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Signatures of fluid–fluid displacement in porous media: wettability, patterns and pressures

Published online by Cambridge University Press:  26 July 2019

Bauyrzhan K. Primkulov ,
Amir A. Pahlavan Open the ORCID record for Amir A. Pahlavan [Opens in a new window] ,
Xiaojing Fu ,
Benzhong Zhao ,
Christopher W. MacMinn Open the ORCID record for Christopher W. MacMinn [Opens in a new window]  and
Ruben Juanes Open the ORCID record for Ruben Juanes [Opens in a new window]
Bauyrzhan K. Primkulov
Affiliation:
Department of Civil and Environmental Engineering, Massachusetts Institute of Technology, Cambridge, MA 02139, USA
Amir A. Pahlavan
Affiliation:
Department of Mechanical and Aerospace Engineering, Princeton University, Princeton, NJ 08540, USA
Xiaojing Fu
Affiliation:
Department of Earth and Planetary Science, University of California at Berkeley, Berkeley, CA 94720, USA
Benzhong Zhao
Affiliation:
Department of Civil Engineering, McMaster University, Hamilton, ON, L8S 4L7, Canada
Christopher W. MacMinn
Affiliation:
Department of Engineering Science, University of Oxford, Oxford OX1 3PJ, UK
Ruben Juanes*
Affiliation:
Department of Civil and Environmental Engineering, Massachusetts Institute of Technology, Cambridge, MA 02139, USA
*
†Email address for correspondence: [email protected]
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Abstract

We develop a novel ‘moving-capacitor’ dynamic network model to simulate immiscible fluid–fluid displacement in porous media. Traditional network models approximate the pore geometry as a network of fixed resistors, directly analogous to an electrical circuit. Our model additionally captures the motion of individual fluid–fluid interfaces through the pore geometry by completing this analogy, representing interfaces as a set of moving capacitors. By incorporating pore-scale invasion events, the model reproduces, for the first time, both the displacement pattern and the injection-pressure signal under a wide range of capillary numbers and substrate wettabilities. We show that at high capillary numbers the invading patterns advance symmetrically through viscous fingers. In contrast, at low capillary numbers the flow is governed by the wettability-dependent fluid–fluid interactions with the pore structure. The signature of the transition between the two regimes manifests itself in the fluctuations of the injection-pressure signal.

JFM classification

Low-Reynolds-number flows: Porous media Interfacial Flows (free surface): Fingering instability Interfacial Flows (free surface): Capillary flows
Type
JFM Rapids
Information
Journal of Fluid Mechanics , Volume 875 , 25 September 2019 , R4
Copyright
© 2019 Cambridge University Press 

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Primkulov Supplementary Movie 1

Video shows the fluid-fluid displacement at Ca=1e-6 and contact angle of 90 deg. The pore-space is colored based on the local pressure, where tones of black, yellow, and white stand for high, intermediate, and low pressures, respectively. The rapid advance of the local interface after the pore-invasion event pressurizes the defending fluid ahead. This overpressure then dissipates. The size of the colored circles at the fluid-fluid front stands for the status of filling: increasing/decreasing size of the colored circle indicates filling/emptying of the pore throat. When the size of the colored circle matches the size of the post, the throat is full. The red, blue, and green colors stand for ``burst'', ``touch'', and ``overlap'' events. The mean radius of the pillars is 1055 microns; the mean hydraulic radius of the throats is 169 microns; the mean distance between the pore centers is 1577 microns.

Download Primkulov Supplementary Movie 1(Video)
Video 28.3 MB

Primkulov Supplementary Movie 2

Video shows the fluid-fluid displacement at Ca=1e-3 and contact angle of 46 deg. The network of throats is colored based on the local flow rates, where the color changes from red to yellow as flowrate changes from high to low. The dominant flow channels are the chains with the darkest colors. In the limit of high capillary numbers, the locations of the dominant flow channels change as the viscous fingers grow. This is best seen by observing the change in colors at a fixed spot ahead of the invading front. The size of the colored circles at the fluid-fluid front stands for the status of filling: increasing/decreasing size of the colored circle indicates filling/emptying of the pore throat. When the size of the colored circle matches the size of the post, the throat is full. The red, blue, and green colors stand for ``burst'', ``touch'', and ``overlap'' events. The mean radius of the pillars is 1055 microns; the mean hydraulic radius of the throats is 169 microns; the mean distance between the pore centers is 1577 microns.

Download Primkulov Supplementary Movie 2(Video)
Video 7.7 MB