Scale-Up Of Reservoir Model Relative Permeability Using A Global Method
- D. Li (Mobil E&P Technical Center) | A.S. Cullick (Mobil E&P Technical Center) | L.W. Lake (University of Texas at Austin)
- Document ID
- Society of Petroleum Engineers
- SPE Reservoir Engineering
- Publication Date
- August 1996
- Document Type
- Journal Paper
- 149 - 157
- 1996. Society of Petroleum Engineers
- 5.6.3 Deterministic Methods, 5.5.2 Construction of Static Models, 5.4.9 Miscible Methods, 4.3.4 Scale, 5.2 Reservoir Fluid Dynamics, 5.1 Reservoir Characterisation, 5.6.4 Drillstem/Well Testing, 5.1.5 Geologic Modeling, 5.5 Reservoir Simulation, 5.4.1 Waterflooding, 5.3.2 Multiphase Flow
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Geoscientists and engineers commonly build geologic or geostatistical reservoir models that contain more than 106 grid cells. For flow simulation the number of grid cells must be reduced by a factor of ten or more. Such scaling up necessarily involves a loss of information that must be restored through the use of effective or pseudo relative permeabilities. This paper describes an approach to generate such functions that, when combined with global absolute permeability scale-up, offers a significant improvement over existing "dynamic pseudo" methods that require extensive fine-grid simulation and that are very sensitive to flow conditions.
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 scale-up 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 simulations. 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.
Advanced reservoir characterization techniques can now describe a petroleum reservoir in great detail with millions of fine-grid cells, each populated with porosity, permeability, fluid saturation, and relative permeability and capillary pressure functions. However, reservoir simulation must be performed with a factor of ten or fewer simulation grid cells. Scale-up of the fine-grid reservoir model to a coarse-grid simulation model which preserves as much as possible the fluid flow performance is needed. For a multi-phase flow process, e.g. waterflooding, scale-up of the saturation-dependent functions relative permeability and capillary pressure are critical to accurate model scale-up.
Earlier relative permeability scale-up work concentrated on reducing simulation model dimensionality. For example, Coats et al. used the vertical equilibrium concept to calculate pseudo relative permeability and capillary pressure for two-dimensional simulation of three-dimensional reservoir models. Jacks et al. introduced dynamic pseudos, which are applicable over a wide range of flow rates and over the complete range of fluid saturations, and that are determined by using detailed simulations.
Kyte and Berry extended the dynamic pseudo concepts to account for both dimension reduction and areal scale-up.
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