To obtain a reliable characterization of complex reservoirs, geoscientists and petroleum engineers commonly build geologic or geostatistical reservoir models which contain more than a million grid cells. However, for flow simulation such a detailed description demands a great deal of information and processing time. Therefore, less complex models are usually preferred where the number of grid cells must be reduced by a factor of 10 or more. Such scaling up necessarily involves a loss of information that must be captured through upscaling porosity permeability and the use of pseudofunctions. The main objective of this paper is to determine a general methodology for using pseudofunctions for upscaling multiphase flow in 3D anisotropic heterogeneous reservoirs with different capillary and gravity numbers and applying the method to a real field case "Hassi Messaoud Field - Algeria"

The performance of different kinds of pseudofunctions is evaluated under different capillary and gravity numbers, and upscaling levels. A variety of homogeneous fine grid models representing different existent flow regimes were considered in this study and the performance of several pseudofunction methods was compared. All the pseudo function methods succeeded in reproducing the fine grid water cut and oil production plateau for the capillary dominated, equilibrium, viscous dominated flows, however, for the gravity dominated flow they failed to match the fine grid curve exactly. Although this shortcoming of the pseudofunction curves gives better results than the rock curves.

Next in this study, the results of the waterflood of a heterogeneous 3-D model of HMD Zone 17 are presented. This real field model confirmed the homogeneous case results: for high flow rates the pseudofunctions can be applied successfully to upscale from fine to coarse grid simulation.


As the clock is ticking geostatistical models scales are becoming finer and finer. Unfortunately the development of reservoir flow simulators is not moving at the same pace to handle such a large fine scale model. A revolution in the computational hardware or modification to the way the simulation is done is, therefore, necessary. A typical grid block size is 100 m areally and 1–10 m vertically. Such a large grid block may include a lot of heterogeneity. If we use rock curve for simulation with such large grid blocks, the important effects of heterogeneity will be omitted. Large simulation grid blocks will also cause large numerical dispersion. So, under such circumstances, dynamic pseudo functions are needed to replace the rock curves. Through the use of dynamic pseudo functions, one attempts to capture the effects of heterogeneity below the scale of a simulation grid block, and reduce the effects of numerical dispersion. One common use of pseudo functions is to reduce the number of grid blocks used in the simulation, and sometimes even reduce the dimension of the problem, such as reducing a 3-D field case model to a 2-D cross-sectional model. By doing so, we hope to retain fine grid information while performing coarse grid simulations.

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