Mathematical Modeling of Heat Frozen Earth
In-situ leaching is a mining process used to recover minerals such as copper and uranium through boreholes drilled into a deposit, in situ. Water permeability of orebody is a necessary condition of in-situ leaching. Permafrost or cryotic soil is soil at or below the freezing point of water for two or more years. Most permafrost is located in high latitudes. Ground ice is not always present, but it frequently occurs and it may be in amounts exceeding the potential hydraulic saturation of the ground material. Under these conditions it is necessary for the successful leaching warm orebody and melt the ice. Mathematical model of heating permafrost is considered taking into account the Stefan condition at the boundary of melting. An equivalent formulation of the problem is shown. We proposed numerical algorithm for analyzing this process. Computation module is produced on an open architecture with the use of object-oriented programming language OpenFOAM. Verification of the computation module carried using the known exact solutions of simplified tasks. Evolution of permafrost melting in the case of one, three and four cylindrical heaters is presented. The main result of this study is the time required for melting the solid of permafrost by four heaters. The time to complete defrosting orebody in the space between the heaters is shown.