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Prediction of spontaneous imbibition with gravity in porous media micromodels

Published online by Cambridge University Press:  18 November 2022

Sheng Li ,
Haihu Liu Open the ORCID record for Haihu Liu [Opens in a new window] ,
Rui Wu ,
Jianchao Cai ,
Guang Xi  and
Fei Jiang
Sheng Li
Affiliation:
School of Energy and Power Engineering, Xi'an Jiaotong University, 28 West Xianning Road, Xi'an 710049, PR China
Haihu Liu*
Affiliation:
School of Energy and Power Engineering, Xi'an Jiaotong University, 28 West Xianning Road, Xi'an 710049, PR China Heilongjiang Provincial Key Laboratory of Reservoir Physics & Fluid Mechanics in Porous Medium, Daqing 163712, PR China
Rui Wu
Affiliation:
School of Mechanical Engineering, Shanghai Jiao Tong University, Shanghai 200240, PR China
Jianchao Cai
Affiliation:
State Key Laboratory of Petroleum Resources and Prospecting, China University of Petroleum, Beijing 102249, PR China
Guang Xi
Affiliation:
School of Energy and Power Engineering, Xi'an Jiaotong University, 28 West Xianning Road, Xi'an 710049, PR China
Fei Jiang
Affiliation:
Graduate School of Sciences and Technology for Innovation, Yamaguchi University, Yamaguchi 755-8611, Japan
*
†Email address for correspondence: haihu.liu@mail.xjtu.edu.cn
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Abstract

In this work, theoretical modelling, quasi-three-dimensional (quasi-3D) simulations and micromodel experiments are conducted to study spontaneous imbibition with gravity in porous media micromodels. By establishing the force balance governing the spontaneous imbibition process, we develop a theoretical model for predicting the imbibition length against time in a rectangular capillary. The theoretical model is then extended to the prediction of a compact displacement process in a micromodel by using an equivalent width, which is derived by analogising the micromodel to a rectangular capillary. By simulating spontaneous imbibition in a rectangular capillary with various aspect ratios ($\varepsilon$), we show that the application condition of the quasi-3D method is $\varepsilon \leqslant 1/3$. Next, we simulate spontaneous imbibition in micromodels with various geometries and flow conditions. Fingering and compact displacement are identified for varying viscosity ratios and gravitational accelerations. At low (high) viscosity ratio of wetting to non-wetting fluids, an upward (downward) gravity can promote the stability of the wetting front, favouring the transition from fingering to compact displacement. In addition, we find that the depth-oriented interface curvature dominates the capillary effect during the imbibition, and such a mechanism is considered by introducing an equivalent contact angle into the theoretical model. With the help of equivalent width and contact angle, the theoretical model is shown to provide satisfactory prediction of the compact displacement process. Finally, a micromodel experiment is presented to further verify the developed theoretical model and the quasi-3D simulation.

JFM classification

Low-Reynolds-number flows: Porous media Interfacial Flows (free surface): Capillary flows Multiphase and Particle-laden Flows: Multiphase flow
Type
JFM Papers
Information
Journal of Fluid Mechanics , Volume 952 , 10 December 2022 , A9
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© The Author(s), 2022. Published by Cambridge University Press

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References

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