Baleanu, DumitruRazminia, KambizRazminia, AbolhassanBaleanu, Dumitru2020-02-282020-02-282019Razminia, Kambiz; Razminia, Abolhassan; Baleanu, Dumitru, "Fractal-fractional modelling of partially penetrating wells", Chaos Solitons & Fractals, Vol. 119, pp. 135-142, (2019).0960-0779https://hdl.handle.net/20.500.12416/2573In 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.eninfo:eu-repo/semantics/closedAccessFractional CalculusGreen's FunctionPartially Penetrating WellFractal ReservoirArticle11913514210.1016/j.chaos.2018.12.020