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An analytical model for injectivity tests in multilayered reservoir with formation crossflow

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Abstract

Injectivity tests involve injecting fluid through wells into an oil reservoir to gather information about its parameters. This knowledge can be valuable for improving oil production. As such, several studies on injectivity tests in multilayered reservoirs have been conducted. Typically, these studies focus only on commingled systems, which are layers separated by impermeable barriers. The present work developed an analytical model in the Laplace space for multilayered reservoirs under injectivity tests, considering formation crossflow across all layers. The accuracy of the proposed solution was verified by comparing it with a finite difference flow simulator. The results from the analytical model and numerical data are consistently similar. Additionally, the analytical solution’s data is used to estimate the reservoir’s equivalent permeability, which yields satisfactory accuracy for all tested cases.

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References

  • Barreto, A.B., Peres, A.M., Pires, A.P., et al.: Water injectivity tests on multilayered oil reservoirs (2011)

  • Bela, R.V., Pesco, S., Barreto, A., Jr.: Modeling falloff tests in multilayer reservoirs. J. Petrol. Sci. Eng. 174, 161–168 (2019)

    Article  Google Scholar 

  • Bittencourt Neto, L.F., Vieira Bela, J., esco, S., Barreto, A.: Pressure behavior during injectivity tests: a composite reservoir approach. In: SPE Latin America and Caribbean Petroleum Engineering Conference D021S010R002 (2020). https://doi.org/10.2118/198983-MS

  • Bittencourt Neto, L.F., Vieira Bela, J., Pesco, S., Barreto, A.: Laplace domain pressure behavior solution for multilayered composite reservoirs. In: SPE Latin America and Caribbean Petroleum Engineering Conference D051S042R003 (2020). https://doi.org/10.2118/199018-MS

  • Boughrara, A.A., Peres, A.M., Chen, S., Machado, A.A., Reynolds, A.C.: Approximate analytical solutions for the pressure response at a water-injection well. SPE J. 12(01), 19–34 (2007)

    Article  CAS  Google Scholar 

  • Bratvold, R.B., Horne, R.N.: Analysis of pressure-falloff tests following cold-water injection. SPE Form. Eval. 5(03), 293–302 (1990)

    Article  Google Scholar 

  • Buckley, S.E., Leverett, M., et al.: Mechanism of fluid displacement in sands. Trans. AIME 146(01), 107–116 (1942)

    Article  Google Scholar 

  • CMG.: IMEX User Guide, Computer Modeling Group (2010)

  • Cobb, W.M., Ramey, H., Jr., Miller, F.G., et al.: Well-test analysis for wells producing commingled zones. J. Petrol. Technol. 24(01), 27–37 (1972)

    Article  Google Scholar 

  • Ehlig-Economides, C.A., Joseph, J.: A new test for determination of individual layer properties in a multilayered reservoir. SPE Form. Eval. 2(03), 261–283 (1987)

    Article  Google Scholar 

  • Escobar, F.H., Navia, J.J., Suescún-Diaz, D.: Pressure and pressure derivative interpretation of a well in a completed-perforated multilayer reservoir with crossflow. Dyna 88(219), 94–101 (2021)

    Article  Google Scholar 

  • Kamal, M.: Transient well testing. spe monograph. vol. 23, henry l. doherty series, society of petroleum engineers (2009)

  • Lee, J., Rollins, J.B., Spivey, J.P.: Pressure transient testing (ebook). SPE textbook series, vol. 9 (2003)

  • Lefkovits, H., Hazebroek, P., Allen, E., Matthews, C., et al.: A study of the behavior of bounded reservoirs composed of stratified layers. Soc. Petrol. Eng. J. 1(01), 43–58 (1961)

    Article  Google Scholar 

  • Lu, J., Rahman, M.M., Yang, E., Alhamami, M.T., Zhong, H.: Pressure transient behavior in a multilayer reservoir with formation crossflow. J. Petrol. Sci. Eng. 208, 109376 (2022)

    Article  CAS  Google Scholar 

  • Nie, R.-S., et al.: New modelling of transient well test and rate decline analysis for a horizontal well in a multiple-zone reservoir. J. Geophys. Eng. 8, 464–476 (2011). https://doi.org/10.1088/1742-2132/8/3/007

    Article  Google Scholar 

  • Peres, A., Boughrara, A., Chen, S., Machado, A., Reynolds, A.: Approximate analytical solutions for the pressure response at a water injection well (2004)

  • Peres, A.M., Boughrara, A.A., Reynolds, A.C.: Rate superposition for generating pressure falloff solutions. SPE J. 11(03), 364–374 (2006)

    Article  Google Scholar 

  • Prijambodo, R., Raghavan, R., Reynolds, A., et al.: Well test analysis for wells producing layered reservoirs with crossflow. Soc. Petrol. Eng. J. 25(03), 380–396 (1985)

    Article  Google Scholar 

  • Stehfest, H.: Algorithm 368: numerical inversion of laplace transforms [d5]. Commun. ACM 13(1), 47–49 (1970)

    Article  Google Scholar 

  • Sun, H., Gao, C.: Well Test Analysis for Multilayered Reservoirs with Formation Crossflow, Gulf Professional Publishing (2017)

Download references

Funding

This study was financed in part by the Coordenação de Aperfeiçoamento de Pessoal de Nível Superior-Brasil (CAPES)-Finance Code 001 and by Petrobras, as part of the contract PT-120. 01.14053-SAP4600567308;

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Correspondence to Malú Grave.

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Viana, I.V., Bela, R.V., Grave, M. et al. An analytical model for injectivity tests in multilayered reservoir with formation crossflow. Int J Geomath 15, 6 (2024). https://doi.org/10.1007/s13137-024-00247-y

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