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

Abstract

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 V p /S, permeability to fluid flow k, exchange cation molarity Q v , and proton NMR decay constant T 1 in water-saturated rocks (see Figure 1): k=10 (super 6.59) ((phi m V p /S)) (super 2.08) , R=0.90, Q (sub ) =10 (super -1.61) ((V p /S)) (super -0.75) , R=0.79, T 1 =10 (super 3.08) ((V p /S)) (super 0.9) , R=0.87, k=10 (super 2.65) ((phi m /Q (sub ) )) (super 2.11) , R=0.88, k=10 (super -0.1) ((phi m T 1 )) (super 2.15) , R=0.94, Q (sub ) =10 (super .8) T (sub 1 (super -0.74) ) , R=0.77. Here R is the regression coefficient, phi is the porosity and m the conductivity exponent; Q v in normality (meq/ml), k in millidarcies, and T 1 in milliseconds, V p /S in mu m.Including the tortuosity factor phi m in conjunction with a pore-size parameter as represented by V p /S, T 1 , or Q v improves the correlation with permeability and reduces the residual error. The best predictor for log k is log (phi m T 1 ). 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.