Discontinuous

At pressures above the highest real data point, the extrapolated data were generated by the correlation of Lyckman et al. (1965), modified slightly to eliminate any discontinuity between the real and generated data. This modification is small, only a few percent, well within the uncertainties of the Lyckman method. The Lyckman correlation was always used within its recommended limits of validity--that is, at reduced temperatures no greater than 1.5 to 2.0. 

In a batch process, the main steps operate discontinuously. In contrast with a continuous process, a batch process does not deliver its product continuously but in discrete amounts. This means that... 

It was used as an end component in a few azo-dyes, but this use has been discontinued because of its carcinogenic character. 

Initial portion of the TBP curve of a Saharan crude oil (Note the discontinuities due to the presence of aromatics benzene B, toluene T, xylenes X). 

Normal pressure regimes follow a hydrostatic fluid gradient from surface, and are approximately linear. Abnormal pressure regimes include overpressured and underpressured fluid pressures, and represent a discontinuity in the normal pressure gradient. Drilling through abnormal pressure regimes requires special care. 

If a pressure measuring device were run inside the capillary, an oil gradient would be measured in the oil column. A pressure discontinuity would be apparent across the interface (the difference being the capillary pressure), and a water gradient would be measured below the interface. If the device also measured resistivity, a contact would be determined at this interface, and would be described as the oil-water contact (OWC). Note that if oil and water pressure measurements alone were used to construct a pressure-depth plot, and the gradient intercept technigue was used to determine an interface, it is the free water level which would be determined, not the OWC. 

Horizontal wells have a large potential to connect laterally discontinuous features in heterogeneous or discontinuous reservoirs. If the reservoir quality is locally poor, the subsequent section of the reservoir may be of better quality, providing a healthy productivity for the well. If the reservoir is faulted or fractured a horizontal well may connect a series of fault blocks or natural fractures In a manner which would require many vertical wells. The ultimate recovery of a horizontal well is likely to be significantly greater than for a single vertical well. 

Beside this pre-warning feature AE can be used parallel as a NDT technique to detect, locate and roughly grade any active (growing) discontinuity in the structure under test. 

Figure 6 shows the histogram of localized AE events vs axial position for the same time period as in fig.5. The location of the AE source corresponds, within source location errors (< 10-15 cm), to one of the welds under surveillance. The weld was known by ultrasonic examination to be affected by internal discontinuities. However, the position of the source could also correspond to one of the hangers. The steps observed in EA event accumulation have taken place during steady load operation, which normally corresponds to very low background noise conditions. This type of event, however, has not been observed afterwards. 

A new one-dimensional mierowave imaging approaeh based on suecessive reeonstruetion of dielectrie interfaees is described. The reconstruction is obtained using the complex reflection coefficient data collected over some standard waveguide band. The problem is considered in terms of the optical path length to ensure better convergence of the iterative procedure. Then, the reverse coordinate transformation to the final profile is applied. The method is valid for highly contrasted discontinuous profiles and shows low sensitivity to the practical measurement error. Some numerical examples are presented. 

There have been numerous efforts to inspect specimens by ultrasonic reflectivity (or pulse-echo) measurements. In these inspections ultrasonic reflectivity is often used to observe changes in the acoustical impedance, and from this observation to localize defects in the specimen. However, the term defect is related to any discontinuity within the specimen and, consequently, more information is needed than only ultrasonic reflectivity to define the discontinuity as a defect. This information may be provided by three-dimensional ultrasonic reflection tomography and a priori knowledge about the specimen (e.g., the specimen fabrication process, its design, the intended purpose and the material). A more comprehensive review of defect characterization and related nondestructive evaluation (NDE) methods is provided elsewhere [1]. 

In this paper, discontinuities in cylindrical specimens were studied by ultrasonic reflection tomography. The aim was threefold. First, to localize discontinuities from circular C-scan images. Second, to reconstruct quantitative cross-sectional images from circular B-scan profiles (i.e., reflection tomograms). Finally, to obtain three-dimensional information (i.e., discontinuity location, dimension and type) by stacking these reflection tomograms in multiple planes, in the third dimension. 

In order to ensure perpendicular beam incidence on the cylindrical specimen, the circular B-scan profiles were acquired by high frequency (narrow beam) transducers in a synthetic circular aperture array. From these profiles two-dimensional reflection tomograms were reconstructed using a filtered backprojection technique. Straight line propagation was assumed. Several artificial discontinuity types in a cylindrical Plexiglas (Perspex) specimen were compared with similar artificial discontinuities in a cylindrical A/Si-alloy [2]. Furthermore, examples of real discontinuities (an inclusion and a feed head) in the cylindrical AlSi-alloy are presented. 

Some of the problems often encountered during ultrasonic inspection of plane specimens are also found on cylindrical specimens. For example, problems associated with the directional characteristic of the ultrasonic transducer. Furthermore, the discontinuity influences the shape and propagation direction of a reflected pulse, causing wave mode transformation. In addition, the specimen influences the shape and amplitude of the reflected pulse by sound absorption. 

