An Embedded Grid-Free Approach for Near-Wellbore Streamline Simulation
- Bin Wang (University of Louisiana, Lafayette) | Yin Feng (University of Louisiana, Lafayette) | Juan Du (China National Offshore Oil Corporation) | Yihui Wang (University of Louisiana, Lafayette) | Sijie Wang (University of Louisiana, Lafayette) | Ruiyue Yang (China University of Petroleum, Beijing)
- Document ID
- Society of Petroleum Engineers
- SPE Journal
- Publication Date
- April 2018
- Document Type
- Journal Paper
- 567 - 588
- 2018.Society of Petroleum Engineers
- Streamline Tracing, Boundary Element Method, Reactive Transport, Complex Grid, Streamline Simulation
- 1 in the last 30 days
- 221 since 2007
- Show more detail
- View rights & permissions
|SPE Member Price:||USD 5.00|
|SPE Non-Member Price:||USD 35.00|
Reactive-transport phenomena, such as carbon dioxide sequestration and microbial enhanced oil recovery (EOR), have been of interest in streamline-based simulation (SLS). Tracing streamlines launched from a wellbore is important, especially for time-sensitive transport behaviors. However, discretized gridblocks are usually too large compared with the wellbore radius. Field-scale simulations with local-grid-refinement (LGR) models often consume huge computational time. An embedded grid-free approach to integrate near-wellbore transport behaviors into streamline simulations is developed, comprising two stages of development: tracing streamlines in a wellblock (a gridblock containing wells) and coupling streamlines with neighboring grids. The velocity field in a wellblock is produced using a gridless virtual-boundary-element method (VBEM), where streamlines are numerically traced with the fourth-order Runge-Kutta (RK4) method (Butcher 2008). The local streamline system is then connected with the global streamline system, which is produced with the Pollock (1988) algorithm. Finally, the reactive-transport equation will be solved along these streamlines.
The algorithm presented for solving near-wellbore streamlines is verified by both a commercial finite-element simulator and a Pollock-algorithm-based 3D streamline simulator. A series of computational cases of reactive-transport simulation is studied to demonstrate the applicability, accuracy, and efficiency of the proposed method. Velocity field, time-of-flight (TOF), streamline pattern, and concentration distribution produced by different approaches are analyzed. Results show that the presented method can accurately perform near-wellbore streamline simulations in a time-effective manner. The algorithm can be directly applied to one grid containing multiple wells or to off-center wells. Furthermore, assuming streamlines are evenly launched from the gridblock boundary or ignoring transport in the wellblock is not always reasonable, and may lead to a significant error.
This study provides a simple and grid-free solution, but is capable of capturing the flow field near the wellbore with significant accuracy and computational efficiency. The method is promising for reservoir SLS with time-sensitive transport, and other simulations requiring an accurate assessment of interactions between wells in one particular gridblock.
|File Size||1 MB||Number of Pages||22|
Ahrens, J., Geveci, B., and Law, C. 2005. ParaView: An End-User Tool for Large-Data Visualization. In The Visualization Handbook, ed. C. D. Hansen and C. R. Johnson, Chap. 36, 717–731. Amsterdam: Elsevier.
AlSofi, A. M. and Blunt, M. J. 2010. Streamline-Based Simulation of Non-Newtonian Polymer Flooding. SPE J. 15 (4): 895–905. SPE-123971-PA. https://doi.org/10.2118/123971-PA.
Batycky, R. P. 1997. A Three-Dimensional Two-Phase Field Scale Streamline Simulator. PhD dissertation, Stanford University, Stanford, California.
Brebbia, C. A. and Dominguez, J. 1977. Boundary Element Methods for Potential Problems. Appl. Math. Model. 1 (7): 372–378. https://doi.org/10.1016/0307-904X(77)90046-4.
Bruch, E. K. 1991. The Boundary Element Method for Groundwater Flow, Vol. 70 of Lecture Notes in Engineering series. Heidelberg, Germany: Springer-Verlag Berlin.
