High-Order Multiscale Modeling of Hydro-Mechanical Coupling in Porous Media: Bridging Micro to Macro Dynamics

Understanding the interaction between fluid flow and solid mechanics in porous media is essential in the success of many engineering operations such as hydraulic fracturing, geothermal energy extraction, carbon capture and storage, and subsurface fluid dynamics. These systems are characterized by their inherent multiscale and heterogeneous nature which cause major challenge in accurately modeling the hydro-mechanical (HM) coupling processes that govern their behavior. One important to mention is the difficulty in bridging the micro- and macro-scales in a way that captures the complex interactions between fluid pressures, stress fields, and solid displacements because the fluid flow through pores or fractures and the deformation of the solid matrix are strongly interdependent which makes accurate prediction of system behavior really hard. Traditional models including continuum-based methods fail to fully capture the complexity of these interactions especially when rapid changes occur at the micro or meso-scale such as local oscillations in gas flow and sharp stress gradients. First-order homogenization methods have been developed to improve upon simpler models, but these too are limited in their ability to account for finer details, leading to reduced accuracy in critical applications like fracture propagation in hydraulic fracturing or subsurface carbon storage. Given the limitations of existing methods, researchers thought to explore more sophisticated models that can address these challenges. To this account, new study published in International Journal for Numerical Methods in Engineering and conducted by Hong Zuo Assistant Professor of China University of Mining and Technology, Associate Professor Zhiqiang Yang from the Harbin Institute of Technology and co-authors Junzhi Cui, Shouchun Deng, Haibo Li, and Zitao Guo, the researchers developed novel high-order multiscale asymptotic models that can bridge the gap between different scales and better predict both global and local behaviors. By incorporating high-order correctors, they aimed to capture the nonlinear and oscillatory phenomena that are often missed by traditional methods.

The researchers demonstrated that their models could outperform traditional methods by accurately capturing the local and global behaviors of fluid flow and solid deformation. To achieve this, the team designed representative cases that featured varying contrasts in material properties and constitutive coefficients. These cases were selected to test the models’ ability to predict the behavior of systems with significant heterogeneity and multi-scale interactions, which are common in real-world applications like hydraulic fracturing and subsurface fluid dynamics. One key aspect of this work was the development of a high-order asymptotic expansion technique, which allowed the researchers to introduce correctors at different scales macro, meso, and micro. They applied this method to several benchmark problems where traditional models typically struggle, particularly in cases involving sharp pressure gradients and strong local stress concentrations. For example, one case involved simulating gas transport in a porous medium with micro/nanopores, where slippage effects and high-stress zones would normally be difficult to model accurately. By using their high-order models, the researchers found that they could predict gas flow patterns with a level of precision that far exceeded first-order homogenization approaches. The models successfully captured the intricate variations in pressure and deformation fields, proving their value in accurately resolving both large-scale behavior and small-scale fluctuations.

The authors validated the model’s performance in predicting macro effective properties in fractured media, a complex phenomenon that is vital in applications like hydraulic fracturing. Traditional models often overlook the early stages of crack initiation at the micro-scale, where tiny fractures grow and coalesce into larger cracks that can influence the entire system. In this case, the high-order correctors allowed the model to predict the localized stress concentrations that lead to micro-crack propagation. They observed that their model could simulate the transition from micro to macro-scale more accurately than lower-order models, which tended to smooth out these critical local variations. This was a significant finding, as it suggested that the high-order models could be applied to optimize hydraulic fracturing techniques by improving the precision of crack predictions. Additionally, the researchers also investigated the behavior of stress-sensitive porous media where variations in pore pressure could lead to changes in permeability and overall fluid transport. In these experiments, the team compared their model’s predictions with data obtained from traditional numerical methods, such as finite element modeling. Their model consistently outperformed the standard approaches, especially in scenarios where rapid changes in pressure and stress occurred. For example, the high-order models were able to capture the effects of gas slippage and pressure-induced permeability changes, providing insights that could be crucial for industries like natural gas extraction or geothermal energy. The findings from these experiments reinforced the model’s robustness and versatility, confirming that it could handle complex nonlinearities and interactions across multiple scales. We noticed that throughout their study, the researchers emphasized the importance of validating their models against high-accuracy results obtained through direct numerical simulations (DNS). These simulations, performed with extremely fine meshes, served as the benchmark for comparing the performance of the high-order models. In each case, the researchers found that their models closely matched the DNS results, often with significantly less computational cost and higher efficiency. This was particularly important because one of the key challenges in modeling HM coupling in porous media is the computational expense associated with solving problems across multiple scales. The high-order models offered a solution that was not only more accurate but also more computationally feasible, making them a practical tool for real-world engineering applications.

In conclusion, Professor Hong Zuo and Zhiqiang Yang and the co-authors developed high-order models and high-order correctors that provide an unprecedented level of detail in capturing local oscillations and sharp gradients, which are often critical for determining the overall system behavior. These are very important solutions in hydraulic fracturing, geothermal energy, and carbon capture: the accurate prediction of fluid flow and solid deformation across multiple scales. In our opinion another important implication of the new study its potential to significantly improve the accuracy and efficiency of engineering simulations where for instance in oil and gas extraction it can predict where cracks will initiate and propagate can optimize the hydraulic fracturing process and by this reduces costs and minimize environmental impacts. Similarly, in geothermal energy systems the enhanced modeling of fluid flow and heat transfer in fractured rock can lead to more efficient energy extraction. Moreover, understanding the behavior of stored gases in subsurface reservoirs in say carbon capture and storage is vital in ensuring long-term stability and preventing leakage. We have to highlight a major advantage of the versatility of the reported high-order models which can be easily adapted to other multi-physical field problems, such as thermal-hydro-mechanical coupling and make them a valuable tool in many engineering domains.