ISSN 1608-5078 (Online)

##### Pages

##### Download article

Local Refinement of the Super Element Model of Oil Reservoir

*A.B. Mazo, K.A. Potashev*

Original article

open access

In this paper, we propose a two-stage method for petroleum reservoir simulation. The method uses two models with different degrees of detailing to describe hydrodynamic processes of different space-time scales. At the first stage, the global dynamics of the energy state of the deposit and reserves is modeled (characteristic scale of such changes is km / year). The two-phase flow equations in the model of global dynamics operate with smooth averaged pressure and saturation fields, and they are solved numerically on a large computational grid of super-elements with a characteristic cell size of 200-500 m. The tensor coefficients of the super-element model are calculated using special procedures of upscaling of absolute and relative phase permeabilities. At the second stage, a local refinement of the super-element model is constructed for calculating small-scale processes (with a scale of m / day), which take place, for example, during various geological and technical measures aimed at increasing the oil recovery of a reservoir. Then we solve the two-phase flow problem in the selected area of the measure exposure on a detailed three-dimensional grid, which resolves the geological structure of the reservoir, and with a time step sufficient for describing fast-flowing processes. The initial and boundary conditions of the local problem are formulated on the basis of the super-element solution. This approach allows us to reduce the computational costs in order to solve the problems of designing and monitoring the oil reservoir. To demonstrate the proposed approach, we give an example of the two-stage modeling of the development of a layered reservoir with a local refinement of the model during the isolation of a water-saturated high-permeability interlayer. We show a good compliance between the locally refined solution of the super-element model in the area of measure exposure and the results of numerical modeling of the whole history of reservoir development on a detailed grid.

super elements method, numerical simulation, petroleum reservoir, local refinement, reservoir treatments simulation, two phase flow, downscaling

