Scaleup of reservoir-model relative permeability with a global method

Geoscientists and engineers commonly build geologic or geostatistical reservoir models that contain more than 10(6) grid cells. For flow simulation, 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 restored through the use of effective or pseudorelative permeabilities. This paper describes an approach to generate such functions that, when combined with global absolute permeability scaleup,(1) offers a significant improvement over existing ''dynamic pseudo'' methods that require extensive fine-grid simulation and that are very sensitive to flow conditions.(1) The method builds on previous work to scale up absolute permeability through a global technique that minimizes the loss of permeability variance and the spatial correlation in an unequally sized grid system. This paper shows that, when the residual permeability following global absolute permeability scaleup is spatially uncorrelated, the velocity of a fluid-displacement shock front correlates with a well-defined universal heterogeneity number that is related to the permeability distribution. The paper presents an analytic computation of the pseudo as a superposition of the shock velocities for the residual field, found from a table look-up, and the fine-grid field when the fine-grid relative permeabilities (usually based on measured relative permeabilities) have the same normalized form. The method is then generalized to multiple functional forms of fine-grid-cell relative permeabilities with new relative permeability and capillary pressure averaging methods. The procedure eliminates the need for fine-scale simulation and is equally applicable to geologic deterministic or stochastic models. The paper describes the technique in detail and demonstrates the procedure with one two-dimensional (2D) and one three-dimensional (3D) reservoir model waterflood simulation. In the latter case, the number of cells is reduced from 23,600 (fine scale) to 4,000 (coarse scale) with very little change in the water breakthrough and water-cut behavior.