# An Upscaling–Static-Downscaling Scheme for Simulation of Enhanced Oil Recovery Processes

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## Abstract

We investigate whether upscaling errors for EOR simulation can be reduced by an upscaling–static-downscaling method where the scales of simulation for the pressure and saturation/concentration switch between coarse simulation model and fine geological model. We apply a static downscaling that has been previously shown to be reliable for water flooding. We use the same algorithm of static downscaling for EOR processes that have been used for water flooding. Different EOR processes are considered: polymer, surfactant and thermal. This range of flooding processes ensures that we are examining more physically complicated systems than water flooding. For these processes, one major difference from water flooding is existence of a secondary front. The effective capturing of this front is a criterion of accuracy for upscaling because, for this front, the coupling of dispersion with the fractional flow creates excessive smearing. A scheme for numerical dispersion control is implemented to both upscaled and downscaled models to determine and reduce the sensitivity to dispersion errors.

## Keywords

Upscaling Static downscaling Flux reconstruction EOR processes Heterogeneous porous media## Notes

### Acknowledgments

The authors would like to thank the editor and the anonymous reviewers for their valuable comments and suggestions to improve the quality of the paper. M.B. also sincerely thanks Prof. M.J. Blunt at Imperial College for constructive suggestions mainly on readability and structure of the paper. Finally, M.B. gratefully appreciates ESPRC-Shell Dorothy Hodgkin Postgraduate scholarship that has enabled him to undertake research at Imperial College London.