- Aarnes J.E., Kippe V., Lie K.-A. Mixed multiscale finite elements and streamline methods for reservoir simulation of large geomodels. Adv. in Water. Res. 2005. V. 28 (3). Pp. 257-271.
- Arbogast T. Numerical subgrid upscaling of two-phase flow in porous media. Numerical treatment of multiphase flows in porous media. 2000. V. 552 of Lecture Notes in Phys. Berlin: Springer. Pp. 35-49.
- Beliaev A.Yu. Averaging in problems of the theory of fluid flow in porous media. Moscow: Science. 2004. 200 p. (In Russ.)
- Bulygin V.Ya. Hydromechanics of the oil reservoir. Moscow: Science. 1974. 232 p. (In Russ.)
- Bulygin D.V., Mazo A.B., Potashev K.A., Kalinin E.I. Geological and technical aspects of super element method of petroleum reservoir simulation. Georesursy = Georesources. 2013. No. 3(53). Pp. 27-30. (In Russ.)
- Bulygin D.V., Mardanov R.F. Three-dimensional visualization of complex oil and gas reservoirs. Certificate of state registration of the computer program No. 2007612386. 06/07/2007. (In Russ.)
- Daigle H., Dugan B. Extending NMR data for permeability estimation in fine-grained sediments. Marine and Petroleum Geology. 2009. V. 26. Pp. 1419-1427.
- Durlofsky L.J. Coarse scale models of two phase flow in heterogeneous reservoirs: volume averaged equations and their relationship to existing upscaling techniques. Computational Geosciences. 1998. V. 2. Pp. 73-92.
- Dykstra H. and Parsons R.L. The Prediction of Oil Recovery by Waterflooding. Secondary Recovery of Oil in the United States. Smith J. Second edition. API. New York. 1950. 160 p.
- Efendiev Y., Ginting V., Hou T., and Ewing R. Accurate multiscale finite element methods for two-phase flow simulations. J. Comput. Phys. 2006. V. 220 (1). Pp. 155-174.
- Eymard R., Gallouet T., Herbin R. Finite Volume Methods. Handbook of Numerical Analysis. North Holland. 2000. Pp. 713-1020.
- Gautier Y., Blunt M.J., and Christie M.A. Nested gridding and streamline-based simulation for fast reservoir performance prediction. Comput. Geosci. 1999. V.3 (3-4). Pp. 295-320.
- Jenny P., Lee S., and Tchelepi H. Adaptive fully implicit multi-scale finite-volume methods for multi-phase flow and transport in heterogeneous porous media. J. Comput. Phys. 2006. V. 217 (2). Pp. 627-641.
- Kozeny J. Ueber kapillare Leitung des Wassers im Boden. Aufstieg, Versickerung und Anwendung auf die Bewaesserung. Sitzungsberichte der Akademie der Wissenschaften in Wien. 1927. 136. Pp. 271-306.
- Mazo A.B., Bulygin D.V. Superelements. New approach to oil reservoir simulation. Neft. Gaz. Novatsii. 2011. No. 11. Pp. 6-8. (In Russ.)
- Mazo A.B., Potashev K.A. (а) Absolute permeability upscaling for a super-element oil reservoir model. Matematicheskoe modelirovanie. 2017. V. 29 (6). Pp. 89-102. (In Russ.)
- Mazo A.B., Potashev K.A. Upscaling of absolute permeability for a super-element model of petroleum reservoir. IOP Conference Series: Materials Science and Engineering. 2016. 158 (012068). Pp. 1-6. (In Russ.)
- Mazo A.B., Potashev K.A. (b) Upscaling of relative phase permeabilities for superelement modeling of petroleum reservoir. Matematicheskoe modelirovanie. 2017. V. 29 (3). Pp. 81-94. (In Russ.)
- Mazo A.B., Potashev K.A., Baushin V.V., Bulygin D.V. Numerical Simulation of Oil Reservoir Polymer Flooding by the Model of Fixed Stream Tube. Georesursy = Georesources. 2017. V. 19. No. 1. Pp. 15-20.
- Mazo A.B., Potashev K.A., Bulygin D.V. DeltaIntegra. Super element model of oil reservoir. Certificate of state registration of the computer program No. 2012660559. 11/23/2012. (In Russ.)
- Mazo A., Potashev K., Kalinin E.. Petroleum reservoir simulation using Super Element Method. Procedia Earth and Planetary Science. 2015. V. 15. Pp. 482-487. (In Russ.)
- Mazo A.B., Potashev K.A., Kalinin E.I., Bulygin D.V. Modeling the petroleum deposits using the superelement method. Matematicheskoe modelirovanie. 2013. V. 25 (8). Pp. 51-64. (In Russ.)
- Mardanov R.F., Bulygin D.V. DeltaIntegra. Construction of a three-dimensional geological model. Certificate of state registration of the computer program No. 2012660561. 11/23/2012. (In Russ.)
- Panfilov M.B., Panfilova I.V. Averaged models of fluid flow in porous media with an inhomogeneous internal structure. Moscow: Science. 1996. 383 p. (In Russ.)
- Pergament A.Kh., Semiletov V.A., Tomin P.Yu. On Some Multiscale Algorithms for Sector Modeling in Multiphase Flow in Porous Media. Mathematical Models and Computer Simulations. 2011. V.3 (3). Pp. 365‑374. (In Russ.)
- Potashev K. The Use of ANN for the Prediction of the Modified Relative Permeability Functions in Stratified Reservoirs. Lobachevskii Journal of Mathematics. 2017. V. 38 (5). Pp. 843-848.
- Potashev K.A., Abdrashitova L.R. Account for the heterogeneity of waterflooding in the well drainage area for large-scale modeling of oil reservoir. Uchenye zapiski Kazanskogo universiteta. Serija fiz.-mat. nauki. 2017. 159 (1). Pp. 116-129. (In Russ.)
- Potashev K.A., Mazo A.B., Ramazanov R.G., Bulygin D.V. Analysis and design of a section of an oil reservoir using a fixed stream tube model. Neft’. Gaz. Novacii. 2016. V. 187 (4). Pp. 32-40. (In Russ.)
- Stiles W.E. Use of Permeability Distribution in Waterflood Calculations. J. Petrol. Technol. 1949. V. 1 (1). Pp. 9-13.
- Yang Y., Aplin A.C. Permeability and petrophysical properties of 30 natural mudstones. Journal of Geophysical Research B: Solid Earth. 2007. V. 112 (3). Pp. 1-14.

Kazan Federal University, Kazan, Russia

#### For citation:

Mazo A.B., Potashev K.A. Local Refinement of the Super Element Model of Oil Reservoir. Georesursy = Georesources. 2017. V. 19. No. 4. Part 1. Pp. 323-330. DOI: https://doi.org/10.18599/grs.19.4.4