Ties, tying

The SRTS sequence consists of a preparatory pulse and an arbitrary long train of the phase-coherent RF pulses of the same flip angle applied with a constant short-repetition time. As was noted above, the "short time" in this case should be interpreted as the pulse spacing T within the sequence that meets the condition T T2 Hd. The state that is established in the spin system after the time, T2, is traditionally defined as the "steady-state free precession" (SSFP), ° and includes two other states (or sub-states) quasi-stationary, that exists at times T2effective relaxation time) and stationary, that is established after the time " 3Tie after the start of the sequence.The SSFP is a very particular state which requires a specific mechanism for its description. This mechanism was devised in articles on the basis of the effective field concept and canonical transformations. Later approaches on the basis of the average-Hamiltonian theory were developed. ... 

UNIQUAC equation with binary parameters estimated by supplementing binary VLE data with ternary tie-line data. 

To illustrate the criterion for parameter estimation, let 1, 2, and 3 represent the three components in a mixture. Components 1 and 2 are only partially miscible components 1 and 3, as well as components 2 and 3 are totally miscible. The two binary parameters for the 1-2 binary are determined from mutual-solubility data and remain fixed. Initial estimates of the four binary parameters for the two completely miscible binaries, 1-3 and 2-3, are determined from sets of binary vapor-liquid equilibrium (VLE) data. The final values of these parameters are then obtained by fitting both sets of binary vapor-liquid equilibrium data simultaneously with the limited ternary tie-line data. 

The estimated true values must satisfy the appropriate equilibrium constraints. For points 1 through L, there are two constraints given by Equation (2-4) one each for components 1 and 2. For points L+1 through M the same equilibrium relations apply however, now they apply to components 2 and 3. The constraints for the tie-line points, M+1 through N, are given by Equation (2-6), applied to each of the three components. 

In most cases only a single tie line is required. When several are available, the choice of which one to use is somewhat arbitrary. However, our experience has shown that tie lines which are near the middle of the two-phase region are most useful for estimating the parameters. Tie lines close to the plait point are less useful, since no common models for the excess Gibbs energy can adequately describe the flat region near the... 

The continuous line in Figure 16 shows results from fitting a single tie line in addition to the binary data. Only slight improvement is obtained in prediction of the two-phase region more important, however, prediction of solute distribution is improved. Incorporation of the single ternary tie line into the method of data reduction produces only a small loss of accuracy in the representation of VLE for the two binary systems. 

Figure 4-16. Representation of ternary liquid-liquid equilibria using the UNIQUAC equation is improved by incorporating ternary tie-line data into binary-parameter estimation. Representation of binary VLB shows small loss of accuracy. ---- Binary...

Binary data only. ----- One tie-line plus binary data. 

Figure 17 shows results for the acetonitrile-n-heptane-benzene system. Here, however, the two-phase region is somewhat smaller ternary equilibrium calculations using binary data alone considerably overestimate the two-phase region. Upon including a single ternary tie line, satisfactory ternary representation is obtained. Unfortunately, there is some loss of accuracy in the representation of the binary VLB (particularly for the acetonitrile-benzene system where the shift of the aceotrope is evident) but the loss is not severe. 

Two further examples of type I ternary systems are shown in Figure 19 which presents calculated and observed selectivities. For successful extraction, selectivity is often a more important index than the distribution coefficient. Calculations are shown for the case where binary data alone are used and where binary data are used together with a single ternary tie line. It is evident that calculated selectivities are substantially improved by including limited ternary tie-line data in data reduction. 

Figure 4-19. Calculated selectivities in two ternary systems show large improvements when tie-line data are used to supplement binary VLB data for estimating binary parameters.

Type C. Component 1 is only partially miscible with coin -ponents 3 through m, but it is totally miscible with component 2. Components 2 through m are miscible with each other in all proportions. Again, both binary data and ternary tie-line data are needed ... 

Using the ternary tie-line data and the binary VLE data for the miscible binary pairs, the optimum binary parameters are obtained for each ternary of the type 1-2-i for i = 3. .. m. This results in multiple sets of the parameters for the 1-2 binary, since this binary occurs in each of the ternaries containing two liquid phases. To determine a single set of parameters to represent the 1-2 binary system, the values obtained from initial data reduction of each of the ternary systems are plotted with their approximate confidence ellipses. We choose a single optimum set from the intersection of the confidence ellipses. Finally, with the parameters for the 1-2 binary set at their optimum value, the parameters are adjusted for the remaining miscible binary in each ternary, i.e. the parameters for the 2-i binary system in each ternary of the type 1-2-i for i = 3. .. m. This adjustment is made, again, using the ternary tie-line data and binary VLE data. 

