Theoretical studies in rock physics: 1. Pore space geometry and fluid magnetization. 2. Elasticity in a borehole geometry.

摘要

1a. Two model porous media and a precise drying protocol are employed in numerical simulation of fluid configurations in partially saturated porous media. Over a substantial range of partial saturation {dollar}Nsb{lcub}L{rcub},{dollar} the liquid-vapor configurations are inhomogeneous on a length scale that is a sensitive function of {dollar}Nsb{lcub}L{rcub}.{dollar} Several measures of the characteristics of fluid configurations are developed. Details of the fluid configurations are found in the study of {dollar}p(x;ell,Nsb{lcub}L{rcub}),{dollar} the probability density for a porous medium of partial saturation {dollar}Nsb{lcub}L{rcub}{dollar} to contain a piece of material of size {dollar}ellsp{lcub}d{rcub}{dollar} having partial saturation x. This probability density is a gauge of inhomogeneity and appears importantly in NMR studies of porous media.; 1b. The equations governing magnetization evolution in fluid filled pore systems are developed. In pore systems with a range of pore sizes (and/or decay rates) the magnetization evolution is described exactly by a spectrum of decay rates, leading to multiple exponential decay. We study this spectrum of decay rates as a function of coupling strength between pores using perturbation theory, effective medium theory, and matrix diagonalization. The spectrum of decay rates evolves from the individual pore decay rate distribution, at zero coupling, to a delta function distribution, at infinite coupling. The effect of coupling between pores is important in NMR studies of temperature dependence of characteristic decay rates in porous media.; 2. The equation of motion describing a borehole elastic system (BES) is studied in the form of a perturbation problem, i.e. as the sum of terms describing a model elastic system (MES) and terms describing the departure of the BES being studied from the MES. The MES is chosen such that the departure terms in the BES equation of motion are small. The Green tensor for an infinite, azimuthally symmetric borehole is developed. As an illustration of the perturbation technique, the consequences of a mudcake layer on the borehole wall are explored. Comparison of first order perturbation calculations confirms the perturbation method is a valid technique for probing small changes to a model elastic system.