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Previous studies optimized the dimensions of coaxial heat exchangers using constant mass fow rates as a boundary condition. They show a thermal optimal circular ring width of nearly zero. Hydraulically optimal is an inner to outer pipe radius ratio of 0.65 for turbulent and 0.68 for laminar fow types. In contrast, in this study, fow conditions in the circular ring are kept constant (a set of fxed Reynolds numbers) during optimization. This approach ensures fxed fow conditions and prevents inappropriately high or low mass fow rates. The optimization is carried out for three objectives: Maximum energy gain, minimum hydraulic efort and eventually optimum net-exergy balance. The optimization changes the inner pipe radius and mass fow rate but not the Reynolds number of the circular ring. The thermal calculations base on Hellström’s borehole resistance and the hydraulic optimization on individually calculated linear loss of head coefcients. Increasing the inner pipe radius results in decreased hydraulic losses in the inner pipe but increased losses in the circular ring. The net-exergy diference is a key performance indicator and combines thermal and hydraulic calculations. It is the difference between thermal exergy fux and hydraulic efort. The Reynolds number in the circular ring is instead of the mass fow rate constant during all optimizations. The result from a thermal perspective is an optimal width of the circular ring of nearly zero. The hydraulically optimal inner pipe radius is 54% of the outer pipe radius for laminar fow and 60% for turbulent fow scenarios. Net-exergetic optimization shows a predominant infuence of hydraulic losses, especially for small temperature gains. The exact result depends on the earth’s thermal properties and the fow type. Conclusively, coaxial geothermal probes’ design should focus on the hydraulic optimum and take the thermal optimum as a secondary criterion due to the dominating hydraulics.
Non-nuclear and non-fossil energy resources and their possibilities for future power generation
(1975)
It must be stressed that the assessment of the exploitation possibilities of the energy resources discussed in this paper requires further studies. With this proviso, the situation can be provisionally summarised as follows: The total potential of known geothermal steam sources is only 64 GW. Geothermal energy could therefore only make a significant contribution to covering the worldwide power needs if we succeed in exploiting dry geothermal reservoirs. Exploitation of tidal energy is limited to a few geographically favourable locations. The power generation potential at these locations is only about 64 GW. An important drawback of tidal power is discontinuous power generation. Large scale exploitation of wind, wave and glacier energy, and of ocean heat, requires solution of a number of technological problems. The environmental effects of exploitation of these energy resources are to some extent of a qualitatively different nature from those of operation of fossil-fuel-fired and of nuclear power plants. The scanty knowledge in this area often results in these effects being underestimated. In any case, however, it would be deliberately misleading to postulate that any form of power generation is possible without some detrimental effects on the environment. It may be stated in conclusion that, owing to their small potential or to the as yet insufficiently advanced technological development, none of the energy resources discussed in this paper can make a significant contribution to the solution of middle-term energy supply problems, i.e., to a rapid replacement of mineral oil and natural gas.