Skip to main content
Log in

An Anisotropic Permeability Model for Shale Gas Recovery Considering Slippage Effect and Embedded Proppants

  • Original Paper
  • Published:
Natural Resources Research Aims and scope Submit manuscript

Abstract

Hydraulic fracturing has been widely adopted to improve shale gas recovery. A main issue in the implementation of hydraulic fracturing techniques is that proppants made from a variety of materials are normally introduced for the purpose of permeability enhancement. An embedded proppant can significantly alter the original gas flow behavior of shale, which should be taken into account when estimating shale permeability. In this paper, we propose a shale anisotropic permeability model that considers the effect of proppant embedding. Moreover, because the slippage factor is usually not fixed owing to the combined effect of proppant embeddings, any adsorption-induced swelling and stress, a slippage factor formulation is developed to consider the embedded proppant. Finally, an improved shale anisotropic permeability model that considers the combined effect of proppants and slippage is proposed. The validity of the model presented in this paper was assessed by comparing the results with previous experiments, and good agreement was found for the proposed model. The developed model can estimate accurately shale anisotropic permeability, when both the proppant and slippage effect are considered, and can be used to study related problems in the recovery of shale gas resources.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Figure 1
Figure 2
Figure 3
Figure 4
Figure 5
Figure 6
Figure 7
Figure 8
Figure 9
Figure 10
Figure 11
Figure 12
Figure 13
Figure 14
Figure 15

Similar content being viewed by others

References

  • Alramahi, B., & Sundberg, M. I. (2012). Proppant embedment and conductivity of hydraulic fractures in shales. In 46th US Rock Mechanics/Geomechanics Symposium. American Rock Mechanics Association.

  • Cai, J., Lin, D., Singh, H., Zhou, S., Meng, Q., & Zhang, Q. (2019). A simple permeability model for shale gas and key insights on relative importance of various transport mechanisms. Fuel, 252, 210–219.

    Google Scholar 

  • Cao, P., Liu, J., & Leong, Y. K. (2016). General gas permeability model for porous media: Bridging the gaps between conventional and unconventional natural gas reservoirs. Energy & Fuels, 30(7), 5492–5505.

    Google Scholar 

  • Chen, Z., Liu, J., Pan, Z., Connell, L. D., & Elsworth, D. (2012). Influence of the effective stress coefficient and sorption-induced strain on the evolution of coal permeability: Model development and analysis. International Journal of Greenhouse Gas Control, 8, 101–110.

    Google Scholar 

  • Chen, D., Pan, Z., & Ye, Z. (2015). Dependence of gas shale fracture permeability on effective stress and reservoir pressure: Model match and insights. Fuel, 139, 383–392.

    Google Scholar 

  • Chen, D., Ye, Z., Pan, Z., Zhou, Y., & Zhang, J. (2017). A permeability model for the hydraulic fracture filled with proppant packs under combined effect of compaction and embedment. Journal of Petroleum Science and Engineering, 149, 428–435.

    Google Scholar 

  • Cho, J. W., Kim, H., Jeon, S., & Min, K. B. (2012). Deformation and strength anisotropy of Asan gneiss, Boryeong shale, and Yeoncheon schist. International Journal of Rock Mechanics and Mining Sciences, 50, 158–169.

    Google Scholar 

  • Civan, F. (2010). Effective correlation of apparent gas permeability in tight porous media. Transport in Porous Media, 82(2), 375–384.

    Google Scholar 

  • Cui, G., Liu, J., Wei, M., Feng, X., & Elsworth, D. (2018). Evolution of permeability during the process of shale gas extraction. Journal of Natural Gas Science and Engineering, 49, 94–109.

    Google Scholar 

  • Ertekin, T., King, G. A., & Schwerer, F. C. (1986). Dynamic gas slippage: A unique dual-mechanism approach to the flow of gas in tight formations. SPE formation evaluation, 1(01), 43–52.

    Google Scholar 

  • Fathi, E., Tinni, A., & Akkutlu, I. Y. (2012). Correction to Klinkenberg slip theory for gas flow in nano-capillaries. International Journal of Coal Geology, 103, 51–59.

    Google Scholar 

  • Fink, R., Amann-Hildenbrand, A., Bertier, P., & Littke, R. (2018). Pore structure, gas storage and matrix transport characteristics of lacustrine Newark shale. Marine and Petroleum Geology, 97, 525–539.

