KJ8210 - Flows in Porous Media

About

New from the academic year 2018/2019

Examination arrangement

Examination arrangement: Portfolio assessment
Grade: Passed/Failed

Evaluation form Weighting Duration Examination aids Grade deviation
Assignment 10/100
Approved report 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

Goal: Bring the student to understand the hydrodynamics of flows in porous media, including thermal gradients and concentration gradients. Also, the student will get a toolbox to simulate the flow in porous media on different scales. The course will support the experimental course in PoreLab. But it does not depend on this course.

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

Specific conditions

Exam registration requires that class registration is approved in the same semester. Compulsory activities from previous semester may be approved by the department.

Required previous knowledge

A basic course in thermodynamics and knowledge corresponding to mathematics 1-3 are required for participation.

Course materials

Texts will be made available

Timetable

Detailed timetable

Examination

Examination arrangement: Portfolio assessment

Term Statuskode Evaluation form Weighting Examination aids Date Time Room *
Autumn ORD Assignment 10/100
Autumn ORD Approved report 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.