Intelligent Optimization of Stage and Cluster Parameters Based on Toeplitz Inverse Covariance-Based Clustering

ABSTRACT: The design of multi-stage and multi-cluster parameters in hydraulic fracturing is critical for optimizing unconventional shale oil and gas extraction. Traditional methods based on geological or well logging data are often subjective and limited. To address this, we propose the Toeplitz inverse covariance clustering (TICC) algorithm, which treats logging and shale evaluation data as time series to optimize stage and cluster design. The TICC algorithm employs multivariate time series segmentation and clustering, representing each category as a Markov random field with a Toeplitz matrix. It incorporates a penalty term to ensure continuity and interpretability, enhancing the scientific rationale behind fracturing designs. Applied to well Y in the Zijinba block, the TICC algorithm integrates four geological and four engineering sweet spot parameters to predict high-quality fracturing sections. Using FrSmart numerical simulation software, non-planar fracture extension and post-fracturing production simulations were conducted for both TICC and on-site designs. Results show that the TICC-designed scheme achieves a 4.44% higher cumulative production rate after five years, with cluster production rates better aligned with sweet spot predictions. This demonstrates the TICC algorithm's effectiveness in improving reservoir quality and production, offering a valuable tool for optimizing fracturing designs in unconventional reservoirs.