Advertisement

Stochastic inverse modeling and global sensitivity analysis to assist interpretation of drilling mud losses in fractured formations

  • A. RussianEmail author
  • M. Riva
  • E. R. Russo
  • M. A. Chiaramonte
  • A. Guadagnini
Original Paper
  • 77 Downloads

Abstract

This study is keyed to enhancing our ability to characterize naturally fractured reservoirs through quantification of uncertainties associated with fracture permeability estimation. These uncertainties underpin the accurate design of well drilling completion in heterogeneous fractured systems. We rely on monitored temporal evolution of drilling mud losses to propose a non-invasive and quite inexpensive method to provide estimates of fracture aperture and fracture mud invasion together with the associated uncertainty. Drilling mud is modeled as a yield power law fluid, open fractures being treated as horizontal planes intersecting perpendicularly the wellbore. Quantities such as drilling fluid rheological properties, flow rates, pore and dynamic drilling fluid pressure, or wellbore geometry, are often measured and available for modeling purposes. Due to uncertainty associated with measurement accuracy and the marked space–time variability of the investigated phenomena, we ground our study within a stochastic framework. We discuss (a) advantages and drawbacks of diverse stochastic calibration strategies and (b) the way the posterior probability densities (conditional on data) of model parameters are affected by the choice of the inverse modeling approach employed. We propose to assist stochastic model calibration through results of a moment-based global sensitivity analysis (GSA). The latter enables us to investigate the way parameter uncertainty influences key statistical moments of model outputs and can contribute to alleviate computational costs. Our results suggest that combining moment-based GSA with stochastic model calibration can lead to significant improvements of fractured reservoir characterization and uncertainty quantification.

Keywords

Stochastic calibration Drilling mud losses Parameter uncertainty Global sensitivity analysis Fractured formations 

Notes

Acknowledgements

The Authors acknowledge funding from Geolog Srl (Project: Feedback between mud losses and fractures during along wellbores in fractured formations).

Compliance with ethical standards

Conflict of interest

The authors declare no conflict of interest in preparing this article.

