3D Finite-Difference Based Electromagnetic Modelling Multidisciplinary Applications

This dissertation mainly focused on the multidisciplinary applications of a 3D finite-difference based electromagnetic modeling which included applications in oil & gas industry as well as medical industry. For applications in oil & gas industry, we focused on the electromagnetic modeling aspect of the digital rock physics (DRP) to understand the relationship between the micro-structures and contents within the structure to their electrical properties. This is achieved via using the 3D rock micro-CT images and performing electromagnetic modeling using the 3D numerical mixing law (finite difference method based), which is a robust numerical method with high efficiency. Based on the results of this investigation, one can establish the relationship between the rock structure/porous space filling materials and the buck electrical properties, such as the permittivity and the conductivity. Additionally, conventional methods to extract the electrical properties from Micro-CT rock images require significant computational resources. This thesis also includes a novel multi-scale method for such large-scale modeling based on a hierarchy approach. Without losing any information from the original Micro-CT images, the method uses the mixing theory to extract equivalent rock electrical properties at multi-level and cascades all results at different level to achieve the overall rock properties. The method proposed in this application effectively overcome previous approximation that needs to decimate the original images and all vital information will be remained. Modelling and simulations are performed at multi-scale with different choices of sub model sizes to understand the effect of partition on the overall accuracy. For the application in medical industry, we focused on the spinal cord stimulation. Spinal cord stimulation (SCS) is a type of neuro-stimulation therapy proven to be effective for many chronic pain suffers; it helps mask pain by blocking or modifying pain signals before they reach the brain. The main purpose of this research is to evaluate the dorsal column (DC) activation region that relate to dermatomal coverage. A paddle lead with 4×5 contact array was utilized to achieve expected coverage of DC fibers. An efficient 3D finite-difference-based method was applied to obtain the field potentials inside the spinal cord, which can be coupled to the second step biophysical mammalian myelinated fiber model to identify the DC activation region.