Thermodynamics of flow in porous media


Objective: To provide a set of equations and relations for immiscible two-phase flow in porous media connecting the physics at the pore scale with the macroscopic level where the porous medium may be described as a homogeneous continuum.

A Monte Carlo algorithm for immiscible two-phase flow in porous media. In the steady state, as statistics depends on a small number of macroscopic parameters, all steady-state properties therefore should be possible to describe completely by the ensemble distribution. Here we propose a Monte Carlo algorithm for two-phase flow based on the configurational probability and compare the results with time stepping. The figure show the implementation. Picture courtesy: Isha Savani, et. al.

Principal Investigator WP1: Professor Alex Hansen. Partners: Profs. Jan Øystein Haavig Bakke, Dick Bedeaux, Sarah Codd, Eirik Grude Flekkøy, Signe Kjelstrup, Knut Jørgen Måløy, Miguel Rubi, Laurent Talon, Renaud Toussaint, Marios Valavanides. Associate professor: Per Arne Slotte. PhD-candidates: Magnus Aashammer Gjennestad. 

Description: This field covers a range of scales and the results are both about the steady state distributions and about the transport laws. The former subject is the analog of equilibrium statistical physics, while the latter addresses the question of how these statistical mechanical results may form or constrain the macroscopic laws of displacement.

We aim to derive the set of thermodynamic equations for immiscible two-phase flow in porous media. The ensemble distribution for steady-state immiscible flow we have derived corresponds to the microcanonical ensemble. The corresponding one for a representative elementary volume would be the canonical ensemble. We will establish ergodicity for the Monte Carlo method for network models.

We will pursue the transport laws along several routes, one of which is based on network simulator for flow in porous media. In this context, we expect to find a non-linear relationship between flow rate and pressure drop for both two- and three-dimensional porous media.

We have recently established that an interesting new class of Onsager reciprocity relations may be derived from time-reversibility at a mesoscopic- rather than microscopic level. These relations serve to constrain the macroscopic laws of dispersion in porous media flow.

Plenary lectures at international conferences and distinguished lectures

Media coverage

  1. Geoforskning: Fremragende forskning på porenivå, 17 March 2017
  2. Titan: Kunnskap om olje skal gi verden rent vann, 10 March 2017

Selected articles before center launch

Selected articles from 2017

  1. E.G. Flekkoy, S.R. Pride and R. Toussaint “Onsager symmetry from mesoscopic time reversibility and the hydrodynamic dispersion tensor for coarse-grained systems Phys. Rev. E 95 (2017).  DOI:10.1103/PhysRevE.95.022136


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