Abstract

Fluid permeability is one of the most important characteristics of a hydrocarbon reservoir, and is described by a number of empirical and theoretical models. We have taken four of the most important models, each of which is derived from a different physical approach, and have rewritten them in a generic form that implies a characteristic scale length and scaling constant for each model. The four models have been compared theoretically and using experimental data from 22 bead packs and 188 rock cores from a sand-shale sequence in the U. K. sector of the North Sea. The Kozeny-Carman model did not perform well because it takes no account of the connectedness of the pore network and should no longer be used. The other three models (Schwartz, Sen, and Johnson [SSJ]; Katz and Thompson [KT]; and the Revil, Glover, Pezard, and Zamora [RGPZ]) all performed well when used with their respective length scales and scaling constants. Surprisingly, we found that the SSJ and KT models are extremely similar, such that their characteristic scale lengths and scaling constants are almost identical even though they are derived using extremely different approaches: The SSJ model by weighting the Kozeny-Carman model using the local electrical field, and the KT model by using entry radii from fluid imbibition measurements. The experimentally determined scaling constants for each model were found to be cSSJcKT8/3cRGPZ/3. Use of these models with AC electrokinetic theory has also allowed us to show that these scaling constants are also related to the a value in the RGPZ model and the m value in time-dependent electrokinetic theory and then to derive a relationship between the electrokinetic transition frequency and the RGPZ scale length, which we have validated using experimental data. The practical implication of this work for permeability prediction is that the KT model should be used when fluid imbibition data are available, whereas the RGPZ model should be used when electrical data are available.

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