A fractional derivative perspective on transient pulse test for determining the permeability of rocks

Yang, Shuai; Zhou, Hongwei; Zhang, S.Q.; Ren, W.G.

doi:10.1016/j.ijrmms.2018.11.013

Cited by 36 publications

(16 citation statements)

References 53 publications

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“…For subdiffusive flows, fractional flux laws of the form proposed here have been used for many years in a variety of contexts concerning diffusion: in biophysics (Magin et al, 2013), fractal structures (Dassas and Duby, 1995;Metzler et al, 1994), flow in porous media (Albinali et al, 2016;Lẽ Mehautẽ and Crepy, 1983;Nigmatullin, 1984a, b;Płociniczak, 2015;Raghavan, 2011;Raghavan and Chen, 2017;Su, 2014;Su et al, 2015), contaminant transport (Fomin et al, 2011;Kim et al, 2015;Molz et al, 2002;Suzuki et al, 2016), heat transmission (Angulo et al, 2000;Gurtin and Pipkin, 1968;Moodie and Tait, 1983;Norwood, 1972). Experimental aspects are discussed in Tao et al (2016), Strizhak (2018, 2019) and Yanga et al (2019). Additional options are available to modify equation ( 10) should one address phenomena such as truncation (Odling et al, 1999) to model structures that are discontinuous resulting in the variation of permeability around faults.…”

Section: The Darcy Law Subdiffusive Flowmentioning

confidence: 99%

Subdiffusive flow in a composite medium with a communicating (absorbing) interface

Raghavan

Chen²

2020

Oil Gas Sci. Technol. – Rev. IFP Energies nouvelles

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Two-dimensional subdiffusion in media separated by a partially communicating interface is considered. Starting with the appropriate Green’s functions, solutions are developed in terms of the Laplace transformation reflecting two circumstances at the interface: situations where there is perfect contact and situations where the interface offers a resistance. Asymptotic solutions are derived; limiting forms of the expressions reduce to known solutions for both classical diffusion and subdiffusion. Specifics are analyzed in depth with reference to flow in porous media with potential applications to the evaluation of the role of subsurface faults and flow in fractured rocks. Characteristics of the derivative responses are documented extensively as they are the linchpin for evaluation of pressure tests. Results given here may be used for evaluation at the Theis (1935; Eos Trans. AGU 2, 519–524) scale along with geological and geophysical properties, and production statistics. Yet a subdiffusive model does not imply a single value for properties. The method presented here may be extended to multiple contiguous media and to subdiffusive transport in many contexts (complex wellbores such as inclined, fractured and horizontal wells, situations such as sequestration, production of geothermal systems, etc.).

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Section: The Darcy Law Subdiffusive Flowmentioning

confidence: 99%

Subdiffusive flow in a composite medium with a communicating (absorbing) interface

Raghavan

Chen²

2020

Oil Gas Sci. Technol. – Rev. IFP Energies nouvelles

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“…Recently, the presence of temporal memory kernels on descriptions of physical systems has been an interesting mathematical tool to investigate complexity in nature [55][56][57][58][59]. In this sense, a series of news kernels was proposed to approach mathematical models that have become limited.…”

Section: Preliminaries Concepts: Fractional Derivativesmentioning

confidence: 99%

Mittag–Leffler Memory Kernel in Lévy Flights

Santos

2019

Mathematics

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In this article, we make a detailed study of some mathematical aspects associated with a generalized Lévy process using fractional diffusion equation with Mittag–Leffler kernel in the context of Atangana–Baleanu operator. The Lévy process has several applications in science, with a particular emphasis on statistical physics and biological systems. Using the continuous time random walk, we constructed a fractional diffusion equation that includes two fractional operators, the Riesz operator to Laplacian term and the Atangana–Baleanu in time derivative, i.e., a A B D t α ρ ( x , t ) = K α , μ ∂ x μ ρ ( x , t ) . We present the exact solution to model and discuss how the Mittag–Leffler kernel brings a new point of view to Lévy process. Moreover, we discuss a series of scenarios where the present model can be useful in the description of real systems.

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“…According to triaxial compression tests of the fractured rock, the progressive failure is often accompanied by the compression, crack, expansion, and mutual intersection of internal fractures [31,32]. e permeability changes obviously with the formation of the fractured networks, owing to the expansion and the penetration of primary cracks.…”

Section: Seepage Characteristics Of the Fractured Rock Massmentioning

confidence: 99%

Seepage Evolution Model of the Fractured Rock Mass under High Seepage Pressure in Dam Foundation

Zhao

Jiang

2021

Advances in Civil Engineering

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The seepage of the fractured rock mass in dam foundations involves complex fluid-structure coupling behavior, due to practical hydrogeological conditions. In this work, the seepage characteristics of the fractured rock mass and their correlations with the structural permeable mediums are experimentally explored to reveal the cracking effect on the hydromechanical properties firstly. Subsequently, the tangential and the compression creep damage constitutive models are, respectively, established by introducing a nonlinear viscoplastic body to improve the Nishihara model. Afterwards, an innovative evolution equation of the permeability coefficient considering the creep damage is proposed. It can indicate the time effect of the porosity, the permeability, and damage variables of the fractured rock mass under the long-term infiltration action of the hydraulic pressures. Ultimately, the proposed methods are applied to the seepage simulation on the dam foundation of the Longyangxia hydropower station and the significantly increased leakage is in good agreement with the measured values during the storage period. It was further confirmed that the crack expansion and penetration in the rock masses can be constantly intensified by the seepage pressures. The research results can provide a reference for engineering repair and supervision through controlling the permeability performance for long-term operations.

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A fractional derivative perspective on transient pulse test for determining the permeability of rocks

Cited by 36 publications

References 53 publications

Subdiffusive flow in a composite medium with a communicating (absorbing) interface

Subdiffusive flow in a composite medium with a communicating (absorbing) interface

Mittag–Leffler Memory Kernel in Lévy Flights

Seepage Evolution Model of the Fractured Rock Mass under High Seepage Pressure in Dam Foundation

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