Some discontinuities may be identified by a conventional two-dimensional ultrasonic technique, from which the well-known C-scan image is the most popular. The C-scan technique is relatively easy to implement and the results from several NDE studies have been very encouraging [1]. In the case of cylindrical specimens, a circular C-scan image is convenient to show discontinuity information. The circular C-scan image shows the peak amplitude of a back-scattered pulse received in the circular array. The axial scan direction is shown as a function of transducer position in the circular array. The circular C-scan image serves also as an initial step for choosing circular B-scan profiles. The latter provides a mapping between distance to the discontinuity and transducer position in the circular array. 

Fig. 2. Three time gates set to measure backseattered pulse from cylinder interface echo (gate 1), echo from discontinuity (gate 2) and back echo (gate 3).

Fig. 3. Circular C-scan image of A/Si-alloy cylinder showing six discontinuity types. Grey scale in [dB] of echo from discontinuity (gate 2).

Although the discontinuities may be seen clearly in the circular C-scan image, the image represents only a projection of discontinuities in a specific direction (i.e., a shadow of overlapping discontinuities). More information of the discontinuities according to location, dimension and type may be achieved by ultrasonic computed tomography (UCT) imaging. 

Fig. 5. shows six ultrasonic reflection tomograms. Three of these are from the Plexiglas specimen (shown left) and three are from the AlSi-alloy (shown right). The tomograms are reconstructed from reflection data measured across the plane (b), (c) and (e), respectively. The dark regions indicate high reflectivity and represent specimen interfaces and discontinuities. 

The reflection tomograms (c) show the axial hole in the Plexiglas specimen, but also a real discontinuity in the A/5i -alloy. The internal discontinuity is located 6 mm from the edge, 50° from the axial hole and its dimension is about 1-2 mm. This may be an inclusion or a porosity (void). Multiple reflections from the measurement were ignored in the calculation of the Plexiglas tomogram (left). This is seen as a bright circle. 

The three pairs of reflection tomograms are listed in Table 2, showing the artificial and real discontinuities in the Plexiglas and A/5i-alloy cylinder, respectively. 

Table 2. Discontinuities in Plexiglas specimen and AZ5i-alloy.

Several discontinuity types in Plexiglas and A/SZ-alloy cylindrical specimens were studied by... 

First, by circular array imaging A synthetic circular aperture array was used to obtain circular C-scan images. These images displayed the location of different discontinuity types, although only shadow images were obtained. 

Secondly, the linearized inverse problem is, as well as known, ill-posed because it involves the solution of a Fredholm integral equation of the first kind. The solution must be regularized to yield a stable and physically plausible solution. In this apphcation, the classical smoothness constraint on the solution [8], does not allow to recover the discontinuities of the original object function. In our case, we have considered notches at the smface of the half-space conductive media. So, notche shapes involve abrupt contours. This strong local correlation between pixels in each layer of the half conductive media suggests to represent the contrast function (the object function) by a piecewise continuous function. According to previous works that we have aheady presented [14], we 2584... 

An implicit edge process is involved in the regularization process where A acts as a scale parameter which gives a constraint on the size of the homogeneous patches and p. comes from ho = -y/ p/A where ho is the threshold above which a discontinuity is introduced. We propose, then to combine these two functionals to obtain a satisfactory solution ... 

Electromagnetic Evaluation of Material Discontinuities Shape and Severity. 

This work presents the theoretieal results and their experimental verifications concerning two possible methods for predicting the material discontinuities shape and severity. The methods are developed for the case of the eddy current transducer with orthogonal coils, for two situations for long crack-tjfpe discontinuities, a metod based on the geometrical diffraction has been used, while in the ease of short discontinuities the holographic method is prefered. 

The purpose of the nondestructive control consists in detecting local modifications of the material parameters which, by their presence can endanger the quality of the half-finished or finished products. The electromagnetic nondestructive control permits to render evident surface and subsurface discontinuities in the electroconductive material under test. The present tendency of this control is to pass from a qualitative evaluation (the presence or absence of the material discontinuities which give at the output of the control equipment a signal higher or at least equal to that coming from a standard discontinuity whose shape and severity has been prescribed by the product standards) to a quantitative one, which enables to locate as exactly as possible the discontinuity and to make predictions over its shape and severity. 

This work presents two procedures of quantitative evaluation of the material discontinuities, using the eddy current method. One of the procedures concerns the long surface or subsurface crack-type discontinuities in a flat conductive body. The second procedure allows a quantitative evaluation of short discontinuities, such as voids, inclusions etc. 

Let us consider a conductive material of conductivity o in which a long, very narrow discontinuity was machined under the examined material surface The surface examination is accomplished with a transducer with orthogonal coils, the coil parallel to the inspected surface serving as emission coil, and the coil perpendicular to the surface being the reception coil. 

The problem consists in finding as precisely as possible the discontinuity position and in estimating its sub-surface depth. For this reason, a method has been developed based on the general theory of electromagnetic wave diffraction on the discontinuity [6], [7]. 

In this theory, the fundamental notion is the concept of beam introduced similarly to that ft om the geometrical optics. The faces of the discontinuity will reflect all the electromagnetic beams due to the zero conductivity of the air filling the discontinuity The edge of the discontinuity will diffract the incident beam similarly to the Fresnel diffraction in optics. 

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