Corey-type equation

This section uses the Corey-type (Brooks and Corey, 1966) equation (Eq. 7.125) to describe relative permeabilities. We first use this type of equation to see the effect of IFT on the k, ratio in two-phase flow. Figure 7.37 compares the three k, ratios normal water/oil k miscible k and k between. Their parameters are presented in Table 7.10. The figure clearly shows that as the IFT is increased from the normal waterflooding high IFT to the intermediate IFT to the miscible flooding low IFT, the ratio of kj to k increases in the low Sw... 

Pioneering work on the desulphonylation of jS-ketosulphones was carried out by Corey and Chaykovsky - . This reaction was part of a sequence which could be used in the synthesis of ketones, as shown in equation (53). The main thrust of this work was in the use of sulphoxides, but Corey did stress the merits of both sulphones and sulphonamides for different applications of this type of reaction. The method soon found application by Stetter and Hesse for the synthesis of 3-methyl-2,4-dioxa-adamantane , and by House and Larson in an ingenious synthesis of intermediates directed towards the gibberellin skeleton, and also for more standard applications . Other applications of the method have also been madealthough it does suffer from certain limitations in that further alkylation of an a-alkyl- -ketosulphone is a very sluggish, inefficient process. Kurth and O Brien have proposed an alternative, one-pot sequence of reactions (equation 54), carried out at — 78 to — 50°, with yields better than 50%. The major difference between the two routes is that the one-pot process uses the desulphonylation step to generate the enolate anion, whereas in the Corey-House procedure, the desulphonylation with aluminium amalgam is a separate, non-productive step. 

Although the approach is theoretically sound, both the proposed relationships between capillary pressure and saturation (Equations 6.23 and 6.24) are highly nonlinear and limited in practicality by the requirement of multiparameter identification. In addition, due to the inherent soil heterogeneities and difference in LNAPL composition, the identified parameters at one location cannot be automatically applied to another location at the same site, or less so at another site. For example, Farr et al. (1990) has reported the Brooks-Corey and van Genutchen parameters, X, ii, and o.a0, for seven different porous media based on least-square regression of laboratory data. The parameters are found to vary about one order of magnitude and do not show any specific correlation for a particular soil type. 

There are several scattered instances of [4 + 2] cycloadditions with charged thienium dienophiles. " The first reported example of this type of Diels-Alder reaction was by Corey and Walinsky, who used dithienium compound (191) in cycloadditions. For instance, (191) reacts at low temperature with iso-prene regioselectively to afford adduct (192) (equation 96). This compound can be converted to cyclo-... 

Variouspolyfimciioual compounds. Corey et al. have reported useful syntheses of various types from metallated N,N-dimethylhydrazones. Typical results are summarized in the equations. 

A similar effect has been reported by Corey et al. using tryptophan-derived oxaz-aborolidinone (OXB) catalysts of type 5 (Equation 22) [19], which are especially efficient in asymmetric catalysis of the cydoaddition between 2-bromoacrolein and various dienes (>90-95% ee). Attractive interactions between the indolyl moiety and the Jt-acidic dienophile protect one face of the dienophile. This effect is well supported by the discovery that replacement of the indole group by a cydohexyl or an isopropyl group gives the cycloadduct with an opposite configuration (70% ee). 

Corey and coworkers further expanded the utility of their catalyst (14) toward other types of dienophiles such as acrylic acids, a,P-unsaturated esters, and a,P-unsaturated ketones (Equations 6 and 7) [15]. 

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