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The Transient Flow Analysis of Fluid in a Fractal, Double-Porosity Reservoir

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Abstract

The mathematical model for transient fluid flow in porous media is based in general on mass conservation principle. Because of the small compressibility of formation fluid, the quadratic term of pressure gradient is always ignored to linearize the non-linear diffusion equation. This may result in significant errors in model prediction, especially at large time scale. In order to solve this problem, it may be necessary to keep the quadratic term in the non-linear equations. In our study, the quadratic term is reserved to fully describe the transient fluid flow. Based on this rigorous treatment, the mathematical models are established to analyze the transient flow behavior in a double porosity, fractal reservoir with spherical and cylindrical matrix. In addition, Laplace transformation method is employed to solve these mathematical models and the type curves are provided to analyze the pressure transient characteristics. This study indicates that the relative errors in calculated pressure caused by ignoring the quadratic term may amount to 10 % in a fractal reservoir with double porosity, which can’t be neglected in general for fractal reservoirs with double porosity at large time scale.

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References

  • Aprilian S., Abdassah D., Mucharan L. et al.: Application of fractal reservoir model for interference test analysis in Kamojang geothermal field (Indonesia). SPE Form. Eval. 27(4), 7–14 (1993)

    Google Scholar 

  • Barenblatt G., Zheltov I., Kochina I.: Basic concept in the theory of homogeneous liquids in fractured rocks. Int.J. Appl. Math. Mech. 24, 1286–1303 (1960)

    Article  Google Scholar 

  • Beier, R.A.: Pressure transient field date showing fractal reservoir structure. The 1990 International Technical Meeting of the SPE, 10–13 June 1990

  • Bourdet, D., Gringarten, A.: Determination of fissure volume and block size in fractured reservoirs by type-cure analysis. In: This paper was presented at the 55th Annual Fall Technical Conference and Exhibition of the Society of Petroleum Engineers of AIME, held in Dallas, TX, 21–24 September 1980

  • Braeuning S., Jelmert T.A., Vik S.A.: The effect of the quadratic gradient term on variable-rate well-tests. J. Pet. Sci. Eng. 21(2), 203–222 (1998)

    Article  Google Scholar 

  • Chakrabarty C., Farouq S.M., Tortike W.S.: Analytical solutions for radial pressure distribution including the effects of quadratic-gradient term. Water Resour. Res. 29(4), 1171–1177 (1993)

    Article  Google Scholar 

  • Chakrabarty, C., Farouq, S.M., Tortike, W.S.: Transient flow behavior of non-Newtonian power-law fluid in fractal reservoirs. In: Annual Technical Meeting of the Petroleum Society of CIM, Calgery, AB, 9–11 May 1993

  • Chang J., Yortsos Y.C.: Pressure transient analysis of fractal reservoir. SPE Form. Eval. 5(1), 31–38 (1990)

    Google Scholar 

  • Finjord J., Adanoy B.S.: Effects of the quadratic gradient term in steady-state and semi steady-state solutions for reservoir pressure. SPE Form. Eval. 4(3), 413–417 (1989)

    Google Scholar 

  • Ge J., Liu Y., Yao Y.: The Modern Mechanics of Fluid Flow in Oil Reservoir. Petroleum Industry Press, Beijing (2003) (in Chinese)

    Google Scholar 

  • Gonzales, F., Ilk, D., Blasingame, T.: A quadratic cumulative production model for the material balance of an abnormally pressured gas reservoir. In: 2008 SPE Western Regional and Pacific Section AAPG Joint Meeting held in Bakersfield, CA, USA, 31 March–2 April 2008

  • Jelmert, T.: Improved well test modeling of naturally fractured reservoirs, In: 2nd Nordic Symposium on Petrophysics and Reservoir Modeling, Chalmers University of Technology, 25–26 Jan 1996, pp. 7–9. Gothenburg, Sweden (1996)

  • Jelmert T., Vik S.: Analytic solution to the non-linear diffusion equation for fluids of constant compressibility. J. Pet. Sci. Eng. 14(2), 231–233 (1996)

    Article  Google Scholar 

  • Mattews C.S., Russel D.G.: Pressure buildup and flow tests in wells. Soc. Pet. Eng. 27(4), 7–14 (1967)

    Google Scholar 

  • Najurieta H.: A theory for the pressure transient analysis in naturally fractured reservoirs. J. Pet. Tech. 32(7), 1241–1250 (1980)

    Google Scholar 

  • Nie, R., Jia, Y.: The transient well test analysis of fractured-Vuggy triple-porosity reservoir With the quadratic pressure gradient term. In: 2009 SPE Latin American and Caribbean Petroleum Engineering Conference held in Cartagena, Colombia, 31 May–3 June 2009

  • Stehfest H.: Algorithm 368 numerical inversion of Laplace transforms. Int. J. Commun. ACM 13, 47–49 (1970a)

    Article  Google Scholar 

  • Stehfest H.: Remark on algorithm 368 numerical inversion of Laplace transform. Int.J. Commun. ACM 13, 624–625 (1970b)

    Article  Google Scholar 

  • Swaano A.: Analytical solution for determining naturally fractured reservoir properties by well testing. Soc. Pet. Eng. J. 16(3), 117–122 (1976)

    Google Scholar 

  • Tong, D.: The study on the seepage mechanics of fractal reservoir. PhD, China University of Petroleum (in Chinese) (1997)

  • Tong D.: The Fluid Mechanics of Nonlinear Flow in Porous Media, pp. 1–19. Petroleum Industry Press, Beijing (2003) (in Chinese)

    Google Scholar 

  • Tong D., Liu M.: Non-linear flow fractal analysis on reservoir with double-media. J. Univ. Petroleum, China 27(2), 59–62 (2003) (in Chinese)

    Google Scholar 

  • Tong D., Cai L., Chen Q.: Flow analysis of fluid in double porous media including the effects of quadratic-gradient term. Eng. Mech. 19(3), 99–104 (2002) (in Chinese)

    Google Scholar 

  • Tong D., Cao X., Wang R.: Exact solution for nonlinear transient flow model including a quadratic gradient term. Appl. Math. Mech. 25(11), 102–109 (2004)

    Google Scholar 

  • Wang Y., Dusseault M.B.: The Effect of quadratic gradient on the borehole solution in Vic elastic media. Water Resour. Res. 27(12), 3215–3223 (1991)

    Article  Google Scholar 

  • Warren J., Root P.: Behavior of naturally fractured reservoirs. Soc. Pet. Eng. J. 3(3), 245–255 (1963)

    Google Scholar 

  • Xue L., Tong D.: Fluid characteristics of triple-medium double permeability consider quadratic gradient term effects. Chin. Q. Mech. 26(3), 61–65 (2008) (in Chinese)

    Google Scholar 

  • Zhang X., Tong D.: Analysis for pressure transient of coalbed methane reservoir. Well Test. 26(6), 61–67 (2008) (in Chinese)

    Google Scholar 

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Authors and Affiliations

  1. MOE Key Laboratory of Petroleum Engineering, China University of Petroleum, Beijing, 102249, China

    Yuedong Yao

  2. Department of Petroleum Engineering, Colorado School of Mines, Golden, CO, USA

    Yu-Shu Wu & Ronglei Zhang

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  1. Yuedong Yao
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  2. Yu-Shu Wu
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  3. Ronglei Zhang
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Correspondence to Yuedong Yao.

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Yao, Y., Wu, YS. & Zhang, R. The Transient Flow Analysis of Fluid in a Fractal, Double-Porosity Reservoir. Transp Porous Med 94, 175–187 (2012). https://doi.org/10.1007/s11242-012-9995-y

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