Program Overview

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Course Overview

The course "Flows in Porous Media" is offered at the Norwegian University of Science and Technology (NTNU) with the course code KJ8210.

Course Details

• Credits: 7.5
• Level: Doctoral degree level
• Course Start: Autumn 2025
• Duration: 1 semester
• Language of Instruction: English
• Location: Trondheim
• Examination Arrangement: Assignment

About the Course

Course Content

The course covers various topics including:

• Geometry of porous media
• Hydrodynamics
• Statistical mechanics
• Simulation methods

The specific contents include:

1. Geometry of porous media - Porosity and the packing of spheres - Real Rocks (porosity distributions, correlations, sedimentrary processes) - Fractals (basic theory, examples from mathematics and box-counting)
2. Hydrodynamics - Navier Stokes equation - Examples of low Raynold number flows (Pouiseuille, Couette and Batchelors lubrication theory) - Darcy's law - Karman-Kozeny - Capillarity, droplets and Laplace law (water is adhesive and supports tension) - Youngs law and wetting - Examples of multi-phase flows (Washburn equaton and the Saffman-Taylor instability) - Capillary dominated flow in porous media (application of box-counting) - Viscous fingering (applicationg of box-counting for fractal dimension) Steady states and the justification of REV approaches (when can we assume that the result of averaging is independent of REV size?)
3. Statistical mechanics - Diffusion and the Langevin equation (leading up to the Einstein relation) - Green-Kubo relations (for the measurement of diffusivity and viscosity via MD. Derive for D, generalize to viscosity) - Percolation and invasion percolation
4. Simulation methods - Random walks and the advection diffusion equation - Basic principles of molecular dynamics (Newton, Lennard Jones and the celocity Verlet algorithm) - Lattice Boltzmann methods (Basic algorithm fir Navier Stokes and the additions that introduce diffusive tracers, surface tension and thermal gradients/buoyancy) - Network models (Basix algorithm for the flow of fluids or electric currents as well as the use of Washburn equation) - Invasion percolation: Basix model coded efficiently as well as the added feature of gradients/gravity

Learning Outcome

After completing the course, the candidate will have the following knowledge, skills, and general competence:

• Knowledge: Masters the relevant theory, problem formulations, and methodologies for description of transport in porous media. Is able to evaluate when it is appropriate to use one vs. another method.
• Skills: Can plan and perform a project at an advanced level using the course toolbox.
• General Competence: Can perform research at a high international level. Has knowledge of recent enabling technologies that meet the needs of society, when the field of transport in porous media is concerned.

Learning Methods and Activities

The course includes discussion groups, problem-solving, lectures, and video lectures.

Compulsory Assignments

• Exercises
• Project report

Further on Evaluation

The assessment will be based on the project assignment.

Recommended Previous Knowledge

Assumed background of the students: Equilibrium statistical mechanics. Some students may know about diffusion/Langevin equations/basic theory of Onsager reciprocity relations, others will know the Boltzmann equation.

Required Previous Knowledge

A basic course in thermodynamics and knowledge corresponding to mathematics 1-3 are required for participation. The course will serve as a link to the experimental course in PoreLab. But it does not depend on this course.

Subject Areas

• Chemical Engineering
• Physics
• Geophysics
• Chemistry

Examination

• Examination Arrangement: Assignment
• Grade: Passed / Not Passed
• Ordinary Examination - Autumn 2025: Assignment with a weighting of 100/100. Submission is due at 12:00, and the exam system used is Inspera Assessment.