Study of a Robust SEM-based Domain Decomposition Method for the Analysis of Well-Logging Tools in Multilayered Anisotropic Geophysical Formations

• Grant number: 25/16230-2
• Support Opportunities: Scholarships abroad - Research Internship - Post-doctor
• Start date: January 01, 2026
• End date: December 31, 2026
• Field of knowledge: Engineering - Electrical Engineering - Telecommunications
• Principal Investigator: Guilherme Simon da Rosa
• Grantee: Raul Oliveira Ribeiro
• Supervisor: Adrian Amor-Martin
• Host Institution: Faculdade de Engenharia. Universidade Estadual Paulista (UNESP). Campus São João da Boa Vista. São João da Boa Vista , SP, Brazil
• Institution abroad: Universidad Carlos Iii De Madrid, Campus De Leganés, Spain
• Associated to the scholarship: 24/05690-0 - Modeling of electromagnetic sensors for profiling and inspection of oil wells in anisotropic geophysical formations, BP.PD

Abstract

The prospecting of hydrocarbon reservoirs in deep and complex geophysical formations is a critical task for the oil and gas industry, particularly in the context of intelligent drilling in ultra-deep wells, such as those in the Campos and Santos Basins in Brazil. This scenario demands robust computational methods for solving Maxwell's equations under highly heterogeneous, lossy, and anisotropic media conditions. This project aims to develop efficient numerical techniques for modeling electromagnetic logging sensors for reservoir evaluation. Geophysical formations of interest can be modeled as cylindrical structures with both axial and radial stratifications, often exhibiting strong contrasts in media properties such as conductivity and permittivity. Traditional full-domain 3D discretization approaches, including finite difference and finite element methods, may become computationally prohibitive in these scenarios due to their high memory and CPU demands. To address these challenges, we propose a hybrid numerical strategy combining spectral accuracy and domain decomposition. The problem is partitioned into axial subdomains. Within each axial region, a domain decomposition method (DDM) is applied in the radial direction, where each concentric layer is modeled using the spectral element method (SEM). This enables the use of adaptive polynomial orders tailored to the local properties of each radial layer. Finally, the solutions in different axial subdomains are connected using the mode-matching technique (MMT), ensuring field continuity while maintaining a semi-analytical character. In summary, the project explores the integration of SEM, DDM, and MMT to develop a computationally efficient and robust framework for simulating electromagnetic sensors operating in stratified and anisotropic well-logging environments. (AU)