A Non-Linear Flow Model for Porous Media Based on Conformable Derivative Approach

Gang Lei, Nai Cao, Di Liu and Huijie Wang
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Gang Lei: College Petroleum of Engineering & Geoscience, King Fahd University of Petroleum and Minerals, Dhahran 31261, Saudi Arabia
Nai Cao: College of Petroleum Engineering, China University of Petroleum, Beijing 102249, China
Di Liu: School of Mechanics and Civil Engineering, China University of Mining and Technology, Beijing 100083, China
Huijie Wang: College of Engineering, Peking University, Beijing 100871, China

Energies, 2018, vol. 11, issue 11, 1-11

Abstract: Prediction of the non-linear flow in porous media is still a major scientific and engineering challenge, despite major technological advances in both theoretical and computational thermodynamics in the past two decades. Specifically, essential controls on non-linear flow in porous media are not yet definitive. The principal aim of this paper is to develop a meaningful and reasonable quantitative model that manifests the most important fundamental controls on low velocity non-linear flow. By coupling a new derivative with fractional order, referred to conformable derivative, Swartzendruber equation and modified Hertzian contact theory as well as fractal geometry theory, a flow velocity model for porous media is proposed to improve the modeling of Non-linear flow in porous media. Predictions using the proposed model agree well with available experimental data. Salient results presented here include (1) the flow velocity decreases as effective stress increases; (2) rock types of “softer” mechanical properties may exhibit lower flow velocity; (3) flow velocity increases with the rougher pore surfaces and rock elastic modulus. In general, the proposed model illustrates mechanisms that affect non-linear flow behavior in porous media.

Keywords: porous media; non-linear flow; conformable derivative; fractal (search for similar items in EconPapers)
JEL-codes: Q Q0 Q4 Q40 Q41 Q42 Q43 Q47 Q48 Q49 (search for similar items in EconPapers)
Date: 2018
References: View complete reference list from CitEc
Citations: View citations in EconPapers (3)

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