Surface‐to‐volume ratio, charge density, nuclear magnetic relaxation, and permeability in clay‐bearing sandstones

Abstract

Based on measurements on some 100 sandstone core samples, mainly from oil fields from various parts of the world, we found the following regressions between volume‐to‐surface ratio [Formula: see text], permeability to fluid flow k, exchange cation molarity [Formula: see text], and proton NMR decay constant [Formula: see text] in water‐saturated rocks (see Figure 1): [Formula: see text], [Formula: see text], [Formula: see text], [Formula: see text], [Formula: see text], [Formula: see text]. Here R is the regression coefficient, ϕ is the porosity and m the conductivity exponent; [Formula: see text] in normality (meq/ml), k in millidarcies, and [Formula: see text] in milliseconds, [Formula: see text] in μm. Including the tortuosity factor [Formula: see text] in conjunction with a pore‐size parameter as represented by [Formula: see text], [Formula: see text], or [Formula: see text] improves the correlation with permeability and reduces the residual error. The best predictor for log k is log [Formula: see text]. The exponents in the above correlations agree reasonably with those expected from simple models. These correlations provide a numerical basis for assessing how well some of these quantities can be estimated from others in log interpretation. They also provide a basis for assessing the importance of the factors that interfere with and thereby weaken the correlations.

Influence of drying–wetting cycles on soil-water characteristic curve of undisturbed granite residual soils and microstructure mechanism by nuclear magnetic resonance (NMR) spin-spin relaxation time (T2) relaxometry

“…Some researches obtained ρ 2 values by comparing the T 2 relaxation distribution with POSD data calculated by MIP (Marschall et al 1995;Kleinberg 1996;Kenyon 1997;Li et al 2008;Minagawa, et al 2008; Yao and Liu 2012), Nitrogen Gas Adsorption or Diffusion measurements (Gallegos and Smith 1988;Hurlimann et al 1994;Sorland et al 2007), Cation Exchange Capacity (Sen et al 1990), Differential Thermal Calorimetry (Ramia et al 2010) and Photo Microscopy or Image Analysis (Howard et al 1993;Kenyon 1997;Arns 2004;Wang 2009) by Kenyon et al (1988), is used to obtain the surface relaxivity coefficient (ρ 2 ) which is…”

Geophysical Estimation of Permeability in Sedimentary Media with Porosities from 0 to 50%

“…To illustrate this, we have extracted data from the works of Timur (1968), Waxman and Smits (1968), Turner (1983) and Sen et al (1990) and we have represented the k(Ø) curves, given by Equation (5b), in Figure 5, together with the different cementation exponents that contain the compiled data.…”

“…As stated by Sen et al (1990) "Empirical laws have been extremely useful in geophysical exploration". In the case of the k(Ø) relationship, it has been very common to find an expression that presents the minimum error against empirical data from one or more zones with similar characteristics.…”

“…Data on the positive correlation between k and Ғ for consolidated sands was reflected in the (k, Ғ ) graphs presented by Archie (1942), Winsauer et al (1952), Waxman and Smits (1968), Carothers (1968), Sawyer et al (1971), and Sen et al (1990), among others. Similarly, for unconsolidated media there are also available data on the negative correlation between k and Ғ, of which we have selected those presented by Jones and Buford (1951), Kosinski and Kelly (1981), Urish (1981), Kelly and Frohlich (1985) and Huntley (1986).…”

“…In a large number of studies on oil drilling, the existence of a positive correlation between k and Ø is identified (Archie, 1942;Winsauer et al, 1952;Carothers, 1968;Timur, 1968;Waxman and Smits, 1968;Turner, 1983;Sen et al, 1990;Nelson, 1994;Pape et al, 1999;Ehrenberg et al, 2006;Glover and Walker, 2009). However, in studies of well data in non-consolidated media, this correlation is found to be negative (Jones and Buford, 1951;Baker et al, 1964;Alger, 1966;Croft, 1971;Worthington, 1977;Heigold et al, 1979;Urish, 1981;Worthington, 1983;Kwader, 1985;Kelly and Frohlich, 1985;Huntley, 1986;Detmer, 1995;Díaz-Curiel, 1995;Frohlich et al, 1996;Purvance and Andricevic, 2000) and others (Khalil and Santos, 2009).…”