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Quantifying Uncertainty in Flow Functions Derived from SCAL Data

USS Relative Permeability and Capillary Pressure

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Abstract

Unsteady-state (USS) core flood experiments provide data for deriving two-phase relative permeability and capillary pressure functions. The experimental data is uncertain due to measurement errors, and the accuracy of the derived flow functions is limited by both data and modeling errors.

History matching provides a reasonable means of deriving in-phase flow functions from uncertain unsteady-state experimental data. This approach is preferred to other analytical procedures, which involve data smoothing and differentiation. Data smoothing leads to loss of information while data differentiation is a mathematically unstable procedure, which could be error magnifying. The problem is non-linear, inverse and ill posed. Hence the history-matching procedure gives a non-unique solution.

This paper presents a procedure for quantifying the uncertainty in two-phase flow functions, using unsteady-state experimental data. We validate the methodology using synthetic data.

We investigate the impact of uncertain flow functions on a homogeneous reservoir model using the Buckley–Leverett theory. Using a synthetic, heterogeneous reservoir model, we estimate the uncertainty in oil recovery efficiency due to uncertainty in the flow functions.

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References

  • S. Akin L.M. Castanier W.E. Brigham (1999) ArticleTitleEffect of temperature on heavy oil/water relative permeabilities Soc. Petrol. Eng. J. 54120 1–11

    Google Scholar 

  • J.S. Archer P.G. Wall (1991) Petroleum Engineering: Principles and Practice Graham & Trotman London

    Google Scholar 

  • J. S. Archer S. W. Wong (1973) ArticleTitleUse of a reservoir simulator to interpret laboratory waterflood data Soc. Petrol. Eng. J. 3551 343–347

    Google Scholar 

  • S.E. Buckley M.C. Leverett (1942) ArticleTitleMechanisms of fluid displacement in sands Trans. Am. Inst. Min. Eng. 146 107–116

    Google Scholar 

  • G. Chavent G. Cohen M. Espy (1980) ArticleTitleDetermination of relative permeabilities and capillary pressures by an automatic adjustment method Soc. Petrol. Eng. 9237 1–10

    Google Scholar 

  • G.L. Chierici (1981) ArticleTitleNovel relations for drainage and imbibition relative permeabilities Soc. Petrol. Eng. 10165 1–10

    Google Scholar 

  • M.A. Christie (1996) ArticleTitleUpscaling for reservoir simulation Soc. Petrol. Eng. 37324 1–5

    Google Scholar 

  • M.A. Christie M.J. Blunt (2001) ArticleTitleTenth SPE Comparative Solution Project: a comparison of upscaling techniques Soc. Petrol. Eng. 66599 1–9

    Google Scholar 

  • F. Civan E.C. Donaldson (1987) ArticleTitleRelative permeability from unsteady-state displacements: an analytical interpretation Soc. Petrol. Eng. 16200 139–155

    Google Scholar 

  • Civan F. and Donaldson E. C. (1989). Relative permeability from unsteady-state displacements with capillary pressure included. SPE Form. Eval. (June) 189–193.

  • E.R. Collins (1976) Flow of Fluids through Porous Materials PennWell Books Tulsa, Oklahoma

    Google Scholar 

  • A.T. Corey (1954) ArticleTitleThe Interrelation between gas and oil permeabilities Producers Monthly 19 38–41

    Google Scholar 

  • Craig, F. F. Jr. (1971). The Reservoir Engineering Aspects of Waterflooding, Society of Petroleum Engineers of AIME, New York.

  • Floris, F. J. T., Bush, M. D., Cuypers, M., Roggero, F. and Syversveen, A. R. (1999). Comparison of production forecast uncertainty quantification methods – an integrated study, in: Proceedings of 1st Conference on Petroleum Geostatistics, Toulouse, France, pp. 1–20.

