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Improved discrete element modeling for proppant embedment into rock surfaces

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Abstract

Brinell indentation tests were performed on Montney siltstone, and the results were compared with discrete element indentation simulations that use the micro-parameters calibrated using compression test data from the same siltstone samples. The simulated proppant indentation into the rock surface can be 15% less than the laboratory measurements. A lower effective particle–particle modulus and thus a lower Young’s modulus are needed in discrete element models for proper simulation of indentation. An equation to find the appropriate value of Young’s modulus for indentation simulation is proposed using Brinell indentation tests including 198 laboratory tests and 32 discrete element simulations. This equation can improve the prediction of Young’s modulus and thus the particle–particle effective modulus for indentation simulations to match the measured force–indentation depth curve in the laboratory. Using the improved micro-parameters, a parametric analysis of the influence of rock Young’s modulus and proppant particle size on proppant embedment was performed. An equation to estimate Brinell hardness as a function of Young’s modulus and closure stress was derived. A practical procedure was developed to predict proppant embedment from the estimated hardness. The predictions agree with the laboratory measurements in a case study on the Montney Formation.

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Acknowledgements

The Particle Flow Code was provided by Itasca through an educational partnership. This work was support by grants from the Key Program of National Natural Science Foundation of China (41630643), China Postdoctoral Science Foundation (2018M642952) and Postdoctoral International Exchange Program, British Columbia Oil and Gas Commission, and Mitacs. Trican Geological Solutions (now AGAT Laboratories) contributed to the laboratory measurement work.

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Authors and Affiliations

  1. Faculty of Engineering, China University of Geoscience, 388 Lumo Road, Wuhan, Hubei Province, 430074, People’s Republic of China

    Wenbo Zheng & Xinli Hu

  2. School of Engineering, University of British Columbia, Kelowna, BC, V1V 1V7, Canada

    Wenbo Zheng, Dwayne D. Tannant & Cong Xu

  3. AGAT Laboratories, Calgary, AB, T2E 2M1, Canada

    Xiaojun Cui

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  1. Wenbo Zheng
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  2. Dwayne D. Tannant
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  3. Xiaojun Cui
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  4. Cong Xu
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  5. Xinli Hu
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Correspondence to Xinli Hu.

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Appendix: micro-parameters analysis of bonded siltstone models

Appendix: micro-parameters analysis of bonded siltstone models

See Tables 8, 9 and 10.

Table 8 Combination of different levels of micro-parameters for computation scenarios
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Table 9 Results of 32 scenarios
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Table 10 Estimated contribution of micro-parameters to outputs
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Zheng, W., Tannant, D.D., Cui, X. et al. Improved discrete element modeling for proppant embedment into rock surfaces. Acta Geotech. 15, 347–364 (2020). https://doi.org/10.1007/s11440-019-00819-5

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  • DOI: https://doi.org/10.1007/s11440-019-00819-5

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