Asymptotic regimes in unstable miscible displacements in random porous media |
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| Authors: | ZM Yang YC Yortsos Dominique Salin |
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| Institution: | 1. Petroleum Engineering Program, Department of Chemical Engineering, University of Southern California, Los Angeles, CA 90089-1211, USA;2. Laboratoire FAST, Universite Paris XI, 91405 Orsay Cedex, France;1. Institute for Space and Nuclear Power Studies, University of New Mexico, Albuquerque, NM, USA;2. Nuclear Engineering Department, University of New Mexico, Albuquerque, NM, USA;3. Mechanical Engineering Department, University of New Mexico, Albuquerque, NM, USA;4. Chemical and Biological Engineering Department, University of New Mexico, Albuquerque, NM, USA;1. Department of Mechanical and Product Design Engineering, Swinburne University of Technology, Hawthorn, Victoria 3122, Australia;2. Department of Mechanical Engineering, University of Anbar, Ramadi, Anbar 31001, Iraq;3. Mechanical Engineering Department, College of Engineering, Wasit University, Wasit, Iraq;1. Englander Institute for Precision Medicine, Weill Cornell Medical Center, New York, USA;2. Montreal Cancer Institute, Montreal University Hospital Center (CHUM), Montreal, QC, Canada;3. Knight Cancer Institute, Oregon Health and Science University and VA Portland Health Care System, Portland, USA;4. Department of Oncology, Rambam Health Care Center, Haifa, Israel;5. Department of Oncology, Wayne State University/Karmanos Cancer Institute, Detroit, USA;6. Division of Nuclear Medicine, The Ottawa Hospital, Ottawa, Ontario, Canada;7. Institute of Oncology, Rabin Medical Center-Davidoff Cancer Center, Petah Tikva, Israel;8. Department of Medical Oncology, Crown Princess Mary Cancer Centre, Westmead Hospital, Sydney, Australia;9. Department of Medical Oncology, The Kinghorn Cancer Centre, St. Vincent’s Hospital, Sydney, Australia;10. Department of Medicine, Monash University, Melbourne, Australia;11. Eastern Health, Melbourne, Australia;12. Clinical Statistics Oncology, Bayer HealthCare Pharmaceutical Inc, Whippany, USA;13. Global Clinical Development, Bayer Consumer Care AG, Basel, Switzerland;14. Division of Hematology/Oncology, Robert H. Lurie Comprehensive Cancer Center, Northwestern University Feinberg School of Medicine, Chicago, USA |
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| Abstract: | We study two asymptotic regimes of unstable miscible displacements in porous media, in the two limits, where a permeability-modified aspect ratio, RL=L/H(kv/kh)1/2, becomes large or small, respectively. The first limit is known as transverse (or vertical) equilibrium, the second leads to the problem of non-communicating layers (the Dykstra–Parsons problem). In either case, the problem reduces to the solution of a single integro-differential equation. Although at opposite limits of the parameter RL, the two regimes coincide in the case of equal viscosities, M=1. By comparison with high-resolution simulation we investigate the validity of these two approximations. The evolution of transverse averages, particularly under viscous fingering conditions, depends on RL. We investigate the development of a model to describe viscous fingering in weakly heterogeneous porous media under transverse equilibrium conditions, and compare with the various existing empirical models (such as the Koval, Todd–Longstaff and Fayers models). |
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