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^

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