Deformation and failure of rock samples probed by T1 and T2 relaxation.
The objective of the study was to pinpoint the effect of stress induced rock matrix alterations on NMR-wireline-log measurements by means of laboratory T1 and T2 relaxation time measurements. The research activities were subdivided into two major parts: NMR relaxation measurements on a brine saturated outcrop sandstone (Red Wildmoor Sandstone) during uniaxial compressional tests and NMR relaxation measurements on artificial sandstone samples prepared with defined crack patterns. T1-measurements performed on Red Wildmoor samples during compaction showed a decrease in the mean relaxation rate 1/exp<ln (T1) up to a point assumed to characterize the yield strength of the rock. The rate decreased most probably as a result of the compaction of micropores. This trend was reversed when the rock failed. The relaxation rate increased again, most probably through the generation of fresh mineral surfaces at broken cementations or grain contacts. T2-relaxation was measured on artificial sandstone samples using CPMG pulse sequences with echo times between 175 micros and 1400 micros. Samples with larger crack volumes and crack orientation orthogonal to the B0-field showed consistently smaller exp<ln (T2) than the samples without any cracks. Further calculations indicate that internal magnetic field gradients were largest for samples having a larger number of cracks and crack orientations orthogonal to the B0-field.
Novel Multidimensional Inverse Laplace Nuclear Magnetic Resonance Spectroscopy Techniques
This thesis presents the new development and application of multidimensional inverse Laplace nuclear magnetic resonance spectroscopy techniques. We present a new NMR technique which relates the longitudinal relaxation rate of the NMR signal to the internal gradients in the sample. We perform the experiment on a large range of magnet strengths to provide experimental evidence for the theory of how internal gradient intensity scales with pore size as a function of field strength. We make the first attempt of quantisation of two dimensional inverse Laplace experiments. We perform a transverse relaxation exchange experiment on several samples for a range of mixing times. We then integrate the peaks in the resulting spectra and plot them as a function of mixing time. By fitting the experimental results to theory, we can estimate the molecular exchange between pores of differing sizes. We then modify the transverse relaxation experiment to include diffusion attenuation so that we can see the separate signals for oil and water. We use this to look at the effect wettability has on the movement of the different fluids between pores. We then present the first experiment to combine two inverse Laplace dimensions with a Fourier dimension. We add a propagator dimension to the transverse relaxation exchange experiment to measure how far the molecules move during the mixing time. Quantisation of the results allows us to estimate the exchange rate between pores of similar sizes in addition the exchange rate between pores of different sizes. We are also able to estimate pore radii, inter-pore spacing and tortuosity. Lastly, we attempt a three dimensional inverse Laplace experiment by correlating transverse relaxation, diffusion, and internal gradients. While the three dimensional inversion techniques require more development, the results show resemblance to those seen from two dimensional experiments.
Wave speeds and attenuation of elastic waves in material containing cracks
Summary. Expressions now exist from which may be calculated the propagation constants of elastic waves travelling through material containing a distribution of cracks. The cracks are randomly distributed in position and may be randomly orientated. The wavelengths involved are assumed to be large compared with the size of the cracks and with their separation distances so that the formulae, based on the mean taken over a statistical ensemble, may reasonably be used to predict the properties of a single sample. The results are valid only for small concentrations of cracks. Explicit expressions, correct to lowest order in the ratio of the crack size to a wavelength, are derived here for the overall elastic parameters and the overall wave speeds and attenuation of elastic waves in cracked materials where the mean crack is circular, and the cracks are either aligned or randomly orientated. The cracks may be empty or filled with solid or fluid material. These results are achieved on the basis of simply the static solution for an ellipsoidal inclusion under stress. The extension to different distributions of orientation or to mixtures of different types of crack is quite straightforward.