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Water Injection into a Low-Permeability Rock - 1 Hydrofracture Growth

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Abstract

In this paper, we model water injection through a growing vertical hydrofracture penetrating a low-permeability reservoir. The results are useful in oilfield waterflood applications and in liquid waste disposal through reinjection. Using Duhamel's principle, we extend the Gordeyev and Entov (1997) self-similar 2D solution of pressure diffusion from a growing fracture to the case of variable injection pressure. The flow of water injected into a low-permeability rock is almost perpendicular to the fracture for a time sufficiently long to be of practical interest. We revisit Carter's model of 1D fluid injection (Howard and Fast, 1957) and extend it to the case of variable injection pressure. We express the cumulative injection through the injection pressure and effective fracture area. Maintaining fluid injection above a reasonable minimal value leads inevitably to fracture growth regardless of the injector design and the injection policy. The average rate of fracture growth can be predicted from early injection. A smart injection controller that can prevent rapid fracture growth is needed.

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References

  • Barenblatt, G. I.: 1959a, Concerning equilibrium cracks forming during brittle fracture. The stability of isolated cracks. Relationships with energetic theories, J. Appl. Math. Mech. 23(5), 1273-1282.

    Google Scholar 

  • Barenblatt, G. I.: 1959b, Equilibrium cracks formed during brittle fracture. rectilinear cracks in plane plates. J. Appl. Math. Mech. 23(4), 1009-1029.

    Google Scholar 

  • Barenblatt, G. I.: 1959c, The Formation of equilibrium cracks during brittle fracture. General ideas and hypotheses. Axially-symmetric cracks, J. Appl. Math. Mech. 23(3), 622-636.

    Google Scholar 

  • Barenblatt, G. I.: 1961, On the finiteness of stresses at the leading edge of an arbitrary crack, J. Appl. Math. Mech. 25(4), 1112-1115.

    Google Scholar 

  • Biot, M. A.: 1956, Theory of deformation of a porous viscoplastic anisotropic solid, J. Appl. Phys. 27, 459-467.

    Google Scholar 

  • Biot, M. A.: 1972, Mechanics of finite deformation of porous solids, Indiana Uni. Math. J. 21, 597-620.

    Google Scholar 

  • Carslaw, J. C. and Jaeger, J. C.: 1959, Conduction of Heat in Solids, 2nd edn, Clarendon Press, Oxford.

    Google Scholar 

  • De, A. and Patzek, T.W.: 1999, Waterflood Analyzer, MatLab Software Package, Version, Lawrence Berkley National Lab, Berkeley, CA.

    Google Scholar 

  • Gordeyev, Y. N. and Entov, V. M.: 1997, The pressure distribution around a growing crack, J. Appl. Maths. Mechs. 51(6), 1025-1029.

    Google Scholar 

  • Gordeyev, Y. N. and Zazovsky, A. F.: 1992, Self-similar solution for deep-penetrating hydraulic fracture propagation, Transport in Porous Media 7, 283-304.

    Google Scholar 

  • Hagoort, J., Weatherill, B. D. and Settari, A.: 1980, Modeling the propagation of waterflood-induced hydraulic fractures, SPEJ 8, 293-303.

    Google Scholar 

  • Howard, G. C. and Fast, C. R.: 1957, Optimum fluid characteristics for fracture extension, Drill. Prod. Prac. API 261-270.

  • Ilderton, D., Patzek, T. E. et al.: 1996, Microseismic imaging of hydrofractures in the diatomite, SPE Form. Eval. 3, 46-54.

    Google Scholar 

  • Koning, E. J. L.: 1985, Fractured water injection wells — analytical modeling of fracture propagation, SPE 14684, 1-27.

    Google Scholar 

  • Kovscek, A. R., Johnston, R. M. and Patzek, T.W.: 1996a, Interpretation of hydrofracture geometry—During steam injection using temperature transients, I. Asymmetric hydrofractures, In Situ 20(3), 251-289.

