Application of Homotopy Analysis Method in One-Dimensional Instability Phenomenon Arising in Inclined Porous Media

Kajal K. Patel^1, , M. N. Mehta¹ and Twinkle R. Singh¹

¹Department of Applied Mathematics & Humanities, S. V. National Institute of Technology, Surat, India

Cite this paper

Kajal K. Patel, M. N. Mehta and Twinkle R. Singh. Application of Homotopy Analysis Method in One-Dimensional Instability Phenomenon Arising in Inclined Porous Media. American Journal of Applied Mathematics and Statistics. 2014; 2(3):106-114. doi: 10.12691/AJAMS-2-3-4

Abstract

During secondary oil recovery process when water is injected in inclined oil formatted area then phenomenon of instability occurs due to viscosity difference of water and oil. The non-linear partial differential equation for this instability phenomenon have been obtained. The Homotopy analysis method has been applied to this governing equation by using appropriate initial and boundary conditions. The guess value of saturation of injected water has been satisfying its initial and boundary conditions. The numerical value and graphical presentation are given by using Maple software and it is concluded that the saturation of injected water is increasing during instability phenomenon in inclined porous media when length of fingers and time increases.

Keywords

instability phenomenon, homotopy analysis method, porous matrix, secondary oil recovery process

Copyright

This work is licensed under a Creative Commons Attribution 4.0 International License. To view a copy of this license, visit http://creativecommons.org/licenses/by/4.0/

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