Shape optimization of magnet system for NMR logging-while-drilling sensor via B-spline boundaries and mesh deformation

Abstract Real-time nuclear magnetic resonance (NMR) logging-while-drilling (LWD) is critical for reservoir evaluation. The magnet system, as the core of the NMR-LWD sensor, directly influences signal quality and measurement temperature stability. However, traditional magnet system design methods are based on empirical structures and size optimization, making it difficult to obtain a novel and excellent magnet system. This study proposed a novel shape optimization method via B-spline boundaries and mesh deformation. First, the boundaries of the magnet system are controlled by the B-spline curves to present more novel structures. To improve the efficiency of finite element analysis (FEA) and guarantee a seamless optimization, the radial basis function-based mesh deformation method is applied to obtain the mesh for different shapes without time-consuming remeshing. Finally, the multi-objective optimization is conducted. The performance of some typical Pareto solutions is evaluated and compared with that from traditional size optimization based on FEA. It is found that the proposed shape optimization yields a magnet system that is superior to its size optimization counterpart, providing a 10% stronger magnetic field and 56% better stability in signal strength against temperature variations.