A remote island wants a firm renewable supply averaging over a planning horizon of

PHYSICS · Multi-part · Fermi University Physics · Earth, Climate & Energy Physics · Energy resources and conversion · Energy resources and conversion

Energy from Physics, Ch Natural energy flows: rotors, turbines, waves, channels and hot rock

Problem

A remote island wants a firm renewable supply averaging 5 MWe5\,\mathrm{MW_e} over a planning horizon of 25 years25\,\mathrm{years}. Two schemes are proposed, to run together. A fence of tidal-stream turbines across a nearby strait, with tidal head amplitude a0=0.6 ma_0 = 0.6\,\mathrm{m} and natural peak flow Qmax⁡=3000 m3 s−1Q_{\max} = 3000\,\mathrm{m^3\,s^{-1}}. Take seawater density ρ=1025 kg m−3\rho = 1025\,\mathrm{kg\,m^{-3}} and the Garrett-Cummins coefficient γGC=0.22\gamma_{\rm GC} = 0.22. Take the channel's power limit as the electrical power delivered, ignoring turbine and generator losses. A binary geothermal plant drawing brine at m˙=40 kg s−1\dot m = 40\,\mathrm{kg\,s^{-1}} from a well at T=420 KT = 420\,\mathrm{K}, with specific heat c=4.2 kJ kg−1 K−1c = 4.2\,\mathrm{kJ\,kg^{-1}\,K^{-1}}, against a dead-state temperature T0=300 KT_0 = 300\,\mathrm{K}. Its binary cycle converts a fraction ηx=0.45\eta_{\rm x} = 0.45 of the delivered exergy into electricity. The reservoir rock has volume V=0.5 km3V = 0.5\,\mathrm{km^3}, volumetric heat capacity ρc=2.6 MJ m−3 K−1\rho c = 2.6\,\mathrm{MJ\,m^{-3}\,K^{-1}}, and is taken to be exhausted once it has cooled by ΔT=60 K\Delta T = 60\,\mathrm{K}. Only a recovery factor Rf=0.15R_f = 0.15 of the heat released by that cooling can in practice be brought to the surface, at the constant flow rate m˙\dot m stated above, before the field must be judged spent. ((a)) Find the long-run average power the turbine fence can deliver. ((b)) Find the electrical power the binary plant delivers while the field is fresh. ((c)) Find how many years that electrical output can be sustained at the stated recovery factor. ((d)) State whether the combined scheme meets the island's 5 MWe5\,\mathrm{MW_e} target over the full 2525-year horizon, and identify which of the two resources is a flow and which is a store, and how that difference shows up in the answer.

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