable assumptions for field life fall between 

 25 and 50 years. 



Even if one restricts resource discussion to heat 

 and thus avoids the possible ambiguity of electrical 

 units, one must be careful to specify whether the 

 heat considered is total heat in a specified volume 

 of ground, heat in the fluid phase only, heat that 



actually can be extracted from the ground, or heat 

 actually delivered to a turbine. 



To illustrate these differences, consider a hypo- 

 thetical hot-water geothermal system to a depth of 

 3 km, with temperatures controlled by the boiling- 

 point curve to a base temperature of 260 °C. 1 

 assume a rock particle density of 2.6 g cm-% a rock 

 specific heat of 0.2 cal g-^ °C-\ and all calculations 

 referred to 15°C. Using steam table data (Keenan 

 and others, 1969) and the boiling-point curve for 

 pure water at sea level (Haas, 1971), one can cal- 

 culate incrementally that the heat contained in the 

 geothermal system at temperatures less than 260°C 

 (that is, at depths shallower than 0.5518 km) is 

 6.3 X 10^'' cal km-^ The heat stored at 260°C from 

 0.5518 to 3.0 km is 34.0 X lO^'' cal km-^ Therefore, 

 the total heat in the geothermal system above 15° C 

 is approximately 40.3 X 10'^ cal km-^ 



The amount of heat remaining after exploitation 

 perhaps can be approximated by assuming that the 

 geothermal system drops to a base temperature of 

 180°C; the calculations are similar to those just 

 shown. The heat withdrawn during exploitation is 

 then the difference between the heat at the initial 

 state (40.3 X 10'' cal km-^) and the heat at the 

 final (depleted) state (28.5 X 10" cal km-^), or 

 11.8 X lO'** cal km-^ This figure is undoubtedly too 

 high, perhaps by a factor of 2, owing to inefficient 

 extraction because of impermeable rock, insufficient 

 number of drill holes, and drilling spacing that is 

 not optimum. Therefore, the heat actually delivered 

 to the surface wells will be approximately 5.9 X 

 10" cal km--, about 15 percent of the heat actually 

 stored in the initial geothermal system above 15°C. 

 Taking into account the 14.3 percent thermal effi- 

 ciency of generation and the heat wasted in hot 

 water (41 percent), we find that only 1 percent of 

 the heat contained in this hot-water geothermal 

 system can be converted into electricity. 



The amount of heat and water recharge assumed 

 to enter the system from greater depths should also 

 be specified in the estimation of the geothermal 

 resources or reserves of any area. Calculations such 

 as the above do not take into account the possibility 

 of recharge, and therefore give only a minimum 

 figure for the heat that may ultimately be derived 

 from a geothermal system. At Wairakei, New Zea- 

 land, recharge is significant. Hunt (1970), using 

 precise gravity and leveling techniques at various 

 times during exploitation of the field, has shown 

 that about 20 percent of the water drawn off from 

 the Wairakei field from 1961 to 1967 was replaced 

 by recharge. Although recharge is clearly a signifi- 

 cant factor in geothermal reserve estimations, its 



