Saturation fraction

As the temperatures of the distillation cuts increase, the problems get more complicated to the point where preliminary separations are required that usually involve liquid phase chromatography (described earlier). This provides, among others, a saturated fraction and an aromatic fraction. Mass spectrometry is then used for each of these fractions. 

A wheat germ, cell-free, translation extract was fractionated into three concentrated parts using ammonium sulfate the 0 - 40 % saturated fraction, the 40 - 60 % saturated fraction, and the ribosome fraction. These fractions were tested for their ability to enhance the translational activity of the wheat germ, cell-free extract for dihydrofolate reductase. The fortified cell-free system supplemented with the 0 - 40 % ammonium sulfate fraction enhanced the efficiency of protein synthesis by 50 %. 

For oil A, slight differences in composition exist the aromatic and resin fractions hardly decrease to form lighter saturate compounds. The effects are quite similar to those on oil B whose global composition does not change. But in the saturate fraction, the amount of n and iso alkanes is three times higher in the recovered samples than in the initial one (Fig. 11). 

The fractions from elution chromatography were studied by a number of spectroscopic methods, n.m.r., i.r., u.v., fluorescence and phosphorescence spectroscopy. Equivalent fractions from chromatographic separation of the various oils showed no significant differences in their spectra and it appears that the composition of the fractions was independent of the catalyst concentration used to produce the oil. Though, as previously mentioned the amounts of the various fractions especially the polar fractions differ with the catalyst concentration. G.1.C. analysis of the saturate fractions also indicated no changes with different catalyst concentrations. 

Another relevant feature of the gas chromographic profile is the acyclic isoprenoid hydrocarbon pattern that is made evident with capillary columns or by the inclusion of the saturated fraction in 5 A (0.5 nm) molecular sieves or in urea. The predominant peaks usually correspond to the C19 (pristaine) and C20 (phytane) isomers, which ratios serve as an identification parameter [87], although the series extends to lower and higher homologues. 

The methods include the use of mass spectrometry to determine (1) the hydrocarbon types in middle distillates (ASTM D2425) (2) the hydrocarbon types of gas oil saturate fractions (ASTM D2786) (3) the hydrocarbon types in low-olefin gasoline (ASTM D2789) and (d) the aromatic types of gas oil aromatic fractions (ASTM D3239). 

Most screening designs are based on saturated fractional factorial designs. The firactional factorial designs in Section 14.8 are said to be saturated by the first-order factor effects (parameters) in the four-parameter model (Equation 14.27). In other words, the efficiency E = p/f = 4/4 = 1.0. It would be nice if there were 100% efficient fractional factorial designs for any number of factors, but the algebra doesn t work out that way. 

Notice that this is an orthogonal design in coded factor space (-1 and +1) any one column multiplied by any other column will give a vector product of zero. Other saturated fractional factorial designs may be found in the literature [Box and Hunter (1961a, 1961b), Anderson and McLean (1974), Barker (1985), Bayne and Rubin (1986), Wheeler (1989), Diamond (1989)]. 

The saturated fractional factorial designs are satisfactory for exactly 3, or 7, or 15, or 31, or 63, or 127 factors, but if the number of factors is different from these, so-called dummy factors can be added to bring the number of factors up to the next largest saturated fractional factorial design. A dummy factor doesn t really exist, but the experimental design and data treatment are allowed to think it exists. At the end of the data treatment, dummy factors should have very small factor effects that express the noise in the data. If the dummy factors have big effects, it usually indicates that the assumption of first-order behavior without interactions or curvature was wrong that is, there is significant lack of fit. 

As an example of the use of dummy factors with saturated fractional factorial designs, suppose there are 11 factors to be screened. Just add four dummy factors and... 

Now suppose there are 16 factors to be screened. We would have to add 15 dummy factors and use the 2 " saturated fractional factorial design, but this would give an efficiency of only 17/32 = 53%. This is not very efficient. Most researchers would rather eliminate one of their original 16 factors to give only 15 factors. There is a saturated fractional factorial design that will allow these factors to be screened in only 16 experiments. 

A seven-factor saturated fractional factorial design. 

The relationship of saturated fractional factorial and Plackett-Burman designs. 

Plackett-Burman and saturated fractional factorial designs. 

Using row and column operations, convert the following 7-factor Plackett-Burman design to the saturated fractional factorial design shown in Table 14.7. 

Hint row 8 of this design and row 8 of the saturated fractional factorial design in Table 14.7 suggest that the reflection or foldover must be carried out first. Repetitions of switching one row with another, and switching one column with another, will eventually yield the desired result. Retain the identities of the rows and columns. 

The zone between land surface and the water table, which forms the upper boundary of the groundwater region, is known as the vadose zone. This zone is mostly unsaturated— or more precisely, partially saturated— but it may contain a saturated fraction in the vicinity of the water table due to flucmations in water levels or capillary rise above the water table. The near-surface layer of this zone—the soil—is generally partially saturated, although it can exhibit periods of full saturation. Soil acts as a buffer that controls the flow of water among atmosphere, land, and sea and functions as a sink for anthropogenic contaminants. 

Fig. 13. Salient features of the GC-MS data for the saturated fraction of a hydrothermal bitumen sam pie from the Mid-Atlantic Ridge (a) TIC - background trace, (b) ra/z 85 fragmentogram (key ion for 3-ethyl-3-methylalkanes and -alkanes), (c) mjz 99, key ion for 3,3-diethylalkanes with -alkanes, and (d) m/z 127, key ion for 5,5-diethylalkanes with w-alkanes. (Numbers refer to total carbon number, dots ovet peaks are -alkanes.)... 

For this reason one prefers to apply an experimental design. In the literature a number of different designs are described, such as saturated fractional factorial designs and Plackett-Burman designs, full and fractional factorial designs, central composite designs and Box-Behnken designs [5]. 

A Plackett-Burman design with N experiments can examine up to N-1 factors. This is a difference with fractional factorial designs. Some saturated fractional factorial designs however contain also N-1 factors (e.g. the design of Table 3.14) but this is not always the case. The saturated design for 5 factors, for example, is the 2 design. In this design only 5 factors are examined in 8 experiments. 

M. Mulholland, J. Waterhouse, Investigation of the limitations of saturated fractional factorial experimental designs, with confounding effects for an HPLC ruggedness test, Chromatographia, 25 (1988) 769-774. 

The most commonly used designs are half-fractional designs and saturated fractional designs. 

Saturated fractional designs are constructed on the assumption that all interaction effects can be assumed to be insignificant and the number of experiments is now reduced to k +1. 

These limitations can be seen by comparing the experimental procedure for a three factor, three level star design, shown in Table 5.10, with the experimental procedure for a reflected saturated fractional design, which also tests three factors at three levels, shown in Table 5.11. 

The experimental scheme for a three level reflected saturated fractional design for seven factors is shown in Table 5.15 ( note that one factor was retained as a dummy factor to be used as an additional error check). The experimental order of the scheme was sorted on acid type as this required long equilibration times, this ordering loses some of the features of the initial design but is a compromise that can be justified on the fact that... 

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