Hybrid Proxy Model for Extrapolating Cumulative Oil Production with Different Locations: Polynomial-Fast Marching Method

Abstract

Well-placement optimization is a complex problem critical for maximizing hydrocarbon recovery while minimizing operational costs. The traditional methods that are used for evaluation have drawbacks such as full-physics simulation while accurate is computationally expensive, reduced-physics proxy models are less accurate, deep learning as a proxy model needs many run simulations, and Tree-based machine learning models like Extreme Gradient Boosting (XGBoost), although efficient, struggle with extrapolation, limiting their utility in scenarios where predictions extend beyond training data. To address these limitations, we apply a new hybrid approach that combines the Fast Marching Method (FMM) and Polynomial-XGBoost (linear-based) to enhance the extrapolation capabilities as an evaluation tool for well placement problems. Our approach incorporates polynomial features to capture non-linear relationships between reservoir properties (e.g., permeability, porosity) and cumulative oil production. We evaluated our approach using the SPE10 model, focusing on both interpolation and extrapolation datasets. Cross-validation results demonstrate that the proposed model significantly outperforms traditional XGBoost, achieving an average R² of 94% compared to 88% for XGBoost in interpolation scenarios. In extrapolation tests, our model showed an average R² of 83.9%, well above XGBoost's 56.3%, highlighting its superior ability to predict well performance beyond the training data range. This study shows that the integration of FMM and Polynomial-XGBoost offers a more reliable and computationally efficient alternative to existing proxy models, particularly in complex reservoirs. Our hybrid model significant improvement and shows promising results as a proxy model.