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Upscaling Flow Properties

  • Philip Ringrose
  • Mark Bentley
Chapter

Abstract

To upscale flow properties means to estimate large-scale flow behaviour from smaller-scale measurements. Typically, we start with a few measurements of rock samples (lengthscale ~3 cm) and some records of flow rates and pressures in test wells (~100 m). Our challenge is to estimate how the whole reservoir will flow (~1 km).

Flow properties of rocks vary enormously over a wide range of length-scales, and estimating upscaled flow properties can be quite a challenge. Unfortunately, many reservoir modellers choose to overlook this problem and blindly hope that a few measurements will correctly represent the whole reservoir. The aim of this chapter is to help make intelligent estimates of large-scale flow properties. In the words of Albert Einstein:

Two things are infinite: the universe and human stupidity; and I’m not sure about the universe.

Keywords

Capillary Pressure Relative Permeability Representative Elementary Volume Flow Property Reservoir Model 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

References

  1. Abbaszadeh M, Fujii H, Fujimoto F (1996) Permeability prediction by hydraulic flow units – theory and applications. SPE Form Eval 11(4):263–271CrossRefGoogle Scholar
  2. Bakke S, Øren P-E (1997) 3-D pore-scale modelling of sandstones and flow simulations in pore networks. SPE J 2:136–149CrossRefGoogle Scholar
  3. Barker JW, Thibeau S (1997) A critical review of the use of pseudo relative permeabilities for upscaling. SPE Reserv Eng 12(5):138–143CrossRefGoogle Scholar
  4. Bear J (1972) Dynamics of fluids in porous media. Elsevier, New YorkGoogle Scholar
  5. Behbahani H, Blunt MJ (2005) Analysis of imbibition in mixed-wet rocks using pore-scale modeling. SPE J 10(4):466–474CrossRefGoogle Scholar
  6. Blunt MJ (1997) Effects of heterogeneity and wetting on relative permeability using pore level modeling. SPE J 2(1):70–87CrossRefGoogle Scholar
  7. Bourbiaux B, Basquet R, Cacas M-C, Daniel J-M, Sarda S (2002) An integrated workflow to account for multi-scale fractures in reservoir simulation models: implementation and benefits. SPE paper 78489 presented at Abu Dhabi international petroleum exhibition and conference, Abu Dhabi, United Arab Emirates, 13–16 OctoberGoogle Scholar
  8. Brandsæter I, Wist HT, Næss A, Li O, Arntzen OJ, Ringrose P, Martinius AW, Lerdahl TR (2001a) Ranking of stochastic realizations of complex tidal reservoirs using streamline simulation criteria. Pet Geosci 7:53–63CrossRefGoogle Scholar
  9. Brandsæter I, Ringrose PS, Townsend CT Omdal S (2001b) Integrated modelling of geological heterogeneity and fluid displacement: Smørbukk gas-condensate field, Offshore Mid-Norway. SPE paper 66391 presented at the SPE reservoir simulation symposium, Houston, TX, 11–14 Feb 2001Google Scholar
  10. Brandsæter I, McIlroy D, Lia O, Ringrose PS (2005) Reservoir modelling of the Lajas outcrop (Argentina) to constrain tidal reservoirs of the Haltenbanken (Norway). Pet Geosci 11:37–46CrossRefGoogle Scholar
  11. Bryant S, Blunt MJ (1992) Prediction of relative permeability in simple porous media. Phys Rev A 46:2004–2011CrossRefGoogle Scholar
  12. Bryant S, King PR, Mellor DW (1993) Network model evaluation of permeability and spatial correlation in a real random sphere packing. Transp Porous Media 11:53–70CrossRefGoogle Scholar
  13. Campbell CV (1967) Lamina, laminaset, bed, bedset. Sedimentology 8:7–26CrossRefGoogle Scholar
  14. Chierici GL (1994) Principles of petroleum reservoir engineering, vol 1 & 2. Springer, BerlinCrossRefGoogle Scholar
  15. Coats KH, Dempsey JR, Henderson JH (1971) The use of vertical equilibrium in two-dimensional simulation of three-dimensional reservoir performance. Soc Petrol Eng J 11(01):63–71CrossRefGoogle Scholar
