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A Fractal Model for Oil Transport in Tight Porous Media

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Abstract

Tight porous media are mainly composed of micro/nano-pores and throats, which leads to obvious microscale effect and nonlinear seepage characteristics. Based on the capillary bundle model and the fractal theory, a new nonlinear seepage equation was deduced, and a further fractal permeability model was obtained for oil transport in tight porous media by considering the effect of the boundary layer. The predictions of the model were then compared with experimental data to demonstrate that the model is valid. This model clarifies the oil transport mechanisms in tight porous media: the effective permeability is no longer a constant value and is governed by properties of tight porous media and oil. Furthermore, parameters influencing effective permeability were analyzed. The model can accurately present the seepage characteristics of the oil in tight porous media and provide a reliable basis for the development of unconventional reservoirs.

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References

  • Cai, J.C.: The fractal study of the non-darcy seepage properties for low permeability reservoir. MS thesis. Huazhong University of Science and Technology (2007). (in Chinese)

  • Cai, J.C.: A fractal approach to low velocity non-Darcy flow in a low permeability porous medium. Chin. Phys. B 23(4), 044701 (2014)

    Article  Google Scholar 

  • Civan, F.: A triple-mechanism fractal model with hydraulic dispersion for gas permeation in tight reservoirs. In: SPE International Petroleum Conference and Exhibition in Mexico. Society of Petroleum Engineers (2002)

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

    Article  Google Scholar 

  • Dadmohammadi, Y., Misra, S., Sondergeld, C. H., et al.: Improved petrophysical interpretation of laboratory pressure-step-decay measurements on ultra-tight rock samples. In: Unconventional Resources Technology Conference (2016)

  • Dadmohammadi, Y., Misra, S., Sondergeld, C.H., et al.: Petrophysical interpretation of laboratory pressure-step-decay measurements on ultra-tight rock samples. Part 1–in the presence of only gas slippage. J. Pet. Sci. Eng. 156, 381–395 (2017)

    Article  Google Scholar 

  • Deng, Y.E., Liu, C.Q.: Mathematical model of nonlinear flow in low permeability porous media and its application. Acta Pet. Sin. 22(4), 72–77 (2001). (in Chinese)

    Google Scholar 

  • Freeman, C.M., Moridis, G.J., Blasingame, T.A.: A numerical study of microscale flow behavior in tight gas and shale gas reservoir systems. Transp. Porous Media 90(1), 253–268 (2011)

    Article  Google Scholar 

  • Huang, Y.Z.: Nonlinear percolation feature in low permeability reservoir. Spec. Oil Gas Reserv. 4(1), 9–14 (1997). (in Chinese)

    Google Scholar 

  • Huang, Y.Z., Yang, Z.M., He, Y., et al.: Nonlinear porous flow in low permeability porous media. Mech. Eng. 35(5), 1–8 (2013). (in Chinese)

    Google Scholar 

  • Javadpour, F.: Nanopores and apparent permeability of gas flow in mudrocks (shales and siltstone). J. Can. Pet. Technol. 48(08), 16–21 (2009)

    Article  Google Scholar 

  • Jia, C.Z., Zou, C.N., Li, J.Z., et al.: Assessment criteria, main types, basic features and resource prospects of the tight oil in China. Acta Pet. Sin. 33(3), 343–350 (2012). (in Chinese)

    Google Scholar 

  • Jiang, R.Z., Li, L.K., Xu, J.C., et al.: A nonlinear mathematical model for low-permeability reservoirs and well-testing analysis. Acta Pet. Sin. 33(2), 264–268 (2012). (in Chinese)

    Google Scholar 

  • Jin, X., Meng, D.P., Liu, X.D., et al.: Understanding the interfacial wettability of reservoir rock at nanoscale. J. Nanosci. Nanotechnol. 16(9), 9779–9783 (2016)

    Article  Google Scholar 

  • Lei, H., Yang, S.L., Zu, L.H., et al.: Oil Recovery Performance and \(\text{ CO }_{2}\) Storage Potential of \(\text{ CO }_{2}\) Water-Alternating-Gas Injection after Continuous \(\text{ CO }_{2}\) Injection in a Multilayer Formation. Energy Fuels 30(11), 8922–8931 (2016)

    Article  Google Scholar 

  • Li, Y.: Study of microscale nonlinear flow characteristics and flow resistance reducing methods. PhD thesis. Chinese Academy of Sciences (Institute of porous flow and fluid mechanics) (2010). (in Chinese)

  • Li, Z.F., He, S.L.: Influence of boundary layers upon filtration law in low-permeability oil reservoirs. Pet. Geol. Oilfield Dev. Daqing 24(2), 57–59 (2005). (in Chinese)

