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Abstract

Summary

Dynamic Local Grid Refinement (DLGR) is a well-known computational method to improve the performance of reservoir simulations by dynamically adapting the grid resolution to local physical phenomena at each location in time. This enables reservoir simulators to achieve similar accuracy with only a fraction of the number of grid cells that it would otherwise utilize. This is particularly useful for IOR/EOR processes due to the small scale and complexity of the physical and chemical processes involved.

A challenge in using DLGR is the adaptation of the local grid resolution in advance of dynamic changes in physical phenomena, such as moving thermal or oil displacement fronts. Failure to intercept such changes up front by a locally high resolution grid will lead to loss of numerical accuracy. A Repeat Time Step (RTS) method that iteratively repeats time steps to implicitly evaluate the grid adaptation criteria at the next time node was previously proposed. However, the results in this paper show that using the RTS method for DLGR leads on average to considerably higher computational time spent in the linear solver. As a result, it was found that it is more efficient in most cases to tighten the tolerances for the grid adaptation criteria in order to create a buffer zone of fine grid cells in regions that require high grid resolution instead of using the RTS method.

This report proposes an iDLGR-ANM method in which an Adaptive Newton's Method (ANM) is used to further reduce computational overhead spent in repeat time steps performed by DLGR. The ANM leads to reduced simulation times by only considering unconverged and adjacent grid cells in each NR iteration. Furthermore, the added benefit of ANM to the RTS method is that ANM can immediately be restricted to refined grid cells and adjacent cells from the first NR iteration in the repeat time steps rather than solving the full system of linearized equations. In order to compare the performance of the RTS method with and without the ANM, eight examples are considered involving various IOR/EOR applications and numerical schemes. Results show that iDLGR-ANM is nearly as fast in terms of CPU time spent in the linear solver as DLGR without using the RTS method. Moreover, if a post-Newton material balance smoothing technique is applied, iDLGR-ANM results in production forecasts with the same accuracy as DLGR when the RTS method is used without ANM, with differences within machine accuracy.

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/content/papers/10.3997/2214-4609.201900135
2019-04-08
2024-04-19