  16. Corbett PWM, Jensen JL (1992) Estimating the mean permeability: how many measurements do you need? First Break 10:89–94CrossRefGoogle Scholar
  17. Corbett PWM, Ringrose PS, Jensen JL, Sorbie KS (1992) Laminated clastic reservoirs: the interplay of capillary pressure and sedimentary architecture. SPE paper 24699, presented at the SPE annual technical conference, Washington, DCGoogle Scholar
  18. Dake LP (2001) The practice of reservoir engineering (Rev edn). Elsevier, AmsterdamGoogle Scholar
  19. Davis JC (2003) Statistics and data analysis in geology, 3rd edn. Wiley, New York, 638 pagesGoogle Scholar
  20. Dengen Z, Fayers FJ, Orr FM Jr (1997) Scaling of multiphase flow in simple heterogeneous porous media. SPE Reserv Eng 12(3):173–178Google Scholar
  21. Doyen PM (2007) Seismic reservoir characterisation. EAGE Publications, HoutenGoogle Scholar
  22. Durlofsky LJ, Milliken WJ, Bernath A (2000) Scaleup in the near-well region. SPE J 5(1):110–117CrossRefGoogle Scholar
  23. Ekran S, Aasen JO (2000) Steady-state upscaling. Transp Porous Media 41(3):245–262CrossRefGoogle Scholar
  24. England WA, Townsend C (1998) The effects of faulting on production form a shallow marine reservoir – a study of the relative importance of fault parameters. Soc Petrol Eng. doi: 10.2118/49023-MS
  25. Haldorsen HH (1986) Simulator parameter assignment and the problem of scale in reservoir engineering. In: Lake LW, Caroll HB (eds) Reservoir characterization. Academic, Orlando, pp 293–340CrossRefGoogle Scholar
  26. Haldorsen HH, Lake LW (1984) A new approach to shale management in field-scale models. Soc Petrol Eng J 24:447–457CrossRefGoogle Scholar
  27. Huang Y, Ringrose PS, Sorbie KS (1995) Capillary trapping mechanisms in water-wet laminated rock. SPE Reserv Eng 10:287–292CrossRefGoogle Scholar
  28. Huang Y, Ringrose PS, Sorbie KS, Larter SR (1996) The effects of heterogeneity and wettability on oil recovery from laminated sedimentary. SPE J 1(4):451–461CrossRefGoogle Scholar
  29. Isaaks EH, Srivastava RM (1989) Introduction to applied geostatistics. Oxford University Press, New YorkGoogle Scholar
  30. Jackson MD, Muggeridge AH, Yoshida S, Johnson HD (2003) Upscaling permeability measurements within complex heterolithic tidal sandstones. Math Geol 35(5):499–519CrossRefGoogle Scholar
  31. Jacobsen T, Agustsson H, Alvestad J, Digranes P, Kaas I, Opdal S-T (2000) Modelling and identification of remaining reserves in the Gullfaks field. Paper SPE 65412 presented at the SPE European petroleum conference, Paris, France, 24–25 OctoberGoogle Scholar
  32. Jensen JL, Lake LW, Corbett PWM, Goggin DJ (2000) Statistics for petroleum engineers and geoscientists, 2nd edn. Elsevier, AmsterdamGoogle Scholar
  33. Jones A, Doyle J, Jacobsen T, Kjønsvik D (1993) Which sub-seismic heterogeneities influence waterflood performance? A case study of a low net-to-gross fluvial reservoir. In: De Haan HJ (ed) New developments in improved oil recovery, vol 84, Geological Society special publication. Geological Society, London, pp 5–18Google Scholar
  34. King MJ, Mansfield M (1999) Flow simulation of geologic models. SPE Reserv Eval Eng 2(4):351–367CrossRefGoogle Scholar
  35. Kjønsvik D, Doyle J, Jacobsen T, Jones A (1994) The effect of sedimentary heterogeneities on production from a shallow marine reservoir – what really matters?. SPE paper 28445 presented at the European petroleum conference, London, 25–27 Oct 1994Google Scholar
  36. Kløv T, Øren P-E, Stensen JÅ, Lerdahl TR, Berge LI, Bakke S, Boassen T, Virnovsky G (2003) SPE paper 84549 presented at the SPE annual technical conference and exhibition, Denver, CO, USA, 5–8 OctoberGoogle Scholar
  37. Kyte JR, Berry DW (1975) New pseudofunctions to control numerical dispersion. SPE J 15:276–296Google Scholar
