A level set method for drainage and imbibition in realistic porous media
Maša Prodanović, Center for Petroleum and Geosystems Engineering, University of Texas at
Austin
An accurate description of the mechanics of pore level displacement of immiscible fluids could
significantly improve the macroscopic parameter predictions such as capillary pressure saturation interfacial area relationships in real porous media.
Slow displacement can be modeled as a quasi-static, capillarity-controlled process. At constant pressure
and interfacial tension, pore scale fluid-fluid interfaces are modeled as constant mean curvature
surfaces. For a given location in the pore space geometry, such surfaces need not be stable (in which
case a fluid typically moves until it finds an appropriate location) nor easy to calculate. Furthermore,
tracking the topological changes of the interface, such as splitting or merging, is a significant challenge.
The irregular pore spaces in natural porous media admit many such changes.
Assuming quasi-static displacement, we recently developed ([1-3]) a simple but robust model based on
the level set method for determining fluid interface position during both drainage and imbibition. The
original method assumed zero-contact angle and arrived at geometrically correct interfaces. At the
same time, the level set based description allows for robust handling of topology changes and
independence from the pore space complexity. We show many examples of 2D and 3D displacements
in individual pores (openings) and throat (narrow constrictions), as well as simulations in imaged
porous samples and comparison to experimental results. Haines jumps at drainage and pore body
imbibition events are readily identified, as well as snap-off and trapping of the non-wetting phase.
We further discuss the extension of the method to handle non-zero contact angles. Finally, we touch
upon some applications and future directions: investigating fracture matrix transfer [4], coupling with
sediment mechanics with implications for methane hydrate growth [5-6] and determination of the
residual saturations using paramagnetic nanoparticles and magnetic field.
1. M. Prodanović and S. L. Bryant. A level set method for determining critical curvatures for drainage and
imbibition. Journal of Colloid and Interface Science, 304 (2006) 442--458.
2. M. Prodanović and S.L. Bryant. In Focus on Water Resource Research ed. E. Heikkinen, Nova Science
Publishers, Hauppage, New York chap. Resolving Meniscus Movement Within Rough Confining
Surfaces Via the Level Set Method. (in press)
3. M. Prodanović and S.L. Bryant. Physics-driven Interface Modeling for Drainage and Imbibition in
Fractures. SPE paper 110448, prepared for SPE Annual Technical Conference and Exhibition, Anaheim,
California, U.S.A., 11–14 November 2007.
4. M. Prodanović, S.L. Bryant and Z. T. Karpyn. Investigating Matrix-Fracture Transfer via a Level Set
Method for Drainage and Imbibition. SPE paper 116110 prepared for SPE Annual Technical Conference
and Exhibition held in Denver, Colorado, U.S.A., 21–24 September 2008.
5. J. Behseresht, Y. Peng, M. Prodanović, S.L. Bryant, A. Jain and R. Juanes. Mechanisms by Which
Methane Gas and Methane Hydrate Coexist in Ocean Sediments. OTC paper 19332 prepared for
Offshore Technology Conference, Houston, TX, USA, May 4-8, 2008.
6. M. Prodanović, S.L. Bryant. Capillarity Controlled Displacements in Sediments with Movable Grains:
Implications for Growth of Methane Hydrates. SPE paper 116663 prepared for SPE Annual Technical
Conference and Exhibition held in Denver, Colorado, U.S.A., 21–24 September 2008.
Short Biography:
Maša Prodanović holds a Bachelor of Science in Applied Mathematics from the University of Zagreb,
Croatia and a PhD in Computational Applied Mathematics from the Stony Brook University, USA.
Following a two-year Postdoctoral Fellowship at the Institute of Computational Engineering and
Sciences (ICES), located at the University of Texas at Austin, she moved to her current Research
Associate position in the Center for Petroleum and Geosystems Engineering (UT Austin) in 2007. Her
research interests include fluids displacement in porous media, the level set method, porous media
characterization, pore network modeling and image analysis.
For more info see http://www.ices.utexas.edu/~masha
Contact: masha@ices.utexas.edu