A model is developed that allows accurate prediction of the permeability of a core sample of sedimentary rock, based solely on two-dimensional image analysis of its pore structure. The only required input data are the areas and perimeters of the pores observed in, for example, an SEM image. The hydraulic radius approximation is used to estimate the individual pore conductances. Prior to this, stereological corrections are used to convert apparent pore geometries, and various hydraulic corrections are applied to account for converging–diverging flow paths. These various corrections are the principal and crucial differences between our approach and previous methods based on two-dimensional images. Finally, Kirkpatrick's effective medium approximation is used to find the effective value of the hydraulic conductances of the individual pores.

The method has been applied to several data sets, including consolidated North Sea reservoir sandstones, outcrop sandstones, outcrop carbonates, and carbonates from Middle East oil and gas fields. The permeabilities of this entire data set range from 0.5-1377 mD, which covers a significant portion of the range of permeabilities that are relevant in reservoir engineering. In 80% of the cases, the permeabilities predicted by our method are within a factor of two of the measured values, and the predictions are within a factor of three in over 90% of the cases. The method requires minimal data manipulation and computation when compared to approaches that require three-dimensional imaging and/or full solution of the Navier-Stokes equations, and is much more accurate than primitive empirical methods such as the Kozeny-Carman equation.

Aside from giving insight into the influence of pore structure on permeability, our method offers the potential of permitting permeability predictions to be made using drill cuttings, in situations where it is not possible to recover intact core. Another possible future application is to use downhole borehole imaging technology to provide an image with the appropriate resolution, thereby allowing in situ permeability estimation, without the need for core samples.

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