Paper contribution

Effect of Biot–Willis Coefficient in Coupled Hydro-Mechanical Hydraulic Fracturing Analysis

Kiyoshi Kishida; Yuki Tatemura; Sho Ogata; Hideaki Yasuhara

Proceedings
EUROCK 2026
Pages
529-534
Submitted
28 January 2026
Accepted
15 June 2026
Published
12 August 2026

Summary

Abstract

Hydraulic fracturing is widely used for in-situ stress measurements and the development of enhanced geothermal systems, where fluid is injected to artificially create and propagate fractures. To accurately evaluate the stress state and fracture propagation behavior, it is essential to establish a simulation framework that can reliably reproduce the coupled interaction between fluid flow and rock deformation. This study develops a fully coupled hydro-mechanical simulation model for flow-rate–controlled hydraulic fracturing, in which the penetration of pore pressure within a porous rock mass and the resulting mechanical response are simultaneously considered. In poroelastic theory, the Biot–Willis coefficient α represents the magnitude of pore pressure contribution to the effective stress in the solid skeleton and is therefore a key parameter governing fluid–solid interaction. However, despite its fundamental role, the influence of α on hydraulic-fracturing behavior, particularly on injection pressure evolution, has not been systematically investigated in previous studies, where α was typically assumed as a fixed value without sensitivity analysis. To address this gap, the present study conducts numerical simulations to quantify the effect of α on injection pressure during fracture initiation and early propagation. The results demonstrate that the injection pressure decreases as α increases, reflecting the enhanced contribution of pore pressure to the rock matrix stress. The reduction in injection pressure becomes less pronounced when α approaches approximately 0.9, beyond which the effect saturates and the injection pressure remains nearly constant. These findings highlight that the predicted breakdown and injection pressures in hydraulic-fracturing simulations are highly sensitive to the assumed Biot–Willis coefficient. The outcomes provide important guidance for selecting appropriate α values in coupled simulation frameworks, contributing to improved accuracy in in-situ stress determination and geothermal reservoir stimulation analysis.

Contributors

Authors

  1. Kiyoshi Kishida Kyoto University, Japan ORCID 0000-0003-1588-4024
  2. Yuki Tatemura Kyoto University, Japan ORCID 0000-0003-4557-4692
  3. Sho Ogata Osaka University, Japan
  4. Hideaki Yasuhara Kyoto University, Japan

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References

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