Chapter 2 - Porosity PIA NMR BET

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1 2.5 Pore tructure Measurement Alication of the Carmen-Kozeny model requires recise measurements of ore level arameters; e.g., secific surface area and tortuosity. Numerous methods have been develoed to measure the secific surface area of a samle from early statistical methods to current day imaging techniques. The advanced technology has imroved the estimation of secific surface area. Tortuosity measurements have been confined to electrical resistivity measurements on samles with the underlying assumtion that the electrical ath and fluid flow ath are the same. In most measurement techniques, a hysical samle must be extracted from the reservoir; i.e., core for the analysis. Recent advances in NMR logging; however, have rovided an alternative to this requirement. This section will exlain the various measurement techniques for these arameters and discuss the relevant advantages and limitations. Methods for ecific urface Area Accurate secific surface area measurements of orous media are required when redicting ermeability using the Kozeny or Kozeny-Carman equations. The three common techniques for estimating secific surface area er unit volume are: Petrograhic Image Analysis (PIA), gas adsortion 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 ore level. Figure 2.25 illustrates the result of these different levels of measurement on a hyothetical ore body. PIA NMR BET Figure Hyothetical examle of secific surface area measurements Due to the additional surface area measured, the resulting relationshi is valid: A s (NMR) > A s (BET) > A s (PIA). However, the extra surface area measured by the NMR is not relative, 2.39

2 because it does not affect flow. The referred method is the PIA because it is a ore-level measurement, which is directly related to flow. tatistical Methods One of the earliest techniques, but not very accurate, was to reeatedly dro a needle on a thin section and count the times a ore surface is intersected by the needle and the number of times the end of the needle falls within the ore sace. The robability of selecting a ore or ore erimeter is given by [Perez-Rosales,1967]: where c n L M bv = the number of erimeter intersections = number of oints in ores = needle length = magnification 4 c m (2.32) nl The lack of scientific background and reliance on robability made this method unoular. Adsortion method These methods rely on the measurement of the volume of hysical adsortion of an inert gas (Argon or Nitrogen) on the solid surface at reduced ressure and temerature, near the normal liquefaction temerature of the gas. Isothermal adsortion theory develoed 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 (A s ) is given by: A s n* (2.33) where is the effective surface area covered by a molecule of gas (15.2 Å 2 for nitrogen and 13.6 for Argon), and n is the number of molecules in the volume of gas to form a monomolecular layer. where, V m N = volume of gas to form a mono-molecular layer, cc. = density, gm/cc = avagadros number, 6.023x10 23 molecules/gm-mole V m N n (2.34) M 2.40

3 M = molecular weight, gm/gm-mole A literature survey reveals that there are few reorted measurements on secific surface area of geological orous material. Brooks and Purcell [1952] and Tignot et al. [1952] reorted surface areas of a few sandstones and also comared the direct measurement method develoed by Brunauer Emmett Teller (BET) against redicted value of secific surface area calculated using the Kozeny equation. Brooks and Purcell first investigated secific surface area for an unconsolidated ack of uniform, sherical glass beads. Using mercury caillary ressure curves, the effective zoning factor was determined, where, k T c = caillary ressure, dynes/cm 2 k = interfacial tension, dynes/cm = ermeability, md 2 ( cos ) 1 d x10 k 0 2 c (2.35) ubstitution of k T into Carman-Kozeny equation results in determination of secific surface area. The results by this method are slightly greater (1.05 to 1.35) than geometrically comuted values. The difference is attributed to minor imerfections of the sherical beads; therefore the true surface area is greater than the comuted value; and to an assumed contact angle of 140. The second ste was to analyze secific surface area for consolidated orous solids. Using the same rocedure as above, k T was determined to be 8 to 40. In comarison, Kozeny = 2 Carman = 5 Glass beads = 3 to 4 The increased tortuosity is considered the reason for the discreancy in values. A further ste was to comare the secific surface from gas adsortion with the CK equation. Brooks and Purcell reorted that observed surface areas as determined by gas adsortion are from 5 to 100 times larger than the areas calculated from the Kozeny equation for consolidated sand and heterogeneous rocks. The discreancy was attributed to variations in ore structure when glass beads were relaced with a naturally occurring orous media. Furthermore, the Kozeny equation only alies to external surface area of the solid 2.41

