Gerald A. LaTorraca

An analysis of the magnetotelluric impedance for three‐dimensional conductivity structures

The eigenstate analysis of Lanczos, also known as singular value decomposition (SVD), is used to define eight parameters which uniquely describe the magnetotelluric impedance Z. These parameters are independent of a priori assumptions about Z and can be interpreted in terms of three‐dimensional conductivity structures. Through SVD, the impedance is represented by two characteristic states. These states consist of two pairs (E and H) of complex vectors and two corresponding, real, singular values which together describe the extremal properties of Z. The singular values are the maximum and minimum |E|/|H| ratios possible at the observation site and therefore yield the true maximum and minimum apparent resistivities. We use a variation of SVD analysis by incorporating phases in the singular values, which are then called characteristic values. These phases reflect the delay (caused by the earth’s conductivity) of the electric fields relative to their associated magnetic fields. In this analysis of Z, the char...

Low-field NMR determinations of the properties of heavy oils and water-in-oil emulsions

Low-field (< 50 mT) nuclear magnetic resonance (NMR) well-logging measurements are beginning to be used to obtain estimates of oil viscosity in situ. To build an interpretive capability, we made laboratory T1 and T2 relaxation measurements on a suite of high-density, high-viscosity crude oils. These measurements were also used to estimate oil viscosity and water fraction from T1 and T2 measurements on stable, water-in-oil emulsions. High-density, high-viscosity oils have components that relax faster than can be measured by nuclear magnetic resonance logging tools. This requires corrections to T2 logging measurements for accurate estimates of oil saturation and porosity.

Permeability relation with other petrophysical parameters for periodic porous media

We modeled permeability (k) estimation based on porosity (ϕ), electrical formation factor (F), and nuclear magnetic resonance (NMR) relaxation time (T), using periodic structures of touching and overlapping spheres. The formation factors for these systems were calculated using the theory of bounds of bulk effective conductivity for a two‐component composite. The model allowed variations in grain consolidation (degree of overlap), scaling (grain size), and NMR surface relaxivity. The correlation of the permeability (k) with the predictor a aTbFc was slightly higher than aTbϕc (i.e., a correlation coefficient of 0.98 versus 0.95). The exponent b ranged from 1.4 for a pure grain consolidation system to 2 for a pure scaling system. Variations in surface relaxivity are shown to cause significant scatter in the correlations.

PERMEABILITY RELATION FOR PERIODIC STRUCTURES

The permeability relation for periodic porous media is studied with respect to other petrophysical parameters such as formation factor, porosity, surface-to-volume ratio, and nuclear magnetic resonance (NMR) relaxation time. All these quantities were computed for periodic structures of simple, body-centered, and face-centered cubic arrays of touching and overlapping spheres. The formation factors were calculated by using a method which is based on a Fourier-space representation of an integral equation for the electric potential in a two-component composite. The nuclear magnetic resonance relaxation time for the case where surface-enchanced relaxation plays a dominant role is known to be V P/rho S (VP is the pore volume, S is the pore surface, is the surface relaxation strength) when rho is not too large. Previously calculated permeabilities for these structures from the literature were used for correlation studies with other petrophysical parameters. Various correlation schemes among these quantities, such as k = aTbFc, and k = aTb phi c, were investigated, where k is permeability, T is the NMR relaxation time, phi is the porosity, and F is the formation factor.

Magnetic field nonuniformities and NMR of protons diffusing in a porous medium

Magnetic field inhomogeneity can arise either because of an externally applied field gradient or because of spatial variations in magnetic susceptibility. The latter are most important when the solid matrix includes paramagnetic substances and when the uniform applied field, and, consequently, also the Larmor precession frequency are very large. Both types of field inhomogeneity add extra phase shifts to the precessing spins. These phase shifts vary with time and position in a complex and random fashion as a result of the diffusive motion of the spins. We have studied these effects by performing detailed calculations for the case of a fluid filled porous medium with a periodic microstructure. Special attention was devoted to the question of whether the statistical distribution of the phase shifts encountered in a Hahn spin echo experiment or in a Carr-Purcell-Meiboom-Gill (CPMG) spin-echo train can be approximated as a Gaussian. The mean square phase shift is measured in such experiments as an enhanced relaxation rate of the precessing transverse magnetization. We determine this mean square phase shift for periodic composites from the diffusion eigenstates, which were calculated using a previously developed Fourier expansion method. The enhanced relaxation rate depends on the echo spacing time tau in a way that can be correlated with important length scales of the porous microstructure. Those correlations can be extended also to disordered microstructures, like the ones that are found in natural rocks. We compare these theoretically predicted correlations with CPMG measurements performed on protons in laboratory samples of brine saturated sandstone.