  38. Lescoffit G, Townsend C (2005) Quantifying the impact of fault modeling parameters on production forecasting for clastic reservoirs. In: Evaluating fault and cap rock seals, vol 2, AAPG special volume Hedberg series. AAPG, Tulsa, pp 137–149Google Scholar
  39. Li D, Lake LW (1995) Scaling fluid flow through heterogeneous permeable media. SPE Adv Technol Ser 3(1):188–197CrossRefGoogle Scholar
  40. Li D, Cullick AS, Lake LW (1996) Scaleup of reservoir-model relative permeability with a global method. SPE Reserv Eng 11(3):149–157CrossRefGoogle Scholar
  41. Mallet JL (2008) Numerical earth models. European Association of Geoscientists and Engineers, Houten, p 147Google Scholar
  42. Manzocchi T, Heath AE, Walsh JJ, Childs C (2002) The representation of two-phase fault-rock properties in flow simulation models. Pet Geosci 8:119–132CrossRefGoogle Scholar
  43. McDougall SR, Sorbie KS (1995) The impact of wettability on waterflooding: pore-scale simulation. SPE Reserv Eng 10(3):208–213CrossRefGoogle Scholar
  44. Miall AD (1985) Architectural-element analysis: a new method of facies analysis applied to fluivial deposits. Earth-Sci Rev 22:261–308CrossRefGoogle Scholar
  45. Neasham JW (1977) The morphology of dispersed clay in sandstone reservoirs and its effect on sandstone shaliness, pore space and fluid flow properties. SPE paper 6858 presented at the SPE annual technical conference and exhibition, Denver, CO, 9–12 Oct 1977Google Scholar
  46. Nordahl K, Ringrose PS (2008) Identifying the representative elementary volume for permeability in heterolithic deposits using numerical rock models. Math Geosci 40(7):753–771CrossRefGoogle Scholar
  47. Nordahl K, Ringrose PS, Wen R (2005) Petrophysical characterisation of a heterolithic tidal reservoir interval using a process-based modelling tool. Pet Geosci 11:17–28CrossRefGoogle Scholar
  48. Øren P-E, Bakke S (2003) Process-based reconstruction of sandstones and prediction of transport properties. Transp Porous Media 12(48):1–32Google Scholar
  49. Pickup GE, Stephen KS (2000) An assessment of steady-state scale-up for small-scale geological models. Pet Geosci 6:203–210CrossRefGoogle Scholar
  50. Pickup GE, Ringrose PS, Sharif A (2000) Steady-state upscaling: from lamina-scale to full-field model. SPE J 5:208–217CrossRefGoogle Scholar
  51. Pickup GE, Stephen KD, Zhang M, Ma J, Clark JD (2005) Multi-stage upscaling: selection of suitable methods. Transp Porous Media 58:119–216CrossRefGoogle Scholar
  52. Rapoport LA (1955) Scaling laws for use in design and operation of water-oil flow models. Am Inst Min Metallur Petrol Eng Trans 204:143–150Google Scholar
  53. Renard P, de Marsily G (1997) Calculating equivalent permeability: a review. Adv Water Resour 20:253–278CrossRefGoogle Scholar
  54. Ringrose PS (1994) Structural and lithological controls on coastline profiles in Fife, Eastern Britain. Terra Nova 6:251–254CrossRefGoogle Scholar
  55. Ringrose PS, Corbett PWM (1994) Controls on two-phase fluid flow in heterogeneous sandstones. In: Parnell J (ed) Geofluids: origin, migration and evolution of fluids in sedimentary basins, vol 78, Geological Society special publication. Geological Society, London, pp 141–150Google Scholar
  56. Ringrose PS, Sorbie KS, Corbett PWM, Jensen JL (1993) Immiscible flow behaviour in laminated and cross-bedded sandstones. J Petrol Sci Eng 9:103–124CrossRefGoogle Scholar
  57. Ringrose PS, Jensen JL, Sorbie KS (1996) Use of geology in the interpretation of core-scale relative permeability data. SPE Form Eval 11(03):171–176CrossRefGoogle Scholar
  58. Ringrose PS, Skjetne E, Elfeinbein C (2003) Permeability estimation functions based on forward modeling of sedimentary heterogeneity. SPE 84275, Presented at the SPE annual conference, Denver, USA, 5–8 Oct 2003Google Scholar
