# KJ8210 - Flows in Porous Media

### Examination arrangement

Examination arrangement: Portfolio assessment

Evaluation Weighting Duration Grade deviation Examination aids
Oppgave 10/100
Rapport 90/100

### Course content

Motivation in terms of ground water flows, biological tissue, hydrocarbon management, fuel cells, electrophoresis, building materials and the quest for the governing equations.

Contents
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 (Could be left entirely for the next chapter?)
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: (i) Masters the relevant theory, problem formulations and methodologies for description of transport in porous media (ii) 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: (i) Can perform research at a high international level. (ii) Has knowledge of recent enabling technologies that meets the needs of society, when the field of transport in porous media is concerned.

### Learning methods and activities

Dicsussion groups, problemsolving, lectures and video lectures

### Compulsory assignments

• Project report

### Further on evaluation

The assessment will be based on the delivered exam, and on the participation in the excercises

### 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.

### Course materials

More on the course
Facts

Version: 1
Credits:  7.5 SP
Study level: Doctoral degree level

Coursework

Term no.: 1
Teaching semester:  AUTUMN 2019

Language of instruction: English

Location: Trondheim

Subject area(s)
• Chemical Engineering
• Physics
• Geophysics
• Chemistry
Contact information
Course coordinator:

Department of Chemistry

# Examination

#### Examination arrangement: Portfolio assessment

Term Status code Evaluation Weighting Examination aids Date Time Examination system
Autumn ORD Oppgave 10/100
Autumn ORD Rapport 90/100
• * The location (room) for a written examination is published 3 days before examination date. If more than one room is listed, you will find your room at Studentweb.
Examination

For more information regarding registration for examination and examination procedures, see "Innsida - Exams"

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