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Supervisor
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Date
2026-03-09
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Abstract
Porous media flow plays a fundamental role in a wide range of scientific and engineering applications, including groundwater hydrology, petroleum reservoir simulation, environmental remediation, and subsurface heat storage. Single-phase flow, in particular, serves as a foundational concept in understanding more complex multiphase and reactive transport processes. It describes the movement of a single fluid, such as water, oil, or gas, through a porous solid matrix under the influence of pressure gradients and physical properties of the medium. This chapter provides an exploration of incompressible single-phase flow through porous media, combining analytical derivations, numerical modeling, and computational implementation. Beginning with the formulation of the governing equations based on Darcy's law and the principle of mass conservation, the chapter builds toward solving these equations under various boundary and initial conditions. Analytical solutions are first presented for simplified geometries, offering insights into pressure distribution and the influence of key physical parameters such as permeability, viscosity, and flow rate. These solutions serve as validation benchmarks for more sophisticated numerical approaches. Subsequently, numerical methods, including finite difference and finite element methods, are introduced to solve the pressure equation in higher-dimensional and more realistic settings. To bridge theory and application, this chapter also presents MATLABĀ® and Python implementations for simulating flow in two-dimensional domains, supported by graphical visualizations. Furthermore, advanced topics such as solute transport, desiccant-based water harvesting, and stability criteria are introduced to highlight the relevance of single-phase flow modeling in both environmental and industrial contexts.
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Book title
Numerical Methods in Porous Media MATLABĀ® and Python Approaches