Correlated calculations 574 INDEX

The TOTAL correlations calculate aromatic carbon content, hydrogen content, molecular weight, and refractive index using routine laboratory tests. The TOTAL correlations are listed below and are also in Appendix 3. Example 2-2 illustrates the use of TOTAL correlations. 

Jensen [9] indicated that there is no evidence that Drago s parameters reflect the relative electrostatic and covalent contributions to the bonding in resulting adducts. They were not correlated with either a physical property (dipole moment, ionization potential) or with a quantum-mechanically calculated index. Drago s approach is a purely empirical method of calculating enthalpy of formation for molecular adducts. Fowkes applied the Lewis E C equation [19] and has attempted to determine E and C parameters for both polymers and surfaces. However, Jensen [9] indicated the potential problem connected... 

Table 9.1. Experimental dielectric constants e(exp), the quantities (cohesive energy Ecohl in J/mole, correction index Ndc> and van der Waals volume Vw in cc/mole) used in the correlation for e, and fitted dielectric constants e(fit), for 61 polymers. Ecohl is calculated from equations 5.8-5.10, and Vw is calculated from equations 3.10 and 3.11, for use in this correlation. Calculations on random copolymers are discussed in Section 17.E. 

The local MP2 electron-correlation method for nonconducting crystals [109] is an extension to crystalline solids of the local correlation MP2 method for molecules (see Sect. 5.1.5), starting from a local representation of the occupied and virtual HF subspaces. The localized HF crystalline orbitals of the occupied states are provided in the LCAO approximation by the CRYSTAL program [23] and based on a Boys localization criterion. The localization technique was considered in Sect. 3.3.3. The label im of the occupied localized Wannier functions (LWF) Wim = Wj(r — Rm) includes the type of LWF and translation vector Rm, indicating the primitive unit cell, in which the LWF is centered (m = 0 for the reference cell). The index i runs from 1 to A i, the number of filled electron bands used for the localization procedure the correlation calculation is restricted usually to valence bands LWFs. The latter are expressed as a linear combination of the Gaussian-type atomic orbitals (AOs) Xfiif Rn) = Xfin numbered by index = 1,..., M M is the number of AOs in the reference cell) and the cell n translation vector... 

In the case of metals (but also in the case of insulators) one can take a grid in k in each band and perform the excitations between the chosen k values. (One can take either an equidistant grid in k, or one can also apply a non-equidistant grid in which case one can subdivide the band according to the DOS distribution for details see the first reference of /4/.) To be able to perform the four index transformation necessary for any correlation calculation one can expand the LCAO coefficients c(k)p g occurring in equ. (1) in a simple trigonometric series /22/. 

An important application of this type of analysis is in the determination of the calculated cetane index. The procedure is as follows the cetane number is measured using the standard CFR engine method for a large number of gas oil samples covering a wide range of chemical compositions. It was shown that this measured number is a linear combination of chemical family concentrations as determined by the D 2425 method. An example of the correlation obtained is given in Figure 3.3. 

Cetane number is difficult to measure experimentally. Therefore, various correlation equations have been developed to predict cetane number from fuel properties. One such equation may be found in ASTM D4737 to calculate a cetane index (Cl). ASTM D975 allows use of Cl as an approximation if cetane numbers are not available. 

The critical characteristic on each component was analysed, calculated from the analysis and the value obtained was plotted against the process capability indices, Cpk and Cp, for the characteristic in question. See Appendix V for descriptions of the 21 components analysed, including the values of Cp and Cp from the SPC data supplied. Note that some components studied have a zero process capability index. This is a default value given if the process capability index calculated from the SPC data had a mean outside either one of the tolerance limits, which was the case for some of the components submitted. Although it is recognized that negative process capability indices are used for the aim of process improvement, they have little use in the analyses here. A correlation between positive values (or values which are at least within the tolerance limits) will yield a more deterministic relationship between design capability and estimated process capability. 

The n-d-M correlation is an ASTM (D-3238) method that uses refractive index (n), density (d), average molecular weight (MW), and sulfur (S) to estimate the percentage of total carbon distribution in the aromatic ring structure (% C ), naphthenic ring structure (Cj,), and paraffin chains (% Cp). Both refractive index and density are either measured or estimated at 20°C (68°F). Appendix 4 shows formulas used to calculate carbon distribution. Note that the n-d-M method calculates, for example, the percent of carbon in the aromatic ring... 

Step 2 Calculate refractive index 20°C from the TOTAL correlation. 

Cetane number is measured in a single-cylinder laboratory engine, but cetane index (Cl) is more commonly used. Cetane index is a calculated value and correlates adequately with the cetane number. Most refiners use the ASTM equation (Method D-976-80) to calculate the cetane index. The equation uses the 50% boiling point and API gravity (Example 6-1). 

Figure 9.2 displays a division of the mass range into 13 intervals. After multiplication of all the individual normalized correlation values, the composite correlation index is smaller and the method achieves more selectivity than it would if a single correlation function were calculated over the full mass range. A lower limit of 0.0001 was placed on the value for each normalized interval comparison to prevent the method from generating absurdly low values. These... 

Body mass index (BMI) is another index of weight-for-height that is highly correlated with body fat. Interpretation of BMI should include consideration of gender, frame size, and age. BMI values greater than 25 kg/m2 are indicative of overweight, and values less than 18.5 kg/m2 are indicative of undernutrition. BMI is calculated as follows ... 

Fig. 2. The distribution of the calculated FeS index from groundwater results at the Teutonic Bore / Jaguar VMS camp. Results correlate closely with known ore bodies and prospects.

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