Similarity solution of axisymmetric flow in porous media |
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| Affiliation: | 1. School of Engineering, The University of Queensland, Brisbane 4072, Australia;2. Centre for Eco-Environmental Modelling, Hohai University, Nanjing 210098, P.R. China;3. École Polytechnique Fédérale de Lausanne (EPFL), School of Architecture, Civil and Environmental Engineering, Ecublens 1015-CH, Switzerland;4. School of Ecology and Environment, Deakin University, P.O. Box 423,Warrnambool, Vic. 3280, Australia;5. Department of Civil Engineering, The University of Sydney, NSW 2006, Australia;6. Bioengineering Department, Oregon State University, Corvallis, OR 13906, USA;7. Department of Mathematics, University of Nevada, Reno, NV 89557-0042, USA;8. Department of Biological and Environmental Engineering, Cornell University, Ithaca, NY 14853-5701, USA |
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| Abstract: | Applications of the axisymmetric Boussinesq equation to groundwater hydrology and reservoir engineering have long been recognised. An archetypal example is invasion by drilling fluid into a permeable bed where there is initially no such fluid present, a circumstance of some importance in the oil industry. It is well known that the governing Boussinesq model can be reduced to a nonlinear ordinary differential equation using a similarity variable, a transformation that is valid for a certain time-dependent flux at the origin. Here, a new analytical approximation is obtained for this case. The new solution,, which has a simple form, is demonstrated to be highly accurate. |
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