Scaling and Upscaling of Fluid Flow Through Permeable Media

by
Dachang Li, Ph.D.

University of Texas at Austin, 1995
Supervisor: Larry W. Lake

This dissertation presents a general procedure of inspectional analysis that derives the minimum number of the most succinct form of independent dimensionless groups. Two new geostatistic tools, a moving window semi-variance estimator and a type curve approach to estimating p for a p-normal transformation, have been developed to provide more precise reservoir heterogeneity description. Based on inspectional analysis and geostatistic techniques, this dissertation presents, for the first time, a general method to scale immiscible and miscible flows through heterogeneous permeable media. The concepts of heterogeneity and scale have been clarified , and heterogeneity scaling groups have been separated from flow scaling groups. The causes of the inefficiency for the East Velma West Block Sims Sand Unit located in the south central part of Stephens County, Oklahoma, have been determined by using the scaling results in conjunction with reservoir simulation, and possible remedial actions have been recommended.

A new method for absolute permeability upscaling is presented. The method, referred to as global upscaling, focuses on the spatial connections within a global permeability field. Conventional methods, referred to as local upscaling, concentrate on local areas which can lead to loss of geologically important structural information. The method has been implemented in a three-dimensional algorithm that uses a moving window technique to detect boundaries of large permeability variance and then constructs a coarse-scale grid. The gridding method produces locally refined Cartesian grids for the upscaled model. Based on the global upscaling concept, this dissertation has developed a new approach for relative permeability and capillary pressure upscaling. The technique uses a table of "shock velocity" values that are correlated with a universal heterogeneity number and the effective aspect ratio of a residual permeability field. This table look-up eliminates the need for fine-grid numerical simulation. The approach has the potential to be a significant improvement over existing upscaling methods that require extensive fine-grid simulation. Water flood and tracer flood simulation on several 2D and 3D examples show that the global method reproduces the fine-grid flow behavior better than local upscaling methods.

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