Towards a Characteristic Equation for Permeability Conference Paper uri icon


  • Abstract 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(f,z) — porosity (f) and z. Where, for this work, z is either the water saturation (Sw) or the Archie Formation Factor (F). Our rationale in considering k = f(f,z) is two-fold — first, such a formulation is a fundamental extension of the k = f(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 plus another variable. We demonstrate and validate our concept of a characteristic permeability relation (CPR) 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 can be used to segregate petrophysical data into depositional flow sequences. Objectives The objectives of this work are:To propose and develop a family of "characteristic permeability relations" — specifically, functional forms based on the original observations of Archie (power law and exponential behavior of numerous permeability-porosity data sets).To validate these "characteristic permeability relations" using data from literature and industry sources for consolidated rocks, as well as data for other materials.To provide a general methodology for applying the "characteristic permeability relations" in practice, including methods to distinguish poor data from correlation efforts. Statement of the Problem There have been exhaustive attempts to correlate permeability with porosity and other variables — this is one of the most intractable problems in the petroleum industry. Our goal is not to provide a "universal" relation or concept, but rather, to provide "characteristic relations" that can accurately represent a correlation of permeability with other variables. A typical "characteristic relation" will use either the power law or exponential models proposed by Archie [1950]. ("Power Law Model") (1) ("Exponential Model") (2) Our motivation for this work is derived from our observation that many correlations of permeability, porosity, and other variables can yield inconsistent and/or inaccurate results — especially for low permeability rock samples. As we are pursuing opportunities in very low permeability (k>0.01 md) and ultralow permeability (k>0.001) reservoirs, the potential for using such correlations to establish/verify reservoir quality becomes significant. We also believe that for ultra-low per-meability samples, it will be increasingly difficult to physically measure permeability on a routine basis — making the correlation of permeability a priority (based on a few key measurements of permeability).

name of conference

  • SPE Eastern Regional/AAPG Eastern Section Joint Meeting

published proceedings

  • All Days

author list (cited authors)

  • Siddiqui, A. A., Ilk, D., & Blasingame, T. A

complete list of authors

  • Siddiqui, Adil Ahmed||Ilk, Dilhan||Blasingame, Thomas Alwin

publication date

  • January 1, 2008 11:11 AM


  • SPE  Publisher