Butcher, J. 2008. Numerical Methods for Ordinary Differential Equations. New York: John Wiley & Sons.
Caudle, B. H. 1967. Fundamentals of Reservoir Engineering. Richardson, Texas: Society of Petroleum Engineers.
Chan, H. C. M., Li, V., and Einstein, H. H. 1990. A Hybridized Displacement Discontinuity and Indirect Boundary Element Method to Model Fracture Propagation. Int. J. Fracture 45 (4): 263–282. https://doi.org/10.1007/BF00036271.
Clement, T. P. 1997. RT3D, A Modular Computer Code for Simulating Reactive Multispecies Transport in 3-Dimensional Groundwater Aquifers. Report, prepared for the US Department of Energy, Contract No. DE-AC06-76RLO 1830. Pacific Northwest National Laboratory, Richland, Washington.
Collins, R. E. 1976. Flow of Fluids Through Porous Materials. Tulsa: The Petroleum Publishing Company.
Courant, R., Friedrichs, K., and Lewy, H. 1967. On the Partial Difference Equations of Mathematical Physics. IBM Journal of Research and Development 11 (2): 215–234. https://doi.org/10.1147/rd.112.0215.
Crane, M. J. and Blunt, M. J. 1999. Streamline-Based Simulation of Solute Transport. Water Resour. Res. 35 (10): 3061–3078. https://doi.org/10.1029/1999WR900145.
Datta-Gupta, A. and King, M. J. 1995. A Semianalytic Approach to Tracer Flow Modeling in Heterogeneous Permeable Media. Adv. Water Resour. 18 (1): 1–9. https://doi.org/10.1016/0309-1708(94)00021-V.
Datta-Gupta, A. and King, M. J. 2007. Streamline Simulation: Theory and Practice. Richardson, Texas: Textbook Series, Society of Petroleum Engineers.
Delong, Q. and Guangting, L. 1996. Solution of Periodic Heat Conduction by Indirect Boundary Element Method Based on Fictitious Heat Source. Int. J. Numer. Meth. Biomed. Eng. 12 (10): 673–682. https://doi.org/10.1002/(SICI)1099-0887(199610)12:10<673::AID-CNM21>3.0.CO;2-1.
Delshad, M., Pope, G. A., and Sepehrnoori, K. 2000. Volume II: Technical Documentation for UTCHEM-9.0, A Three-Dimensional Chemical Flood Simulator. Technical Documentation, Center for Petroleum and Geosystems Engineering, The University of Texas at Austin, Austin, Texas (July 2000), http://www.cpge.utexas.edu/utchem/UTCHEM_-Tech_Doc.pdf (accessed 20 January 2016).
Diersch, H. J. 2013. FEFLOW: Finite Element Modeling of Flow, Mass and Heat Transport in Porous and Fractured Media. Heidelberg, Germany: Springer Science & Business Media.
Fogler, H. S. 2006. Elements of Chemical Reaction Engineering. London: Pearson Education.
Gautier, Y., Noetinger, B., and Roggero, F. 2004. History Matching Using a Streamline-Based Approach and Gradual Deformation. SPE J. 9 (1): 88–101. SPE-87821-PA. https://doi.org/10.2118/87821-PA.
Hægland, H., Dahle, H. K., Eigestad, G. T. et al. 2007. Improved Streamlines and Time-of-Flight for Streamline Simulation on Irregular Grids. Adv. Water Resour. 30 (4): 1027–1045. https://doi.org/10.1016/j.advwatres.2006.09.002.
Herrera, P. A., Valocchi, A. J., and Beckie, R. D. 2010. A Multidimensional Streamline-Based Method to Simulate Reactive Solute Transport in Heterogeneous Porous Media. Adv. Water Resour. 33 (7): 711–727. https://doi.org/10.1016/j.advwatres.2010.03.001.
