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  [c.37]

Since the accuracy of experimental data is frequently not high, and since experimental data are hardly ever plentiful, it is important to reduce the available data with care using a suitable statistical method and using a model for the excess Gibbs energy which contains only a minimum of binary parameters. Rarely are experimental data of sufficient quality and quantity to justify more than three binary parameters and, all too often, the data justify no more than two such parameters. When data sources (5) or (6) or (7) are used alone, it is not possible to use a three- (or more)-parameter model without making additional arbitrary assumptions. For typical engineering calculations, therefore, it is desirable to use a two-parameter model such as UNIQUAC.  [c.43]

In Equation (24), a is the estimated standard deviation for each of the measured variables, i.e. pressure, temperature, and liquid-phase and vapor-phase compositions. The values assigned to a determine the relative weighting between the tieline data and the vapor-liquid equilibrium data this weighting determines how well the ternary system is represented. This weighting depends first, on the estimated accuracy of the ternary data, relative to that of the binary vapor-liquid data and second, on how remote the temperature of the binary data is from that of the ternary data and finally, on how important in a design the liquid-liquid equilibria are relative to the vapor-liquid equilibria. Typical values which we use in data reduction are Op = 1 mm Hg, = 0.05°C, = 0.001, and = 0.003  [c.68]

The method described here is based on the high degree of correlation of model parameters, in this case, UNIQUAC parameters. Thus, although a certain set of binary parameters may be best for VLE data, we are able to find other sets of binary parameters for the miscible binaries which significantly improve ternary LLE prediction while only slightly decreasing accuracy of representation of the binary VLE. Fitting ternary LLE data only, may yield unrealistic parameters that predict grossly erroneous results when used in regions not identical to those employed in data reduction. By contrast, fitting ternary LLE data simultaneously with binary VLE data, effectively provides constraints on the binary parameters, preventing them from attaining arbitrary values of little physical significance. Determination of a single set of parameters which can adequately represent both VLE and LLE is particularly important in three-phase distillation.  [c.69]

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.  [c.69]

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 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
Figure 4-17. 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 some loss of accuracy. Figure 4-17. 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 some loss of accuracy.
The accuracy of the calculations depends directly on the reliability of the experimental data. The correlated data presented in the Appendices were taken from standard literature sources while these data are probably reliable for most fluids, it is not possible to be certain that they are reliable for all.  [c.95]

While many methods for parameter estimation have been proposed, experience has shown some to be more effective than others. Since most phenomenological models are nonlinear in their adjustable parameters, the best estimates of these parameters can be obtained from a formalized method which properly treats the statistical behavior of the errors associated with all experimental observations. For reliable process-design calculations, we require not only estimates of the parameters but also a measure of the errors in the parameters and an indication of the accuracy of the data.  [c.96]

In many process-design calculations it is not necessary to fit the data to within the experimental uncertainty. Here, economics dictates that a minimum number of adjustable parameters be fitted to scarce data with the best accuracy possible. This compromise between "goodness of fit" and number of parameters requires some method of discriminating between models. One way is to compare the uncertainties in the calculated parameters. An alternative method consists of examination of the residuals for trends and excessive errors when plotted versus other system variables (Draper and Smith, 1966). A more useful quantity for comparison is obtained from the sum of the weighted squared residuals given by Equation (1).  [c.107]

C. These values are su but are not reliable for high accuracy in molar volumes.  [c.139]

Appendix C-6 gives parameters for all the condensable binary systems we have here investigated literature references are also given for experimental data. Parameters given are for each set of data analyzed they often reflect in temperature (or pressure) range, number of data points, and experimental accuracy. Best calculated results are usually obtained when the parameters are obtained from experimental data at conditions of temperature, pressure, and composition close to those where the calculations are performed. However, sometimes, if the experimental data at these conditions are of low quality, better calculated results may be obtained with parameters obtained from good experimental data measured at other conditions.  [c.144]

It must be emphasized that Eq. (6.7) is only an approximate method for calculating the performance of refrigeration cycles. If greater accuracy is required, the refrigeration cycle must be followed using thermodynamic properties of the refrigerant being used. °  [c.209]

