Fractal Analysis for Wave Propagation in Combustion–Explosion Fracturing Shale Reservoir

Author:

Shang Xiaoji,Zhang ZhizhenORCID,Yang Weihao,Wang J. G.ORCID,Zhai Cheng

Abstract

The in-situ combustion–explosion fracturing technology in shale reservoirs can promote continuous fracture expansion with a radial detonation wave first converging into a shock wave and then decaying into an elastic wave. The transformation scale of the shale reservoir is determined by the range of wave propagation during combustion–explosion. As wave propagation paths are usually tortuous and fractal, the previous integer wave models are not competent to describe the wave propagation and estimate the impact range of the combustion–explosion fracturing process. This study develops two fractional wave propagation models and seeks analytical solutions. Firstly, a novel fractional wave model of rotation angle is proposed to describe the process of detonation waves converting into shock waves in a bifurcated structure. The radial displacement gradient of the detonation wave is represented by the internal expansion and rotation deformation of the shale. Secondly, another fractional wave propagation model of radial displacement is proposed to show the process of a shock wave decaying into an elastic wave. Thirdly, the proposed models are analytically solved through the fractional variable separation method and variational iteration method, respectively. Analytical solutions for rotation angle and radial displacement with fractal time and space are obtained. Finally, the impacts of the branching parameter of the detonation wave converge bifurcation system, aggregation order of detonation compression wave, and different types of explosives on the rotation angle of the shock wave are investigated. The propagation mechanism of the primary wave (P-wave) with time and space is analyzed. The analytical solutions can well describe the wave propagation process in fractured shales. The proposed fractional wave propagation models can promote the research of wave propagation in the combustion–explosion fracturing process of shale reservoirs.

Funder

National Key R&D Program of China

National Natural Science Foundation of China

Natural Science Foundation of Jiangsu Province for Youth Foundation

China Postdoctoral Science Foundation

Publisher

MDPI AG

Subject

Statistics and Probability,Statistical and Nonlinear Physics,Analysis

Reference29 articles.

同舟云学术

1.学者识别学者识别

2.学术分析学术分析

3.人才评估人才评估

"同舟云学术"是以全球学者为主线,采集、加工和组织学术论文而形成的新型学术文献查询和分析系统,可以对全球学者进行文献检索和人才价值评估。用户可以通过关注某些学科领域的顶尖人物而持续追踪该领域的学科进展和研究前沿。经过近期的数据扩容,当前同舟云学术共收录了国内外主流学术期刊6万余种,收集的期刊论文及会议论文总量共计约1.5亿篇,并以每天添加12000余篇中外论文的速度递增。我们也可以为用户提供个性化、定制化的学者数据。欢迎来电咨询!咨询电话:010-8811{复制后删除}0370

www.globalauthorid.com

TOP

Copyright © 2019-2024 北京同舟云网络信息技术有限公司
京公网安备11010802033243号  京ICP备18003416号-3