Models of polymer flooding account for several processes such as concentration dependent viscosity, adsorption, incomplete mixing, inaccessible pore space, and reduced permeability effects, which altogether gives strongly coupled nonlinear systems that are challenging to solve numerically. Herein, we use a sequentially implicit solution strategy that splits the equation system into a pressure and a transport part. Our objective is to improve convergence rates for the transport subproblem, which contains many of the essential nonlinearities caused by the addition of polymer. Convergence failure for the Newton solver is usually caused by steps that pass inflection points and discontinuities in the fractional flow functions. The industry-standard approach is to heuristically chop time steps and/or dampen saturation updates suggested by the Newton solver if these exceed a predefined limit. An improved strategy is to use trust regions to determine safe saturation updates that stay within regions having the same curvature for the numerical flux. This approach has previously been used to obtain unconditional convergence for waterflooding scenarios and multicomponent problems with realistic property curves. Herein, we extend the method to polymer flooding, and study the performance of the method for a wide range of polymer parameters and reservoir configurations.


Article metrics loading...

Loading full text...

Full text loading...


  1. AlSofi, A.M. and Blunt, M.J.
    [2010] Streamline-based simulation of non-Newtonian polymer flooding. SPE J., 15(4), 895–905.
    [Google Scholar]
  2. Bao, K., Lie, K.A., Møyner, O. and Liu, M.
    [2017] Fully implicit simulation of polymer flooding with MRST. Comput. Geosci. Accepted.
    [Google Scholar]
  3. Brenier, Y. and Jaffré, J.
    [1991] Upstream differencing for multiphase flow in reservoir simulation. SIAM J. Numer. Anal., 28(3), 685–696.
    [Google Scholar]
  4. Christie, M.A. and Blunt, M.J.
    [2001] Tenth SPE comparative solution project: A comparison of upscaling techniques. SPE Reservoir Eval. Eng., 4, 308–317.
    [Google Scholar]
  5. Clemens, T., Abdev, J. and Thiele, M.R.
    [2011] Improved polymer-flood management using streamlines. SPE J., 14(2), 171–181.
    [Google Scholar]
  6. Hilden, S.T., Møyner, O., Lie, K.A. and Bao, K.
    [2016] Multiscale simulation of polymer flooding with shear effects. Transp. Porous Media, 113(1), 111–135.
    [Google Scholar]
  7. Hoteit, H. and Chawathé, A.
    [2016] Making field-scale chemical enhanced-oil-recovery simulations a practical reality with dynamic gridding. SPE J., 21(6), 2220–2237.
    [Google Scholar]
  8. IO Center, NTNU
    [2012] The Norne benchmark case. http://www.ipt.ntnu.no/~norne/.
  9. Jenny, P., Tchelepi, H.A. and Lee, S.H.
    [2009] Unconditionally convergent nonlinear solver for hyperbolic conservation laws with S-shaped flux functions. J. Comput. Phys., 228(20), 7497–7512.
    [Google Scholar]
  10. Krogstad, S., Lie, K.A., Møyner, O., Nilsen, H.M., Raynaud, X. and Skaflestad, B.
    [2015] MRST-AD – an open-source framework for rapid prototyping and evaluation of reservoir simulation problems. In: SPE Reservoir Simulation Symposium, 23–25 February, Houston, Texas.
    [Google Scholar]
  11. Krogstad, S., Lie, K.A., Nilsen, H.M., Berg, C.F. and Kippe, V.
    [2016] Flow diagnostics for optimal polymer injection strategies. In: ECMOR XV– 15th European Conference on the Mathematics of Oil Recovery, Amsterdam, Netherlands, 29 Aug–1 Sept.
    [Google Scholar]
  12. Li, B. and Tchelepi, H.A.
    [2014] Unconditionally convergent nonlinear solver for multiphase flow in porous media under viscous force, buoyancy, and capillarity. Energy Procedia, 59, 404–411.
    [Google Scholar]
  13. Lie, K.A., Nilsen, H.M., Rasmussen, A.F. and Raynaud, X.
    [2012] An unconditionally stable splitting method using reordering for simulating polymer injection. In: ECMOR XIII – 13th European Conference on the Mathematics of Oil Recovery, Biarritz, France, 10–13 September 2012, B25.
    [Google Scholar]
  14. [2014] Fast simulation of polymer injection in heavy-oil reservoirs based on topological sorting and sequential splitting. SPE J., 19(6), 991–1004.
    [Google Scholar]
  15. Møyner, O.
    [2016] Nonlinear solver for three-phase transport problems based on approximate trust regions. In: ECMOR XV – 15th European Conference on the Mathematics of Oil Recovery, Amsterdam, Netherlands, 29 Aug–1 Sept.
    [Google Scholar]
  16. Nasiri, H. and Henriquez, A.
    [2014] Challenges in implementation of chemical EOR in Norway. FORCE: – EOR competence group: EOR Process Modeling Workshop, 26 May 2014, Stavanger, Norway.
    [Google Scholar]
  17. Natvig, J.R. and Lie, K.A.
    [2008] Fast computation of multiphase flow in porous media by implicit discontinuous Galerkin schemes with optimal ordering of elements. J. Comput. Phys., 227(24), 10108–10124.
    [Google Scholar]
  18. SINTEF
    [2016] The MATLAB Reservoir Simulation Toolbox, 2016b. http://www.sintef.no/MRST/.
  19. The Open Porous Media Initative
    [2015] The Norne dataset. https://github.com/OPM/opm-data.
  20. Todd, M.R. and Longstaff, W.J.
    [1972] The development, testing, and application of a numerical simulator for predicting miscible flood performance. J. Petrol. Tech., 24(7), 874–882.
    [Google Scholar]
  21. Voskov, D.V. and Tchelepi, H.
    [2011] Compositional nonlinear solver based on trust regions of the flux function along key tie-lines. In: SPE Reservoir Simulation Symposium, 21–23 February, The Woodlands, Texas, USA.
    [Google Scholar]
  22. Wang, X. and Tchelepi, H.A.
    [2013] Trust-region based solver for nonlinear transport in heterogeneous porous media. J. Comput. Phys., 253, 114–137.
    [Google Scholar]

Data & Media loading...

This is a required field
Please enter a valid email address
Approval was a Success
Invalid data
An Error Occurred
Approval was partially successful, following selected items could not be processed due to error