References

  1. Al-Adwani T, Singh S, Khan B, Dashti J, Ferroni G, Martocchia A (2012) Real time advanced surface flow analysis for detection of open fractures. In: EAGE annual conference & exhibition incorporating SPE Europec.  https://doi.org/10.2118/154927-MS
  2. Alcolea A, Carrera J, Medina A (2006) Pilot points method incorporating prior information for solving the groundwater flow inverse problem. Adv Water Resour 29:1678–1689.  https://doi.org/10.1016/j.advwatres.2005.12.009 CrossRefGoogle Scholar
  3. ANSYS Inc. (2009) ANSYS® FLUENT® User’s guide, Rel. 12.1Google Scholar
  4. Campolongo F, Cariboni J, Saltelli A (2007) An effective screening design for sensitivity analysis of large models. Environ Model Softw 22:1509–1518.  https://doi.org/10.1016/j.envsoft.2006.10.004 CrossRefGoogle Scholar
  5. Carrera J, Neuman SP (1986) Estimation of aquifer parameters under transient and steady state conditions: 2. Uniqueness, stability, and solution algorithms. Water Resour Res 22(2):211–227.  https://doi.org/10.1029/WR022i002p00211 CrossRefGoogle Scholar
  6. Carrera J, Alcolea A, Medina A, Hidalgo J, Slooten LJ (2005) Inverse problem in hydrogeology. Hydrogeol J 13(1):206–222.  https://doi.org/10.1007/s10040-004-0404-7 CrossRefGoogle Scholar
  7. Chen M, Izady A, Abdalla OA, Amerjeed M (2018) A surrogate-based sensitivity quantification and Bayesian inversion of a regional groundwater flow model. J Hydrol 557:826–837.  https://doi.org/10.1016/j.jhydrol.2017.12.071 CrossRefGoogle Scholar
  8. Dell’Oca A, Riva M, Guadagnini A (2017) Moment-based metrics for global sensitivity analysis of hydrological systems. Hydrol Earth Syst Sci 21:1–16.  https://doi.org/10.5194/hess-21-6219-2017 CrossRefGoogle Scholar
  9. API Draft (2009) Rheology and hydraulics of oil-well draft. In API recommended practice 13D Draft, p 16Google Scholar
  10. Faysal A, Shahriar M, Sheikh ZI (2019) Computational fluid dynamics study of yield power law drilling fluid flow through smooth-walled fractures. J Pet Explor Prod Technol.  https://doi.org/10.1007/s13202-019-0646-5 CrossRefGoogle Scholar
  11. Galvis Barros NE (2018) Geomechanics, fluid dynamics and well testing, applied to naturally fractured carbonate reservoirs, extreme naturally fractured reservoirs. Springer theses. Springer, New York.  https://doi.org/10.1007/978-3-319-77501-2 CrossRefGoogle Scholar
  12. Keller JB (1976) Inverse problems. Am Math Mon 83:107–118CrossRefGoogle Scholar
  13. Kennedy J, Eberhart R (1995) Particle swarm optimization. In: Proceedings of the IEEE international conference on neural networks, vol 4, pp 1942–1948. http://dx.doi.org/10.1109/ICNN.1995.488968
  14. Kullback S (1959) Information theory and statistics. Wiley, New YorkGoogle Scholar
  15. Lagarias JC, Reeds JA, Wright MH, Wright PE (1998) Convergence properties of the Nelder–Mead simplex method in low dimensions. SIAM J Optim 9(1):112–147.  https://doi.org/10.1137/S1052623496303470 CrossRefGoogle Scholar
  16. Laloy E, Rogiers B, Vrugt JA, Mallants D, Jacques D (2013) Efficient posterior exploration of a high-dimensional groundwater model from two-stage Markov chain Monte Carlo simulation and polynomial chaos expansion. Water Resour Res 49:2664–2682.  https://doi.org/10.1002/wrcr.20226 CrossRefGoogle Scholar
  17. Lavrov A (2014) Radial flow of non-Newtonian power-law fluid in a rough-walled fracture: effect of fluid rheology. Transp Porous Med 105(3):559–570.  https://doi.org/10.1007/s11242-014-0384-6 CrossRefGoogle Scholar
  18. Majidi R, Miska SZ (2011) Fingerprint of mud losses into natural or induced fractures. SPE 143854 SPE European formation damage conference held in Noordwijk, The Netherlands, 7–10 June 2011Google Scholar
  19. Majidi R, Miska SZ, Ahmed R, Yu M, Thompson LG (2010) Radial flow of yield-power-law fluids: numerical analysis, experimental study and the application for drilling fluid losses in fractured formations. J Pet Sci Eng 70(3):334–343.  https://doi.org/10.1016/j.petrol.2009.12.005 CrossRefGoogle Scholar
  20. Mara TA, Fajraoui N, Guadagnini A, Younes A (2017) Dimensionality reduction for efficient Bayesian estimation of groundwater flow in strongly heterogeneous aquifers. Stoch Environ Res Risk Assess 31:2313–2326.  https://doi.org/10.1007/s00477-016-1344-1 CrossRefGoogle Scholar
  21. Medina A, Carrera J (1996) Coupled estimation of flow and solute transport parameters. Water Resour Res 32(10):3063–3076.  https://doi.org/10.1029/96wr00754 CrossRefGoogle Scholar
