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Numerical modelling of the dynamic process of oil displacement by water in sandstone reservoirs with random pore structures
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Abstract: In order to maintain the production rate of a reservoir and improve the displacement efficiency, it is crucial to have an in-depth understanding of the process of oil displacement by water. However, with respect to the conceptualization of porous media of a reservoir, very limited efforts have been made to the pore structures inside the reservoirs. In this paper, the pore structures of a sandstone reservoir were generated by using the method of random growth algorithm. Based on the randomly generated model, a theoretical model to describe the dynamic process of oil displacement by water in the sandstone reservoir was established, and then corresponding numerical modelling was performed. The effects of the displacement velocity, the viscosity ratio of oil-water phase and the porosity of reservoirs on the displacement performance were also analyzed. Results show that due to a great difference in the viscosity between oil and water phases, the moving interface of water phase is not uniform, and the viscous fingering occurs, tending to proceed along the direction with the minimum flow resistance. There is not a linear relationship between the displacement velocity and the displacement efficiency. Too high displacement velocities do not lead to much better displacement efficiency, while a higher pressure drop is caused. Choosing a proper displacement velocity is indispensable in practical engineering. A lower oil-water viscosity ratio is more favorable to obtain high displacement efficiency. Under the present simulation conditions, when the viscosity ratio is 1.2, the displacement efficiency reaches 96.2% at a moderate Reynolds number. The porosity is not a sole factor determining the displacement performance. Even for the same porosity, the shape and length of preferential flow paths are different and randomly distributed, causing a different displacement performance. A large tortuosity tends to result in a low hydraulic conductivity and displacement efficiency.
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Figure 1. Eight growth directions of each cell for randomly-generated 2-D porous media
Figure 3. Comparison of the outlet oil phase saturation between the simulation and experimental results
Figure 4. Comparison of simulation results under different sizes of computational domain
Figure 5. Distribution of water phase during the process of oil displacement (Re=14.8)
Note: The white, red and blue colours represent the matrix of the reservoir, the water phase and the oil phase, respectively, and the transition zone of water-oil phase is shown as the green or yellow colour.
Figure 6. Variations of the pressure drop and the saturation of oil phase between the inlet and outlet under different displacement velocities of water phase
Figure 7. Variations of the pressure drop and the saturation of oil phase between the inlet and outlet under different viscosity ratios of oil-water phase
Figure 8. Variations of the pressure drop and displacement efficiency with oil-water viscosity ratios
Figure 9. Distribution of oil phase at 180 s during the process of oil displacement (Re=58.7)
Figure 10. Variations of the average velocity of water and oil phase under different porosities
Figure 11. Variations of the pressure drop and the saturation of oil phase between the inlet and outlet under different porosities
Figure 12. Fine throats along preferential flow paths (Φ=0.384) and variations of tortuosity with porosity of porous media with random pores
Table 1. Major physical parameters for simulation
Item Unit Value Item Unit Value Water density kg/m3 1000 Water viscosity Pa·s 0.001 Oil density kg/m3 900 Oil viscosity Pa·s 0.048 Sandstone density kg/m3 2500 Sandstone porosity - 0.327 Surface tension N/m 0.035 Initial saturation - 1.0 
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Table 2. Parameters for different simulation situations
No Porosity Oil-water viscosity ratio Re number 1 0.327 48 14.8, 29.4, 58.7, 73.4, 95.4 2 0.327 1.2, 26, 48, 70 58.7 3 0.327, 0.351, 0.384 48 58.7
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Table 3. Displacement efficiency under different Re numbers of water phases
Item Re =14.8 Re =29.4 Re =58.7 Re =73.4 Re =95.4 Displacement efficiency(%) 65.2 69.7 74.3 77.0 79.0
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