An equivalent mathematical model for 2D stimulated reservoir volume simulation of hydraulic fracturing in unconventional reservoirs

ABSTRACT

Stimulated reservoir volume (SRV) is a key parameter affecting the post-fracturing production of ultra-low permeability reservoirs. Accurate prediction of the SRV shape and size is of vital significance for pre-fracturing stimulation design and post-fracturing effect evaluation. In this paper, an equivalent mathematical model for simulating two-dimensional SRV growth is proposed by integrating the fracture width equation, tensor permeability conversion, cubic law and calculation method of fracture porosity with mass conservation equation of injected fluid in natural fracture system. The finite difference method is used to derive the numerical discrete equation, and the fluid pressure and average fracture width in each grid block are obtained by solving the coupled fluid conservation equation and fracture width equation. The model is validated by comparing the results obtained from this work with others from literature. A parametric sensitivity study was performed to analyze the effects of some factors incorporating approaching angle, natural fracture spacing, horizontal principal stress difference, pumping rate and fracturing fluid viscosity on the SRV (including size, aspect ratio, and arithmetic mean fracture width in SRV region). The results show that SRV increases with the decrease of approaching angle, principal stress difference, injection rate, viscosity of fracturing fluid and fracture density. The width of branch fracture decreases with the increasing approaching angle and principal stress difference but increases with the increasing pumping rate and fluid viscosity.

KEYWORDS:

• Natural fracture
• stimulated reservoir volume
• permeability tensor
• unconventional reservoirs
• mathematical model

Acknowledgments

The authors would like to acknowledge the financial support of the Chongqing Research Program of Basic Research and Frontier Technology Study (cstc2016jcyjA0293, cstc2018jcyjAX0700), The Key Projects of Chongqing Natural Science Foundation (cstc2019jcyj-zdxm0064), National Natural Science Foundation of China Youth Fund (51604053) and The Major National Science and Technology Projects (2016ZX05047004004). We would also like to express our gratitude to the reviewers for their careful review of this manuscript. Their comments on this manuscript are greatly valuable for our future research.

Additional information

Funding

This work was supported by the Chongqing Research Program of Basic Research and Frontier Technology [cstc2016jcyjA0293, cstc2018jcyjAX0700]; The Major National Science and Technology Projects [2016ZX05047004004];The Key Projects of Chongqing Natural Science Foundation [cstc2019jcyj-zdxm0064] ;National Natural Science Foundation of China Youth Fund [51604053].

Notes on contributors

Zhiqiang Li

Zhiqiang Li, a postdoctoral researcher of chongqing university, graduated from southwest petroleum university with a doctorate degree in oil and gas field development engineering. He is mainly engaged in numerical simulation of hydraulic fracturing, seepage mechanism and productivity evaluation in unconventional reservoirs.

Zhilin Qi

Zhilin Qi, a professor of chongqing university of science and technology, graduated from southwest petroleum university with a  doctorate degree in oil and gas field development engineering. He is mainly engaged in numerical simulation and oil and gas seepage mechanism.

Wende Yan

Wende Yan, an associate professor of chongqing university of science and technology, graduated from southwest petroleum university with a doctorate degree in oil and gas field development engineering. He is mainly engaged in the research of oil and gas seepage mechanism.

Qianhua Xiao

Qianhua Xiao, an associate professor of chongqing university of science and technology, graduated from  the university  of chinese academy of sciences with a Ph.D. in fluid mechanics. At present, he is mainly engaged in the research of oil and gas percolation mechanism.

Zuping Xiang

Zuping Xiang, a professor of chongqing university of science and technology, graduated from southwest petroleum university with a doctorate degree in oil and gas field development. He is mainly engaged  in reservoir numerical simulation and reservoir engineering.

Zhengwu Tao

Zhengwu Tao, reservoir engineer, graduated from southwest petroleum university with a doctorate degree in oil and gas field development. He is mainly engaged in reservoir engineering, production performance analysis, development program and other related studies.