Fractal analysis for heat extraction in geothermal system

Author:

Shang Xiaoji1,Wang Jianguo2,Yang Xiaojun2

Affiliation:

1. China University of Mining and Technology, State Key Laboratory for Geomechanics and Deep Underground Engineering, Xuzhou, China

2. China University of Mining and Technology, School of Mechanics and Civil Engineering, Xuzhou, China

Abstract

Heat conduction and convection play a key role in geothermal development. These two processes are coupled and influenced by fluid seepage in hot porous rock. A number of integer dimension thermal fluid models have been proposed to describe this coupling mechanism. However, fluid flow, heat conduction and convection in porous rock are usually non-linear, tortuous and fractal, thus the integer dimension thermal fluid flow models can not well describe these phenomena. In this study, a fractal thermal fluid coupling model is proposed to describe the heat conduction and flow behaviors in fractal hot porous rock in terms of local fractional time and space derivatives. This coupling equation is analytically solved through the fractal travelling wave transformation method. Analytical solutions of Darcy?s velocity, fluid temperature with fractal time and space are obtained. The solutions show that the introduction of fractional parameters is essential to describe the mechanism of heat conduction and convection.

Publisher

National Library of Serbia

Subject

Renewable Energy, Sustainability and the Environment

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