4 articles that would be contacted by a moving fluid. Thus any surfaces that are exosed but not in contact with a moving fluid (i.e. dead-end ores) would not be counted using the Kozeny relationshi, but would be measured using a gas adsortion method. It was ostulated from these findings that "the lack of uniform ore size in naturally occurring rocks may limit the alicability of Kozeny equation to such orous solids and may contribute, in art to the observed differences between the Kozeny and gas adsortion surface areas". Donaldson et al. [1975] using an aaratus modified from Nelson and Eggertsen for orous media, found excellent agreement between the surface areas obtained from Kozeny-Carman equation and nitrogen adsortion on glass beads, and good agreement for crushed sand. Donaldson et al. attributed this agreement of crushed sand to the grinding rocess, which rounded the grains. It should be noted that no author has attributed any discreancy to the assumtions made when using the Kozeny relationshi. The constant in the Kozeny or Kozeny-Carman equations, which suosedly comensates for tortuosity, shae factor, sizing and in turn generalizing the equation for non-ideal systems has to date not been considered as a source for these inconsistencies. The gas adsortion method is widely used in the determination of secific surface areas of orous solids. However, it should be limited to orous media, which do not have large secific surface, and the grains of the matrix are singularly smooth and regular. Consequently, it can be safely assumed that the adsortion method, as currently racticed, does not measure the same surface area as that involved in fluid flow exeriments of most orous rocks; esecially when the rock samles are crushed. However, for unconsolidated orous systems, the secific surface area obtained by the gas adsortion method is adequate. Fig shows a log-log lot of gv, versus d g data obtained exerimentally. The equation of the straight line is, gv 4.27 (2.36) d g where gv = secific surface area er unit grain volume; cm -1 dg = grain diameter, cm 2.42

5 Figure 2.26 Relationshi between secific surface area and grain size from gas adsortion method. It is obvious from Fig that the secific surface area of the rock material increases as the size of the constituent grains decreases, with the result in a loss in ermeability. Furthermore, for orous media comosed of clay minerals, which have large secific surface areas, a reduction in ermeability will also occur. The following list [Lake, 1998] contains measured gv for various media illustrating two orders of magnitude in difference for clays in comarison to sandstones. It is therefore a common observation that ermeability will be inversely roortional to clay content. 2.43

6 Material gv, cm -1 Berea 20 Toredo 80 Kaolinite 500 Illite 2800 mectite 1300 From mathematical rinciles the secific surface area of a sherical glass bead is: gv 6 (2.37) d g The difference between the comute value of 6 and the emirical value of 4.27 is due to the roughness and irregular shae of the grains; consequently the total surface area exosed to fluid is areciably reduced by contacts between grains. A general equation can be derived for gv in the form of, K sg gv (2.38) d g where K sg is the effective grain shae factor. A similar analysis can be alied to ores for uniform ore-sized media, i.e.: K s v (2.39) d where K s is the effective ore shae factor and d is the mean ore diameter. Petrograhic Image Analysis The Petrograhic Image Analysis method relies on sohisticated imaging techniques of thin sections to determine surface area [Clelland & Fens, 1991]. X-ray, back-scattered electrons, and EM are imaging methods currently used. Equiment consists of an imagerocessing system, etrograhic microscoe and a camera. It has the advantages of requiring a small samle, 5 to 10 mm 2 and fast measurement time, 20 to 30 minutes. PIA method may be used to characterize the orous rock if samles are reared with good otical contrast 2.44

7 between the ores and grains, and the thin sections are obtained at overburden conditions. The secific ore surface can be determined as: v 4 L (2.40) A where L and A are the ore erimeter and the ore cross-section, resectively. Using PIA a ore shae factor can be determined as [Tiab, 1994], [Bekri, et al. 2000]: f s 2 L (2.41) 4 A The factor f s indicates what the erimeter L would be if the lanar feature was a given shae. For examle, if the 2D ore shae is a circle, then substituting for L = 2 r and A = r 2 results in f s = 1. To convert to 3D sace, K s = 6*f s. The table below shows f s and K s values for a variety of ore shaes. Pore hae f s (2D) K s (3D) Nuclear Magnetic Resonance The NMR (Nuclear Magnetic Resonance) method can also be used to estimate the secific surface area from: gv A * nmr ma (2.42) where A NMR ma = NMR surface area of dry material, m 2 /gm = grain-matrix density, gm/cc 2.45

8 v and gv values obtained from NMR are considerably higher than values obtained by PIA, or the gas adsortion technique. everal studies have found that the secific surface area, measured with any of the three methods, i.e., the adsortion method, PIA and NMR, is related to the irreducible water saturation or simly water saturation by a relationshi of the general form: b a (2.43) v w where a and b are constants of correlations. Zemanek investigated low-resistivity sandstone reservoirs and found surface areas measured with the NMR technique were quantitatively consistent with the irreducible water saturations from the caillary ressure curve data. Figs and 2.28 demonstrate an excellent correlation between v and wi and w. Figure 2.27 Relationshi between surface area and wi for a sandstone formation Figure 2.28 Relationshi between surface area and w for a sandstone formation 2.46