A Novel Framework for Reservoir Permeability Prediction Using GPR with Grey Relational Grades and Uncertainty Quantification

Reservoir permeability prediction is crucial for hydrocarbon exploration and production. Traditional methods have limitations, and Gaussian Process Regression (GPR) offers a powerful alternative. However, GPR can be sensitive to kernel parameters. This paper proposes a novel framework, GPR with Grey Relational Lengthscale Adaptation (GRLA-GPR), that incorporates Grey Relational Grades (GRG) from NMR log data into GPR lengthscale updates to improve permeability prediction with a focus on uncertainty quantification. The framework utilizes a Radial Basis Function (RBF) and Matern kernels' GPR model and calculates GRG to capture relationships between NMR data sequences. The calculated GRG values are then used to update the GPR lengthscale during training. A validation strategy is employed to evaluate the performance. The effectiveness of the framework is assessed using accuracy metrics (mean absolute error, mean squared error and <tex xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">$R^{2})$</tex> and uncertainty quantification metrics (variance and prediction interval normalized average width). The results are compared to a baseline GPR model without GRG-based updates. The proposed framework achieved a better performance in terms of accuracy and uncertainty quantification, providing more reliable permeability estimates for informed decision-making in reservoir characterization.