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Research Papers

Analytical Solution of Fractional Order Diffusivity Equation With Wellbore Storage and Skin Effects

[+] Author and Article Information
Kambiz Razminia

Department of Petroleum Engineering,
Petroleum University of Technology,
Ahwaz, Iran
e-mail: kambiz.razminia@gmail.com

Abolhassan Razminia

Dynamical Systems & Control (DSC)
Research Laboratory,
Department of Electrical Engineering,
School of Engineering,
Persian Gulf University,
P.O. Box 75169,
Bushehr, Iran
e-mail: razminia@pgu.ac.ir

J. A. Tenreiro Machado

Department of Electrical Engineering,
Institute of Engineering,
Polytechnic of Porto,
Rua Dr. Antonio Bernardino de Almeida, 431,
Porto 4200-072, Portugal
e-mail: jtenreiromachado@gmail.com

1Corresponding author.

Contributed by the Design Engineering Division of ASME for publication in the JOURNAL OF COMPUTATIONAL AND NONLINEAR DYNAMICS. Manuscript received June 21, 2014; final manuscript received May 2, 2015; published online June 30, 2015. Assoc. Editor: Hiroshi Yabuno.

J. Comput. Nonlinear Dynam 11(1), 011006 (Jan 01, 2016) (8 pages) Paper No: CND-14-1160; doi: 10.1115/1.4030534 History: Received June 21, 2014; Revised May 02, 2015; Online June 30, 2015

This paper addresses the model, solution, and analysis of fluid flow behavior in fractal reservoirs considering wellbore storage and skin effects (WS–SE). In the light of the fractional calculus (FC), the general form of fluid flow model considering the history of flow in all stages of production is presented. On the basis of Bessel functions theory, analytical solutions in the Laplace transform domain under three outer-boundary conditions, assuming the well is producing at a constant rate, are obtained. Based on the analytical solutions, various examples, discussing the pressure-transient behavior of a well in a fractal reservoir, are presented.

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References

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Figures

Grahic Jump Location
Fig. 1

The effect of dmf and θ on pressure behavior in a fractal reservoir based on FFD model with infinite-acting behavior

Grahic Jump Location
Fig. 2

The effect of dmf and θ on pressure behavior in a fractal reservoir based on FFD model with no flow across the exterior boundary

Grahic Jump Location
Fig. 3

The effect of dmf and θ on pressure behavior in a fractal reservoir based on FFD model with CPOB

Grahic Jump Location
Fig. 4

Type curve match of the pressure data from the pressure-buildup test example

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