Heat exchanger cost laws often can be adjusted with little loss of accuracy such that the coefficient c is constant for different specifications, i.e.. Cl = Ca = c. In this case, Eq. (7.23) simplifies to  [c.230]

Choose a reference cost law for the heat exchangers. Greatest accuracy results if the category of streams which makes the largest contribution to capital cost is chosen as reference.  [c.230]

Overall, the accuracy of the capital cost targets is more than good enough for the purposes for which they are used  [c.233]

Information contained in this work has been obtained by McGraw-Hill, Inc., from sources believed to be reliable. However, neither McGraw-Hill nor its authors guarantees the accuracy or completeness of any information published herein, and neither McGraw-Hill nor its authors shall be responsible for any errors, omissions, or damages arising out of use of this information. This work is pubhshed with the understanding that McGraw-Hill and its authors are supplying information, but are not attempting to render engineering or other professional services. If such services are required, the assistance of an appropriate professional should be sought.  [c.464]

With regard to hydrogen, the accuracy is deemed insufficient for obtaining the hydrogen balance in a refining process. A rather cumbersome answer used at times is to determine the content by macro analysis. The hydrogen content in approximately one gram of sample is calculated by weighing the water formed. More recently, a totally different technique has appeared, hydrogen analysis by nuclear magnetic resonance. Refer to article The order of magnitude of the absolute error is 0.05%.  [c.29]

In all these methods, the accuracy depends on the sulfur concentration in relative value, the error is estimated to be about 0.1%.  [c.32]

The choice between X-ray fluorescence and the two other methods will be guided by the concentration levels and by the duration of the analytical procedure X-ray fluorescence is usually less sensitive than atomic absorption, but, at least for petroleum products, it requires less preparation after obtaining the calibration curve. Table 2.4 shows the detectable limits and accuracies of the three methods given above for the most commonly analyzed metals in petroleum products. For atomic absorption and plasma, the figures are given for analysis in an organic medium without mineralization.  [c.38]

As stated earlier, these hydrocarbons are difficult to quantify with accuracy. The FIA method, which is a chromatographic adsorption on silica, gives volume percentages of saturated hydrocarbons, olefins and aromatics.  [c.81]

Because of the existence of numerous isomers, hydrocarbon mixtures having a large number of carbon atoms can not be easily analyzed in detail. It is common practice either to group the constituents around key components that have large concentrations and whose properties are representative, or to use the concept of petroleum fractions. It is obvious that the grouping around a component or in a fraction can only be done if their chemical natures are similar. It should be kept in mind that the accuracy will be diminished when estimating certain properties particularly sensitive to molecular structure such as octane number or crystallization point.  [c.86]

The method of contributing groups does not apply with sufficient accuracy for the following calculations  [c.93]

The accuracy of the conversion depends on the smoothness of the D 86 curve. Errors affect essentially the points in the low % distilled ranges. Average error is on the order of 5°C for conversion of a smooth curve.  [c.100]

The error is about 3% when the are known with accuracy.  [c.116]

This relation should not be applied for temperatures less than 0°C. Its average accuracy is on the order of 5%. For a Watson factor ot 11.8, the C j can be obtained from the curve shown in Figure 4.4. For different K, values, the following correction is used (  [c.121]

Liquid viscosity is one of the most difficult properties to calculate with accuracy, yet it has an important role in the calculation of heat transfer coefficients and pressure drop. No single method is satisfactory for all temperature and viscosity ranges. We will distinguish three cases for pure hydrocarbons and petroleum fractions  [c.126]

The Mehrotra and ASTM methods apply with acceptable accuracy only for viscosities between 1 and 1000 mPa s. The average error is about 20%. The largest spreads are obtained at low and very high viscosities.  [c.129]

It is difficult to judge the accuracy of these methods because data are scarce. Table 4.9 compares the values obtained by different weighting methods with experimental values for a mixture of n-hexane-n-hexadecane at 25°C. The ASTM method shows results very close to those obtained experimentally.  [c.131]

There have been several equations of state proposed to express the compressibility factor. Remarkable accuracy has been obtained when specific equations for certain components are used however, the multitude of their coefficients makes their extension to mixtures complicated.  [c.138]

