{"id":12917,"date":"2025-05-22T16:46:00","date_gmt":"2025-05-22T15:46:00","guid":{"rendered":"https:\/\/icertpublication.com\/?page_id=12917"},"modified":"2026-04-03T09:30:43","modified_gmt":"2026-04-03T04:00:43","slug":"mathematical-approaches-for-modelling-flow-and-transport-porous-media-enhancing-groundwater-resource-development","status":"publish","type":"page","link":"https:\/\/icert.org.in\/index.php\/shodh-sari-2\/mathematical-approaches-for-modelling-flow-and-transport-porous-media-enhancing-groundwater-resource-development\/","title":{"rendered":"Mathematical Approaches for Modelling Flow and Transport Porous Media: Enhancing Groundwater Resource Development"},"content":{"rendered":"\t\t
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Shodh Sari-An International Multidisciplinary Journal<\/h1>\t\t\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t
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Vol-04, Issue-02 (Apr-Jun 2025)<\/h2>\t\t\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t
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An International scholarly\/ academic journal, peer-reviewed\/ refereed journal, ISSN : 2959-1376<\/h5>\t\t\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t\t<\/div>\n\t\t<\/div>\n\t\t\t\t\t<\/div>\n\t\t<\/section>\n\t\t\t\t
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Mathematical Approaches for Modelling Flow and Transport Porous Media: Enhancing Groundwater Resource Development<\/h4>\t\t\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t
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Bansal, Rekha<\/span><\/p>

Assistant Professor (Department of Mathematics), Pt. Deen Dayal Upadhyaya Rajkiya Mahila Mahavihalya Farah Mathura<\/span><\/p>\t\t\t\t\t\t\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t\t<\/div>\n\t\t<\/div>\n\t\t\t\t\t<\/div>\n\t\t<\/section>\n\t\t\t\t

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DOI: <\/span>https:\/\/doi.org\/10.59231\/SARI7832<\/span><\/a><\/p>

Subject: Applied Mathematics \/ Hydrology \/ Environmental Engineering<\/span><\/p>

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Received: January 20, 2025<\/span><\/p>

Accepted: March 05, 2025<\/span><\/p>

Published: April 01, 2025<\/span><\/p>\t\t\t\t\t\t\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t

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Thematic Classification: Mathematical Modelling, Porous Media Flow, Transport Phenomena, Groundwater Resource Development, Hydrogeology, Environmental Fluid Mechanics.<\/span><\/p>\t\t\t\t\t\t\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t\t<\/div>\n\t\t<\/div>\n\t\t\t\t\t<\/div>\n\t\t<\/section>\n\t\t\t\t\t<\/div>\n\t\t<\/div>\n\t\t\t\t\t<\/div>\n\t\t<\/section>\n\t\t\t\t

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Abstract\n<\/h6>\t\t\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t
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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\u2019s 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\u2019s 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.<\/span><\/p>

Keyboards:<\/span> Hydrocarbon, Multiphase, Environmental, Challenges, Resource Development<\/span><\/p>\t\t\t\t\t\t\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t\t<\/div>\n\t\t<\/div>\n\t\t\t\t\t<\/div>\n\t\t<\/section>\n\t\t\t\t

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Impact Statement<\/h6>\t\t\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t
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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.<\/span><\/p>

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.<\/span><\/p>

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\u2019s most vital natural resources\u2014groundwater.<\/span><\/p>\t\t\t\t\t\t\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t\t<\/div>\n\t\t<\/div>\n\t\t\t\t\t<\/div>\n\t\t<\/section>\n\t\t\t\t

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About The Author<\/h6>\t\t\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t
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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.<\/span><\/p>\t\t\t\t\t\t\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t\t<\/div>\n\t\t<\/div>\n\t\t\t\t\t<\/div>\n\t\t<\/section>\n\t\t\t\t

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Cite this Article\n<\/h6>\t\t\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t
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APA 7th Style<\/span>\u00a0<\/span><\/p>

