THE CONSTITUTIVE RELATIONSHIP BETWEEN STRESS DISTURBANCES AND HYDRAULIC FRACTURING VOLUME OPENINGS AND EFFECTS CONTROLLING

Wang Li; Nan Yakun; Xu Shuo; Cao Yunxing; Tian Lin; Zhang Junsheng; Shi Bin

doi:10.6052/0459-1879-23-631

Volume 56 Issue 7

Jul. 2024

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Chinese Journal of Theoretical and Applied Mechanics > 2024 > 56(7): 2150-2163. > DOI: 10.6052/0459-1879-23-631 CSTR: 32045.14.0459-1879-23-631

Wang Li, Nan Yakun, Xu Shuo, Cao Yunxing, Tian Lin, Zhang Junsheng, Shi Bin. The constitutive relationship between stress disturbances and hydraulic fracturing volume openings and effects controlling. Chinese Journal of Theoretical and Applied Mechanics, 2024, 56(7): 2150-2163. DOI: 10.6052/0459-1879-23-631

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THE CONSTITUTIVE RELATIONSHIP BETWEEN STRESS DISTURBANCES AND HYDRAULIC FRACTURING VOLUME OPENINGS AND EFFECTS CONTROLLING

Wang Li^*, ,,
Nan Yakun^*,
Xu Shuo^*,
Cao Yunxing^†,
Tian Lin^†,
Zhang Junsheng^†,
Shi Bin^†

*.
School of Civil Engineering, Henan Polytechnic University, Jiaozuo 454000, Henan, China
†.
School of Resources& Environment, Henan Polytechnic University, Jiaozuo 454000, Henan, China

Received Date: December 26, 2023
Accepted Date: May 15, 2024
Available Online: May 15, 2024
Published Date: May 16, 2024

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Abstract

Abstract

Hydraulic fracturing volumetric openings and stress disturbances are concomitant mechanical behaviors in hydraulic fracturing process. The former create hydraulically crack net-works including the main fracture and branching crack net-works, which provide passages for free gas transportation. The latters are increments of compressive stresses on the skeleton matrix, including the main fracture stress disturbance and hydrostatic stress disturbance, which are resulted from main fracture volumetric opening and crack net-work volumetric opening, respectively. Stress disturbances control the passages for gas desorption and diffusion by producing shear dilation in brittle formations or irreversible compression deformation in plastic formations. Therefore, the both mechanical behaviors are jointed together to control the hydraulic fracturing effects. In this paper, in order to establish a controlling mechanisms of gas production, the constitutive relationship between the two mechanical behaviors are established, which includes the meso-mechanisms of stress disturbances stimulated by hydraulic fracturing volumetric openings, the mathematical expressions between stress disturbances and hydraulic volumetric openings, and the method of applying fluid load. By this model, the multitudinous influence factors on the HF effects are integrated into a unified model. As examples, two limiting hydraulic fracturing cases, which respectively belong to the viscosity-storage dominated regime $M$ and viscosity-leak-off dominated regime $\tilde M$ , are employed to demonstrate the constitutive behaviors under varied injection flow rates and fracturing liquids such as water, liquid CO₂, supercritical CO₂, and nitrogen gas N₂. It shows that with the total hydraulic volumetric opening increasing, the hydrostatic stress disturbance firstly goes up to a peak value linearly, then falls to a low level, while the main fracture stress disturbance goes up monotonously following a power law with the exponent larger than 1, and that in $M$ regime, the change paths of stress disturbances are coincident in a line under varied injection flow rates, but in $\tilde M$ regime, these paths are divergent, and the values in $M$ regime are far smaller than in $\tilde M$ regime, and that with the fracturing medium change from liquid to supercritical state and to gas, the hydraulic volumetric openings and stress disturbances become smaller and the final stress disturbance from fracture stress dominated changes to hydrostatic stress dominated. This constitutive relationship establish the base for a controlling mechanism: injection fluid load-hydraulic volume openings-stress disturbances-long term gas production.
- hydraulic fracture,
- hydraulic volume opening,
- stress disturbance,
- constitutive relation,
- fracturing effects controlling

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