Study on Physical Dimensions of Some Expressions of Petrophysics

Abstract

This study arose during the survey of a large number of works aiming to prepare a permeability model that presented a better accuracy than those consecrated in the literature for different types of reservoir rocks in the petrophysical area. The methodology used was to appreciate the mathematical expressions replacing physical quantities by their dimensions in the LMT system. After replacing length by L, mass by M and time by T, we compare the first members of the equations with the second to verify the homogeneity of the magnitudes involved in each mathematical formula. When these expressions are tested with experimental data, were identified formulas that did not show equilibrium in dimensions of their magnitudes, where it was observed that the permeability values found did not exhibit units of squared length. It has been used the phase spatial encoding in the Nuclear Magnetic Resonance Tool with experimental data of porosity, irreducible fluid volume, free fluid volume and transverse relaxation time. This distortion led us to conclude that the equations did not present their homogeneous physical dimensions, motivating a deep study in the identification of expressions used in the permeability calculation, in sandstone and carbonate rocks, with no equilibrium in their dimensional equations in any unit system. This review aims to identify the constants used in the equations equilibrium suggesting modifications that can be obtained through pre-established relationships to increase the reliability of the equations previously used.