Bansal, R. (2025). Mathematical approaches for modelling flow and transport porous media: Enhancing groundwater resource development. <\/span>Shodh Sari-An International Multidisciplinary Journal<\/span>, <\/span>4<\/span>(02), 407\u2013425. <\/span>https:\/\/doi.org\/10.59231\/SARI7832<\/span><\/a><\/p>

Chicago 17th Style<\/span>\u00a0<\/span><\/p>

Bansal, Rekha. “Mathematical Approaches for Modelling Flow and Transport Porous Media: Enhancing Groundwater Resource Development.” <\/span>Shodh Sari-An International Multidisciplinary Journal<\/span> 4, no. 2 (2025): 407\u2013425. <\/span>https:\/\/doi.org\/10.59231\/SARI7832<\/span><\/a>.<\/span><\/p>

MLA 9th Style<\/span>\u00a0<\/span><\/p>

Bansal, Rekha. “Mathematical Approaches for Modelling Flow and Transport Porous Media: Enhancing Groundwater Resource Development.” <\/span>Shodh Sari-An International Multidisciplinary Journal<\/span>, vol. 4, no. 2, 2025, pp. 407-425, <\/span>https:\/\/doi.org\/10.59231\/SARI7832<\/span><\/a>.<\/span><\/p>\t\t\t\t\t\t\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t\t<\/div>\n\t\t<\/div>\n\t\t\t\t\t<\/div>\n\t\t<\/section>\n\t\t\t\t

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Statements & Declarations\n<\/h6>\t\t\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t
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Review Method:<\/span> This article underwent a double-blind peer-review process by two independent external experts in Fluid Dynamics and Environmental Mathematics to ensure the mathematical rigor of the differential equations used and the physical validity of the porous media transport models.<\/span><\/p>

Competing Interests:<\/span> The author (Rekha Bansal) declares that there are no financial, personal, or professional conflicts of interest that could have inappropriately influenced the research findings or the mathematical derivations presented in this study.<\/span><\/p>

Funding:<\/span> This research was conducted as part of the author’s academic and professional activities at Pt. Deen Dayal Upadhyaya Rajkiya Mahila Mahavihalya, Mathura. No specific external grants or commercial funding were received for this work.<\/span><\/p>

Data Availability:<\/span> The analysis is based on theoretical mathematical models, including Darcy’s Law and the Advection-Dispersion Equation. Numerical simulations and parameters used for modeling groundwater flow are detailed within the manuscript. Any additional data are available from the author upon reasonable request.<\/span><\/p>

License:<\/span> Mathematical Approaches for Modelling Flow and Transport Porous Media: Enhancing Groundwater Resource Development<\/span> \u00a9 2025 by Rekha Bansal is licensed under <\/span>CC BY-NC-ND 4.0<\/span>. This work is published by the International Council for Education Research and Training (ICERT).<\/span><\/p>

Ethics Approval:<\/span> As this study is a theoretical and mathematical analysis and does not involve direct experimentation on human participants or animals, it was deemed exempt from formal ethical review by the Institutional Research Committee.<\/span><\/p>\t\t\t\t\t\t\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t\t<\/div>\n\t\t<\/div>\n\t\t\t\t\t<\/div>\n\t\t<\/section>\n\t\t\t\t

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References<\/h6>\t\t\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t
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    \n\t\t\t\t\t\n\t\t\t\t\t\t\n\t\t\t\t\t\t\t\t\tBack<\/span>\n\t\t\t\t\t<\/span>\n\t\t\t\t\t<\/a>\n\t\t\t\t<\/div>\n\t\t\t\t\t\t\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t\t<\/div>\n\t\t<\/div>\n\t\t\t\t\t<\/div>\n\t\t<\/section>\n\t\t\t\t<\/div>\n\t\t","protected":false},"excerpt":{"rendered":"

