Stability of the Solidified Magma Region for Direct Utilization of Magma Energy

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Stability of the solidified region for the direct extraction of energy from molten magma was examined from the view point of solid mechanics. Firstly, the constitutive law of the solidified magma was investigated, by using the Norton law to express the dependency of creep strain on stress, for the uni-axial stress-creep strain relation. With regard to the dependency of creep strain on time, the creep strain was set to be linear with respect to time as usually used in the secondary creep stage and the Arrhenius law is introduced to express the temperature dependency of creep strain. Based on the uni-axial stress-creep strain relation, the constitutive equation was constructed by employing the J_2 flow theory which utilized the second invariant of deviatric stress the creep potential. Three kinds of rock, i.e. granite, anorthosite and olivine, were introduced. As for the temperature condition, following two cases was considered. The first case is that convection of molten magma flow is very weak and thus the size of the solidified region is primarily determined by the solidus temperature. The second case is that the convection of magma is sufficiently strong so that the size of the solidified magma is almost determined by the heat balance between the heat extracted and the heat supplied by the convective magma from the outside of the solidified region. The temperature distribution was analyzed for the both cases and the stress distribution and the deformation were clarified, shedding light on the formation of fracture network within the solidified region, based on the constitutive equations and the temperature fields mentioned above. It was revealed that, for both of the two cases, olivine was the most potential candidate from the view point of formation of fracture network and anorthosite came next. Granite would not be appropriate for the direct extraction of magma energy.