Aquifer Acceleration in Parallel Implicit Field-Scale Reservoir Simulation
- Shouhong Du (Saudi Aramco) | Larry S. K. Fung (Saudi Aramco) | Ali H. Dogru (Saudi Aramco)
- Document ID
- Society of Petroleum Engineers
- SPE Journal
- Publication Date
- April 2018
- Document Type
- Journal Paper
- 614 - 624
- 2018.Society of Petroleum Engineers
- Aquifer Acceleration, Vertical Equilibrium
- 2 in the last 30 days
- 221 since 2007
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Grid coarsening outside of the areas of interest is a common method to reduce computational cost in reservoir simulation. Aquifer regions are candidates for grid coarsening. In this situation, upscaling is applied to the fine grid to generate coarse-grid flow properties. The efficacy of the approach can be judged easily by comparing the simulation results between the coarse-grid model and the fine-grid model. For many reservoirs in the Middle East bordered by active aquifers, transient water influx is an important recovery mechanism that needs to be modeled correctly. Our experience has shown that the standard grid coarsening and upscaling method do not produce correct results in this situation. Therefore, the objective of this work is to build a method that retains the fine-scale heterogeneities to accurately represent the water movement, but to significantly reduce the computational cost of the aquifer grids in the model.
The new method can be viewed as a modified two-level multigrid (MTL-MG) or a specialized adaptation of the multiscale method. It makes use of the vertical-equilibrium (VE) concept in the fine-scale pressure reconstruction in which it is applicable. The method differs from the standard grid coarsening and upscaling method in which the coarse-grid properties are computed a priori. Instead, the fine-scale information is restricted to the coarse grid during Newton’s iteration to represent the fine-scale flow behavior. Within the aquifer regions, each column of fine cells is coarsened vertically based on fine-scale z-transmissibility. A coarsened column may consist of a single amalgamated aquifer cell or multiple vertically disconnected aquifer cells separated by flow barriers. The pore volume (PV), compressibility, and lateral flow terms of the coarse cell are restricted from the fine-grid cells. The lateral connectivity within the aquifer regions and the one between the aquifer and the reservoir are honored, inclusive of the fine-scale description of faults, pinchouts, and null cells. Reservoir regions are not coarsened. Two alternatives exist for the fine-scale pressure reconstruction from the coarse-grid solution. The first method uses the VE concept. When VE applies, pressure variation can be analytically computed in the solution update step. Otherwise, the second method is to apply a 1D z-line solve for the fine-scale aquifer pressure from the coarse-grid solution.
Simulation results for several examples are included to demonstrate the efficacy and efficiency of the method. We have applied the method to several Saudi Arabian complex full-field simulation models in which the transient aquifer water influx has been identified as a key factor. These models include dual-porosity/dual-permeability (DPDP) models, as well as models with faults and pinchouts in corner-point-geometry grids, for both history match and prediction period. The method is flexible and allows for the optional selection of aquifer regions to be coarsened, either only peripheral aquifers or both the peripheral and bottom aquifers. The new method gives nearly identical results compared with the original runs without coarsening, but with significant reduction in computer time or hardware cost. These results will be detailed in the paper.
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Alpak, F. O., Pal, M., and Lie, K. A. 2012. A Multiscale Adaptive Local-Global Method for Modeling Flow in Stratigraphically Complex Reservoirs. SPE J. 17 (4): 10–56. SPE-140403-PA. https://doi.org/10.2118/140403-PA.
Andersen, O. A., Nilsen, H. M., and Gasda, S. E. 2017. Vertical Equilibrium Flow Models With Fully Coupled Geomechanics for CO2 Storage Modeling, Using Precomputed Mechanical Response Functions. Energy Procedia 114: 3113–3131. https://doi.org/10.1016/j.egypro.2017.03.1440.
Arbogast, T. and Bryant, S. L. 2001. Numerical Subgrid Upscaling for Waterflood Simulations. Presented at the SPE Reservoir Simulation Symposium, Houston, 11–14 February. SPE-66375-MS. https://doi.org/10.2118/66375-MS.
Audigane, P. and Blunt, M. J. 2003. Dual Mesh Method in Upscaling. Presented at the SPE Reservoir Simulation Symposium, Houston, 3–5 February. SPE-79681-MS. https://doi.org/10.2118/79681-MS.
Carter, R. D. and Tracy, G. W. 1960. An Improved Method for Calculating Water Influx. Petroleum Trans., AIME 219: 415–417. SPE-1626-G. https://doi.org/10.2118/1626-G.
Chen, Z. and Hou, T. 2003. A Mixed Multiscale Finite Element Method for Elliptic Problems With Oscillating Coefficients. Mathematics of Computation 72 (242): 541–576. https://doi.org/10.1090/S0025-5718-02-01441-2.
Coats, K. H., Nielsen, R. L., Terune, M. H. et al. 1967. Simulation of Three-Dimensional, Two-Phase Flow in Oil and Gas Reservoirs. SPE J. 7 (4): 377–388. SPE-1961-PA. https://doi.org/10.2118/1961-PA.
Coats, K. H., Dempsey, J. R., and Henderson, J. H. 1971. The Use of Vertical Equilibrium in Two-Dimensional Simulation of Three-Dimensional Reservoir Performance. SPE J. 11 (1): 63–71. SPE-2797-PA. https://doi.org/10.2118/2797-PA.