  22. Mitsoulis E, Abdali SS (1993) Flow Simulation of Herschel–Bulkley fluids through extrusion dies. Can J Chem Eng 71:147–160.  https://doi.org/10.1002/cjce.5450710120 CrossRefGoogle Scholar
  23. Neuman SP (1973) Calibration of groundwater flow models viewed as a multiple-objective decision process under uncertainty. Water Resour Res 9(4):1006–1021.  https://doi.org/10.1029/WR009i004p01006 CrossRefGoogle Scholar
  24. Pianosi F, Beven K, Freer J, Hall JW, Rougier J, Stephenson DB, Wagener T (2016) Sensitivity analysis of environmental models: a systematic review with practical workflow. Environ Model Softw 79:214–232.  https://doi.org/10.1016/j.envsoft.2016.02.008 CrossRefGoogle Scholar
  25. Rahmat-Samii Y, Michielsen E (1999) Electromagnetic optimization by genetic algorithms. Wiley, New YorkGoogle Scholar
  26. Ratto M, Tarantola S, Saltelli A (2001) Sensitivity analysis in model calibration: GSA-GLUE approach. Comput Phys Commun 136:212–224.  https://doi.org/10.1016/S0010-4655(01)00159-X CrossRefGoogle Scholar
  27. Razavi S, Gupta HV (2015) What do we mean by sensitivity analysis? The need for comprehensive characterization of ‘‘global’’ sensitivity in Earth and Environmental systems models. Water Resour Res 51:3070–3092.  https://doi.org/10.1002/2014WR016527 CrossRefGoogle Scholar
  28. Razavi O, Lee HP, Olson JE, Schultz RA (2017) Drilling mud loss in naturally fractured reservoirs: theoretical modelling and field data analysis. SPE-187265-MS.  https://doi.org/10.2118/187265-MS
  29. Rehm B, Haghshenas A, Paknejad AS, Al-Yami A, Hughes J, Shubert J (2012) Underbalanced drilling: Limits and extremes. Gulf Publishing Company, HoustonGoogle Scholar
  30. Robinson J, Rahmat-Samii Y (2004) particle swarm optimization in electromagnetics. IEEE Trans Antennas Propag 52(2):397–407.  https://doi.org/10.1109/TAP.2004.823969 CrossRefGoogle Scholar
  31. Roehl P, Choquette P (1985) Carbonate petroleum reservoir. Springer, New YorkCrossRefGoogle Scholar
  32. Russo E, Colombo I, Nicolotti I (2018) Uncertainty quantification of fracture characterization in naturally fractured reservoirs. Presented at FRONTUQ18 Pavia, ItalyGoogle Scholar
  33. Saltelli A, Ratto M, Andres T, Campolongo F, Cariboni J, Gatelli D (2008) Global sensitivity analysis: the primer. Wiley, ChichesterGoogle Scholar
  34. Sobol IM (1993) Global sensitivity indices for nonlinear mathematical models and their Monte Carlo estimates. Math Comput Simul 55:271–280.  https://doi.org/10.1016/S0378-4754(00)00270-6 CrossRefGoogle Scholar
  35. Sochala P, Le Maître OP (2013) Polynomial chaos expansion for subsurface flows with uncertain soil parameters. Adv Water Resour 62:139–154.  https://doi.org/10.1016/j.advwatres.2013.10.003 CrossRefGoogle Scholar
  36. Song X, Zhang J, Zhan C, Xuan Y, Ye M, Xu C (2015) Global sensitivity analysis in hydrological modeling: review of concepts, methods, theoretical framework, and applications. J Hydrol 523:739–757.  https://doi.org/10.1016/j.jhydrol.2015.02.013 CrossRefGoogle Scholar
  37. Sudret B, Marelli S, Wiart J (2017) Surrogate models for uncertainty quantification: an overview. In: 11th European conference on antennas and propagation (EUCAP), Paris, pp 793-797.  https://doi.org/10.23919/eucap.2017.7928679
  38. Tang J, Zhuang Q (2009) A global sensitivity analysis and Bayesian inference framework for improving the parameter estimation and prediction of a process-based Terrestrial Ecosystem Model. J Geophys Res 114:D15303.  https://doi.org/10.1029/2009JD011724 CrossRefGoogle Scholar
  39. Van Griensven A, Meixner T, Grunwald S, Bishop T, Diluzio M, Srinivasan R (2006) A global sensitivity analysis tool for the parameters of multi-variable catchment models. J Hydrol 324:10–23.  https://doi.org/10.1016/j.jhydrol.2005.09.008 CrossRefGoogle Scholar
  40. World Energy Outlook (2006) International energy agency. https://www.iea.org/publications/freepublications/publication/weo2006.pdf
  41. Zhou H, Gómez-Hernández JJ, Li L (2014) Inverse methods in hydrogeology: evolution and recent trends. Adv Water Resour 63:22–37.  https://doi.org/10.1016/j.advwatres.2005.12.009 CrossRefGoogle Scholar

Copyright information

© Springer-Verlag GmbH Germany, part of Springer Nature 2019

Authors and Affiliations

  • A. Russian
    • 1
    Email author
  • M. Riva
    • 1
    • 2
  • E. R. Russo
    • 3
  • M. A. Chiaramonte
    • 3
  • A. Guadagnini
    • 1
    • 2
  1. 1.Department of Civil and Environmental EngineeringPolitecnico di MilanoMilanItaly
  2. 2.Department of Hydrology and Atmospheric SciencesUniversity of ArizonaTucsonUSA
  3. 3.Geolog SrlSan Giuliano Milanese, MilanItaly

Personalised recommendations