  • S.C. Gabbanelli A.G. Mezzatesta M.S. Bidner (1982) ArticleTitleOne-dimensional numerical simulation of waterflooding an oil reservoir Lat. Am. J. Heat Mass. Transf. 6 251–273

    Google Scholar 

  • S. Geman D. Geman (1984) ArticleTitleStochastic relaxation, Gibbs distributions and the Bayesian restoration of images IEEE Trans. Pattern Anal. Mach. Int. 6 721–741 Occurrence Handle10.1109/TPAMI.1984.4767596

    Article  Google Scholar 

  • P.E. Gill W. Murray (1981) Practical Optimization Academic Press New York City

    Google Scholar 

  • J. Glimm S. Hou Y.H. Lee D. Sharp K. Ye (2001) ArticleTitlePrediction of oil preduction with confidence intervals Soc. Petrol. Eng. 66350 1–15

    Google Scholar 

  • J. Glimm S. Hou H. Kim D.H. Sharp (2001) ArticleTitleA probability model for errors in the numerical solutions of a partial differential equation Fluid Dyn. J. 9 485–493

    Google Scholar 

  • C.A. Grattoni M.S. Bidner (1990) ArticleTitleHistory matching of unsteady-state corefloods for determining capillary pressure and relative permeabilities Soc. Petrol. Eng. 21135 1–8

    Google Scholar 

  • K.M. Hansen G.S. Cunningham R.J. McKee (1977) ArticleTitleUncertainty assessment for reconstruction based on deformable geometry Int. J. Imag. Syst. Technol. 8 506–512 Occurrence Handle10.1002/(SICI)1098-1098(1997)8:6<506::AID-IMA2>3.0.CO;2-E

    Article  Google Scholar 

  • M. Honarpour L. Koederitz A.H. Harvey (1986) Relative Permeability of Petroleum Reservoirs CRC Press, Inc. Boca Raton, Florida

    Google Scholar 

  • E.F. Johnson D.P. Bossler V.O. Naumann (1959) ArticleTitleCalculation of relative permeability from displacement experiments Trans. Am. Inst. Min. Eng. 216 370–372

    Google Scholar 

  • P.D. Kerig A.T. Watson (1987) ArticleTitleA new algorithm for estimating relative permeabilities from displacement experiments Soc. Petrol. Eng. Reserv. Eval. 2 IssueID1 103–112

    Google Scholar 

  • D.J. MacMillan (1987) ArticleTitleAutomatic history matching of laboratory corefloods to obtain relative-permeability curves Soc. Petrol. Eng. Reserv. Eval. 2 IssueID1 85–91

    Google Scholar 

  • C. M. Marle (1981) Multiphase Flow in Porous Media Gulf Pub. Co. Texas

    Google Scholar 

  • J.S. Osoba J.G. Richardson J.K. Kerver J.A. Hafford P.M. Blair (1951) ArticleTitleLaboratory measurements of relative permeability Trans. Am. Ins. Min. Eng. 192 47–56

    Google Scholar 

  • J.G. Richardson J.K. Kerver J.A. Hafford J.S. Osoba (1952) ArticleTitleLaboratory determination of relative permeability Trans. Am. Inst. Min. Eng. 195 187–196

    Google Scholar 

  • P.C. Richmond A.T. Watson (1990) ArticleTitleEstimation of multiphase flow functions from displacement experiments Soc. Reserv. Eng. 18569 1–7

    Google Scholar 

  • M. Sambridge (1998) ArticleTitleExploring multidimensional landscapes without a map Inverse Probl. 14 427–440 Occurrence Handle10.1088/0266-5611/14/3/005

    Article  Google Scholar 

  • M. Sambridge (1999) ArticleTitleGeophysical inversion with a neighbourhood algorithm – 1. Searching a parameter space Geophys. J. Int. 138 479–494 Occurrence Handle10.1046/j.1365-246X.1999.00876.x

    Article  Google Scholar 

  • M. Sambridge (1999) ArticleTitleGeophysical inversion with a neighbourhood algorithm – II. Appraising the ensemble Geophys. J. Int. 138 727–745 Occurrence Handle10.1046/j.1365-246x.1999.00900.x

