Correlation effects on Raman scattering from lowenergy vibrational modes in fractal and disordered systems. I. TheoryThe frequencies and intensities of the Raman spectrum of thermally polymerizing styrene were measured in order to confirm (or correct) the mode assignments in the literature and to observe the effect of polymerization on the Raman active modes. The spectra were measured over a period of three weeks while an originally highly purified sample of monostryrene was kept at about 100 'C. The polymer vibrations are identified with their monomer "origins" which are in turn compared to known benzene (or benzene derivatives) and ethylene (or vinyl group) vibrations.
Summary. This paper discusses the main reservoir engineering and fracture mechanics aspects of fracturing horizontal wells. Specifically, the paper discusses fracture orientation with respect to a horizontal wellbore, locating a horizontal well to optimize fracture height, determining the optimum number of fractures intercepting a horizontal well, and the mechanism of fluid flow into a fractured horizontal well. Introduction Interest in horizontal well drilling and completions has increased during the last few years. The significant advances in drilling and monitoring technology have made it possible to drill, guide, and monitor horizontal holes, making horizontal drilling not only possible but also consistently successful. Most wells have been completed as drainholes. These drainholes have been used in primary production and in EOR. Papers on drilling, completion, well testing, and increased production of horizontal vs. vertical wells have been presented in the petroleum literature. Many papers have dealt with steady-state production increase of horizontal wells over vertical wells Graphs and equations have been presented for calculating steady-state ratios for both fractured and unfractured wells. Ref. 2 provides a recent review of this technology. Other authors have studied the transient behavior of pressure response during a drawdown or a buildup of a drainhole. The literature lacks comprehensive studies on fracturing horizontal wells, and none of the studies cited above discussed this subject. Only Karcher et al. studied production increase caused by multiple fractures intercepting a horizontal hole. Using a numerical simulator, Karcher studied steady-state behavior of infinite-conductivity fractures. Stability of horizontal holes during drilling is another important aspect of horizontal well technology. It has been found that the degree of stability of horizontal holes depends on the relative magnitude of the three principal stresses and the orientation of the wellbore with respect to the minimum horizontal stress. Although productivity of horizontal wells could be two to five times higher than productivity of vertical wells, fracturing a horizontal well may further enhance its productivity, especially when formation permeability is low. Presence of shale streaks or low vertical permeability that impedes fluid flow in the vertical direction could make fracturing a horizontal well a necessity. This paper discusses fracturing horizontal wells from both reservoir engineering and fracture mechanics points of view. Our goal is to shed some light on important aspects of fracturing horizontal wells. Stress Magnitude and Orientation The first parameter to be determined is the fracture orientation with respect to the wellbore. Because fractures are always perpendicular to the least principal stress, the questions actually concern wellbore- and stress-orientation measurements. In what direction will induced fractures occur? What is the anticipated fracture geometry? What is the optimum length of the perforation interval? What is the optimum treatment size? What are the expected fracturing pressures? Data necessary for planning a fracturing treatment are the mechanical properties of the formation, the orientation and magnitude of the least principal stress, the variation in stresses above and below the target formaation, and the leakoff characteristics of the formation. It is commonly accepted that, at depths usually encountered in the oil field, the least principal stress is a horizontal stress. It also can be shown that the induced fracture will be oriented perpendicular to the least principal stress. The result is that a fracture created by a treatment will be in a vertical plane. If the horizontal segment is drilled in the direction of the least stress, several vertical fractures may be spaced along its axis wherever perforations are present. This spacing is one of the design parameters to be selected. Usually, this is investigated with numerical simulators. If the horizontal segment is drilled perpendicular to the least stress, one vertical fracture will be created parallel to the well. Figs. 1 and 2 show fracture direction vs. well direction. When the wellbore is not in one of these two major directions, several scenarios may occur, depending on the angle between the wellbore and the stress direction and on the perforation distribution and density. JPT P. 966⁁
Adiabatic values for a selection of energy levels and matrix elements of the quadrupole moment and the polarizability of H2, HD, D2, HT, DT, and T2 are presented. Additional energy levels and matrix elements are available for a minimal charge upon request from the Depository of Unpublished Data, C.I.S.T.I., National Research Council of Canada, Ottawa, Ont., Canada K1A 0S2.
Delta algorithms compress data by encoding one file in terms of another. This type of compression is useful in a number of situations: storing multiple versions of data, displaying differences, merging changes, distributing updates, storing backups, transmitting video sequences, and others. This article studies the performance parameters of several delta algorithms, using a benchmark of over 1,300 pairs of files taken from two successive releases of GNU software. Results indicate that modern delta compression algorithms based on Ziv-Lempel techniques significantly outperform diff, a popular but older delta compressor, in terms of compression ratio. The modern compressors also correlate better with the actual difference between files without sacrificing performance.
The Hamiltonian describing the rotation and vibration of a homonuclear diatomic molecule in the field of a point charge at a fixed distance from its centre-of-mass is given. Numerical results for the Stark shift of the molecular levels due to a point charge of either sign are listed for H2, D2, and T2 as a function of the separation of the point charge from the molecule. The intensity associated with transitions between perturbed levels is discussed briefly.
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