1887

Abstract

Summary

Uncertainty quantification is typically accomplished by simulating multiple geological realizations, which can be very expensive computationally if the flow process is complicated and the models are highly resolved. Upscaling procedures can be applied to reduce computational demands, though it is essential that the resulting coarse-model predictions correspond closely to reference fine-scale solutions. In this work, we develop an ensemble level upscaling (EnLU) procedure for compositional systems, which enables the efficient generation of multiple coarse models for use in uncertainty quantification. This requires us to first develop an accurate global compositional upscaling method for individual realizations. This global upscaling entails transmissibility and relative permeability upscaling, along with the computation of α-factors to capture component fluxes. A procedure for iterating on coarse-scale α-factors is introduced, and this is shown to improve accuracy. In EnLU, global upscaling is applied for only a few selected realizations. For 90% or more of the realizations, upscaled functions are assigned statistically based on quickly-computed flow and permeability attributes. A sequential Gaussian co-simulation procedure is incorporated to provide coarse models that honor the spatial correlation structure of the upscaled properties. The resulting EnLU procedure is applied for multiple realizations of 2D models, for both Gaussian and channelized permeability fields. Results demonstrate that EnLU provides P10, P50 and P90 results for phase and component production rates that are in close agreement with reference fine-scale results. Less accuracy is observed in realization-by-realization comparisons, though the models are still much more accurate than those generated using standard coarsening procedures.

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/content/papers/10.3997/2214-4609.20141860
2014-09-08
2024-04-25
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References

