Magnetic resonance imaging in laboratory petrophysical core analysis

Magnetic resonance imaging (MRI) is a well-known technique in medical diagnosis and materials science. In the more specialized arena of laboratory-scale petrophysical rock core analysis, the role of MRI has undergone a substantial change in focus over the last three decades. Initially, alongside the continual drive to exploit higher magnetic field strengths in MRI applications for medicine and chemistry, the same trend was followed in core analysis. However, the spatial resolution achievable in heterogeneous porous media is inherently limited due to the magnetic susceptibility contrast between solid and fluid. As a result, imaging resolution at the length-scale of typical pore diameters is not practical and so MRI of core-plugs has often been viewed as an inappropriate use of expensive magnetic resonance facilities. Recently, there has been a paradigm shift in the use of MRI in laboratory-scale core analysis. The focus is now on acquiring data in the laboratory that are directly comparable to data obtained from magnetic resonance well-logging tools (i.e., a common physics of measurement). To maintain consistency with well-logging instrumentation, it is desirable to measure distributions of transverse (_T2$T_2$) relaxation time–the industry-standard metric in well-logging–at the laboratory-scale. These _T2$T_2$ distributions can be spatially resolved over the length of a core-plug. The use of low-field magnets in the laboratory environment is optimal for core analysis not only because the magnetic field strength is closer to that of well-logging tools, but also because the magnetic susceptibility contrast is minimized, allowing the acquisition of quantitative image voxel (or pixel) intensities that are directly scalable to liquid volume. Beyond simple determination of macroscopic rock heterogeneity, it is possible to utilize the spatial resolution for monitoring forced displacement of oil by water or chemical agents, determining capillary pressure curves, and estimating wettability. The history of MRI in petrophysics is reviewed and future directions considered, including advanced data processing techniques such as compressed sensing reconstruction and Bayesian inference analysis of under-sampled data. Although this review focuses on rock core analysis, the techniques described are applicable in a wider context to porous media in general, such as cements, soils, ceramics, and catalytic materials.     

Approximation of a laminated microstructure for a rotationally invariant,double well energy density

Summary. We give error estimates for the approximation of a laminated microstructure which minimizes the energy for a rotationally invariant, double well energy density . We present error estimates for the convergence of the deformation in the convergence of directional derivatives of the deformation in the “twin planes,” the weak convergence of the deformation gradient, the convergence of the microstructure (or Young measure) of the deformation gradients, and the convergence of nonlinear integrals of the deformation gradient. Received July 25, 1995 / Revised version received November 20, 1995     

Finite difference methods of solution of the von mises boundary layer equation with special reference to conditions near a singularity

Zusammenfassung Frühere Forscher haben die Misessche Gleichung als Mittel zur Lösung des Problems der Grenzschicht an der längsangeströmten ebenen Platte mit Druckanstieg nicht verwendet wegen ihrer unangenehmen Singularität an der Platte. In der vorliegenden Untersuchung wird eine Geschwindigkeitsverteilung berechnet, welche die Plattenbindungen berücksichtigt und folglich den Hautreibungswert durch die Geschwindigkeitswerte in der Grenzschicht berechnen lässt. Diese Werte werden ermittelt durch ein Fortsetzungsdifferenzenverfahren auf der Grundlage der Misesschen Gleichung sowie durch ein modifiziertes Differenzenverfahren in der Nähe der Platte. Dieses letzte Verfahren ist nötig wegen der Instabilität der ursprünglichen Fortsetzungsberechnung in der Nähe der Platte. Angesichts der verhältnismässig geringen Rechnungsarbeit stimmen die Ergebnisse gut überein mit den Lösungen anderer Forscher, die andere Formen der Grenzschichtgleichung benutzten. Die Genauigkeit der in dieser Untersuchung erreichten Ergebnisse lässt sich natürlich noch vermehren durch Anwendung einer kleineren Schrittweite bei der ersten Fortsetzungsberechnung.     

