Advanced Techniques for Reservoir Simulation and Modeling of Nonconventional Wells

Research results for a five year project on the development of improved modeling techniques for nonconventional (e.g., horizontal, deviated, multilateral or “smart”) wells are presented. The overall program entails the development of enhanced well modeling and general simulation capabilities. The development and features of a new general purpose research simulator (GPRS) are described. The simulator accommodates varying degrees of solution implicitness, handles structured and unstructured grids, and can additionally be used for modeling fractured reservoirs. Advanced linear solution techniques were also implemented. A general gridding and upscaling procedure for unstructured models is presented. The method includes a streamline simulation technique that can be used to assess the accuracy of the coarse model. A semianalytical technique for the modeling of nonconventional wells was developed. This model, implemented into an advanced well modeling software package (AdWell), provides an approximate treatment of reservoir heterogeneity and is able to model downhole inflow control devices and wellbore pressure losses. The well index, which is a key parameter in finite difference well models, can also be computed from AdWell. A drift-flux model for the description of multiphase wellbore flow is presented. Parameters applicable for use in practical systems are determined through tuning to unique experimental data (obtained outside of this DOE sponsored research) on largediameter pipes. The optimum deployment of nonconventional wells is considered next. A genetic algorithm for determining the optimum well type and location is described. A technique for the optimization of smart well control is then presented. The linkage of the method with a historymatching procedure provides a prototype real-time well control strategy. Papers resulting from DOE funded and related research: 1. Aitokhuehi, I., Durlofsky, L.J., Artus, V., Yeten, B., Aziz, K.: “Optimization of advanced well type and performance,” Proceedings of the 9th European Conference on the Mathematics of Oil Recovery, Cannes, France, Aug. 30 Sept. 2, 2004. 2. Cao, H., Aziz, K.: “Performance of IMPSAT and IMPSAT-AIM models in compositional simulation,” SPE paper 77720, presented at the SPE Annual Technical Conference and Exhibition, San Antonio, Sept. 29 Oct. 2, 2002. 3. Castellini, A., Edwards, M.G., Durlofsky, L.J.: “Flow based modules for grid generation in two and three dimensions,” Proceedings of the 7th European Conference on the Mathematics of Oil Recovery, Baveno, Italy, Sept. 5-8, 2000. 4. Chen, Y., Durlofsky, L.J.: “Adaptive local-global upscaling for general flow scenarios in heterogeneous formations” (in review for Transport in Porous Media). 5. Chen, Y., Durlofsky, L.J., Gerritsen, M., Wen, X.H.: “A coupled local-global upscaling approach for simulating flow in highly heterogeneous formations,” Advances in Water Resources, 26, 1041-1060, 2003. 6. Chen, Y., Durlofsky, L.J., Wen, X.H.: “Robust coarse scale modeling of flow and transport in heterogeneous reservoirs,” to appear in the Proceedings of the 9th European Conference on the Mathematics of Oil Recovery, Cannes, France, Aug. 30 Sept. 2, 2004. 7. Durlofsky, L.J.: “An approximate model for well productivity in heterogeneous porous media,” Mathematical Geology, 32, 421-438, 2000. 8. Durlofsky, L.J.: “Upscaling of geological models for reservoir simulation: issues and approaches,” Computational Geosciences, 6, 1-4, 2002. 9. Durlofsky, L.J.: “Upscaling of geocellular models for reservoir flow simulation: a review of recent progress,” Proceedings of the 7 International Forum on Reservoir Simulation, Bühl/Baden-Baden, Germany, June 23-27, 2003. 10. Edwards, M.G.: “M-matrix flux splitting for general full tensor discretization operators on structured and unstructured grids,” J. Computational Physics, 160, 1-28, 2000. 11. Edwards, M.G.: “Split full tensor discretization operators for structured and unstructured grids in three dimensions,” SPE paper 66358, presented at the SPE Reservoir Simulation Symposium, Houston, Feb. 11-14, 2001. 12. He, C., Edwards, M.G., Durlofsky, L.J.: “Numerical calculation of equivalent cell permeability tensors for general quadrilateral control volumes,” Computational Geosciences, 6, 29-47, 2002. 