Voorhies correlation

There is one interesting fact however the transients set up operation, and however one obtains steady state, under deactivation conditions, with time, most pellets follow the Voorhies correlation, more or less. 

An alternative approach to the correlation of catalyst deactivation kinetics has been widely employed for coking mechanisms. Here the precise reactions that cause deactivation may be more complex or difficult to identify than in chemical poisoning, and one may not write such precise expressions as equation (3-94) for (—r ). The practice generally has been to relate activity to the time of utilization or time-on-stream , and a number of mathematical forms have been employed. The best known is the Voorhies correlation [A. Voorhies, Jr., Ind. Eng. Chem., 37, 318 (1945)], which relates the weight of coke on the catalyst to a power of time on stream. 

The empirical Voorhies correlation for coking in the catalytic cracking of gas oil... 

Figure 1, (a) Voorhies correlation of coke formation, cumene cracking on H-mordenite, 260 -350 C, 0.33 gihr-g (13) (b) effective diffusivity (SFg) variation with coke content... 

The amount of coke deposited on the catalytic surface has been correlated to the time on stream (Voorhies, 1945) ... 

VSXC van Voorhis and Scuseria s MGGA exchange-correlation functional. van Voorhis, T. and Scuseria, G. E. 1998. J. Chem. Phys., 109, 400. 

VSXC Exchange-correlation functional of van Voorhis and Scuseria... 

Instead, they proposed a time on stream theory to model the catalyst deactivation. However, in an earlier work by Voorhies (2), a linear correlation between conversion and coke on catalyst for fixed-bed catalytic cracking was derived. Rudershausen and Watson (3) also observed the similar behavior. Coke on catalyst can reduce the activity by covering the active sites and blocking the pores. The effects of pore size on catalyst performance during hydrotreating coal oils in trickle-bed reactors have been studied experimentally by Ahmed and Crynes (4) and by Sooter (5). The pore size effects in other studies are also reported 7, 8). Prasher et al. (9) observed that the effective diffusivities of oils in aged catalysts were severely reduced by coke deposition. 

Using the time dependent Voorhies-description (Eq.4) the activity function can be correlated vs. time on streamAs shown in Fig.8 several curves are necessary to describe the activity decline at different temperatures.This strikes out the apparent advantage of a deactivation description based only on coke content... 

Figure 1 illustrates the extent of n-heptane conversion over those catalysts as a function of time-on-stream, working under deactivation conditions. The catalyst deactivation was modeled by the well-known Voorhies equation C= Af [6], where C denotes percentage conversion, t denotes time-on-stream (min), and A and B are empirical parameters. Even though the Voorhies equation was originally used to correlate the coke content with time, the use of the equation for correlating activity and time was also confirmed by Magnoux et. al. [7]. 

It can be seen from Figoire 1 that the Voorhies model correlates well with the performance of those catalysts. The values of the parameters obtained are summarized in Table 1. It is demonstrated that the composite catalysts possess higher activities than either Pt-Re/Al203 or ZSM-5, with the mixed catalyst (mode M) being the highest. These results may suggest different reaction paths for n-heptane over those catalysts. 

Evans J, Vydrov O, Van Voorhis T (2009) Exchange and correlation in molecular wire conductance nonlocality is the key. J Chem Phys 131 034106... 

For the VS98 correlation. Van Voorhis and Scuseria [213] assumed the general form of Eq. (174) and (175) with the Perdew-Wang parametrization [114] of p j). 

The HCTH functional has been extended to also include the kinetic energy density as a variable, producing the acronym t-HCTH. The VSXC (Voorhis-Scuseria eXchange-Correlation) functional similarly includes the kinetic energy density and contains 21 parameters that are fitted to experimental data. The TPSS... 

Therefore, the effect of the density Laplacian is included implicitly in the kinetic energy density. It is natural that the next step in density gradient correction is the kinetic energy density correction on Jacob s ladder (see Sect. 5.1). Major meta-GGA functionals include the van Voorhis-Scuseria 1998 (VS98) meta-GGA exchange-correlation (van Voorhis and Scuseria 1998), the Perdew-Kurt-Zupan-Blaha (PKZB) meta-GGA exchange-correlation (Perdew et al. 1999), and the Tao-Perdew-Staroverov-Scuseria (TPSS) meta-GGA exchange-correlation (Tao et al. 2003) functionals. 

The VS98 meta-GGA exchange-correlation functional (van Voorhis and Scuseria 1998) is the first exchange functional incorporating the kinetic energy density. Similarly to the PF exchange functional (see Sect. 5.2), this functional is derived from the analytical expansion of the density matrix in Eq.(5.7) (Negele and Vautherin 1972),... 

This functional contains 7 semiempirical parameters (a through / and a) for each exchange, parallel-spin or opposite-spin pair correlation functional, and consequently has 21 semiempirical parameters in total (for the parameter values, see van Voorhis and Scuseria 1998). Therefore, this functional is also classified as a semiempirical functional (see Sect. 5.6) and is actually taken as the first meta-GGA semiempirical functional using Za- This functional is also characteristic in associating the correlation functional with the exchange one through the same hg. 

A variety of modern (meta-)GGA (generalized gradient approximation) exchange-correlation (xc) energy functionals, such as the van Voorhis Scuseria functional, are evaluated. For reliable property calculations, improved xc potentials with correct asymptotic behavior, such as SAOP" and GRAC," have been developed. 

The earliest effort to correlate the time dependence of activity was that of Voorhies (1945). He found ... 

Vydrov and van Voorhis proposed considerable modification of the original vdW-DFl [55] called the vdW-DF-09 [67]. A new dispersion model, second-order gradient-coefficient of and a new local functional part were introduced. Specifically, the LC-mPBE exchange-correlation functional was adopted for the nonlocal part of vdW-DF-09. Thus, vdW-DF-09 is defined as... 

The second family of nonlocal functionals was developed by the van Voorhis group. The new nonlocal correlation functional "VV simple analytic form... 

Weston D, Patel B, Van Voorhis WC (1999) Virulence in Xrypanosoma cruzi infection correlates with the expression of a distinct family of sialidase superfamily genes. Mol Biochem Parasitol 98 105-16. 

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