Dynamics of Finger Formation in Laplacian Growth Without Surface Tension

We study the dynamics of “finger” formation in Laplacian growth without surface tension in a channel geometry (the Saffman–Taylor problem). We present a pedagogical derivation of the dynamics of the conformal map from a strip in the complex plane to the physical channel. In doing so we pay attention to the boundary conditions (no flux rather than periodic) and derive a field equation of motion for the conformal map. We first consider an explicit analytic class of conformal maps that form a basis for solutions in infinitely long channels, characterized by meromorphic derivatives. The great bulk of these solutions can lose conformality due to finite time singularities. By considerations of the nature of the analyticity of these solutions, we show that those solutions which are free of such singularities inevitably result in a single asymptotic “finger” whose width is determined by initial conditions. This is in contradiction with the experimental results that indicate selection of a finger of width 1/2. In the last part of this paper we show that such a solution might be determined by the boundary conditions of a finite body of fluid, e.g. finiteness can lead to pattern selection.     

Miscibility studies of the smectic phases of trans,trans-4'-alkylbicyclohexyl-4-carbonitrile (CCH) liquid crystals

Complete temperature-composition phase diagrams for binary mixtures of 4'-ethyl-, 4'-propyl-, and 4'-butylbicyclohexyl-4-carbonitrile (CCH-2, CCH-3, and CCH-4, respectively) in each of the three possible combinations have been constructed from differential scanning calorimetry and thermal microscopy data. The highest temperature smectic phases of each of the pure mesogens are immiscible with one another, even though CCH-3 and CCH-4 have both been previously assigned the bilayer crystal-B structure on the basis of X-ray diffraction studies. The present studies indicate that the enantiotropic smectic phase of CCH-4 is slightly higher-ordered than is the monotropic smectic phase of CCH-3. The smectic phase of CCH-2, which previously has been found to be characterized by rhombohedral packing on the basis of X-ray diffraction data, is miscible with the second, previously uncharacterized (monotropic) smectic phase (S₂) of CCH-3. Photographs illustrating the subtle differences in the microscopic textures of these smectic phases are also presented.     

High-performance liquid chromatographic determination of 4-methylimidazole in sheep plasma and in ammoniated tall fescue hay

A method for 4-methylimidazole (4MI) extraction and quantitation in body fluids and forage samples was developed. The procedures involve ion-pair extraction of the compound with the quantitation done by ion-pair liquid chromatography. The results indicate that this high-performance liquid chromatographic method is sensitive, reproducible and more rapid than others that have been previously used. The mean recovery of 4MI from plasma and tall fescue (Festuca arundinacea) hay samples were above 95 and 85%, respectively. The versatility of the procedure makes it suitable for the determination of 4MI in body fluids and in forage samples.     

Liquid crystal elastomers: Synthesis and characterization

The synthesis is described of some acrylate based polymers containing both a mesogenic group (4-cyanophenyl benzoate) connected to the polymer backbone by a flexible spacer, and varying degrees of crosslinking, introduced by copolymerization. Optical and calorimetric techniques are used to determine the phase behavior, which is found to depend strongly on the crosslink density (and the flexible spacer length); though (nominally) a relatively high degree of crosslinking is possible without completely destroying the liquid crystal phase. Mechanical measurements in conjunction with supplementary analytical data, where available, are used to determine the efficiency of copolymerization at introducing intermolecular crosslinking. Some possible explanations for the unexpectedly low efficiency of this process are discussed. The properties of materials prepared in this fashion are compared briefly with some examples where crosslinking is introduced after polymerization; this latter process is seen to be rather more efficient.     

Some algorithms of the projective-Newton method for the finite element space

The paper presents the projective-Newton method in the finite element space with curved finite elements along the boundary. The properties of this method are studied when the integrals are calculated by numerical quadrature. Some algorithms are derived when ω = {x ? R²: 0 < x₁, x₂ < 1}.