13. Karimi-Fard, M.: “Growing region technique applied to grid generation of complex fractured porous media,” Proceedings of the 9th European Conference on the Mathematics of Oil Recovery, Cannes, France, Aug. 30 Sept. 2, 2004. 14. Karimi-Fard, M., Durlofsky, L.J., Aziz, K.: “An efficient discrete fracture model applicable for general purpose reservoir simulators,” SPEJ, 9, 227-236, 2004 (also SPE paper 79699). 15. Mascarenhas, O., Durlofsky, L.J.: “Coarse scale simulation of horizontal wells in heterogeneous reservoirs,” Journal of Petroleum Science and Engineering, 25, 135-147, 2000. 16. Prevost, M., Edwards, M.G., Blunt, M.J.: “Streamline tracing on curvilinear structured and unstructured grids,” SPEJ, 7, 139-148, 2002 (also SPE paper 66347). 17. Prevost, M., Lepage, F., Durlofsky, L.J., Mallet, J.-L.: “Unstructured 3D gridding and upscaling for coarse modeling of geometrically complex reservoirs,” Proceedings of the 9th European Conference on the Mathematics of Oil Recovery, Cannes, France, Aug. 30-Sept. 2, 2004. 18. Sarma, P., Aziz, K.: “Simulation of Naturally Fractured Reservoirs With Dual Porosity Models: Part I-Single-Phase Flow,” SPE paper 90231, to be presented at the SPE Annual Technical Conference and Exhibition, Houston, Sept. 26-29, 2004. 19. Shi, H., Holmes, J.A., Diaz, L.R., Durlofsky, L.J., Aziz, K.: “Drift-flux parameters for threephase steady-state flow in wellbores,” SPE paper 89836, to be presented at the SPE Annual Technical Conference and Exhibition, Houston, Sept. 26-29, 2004. 20. Shi, H., Holmes, J.A., Durlofsky, L.J., Aziz, K., Diaz, L.R., Alkaya, B., Oddie, G.: “Driftflux modeling of multiphase flow in wellbores,” SPE paper 84228, presented at the SPE Annual Technical Conference and Exhibition, Denver, Oct. 5-8, 2003. 21. Valvatne, P.H., Durlofsky, L.J., Aziz, K.: “Semi-analytical modeling of the performance of intelligent well completions,” SPE paper 66368, presented at the SPE Reservoir Simulation Symposium, Houston, Feb. 11-14, 2001. 22. Valvatne, P.H., Serve, J., Durlofsky, L.J., Aziz, K.: “Efficient modeling of non-conventional wells with downhole inflow control devices,” Journal of Petroleum Science and Engineering, 39, 99-116, 2003. 23. Wen, X.H., Durlofsky, L.J., Edwards, M.G.: “Upscaling of channel systems in two dimensions using flow-based grids,” Transport in Porous Media, 51, 343-366, 2003. 24. Wolfsteiner, C., Aziz, K., Durlofsky, L.J.: “Modeling conventional and non-conventional wells,” Proceedings of the 6 International Forum on Reservoir Simulation, Hof/Salzburg, Austria, Sept. 3-7, 2001 (also appearing in the Proceedings of the International Energy Agency Symposium on Enhanced Oil Recovery, Vienna, Austria, Sept. 9-12, 2001). 25. Wolfsteiner, C., Durlofsky, L.J.: “Near-well radial upscaling for the accurate modeling of nonconventional wells,” SPE paper 76779, presented at the SPE Western Regional Meeting, Anchorage, May 20-22, 2002. 26. Wolfsteiner, C., Durlofsky, L.J., Aziz, K.: “Calculation of well index for non-conventional wells on arbitrary grids,” Computational Geosciences, 7, 61-82, 2003. 27. Wolfsteiner, C., Durlofsky, L.J., Aziz, K.: “Approximate model for productivity of nonconventional wells in heterogeneous reservoirs, SPEJ, 5, 218-226, 2000 (also SPE paper 56754). 28. Wolfsteiner, C., Durlofsky, L.J. and Aziz, K.: “Efficient estimation of the effects of wellbore hydraulics and reservoir heterogeneity on the productivity of non-conventional wells,” SPE paper 59399, presented at the SPE Asia Pacific Conference, Yokohama, Japan, April 25-26, 2000. 29. Yeten, B., Brouwer, D.R., Durlofsky, L.J., Aziz, K.: “Deployment of smart wells in the presence of geological and engineering uncertainty” (to appear in Journal of Petroleum Science and Engineering). 30. Yeten, B., Durlofsky, L.J., Aziz, K.: “Optimization of smart well control,” SPE paper 79031, presented at the SPE International Thermal Operations and Heavy Oil Symposium and International Horizontal Well Technology Conference, Calgary, Nov. 4 – 7, 2002. 31. Yeten, B., Durlofsky, L.J., Aziz, K.: “Optimization of intelligent well control,” World Oil, 224, 35-40, March 2003. 32. Yeten, B., Durlofsky, L.J., Aziz, K.: “Optimization of nonconventional well type, location and trajectory,” SPEJ, 8, 200-210, 2003 (also SPE paper 77565). 33. Yeten, B., Wolfsteiner, C., Durlofsky, L.J., Aziz, K.: “Approximate finite difference modeling of the performance of horizontal wells in heterogeneous reservoirs,” SPE paper 62555, presented at the SPE Western Regional Meeting, Long Beach, June 19-23, 2000.