Thermal energy from the earths crust

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Abstract
The theory of conductive heat flow is used to calculate the efficiency of extraction of energy from large impermeable masses of hot rock, by circulation of a heat-transfer fluid through localised fissures or joints.The cases considered are a single plane fissure in an infinite medium, a plane slab cooled on both faces, and a cube cooled on all faces.The time variation of heat flow through the cooling surface to the transfer fluid is controlled by the fluid temperature; and, by a simple theoretical device, this time variation is made to take an easily calculable form, which also gives a fairly constant power output over the chosen period of cooling of the rock.The calculations show that the form of cooling cycle chosen will allow about 70% of the theoretical energy content to be recovered from the first few tens of metres of rock along the walls of a single fissure over a 20-year drawoff period.Both the thickness of rock drawn upon and the total energy available increase with the square root of the length of the drawoff period. In average rock at an initial temperature of 400°c, a mean power output of about 13 megawatts per square kilometre of fissure would be produced throughout the 20-year period. In slabs and cubes with dimensions (thickness) ranging from about 40 to 60 metres, extraction efficiencies of between 80% and 90% are obtainable with a 20-year drawoff period.The mean power output ranges from about 330 to 370 megawatts per cubic kilometre of rock.For a given efficiency, the permissible dimensions vary as the square root of the drawoff period, and the power output per unit volume varies inversely as the square root of the period Application of this theory to the Wairakei production area, New Zealand, taking account only of the observed spacing of surface faults, indicates that if the relation between the heat storage volume and projected drawoff rate is such that a life of between 100 and 200 years can be expected (and evidence to date suggests that at least this life is probable), much of the stored heat can be extracted with high efficiency.

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