Chapter 2 - Porosity 2.39 2.5 Pore Structure Measurement Application of the Carmen-Kozeny model requires precise measurements of pore level parameters; e.g., specific surface area and tortuosity. Numerous methods have been developed to measure the specific surface area of a sample from early statistical methods to current day imaging techniques. The advanced technology has improved the estimation of specific surface area. Tortuosity measurements have been confined to electrical resistivity measurements on samples with the underlying assumption that the electrical path and fluid flow path are the same. In most measurement techniques, a physical sample must be extracted from the reservoir; i.e., core for the analysis. Recent advances in NMR logging; however, have provided an alternative to this requirement. This section will explain the various measurement techniques for these parameters and discuss the relevant advantages and limitations. Methods for Specific Surface Area Accurate specific surface area measurements of porous media are required when predicting permeability using the Kozeny or Kozeny-Carman equations. The three common techniques for estimating specific surface area per unit volume are: Petrographic Image Analysis (PIA), gas adsorption method and Nuclear Magnetic Resonance (NMR). Each method measures at a different scale: NMR at sub-electron level, BET at the electron level, and PIA at the pore level. Figure 2.25 illustrates the result of these different levels of measurement on a hypothetical pore body. NMRPIABET Figure 2.25. Hypothetical example of specific surface area measurements Due to the additional surface area measured, the resulting relationship is valid: As(NMR) > As(BET) > As(PIA). However, the extra surface area measured by the NMR is not relative,Chapter 2 - Porosity 2.40 because it does not affect flow. The preferred method is the PIA because it is a pore-level measurement, which is directly related to flow. Statistical Methods One of the earliest techniques, but not very accurate, was to repeatedly drop a needle on a thin section and count the times a pore surface is intersected by the needle and the number of times the end of the needle falls within the pore space. The probability of selecting a pore or pore perimeter is given by [Perez-Rosales,1967]: mnLcbvS4 (2.32) where c = the number of perimeter intersections n = number of points in pores L = needle length M = magnification The lack of scientific background and reliance on probability made this method unpopular. Adsorption method These methods rely on the measurement of the volume of physical adsorption of an inert gas (Argon or Nitrogen) on the solid surface at reduced pressure and temperature, near the normal liquefaction temperature of the gas. Isothermal adsorption theory developed by Brunauer-Emmett-Teller (BET) allows for the determination of the amount of gas to cover the solid surface with a single layer of gas molecules. The total surface area (As) is given by: *nsA  (2.33) where  is the effective surface area covered by a molecule of gas (15.2 Å2 for nitrogen and 13.6 for Argon), and n is the number of molecules in the volume of gas to form a mono-molecular layer. MNmVn (2.34) where, Vm = volume of gas to form a mono-molecular layer, cc.  = density, gm/cc N = avagadros number, 6.023x1023 molecules/gm-moleChapter 2 - Porosity 2.41 M = molecular weight, gm/gm-mole A literature survey reveals that there are few reported measurements on specific surface area of geological porous material. Brooks and Purcell [1952] and Tignot et al. [1952] reported surface areas of a few sandstones and also compared the direct measurement method developed by Brunauer Emmett Teller (BET) against predicted value of specific surface area calculated using the Kozeny equation. Brooks and Purcell first investigated specific surface area for an unconsolidated pack of uniform, spherical glass beads. Using mercury capillary pressure curves, the effective zoning factor was determined, 102121087.92)cos(SScpdSkxTk (2.35) where, pc = capillary pressure, dynes/cm2  = interfacial tension, dynes/cm k = permeability, md Substitution of kT into Carman-Kozeny equation results in determination of specific surface area. The results by this method are slightly greater (1.05 to 1.35) than geometrically computed values. The difference is attributed to minor imperfections of the spherical beads; therefore the true surface area is greater than the computed value; and to an assumed contact angle of 140. The second step was to analyze specific surface area for consolidated porous solids. Using the same procedure as above, kT was determined to be 8 to 40. In comparison, Kozeny = 2 Carman = 5 Glass beads = 3 to 4 The increased tortuosity is considered the reason for the discrepancy in values. A further step was to compare the specific surface from gas adsorption with the CK equation. Brooks and Purcell reported that observed surface areas as determined by gas adsorption are from 5 to 100 times larger than the areas calculated from the Kozeny equation for consolidated sand and heterogeneous rocks. The discrepancy was attributed to variations in pore structure when glass beads were replaced with a naturally occurring porous media. Furthermore, the Kozeny equation only applies to external surface area of the solidChapter 2 - Porosity 2.42 particles that would be contacted by a moving fluid. Thus any surfaces that are exposed but not in contact with a moving fluid (i.e. dead-end pores) would not be counted using the Kozeny relationship, but would be measured using a gas adsorption method. It was postulated from these findings that "the lack of uniform pore size in naturally occurring rocks may limit the applicability of Kozeny equation to such porous solids and may contribute, in part to the observed differences between the Kozeny and gas adsorption surface areas". Donaldson et al. [1975] using an apparatus modified from Nelson and Eggertsen for porous media, found excellent agreement between the surface areas obtained from Kozeny-Carman equation and nitrogen