Porous and Dispersed Media Course

Lesson 1 • Natural and Engineered Media Examples

Surveys real-world porous and dispersed media from geology, biology, and industry. Grounds abstract concepts in tangible applications.

Lesson 2 • Microstructure and Morphology

Examines internal geometry of porous and dispersed media at micro and macro scales. Connects morphology to transport and mechanical behavior.

Lesson 3 • Key Physical Properties

Covers porosity, void fraction, bulk density, and specific surface area as primary characterization parameters. Links each property to practical measurement methods.

Lesson 1 • Fractal and Multiscale Descriptions

Introduces fractal geometry for self-similar porous structures and multiscale modeling strategies. Extends classical descriptions to irregular media.

Lesson 2 • Network and Graph Models

Presents pore network models as simplified representations of complex media. Connects network topology to transport predictions.

Lesson 3 • Continuum and Averaging Approaches

Covers volume averaging and homogenization to derive continuum equations from pore-scale physics. Bridges micro-scale detail to macro-scale models.

Lesson 1 • Stokes Flow at the Pore Scale

Analyzes viscous flow at the pore scale using Stokes equations and lubrication theory. Connects pore-scale physics to macroscopic permeability.

Lesson 2 • Darcy's Law and Permeability

Derives Darcy's law from first principles and defines intrinsic permeability. Establishes the central transport law for saturated porous flow.

Lesson 3 • Boundary Conditions and Flow Geometry

Covers boundary condition formulation for porous media flow problems in various geometries. Prepares students for numerical and analytical solution strategies.

Lesson 4 • Non-Darcy and Inertial Flow Regimes

Examines Forchheimer and Brinkman extensions for high-velocity and transitional flows. Identifies conditions where Darcy's law breaks down.

Lesson 1 • Capillary Pressure and Interfacial Phenomena

Introduces capillary pressure, Young-Laplace equation, and interfacial tension in porous media. Establishes the driving forces for multiphase flow.

Lesson 2 • Relative Permeability Concepts

Defines relative permeability functions and their dependence on saturation and wettability. Links pore-scale fluid distribution to macroscopic flow resistance.

Lesson 3 • Buckley-Leverett Theory and Extensions

Applies fractional flow theory to immiscible displacement in one dimension. Provides analytical tools for predicting saturation fronts.

Lesson 4 • Drainage and Imbibition Processes

Examines pore-scale mechanisms of drainage and imbibition, including snap-off and cooperative filling. Connects pore events to macroscopic saturation changes.

Lesson 1 • Non-Fickian and Anomalous Transport

Introduces non-Fickian transport phenomena including tailing, early breakthrough, and anomalous diffusion. Presents CTRW and dual-porosity models.

Lesson 2 • Hydrodynamic Dispersion Mechanisms

Analyzes mechanical dispersion arising from velocity heterogeneity at pore and field scales. Connects pore-scale velocity distributions to macroscopic dispersion coefficients.

Lesson 3 • Advection-Diffusion-Reaction Equations

Formulates the advection-diffusion-reaction equation for reactive solute transport. Provides analytical and numerical solution strategies.

Lesson 4 • Colloidal and Particle Transport

Examines transport, filtration, and deposition of colloids and fine particles in porous media. Addresses clogging and mobilization in environmental and industrial contexts.

Lesson 1 • Local Thermal Equilibrium and Non-Equilibrium

Distinguishes local thermal equilibrium from two-temperature models for solid and fluid phases. Identifies conditions requiring non-equilibrium treatment.

Lesson 2 • Natural Convection and Instabilities

Examines buoyancy-driven flow and onset of convective instability in porous layers. Applies Horton-Rogers-Lapwood analysis to stability problems.

Lesson 3 • Forced Convection in Porous Media

Analyzes forced convection heat transfer using Darcy and Brinkman flow models. Provides correlations and solutions for engineering design.

Lesson 4 • Effective Thermal Conductivity

Derives effective thermal conductivity of porous media using mixing rules and homogenization. Connects microstructure to macroscopic thermal performance.

Lesson 1 • Mercury Intrusion and Gas Adsorption

Presents mercury intrusion porosimetry and gas adsorption for pore size distribution measurement. Addresses assumptions, artifacts, and data interpretation.

Lesson 2 • Mechanical and Thermal Property Testing

Introduces uniaxial compression, triaxial testing, and thermal conductivity measurement for porous solids. Connects mechanical and thermal data to structural parameters.

Lesson 3 • Permeability and Flow Measurement

Describes steady-state and transient permeability measurement methods for liquids and gases. Covers core flooding apparatus and data quality assurance.

Lesson 4 • Transport and Dispersion Experiments

Covers tracer injection, breakthrough curve analysis, and NMR diffusometry for transport characterization. Links experimental data to model parameters.

Lesson 1 • Continuum-Scale Finite Element Methods

Applies finite element methods to Darcy flow, transport, and heat transfer at the continuum scale. Addresses mesh generation for heterogeneous domains.

Lesson 2 • Multiscale and Upscaling Algorithms

Introduces multiscale finite element and numerical upscaling methods for heterogeneous porous media. Bridges pore-scale and field-scale simulations.

Lesson 3 • Finite Volume and Finite Difference Methods

Presents finite volume and finite difference discretization for porous media equations. Emphasizes conservation properties and practical implementation.

Lesson 4 • Validation, Benchmarking, and Workflow

Establishes best practices for simulation validation, benchmarking against analytical solutions, and reproducible computational workflows. Prepares students for professional simulation practice.