Gridblock-scale stress-permeability

Two methods are developed for calculating gridblock-scale stress-permeability relationships. Although the first method is developed by assuming identical properties for individual hactures and spatially variable fracture densities, it can be mathematically shown that the model is also valid for individual fractures with different aperture parameters (e.g., b, and bmu) as long as Rb is the same for individual fractures. 

Figured. Outline of stochastic stress and fluid flow analysis for upscaling the srrmll-scale (e.g.. 1.56 m x 1.56 m) stress-permeability relation to a gridblock scale for a large-scale model.

For a given mean initial log(K) for the 1.56 m x 1.56 m blocks (Figure 4), we can simulate effective permeability ratios for the gridblock for different initial stresses and stress changes. Based on Equations 4 and 5, the local scale Rb is given by... 

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