Miscible displacements in Hele–Shaw cells: Nonmonotonic viscosity profiles |
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| Institution: | 1. Center for Experimental Study of Subsurface Environmental Processes (CESEP), Colorado School of Mines, Golden, CO 80401, USA;2. Earth Sciences Division, Lawrence Berkeley National Laboratory, University of California, Berkeley, CA 94720, USA;3. Department of Earth Sciences, Uppsala University, Villavägen 16, 75236 Uppsala, Sweden;1. Department of Mechanical Systems Engineering, University of the Ryukyus, 1 Senbaru, Nishihara, Okinawa 903-0213, Japan;2. Department of Materials Engineering Science, Graduate School of Engineering Science, Osaka University, 1-3 Machikaneyama, Toyonaka, Osaka 560-8531, Japan;3. Crystal Growth Laboratory, University of Victoria, Victoria, BC, Canada V8W 3P6;1. Zhejiang University, State Key Laboratory of Fluid Power and Mechatronic Systems, Mechanical Engineering, 38 Zheda Road, Hangzhou 310027, China;2. Shanghai Key Laboratory of Aerospace Intelligent Control Technology, Shanghai Institute of Spaceflight Control Technology, Shanghai, China;1. College of Petroleum Engineering, China University of Petroleum (East China), Qingdao, Shandong 266580, People’s Republic of China;2. Petroleum Systems Engineering, Faculty of Engineering and Applied Science, University of Regina, Regina, Saskatchewan S4S 0A2, Canada;3. Institute for Energy, Environment and Sustainable Communities, University of Regina, Regina, Saskatchewan S4S 0A2, Canada |
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| Abstract: | The influence of nonmonotonic viscosity–concentration relationships on viscous fingering of neutrally buoyant, miscible fluids in a Hele–Shaw cell has been investigated. In a first step, quasisteady base states are obtained by means of nonlinear Stokes simulations. The properties of these base states are analyzed as a function of the Péclet number, the viscosity ratio, and the profile parameters. Subsequently, the stability of these base states is investigated by means of a linear stability analysis. Overall, the nonmonotonicity of the viscosity–concentration relationship is seen to have a much smaller influence on Hele–Shaw displacements than on corresponding Darcy flows. The reason for this difference lies in the nature of the respective base states. For Darcy flows, the base state is characterized by constant velocity and a diffusively decaying concentration (and hence viscosity) profile. This base viscosity profile is strongly affected by the nonmonotonicity. On the other hand, for Hele–Shaw displacements the quasisteady base states are convectively dominated and characterized by sharp fronts, so that their shape depends only weakly on the details of the viscosity–concentration relationship. Hence, for Hele–Shaw displacements both the eigenfunctions and the associated growth rates are quite similar for monotonic and nonmonotonic profiles, in contrast to the findings by O. Manickam, G.M. Homsy, Stability of miscible displacements in porous media with nonmonotonic viscosity profiles, Phys. Fluids A 5 (1993) 1356–1367] for Darcy flows. |
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