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Abstract
Linking a fine-scale geologic description to a coarse-scale reservoir simulation model requires accurate and efficient scale-up. Advanced techniques are necessary to construct reservoir models that incorporate geologic and production data gathered at different scales.

In this paper, we present a new global scale-up technology for calculating effective permeability and/or transmissibility and its applications to reservoir modeling. This technology involves using global flow solutions on the fine-scale model to improve scale-up accuracy and reusing them to improve scale-up efficiency for re-gridded coarser models.

Global scale-up was initially proposed about 20 years ago [1]. Its potential benefits have been demonstrated for simple models in the literature. Until now, significant technical challenges associated with applying global scale-up to real reservoir models have prevented its adoption by the industry. Real reservoir models are often characterized by complex geometry and connectivity, caused by faults, pinch-outs, and flow barriers. Here, we present industry's first commercial global scale-up technology that overcomes these difficulties.

Our studies show that the new global scale-up technology leads to significant improvements in scale-up accuracy. Our global scale-up method preserves complex fine-scale connectivity much more accurately than the industry-standard, local scale-up methods. Moreover, the reuse of flow solutions makes it very efficient to scale-up a fine-scale reservoir model to different coarse-scale models. These advantages enable us to build more accurate reservoir models at different scales and optimize these models for different business objectives. Several applications of global scale-up to the reservoir modeling are presented.

Introduction
Reservoir modeling involves integrating all available geologic and engineering information that are known to or believed to affect the flow behavior in a reservoir. Static reservoir models, i.e., rock property models, are constructed using data measured at different resolutions and covering different vertical and lateral extents. For example, core analysis describes rock property at centimeter scale and covers a large vertical extent of a reservoir. Seismic data provides indirect rock property measures and covers large lateral and vertical extents; however, it lacks vertical resolution. In addition to measured data, geologic concepts at multiple scales are used in building reservoir models. These concepts are required to interpolate the sparse, measured data to fill the 3D model space.

In most reservoirs, rock properties are heterogeneous over many spatial scales and therefore, they are scale dependent. This makes it difficult to consistently incorporate rock property data measured at 0.01~1 meter scale into reservoir models with cell sizes of 50 to 100s of meters. Therefore, an accurate scale-up is required to bridge this wide gap. Often, scale-up needs to be performed recursively at intermediate scales before fine-scale data can be brought into coarse-scale models (see e.g., [2-4]).

Permeability, a key rock property which directly affects the flow, is particularly challenging to model since coarse-scale permeability relates to fine-scale permeability through Darcy's flow and cannot be accurately calculated using simple averages of the fine-scale permeability. Therefore, flow-based scale-up has been widely used in the industry for modeling permeability at different scales. Simply put, the procedure entails solving flows in a volume of interest, e.g., a gridblock, and using the flow solutions to calculate the "effective" permeability of that volume, see [5] for a recent review of development in this area.

In the following, we present an overview of a global scale-up technology, we recently developed [4], and its applications to reservoir modeling.

Global Scale-up
Different from standard flow-based scale-up, global scale-up uses flow solutions obtained in the entire model domain to calculate effective permeability on a set of volumes of interest (e.g., gridblocks) in the domain. In contrast, standard local scale-up methods use flow solutions calculated from local boundary conditions imposed on each individual volume of interest. In this section, we explain the rationale behind global scale-up, then we review our global scale-up procedure and the technology required for its commercial applications.