## References

- Aarnes, J.E.: On the use of a mixed multiscale finite element method for greater flexibility and increased speed or improved accuracy in reservoir simulation. Multiscale Model. Simul.
**2**, 421–439 (2004)CrossRefGoogle Scholar - Aarnes, J.E., Efendiev, Y.: An adaptive multiscale method for simulation of fluid flow in heterogeneous porous media. Multiscale Model. Simul.
**5**(3), 918 (2006)CrossRefGoogle Scholar - AlSofi, A.M., Blunt, M.J.: Control of numerical dispersion in simulations of augmented water flooding. In: SPE Paper 129658-MS, Proceedings of SPE Symposium on Improved Oil Recovery, Tulsa, Oklahoma, 2010Google Scholar
- AlSofi, A.M., Blunt, M.J.: A segregated flow scheme to control numerical dispersion for multi-component flow simulations. Comput. Geosci.
**16**(2), 1–16 (2012)CrossRefGoogle Scholar - Audigane, P., Blunt, M.J.: Dual mesh method for upscaling in waterflood simulation. Transp. Porous Media
**55**(1), 71–89 (2004)CrossRefGoogle Scholar - Babaei, M., King, P.R.: A modified nested-gridding for upscaling downscaling in reservoir simulation. Transp Porous Media
**93**(3), 753–775 (2012)CrossRefGoogle Scholar - Batycky, R.P., Blunt, M.J., Thiele, M.R.: A 3D field-scale streamline-based reservoir simulator. SPE Reserv. Eng.
**12**(4), 246–254 (1997)Google Scholar - Begg, S.H., Carter, R.R., Dranfield, P.: Assigning effective values to simulator gridblock parameters for heterogeneous reservoirs. SPE Reserv. Eng.
**4**(4), 455–463 (1989)Google Scholar - Bratvold, R.B.: An analytical study of reservoir pressure response following cold water injection. PhD thesis, Stanford University (1989)Google Scholar
- Buckley, S.E., Leverett, M.C.: Mechanism of fluid displacement in sands. Trans. AIME
**146**, 107–116 (1942)Google Scholar - Chen, Y., Durlofsky, L.J.: Adaptive local-global upscaling for general flow scenarios in heterogeneous formations. Transp. Porous Media
**62**(2), 157–185 (2006)CrossRefGoogle Scholar - Chen, Y., Durlofsky, L.J., Gerritsen, M., Wen, X.-H.: A coupled local-global upscaling approach for simulating flow in highly heterogeneous formations. Adv. Water Resour.
**26**(10), 1041–1060 (2003)CrossRefGoogle Scholar - Chen, Z., Hou, T.Y.: A mixed multiscale finite element method for elliptic problems with oscillating coefficients. Math. Comput.
**72**(242), 541–576 (2003)Google Scholar - Christie, M.A.: Upscaling for reservoir simulation. J. Petroleum Technol.
**48**(11), 1004–1010 (1996)Google Scholar - Christie, M.A., Blunt, M.J.: Tenth SPE comparative solution project: a comparison of upscaling techniques. SPE Reserv. Eval. Eng.
**4**(4), 308–317 (2001)Google Scholar - Dindoruk, D., Dindoruk, B.: Analytical solution of nonisothermal Buckley-Leverett flow including tracers. SPE Reserv. Eval. Eng.
**11**(3), 555–564 (2008)Google Scholar - Durlofsky, L.J.: Numerical calculation of equivalent grid block permeability tensors for heterogeneous porous media. Water Resour. Res.
**27**(5), 699–708 (1991)CrossRefGoogle Scholar - Gautier, Y., Blunt, M.J., Christie, M.A.: Nested gridding and streamline-based simulation for fast reservoir performance prediction. Comput. Geosci.
**3**(3), 295–320 (1999)CrossRefGoogle Scholar - Green, D.W., Willhite, G.P.: Enhanced Oil Recovery, SPE Textbook Series, vol. 6. Society of Petroleum Engineers, Richardson, TX (1998)Google Scholar
- Guérillot, D.R., Verdière, S.: Different pressure grids for reservoir simulation in heterogeneous reservoirs. In: SPE Paper 29148-MS, Proceedings of SPE Reservoir Simulation Symposium, San Antonio, Texas, 1995Google Scholar
- Hauge, V.L., Lie, K.A., Natvig, J.R.: Flow-based coarsening for multiscale simulation of transport in porous media. Comput. Geosci.
**16**(2), 391–408 (2012)CrossRefGoogle Scholar - Jenny, P., Lee, S.H., Tchelepi, H.A.: Multiscale finite-volume method for elliptic problems in subsurface flow simulation. J. Comput.l Phys.
**187**(1), 47–67 (2003)CrossRefGoogle Scholar - Jenny, P., Lee, S.H., Tchelepi, H.A.: Adaptive multiscale finite-volume method for multiphase flow and transport in porous media. Multiscale Model. Simul.
**3**(1), 50–64 (2005)CrossRefGoogle Scholar - Kippe, V., Aarnes, J.E., Lie, K.A.: A comparison of multiscale methods for elliptic problems in porous media flow. Comput. Geosci.
**12**(3), 377–398 (2008)CrossRefGoogle Scholar - Lake, L.W.: Enhanced Oil Recovery. Old Tappan, Prentice Hall Inc, NJ (1989)Google Scholar
- Papanicolau, G., Bensoussan, A., Lions, J.L.: Asymptotic Analysis for Periodic Structures, vol. 5. North Holland (1978)Google Scholar
- Pickup, G.E., Ringrose, P.S., Jensen, J.L., Sorbie, K.S.: Permeability tensors for sedimentary structures. Math. Geol.
**26**(2), 227–250 (1994)CrossRefGoogle Scholar - Ramé, M., Killough, J.E.: A new approach to flow simulation in highly heterogeneous porous media. SPE Form. Eval.
**7**, 247–254 (1992)Google Scholar - Sorbie, K.S.: Polymer-Improved Oil Recovery. Springer, Berlin (1991)Google Scholar
- Talash, A.W.: Experimental and calculated relative permeability data for systems containing tension additives. In: SPE Paper 5810-MS, Proceedings of SPE Improved Oil Recovery Symposium, Tulsa, Oklahoma, 1976Google Scholar
- Wen, X.-H., Durlofsky, L.J., Chen, Y.: Efficient 3D implementation of local-global upscaling for reservoir simulation. SPE J.
**11**(4), 443–453 (2006)Google Scholar