### Potashev K.A. Mazo A.B.

## Modifying of Relative Phase Permeability Functions for Two-Phase Flow Problem Solving by Superelement Method

### Reporter: Potashev K.A.

Upscaling method for relative phase permeabilities functions (RPP) is formulated. Result of such procedure minimizes the error of phase flow rates approximation at superelement simulation of oil reservoir [1]. A feature of this simulation is to perform calculations on large unstructured meshes with the areal size of the blocks (superelement, SE), comparable to the distance between the holes (hundreds of meters). The vertical size of SE corresponds to the thickness of the reservoir consisting of several layers (tens of meters).

RPP upscaling is performed based on solving a series of two-dimensional problems on a detailed grid. To construct the modified RPP functions (MRPP) proposed a special functional form of dependencies. These coefficients are found by minimizing the functional of differences between averaged and approximated phase velocities at the sites corresponding to the faces of SE.

The case of layered oil reservoir is discussed. The effectiveness of the MRPP application demonstrated at example superelement modeling of the three-dimensional two-phase filtration problems in the reservoir sector developed by the system of injection and production wells. The comparison with the upscaling procedure, neglecting vertical cross flow between the layers [2], is perfomed.

The work was supported by the RFBR and the Government of the Republic of Tatarstan (No. 15-41-02698), BP Exploration (№ 063100027).

REFERENCES

1. Mazo A.B., Potashev K.A., Kalinin E.I., Bulygin D.V. Oil reservoir simulation by superelement method // Mathematical modeling. 2013. V. 25, No. 8. P. 51-64. (In Russian. Modelirovanie razrabotki neftianykh mestorozhdeniy metodom superelementov).

2. Potashev K.A. Upscaling of relative phase permeabilities in noncommunicated layered reservoir // Uchenye zapiski kazanskogo universiteta. Physical-mathematical sciences series. 2014, V. 156 (2). – P. 120-134. (In Russian. Upscaling otnositelnykh phazovykh pronitsaemostei v nesoobschauschemsja sloistom plaste).

To reports list