  1. Ballin, R.R. and Clifford, P. J.
    [2002] Cupiagua: modeling of a complex fractured reservoir using compositional upscaling. SPE Reservoir Evaluation & Engineering, 5, 498–.
    [Google Scholar]
  2. Barker, J.W. and Dupouy, P.
    [1999] An analysis of dynamic pseudo-relative permeability methods for oil-water flows. Petroleum Geoscience, 5, 394–.
    [Google Scholar]
  3. Barker, J.W. and Fayers, F.J.
    [1994] Transport coefficients for compositional simulation with coarse grids in heterogeneous media. SPE Advanced Technology Series, 2, 112–.
    [Google Scholar]
  4. Camy, J.P. and Emanuel, A.S.
    [1977] Effect of grid size in the compositional simulation of CO2 injection. Paper SPE 6894 presented at the SPE Annual Technical Conference and Exhibition, Denver, Colorado, USA.
    [Google Scholar]
  5. Cao, H.
    [2002] Development of Techniques for General Purpose Simulators. Ph.D. thesis, Stanford University.
    [Google Scholar]
  6. Chen, T., Gerritsen, M.G., Lambers, J.V and Durlofsky, L.J.
    [2010] Global variable compact multipoint methods for accurate upscaling with full-tensor effects. Computational Geosciences, 14, 81–.
    [Google Scholar]
  7. Chen, Y. and Durlofsky, L.J.
    [2006] Efficient incorporation of global effects in upscaled models of two-phase flow and transport in heterogeneous formations. Multiscale Modeling & Simulation, 5, 475–.
    [Google Scholar]
  8. [2008] Ensemble-level upscaling for efficient estimation of fine-scale production statistics. SPE Journal, 13, 411–.
    [Google Scholar]
  9. Chen, Y., Durlofsky, L.J., Gerritsen, M. and Wen, X.H.
    [2003] A coupled local-global upscaling approach for simulating flow in highly heterogeneous formations. Advances in Water Resources, 26, 1060–.
    [Google Scholar]
  10. Chen, Y. and Li, Y.
    [2009] Local-global two-phase upscaling of flow and transport in heterogeneous formations. Multiscale Modeling & Simulation, 8, 153–.
    [Google Scholar]
  11. Chen, Y., Mallison, B.T. and Durlofsky, L.J.
    [2008] Nonlinear two-point flux approximation for modeling full-tensor effects in subsurface flow simulations. Computational Geosciences, 12, 335–.
    [Google Scholar]
  12. Chen, Y., Park, K. and Durlofsky, L.J.
    [2011] Statistical assignment of upscaled flow functions for an ensemble of geological models. Computational Geosciences, 15, 51–.
    [Google Scholar]
  13. Christie, M.A. and Clifford, P.J.
    [1998] Fast procedure for upscaling compositional simulation. SPE Journal, 3, 278–.
    [Google Scholar]
  14. Darman, N.H., Pickup, G.E. and Sorbie, K.S.
    [2002] A comparison of two-phase dynamic upscaling methods based on fluid potentials. Computational Geosciences, 6, 27–.
    [Google Scholar]
  15. Deutsch, C.V. and Journel, A.G.
    [1998] GSLIB: Geostatistical Software Library and User’s Guide, 2nd edition. Oxford University Press.
    [Google Scholar]
  16. Ding, Y.
    [1995] Scaling-up in the vicinity of wells in heterogeneous field. Paper SPE 29137 presented at the SPE Reservoir Simulation Symposium, San Antonio, Texas, USA.
    [Google Scholar]
  17. Durlofsky, L.J. and Chen, Y.
    [2012] Uncertainty quantification for subsurface flow problems using coarse-scale models. In: Graham, I.G., Hou, T.Y., Lakkis, O. and Scheichl, R. (Eds.) Numerical Analysis of Multiscale Problems. Springer, vol. 83 of Lecture Notes in Computational Science and Engineering, 163–202.
    [Google Scholar]
  18. Durlofsky, L.J., Milliken, W.J. and Bernath, A.
    [2000] Scaleup in the near-well region. SPE Journal, 5, 117–.
    [Google Scholar]
  19. Fayers, F. J., Barker, J.W. and Newley, T.M.J.
    [1989] Effects of heterogeneities on phase behaviour in enhanced oil recovery. Proceedings of the 1st European Conference on the Mathematics of Oil Recovery, Cambridge, UK.
    [Google Scholar]
  20. Gringarten, E. and Deutsch, C.V
    [2001] Teacher’s aide variogram interpretation and modeling. Mathematical Geology, 33, 534–.
    [Google Scholar]
  21. Hui, M. and Durlofsky, L.J.
    [2005] Accurate coarse modeling of well-driven, high-mobility-ratio displacements in heterogeneous reservoirs. Journal of Petroleum Science and Engineering, 49, 56–.
    [Google Scholar]
  22. Jiang, Y.
    [2007] Techniques for Modeling Complex Reservoirs and Advanced Wells. Ph.D. thesis, Stanford University.
    [Google Scholar]
  23. Kolyukhin, D. and Espedal, M.
    [2010] Modified adaptive local-global upscaling method for discontinuous permeability distribution. Computational Geosciences, 14, 689–.
    [Google Scholar]
  24. Li, H., Chen, Y., Rojas, D. and Kumar, M.
    [2014] Development and application of near-well multiphase upscaling for forecasting of heavy oil primary production. Journal of Petroleum Science and Engineering, 113, 96–.
    [Google Scholar]
  25. Muggeridge, A.H., Cuypers, M., Bacquet, C. and Barker, J.W.
    [2002] Scale-up of well performance for reservoir flow simulation. Petroleum Geoscience, 8, 139–.
    [Google Scholar]
  26. Nakashima, T. and Durlofsky, L.J.
    [2010] Accurate representation of near-well effects in coarse-scale models of primary oil production. Transport in Porous Media, 83, 770–.
    [Google Scholar]
  27. Nakashima, T., Li, H. and Durlofsky, L.J.
    [2012] Near-well upscaling for three phase flows. Computational Geosciences, 16, 73–.
    [Google Scholar]
  28. Ogunlana, D.O. and Mohanty, K.K.
    [2005] Compositional upscaling in fractured reservoirs during gas recycling. Journal of Petroleum Science and Engineering, 46, 21–.
    [Google Scholar]
  29. Remy, N., Boucher, A. and Wu, J.
    [2009] Applied Geostatistics with SGeMS: A User’s Guide. Cambridge University Press.
    [Google Scholar]
  30. Salehi, A., Tchelepi, H. and Voskov, D.
    [2013] Thermodynamically consistent transport coefficients for upscaling of compositional processes. Paper SPE 163576 presented at the SPE Reservoir Simulation Symposium, The Woodlands, Texas, USA.
    [Google Scholar]
  31. Suzuki, S.
    [2011] Pattern-based approach to multiphase flow upscaling using distance-based clustering. Paper SPE 146639 presented at the SPE Annual Technical Conference and Exhibition, Denver, Colorado, USA.
    [Google Scholar]
  32. Wen, X.H., Chen, Y. and Durlofsky, L.J.
    [2006] Efficient 3D implementation of local-global upscaling for reservoir simulation. SPE Journal, 11, 453–.
    [Google Scholar]
  33. White, C.D. and Horne, R.N.
    [1987] Computing absolute transmissibility in the presence of fine-scale heterogeneity. Paper SPE 16011 presented at the SPE Symposium on Reservoir Simulation, San Antonio, Texas, USA.
    [Google Scholar]
  34. Zhang, P., Pickup, G.E. and Christie, M.A.
    [2005] A new upscaling approach for highly heterogeneous reservoirs. Paper SPE 93339 presented at the SPE Reservoir Simulation Symposium, The Woodlands, Texas, USA.
    [Google Scholar]
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