Three-dimensional numerical modeling of geothermal heat conduction

In the last decade or so, there have been some major technological breakthroughs in the applications of geophysical systems. One technological growth area has been in the development and use of deterministic, multi-parameter, numerical simulation models for analyzing the mechanism of transport of heat and fluid through rocks and sediments. In this regard, several forward and inverse problems have been investigated. In particular, a forward problem might consist of identifying the source term that is responsible for causing a given temperature distribution at a given location with prescribed thermal properties. Associated with this is also an inverse problem that consists of solving for the thermal properties for a given temperature distribution in a given location with prescribed heat source. The latter two problems are extremely important in the sense that they provide a feel for the history of the phenomenon that has caused the existing temperature distribution.

In this work, a geothermal heat conduction problem is analyzed via the integral transform technique. Novel and efficient computational algorithms are also developed in three-dimensions to solve both a forward and an inverse heat conduction problem. Numerical models are developed via constrained numerical optimization techniques. Our results establish that the methods developed are both robust and reliable, suggesting that they can be used in conjunction with practical data.