    Google Scholar 

  • Li, L.R., Zhao, Y.Y., Li, Z.X., et al.: Fractal characteristics of micropore structure of porous media and the meaning of fractal coefficient. J. Univ. Pet. China 22(4), 496–498 (2004). (in Chinese)

    Google Scholar 

  • Li, C., Fang, W.Z., Kang, Q.J., et al.: Generalized lattice Boltzmann model for flow through tight porous media with Klinkenberg’s effect. Phys. Rev. E 91(3), 033004 (2015a)

    Article  Google Scholar 

  • Li, Z.F., Ren, X.J., Zhang, Y.: Experimental study of oil and gas permeability measured relationship on low permeability reservoir. J. Liaoning Shihua Univ. 35(2), 50–52 (2015b). (in Chinese)

  • Li, X.G., Yi, L.P., Yang, Z.Z., et al.: A new model for gas transport in fractal-like tight porous media. J. Appl. Phys. 117(17), 174304 (2015c)

    Article  Google Scholar 

  • Li, X.G., Yi, L.P., Yang, Z.Z., et al.: A new model for gas-water two-immiscible-phase transport in fractal-like porous media. J. Appl. Phys. 118(22), 224306 (2015d)

    Article  Google Scholar 

  • Li, P., Zheng, M., Bi, H., et al.: Pore throat structure and fractal characteristics of tight oil sandstone: a case study in the ordos basin, China. J. Pet. Sci. Eng. 149, 665–674 (2017)

    Article  Google Scholar 

  • Mapxacин, И. Л.: The Physical Chemistry Mechanism of Reservoirs. Dianwen Li (translator), Petroleum Industry Press, Beijing (1987). (in Chinese)

  • Neto, C., Evans, D.R., Bonaccurso, E., et al.: Boundary slip in Newtonian liquids: a review of experimental studies. Rep. Prog. Phys. 68(12), 2859 (2005)

    Article  Google Scholar 

  • Ojha, S. P., Misra, S., Sinha, A., et al.: Estimation of pore network characteristics and saturation-dependent relative permeability in organic-rich shale samples obtained from bakken, wolfcamp, and woodford shale formations. In: SPWLA 58th Annual Logging Symposium. Society of Petrophysicists and Well-Log Analysts (2017a)

  • Ojha, S.P., Misra, S., Tinni, A., et al.: Relative permeability estimates for Wolfcamp and Eagle Ford shale samples from oil, gas and condensate windows using adsorption-desorption measurements. Fuel 208, 52–64 (2017b)

    Article  Google Scholar 

  • Prada, A., Civan, F.: Modification of Darcy’s law for the threshold pressure gradient. J. Pet. Sci. Eng. 22(4), 237–240 (1999)

    Article  Google Scholar 

  • Ruan, M., He, Q.X.: He. Low permeability reservoir percolation characteristics and its influence on oil field development. Spec. Oil Gas Reserv. 5(3), 23–28 (1998). (in Chinese)

    Google Scholar 

  • Shi, Y., Yang, Z.M., Huang, Y.Z.: Study on non-linear seepage flow model for low-permeability reservoir. Acta Pet. Sin. 30(5), 731–734 (2009). (in Chinese)

    Google Scholar 

  • Song, F.Q., Wang, J.D., Liu, H.L.: Static threshold pressure gradient characteristics of liquid influenced by boundary wettability. Chin. Phys. Lett. 27(2), 111–120 (2010)

    Article  Google Scholar 

  • Tian, X.F.: Non-linear flow behavior and mathematical model in ultra-low permeability reservoirs. PhD thesis. China University of Petroleum, Beijing (2014). (in Chinese)

  • Tian, X.F., Cheng, L.S., Yan, Y.Q., et al.: An improved solution to estimate relative permeability in tight oil reservoirs. J. Pet. Explor. Prod. Technol. 5(3), 305–314 (2015)

    Article  Google Scholar 

  • Wu, K.L.: Apparent permeability for gas flow in shale reservoirs coupling effects of gas diffusion and desorption. In: Unconventional Resources Technology Conference (URTEC) (2014)

  • Wu, Y.S., Pruess, K., Persoff, P.: Gas flow in porous media with klinkenberg effects. Transp. Porous Media 32(1), 117–137 (1998)

    Article  Google Scholar 

  • Xiong, Y., Yu, J.B., Sun, H.X., et al.: A new non-Darcy flow model for low-velocity multiphase flow in tight reservoirs. Transp. Porous Media 117(3), 367–383 (2017)

    Article  Google Scholar 

  • Xu, S.L., Yue, X.A., Hou, J.R., et al.: Influence of boundary-layer fluid on the seepage characteristic of low-permeability reservoir. J. Xi\(\prime \)an Shiyou Univ. (Nat. Sci. Edn.) 22(2), 26–28 (2007). (in Chinese)

