Multiresolution Dynamic Mode Decomposition (mrDMD) for Hydraulic Fracturing and Reservoir Characterization Applications

Abstract

Fluid flow through heterogeneous porous media and evolving fracture networks play a critical role in subsurface energy and environmental applications. Accurate monitoring and prediction of these flow patterns and fracture processes are essential for effective reservoir characterization and environmental protection in contexts such as hydraulic fracturing, enhanced oil recovery, and geothermal energy extraction. However, conventional monitoring techniques often rely on sparse or indirect measurements, limiting their effectiveness in capturing the complex spatiotemporal dynamics of coupled flow and fracture evolution in subsurface formations.
In this study, we introduce a novel data-driven methodology integrating Dynamic Mode Decomposition (DMD), Fourier Transform (FT), and Compressive Sensing (CS) to monitor and analyze dynamic fluid flow and fracture processes in porous media. Multiresolution DMD (mrDMD), applied to high-resolution experimental images, decomposes complex fluid flow dynamics into dominant spatiotemporal modes, revealing the evolution of flow patterns in heterogeneous porous media. Simultaneously, FT analysis of the corresponding strain fields provides a complementary frequency-domain perspective of the flow behavior, aiding in the identification of key spectral components of the observed flow patterns. To extend this framework to fracture evolution under sparse data conditions, we integrate CS with mrDMD to analyze acoustic emission (AE) data from hydraulic fracturing experiments. This approach enables the reconstruction and tracking of fracture initiation and propagation using only limited, sparsely distributed AE signals, overcoming the limitations of traditional monitoring methods that require dense sensor networks. The combined analysis of high-resolution 2D flow images and sparse 3D AE data allows us to link fluid flow regimes with fracture initiation and propagation, providing a more holistic understanding of these coupled processes.
A key contribution of this work is the introduction of the Temporal Evolution Factor (TEF), a novel parameter derived from DMD eigenvalues and modal amplitudes. TEF provides a dynamic metric to quantify each mode’s dominance and temporal progression. Its inclusion enables more precise identification of critical transitions in flow structure and fracture dynamics, such as mode crossovers, energy redistributions, and localized flow intensifications associated with major changes in flow patterns or fracture activity.
The proposed framework offers a robust approach to understanding subsurface fluid flow and fracture evolution, providing a data-driven strategy for early detection of critical flow or fracture events and improved reservoir characterization. By integrating advanced signal processing techniques with experimental validation, the approach yields physically interpretable results and paves the way for improved reservoir characterization and safer subsurface operations.

Date of Award	2025
Original language	American English
Supervisor	Md Rahman (Supervisor)