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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.

Geophysicists, geologists, and reservoir engineers can now routinely build reservoir geologic models with ten million geologic cells and more than one thousand geologic layers. This explosion in reservoir detail capability presents new challenges for existing upscaling methods. Uplayering (the first step of upscaling) is a technique that provides reservoir engineers with optimal geologic layer-grouping schemes for simulation model construction. Much uplayering is still done by hand by reservoir engineers. Even though some advanced methods can provide automatic tools for uplayering, they are limited in the applicable model size and are also computationally expensive. This paper presents a practical and efficient method for uplayering of multimillion-cell geologic models. The proposed method defines a displacing front conductivity, a combination of porosity, permeability, and facies (in terms of relative permeability, endpoint saturation, and various facies rules), as the uplayering property. Use of the new property ensures that the most important geologic features for fluid flow simulation can be preserved after uplayering. The new method utilizes a residual optimization technique to determine the optimal geologic layer-grouping scenario for a given number of simulation layers. The method is so efficient that multiple optimal grouping scenarios, from the one simulation layer model to the model consisting of all geologic layers, can be generated in a short time, allowing the inspection of all possible combinations of layer-grouping scenarios. A residual curve (the difference of the defined property between the fine-layer and coarse-layer models) is produced from exhaustive analysis of all possible layering combinations. Using the residual curve, engineers are able to determine the number of simulation layers needed based on their tolerance of possible loss of fine-layer geologic features. The uplayering method has been successfully employed in most of recent major reservoir study projects in Mobil and results from three of these studies will be included in this paper. Introduction Simulating a petroleum reservoir directly using multimillion-cell to multibillion-cell geologic models challenges reservoir modeling resources, on both hardware and software. Due to parallel computing techniques, the most advanced reservoir simulators (existing or under development) in the petroleum industry now can handle up to several million cells by using more than one hundred CPUs. Theoretically, one can simulate multimillion to multibillion cells if enough (hundreds to thousands) CPUs are dedicated to reservoir simulation. Unfortunately, reservoir engineers may always find themselves one step behind geologic modeling techniques in terms of the size of a model. This is due, in part, to the fact that geologic models are constructed using static, algebraic systems while reservoir simulation systems are dynamic solutions of partial differential equations. While reservoir engineers are trying hard to simulate multimillion cell models, geologists are building multibillion cell geologic models. The major challenge for reservoir flow modelers is to simulate a reservoir efficiently without a significant loss of reservoir heterogeneities and geologic features. Upscaling provides a solution for this challenge.

Upscaling is necessary because important information about the reservoir is obtained on scales that are finer than the gridblocks of the reservoir simulation. This paper has three themes addressing issues in efficient upscaling: - An overview of simulation model building and hierarchical modeling.–Assessing the effectiveness of simple averaging methods over direct pressure solution upscaling techniques for single- and two-phase flow.–A fast upscaling method for relative permeability that accounts for rate dependence. In theory, one could construct a reservoir model on the core-plug scale. To use this model, one would need to upscale this to a scale suitable for the various types of simulation. This would produce a representation of the reservoir properties of each gridblock. This is not feasible, however, because of the huge memory and processing requirements. The proposed solution, then, is to construct hierarchical models. The translation of fine-scale geostatistical models to more coarsely gridded flow models involves two steps: gridding and upscaling The procedure consists of (1) upgridding, where the main emphasis is to obtain coarse-level gridblocks with minimum subgrid variability and maximum population variability, i.e., as close as possible to the underlying fine-scale variability and (2) upscaling, that incorporates small-scale structure (e.g., permeability and relative permeability are measured at this fine scale) and obtains effective properties in multiple steps on the grid arrived at in (1). Starting at the core scale, a relatively small number of rock types is constructed from core. The effective medium properties of these are determined by numerical simulation. At the next scale, a relatively small number of rock types is constructed from the types at the smaller scale and the upscaled properties are calculated. This process is repeated until the scale of the geological model is reached. At this scale, each block can have different properties from the other blocks, but the blocks still have a well-defined rock type. Orders-of-magnitude reduction in the amount of processing and storage required are thus gained. The effectiveness of averaging techniques was also examined and was found to closely match direct- pressure-solution for the unfractured sandstone reservoirs that were studied. The robustness, accuracy, and speed of two-phase upscaling have been tested by scaling up petrophysical properties in a spatially periodic, mixed-wet, heterogeneous rock and applied to realistic reservoir descriptions. The aim is to accurately represent the properties in the flow simulation model, the results of which are used for economic decisions. To gain the speed and accuracy required when upscaling relative permeability, a balanced set of analytical and numerical approximations were used. Inexpensive asymptotic low- and high-rate 3-D calculations are combined with rate-dependent 1-D calculations to interpolate the 3-D calculations to form a new method: the aw method. 1.0 Introduction This paper has three themes. First, an overview of the issues involved in building a reservoir model by integrating core-level data with geological models at the scale of several meters is given. P. 257^

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-of-magnitude 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.