  • Xu, J.C., Jiang, R.Z., Xie, L.S., et al.: Transient pressure behavior for dual porosity low permeability reservoir based on modified Darcy. In: SPE Latin America and Caribbean Petroleum Engineering Conference. Society of Petroleum Engineers (2012)

  • Xue, H.T., Tian, S.S., Lu, S.F., et al.: The significance of wettability in tight oil exploration and development. Acta Geol. Sin. (Engl. Edit.) 89(s1), 172–174 (2015)

    Article  Google Scholar 

  • Yang, Z.M., Yu, R.Z., Su, Z.X., et al.: Numerical simulation of the nonlinear flow in ultra-low permeability reservoirs. Pet. Expl. Dev. 37(1), 94–98 (2010). (in Chinese)

    Google Scholar 

  • Yang, R.F., Jiang, R.Z., Liu, S.H.: Demonstration of essentiality of considering nonlinear flow in low permeability reservoir. Fault-Block Oil Gas Field 18(4), 493–497 (2011). (in Chinese)

    Google Scholar 

  • Yang, F., Ning, Z.F., Liu, H.Q.: Fractal characteristics of shales from a shale gas reservoir in the Sichuan Basin, China. Fuel 115, 378–384 (2014)

    Article  Google Scholar 

  • Yao, Y.D., Ge, J.L.: New pattern and its rules of oil non-Darcy flow in porous media. Oil Drill. Prod. Technol. 25(5), 40–42 (2003). (in Chinese)

    Google Scholar 

  • Yao, Y.D., Ge, J.L.: Characteristics of non-Darcy flow in low-permeability reservoirs. Pet. Sci. 8(1), 55–62 (2011)

    Article  Google Scholar 

  • Yu, B.M., Li, J.H.: Some fractal characters of porous media. Fractals 9(3), 365–372 (2001)

    Article  Google Scholar 

  • Yu, B.M., Cheng, P.: A fractal permeability model for bi-dispersed porous media. Int. J. Heat Mass Transf. 45(14), 2983–2993 (2002)

    Article  Google Scholar 

  • Yu, B.M., Li, J.H.: A geometry model for tortuosity of flow path in porous media. Chin. Phys. Lett. 21(8), 1569 (2004)

    Article  Google Scholar 

  • Yu, B.M., Cai, J.C., Zou, M.Q.: On the physical properties of apparent two-phase fractal porous media. Vadose Zone J. 8(1), 177–186 (2009)

    Article  Google Scholar 

  • Yuan, Y.D., Doonechaly, N.G., Rahman, S.: An analytical model of apparent gas permeability for tight porous media. Transp. Porous Media 111(1), 193–214 (2016)

    Article  Google Scholar 

  • Yun, M.J.: Research on some flow properties of fluid in porous media. PhD thesis. Huazhong University of Science and Technology (2008). (in Chinese)

  • Yun, M.J., Yu, B.M., Cai, J.C.: A fractal model for the starting pressure gradient for Bingham fluids in porous media. Int. J. Heat Mass Transf. 51(5), 1402–1408 (2008)

  • Zheng, Q., Yu, B.M.: A fractal permeability model for gas flow through dual-porosity media. J. Appl. Phys. 111(2), 024316 (2012)

    Article  Google Scholar 

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

    Article  Google Scholar 

  • Zou, C.N., Tao, S.Z., Bai, B., et al.: Differences and relations between unconventional and conventional oil and gas. China Pet. Explor. 20(1), 1–16 (2015a). (in Chinese)

    Google Scholar 

  • Zou, C.N., Zhu, R.K., Bai, B., et al.: Significance, geologic characteristics, resource potential and future challenges of tight oil and shale oil. Bull. Mineral. Pet. Geochem. 34(1), 3–17 (2015b). (in Chinese)

    Google Scholar 

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Acknowledgements

The authors are grateful to financial support of National Basic Research Program of China (2015CB250900), Program for New Century Excellent Talents in University (Grant No. NCET-13-1030) and the National Natural Science Foundation of China (Grant No. 40974055). We also would like to thank Prof. Yu, School of Physics, Huazhong University of Science and Technology, for value discussion of the study.

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  1. College of Petroleum Engineering, China University of Petroleum, Beijing, 102249, China

    Shan Huang, Yuedong Yao, Shuang Zhang, Jinghao Ji & Ruoyu Ma

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  1. Shan Huang
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Correspondence to Shan Huang.

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Huang, S., Yao, Y., Zhang, S. et al. A Fractal Model for Oil Transport in Tight Porous Media. Transp Porous Med 121, 725–739 (2018). https://doi.org/10.1007/s11242-017-0982-1

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