| Abstract |
Mathematics is a universal language of both science and engineering. Differential equations, mathematical modeling, numerical methods, and computation form the deep infrastructure of sciences and engineering. In this context mathematical modeling using Mathematica (Wolfram Inc. version 7) is a very powerful tool for studying natural systems, and for applications to geothermal engineering. This paper contains a comprehensive overview of how to apply and solve practical models from simple algebraic formulae up to fundamental Partial Differential Equations (PDE) applied to coupled phenomena in non-isothermal poroelastic aquifers. The graphical and computational programmable capabilities of Mathematica are extremely useful for doing research and learning about the flow of mass and energy in deformable porous media. These systems exhibit coupled processes of solid mechanics, heat transfer, fluid flow and solute transport in pores that can be modeled with fundamental PDE and solved with Mathematica. These basic PDE are all classical and range from elliptic, parabolic and hyperbolic type, to a mixture of them. It is therefore possible to provide simultaneously an understanding of complicated coupled phenomena and their modeling with PDE by gradually approaching their solutions using Mathematica. This research technique covers a diverse group of very important applications, including natural resources exploration and exploitation of water resources and geothermal and petroleum reservoirs. |