    Shodh Sari-An International Multidisciplinary Journal Vol-04, Issue-02 (Apr-Jun 2025) An International scholarly\/ academic journal, peer-reviewed\/ refereed journal, ISSN : 2959-1376 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 DOI: https:\/\/doi.org\/10.59231\/SARI7832 Subject: Applied Mathematics \/ […]<\/p>\n","protected":false},"author":1,"featured_media":0,"parent":66,"menu_order":0,"comment_status":"closed","ping_status":"closed","template":"","meta":{"_acf_changed":false,"postBodyCss":"","postBodyMargin":[],"postBodyPadding":[],"postBodyBackground":{"backgroundType":"classic","gradient":""},"site-sidebar-layout":"no-sidebar","site-content-layout":"page-builder","ast-site-content-layout":"default","site-content-style":"default","site-sidebar-style":"default","ast-global-header-display":"","ast-banner-title-visibility":"","ast-main-header-display":"","ast-hfb-above-header-display":"","ast-hfb-below-header-display":"","ast-hfb-mobile-header-display":"","site-post-title":"disabled","ast-breadcrumbs-content":"","ast-featured-img":"disabled","footer-sml-layout":"","theme-transparent-header-meta":"default","adv-header-id-meta":"","stick-header-meta":"","header-above-stick-meta":"","header-main-stick-meta":"","header-below-stick-meta":"","astra-migrate-meta-layouts":"default","ast-page-background-enabled":"default","ast-page-background-meta":{"desktop":{"background-color":"var(--ast-global-color-4)","background-image":"","background-repeat":"repeat","background-position":"center center","background-size":"auto","background-attachment":"scroll","background-type":"","background-media":"","overlay-type":"","overlay-color":"","overlay-opacity":"","overlay-gradient":""},"tablet":{"background-color":"","background-image":"","background-repeat":"repeat","background-position":"center center","background-size":"auto","background-attachment":"scroll","background-type":"","background-media":"","overlay-type":"","overlay-color":"","overlay-opacity":"","overlay-gradient":""},"mobile":{"background-color":"","background-image":"","background-repeat":"repeat","background-position":"center center","background-size":"auto","background-attachment":"scroll","background-type":"","background-media":"","overlay-type":"","overlay-color":"","overlay-opacity":"","overlay-gradient":""}},"ast-content-background-meta":{"desktop":{"background-color":"var(--ast-global-color-5)","background-image":"","background-repeat":"repeat","background-position":"center center","background-size":"auto","background-attachment":"scroll","background-type":"","background-media":"","overlay-type":"","overlay-color":"","overlay-opacity":"","overlay-gradient":""},"tablet":{"background-color":"var(--ast-global-color-5)","background-image":"","background-repeat":"repeat","background-position":"center center","background-size":"auto","background-attachment":"scroll","background-type":"","background-media":"","overlay-type":"","overlay-color":"","overlay-opacity":"","overlay-gradient":""},"mobile":{"background-color":"var(--ast-global-color-5)","background-image":"","background-repeat":"repeat","background-position":"center center","background-size":"auto","background-attachment":"scroll","background-type":"","background-media":"","overlay-type":"","overlay-color":"","overlay-opacity":"","overlay-gradient":""}},"footnotes":""},"class_list":["post-12917","page","type-page","status-publish","hentry"],"acf":[],"_links":{"self":[{"href":"https:\/\/icert.org.in\/index.php\/wp-json\/wp\/v2\/pages\/12917","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/icert.org.in\/index.php\/wp-json\/wp\/v2\/pages"}],"about":[{"href":"https:\/\/icert.org.in\/index.php\/wp-json\/wp\/v2\/types\/page"}],"author":[{"embeddable":true,"href":"https:\/\/icert.org.in\/index.php\/wp-json\/wp\/v2\/users\/1"}],"replies":[{"embeddable":true,"href":"https:\/\/icert.org.in\/index.php\/wp-json\/wp\/v2\/comments?post=12917"}],"version-history":[{"count":9,"href":"https:\/\/icert.org.in\/index.php\/wp-json\/wp\/v2\/pages\/12917\/revisions"}],"predecessor-version":[{"id":31784,"href":"https:\/\/icert.org.in\/index.php\/wp-json\/wp\/v2\/pages\/12917\/revisions\/31784"}],"up":[{"embeddable":true,"href":"https:\/\/icert.org.in\/index.php\/wp-json\/wp\/v2\/pages\/66"}],"wp:attachment":[{"href":"https:\/\/icert.org.in\/index.php\/wp-json\/wp\/v2\/media?parent=12917"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}