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.

The network model consists of a square lattice oriented at 45◦ with respect to the vertical direction; see arrow. The network is periodic in both the vertical and horizontal directions. Hence, fluids that leave the network along the upper border reappear at the bottom border, and fluids that leave along the left border enter at the right border and vice versa. The links are filled with an immiscible mixture of wetting (white) and nonwetting (red) fluids. A pressure difference ΔP = P1 − P2 between the upper and lower borders drives the flow Q in the vertical direction. The nonwetting fluids form channels that span the network once the flow has reached steady state as shown in the figure. Steadystate flow means that the average flow parameters such as Q fluctuate around well-defined constant average values, whereas, at the level of the links, the interfaces between the immiscible fluids move,resulting in fluid clusters constantly merging and breaking up.

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

Bedeaux, Dick; Savani, Isha; Kjelstrup, Signe; Hansen, Alex; Vassvik, Morten; Santanu, Sinha. Ensemble distribution for immiscible two phase flow in porous media. Interpore conference in Rotterdan, Netherlands; 2017-05-07 – 2017-05-11. NTNU

Bedeaux, Dick; Savani, Isha; Kjelstrup, Signe; Hansen, Alex; Vassvik, Morten; Santanu, Sinha. Ensemble Distribution for Immiscible Two- Phase Flow in Porous Media. Opening PoreLab, Oslo, Norway; 2017-09-05 – 2017-09-08. NTNU

Hansen, Alex; Sinha, Santanu; Bedeaux, Dick; Kjelstrup, Signe; Savani, Isha; Vassvik, Morten. Flow in porous materials – as seen from thermodynamics. 9th International Conference on Porous Media; 2017-05-07 – 2017-05-11. NTNU

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 from 2017

S. Sinha, A. T. Bender, M. Danczyk, K. Keepseagle, C. Prather, J. Bray, L. Thrane, J. D. Seymour, S. L. Codd, A. Hansen. Effective Rheology of Two-Phase Flow in Three-Dimensional Porous Media: Experiment and Simulation. Transport in Porous Media 119 (1), 77-94

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

Savani, I.; Sinha, S.; Hansen, A.; Bedeaux, D.; Kjelstrup, S.; Vassvik, M. A Monte Carlo Algorithm for Immiscible Two-Phase Flow in Porous Media. Transport in Porous Media 2017 ;Volum 116.(2) s. 869-888.

I. Savani, D. Bedeaux, S. Kjelstrup, M. Vassvik, S. Sinha, A. Hansen.  “Ensemble distribution for immiscible two-phase flow in porous media” . Phys. Rev. E 95, (2017). DOI = 10.1103/PhysRevE.95.023116.

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