Type C requires the most complex data analysis. To illustrate, we have reduced the data of Henty (1964) for the system furfural-benzene-cyclohexane-2,2,4-trimethylpentane. VLB data were used in conjunction with one ternary tie line for each ternary to determine optimum binary parameters for each of the two type-I ternaries cyclohexane-furfural-benzene and 2,2,4-... 

The optimum parameters for furfural-benzene are chosen in the region of the overlapping 39% confidence ellipses. The ternary tie-line data were then refit with the optimum furfural-benzene parameters final values of binary parameters were thus obtained for benzene-cyclohexane and for benzene-2,2,4-trimethyl-pentane. Table 4 gives all optimum binary parameters for this quarternary system. 

The ternary diagrams shown in Figure 22 and the selectivi-ties and distribution coefficients shown in Figure 23 indicate very good correlation of the ternary data with the UNIQUAC equation. More important, however, Table 5 shows calculated and experimental quarternary tie-line compositions for five of Henty s twenty measurements. The root-mean-squared deviations for all twenty measurements show excellent agreement between calculated and predicted quarternary equilibria. 

The sample is placed in a cqnst a nt magnetic field, Bq, and the variation in frequency throughout the t/omain Tieing expfored excites one by one the different resonances. The scan lasts a few minutes. Inversely, one can maintain a constant frequency and cause the magnetic field to vary. 

In the case of three-phase equilibria, it is also necessary to account for the solubility of hydrocarbon gases in water. This solubility is proportional to the partial pressure of the hydrocarbon or, more precisely, to its partial fugacity in the vapor phase. The relation which ties the solubility expressed in mole fraction to the fugacity is the following ... 

Regarding product characteristics, European specifications were established in 1992. They concern mainly the motor octane number (MON) that limits the olefin content and which should be higher than 89, and the vapor pressure, tied to the C3/C4 ratio which should be less than 1550 mbar at 40°C (ISO 4256). On the other hand, to ensure easy vehicle start-ups, a minimum vapor pressure for winter has been set which is different for each country and depends on climatic conditions. Four classes. A, B, C, and D, are thus defined in Europe with a minimum vapor pressure of 250 mbar, respectively, at -10°C (A), -5 C (B), 0°C (C) and -t-10°C (Z)). France has chosen class A. 

Odor is of prime importance because a petroleum solvent is often used in closed rooms moreover, the idea of odor is tied instinctively in the public image to toxicity. Odor is a function of the solvent s composition and volatility. Generally, the paraffin hydrocarbons are less odorous while the aromatics are more so. 

After often a lengthy period (several months) of acquisition and processing, the data may be loaded onto a seismic workstation for interpretation. These workstations are UNIX based, dual screen systems (sections on one side, maps on the other, typically) where all the trace data is stored on fast access disk, and where the picked horizons and faults can be digitised from the screen Into a database. Of vital Importance is access to all existing well data in the area for establishing the well - seismic tie. 2D data will be interpreted line by intersecting line, and 3D as a volume. 

Appraisal activity should be based upon the information required. The first step is therefore to determine what uncertainties appraisal is trying to reduce, and then what information is required to tie down those uncertainties. For example, if fluid contacts are a major source of uncertainty, drilling wells to penetrate the contacts is an appropriate tool seismic data or well testing may not be. Other examples of appraisal tools are ... 

The field may enter into an economic decline when either income is falling (production decline) or costs are rising, and in many cases both are happening. Whilst there may be scope for further investment in a field in economic decline, it should not tie up funds that can be used more effectively in new projects. A mature development must continue to generate a positive cashflow and compete with other projects for funds. The options that are discussed in this section give some idea of the alternatives that may be available to manage the inevitable process of economic decline, and to extend reservoir and facility life. 

In integrated photoelasticity it is impossible to achieve a complete reconstruction of stresses in samples by only illuminating a system of parallel planes and using equilibrium equations of the elasticity theory. Theory of the fictitious temperature field allows one to formulate a boundary-value problem which permits to determine all components of the stress tensor field in some cases. If the stress gradient in the axial direction is smooth enough, then perturbation method can be used for the solution of the inverse problem. As an example, distribution of stresses in a bow tie type fiber preforms is shown in Fig. 2 [2]. 

Figure 2 Stress distribution in a bow tie type fiber preform.

The intermetallic compound layer shown in Fig. 10 are thought of FerTi and TiC[5]. This Tie is so called though is weak cause of the strength decrease [ 5]. 

Earth Water Air Cosmos Prod- uction Opera -lion Storage Secii- r-ties Arms Explosives, drugs Protection of places ... 

The first scientific-technical publications on NDT issues appeared in Ukraine already at the end of the 40-ties in Automatic iTh/iii g journal, in the subject collections on technical diagnostics and non-destructive testing. 

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