Fung, L. S. K. and Dogru, A. H. 2008a. Distributed Unstructured Grid Infrastructure for Complex Reservoir Simulation. Presented at the EUROPEC/EAGE Conference and Exhibition, Rome, Italy, 9–12 June. SPE-113906-MS. https://doi.org/10.2118/113906-MS.
Fung, L. S. K. and Dogru, A. H. 2008b. Parallel Unstructured-Solver Methods for Simulation of Complex Giant Reservoirs. SPE J. 13 (4): 440–446. SPE-106237-PA. https://doi.org/10.2118/106237-PA.
Fung, L. S. K. and Du, S. 2016. Parallel-Simulator Framework for Multipermeability Modeling With Discrete Fractures for Unconventional and Tight Gas Reservoirs. SPE J. 21 (4): 1370–1385. SPE-179728-PA. https://doi.org/10.2118/179728-PA.
Du, S., Fung, L. S. K., and Dogru, A. H. 2017a. Accelerating Parallel Field-Scale Reservoir Simulation With Peripheral and/or Bottom Aquifers. Presented at the SPE Middle East Oil Show and Conference, Manama, Bahrain, 6–9 March. SPE-183902-MS. https://doi.org/10.2118/183902-MS.
Du, S., Fung, L. S. K., and Dogru, A. H. 2017b. Dual Grid Method for Aquifer Acceleration in Parallel Implicit Field-Scale Reservoir Simulation. Presented at the SPE Reservoir Simulation Conference, Montgomery, Texas, USA, 20–22 February. SPE-182686-MS. https://doi.org/10.2118/182686-MS.
Hou, T. Y. and Wu, X. H. 1997. A Multiscale Finite Element Method for Elliptic Problems in Composite Materials and Porous Media. J. Comput. Phys. 134 (1): 169–189. https://doi.org/10.1006/jcph.1997.5682.
Jenny, P., Lee, S. H., and Tchelepi, H. A. 2003. Multiscale Finite-Volume Method for Elliptic Problems in Subsurface Flow Simulation. J. Comput. Phys. 187 (1): 47–67.
Jenny, P. and Lunati, I. 2009. Modeling Complex Wells With The Multi-Scale Finite-Volume Method. J. Comput. Phys. 228 (3): 687–702.
Karypis, G. and Kumar, V. 1998. A Parallel Algorithm for Multilevel Graph Partitioning and Sparse Matrix Ordering. Journal of Parallel and Distributed Computing 48 (1): 71–95. https://doi.org./10.1006/jpdc.1997.1403.
Lie, K. A., Møyner, O., Natvig, J. R. et al. 2017. Successful Application of Multiscale Methods in a Real Reservoir Simulator Environment. Comput. Geosci. 21 (5–6): 981–998. https://doi.org/10.1007/s10596-017-9627-2.
Lunati, I. and Lee, S. H. 2009. An Operator Formulation of the Multiscale Finite-Volume Method With Correction Function. Multiscale Modeling & Simulation 8 (1): 96–109. https://doi.org/10.1137/080742117.
Marques, J. B. and Trevisan, O. V. 2007. Classic Models of Calculation of Influx: A Comparative Study. Presented at the Latin American & Caribbean Petroleum Engineering Conference, Buenos Aires, Argentina, 15–18 April. SPE-107265-MS. https://doi.org/10.2118/107265-MS.
Martin, J. C. 1958. Some Mathematical Aspects of Two-Phase Flow With Application to Flooding and Gravity Segregation. Prod. Monthly 22 (6): 22–35.
Martin, J. C. 1968. Partial Integration of Equation of Multiphase Flow. SPE J. 8 (4): 370–380. SPE-2040-PA. https://doi.org/10.2118/2040-PA.
Møyner, O. 2014. Construction of Multiscale Preconditioners on Stratigraphic Grids Presented at the ECMOR XIV—14th European Conference on the Mathematics of Oil Recovery, Catania, Sicily, Italy, 8–11 September. https://doi.org/10.3997/2214-4609.20141775.
Møyner, O. and Tchelepi, H. 2017. A Multiscale Restriction-Smoothed Basis Method for Compositional Models. Presented at the SPE Reservoir Simulation Conference, Montgomery, Texas, USA, 20–22 February. SPE-182679-PA. https://doi.org/10.2118/182679-MS.
Nordbotten, J. M. and Celia, M. A. 2012. Geological Storage of CO2: Modeling Approaches for Large-Scale Simulation. Hoboken, Wiley.
Rame, M. and Killough, J. E. 1992. A New Approach to Flow Simulation in Highly Heterogeneous Porous Media. SPE Form & Eval 7 (3): 247–254. SPE-21247-PA. https://doi.org/10.2118/21247-PA.
Wang, Y., Hajibeygi, H., and Tchelepi, H. A. 2014. Algebraic Multiscale Solver for Flow in Heterogeneous Porous Media. J. Comput. Phys. 259: 284–303. https://doi.org/10.1016/j.jcp.2013.11.024.
Zhou, H., Lee, S. H., and Tchelepi, H. A. 2012. Multiscale Finite-Volume Formulation for Saturation Equations. SPE J. 17 (1): 198–211. SPE-119183-PA. https://doi.org/10.2118/119183-PA.