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References

  1. Andrianov, N. and Bratvedt, K.
    [2007] Acceleration of Streamline Simulation Using Adaptive Mesh Refinement along Streamlines. Proceedings of the 2007 SPE Reservoir Simulation Symposium, Houston, TX, U.S.A., SPE 106181.
     [Google Scholar]
  2. Biterge, M. B. and Ertekin, T
    . [1992] Development and Testing of a Static/Dynamic Local Grid Refinement Technique. J. Petr. Techn., 44(4), 487–495.
     [Google Scholar]
  3. Christie, M. A. and Blunt, M. J
    . [2001] Tenth SPE Comparative Solution Project: A Comparison of Upscaling Techniques. SPERes. Eval. Eng., 4(4), 308–317.
     [Google Scholar]
  4. Cusini, M., Gielisse, R., Groot, H., van Kruijsdijk, C. and Hajibeygi, H
    . [2018] Incomplete Mixing in Porous Media: Todd-Longstaff Upscaling Approach versus a Dynamic Local Grid Refinement Method. Comput. Geosci., 1–25.
     [Google Scholar]
  5. Cusini, M., van Kruijsdijk, C. and Hajibeygi, H
    . [2016a] Algebraic Dynamic Multilevel (ADM) Method for Immiscible Multiphase Flow in Heterogeneous Porous Media with Capillarity. Proceedings of ECMOR XV - 15th European Conference on the Mathematics of Oil Recovery, Amsterdam, The Netherlands.
     [Google Scholar]
  6. Cusini, M., van Kruijsdijk, C. and Hajibeygi
    , H. [2016b] Algebraic Dynamic Multilevel (ADM) Method for Fully Implicit Simulations of Multiphase Flow in Porous Media. J. Comp. Phys., 314, 60–79.
     [Google Scholar]
  7. Ding, Y. and Lemonnier, P. A
    . [1993] Development of Dynamic Local Grid-Refinement in Reservoir Simulation. Proceedings of the 12th SPE Symposium on Reservoir Simulation, New Orleans, LA, U.S.A., SPE25279.
     [Google Scholar]
  8. Ding, Y.-X., Shi, A.-F., Lao, H.-S. and Wang, X.-H
    . [2016] Adaptive Mesh Refinement for Non-Isothermal Multiphase Flows in Heterogeneous Porous Media Comprising Different Rock Types with Tensor Permeability. Num. Heat Trans., Part A, 69(1), 31–50.
     [Google Scholar]
  9. Douglas, D., Darlow, B. L., Wheeler, M. and Kendall, R. P
    . [1979] Self-Adaptive Galerkin Methods for One-Dimensional, Two-Phase Immiscible Flow. Proceedings of the1979Society of Petroleum Engineers of AIME Fifth Symposium on Reservoir Simulation, Denver, Colorado, U.S.A., SPE7679.
     [Google Scholar]
  10. Edwards, M.
    G. [1996] A Higher-Order Godunov Scheme Coupled with Dynamical Local Grid Refinement for Flow in a Porous Medium. Comput. Meth. Appl. Mech. Eng., 131, 287–308.
     [Google Scholar]
  11. Edwards, M. G. and Christie, M. A
    . [1993] Dynamically adaptive Godunov schemes with Renormalization in Reservoir Simulation. Proceedings of the 12th SPE Symposium on Reservoir Simulation, New Orleans, LA, U.S.A., SPE25268.
     [Google Scholar]
  12. Espedal, M. S., Langlo, P., Saevareid, O., Gislefoss, E. and Hansen, R
    . [1991] Heterogeneous Reservoir Models: Local Refinement and Effective Parameters. Proceedings of the 11th SPE Symposium on Reservoir Simulation, Anaheim, CA, U.S.A., SPE21231.
     [Google Scholar]
  13. Gerritsen, M. G. and Lambers, J.
    V. [2008] Integration of Local-Global Upscaling and Grid Adaptivity for Simulation of Subsurface Flow in Heterogeneous Formations. Comp. Geosci., 12, 193–218.
     [Google Scholar]
  14. Gonzalez, K. G
    . [2016] Adaptive Grid Refinement Improves Gas Injection Modeling. Proceedings of the SPE Annual Technical Conference and Exhibition, Dubai, UAE, SPE184487.
     [Google Scholar]
  15. Heinemann, Z. E., Gerken, G. and von Hantelmann, G
    . [1983] Using Local Grid Refinement in a Multiple-Application Reservoir Simulator. Proceedings of the Seventh SPE Reservoir Simulation Symposium, San Fransisco, CA, U.S.A., SPE12255.
     [Google Scholar]
  16. Hornung, R. D. and Trangenstein, J. A
    . [1997] Adaptive Mesh Refinement and Multilevel Iteration for Flow in Porous Media. J. Comp. Phys., 136(2), 522–545.
     [Google Scholar]
  17. Hoteit, H. and Chawathé, A
    . [2014] Making Field-Scale Chemical EOR Simulations a Practical Reality Using Dynamic Gridding. Proceedings of the SPE EOR Conference at Oil and Gas West Asia, Muscat, Oman, SPE169688.
     [Google Scholar]
  18. Jensen, O. K. and Finlayson, B. A
