Geostatistical Reservoir Characterization and Scale-Up of Permeability and Relative Permeabilities




Malik, Mohammad Abdul

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In this dissertation several unresolved issues related to reservoir characterization and simulation techniques are investigated so that improvements can be made in their reliability and efficiency. Geostatistical techniques are now commonly used to generate interwell permeability distributions. However, these techniques have not been adequately validated because of scarcity of reference or truth cases for subsurface reservoirs. This study uses detailed deterministic permeability distributions, and corresponding fluid-flow results from an outcrop study as a reference case, to validate stochastic permeability distributions generated by conditional simulation (CS). Only as much data from the outcrop are used as would normally be available in a subsurface reservoir. This is a first of its kind test on the reliability of stochastic permeability distributions. Results indicate that, although CS is highly flexible and generates realistic heterogeneity, it must be adapted to the specific geologic environment for best agreement with deterministic simulations.The reliability of a stochastic permeability distribution depends upon the correct statistical analysis of available data and careful inference of statistical parameters. This study uses core permeability data from an actual producing field to generate a three-dimensional CS permeability distribution. This example serves as a model with practical details for data evaluation, determination of autocorrelation structure and generation of multiple realizations of permeability distribution. The CS permeability distributions are evaluated for their conformity with reservoir geology so that the most realistic realizations can be selected. Millions of fine-scale blocks are required to adequately represent heterogeneity in a typical field. Because fluid-flow simulations on such a large number of blocks are still prohibitively expensive, fine-scale permeability distributions must be scaled-up. This work applies four methods for independent scale-up, of permeability from fine to a practical field-simulation scale. These methods include independent fine-scale simulation (IFS), the electrical network method (ENM), geometric averaging (GA) and the Cardwell-Parsons (CP) method. Permeability is also scaled-up by a dependent fine-scale simulation (DFS) scheme that acknowledges flow through neighboring coarse blocks in the process. Results from independent scale-up of realistic CS permeability cross sections show that IFS is an overall preferable method because of good accuracy and flexibility in application. Especially in low-permeability blocks, IFS and DFS estimates of scaled-up permeability can be significantly different. Closely related to permeability scale-up is the treatment of relative permeability. Laboratory-measured relative permeabilities or rock curves are assumed to apply to fine-scale simulations but they may or may not be applicable in a coarse-scale field simulation. In this research, relative permeabilities are scaled-up by steady-state as well as dynamic fluid-flow simulations. Results show that steady-state scaled-up curves are vii almost the same as the rock curves, while dynamic scaled-up curves are different. Comparison of results from fluid-flow simulations from fine and corresponding coarse cross sections shows that rock curves perform better than dynamic scaled-up curves in coarse simulations, provided the dimensions of the problem are not reduced (2D cross section remains 2D after scale-up) and adequate heterogeneity is retained in the scaled-up field. The small difference in effluent-water fractional flow results from fine and coarse simulations with rock curves appears to be caused by increased numerical dispersion in the coarse simulations.


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