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Phase diagram of quasi-static immiscible displacement in disordered porous media

Published online by Cambridge University Press:  19 July 2019

Ran Hu Open the ORCID record for Ran Hu [Opens in a new window] ,
Tian Lan ,
Guan-Ju Wei  and
Yi-Feng Chen Open the ORCID record for Yi-Feng Chen [Opens in a new window]
Ran Hu*
Affiliation:
State Key Laboratory of Water Resources and Hydropower Engineering Science, Wuhan University, Wuhan 430072, PR China Key Laboratory of Rock Mechanics in Hydraulic Structural Engineering of the Ministry of Education, Wuhan University, Wuhan 430072, PR China
Tian Lan
Affiliation:
State Key Laboratory of Water Resources and Hydropower Engineering Science, Wuhan University, Wuhan 430072, PR China Key Laboratory of Rock Mechanics in Hydraulic Structural Engineering of the Ministry of Education, Wuhan University, Wuhan 430072, PR China
Guan-Ju Wei
Affiliation:
State Key Laboratory of Water Resources and Hydropower Engineering Science, Wuhan University, Wuhan 430072, PR China Key Laboratory of Rock Mechanics in Hydraulic Structural Engineering of the Ministry of Education, Wuhan University, Wuhan 430072, PR China
Yi-Feng Chen*
Affiliation:
State Key Laboratory of Water Resources and Hydropower Engineering Science, Wuhan University, Wuhan 430072, PR China Key Laboratory of Rock Mechanics in Hydraulic Structural Engineering of the Ministry of Education, Wuhan University, Wuhan 430072, PR China
*
†Email addresses for correspondence: whuran@whu.edu.cn, csyfchen@whu.edu.cn
†Email addresses for correspondence: whuran@whu.edu.cn, csyfchen@whu.edu.cn
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Abstract

Immiscible displacement in porous media is common in many practical applications. Under quasi-static conditions, the process is significantly affected by disorder of the porous media and the wettability of the pore surface. Previous studies have focused on wettability effects, but the impact of the interplay between disorder and contact angle is not well understood. Here, we combine microfluidic experiments and pore-scale simulations with theoretical analysis to study the impact of disorder on the quasi-static displacement from weak imbibition to strong drainage. We define the probability of overlap to link the menisci advancements to displacement patterns, and derive a theoretical model to describe the lower and upper bounds of the cross-over zone between compact displacement and capillary fingering for porous media with arbitrary flow geometry at a given disorder. The phase diagram predicted by the theoretical model shows that the cross-over zone, in terms of contact angle range, expands as the disorder increases. The diagram further identifies four zones to elucidate that the impact of disorder depends on wettability. In zone I, increasing disorder destabilizes the patterns, and in zone II, a stabilizing effect plays a role, which is less significant than that in zone I. In the other two zones, invasion morphologies are compact and fingering, respectively, independent of both contact angle and disorder. We evaluate the proposed diagram using pore-scale simulations, experiments in this work and in the literature, confirming that the diagram can capture the effect of disorder on displacement under different wetting conditions. Our work extends the classical phase diagrams and is also of practical significance for engineering applications.

JFM classification

Low-Reynolds-number flows: Porous media Micro-/Nano-fluid dynamics: Microfluidics Interfacial Flows (free surface): Capillary flows
Type
JFM Papers
Information
Journal of Fluid Mechanics , Volume 875 , 25 September 2019 , pp. 448 - 475
Copyright
© 2019 Cambridge University Press 

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