Stochastic analysis of immiscible displacement in porous media |
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| Institution: | 1. Department of Agricultural Engineering, National Taiwan University, Taipei, Taiwan, Republic of China;2. Department of Civil Engineering, National I-Lan Institute of Agriculture and Technology, I-Lan, Taiwan, Republic of China;1. Institute of Geography, Russian Academy of Sciences, 119017 Moscow, Russia;2. Centro de Investigaciones Biologicas del Noroeste, Guaymas, Sonora 85454, Mexico;1. Department of Basic and Applied Sciences for Engineering, Sapienza University of Rome, via A. Scarpa 10, Rome, Italy;2. Department of Basic and Applied Sciences for Engineering, Sapienza University of Rome, via A. Scarpa 16, Rome, Italy;1. Department of Earth Science, University of Florence, Italy;2. Univ. Lille, CNRS, Univ. Littoral Côte d’Opale, UMR 8187, LOG, Laboratoire d’Océanologie et de Géosciences, F 62930 Wimereux, France;1. Faculty of Science and Technology, Universiti Sains Islam Malaysia (USIM), 71800 Nilai, Malaysia;2. Department of Mathematics, Faculty of Science, Universiti Putra Malaysia, 43400 UPM Serdang, Selangor, Malaysia |
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| Abstract: | The interface of two immiscible fluids flowing in porous media may behave in an unstable fashion. This instability is governed by the pore distribution, differential viscosity and interface tension between the two immiscible fluids. This study investigates the factors that control the interface instability at the wetting front. The development of the flow equation is based on the mass balance principle, with boundary conditions such as the velocity continuity and capillary pressure balance at the interface. By assuming that the two-phase fluids in porous media are saturated, a covariance function of the wetting front position is derived by stochastic theory. According to those results, the unstable interface between two immiscible fluids is governed by the fluid velocity and properties such as viscosity and density. The fluid properties that affect the interface instability are expressed as dimensionless parameters, mobility ratio, capillary number and Bond number. If the fluid flow is driven by gravitational force, whether the interface undergoes upward displacement or downward displacement, the variance of the unstable interface decreases with an increasing mobility ratio, increases with increasing capillary number, and decreases with increasing Bond number. For a circumstance in which fluid flow is horizontal, our results demonstrate that the capillary number does not influence the generation of the unstable interface. |
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