Estimated from

Values of Rj, probably close to the required accuracy, can be estimated from the parachor, P the parachor can be calculated from a group-contribution method given by Reid et al. The... 

Figure 4-14. Predicted liquid-liquid equilibria for a typical type-II system shows good agreement with experimental data, using parameters estimated from binary data alone.

Many well-known models can predict ternary LLE for type-II systems, using parameters estimated from binary data alone. Unfortunately, similar predictions for type-I LLE systems are not nearly as good. In most cases, representation of type-I systems requires that some ternary information be used in determining optimum binary parameter. 

Figure 2 shows similar results for ethanol(1)-n-hexane(2) at 1 atm. The liquid-phase enthalpy of mixing was again estimated from UNIQUAC using temperature-independent parameters. 

The primary purpose for expressing experimental data through model equations is to obtain a representation that can be used confidently for systematic interpolations and extrapolations, especially to multicomponent systems. The confidence placed in the calculations depends on the confidence placed in the data and in the model. Therefore, the method of parameter estimation should also provide measures of reliability for the calculated results. This reliability depends on the uncertainties in the parameters, which, with the statistical method of data reduction used here, are estimated from the parameter variance-covariance matrix. This matrix is obtained as a last step in the iterative calculation of the parameters. 

If only two parameters are fit, C must set to some arbitrary value, usually one, and only Pqj and P 2) estimated from the VLE... 

Three parameters are estimated from binary VLE data and correspond to ... 

Execution times for the higher level subroutines FLASH and ELIPS will be highly dependent on the problems involved. The times required per iteration can be estimated from times for lower level subroutines and the descriptions given for FLASH and ELIPS. Computation times for two specific cases calculated with FLASH and one case claculated with ELIPS are included in Table J-1 to show approximate magnitudes required. 

Steam costs vary with the price of fuel. If steam is only generated at low pressure and not used for power generation in steam turbines, then the cost can be estimated from local fuel costs assuming a boiler efficiency of around 75 percent (but can be significantly higher) and distribution losses of perhaps another 10 percent, giving an overall efficiency of around 65 percent. 

The above coefficients are not absolutely required because they can be estimated from other characteristics. 

The standard specific gravity can be estimated from using the followinc relation ... 

Formation permeability around the wellbore can be measured directly on core samples from the reservoir or from well testing (see Section 8.4), or indirectly (estimated) from logs. 

The methods discussed above only give an indication of permeability near the wellbore. Reservoir permeability is usually estimated from production tests and is described in Section 9.4. 

In the experiments, the probabilities were estimated from the processed signal by means of a histogram. It is well known that the entropy is large for nearly uniform distributions and small for distributions with few peaks. Thus it is an interesting candidate as a performance measure when the goal is to process a signal to become more easily interpreted. 

More accurately, as the inverse problem process computes a quadratic error with every point of a local area around a flaw, we shall limit the sensor surface so that the quadratic error induced by the integration lets us separate two close flaws and remains negligible in comparison with other noises or errors. An inevitable noise is the electronic noise due to the coil resistance, that we can estimate from geometrical and physical properties of the sensor. Here are the main conclusions ... 

Wall Thickness Estimation from Digitized Radiographs. 

The visibility level VL of special viewing tasks may be estimated from the the correlations of the quantitative visual recognition. For an adaptation luminance of 10 cd/m2 and given contrasts (C = 0.5 1.0 2.0), VL is described in Fig. 1 in dependance on the object dimension 3 in angular minutes. An object dimension of T represents a circle with a diameter of 0 12 mm in a distance of 0 4 m. 

In a regression approach to material characterization, a statistical model which describes the relation between measurements and the material property is formulated and unknown model parameters are estimated from experimental data. This approach is attractive because it does not require a detailed physical model, and because it automatically extracts and optimally combines important features. Moreover, it can exploit the large amounts of data available. 

Thus each of the elements of the quality system is functioning by means of processes. Each process included in the system has to be estimated from different positions ... 

Benjamin Franklin s experiment is mentioned in the opening paragraphs of this chapter. Estimate, from his results, an approximate value for Avogadro s number make your calculation clear. The answer is a little off explain whether more accurate measurements on Franklin s part would have helped. 

Fig. VI-6. The force between two crossed cylinders coated with mica and carrying adsorbed bilayers of phosphatidylcholine lipids at 22°C. The solid symbols are for 1.2 mM salt while the open circles are for 10.9 roM salt. The solid curves are the DLVO theoretical calculations. The inset shows the effect of the van der Waals force at small separations the Hamaker constant is estimated from this to be 7 1 x 10 erg. In the absence of salt there is no double-layer force and the adhesive force is -1.0 mN/m. (From Ref. 66.)...

Calculate the Hamaker constant for Ar crystal, using Eq. VII-18. Compare your value with the one that you can estimate from the data and equations of Chapter VI. 

Here, x denotes film thickness and x is that corresponding to F . An equation similar to Eq. X-42 is given by Zorin et al. [188]. Also, film pressure may be estimated from potential changes [189]. Equation X-43 has been used to calculate contact angles in dilute electrolyte solutions on quartz results are in accord with DLVO theory (see Section VI-4B) [190]. Finally, the x term may be especially important in the case of liquid-liquid-solid systems [191]. 

The UV-visible absorption spectrum of Ru(2,2 -bipyridine)3 maximum at about 450 nm, from which the energy in volts for process XI-39 may be estimated. The standard reduction potential for the R" /R couple is about 1.26 V at 25°C. Estimate from this information (and standard reduction potentials) the potential in volts for processes XI-40 and XI-41. Repeat the calculation for alkaline solutions. 

The state of an adsorbate is often described as mobile or localized, usually in connection with adsorption models and analyses of adsorption entropies (see Section XVII-3C). A more direct criterion is, in analogy to that of the fluidity of a bulk phase, the degree of mobility as reflected by the surface diffusion coefficient. This may be estimated from the dielectric relaxation time Resing [115] gives values of the diffusion coefficient for adsorbed water ranging from near bulk liquids values (lO cm /sec) to as low as 10 cm /sec. 

A variety of experimental data has been found to fit the Langmuir equation reasonably well. Data are generally plotted according to the linear form, Eq. XVn-9, to obtain the constants b and n from the best fitting straight line. The specific surface area, E, can then be obtained from Eq. XVII-10. A widely used practice is to take to be the molecular area of the adsorbate, estimated from liquid or solid adsorbate densities. On the other hand, the Langmuir model is cast around the concept of adsorption sites, whose spacing one would suppose to be characteristic of the adsorbent. See Section XVII-5B for an additional discussion of the problem. 

The size of the electron-hole pair can be estimated from the Bolu radius for this system ... 

The value of at zero temperature can be estimated from the electron density ( equation Al.3.26). Typical values of the Femii energy range from about 1.6 eV for Cs to 14.1 eV for Be. In temis of temperature (Jp = p//r), the range is approxunately 2000-16,000 K. As a consequence, the Femii energy is a very weak ftuiction of temperature under ambient conditions. The electronic contribution to the heat capacity, C, can be detemiined from... 

The parameters in simple potential models for interactions between unlike molecules A and B are often deduced from tlie corresponding parameters for the A-A and B-B interactions using combination mles . For example, the a and e parameters are often estimated from the Lorentz-Berthelot mles ... 

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