Data interpolation

A typical apphcatiou of a simple batch still might be distillation of an ethanol-water mixture at 101.3 kPa (1 atm). The initial charge is 100 mol of ethanol at 18 mole percent, aud the mixture must be reduced to a maximum ethanol concentration in the stiU of 6 mole percent. By using equilibrium data interpolated from Table 13-1,... 

HETP Prediction HETP can be predicted from mass-transfer models, rules of thumb, and data interpolation. 

Data Interpolation Interpolation of experimental HETP data is the most reliable means of obtaining design HETP values. This is hardly surprising in an area where our understanding of the theory is so poor that rules of thumb can do better than theoretical models. The author believes that it is best to derive HETP from experimental data, and to check it against a rule of thumb. 

Vital et al. (131) present an extensive tabulation of tray efficiency data collected from the published literature, Data interpolation is one of the more reliable methods for obtaining tray efficiency, provided the data are good and the rules recommended for data scale-up (Secs. 7.3,6 and 7.3.7) are followed. 

Flood prediction by interpolation. GPDC interpolation plote are used to interpolate actual flood data. Data interpolation gives accurate flood-point prediction, but can only be used where sufficient flood point data are available. 

Chapter 10 presents a compendium of GPDC data interpolation charts for flood, MOC, and pressure drop prediction, both for random and structured packings. When flood data are absent, pressure drop data can be used for approximating the flood point using Eq. (8.1). 

Which method to use, Data interpolation is generally the most accurate and should be preferred whenever flood data are available. Otherwise either if pressure drop data are available or when pressure drop can be reliably predicted, Eq. (8.1) is recommended. When the packing factor Fp exceeds 60, the Eckert correlation, Fig. 8.17 is recommended. At... 

Both calculations are in good agreement. Since data interpolation is more accurate than correlation, the values calculated by interpolation ... 

This chapter presents an atlas of charts for interpolating flood, pressure drop, and MOC. For random and grid packings (Charts 10.1002 to 10.3517 and 10.8005 to 10.8205), the charts are plots of the Eckert generalized pressure drop correlation (GPDC) curves, with experimental data superimposed on them. These plots permit data interpolation... 

Estimating flood and pressure drop using the GPDC interpolation charts involves data interpolation and extrapolation within the framework of the generalized pressure drop correlation (GPDC) chart (Fig. 8.196 or c), This technique is expected to yield reliable estimates when appropriate data are available in the vicinity of the operating point. The reliability of the estimates will diminish with the extent to which extrapolation is required. Whenever extensive extrapolation is required, the estimates are unreliable, and the calculation is best abandoned. 

Currently, interpolation of experimental HETP data is the most reliable means of obtaining packed-tower design HETPs. Due to our poor understanding of packing hydraulics and mass transfer, rules of thumb outperform theoretical models, while data interpolation outperforms both (Secs. 9.1.4 to 9.1.6). 

The procedure below is based on the axiom that while data interpolation is generally quite reliable, extrapolation seldom is. Extrapolation is best avoided. When unavoidable, it must be performed conservatively and with extreme caution. The following steps are recommended. 

Contrary to a popular belief, Borne distillation characteristics still cannot be satisfactorily predicted by correlation, regardless of the number of correlations available for their prediction, Data interpolation with the aid of an empirical procedure is probably the most reliable means of estimating these characteristics, The last two chapters of this book provide the designer with the data needed. 

Figure 25. (top) Dielectric loss spectra of glycerol, including time domain data, interpolated by applying the GGE distribution, cf. Eq. 36 (solid lines) (bottom) corresponding derivatives of both the data (points) and fit (solid line) (from [142].)... 

To solve the above mentioned problems various tasks are often included within interface modules, as well as data interpolation, meteorological fields downscaling, boundary layer parametrizations and estimation of dispersion coefficients, evaluation of meteorological driven emissions (e.g. biogenic, wind blown dust, sea salt), enhancement of physiographic data. 

Figure 12 The complex permittivity of water and 2.8 molal aqueous glucose solution at 278 K O, t.d.s measurement of e water) , t.ds. measurement of e iyvater) ----------------------,., data interpolated from ref. 24 ...

The present volume is concerned with low-temperature oxidation of hydrocarbons but the data sources cited in this section cover both higher and lower temperature regimes. As indicated earlier most of the direct measurements of rate constants of elementary reactions have been carried out at high temperatures (>1000 K) or temperatures close to ambient. It is only relatively recently that experimental techniques have been modified to produce substantial quantities of data for the intermediate temperatures pertinent to low-temperature oxidation of hydrocarbons, and much of the data for modelling low-temperature oxidation of hydrocarbons must be obtained from extrapolation of low-temperature data, interpolation between high- and low-temperature data, or by estimation methods. Consequently both the evaluations produced for modelling flames and those for atmospheric modelling are relevant. 

LINEST can also be used to find the regression coefficients for equations of higher order. It is sometimes convenient, in the absence of a suitable equation, to fit data to a power series. The equation can then be used for data interpolation. Often a power series y = a + hx + cx + dx is sufficient to fit data of moderate curvature. The lowest order polynomial that produces a satisfactory fit should be used if there are N data points, the highest order polynomial that can be used is of order (N -1). 

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