Mathematical Approaches for Modelling Flow and Transport Porous Media: Enhancing Groundwater Resource Development

Porous media, consisting of interconnected voids or pores, serve as critical frameworks for fluid flow and mass transport in natural and engineered systems. They play a vital role in applications ranging from groundwater resource management and hydrocarbon recovery to carbon capture and environmental remediation. Groundwater, which provides nearly half of the world’s drinking water and supports global agriculture and industry, is increasingly stressed by over-extraction, pollution, and climate change. The spatial heterogeneity of porous media, coupled with the complexity of multiphase flows and reactive transport, poses significant challenges to accurate modelling using traditional approaches like Darcy’s Law. This paper reviews advanced mathematical techniques for modelling flow and transport processes in porous media, emphasizing their application to groundwater management and other critical domains. Key approaches, including numerical methods, multiphase flow models, and reactive transport frameworks, are explored in detail. Emerging technologies, such as enhanced oil recovery (EOR) and carbon capture and storage (CCS), further illustrate the economic and environmental significance of refining porous media models. Additionally, the integration of novel tools such as machine learning and inverse modelling is highlighted as a means to improve parameter estimation and account for system heterogeneity. By addressing the limitations of traditional models and incorporating real-world complexities, this study underscores the importance of developing innovative mathematical frameworks to support sustainable resource management and environmental protection. The findings contribute to enhancing predictive capabilities for groundwater systems and optimizing solutions for energy and environmental challenges.