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There are also some practical difficulties in establishing the coefficients a and b in a reservoir in which the oil/water contact cuts across lithologies because of regional dip or structure. In a reservoir, P c varies with height, and because S wi varies with P c, it is necessary to assume a functional dependence of S wi on P c. 2 were obtained for a fixed value of capillary pressure ( P c). 2, which is based totally on core data, to an oil reservoir. 4 – Permeability/porosity relationship with irreducible water saturation as a parameter, after Timur. 3, and its form on a log 10( k)- Φ plot is shown in Fig. 2 as a predictor of permeability is shown in Fig. 1, it is strictly an empirical relationship. There is no theoretical basis for the substitution of S wi for specific surface area Σ, so although the form of Eq. For b=4.4, the value of a is 0.136 if Φ and S wi are in percent and 8,581 if Φ and S wi are fractional values. 3 and testing the correlation coefficient with respect to Φ b/ S wi 2. Results for b=4.4 produced a fit somewhat better than other values it was obtained by taking the logarithm of both sides of Eq. Timur’s statistical results show that the exponent b can range between 3 and 5 and still give reasonable results. Timur measured irreducible water saturation ( S wi) using a centrifuge and then held k proportional to S wi −2 in the general power-law relationship,Ĭoefficients a and b were determined statistically. The three sandstones exhibit varying degrees of sorting, consolidation, and ranges of porosity. Timur used a database of 155 sandstone samples from three oil fields ( Fig. 1 – Empirical chart relating permeability to porosity with critical interstitial water S ciw as a parameter, after Granberry and Keelan. It was determined from reservoirs in which oil viscosity was approximately twice that of water and requires adjustment for low- or high-gravity oils.įig. 1 cannot be used to estimate permeability from porosity and water saturation as determined from well logs because it reflects only the critical water saturation. Because S ciw is taken from the capillary pressure curve, it is a function of the size of interconnected pores. It is said that if the water saturation in the formation is less than this critical value, the well will produce water free. The S ciw parameter is taken from the "knee" of a capillary pressure curve and is greater than irreducible water saturation, S wi. Their chart, originally presented with S ciw as a function of permeability with porosity as a parameter, is transposed into log( k)- Φ coordinates in Fig. Granberry and Keelan published a set of curves relating permeability, porosity, and "critical water" saturation ( S ciw) for Gulf Coast Tertiary sands that frequently are poorly consolidated.
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Specific surface area as ratio of pore surface to grain volume. Specific surface as ratio of pore surface area to rock volume. 1 have been used as a starting point for predicting permeability from well log data by assuming that residual water saturation is proportional to specific surface area, Σ. Two ideas inherent in Kozeny-Carman are important for later developments: the dependence of k on a power of porosity and on the inverse square of surface area.
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1 Starting from Kozeny-Carman equations.