    Google Scholar 

  • Fink, R., Krooss, B. M., Gensterblum, Y., & Amann-Hildenbrand, A. (2017). Apparent permeability of gas shales–Superposition of fluid-dynamic and poro-elastic effects. Fuel, 199, 532–550.

    Google Scholar 

  • Gao, Q., Tao, J., Hu, J., & Yu, X. B. (2015). Laboratory study on the mechanical behaviors of an anisotropic shale rock. Journal of Rock Mechanics and Geotechnical Engineering, 7(2), 213–219.

    Google Scholar 

  • Gao, C., Xie, L. Z., Xie, H. P., He, B., Jin, W. C., Li, F., et al. (2017). Estimation of the equivalent elastic modulus in shale formation: Theoretical model and experiment. Journal of Petroleum Science and Engineering, 151, 468–479.

    Google Scholar 

  • Gaurav, A., Dao, E. K., & Mohanty, K. K. (2012). Evaluation of ultra-light-weight proppants for shale fracturing. Journal of Petroleum Science and Engineering, 92, 82–88.

    Google Scholar 

  • Ghanizadeh, A., Amann-Hildenbrand, A., Gasparik, M., Gensterblum, Y., Krooss, B. M., & Littke, R. (2014). Experimental study of fluid transport processes in the matrix system of the European organic-rich shales: II. Posidonia Shale (Lower Toarcian, northern Germany). International Journal of Coal Geology, 123, 20–33.

    Google Scholar 

  • Gou, Q., Xu, S., Hao, F., Yang, F., Zhang, B., Shu, Z., et al. (2019). Full-scale pores and micro-fractures characterization using FE-SEM, gas adsorption, nano-CT and micro-CT: A case study of the Silurian Longmaxi Formation shale in the Fuling area, Sichuan Basin, China. Fuel, 253, 167–179.

    Google Scholar 

  • Guo, M., Lu, X., Nielsen, C. P., McElroy, M. B., Shi, W., Chen, Y., et al. (2016). Prospects for shale gas production in China: Implications for water demand. Renewable and Sustainable Energy Reviews, 66, 742–750.

    Google Scholar 

  • Harpalani, S., & Chen, G. (1997). Influence of gas production induced volumetric strain on permeability of coal. Geotechnical and Geological Engineering, 15(4), 303–325.

    Google Scholar 

  • Heid, J., Mc Mahon, J. J., Nielson, R. F., & Yuster, S. T. (1950). In: American Petroleum Institute drilling and production practice (pp. 230–246).

  • Hou, T., Zhang, S., Ma, X., Shao, J., He, Y., Lv, X., et al. (2017). Experimental and theoretical study of fracture conductivity with heterogeneous proppant placement. Journal of Natural Gas Science and Engineering, 37, 449–461.

    Google Scholar 

  • Jia, L., Li, K., Zhou, J., Yan, Z., Wan, F., & Kaita, M. (2019). A mathematical model for calculating rod-shaped proppant conductivity under the combined effect of compaction and embedment. Journal of Petroleum Science and Engineering, 180, 11–21.

    Google Scholar 

  • Jones, F. O., & Owens, W. W. (1980). A laboratory study of low-permeability gas sands. Journal of Petroleum Technology, 32(09), 1–631.

    Google Scholar 

  • Ju, Y., Liu, P., Chen, J., Yang, Y., & Ranjith, P. G. (2016). CDEM-based analysis of the 3D initiation and propagation of hydrofracturing cracks in heterogeneous glutenites. Journal of Natural Gas Science and Engineering, 35, 614–623.

    Google Scholar 

  • Kassis, S., & Sondergeld, C. (2010). Gas shale permeability: Effects of roughness, proppant, fracture offset, and confining pressure. In International Oil and Gas Conference and Exhibition in China.

  • Khanna, A., Kotousov, A., Sobey, J., & Weller, P. (2012). Conductivity of narrow fractures filled with a proppant monolayer. Journal of Petroleum Science and Engineering, 100, 9–13.

    Google Scholar 

  • Klinkenberg, L. J. (1941). The permeability of porous media to liquids and gases. In Drilling and production practice. American Petroleum Institute.

  • Li, J., Chen, Z., Wu, K., Li, R., Xu, J., Liu, Q., et al. (2018). Effect of water saturation on gas slippage in tight rocks. Fuel, 225, 519–532.

    Google Scholar 

  • Li, M., Yin, G., Xu, J., Cao, J., & Song, Z. (2016). Permeability evolution of shale under anisotropic true triaxial stress conditions. International Journal of Coal Geology, 165, 142–148.

