A New Efficient Averaging Technique for Scaleup of Multimillion-Cell Geologic Models

Abstract

Increased resolution in reservoir characterization is driving the need for efficient and accurate upscaling techniques for reservoir simulation on which reservoir performance prediction relies. Unfortunately, the existing averaging methods (i.e. harmonic, arithmetic, power law, geometric or a combination of harmonic and arithmetic methods) are only applicable under the circumstances of perfectly layered or perfectly random heterogeneity distributions, which realistic reservoirs are not. This paper presents a new averaging method that improves the upscaling averaging methods for realistic reservoirs and can substitute for the orders-ofmagnitude slower performance of direct simulation methods, such as pressure solver techniques. The new averaging method first calculates the upper and lower bounds of the effective properties based on the nature of geology and then employs a new correlation, scaling, and rotation technique to estimate the effective properties for the upscaled grid. The approach not only preserves the accuracy of the time consuming simulation methods but also retains the speed of the traditional averaging methods. Five real sandstone and carbonate reservoir geologic models (of which, three of them are multimillion cell models) from Africa, North America, and South America were employed as benchmark and working data sets to develop and validate the new technique. The technique has the advantage of suiting the more irregular geometries i.e. pinchouts, faults, and flexible simulation grids compared to the pressure solver methods which are more suited for relatively simple flow geometries.

Analytical Upgridding Method to Preserve Dynamic Flow Behavior

“…The first step involves design -that is, to determine how to combine various grid blocks so that characteristics of fine scale can be preserved (We call this upgridding) and the second step involves determining the effective properties of combined grid blocks so as to preserve flow characteristics. There have been several papers regarding both upgridding (Testerman 1962, Stern 1999, Li 2000 and calculating the effective properties (Peaceman 1997, Li 1999, Zhang 2006. This paper concentrates with the problem of the upgridding and derivations are based on single phase flow assumptions.…”

“…We do believe that finding the correct effective property is an important step in upscaling process and sometimes can have substantial impact on the ability to reproduce the results of the fine scale model. It is also possible that by defining effective transmissibilities (Li 1999), we may be able to better capture the dynamic results of the fine scale model. In our method we use arithmetic average for K x and K y and harmonic average for K z to find the coarse grid model properties.…”

Duality-based adaptivity in finite element discretization of heterogeneous multiscale problems

“…Warren & Price [49]). For a detailed discussion as well as an overview of newer, more sophisticated averaging methods we refer to Li et al [36] and references therein.…”

Sensitivity-based upscaling for history matching of reservoir models

“…Most of the averaging techniques (arithmetic, harmonic, geometric, power law, pressure solver) are only appropriate under the circumstances of perfectly layered or heterogeneous distributions that are perfectly random and seldom observed in realistic reservoir descriptions. Another method of upscaling is an averaging technique that first computes the lower and upper bounds of the effective properties, based on geology, and then uses a new correlation and scaling technique to estimate the effective properties for the upscaled grid (Li et al 2001). Purely local upscaling methods consider only those finescale grids that are combined in the target coarse-scale grid (Durlofsky 1991;King and Mansfield 1999).…”