Huang, W., Di Donato, G., and Blunt M. J. 2004. Comparison of Streamline-Based and Grid-Based Dual Porosity Simulation. J. Pet. Sci. Eng. 43 (1–2): 129–137. https://doi.org/10.1016/j.petrol.2004.01.002.
Jessen, K. and Orr, F. M. Jr. 2002. Compositional Streamline Simulation. Presented at the SPE Annual Technical Conference and Exhibition, San Antonio, Texas, 29 September–2 October. SPE-77379-MS. https://doi.org/10.2118/77379-MS.
Jimenez, E., Datta-Gupta, A., and King, M. J. 2010. Full-Field Streamline Tracing in Complex Faulted Systems With Non-Neighbor Connections. SPE J. 15 (1): 7–17. SPE-113425-PA. https://doi.org/10.2118/113425-PA.
Jimenez, E., Sabir, K., Datta-Gupta, A. et al. 2005. Spatial Error and Convergence in Streamline Simulation. Presented at the SPE Reservoir Simulation Symposium, The Woodlands, Texas, 31 January–2 February. SPE-92873-MS. https://doi.org/10.2118/92873-MS.
Juanes, R. and Matringe, S. F. 2009. Unified Formulation for High-Order Streamline Tracing on Two-Dimensional Unstructured Grids. J. Sci. Comput. 38 (1): 50–73. https://doi.org/10.1007/s10915-008-9228-2.
Katsikadelis, J. T. 2016. The Boundary Element Method for Engineers and Scientists: Theory and Applications. Oxford, UK: Academic Press.
Lin, J. K. 1972. An Image Well Method for Bounding Arbitrary Reservoir Shapes in the Streamline Model. PhD dissertation, University of Texas at Austin, Austin, Texas.
Matringe, S. F. and Juanes, R. 2005. Streamline Tracing on General Triangular or Quadrilateral Grids. Presented at SPE Annual Technical Conference and Exhibition, Dallas, 9–12 October. SPE-96411-MS. https://doi.org/10.2118/96411-MS.
Natvig, J. R., Lie, K. A., Eikemo, B. et al. 2007. An Efficient Discontinuous Galerkin Method for Advective Transport in Porous Media. Adv. Water Resour. 30 (12): 2424–2438. https://doi.org/10.1016/j.advwatres.2007.05.015.
Numbere, D. T. 1982. A General Streamline Modeling Technique for Homogeneous and Heterogeneous Porous Media with Applications to Steamflood Prediction. PhD dissertation, University of Oklahoma, Norman, Oklahoma.
Obi, E.-O. I. and Blunt, M. J. 2006. Streamline-Based Simulation of Carbon Dioxide Storage in a North Sea Aquifer. Water Resour. Res. 42 (3): W03414. https://doi.org/10.1029/2004WR003347.
Pollock, D. W. 1988. Semianalytical Computation of Pathlines for Finite-Difference Models. Groundwater 26 (6): 743–750. https://doi.org/10.1111/j.1745-6584.1988.tb00425.x.
Prevost, M., Edwards, M. G., and Blunt, M. J. 2001. Streamline Tracing on Curvilinear Structured and Unstructured Grids. Presented at the SPE Reservoir Simulation Symposium, Houston, 11–14 February. SPE-66347-MS. https://doi.org/10.2118/66347-MS.
Qi, R., LaForce, T. C., and Blunt, M. J. 2009. A Three-Phase Four-Component Streamline-Based Simulator to Study Carbon Dioxide Storage. Computat. Geosci. 13 (4): 493–509. https://doi.org/10.1007/s10596-009-9139-9.
Ramirez, W. F. 1987. Application of Optimal Control Theory to Enhanced Oil Recovery, Vol. 21, Developments in Petroleum Science series. Amsterdam: Elsevier Science.
Shahvali, M., Mallison, B., Wei, K. et al. 2012. An Alternative to Streamlines for Flow Diagnostics on Structured and Unstructured Grids. SPE J. 17 (3): 768–778. SPE-146446-PA. https://doi.org/10.2118/146446-PA.