  59. Ringrose PS, Martinius AW, Alvestad J (2008) Multiscale geological reservoir modelling in practice. In: Robinson A et al (eds) The future of geological modelling in hydrocarbon development, vol 309, Geological Society special publications. Geological Society, London, pp 123–134Google Scholar
  60. Rubin DM (1987) Cross-bedding, bedforms and palaeocurrents, vol 1, Concepts in sedimentology and palaeontology. Society of Economic Paleontologists and Mineralogists Special Publication, TulsaCrossRefGoogle Scholar
  61. Rustad AB, Theting TG, Held RJ (2008) Pore-scale estimation, upscaling and uncertainty modelling for multiphase properties. SPE paper 113005, presented at the 2008 SPE/DOE improved oil recovery symposium, Tulsa, OK, UK, 19–23 Apr 2008Google Scholar
  62. Scheiling MH, Thompson RD, Siefert D (2002) Multiscale reservoir description models for performance prediction in the Kuparuk River Field, North Slope of Alaska. SPE paper 76753 presented at the SPE Western Regional/AAPG Pacific Section Joint Meeting, Anchorage, Alaska, 20–22 MayGoogle Scholar
  63. Size WB (ed) (1987) Use and abuse of statistical methods in the earth sciences, IAMG studies in mathematical geology, no. 1. Oxford University Press, OxfordGoogle Scholar
  64. Smith EH (1991) The influence of small-scale heterogeneity on average relative permeability. In: Lake LW et al (eds) Reservoir characterisation II. Academic Press, San DiegoGoogle Scholar
  65. Stone HL (1991) Rigorous black oil pseudo functions. SPE paper 21207, presented at the SPE symposium on reservoir simulation, Anaheim, CA, 17–20 Feb 1991Google Scholar
  66. Tchelepi HA, Jenny P, Lee C, Wolfsteiner C (2005) An adaptive multiscale finite volume simulator for heterogeneous reservoirs. SPE paper 93395 presented at the SPE reservoir simulation symposium, The Woodlands, Texas, 31 January–2 FebruaryGoogle Scholar
  67. Theting TG, Rustad AB, Lerdahl TR, Stensen JÅ, Boassen T, Øren P-E, Bakke S, Ringrose P (2005) Pore-to-field multi-phase upscaling for a depressurization process. Presented at the 13th European symposium on improved oil recovery, Budapest, Hungary, 25–27 Apr 2005Google Scholar
  68. Todd MR, Longstaff WJ (1972) The development, testing, and application of a numerical simulator for predicting miscible flood performance. J Petrol Technol 1972:874–882CrossRefGoogle Scholar
  69. Towler BF (2002) Fundamental principles of reservoir engineering, vol 8, SPE textbook series. Henry L. Doherty Memorial Fund of AIME, Society of Petroleum Engineers, RichardsonGoogle Scholar
  70. Turcotte DL (1992) Fractals and chaos in geology and geophysics. Cambridge University Press, CambridgeGoogle Scholar
  71. Walsh J, Watterson J, Yielding G (1991) The importance of small-scale faulting in regional extension. Nature 351:391–393CrossRefGoogle Scholar
  72. Weber KJ (1986) How heterogeneity affects oil recovery. In: Lake LW, Carroll HB (eds) Reservoir characterisation. Academic, Orlando, pp 487–544CrossRefGoogle Scholar
  73. Weber KJ, van Geuns LC (1990) Framework for constructing clastic reservoir simulation models. J Pet Technol 42:1248–1297CrossRefGoogle Scholar
  74. Wen R, Martinius AW, Næss A, Ringrose PS (1998) Three-dimensional simulation of small-scale heterogeneity in tidal deposits – a process-based stochastic method. In: Buccianti A et al (eds) Proceedings of the 4th annual conference of the international association of mathematical geology, Naples, pp 129–134Google Scholar
  75. Yielding G, Walsh J, Watterson J (1992) The prediction of small-scale faulting in reservoirs. First Break 10(12):449–460Google Scholar

Copyright information

© Springer Science+Business Media B.V. 2015

Authors and Affiliations

  • Philip Ringrose
    • 1
  • Mark Bentley
    • 2
  1. 1.Statoil ASA & NTNUTrondheimNorway
  2. 2.TRACS International Consultancy Ltd.AberdeenUK

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