SINGULAR PERTURBATION SOLUTION OF THE PROBLEM VISCOUS FINGERING PHENOMENON IN MULTIFLUID IMMISCIBLE FLOW

Authors

  • Shailesh S. Patel Professor of Mathematics, Department of Applied Sciences and Humanities, GIDC Degree Engineering College, Navsari, India

DOI:

https://doi.org/10.29121/ijetmr.v5.i4.2018.208

Keywords:

Porous, Fingering, Singular, Partial Differential Equation, Similarity, Perturbation

Abstract

In this paper the phenomenon namely fingering which occurs in the flow problems of oil reservoir engineering has been discussed. The effects arises due to the fingering have been studied by using the Darcy’s law together with different kinds of suitable assumptions and conditions. The problem is then modeled into mathematical form which yields second order partial differential equation. The equation is then solved by using singular perturbation technique together with initial and boundary conditions. The solution is then interpreted in terms of fluid flow terms.

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References

Scheidegger A.E. Canadian Journal of Physics, 39, 2, 1961, 125. DOI: https://doi.org/10.1139/p61-031

Zhangxin Chen, Reservoir Simulation Mathematical techniques in Oil Recovery, SIAM, 2007, 37- 59. DOI: https://doi.org/10.1137/1.9780898717075

Wooding R.A. A.M. Physics, 18, 1962, 255. DOI: https://doi.org/10.1007/BF02148216

Verma A.P. Canadian Journal of Physics, 47, 1969, 2519. DOI: https://doi.org/10.1139/p69-309

Patel S. S. An approximate solution of displacement processes in fluid flow through porous media, Ph.D. Thesis, 1998, 138.

Scheidegger A.E. and Johnson E.F. Canadian journal of physics, 39, 1960, 329.

LeVeque R.J., Finite Difference Methods for Ordinary and Partial Differential Equations, SIAM, 2007, 181-200. DOI: https://doi.org/10.1137/1.9780898717839

Dake L.P., Fundamentals of reservoir Engineering, Elsevier, 1998, 407-413.

Hyden P.E., Similarity Methods for Differential Equations, Cambridge University Press, 2000, 136-149.

Nayfeh A.H. Perturbation Methods, Wiley, New York, 1973, 122-125.

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Published

2018-04-30

How to Cite

Patel, S. (2018). SINGULAR PERTURBATION SOLUTION OF THE PROBLEM VISCOUS FINGERING PHENOMENON IN MULTIFLUID IMMISCIBLE FLOW . International Journal of Engineering Technologies and Management Research, 5(4), 57–61. https://doi.org/10.29121/ijetmr.v5.i4.2018.208