Siavashi, M., Blunt, M. J., Raisee, M. et al. 2014. Three-Dimensional Streamline-Based Simulation of Non-Isothermal Two-Phase Flow in Heterogeneous Porous Media. Comput. Fluid. 103 (1 November): 116–131. https://doi.org/10.1016/j.compfluid.2014.07.014.
Siavashi, M., Pourafshary, P., and Raisee, M. 2012. Application of Space-Time Conservation Element and Solution Element Method in Streamline Simulation. J. Pet. Sci. Eng. 96–97 (October): 58–67. https://doi.org/10.1016/j.petrol.2012.08.005.
Siavashi, M., Tehrani, M. R., and Nakhaee, A. 2016. Efficient Particle Swarm Optimization of Well Placement to Enhance Oil Recovery Using a Novel Streamline-Based Objective Function. J. Energ. Resour. Technol. 138 (5): 052903. https://doi.org/10.1115/1.4032547.
Skinner, J. H. and Johansen, T. 2012. Near Wellbore Streamline Modeling: Its Novelty, Application, and Potential Use. Presented at the SPE International Symposium and Exhibition on Formation Damage Control, Lafayette, Louisiana, 15–17 February. SPE-149962-MS. https://doi.org/10.2118/149962-MS.
Tan, X., Hu, L., Reed, A. H. et al. 2014. Flocculation and Particle Size Analysis of Expansive Clay Sediments Affected by Biological, Chemical, and Hydrodynamic Factors. Ocean Dyn. 64 (1): 143–157. https://doi.org/10.1007/s10236-013-0664-7.
Tan, X. L., Zhang, G. P., Hang, Y. I. N. et al. 2012. Characterization of Particle Size and Settling Velocity of Cohesive Sediments Affected by a Neutral Exopolymer. Int. J. Sediment Res. 27 (4): 473–485. https://doi.org/10.1016/S1001-6279(13)60006-2.
Thiele, M. R. 1994. Modeling Multiphase Flow in Heterogeneous Media Using Streamtubes. PhD dissertation, Stanford University, Stanford, California.
Ueng, S. K., Sikorski, K., and Ma, K. L. 1995. Fast Algorithms for Visualizing Fluid Motion in Steady Flow on Unstructured Grids. Proc., IEEE Conference on Visualization, Atlanta, Georgia, 29 October–3 November. 313. https://doi.org/10.1109/VISUAL.1995.485144.
Wearing, J. L. and Sheikh, M. A. 1988. A Regular Indirect Boundary Element Method for Thermal Analysis. Int. J. Numer. Meth. Eng. 25 (2): 495–515. https://doi.org/10.1002/nme.1620250214.
Weijermars, R., van Harmelen, A., and Zuo, L. 2016. Controlling Flood Displacement Fronts Using a Parallel Analytical Streamline Simulator. J. Pet. Sci. Eng. 139 (March): 23–42. https://doi.org/10.1016/j.petrol.2015.12.002.
Zhang, Y., King, M. J., and Datta-Gupta, A. 2012. Robust Streamline Tracing Using Inter-Cell Fluxes in Locally Refined and Unstructured Grids. Water Resour. Res. 48 (6): W06521. https://doi.org/10.1029/2011WR011396.
Zhu, Z., Gerritsen, M., and Thiele, M. 2010. Thermal Streamline Simulation for Hot Waterflooding. SPE Res Eval & Eng 13 (3): 372–382. SPE-119200-PA. https://doi.org/10.2118/119200-PA.
Zuo, L. H., Lim, J., Chen, R. Q. et al. 2016. Efficient Calculation of Flux Conservative Streamline Trajectories on Complex and Unstructured Grids. Oral presentation given at the 78th EAGE Conference and Exhibition 2016, Vienna, Austria, 30 May–2 June.