Abstract
Due to complex pore structures and ultra-low permeability in unconventional gas reservoirs, the flow consistency between the macro-flow in fracture network and the micro-flow or gas diffusion in matrix may significantly impact the production rate of fractured gas reservoirs. This study investigated the impact of this flow consistency on the production rate through the development of a numerical simulation model and its application to a shale gas reservoir. In this model, a fractured gas reservoir consists of fracture network and matrix. In the fracture network, gas flow was assumed to follow the non-Darcy law. In the matrix, a nonlinear diffusion model was proposed for the gas micro-flow through a non-empirical apparent permeability. This nonlinear diffusion model considered the advection and diffusion of the free-phase gas in nanoporous channels as well as the gas desorption in matrix. Further, the mass exchange rate between fracture network and matrix was calculated via a diffusion time which comprehensively considers both the diffusion capability and the size of matrix block. This numerical model was verified through history matching of the production data from two shale wells and then applied to a typical production well to investigate the effects of pore size in matrix, fracture spacing, and initial fracture permeability on production curve (i.e., production rate versus time). It is found that the production curve is significantly affected by this flow consistency. Pore size and initial fracture permeability play the key roles in this flow consistency. Fracture spacing and fracture permeability can alter the production curve. In this sense, the production curve can be designable through this flow consistency. Production efficiency can be improved through appropriate control of the fracturing degree of shale reservoir. Meanwhile, accurate measurement of shale pore size distribution provides an important parameter to the design of this flow consistency.
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References
Beskok, A., Karniadakis, G.E.: A model for flows in channels, pipes, and ducts at micro and nano scales. Microscale Thermophys. Eng. 3(1), 43–77 (1999)
Bustin, R.M., Bustin, A.M.M.: Importance of rock properties on the producibility of gas shales. Int. J. Coal Geol. 103, 132–147 (2012)
Chen, D., Pan, Z., Ye, Z.: Dependence of gas shale fracture permeability on effective stress and reservoir pressure: model match and insights. Fuel 139, 383–392 (2015)
Civan, F., Rai, C., Sondergeld, C.: Shale-gas permeability and diffusivity inferred by improved formulation of relevant retention and transport mechanisms. Transp. Porous Media 86(3), 925–44 (2011)
Civan, F.: Effective correlation of apparent gas permeability in tight porous media. Transp. Porous Media 82(2), 375–384 (2010)
Cooke Jr, C.E.: Conductivity of fracture proppants in multiple layers. J. Petrol. Technol. 25(9), 1101–1110 (1973). (SPE-4117-PA)
Cooper, S.M., Cruden, B.A., Meyyappan, M., Raju, R., Roy, S.: Gas transport characteristics through a carbon nanotubule. Nano Lett. 4(2), 377–381 (2004)
Cui, X., Bustin, A.M., Bustin, R.: Measurements of gas permeability and diffusivity of tight reservoir rocks: different approaches and their applications. Geofluids 9, 208–223 (2009)
Darabi, H., Ettehad, A., Javadpour, F., Sepehrnoori, K.: Gas flow in ultra-tight shale strata. J. Fluid Mech. 710, 641–658 (2012)
Deng, J., Zhu, W., Ma, Q.: A new seepage model for shale gas reservoir and productivity analysis of fractured well. Fuel 124, 232–240 (2014)
Dongari, N., Sharma, A., Durst, F.: Pressure-driven diffusive gas flows in micro-channels: from the Knudsen to the continuum regimes. Microfluid. Nanofluid. 6(5), 679–692 (2009)
Friedel, T., Voigt, H.D.: Investigation of non-Darcy flow in tight-gas reservoirs with fractured wells. J. Petrol. Sci. Eng. 54(3–4), 112–128 (2006)
Fuentes-Cruz, G., Valko, Peter P.: Revisiting the dual-porosity/dual-permeability modeling of unconventional reservoirs: the induced-interporosity flow field. SPE J. 20(1), 125–141 (2015)
Guo, C., Xu, J., Wu, K., Wei, M., Liu, S.: Study on gas flow through nano pores of shale gas reservoirs. Fuel 143, 107–117 (2015)
Javadpour, F., Fisher, D., Unsworth, M.: Nanoscale gas flow in shale sediments. J. Can. Pet. Technol. 46(10), 55–61 (2007)
Javadpour, F.: Nanopores and apparent permeability of gas flow in mudrocks (shales and siltstone). J. Can. Pet. Technol. 48(8), 16–21 (2009)