The average accuracy of the Lee and Kesler model is much better than that of all cubic equations for pressures higher than 40 bar, as well as those around the critical point.  [c.138]

The accuracy of our calculations is strongly dependent on the accuracy of the experimental data used to obtain the necessary parameters. While we cannot make any general quantitative statement about the accuracy of our calculations for multicomponent vapor-liquid equilibria, our experience leads us to believe that the calculated results for ternary or quarternary mixtures have an accuracy only slightly less than that of the binary data upon which the calculations are based. For multicomponent liquid-liquid equilibria, the accuracy of prediction is dependent not only upon the accuracy of the binary data, but also on the method used to obtain binary parameters. While there are always exceptions, in typical cases the technique used for binary-data reduction is of some, but not major, importance for vapor-liquid equilibria. However, for liquid-liquid equilibria, the method of data reduction plays a crucial role, as discussed in Chapters 4 and 6.  [c.5]

Figure 1 compares data reduction using the modified UNIQUAC equation with that using the original UNIQUAC equation. The data are those of Boublikova and Lu (1969) for ethanol and n-octane. The dashed line indicates results obtained with the original equation (q = q for ethanol) and the continuous line shows results obtained with the modified equation. The original equation predicts a liquid-liquid miscibility gap, contrary to experiment. The modified UNIQUAC equation, however, represents the alcohol/n-octane system with good accuracy.  [c.44]

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.  [c.71]

Combining informativeness and accuracy with readability, Stephanie Yanchinski explores the hopes, fears and, more importantly, the realities of biotechnology - the science of using micro-organisms to manufacture chemicals, drugs, fuel and food.  [c.442]

Knowledge of the overall aromatics content and their distribution in mono-, di-, and polynuclear aromatics in diesel fuels has become necessary because of environmentally-related problems. These components are suspected of being at least p rtly responsible for diesel engine emissions. The need exists for a reliable and easy method (these considerations exclude spectrometry and NMR) to analyze aromatics. The method accepted by a commission of the European Committee of Standardization is liquid chromatography. The fixed phase is a silica modified by NH2 groups, the eluent is normal heptane, and detection is by refractometry although this type of detector has some disadvantages described in section Figure 3.17 shows a chn matpgJ am of a diesel motor fuel. Monoaromatics are quantified by cotfiparing their response to that of an orthoxylene standard, the diaromatics to a standard of a-methylnaphthalene and the polynuclear aromatics to a phenanthrene standard. The accuracy and reproducibility obtained during inter-laboratory round-robin tests are satisfactory and mean this method may be adopted in the near future as a European standard.  [c.81]

The methods that will be described are widely used and, for tbe most part, are integrated into commercial simulation softwares such as PR02, ASPEN + or HYSIM. They constitute the de facto standards and one forgets too often that they do have limited accuracy and range of application. During their integration into software programs, these methods sometimes are subjected to questionable modifications and generalizations.  [c.85]

Using computer programs compiicates the problem because the calculation accuracy is never given for commercial reasons. Furthermore, the ways in which the methods are executed are not explicit and the data banks are often considered secret and inaccessible.  [c.106]

The coefficient can be modified to include an experimental vTscdsIly af a reduced temperature between 0.85 and 0.95. This method applies only if the reduced density is less than 2.5 and the reduced temperature is greater than 0.85. Its average accuracy is about 30%.  [c.127]

See pages that mention the term Accuracy : [c.5]    [c.122]    [c.141]    [c.231]    [c.233]    [c.226]    [c.252]    [c.417]    [c.28]    [c.30]    [c.110]    [c.120]   
See chapters in:

Modern analytical chemistry  -> Accuracy

Cellular automata  -> Accuracy

Computational chemistry (2001) -- [ c.135 , c.137 , c.138 , c.139 , c.140 , c.360 ]

Langes handbook of chemistry (1999) -- [ c.2 , c.118 ]

Modern analytical chemistry (2000) -- [ c.38 ]

Modern Analytical Chemistry (2000) -- [ c.38 ]

Industrial ventilation design guidebook (2001) -- [ c.1130 , c.1404 ]

Chemical kinetics the study of reaction rates in solution (1990) -- [ c.51 ]