    Google Scholar 

  • Liu, H. H., Wei, M. Y., & Rutqvist, J. (2013). Normal-stress dependence of fracture hydraulic properties including two-phase flow properties. Hydrogeology Journal, 21(2), 371–382.

    Google Scholar 

  • McGlade, C., Speirs, J., & Sorrell, S. (2013). Unconventional gas-a review of regional and global resource estimates. Energy, 55, 571–584.

    Google Scholar 

  • McKee, C. R., Bumb, A. C., & Koenig, R. A. (1988). Stress-dependent permeability and porosity of coal and other geologic formations. SPE Formation Evaluation, 3(01), 81–91.

    Google Scholar 

  • Mi, L., Jiang, H., Wang, Y., Pei, Y., Li, J., Gao, S., & Killough, J. (2016). Hydraulic fracture optimization based on discrete fracture network model in shale reservoirs. In International Petroleum Technology Conference.

  • Moghadam, A. A., & Chalaturnyk, R. (2014). Expansion of the Klinkenberg’s slippage equation to low permeability porous media. International Journal of Coal Geology, 123, 2–9.

    Google Scholar 

  • Moghadasi, R., Rostami, A., & Hemmati-Sarapardeh, A. (2019). Application of nanofluids for treating fines migration during hydraulic fracturing: Experimental study and mechanistic understanding. Advances in Geo-Energy Research, 3(2), 198–206.

    Google Scholar 

  • Mukherjee, M., & Misra, S. (2018). A review of experimental research on Enhanced Coal Bed Methane (ECBM) recovery via CO2 sequestration. Earth-Science Reviews, 179, 392–410.

    Google Scholar 

  • Niandou, H., Shao, J. F., Henry, J. P., & Fourmaintraux, D. (1997). Laboratory investigation of the mechanical behaviour of Tournemire shale. International Journal of Rock Mechanics and Mining Sciences, 34(1), 3–16.

    Google Scholar 

  • Pan, Z., Ma, Y., Connell, L. D., Down, D. I., & Camilleri, M. (2015). Measuring anisotropic permeability using a cubic shale sample in a triaxial cell. Journal of Natural Gas Science and Engineering, 26, 336–344.

    Google Scholar 

  • Qu, H., Pan, Z., Peng, Y., & Zhou, F. (2016). Controls on matrix permeability of shale samples from Longmaxi and Niutitang formations, China. Journal of Natural Gas Science and Engineering, 33, 599–610.

    Google Scholar 

  • Shamsi, M. M. M., Nia, S. F., & Jessen, K. (2017). Dynamic conductivity of proppant-filled fractures. Journal of Petroleum Science and Engineering, 151, 183–193.

    Google Scholar 

  • Singh, H., & Cai, J. (2018). A mechanistic model for multi-scale sorption dynamics in shale. Fuel, 234, 996–1014.

    Google Scholar 

  • Sutcu, M. (1992). Orthotropic and transversely isotropic stress-strain relations with built-in coordinate transformations. International Journal of Solids and Structures, 29(4), 503–518.

    Google Scholar 

  • Tan, Y., Pan, Z., Liu, J., Wu, Y., Haque, A., & Connell, L. D. (2017). Experimental study of permeability and its anisotropy for shale fracture supported with proppant. Journal of Natural Gas Science and Engineering, 44, 250–264.

    Google Scholar 

  • Wang, J. G., Hu, B., Liu, H., Han, Y., & Liu, J. (2018). Effects of ‘soft-hard’ compaction and multiscale flow on the shale gas production from a multistage hydraulic fractured horizontal well. Journal of Petroleum Science and Engineering, 170, 873–887.

    Google Scholar 

  • Wang, Y., & Li, C. H. (2017). Investigation of the P-and S-wave velocity anisotropy of a Longmaxi formation shale by real-time ultrasonic and mechanical experiments under uniaxial deformation. Journal of Petroleum Science and Engineering, 158, 253–267.

    Google Scholar 

  • Wang, G., Ren, T., Wang, K., & Zhou, A. (2014a). Improved apparent permeability models of gas flow in coal with Klinkenberg effect. Fuel, 128, 53–61.

    Google Scholar 

  • Wang, K., Zang, J., Wang, G., & Zhou, A. (2014b). Anisotropic permeability evolution of coal with effective stress variation and gas sorption: Model development and analysis. International Journal of Coal Geology, 130, 53–65.

