A.B. Mazo*, K.A. Potashev**
Kazan Federal University, Kazan, 420008 Russia
E-mail: * ABMazo1956@gmail.com, ** KPotashev@mail.ru
Received June 21, 2017
Abstract
In this paper, we propose a two-stage method for petroleum reservoir simulation. The method uses two models with different degrees of detailization to describe the hydrodynamic processes of different space-time scales. At the first stage, the global dynamics of the energy state of the deposit and reserves has been 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 have been calculated using special procedures of upscaling of absolute and relative phase permeabilities. At the second stage, a local refinement of the super-element model has been 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 have been formulated on the basis of the super-element solution. To demonstrate the proposed approach, we have provided 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 have shown a good compliance between the locally refined solution of the super-element model.
Keywords: super-element method, numerical simulation, petroleum reservoir, local refinement, reservoir treatments simulation, two-phased flow, downscaling
Acknowledgments. The study was supported by the Russian Foundation for Basic Research and the Government of the Republic of Tatarstan (projects nos. 15-41-02698 and 15-41-02699).
Figure Captions
Fig. 1. The dynamics of well water-intake capacity at the instant change of bottom-hole pressure: ? – from the solution of equations (5), (6), solid line – from the solution of equations (5), (7).
Fig. 2. The bottom-hole pressure dynamics in the well at the instant change of water-intake capacity: ? – from the solution of equations (5), (6), solid line – from the solution of the equations (5), (7).
Fig. 3. The projection of on the horizontal plane of the model oil deposit with isolation along the oil-bearing contour.
Fig. 4. Super-element grid coverage of the oil-deposit area, the area of model refinement (on the left) and its coverage by the detail grid (on the right).
Fig. 5. The distribution of saturation in the section of the oil bed as of January 2006 based on the model of the whole oil deposit (on the left), based on the local SEM refinement (on the right).
Fig. 6. The calculated open flow of well no. 52: 1 – accurate solution, 2 – SEM, 3 – SEM with refinement.
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For citation: Mazo A.B., Potashev K.A. Petroleum reservoir simulation using super-element mMethod with local detalization of the solution. Uchenye Zapiski Kazanskogo Universiteta. Seriya Fiziko-Matematicheskie Nauki, 2017, vol. 159, no. 3, pp. 327–339.5. (In Russian)
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