Numerical estimation of effective permeability in sand‐shale formations

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Abstract
A numerical approach is used to estimate effective permeability in sand‐shale formations under steady state uniform flow conditions. Permeability is modeled as a binary, second‐order stationary random function taking on two possible values Kss and Ksh in sandstone and shale, respectively. This model is realistic since experience with sandstone reservoirs has shown that randomly dispersed low‐permeability shales are the single dominant heterogeneity affecting flow behavior. The cases of both spatially correlated and uncorrelated permeabilities are considered. For the case of spatially correlated permeability, an autocovariance model was fitted to data from the Assakao fluvial sandstone which outcrops in the Tassili region of the central Sahara. The turning bands method was used to simulate the spatially correlated permeabilities of blocks discretizing the flow field. Effective permeability was found to depend on the shale volume fraction, the spatial covariance structure, and the dimensionality of the flow system. Existing analytical methods for estimating effective permeability in a two‐phase medium are found to be inaccurate when compared to numerical results or unapplicable to stratified environments. In addition to providing a check of analytical work, the numerical approach is found to be a useful tool for exploring the effects of reservoir heterogeneity on flow behavior in a qualitative sense.