A Planar-3D Mathematical Model for Studying the Effect of Heterogeneity of Rock Fracture Toughness on Hydraulic Fracture Propagation: Early-Time Solution including the Stage before Propagation

Kairui Li, Nickolay N. Smirnov (), Chengzhi Qi, Mingyang Wang, Dmitry A. Pestov and Anastasia A. Shamina
Additional contact information
Kairui Li: School of Civil and Transportation Engineering, Beijing University of Civil Engineering and Architecture, Beijing 100044, China
Nickolay N. Smirnov: Faculty of Mechanics and Mathematics, Lomonosov Moscow State University, Moscow 119991, Russia
Chengzhi Qi: School of Civil and Transportation Engineering, Beijing University of Civil Engineering and Architecture, Beijing 100044, China
Mingyang Wang: State Key Laboratory for Explosion & Impact and Disaster Prevention & Mitigation, Faculty of Defense Engineering, Army Engineering University of PLA, Nanjing 210007, China
Dmitry A. Pestov: Scientific Research Institute for System Analysis of the Russian Academy of Sciences, Nakhimovskiy Str. 36-1, Moscow 117218, Russia
Anastasia A. Shamina: Faculty of Mechanics and Mathematics, Lomonosov Moscow State University, Moscow 119991, Russia

Mathematics, 2023, vol. 11, issue 9, 1-27

Abstract: Among the studies of the effect of rock’s heterogeneity on hydraulic fracture propagation, very little information on the effects of the heterogeneity of rock’s fracture toughness is available. The objective of the present paper is to develop a planar-3D model for studying the effect of the heterogeneity of rock’s fracture toughness on hydraulic fracture propagation. Not only the stage of fracture propagation, but also the stage before the fracture propagation is considered in this model. Based on the proposed model, the evolution of hydraulic fracture propagation under a typical heterogeneous distribution of rock’s fracture toughness and the solution at the stage before fracture propagation are analyzed in detail. Furthermore, a series of numerical comparison experiments including five different distributions of rock’s fracture toughness are made in order to study the effect of the heterogeneity of rock’s toughness. The results indicate that the minimum fracture radius and the contrast of rock’s fracture toughness between adjacent layers are important parameters for determining the size and location of the maximum fracture opening. Most importantly, the fracture contour is greatly affected by the heterogeneity of rock’s fracture toughness.

Keywords: planar-3D model; hydraulic fracture; inhomogeneous fracture toughness; early-time solution (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2023
References: View references in EconPapers View complete reference list from CitEc
Citations:

Downloads: (external link)
https://www.mdpi.com/2227-7390/11/9/2083/pdf (application/pdf)
https://www.mdpi.com/2227-7390/11/9/2083/ (text/html)

Related works:
This item may be available elsewhere in EconPapers: Search for items with the same title.

Export reference: BibTeX RIS (EndNote, ProCite, RefMan) HTML/Text

Persistent link: https://EconPapers.repec.org/RePEc:gam:jmathe:v:11:y:2023:i:9:p:2083-:d:1134582

Access Statistics for this article

Mathematics is currently edited by Ms. Emma He

More articles in Mathematics from MDPI
Bibliographic data for series maintained by MDPI Indexing Manager ().