    Google Scholar 

  • Kovscek, A. R., Johnston, R. M. and Patzek, T. W.: 1996b, Interpretation of hydrofracture geometry during steam injection using temperature transients, II. Asymmetric hydrofractures, In Situ 20(3), 289-309.

    Google Scholar 

  • Kuo, M. C. T., Hanson, H. G. and DesBrisay, C. L.: 1984, Prediction of fracture extension during waterflood, Paper SPE 12769, (Long Beach, (SPE)), 377-385.

    Google Scholar 

  • Muskat, M.: 1946, The Flow of Homogeneous Fluids through Porous Media, J. W. Edwards, Ann Arbor, MI.

    Google Scholar 

  • Ovens, J. E. V., Larsen, F. P. and Cowie, D. R.: 1998, Making sense of water injection fractures in the Dan field, SPE Reser. Eval. Engng 1(6), 556-566.

    Google Scholar 

  • Patzek, T.W.: 1992, Surveillance of South Belridge Diatomite, SPE Western Regional Meeting Paper SPE 24040, SPE, Bakersfield.

    Google Scholar 

  • Patzek, T. W.: 2000, Verification of a complete pore network model of drainage and imbibition, Twelfth SPE/DOE Symposium on Improved Oil Recovery, SPE Paper 59312, Tulsa, SPE, OK; SPEJ, July 2001.

    Google Scholar 

  • Patzek, T. W. and Silin, D. B.: 1998, Fluid injection into a low-permeability rock — 1. Hydrofrature growth, SPE/DOE Eleventh Symposium on Improved Oil Recovery, SPE, Tulsa, Oklahoma.

    Google Scholar 

  • Rapoport, L. A. and Leas, W. J.: 1953, Properties of linear waterfloods, Trans. AIME 216, 139-148.

    Google Scholar 

  • Tikhonov, A. N. and Samarskii, A. A.: 1963, Equations of Mathematical Physics. International Series of Monographs in Pure and Applied Mathematics, Vol 39, Macmillan, New York.

    Google Scholar 

  • Valko, P. and Economides, M. J.: 1995, Hydraulic Fracture Mechanics, Wiley, New York.

    Google Scholar 

  • Vinegar, H. J. et al.: 1995, Active and passive seismic imaging of a hydraulic fracture in the diatomite, J. Petrol. Tech., 44, 28.

    Google Scholar 

  • Warpinski, N. R.: 1996, Hydraulic fracture diagnostics, J. Petrol. Tech. 10.

  • Wright, C. A. and Conant, R. A.: 1995, Hydraulic fracture reorientation in primary and secondary recovery from low-permeability reservoirs, SPE Annual Technical Conference & Exhibition, SPE 30484, Dallas, TX.

  • Wright, C. A., Davis, E. J. et al.: 1997, Horizontal hydraulic fractures: Oddball occurrances or practical engineering concern? SPE Western Regional Meeting, SPE 38324, Long Beach, CA.

  • Zheltov, Y. P. and Khristianovich, S. A.: 1955, On hydraulic fracturing of an oil-bearing stratum, Izv. Akad. Nauk SSSR. Otdel Tekhn. Nuk 5, 3-41.

    Google Scholar 

  • Zwahlen, E. D. and Patzek, T.W.: 1997a, Linear transient flow solution for primary oil recovery with infill and conversion to water injection, In Situ 21(4), 297-331.

    Google Scholar 

  • Zwahlen, E. D. and Patzek, T.W.: 1997b, Linear transient flow solution for primary oil recovery with infill and conversion to water injection, 1997 SPE Western Regional Meeting, SPE 38280, SPE, Long Beach.

    Google Scholar 

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Patzek, T.W., Silin, D.B. Water Injection into a Low-Permeability Rock - 1 Hydrofracture Growth. Transport in Porous Media 43, 537–555 (2001). https://doi.org/10.1023/A:1010689016442

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