Abstract

Efficient optimization of unconventional field development necessitates understanding and prediction of the hydraulic fracturing process. Conventional models fall short in capturing dynamic fluid and rock behavior, hindering the optimization of completion designs. Analytical models are often simplistic, while numerical models are computationally inefficient and require inputs for rock and fluid characterization that are not commonly available at scale. This paper aims to introduce a novel workflow that addresses these limitations, offering a refined approach to model hydraulic fracturing processes and assess fracturing performance for practical field applications.

Our proposed workflow comprises two key components: 1) A data-driven and physics-constrained model utilizing routine field measurements to forecast fracturing pressure for various injection rates and schedules. This model is shown to capture complexities associated with single and multi-stage fractures by accounting for both the injection and fall-off periods, and 2) Calculation of injection stimulated reservoir volume (SRV) as a performance metric to evaluate the efficacy of the fracturing job. We employ Sparse Identification of Nonlinear Dynamics (SINDy) to discover the fracturing dynamics by creating a hybrid regression model that combines physics-based and data-driven basis functions.

Validation of the proposed workflow, initially through analytical models and subsequently in complex numerical models, showcases its effectiveness. Hybrid SINDy adeptly captures dynamic functions in both scenarios, exhibiting precision and consistency across various injection rate schedules. The model remains resilient in predicting pressure data, even in the presence of noise, and effectively handles diverse injection time durations. The model performs reasonably well under varying injection rates in single-stage models and produces a robust model for complex rate profiles, addressing the impact of injection rate in multi-stage scenarios. Importantly, the correlation between injection SRV and fracture pore volume underscores its potential as a metric for evaluating fracturing performance.

Our hybrid-model-based workflow not only establishes a physically interpretable governing equation but also provides a practical framework to train and predict fracture pressure for optimizing unconventional completion designs. Demonstrated efficacy through analytical and numerical models reinforces the practical feasibility of this approach. This paper contributes a sophisticated methodology that overcomes existing limitations, paving the way for enhanced decision-making in the complex landscape of hydraulic fracturing optimization for unconventional field development.

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