A one-dimensional model of a heterogeneous material consisting of a matrix with embedded separated particles is considered, and the melting or solidification of the particles is investigated. The matrix is in imperfect contact with the particles, and the lumped capacity approximation applies to each individual particle. Heat is generated inside the particles or is transferred from the matrix to the particles coupled through a contact conductance. The matrix is not allowed to change phase and energy is either generated inside the matrix or transferred from the boundaries, which is initially conducted through the matrix material. The physical model of this coupled, two-step heat transfer process is solved using the energy method. The investigation is conducted in several phases using a building block approach. First, a lumped capacity system during phase transition is studied, then a one-dimensional homogeneous material during phase change is investigated, and finally the one-dimensional heterogeneous material is analyzed. A numerical solution based on the finite difference method is used to solve the model equations. This method allows for any kind of boundary conditions, any combination of material properties, particle sizes and contact conductance. In addition, computer programs, using Mathematica, are developed for the lumped capacity system, homogeneous material, and heterogeneous material. Results show the effects of control volume thickness, time step, contact conductance, material properties, internal sources, and external sources. / Master of Science

In geothermal reservoirs and unconventional gas reservoirs with very low matrix permeability, fractures are the main routes of fluid flow and heat transport, so the fracture permeability change is important. In fact, reservoir development under this circumstance relies on generation and stimulation of a fracture network. This thesis presents numerical simulation of the response of a fractured rock to injection and extraction considering the role of poro-thermoelasticity and joint deformation. Fluid flow and heat transport in the fracture are treated using a finite difference method while the fracture and rock matrix deformation are determined using the displacement discontinuity method (DDM). The fractures response to fluid injection and extraction is affected both by the induced stresses as well as by the initial far-field stress. The latter is accounted for using the non-equilibrium condition, i.e., relaxing the assumption that the rock joints are in equilibrium with the in-situ stress state. The fully coupled DDM simulation has been used to carry out several case studies to model the fracture response under different injection/extractions, in-situ stresses, joint geometries and properties, for both equilibrium and non-equilibrium conditions. The following observations are made: i) Fluid injection increases the pressure causing the joint to open. For non-isothermal injection, cooling increases the fracture aperture drastically by inducing tensile stresses. Higher fracture aperture means higher conductivity. ii) In a single fracture under constant anisotropic in-situ stress (non-equilibrium condition), permanent shear slip is encountered on all fracture segments when the shear strength is overcome by shear stress in response to fluid injection. With cooling operation, the fracture segments in the vicinity of the injection point are opened due to cooling-induced tensile stress and injection pressure, and all the fracture segments experience slip. iii) Fluid pressure in fractures increases in response to compression. The fluid compressibility and joint stiffness play a role. iv) When there are injection and extraction in fractured reservoirs, the cooler fluid flows through the fracture channels from the injection point to extraction well extracting heat from the warmer reservoir matrix. As the matrix cools, the resulting thermal stress increases the fracture apertures and thus increases the fracture conductivity. v) Injection decreases the amount of effective stress due to pressure increase in fracture and matrix near a well. In contrast, extraction increases the amount of effective stress due to pressure drop in fracture and matrix.