    . [1986] A Numerical Technique for Tracking Sharp Fronts in Studies of Tertiary Oil-Recovery Pilots. SPERes. Eng., 1(2), 194–202.
     [Google Scholar]
  19. Lake, L. W
    . [1989] Enhanced Oil Recovery. Englewood Cliffs: Prentice Hall, 1st edition.
     [Google Scholar]
  20. Lambers, J. V., Gerritsen, M. G. andFragola, D. [2009] Multiphase, 3-D Flow Simulation with Integrated Upscaling, MPFA Discretization, and Adaptivity. Proceedings of the
    2009SPE Reservoir Simulation Symposium, Woodlands, TX, U.S.A., SPE118983.
     [Google Scholar]
  21. Lovett, S., Nikiforakis, N. and Monmont
    , F. [2015] Adaptive Mesh Refinement for Compressible Thermal Flow in Porous Media. J. Comp. Phys., 280, 21–36.
     [Google Scholar]
  22. Lu, P. and Beckner, B
    . [2011] An Adaptive Newton's Method for Reservoir Simulation. Proceedings of the SPE Reservoir Simulation Symposium, The Woodlands, TX, U.S.A., SPE141935.
     [Google Scholar]
  23. Manik, J. and Ertekin, T
    . [1997] Development and Application of Dynamic and Static Local Grid Refinement Algorithms for Water Coning Studies. Proceedings of the SPE Eastern Regional Conference and Exhibition, Lexington, KY, U.S.A., SPE39228.
     [Google Scholar]
  24. Matringe, S. F. and Gerritsen, M. G
    . [2004] On Accurate Tracing of Streamlines. Proceedings of the SPE Annual Technical Conference and Exhibition, Houston, TX, U.S.A., SPE89920.
     [Google Scholar]
  25. Michaud, M. C. and Bisshopp, F
    . [1981] Accurate Waterflood Simulation Using Biased Differencing and Selective Grid Refinement, Brown University. USMS9799.
     [Google Scholar]
  26. Mulder, W. A. and Gmelig Meyling, R. H. J
    . [1993] Numerical Simulation of Two-Phase Flow Using Locally Refined Grids in Three Space Dimensions. SPE Advanced Technology Series, 1(1), 36–41.
     [Google Scholar]
  27. Nilsson, J., Gerritsen, M. G. andYounis, R.
    [2005] A Novel Adaptive Anisotropic Grid Framework for Efficient Reservoir Simulation. Proceedings of the2005SPE Reservoir Simulation Symposium, Houston, TX, U.S.A., SPE93243.
     [Google Scholar]
  28. Nilsson, J., Gerritsen, M. G. andYounis, R
    . [2005] Towards an Adaptive, High-Resolution Simulator for Steam Injection Processes. Proceedings of the2005SPE Western Regional Meeting, Irvine, CA, U.S.A., SPE93881.
     [Google Scholar]
  29. Pau, G. S. H., Bell, J. B., Almgren, A. S., Fagnan, K. M. andLijewski, M. J
    . [2012] An Adaptive Mesh Refinement Algorithm for Compressible Two-Phase Flow in Porous Media. Comput. Geosci., 16(3), 577–592.
     [Google Scholar]
  30. Pollock, D. W
    . [1988] Semianalytical Computation of Path Lines for Finite-Difference Models. Ground Water, 26(6), 743–750.
     [Google Scholar]
  31. Sammon, P. H
    . [2003] Dynamically Grid Refinement and Amalgamation for Composotional Simulation. Proceedings of the SPE Reservoir Simulation Symposium, Houston, TX, U.S.A., SPE79683.
     [Google Scholar]
  32. Schmidt, G. H. and Jacobs, F.
    J. [1988] Adaptive Local Grid Refinement and Multi-Grid in Numerical Reservoir Simulation. J. Comp. Phys., 77, 140–165.
     [Google Scholar]
  33. Suicmez, V. S., van Batenburg, D. W., Matsuura, T., Bosch, M. and Boersma, D. M
    . [2011] Dynamic Local Grid Refinement for Multiple Contact Miscible Gas Injection. Proceedings of the International Petroleum Technology Conference, Bangkok, Thailand, IPTC15017.
     [Google Scholar]
  34. van Batenburg, D. W., Bosch, M., Boerrigter, P. M., de Zwart, A. H. and Vink, J. C
    . [2011] Application of Dynamic Gridding Techniques in IOR/EOR Processes. Proceedings of the SPE Reservoir Simulation Symposium, The Woodlands, TX, U.S.A., SPE141711.
     [Google Scholar]
  35. Vikas, S. and Ertekin, T
    . [1996] A Patch-Type Adaptive Local Grid Refinement Technique and Its Application to Horizontal Wells. Proceedings of the SPE Eastern Regional Conference and Exhibition, Columbus, Ohio, U.S.A., SPE37352.
     [Google Scholar]
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An Adaptive Newton's Method for Implicit Dynamic Local Grid Refinement for Simulation of IOR/EOR Processes
Conference Proceedings 2019, 1 (2019); https://doi.org/10.3997/2214-4609.201900135
/content/papers/10.3997/2214-4609.201900135
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