    Article  Google Scholar 

  • G.B. Savioli M.S. Bidner (1982) ArticleTitleThe influence of capillary pressure when determining relative permeability from unsteady-state corefloods Soc. Petrol. Eng. 23698 1–10

    Google Scholar 

  • L.L. Schumaker (1981) Spline Functions: Basic Theory John Wiley & Sons New York

    Google Scholar 

  • P.M. Sigmund F.G. McCaffery (1979) ArticleTitleAn improved unsteady-state procedure for determining the relative-permeability characteristics of heterogeneous porous media Soc. Petrol. Eng. J. 6720 1–14

    Google Scholar 

  • D.S. Sivia (1996) Data Analysis – A Bayesian Tutorial Clarendon Press Oxford

    Google Scholar 

  • Subbey S. (2000). Regularizing the Volterra Integral Equation – the Capillary Pressure Case. PhD thesis. University of Bergen, Norway

  • S. Subbey M. Christie M. Sambridge (2002a) ArticleTitleA strategy for rapid quantification of uncertainty in reservoir performance prediction Soc. Petrol. Eng. 79678 1–12

    Google Scholar 

  • S. Subbey M. Christie M. Sambridge (2002b) ArticleTitleUncertainty reduction in reservoir modeling SIAM Contemp. Math. 295 457–467

    Google Scholar 

  • S. Subbey M. Christie M. Sambridge (2004) ArticleTitleThe impact of uncertain centrifuge capillary pressure on reservoir simulation SIAM J. Sci. Comput. 26 IssueID2 537–557 Occurrence Handle10.1137/S1064827503426747

    Article  Google Scholar 

  • Tao T.M. and Watson A.T. (1984). Accuracy of JBN estimates of relative permeability: part 1 – error analysis. SPEJ (April) 209–214.

  • Tao, T. M. and Watson, A. T.: (1984), Accuracy of JBN estimates of relative permeability: part 2 – algorithms. SPEJ (April) 215–223.

  • A. Tarantola (1987) Inverse Problem Theory, Methods for Data Fitting and Model Parameter Estimation Elsevier Science Publishers Amsterdam, The Netherlands

    Google Scholar 

  • A.T. Watson R. Kulkarni J.-E. Nordtvedt A. Sylte H. Urkedal (1998) ArticleTitleEstimation of porous media flow functions Meas. Sci. Technol. 9 898–905 Occurrence Handle10.1088/0957-0233/9/6/006

    Article  Google Scholar 

  • H.J. Welge (1952) ArticleTitleA simplified method for computing oil recovery by gas or water drive Trans. Am. Inst. Min. Eng. 195 91–98

    Google Scholar 

  • Willhite G. P. (1986). Waterflooding, Society of Petroleum Engineers, Richardson, TX.

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Authors and Affiliations

  1. Institute of Marine Research, PB 1870, Nordnes, N-5817, Bergen, Norway

    S. Subbey

  2. Heriot-Watt Institute of Petroleum Engineering, Edinburgh, EH14 4AS, UK

    H. Monfared

  3. National Iranian Oil Company, Hafez Crossing, Taleghani Avenue, Tehran, Iran

    H. Monfared & M. Christie

  4. Research School of Earth Sciences, Institute of Advanced Studies, Australian National University, Canberra, ACT 0200, Australia

    M. Sambridge

Authors
  1. S. Subbey
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  2. H. Monfared
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  3. M. Christie
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  4. M. Sambridge
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Correspondence to S. Subbey.

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Subbey, S., Monfared, H., Christie, M. et al. Quantifying Uncertainty in Flow Functions Derived from SCAL Data. Transp Porous Med 65, 265–286 (2006). https://doi.org/10.1007/s11242-005-5998-2

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  • DOI: https://doi.org/10.1007/s11242-005-5998-2

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