Connectivity-Constrained Upscaling
Authors: Gajraj Allyson , Lo Tak Sing , Chopra Anil K. 
Published: December 2007

Abstract
The use of upscaling prior to reservoir simulation studies is a common practice, because of the prohibitively high cost of performing high resolution, full-field simulations. In fact, the resolution of the grid may be also limited by the capabilities of the hardware. Invariably, upscaling is undertaken without consideration of the degree of connectivity of the reservoir to the wellbore A new technique is presented in which the discretized fine scale reservoir description is screened using a reservoir connectivity measure prior to performing the upscaling and the theory is presented to validate its appropriateness and accuracy for upscaling reservoirs in which the reservoir connectivity is less than 100%.
The new upscaling approach is applied to a gas reservoir system. Traditional upscaling techniques, such as a pressure solver, are also applied to the fine scale reservoir description and the different sets of upscaled grids are flow simulated — along with the fine scale description. The results of this new upscaling approach are shown to be significantly more accurate in providing an upscaled grid system which more closely approximates the simulation behavior of the fine scale grid.
This methodology has been shown to be applicable to the case of primary recovery from gas reservoirs and, while it has not been tested with more complex recovery mechanisms such as waterflooding, the theory is robust enough that it should be generally applicable as an upscaling technique in which reservoir connectivity is an issue.

Introduction
With current technology and with the much-acclaimed multidisciplinary reservoir management approach, it is now possible to integrate geophysical, geological and reservoir engineering data through geostatistical modeling to create multiple detailed or fine scale reservoir descriptions which honor all these diverse conditioning data sets. These descriptions, insofar as they honor the conditioning data and their statistics, may be considered representative of the underlying reality of the reservoir under study. The objective of creating these descriptions is usually for developing bounds on the uncertainty of the future performance of the reservoir. The accepted methodology for measuring the reservoir performance is the flow simulator. Unfortunately, as alluded to above, this technology is still limited in its capabilities, such that the geostatistical descriptions are typically too large to be easily flow simulated. Table 1 illustrates quite clearly the justification for the use of upscaling: there is a limit on the number of gridblocks we may use for flow simulation for a given computer hardware configuration. Hence there is a need for representative upscaling; i.e. upscaling such that the coarse scale description behaves closely to that of the fine scale one. In a reservoir which is 100% connected, connectivity (defined below) is not an issue in the upscaling Should the reservoir be less than completely connected however, then it becomes important to factor in connectivity into the upscaling Several authors have acknowledged the importance of connectivity in reservoir performance. Alabert and Massonnat have noted that the connectivity of permeable rocks is of major concern for field exploitation and performance forecasting. Thus careful and realistic modeling of connectivities is required to plan future developments, understand and forecast well behaviors and to improve oil recovery. Handyside et al. concurred by stating that an assessment of the impact of sand discontinuities or connectivities in the reservoirs is required for realistic performance predictions and estimation of associated
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