Effect of Variable Saturation Exponent on the Evaluation of Hydrocarbon Saturation

Abstract

Summary. Petrophysical measurements on effectively clean, desaturated core plugs from different fields have shown that the assumption of a constant saturation exponent for a given sample frequently is violated, although the conventional biogarithmic distribution of resistivity-index/water-saturation data is often approximately linear. These variations in saturation exponent are attributed to the effects of pore geometry, in particular the nonuniform distribution of electrolyte within a heterogeneous pore system as desaturation progresses. The data indicate that, if unrecognized, a variable saturation exponent can induce errors of more than 10 saturation units (s.u.) in the petrophysical evaluation of water saturation. Procedures are outlined for the identification of those physicochemical reservoir conditions that can give rise to a variable saturation exponent and for accommodating these variations in reservoir evaluation. Introduction Classic petrophysics holds that the Archie saturation exponent n, is constant for a given (clean) sample of reservoir rock. this presumed constancy forms the basis for the determination water presumed constancy forms the basis for the determination water saturation from resistivity index for a particular lithology. An increasing number of cases are being encountered, however where n has been observed to change with variations in fluid saturation within a given rock. This means that n can be depended on water saturation, the parameter to be evaluated. The nature of this dependence, which has important implications for the evaluation of oil in place, has been investigated through model studies. There also have been several practical syntheses of issue affecting . This paper develops insight into the physical characteristics of n by extending earlier work to demonstrate the implications for formation evaluation of a variable pore geometry can include variations in n. The petrophysical evaluation of water saturation, Sw, is based on the second Archie equation, (1) where IR, the resistivity index, is the ratio of the conductivity o the fully electrolyte-saturated reservoir rock to the conductivity that the rock would possess if partially saturated (to level S) with identical electrolyte. n routinely is presumed constant for a given rock sample. The Archie experimental conditions require a clean (shalefree) rock saturated with high-salinity (NACl) brine and with S greater than 0.15. Eq. 1 is empirical. The Archie equation usually is depicted as a bilogarithmic plot of I vs. S with slope n determined by regression (Fig. 1a). plot of I vs. S with slope n determined by regression (Fig. 1a). The use of logarithmic scales can suppress subtle changes in n. A more informative insight is attainable through an alternative (bilinear) plot of n vs. S, with values of n determined for each individual data point by calculation (Fig. 1b). This approach requires that n be defined as (2) Plots of n vs. S are used in conjunction with the standard Archie representation throughout this paper. At high S values, Eq. 2 becomes unstable, and n is undefined at S = 1. Variable Saturation Exponent Fig. 1 allows comparison of the bilogarithmic and bilinear plots for Sample A of clean sandstone with a unimodal pore-size plots for Sample A of clean sandstone with a unimodal pore-size distribution that contains little microporosity. In particular, Fig. 1b shows that n values calculated from Eq. 2 are effectively constant and that the mean is qualified by the acceptable uncertainty of 0. 1. Table 1 lists the petrophysical characteristics of specific samples. In contrast, Fig. 2, which relates to a clean sandstone, Sample B, with a wider range of pore sizes, reveals a quasilinearity on the bilogarithmic plot of I vs. S but shows a variation in n that trends beyond the limits of uncertainty on the bilinear plot of n vs. S . This comparison emphasizes the diagnostic capability of the bilinear plot and thereby introduces the concept of a variable n that does not conform to the Archie supposition of constancy. Worthington et al. 7 proposed an explanation of variable n for lithologically clean porous media. The premise was that n can increase or decrease with changing S or remain constant, according to the pore-size distribution. Variations in n were particularly pronounced for multimodal porous media that exhibit microporosity. This behavior was porous media that exhibit microporosity. This behavior was attributed to the coexisting effects of tortuosity and surface conduction. In any pore system, tortuosity can be expected to increase as S decreases. In the particular case of a unimodal pore system, where the desaturation of the pore space is fairly uniform, the increase in tortuosity occurs at a rate in accordance with Eq. 1. Thus, n, which is intuitively related to tortuosity, remains effectively constant. However, in the case of a multimodal pore system, where desaturation occurs heterogeneously, the increase in tortuosity can exceed that which is in accordance with Eq. 1. Thus, n increases as desaturation progresses over intermediate values of S . This effect is particularly pronounced where micropores are present. Fig. 3 illustrates the concept of excess tortuosity. A heterogeneous pore system will reflect a range of water saturations for any given bulk value of S that is significantly less than unity. This means that pores with relatively low S will act as severe constraints on current flow to a degree in excess of that associated with the bulk, S . The overall effect is to increase bulk tortuosity beyond the level commensurate with the bulk S . When micropores are present, they exert a gradually increasing influence as S decreases . Their effect is to decrease n so that the excess tortuosity phenomenon no longer is manifested in n. The decrease is related to the degree of surface conduction, which can be highly significant in pore systems characterized by a high surface area. Two more points are noteworthy. First, a significant surface conduction can be manifested in the absence of constituent clay minerals, provided that the medium has a high surface area per unit PV as in microporous systems; the relative magnitude of surface PV as in microporous systems; the relative magnitude of surface conduction increases as S and/or electrolyte salinity decrease. Second, the tortuosity/surface conduction model used to explain variable n provides a means of accounting for a range of identified causes, such as wettability effects, shaliness, Mugginess, and fresh electrolytes, as well as microporosity in its several forms. These observations are in general agreement with the results of other model studies of partially saturated porous systems. Field Examples We now develop these ideas further by considering field examples of effectively clean, multimodal porous media. SPEFE P. 331