Pore-scale direct numerical simulation of Haines jumps in a porous media model
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part of Springer Nature, 2020 https://doi.org/10.1140/epjst/e2020-000008-0
THE EUROPEAN PHYSICAL JOURNAL SPECIAL TOPICS
Regular Article
Pore-scale direct numerical simulation of Haines jumps in a porous media model Adam O’Brien1 , Shahriar Afkhami2,a , and Markus Bussmann1 1
2
Department of Mechanical and Industrial Engineering, University of Toronto, Toronto, ON M5S 3G8, Canada Department of Mathematical Sciences, New Jersey Institute of Technology, Newark, NJ 07102, USA Received 22 January 2020 / Accepted 6 July 2020 Published online 14 September 2020 Abstract. Direct numerical simulations are presented for a porous media model consisting of two immiscible fluids, an invading and defending phase, in a two-dimensional micro-geometry filled with randomly sized and randomly distributed cylinders. First, interface instability and penetration modes are studied when varying the wetting features of a single pore in the porous medium. It is found that the displacement patterns not only change with the capillary number, as previously observed, but also are a function of the contact angle, even for a viscosity ratio of unity. This is an important conclusion suggesting that capillary number and viscosity ratio alone cannot completely describe the pore-scale displacement. Second, rapid pore-scale displacement is considered, where the displacements are accompanied by sudden interface jumps from one site to another, known as Haines jumps. The characteristic time and length scales of a Haines jump are examined to better understand the transient dynamics of the jump. We then focus on analyzing the Haines jump in a simple pore configuration where cylinders of equal size are placed at the vertices of equilateral triangles. We use this geometry to provide more insight into the effect of the contact angle at which the Haines jump is predicted.
1 Introduction The flow of immiscible fluids in porous media has applications in subsurface water flows, tar sands oil production, and CO2 sequestration, to name a few [1]. At the micro-scale, where the capillary forces are dominant, the wetting effects can play a significant role in the displacement dynamics. For example, when a fluid is pushed into a porous medium, displacing an immiscible fluid, the distribution of fluids depends on wetting properties of the medium. In the pioneering work of Lenormand, the displacement patterns of a wetting fluid, which is known as the imbibition scenario, and a non-wetting fluid, known as the drainage scenario, are studied, showing that in slow displacement drainage, fingering like patterns emerge [2]. This condition can lead to the invading phase not being able to completely drain the other (defending) phase, a
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The European Physical Journal Special Topics
resulting in some of the displaced phase becoming trapped in the porous medium [3–5]. The trapping can be important as it affects the saturation of the invading liquid which limits the extent to which the defending fluid can be displaced from the medium [6,
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