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

在岩浆直接取热系统中，工作流体（水）通过流经凝固岩浆热收缩形成的裂隙来取热。骨折的作用有两个方面，即，流体路径和热交换表面。因此，这些裂缝的特征至关重要。在本研究中，裂缝扩展的过程进行了研究。据推测，岩浆房是显着的大相比，热交换系统。采用以下条件作为基本情况，即，该系统的深度为7 km，固相线温度为800℃，杨氏模量乘以线膨胀系数为4.5 × 10 ~（^5）（Pa/℃）。应力场由三个场组成，即，首先是作用在凝固区外边界上的超载压力引起的应力场，其次是作用在凝固区内边界上的压力引起的应力场，最后是热应力场。根据断裂力学进行分析。结果表明，在463℃时，裂纹先扩展，后扩展。第九条断裂的生长温度为457℃。两个温度之间的差异仅为6℃。这意味着裂缝的生长和裂缝网络的形成几乎是同时的，因此是我们无法控制的。影响裂缝网络形成的因素很多，如断裂韧性、井眼半径、弹性常数等，其中换热系统深度对裂缝尺寸的影响最为显着。断裂韧性不太有效。

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.