International Council for Education, Research and Training

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

Bansal, Rekha

Assistant Professor (Department of Mathematics), Pt. Deen Dayal Upadhyaya Rajkiya Mahila Mahavihalya Farah Mathura

Abstract

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.

Keyboards: Hydrocarbon, Multiphase, Environmental, Challenges, Resource Development

Impact Statement

Groundwater resources are critical to global water supply, particularly in arid and semi-arid regions where surface water is scarce. However, their sustainable development and management require a detailed understanding of the complex physical processes governing subsurface flow and contaminant transport. Mathematical modelling offers a powerful framework for simulating these processes, enabling researchers and policymakers to make informed decisions based on predictive analysis and scenario testing.

This research contributes to the advancement of mathematical and computational techniques for modelling flow and transport in porous media, with a focus on applications in groundwater resource development. By integrating partial differential equations, numerical methods, and data-driven calibration techniques, the models developed improve the accuracy and reliability of groundwater assessments. These tools can predict the movement of water and solutes under various environmental conditions, identify optimal extraction strategies, and assess the risk of contamination.

The broader impact of this work lies in its potential to guide sustainable groundwater management practices, inform infrastructure development, and support climate change adaptation strategies. Furthermore, it contributes to the scientific community by advancing mathematical methodologies and fostering interdisciplinary collaboration between hydrologists, engineers, and applied mathematicians. Ultimately, this research empowers stakeholders with better tools to protect and optimize one of Earth’s most vital natural resources—groundwater.

About The Author

Dr. Rekha Bansal is a dedicated academician and author, currently serving as an Assistant Professor in the Department of Mathematics at Pt. Deen Dayal Upadhyaya Rajkiya Mahila Mahavidyalaya, Farah, Mathura. With a strong academic background and a deep passion for mathematics, she has made significant contributions to undergraduate mathematics education. Dr. Bansal is widely respected for her clear and effective teaching methods, which simplify complex mathematical concepts and make them accessible to students. Her textbooks are known for their structured content, accuracy, and student-centric approach, making them valuable resources for B.Sc. mathematics courses. In addition to teaching, she actively participates in academic development through curriculum planning and academic mentoring. Her dedication to the field is evident in her continuous efforts to inspire and guide students toward academic excellence. Through her scholarly work and classroom teaching, Dr. Rekha Bansal plays a vital role in shaping the future of mathematics education in higher institutions.

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