Klinkenberg, L.J.: The permeability of porous media to liquids and gases. In API Drilling and Production Practice, pp. 200–213. (1941)
Lim, K., Aziz, K.: Matrix-fracture transfer shape factors for dual-porosity simulators. J. Petrol. Sci. Eng. 13, 169–178 (1995)
Ma, J., Sanchez, J., Wu, K., Couples, G., Jiang, Z.: A pore network model for simulating non-ideal gas flow in micro- and nano-porous material. Fuel 116, 498–508 (2014)
Mi, L., Jiang, H., Li, J.: The impact of diffusion type on multiscale discrete fracture model numerical simulation for shale gas. J. Nat. Gas Sci. Eng. 20, 74–81 (2014)
Naraghi, M.E., Javadpour, F.: A stochastic permeability model for the shale-gas systems. Int. J. Coal Geol. 140, 111–124 (2015)
Qanbari, F., Clarkson, C.R.: A new method for production data analysis of tight and shale gas reservoirs during transient linear flow period. J. Nat. Gas Sci. Eng. 14, 55–65 (2013)
Qanbari, F., Clarkson, C.R.: Analysis of transient linear flow in stress-sensitive formations. SPE Reserv. Eval. Eng. 17, 98–104 (2014)
Rahmanian, M., Solano, N., Aguilera, R.: Storage and Output Flow From Shale and Tight Gas Reservoirs. SPE Western Regional Meeting, Anaheim, 7–29 May 2010, SPE-133611-MS (2010)
Singh, H., Javadpour, F.: A new non-empirical approach to model transport of fluids in shale gas reservoirs. In Unconventional Resources Technology Conference (In SPE, AAPG and SEG), Denver. doi:10.1190/urtec2013-127 (2013)
Song, H., Yu, M., Zhu, W., Wu, P., Lou, Y., Wang, Y., Killough, J.: Numerical investigation of gas flow rate in shale gas reservoirs with nanoporous media. Int. J. Heat Mass Transf. 80, 626–635 (2015)
Veltzke, T., Thöming, J.: An analytically predictive model for moderately rarefied gas flow. J. Fluid Mech. 698, 406–422 (2012)
Wang, H.T.: Performance of multiple fractured horizontal wells in shale gas reservoirs with consideration of multiple mechanisms. J. Hydrol. 510, 299–312 (2014)
Wang, J.G., Kabir, A., Liu, J., Chen, Z.: Effects of non-Darcy flow on the performance of coal seam gas wells. Int. J. Coal Geol. 93, 62–74 (2012)
Wang, J.G., Peng, Y.: Numerical modeling for the combined effects of two-phase flow, deformation, gas diffusion and \({\rm CO}_{2}\) sorption on caprock sealing efficiency. J. Geochem. Explor. 144, 154–167 (2014)
Wang, J.G., Ju, Y., Gao, F., Peng, Y., Gao, Y.: Effect of \({\rm CO}_{2}\) anisotropic sorption and swelling on caprock sealing efficiency. J. Clean. Prod. 103, 685–695 (2015)
Warren, J., Root, P.: The behavior of naturally fractured reservoirs. Soc. Petrol. Eng. J. 3(3), 245–255 (1963)
Wu, K., Li, X., Wang, C., Yu, W., Guo, C., Ji, D., Ren, G., Chen, Z.: Apparent permeability for gas flow in shale reservoirs coupling effects of gas diffusion and desorption. SPE-2014-1921039-MS, presented at the SPE/AAPG/SEG Unconventional Resources Technology Conference, 25–27 August 2014, Denver, Colorado, USA (2014)
Xiong, X., Devegowda, D., Michel, G., Sigal, R., Civan, F.: A fully-coupled free and adsorptive phase transport model for shale gas reservoirs including non-Darcy flow effects. SPE 159758, presented at the SPE Annual Technical Conference and Exhibition, San Antonio, Texas, USA, 8–10 October, 2012 (2012)
Ye, Z., Chen, D., Wang, J.G.: Evaluation of the non-Darcy effect in coalbed methane production. Fuel 121, 1–10 (2014)
Yu, W., Sepehmoori, K.: Simulation of gas desorption and geomechanics effects for unconventional gas reservoirs. Fuel 116, 455–464 (2014)
Zhang, H.B., Liu, J., Elsworth, D.: How sorption-induced matrix deformation affects gas flow in coal seam: a new FE model. Int. J. Rock Mech. Min. Sci. 4(8), 1226–1833 (2008)
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The authors are grateful to the financial support from Creative Research and Development Group Program of Jiangsu Province (2014), National Natural Science Fund for Distinguished Young Scholars of China (Grant No. 51125017), and National Natural Science Foundation of China (Grant No. 51374213, 51404250).
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Liu, J., Wang, J.G., Gao, F. et al. Flow Consistency Between Non-Darcy Flow in Fracture Network and Nonlinear Diffusion in Matrix to Gas Production Rate in Fractured Shale Gas Reservoirs. Transp Porous Med 111, 97–121 (2016). https://doi.org/10.1007/s11242-015-0583-9
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DOI: https://doi.org/10.1007/s11242-015-0583-9