Fracture Mechanics Approach to the Growth Process of Fracture Network for Direct Heat Heat Extraction from Magma

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In the system of direct heat extraction from magma, working fluid (water) extracts heat by flowing through fractures, which are created by thermal contraction of solidified magma. Role of fractures is two fold, i.e., fluid path and heat exchange surfaces. Thus, the characteristics of these fractures are crucial. In the present research, the process of fracture growth is studied. It is supposed that the magma chamber is significantly large compared with the heat exchange system. The following condition is adopted as the base case, i.e., depth of the system is 7km, solidus temperature 800℃ and the Young's modulus times linear expansion coefficient 4.5X10^5(Pa/℃). The stress field consists of three fields, i.e., firstly the one due to over burden pressure acting on the outer boundary of the solidified region, secondly the one induced by pressure acting on the inner boundary of the solidified region and lastly the thermal stress field. The analysis is performed based on the Fracture Mechanics. It is found that growth of the first two fractures takes place at 463℃ in the base case and is followed by sequential fracture growth. The temperature at which the growth of ninth fracture takes place, is 457℃. The difference is only 6℃ between the two temperatures. This implies that the fracture growth and formation of fracture network would be almost simultaneous and thus be out of our control. There seem to be many factors which have effects on the formation of fracture network, such as fracture toughness, radius of wellbore, elastic constants and so on. Among these factors, depth of the heat exchange system has most significant effect, regarding the fracture size. Fracture toughness is less effective.