Field-Circuit Coupling With Response Surface Model for the Optimization of Flexible Printed RF Coil in Unilateral NMR Logging Sensor

The unilateral wireline nuclear magnetic resonance (NMR) logging sensor is an effective and promising tool for estimating petroleum reservoirs. The flexible printed coil (FPC) is a critical component for the sensor to get a high signal-to-noise ratio (SNR). Unfortunately, because of its intricate multiscale properties, it is difficult to calculate the magnetic field and equivalent circuit parameters of FPC in order to determine the SNR of the sensor. It is, therefore, impossible to achieve rapid optimization of the FPC to increase the SNR of the sensor. This study introduces a novel simulation approach that combines the 2-D field-circuit coupling method with the multiquadric radial basis function (MQ-RBF)-based response surface model. The purpose is to increase the SNR of the sensor by efficiently optimizing the FPC structure. The suggested 2-D field-circuit coupling method allows for quick calculation of FPC, while eliminating the need for sophisticated 3-D finite element simulation. Using the results from the 2-D field-circuit coupling method, the calculation efficiency for the SNR of the sensor with various FPC structures is further enhanced by employing the analytical MQ-RBF-based response surface model. This approach combines the response surface model for SNR prediction with the genetic algorithm (GA) for optimization, enabling the efficient identification of the optimal FPC structure with high SNR. The NMR signals of the sensor equipped with the new FPC and the old FPC were tested and compared using the Carr-Purcell–Meiboom-Gill (CPMG) sequence, with copper sulfate employed as the measurement sample. The experimental results demonstrate that the SNR of the sensor with the new FPC has improved by 32.2% compared to that with the old FPC.