Journal
CHAOS SOLITONS & FRACTALS
Volume 119, Issue -, Pages 135-142Publisher
PERGAMON-ELSEVIER SCIENCE LTD
DOI: 10.1016/j.chaos.2018.12.020
Keywords
Fractional calculus; Green's function; Partially penetrating well; Fractal reservoir
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In this paper, the fractional order dynamical system theory is used to describe the complex behaviour of partially penetrating wells (PPWs) in a typical reservoir whose geometry is governed by fractal tools. The Green's function approach, as a generalised impulse response function, is adopted to model the fluid flow in any type of reservoir with a partially penetrating (vertical) well producing from it. Having obtained the initial description of a typical PPW, using the Laplace transform a new dimensionless constant-flow-rate solution is introduced, when wellbore storage and skin effects are significant. The pressure-transient behaviour of a PPW is discussed following two synthetic examples which illustratively depict the effectiveness of the proposed results. (C) 2019 Elsevier Ltd. All rights reserved.
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