Towards a characteristic equation for permeability

The characterization of reservoir permeability (k) remains the elusive challenge in reservoir engineering. This work considers prior developments in an evolutionary sense, and, as with prior work, our goal is the development of a "characteristic permeability relation" (CPR). To this end, we have developed 5 CPR formulations -- 3 of which could be considered modifications of "historical" models and 2 of which are "weighted" power law-exponential models. In this work, we consider permeability to be only a function of two variables; k = f(?,z) -- porosity (? ) and z, where z is either the water saturation (Sw) or the Archie Formation Factor (F). Our rationale in considering k = f(?,z) is two-fold -- first, such a formulation is a fundamental extension of the k = f( ?) correlation work by Archie (and countless others); and second, our validation datasets are limited to literature cases and cases obtained from industry sources -- none of which would be considered suitable for extension beyond porosity and another variable. We demonstrate and validate our concept of a characteristic permeability relation using various datasets obtained from the literature and from industry sources. In this work we show that each proposed relation has a unique character and performance -- depending on primarily on the data, rather than the functional form of the permeability relation. Using the characteristic permeability relations developed in this work -- the proposed permeability relations can be extended to other and other data types. It may also be possible to develop so-called "hydraulic flow unit" methods which segregate petrophysical data into depositional flow sequences.