    Google Scholar 

  • Wen, Q., Zhang, S., Wang, L., Liu, Y., & Li, X. (2007). The effect of proppant embedment upon the long-term conductivity of fractures. Journal of Petroleum Science and Engineering, 55(3–4), 221–227.

    Google Scholar 

  • Xie, J., Cheng, W., Wang, R., Jiang, G., Sun, D., & Sun, J. (2018). Experiments and analysis on the influence of perforation mode on hydraulic fracture geometry in shale formation. Journal of Petroleum Science and Engineering, 168, 133–147.

    Google Scholar 

  • Xu, R., Zeng, K., Zhang, C., & Jiang, P. (2017). Assessing the feasibility and CO2 storage capacity of CO2 enhanced shale gas recovery using Triple-Porosity reservoir model. Applied Thermal Engineering, 115, 1306–1314.

    Google Scholar 

  • Yang, D., Qi, X., Chen, W., Wang, S., & Dai, F. (2016). Numerical investigation on the coupled gas-solid behavior of coal using an improved anisotropic permeability model. Journal of Natural Gas Science and Engineering, 34, 226–235.

    Google Scholar 

  • Zhang, C. L. (2016). The stress–strain–permeability behaviour of clay rock during damage and recompaction. Journal of Rock Mechanics and Geotechnical Engineering, 8(1), 16–26.

    Google Scholar 

  • Zhang, J., Kamenov, A., Zhu, D., & Hill, A. D. (2015a). Measurement of realistic fracture conductivity in the Barnett shale. Journal of Unconventional Oil and Gas Resources, 11, 44–52.

    Google Scholar 

  • Zhang, R., Ning, Z., Yang, F., Wang, X., Zhao, H., & Wang, Q. (2015b). Impacts of nanopore structure and elastic properties on stress-dependent permeability of gas shales. Journal of Natural Gas Science and Engineering, 26, 1663–1672.

    Google Scholar 

  • Zhang, W., & Wang, Q. (2018). Permeability anisotropy and gas slippage of shales from the Sichuan Basin in South China. International Journal of Coal Geology, 194, 22–32.

    Google Scholar 

  • Zhang, X., Wang, J. G., Gao, F., Ju, Y., & Liu, J. (2017). Impact of water and nitrogen fracturing fluids on fracturing initiation pressure and flow pattern in anisotropic shale reservoirs. Computers and Geotechnics, 81, 59–76.

    Google Scholar 

  • Zheng, Q., Yu, B., Duan, Y., & Fang, Q. (2013). A fractal model for gas slippage factor in porous media in the slip flow regime. Chemical Engineering Science, 87, 209–215.

    Google Scholar 

  • Zhou, Y., Li, Z., Yang, Y., Zhang, L., Si, L., Kong, B., et al. (2016a). Evolution of coal permeability with cleat deformation and variable Klinkenberg effect. Transport in Porous Media, 115(1), 153–167.

    Google Scholar 

  • Zhou, T., Zhang, S., Yang, L., Ma, X., Zou, Y., & Lin, H. (2016b). Experimental investigation on fracture surface strength softening induced by fracturing fluid imbibition and its impacts on flow conductivity in shale reservoirs. Journal of Natural Gas Science and Engineering, 36, 893–905.

    Google Scholar 

  • Ziarani, A. S., & Aguilera, R. (2012). Knudsen’s permeability correction for tight porous media. Transport in Porous Media, 91(1), 239–260.

    Google Scholar 

  • Zou, J., Chen, W., Yang, D., Yu, H., & Yuan, J. (2016). The impact of effective stress and gas slippage on coal permeability under cyclic loading. Journal of Natural Gas Science and Engineering, 31, 236–248.

    Google Scholar 

Download references

Acknowledgments

This study was financially supported by the National Natural Science Foundation of China (Grant Nos. 51804085 and 51911530203) and the Science and Technology Funding Projects of Guizhou Province (No. J2015-2049).

Author information

Authors and Affiliations

Authors

Corresponding author

Correspondence to Bobo Li.

Rights and permissions

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Li, J., Li, B., Wang, Z. et al. An Anisotropic Permeability Model for Shale Gas Recovery Considering Slippage Effect and Embedded Proppants. Nat Resour Res 29, 3319–3333 (2020). https://doi.org/10.1007/s11053-020-09660-0

Download citation

  • Received:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s11053-020-09660-0

Keywords

Navigation