Wetting models

Experimental Verifications of Holdup and Effective Catalyst-Wetting Models... 

The dependence of ln(Cj/C0) on liquid velocity was verified by Skripek and Ballard50 for VGO desulfurization at 45 < GL < 150 g h 1 cm-2. In a series of articles, Paraskos et al.,37 Montagna and Shah,29 and Montagna et al.30 evaluated the applicability of holdup and incomplete catalyst-wetting models to the desulfurization, demetalization, and denitrogenation reactions for a variety of residue and gas oils. Paraskos et al.37 showed that although log log plots of In (Cj/C0) versus 1 /LHSV for the desulfurization, demetalization (i.e., nickel and... 

All these results indicate that although, as predicted by both the holdup and the effective catalyst-wetting models, the conversions in pilot-scale hydroprocessing reactors depend upon the liquid flow rate, and log-log plots of ln(Ci/Cc) versus either l/LHSV or L are straight lines, the slopes of these plots depend upon the nature of the feed, temperature, and the catalyst size. 

Of the holdup and the effective catalyst-wetting models, the latter one appears to be physically more realistic. As indicated earlier, the two models show a... 

Note that the oil-wet results are considerably better than the water-wet EOR recoveries, except for the secondary WAS process in the oil-wet model. The foam results were better for the oil-wet pack for both the secondary and tertiary cases than they were in the water-wet pack. We attribute the poorer performance of the water-wet pack to a higher proportion of oil which is blocked from contact with the 002 at the water saturations which occur in WAG and foam flooding. This apparently cuts the EOR recovery to about half of that observed in the oil-wet pack for equivalent water saturations. 

A two-layer wetting model, according to which the wetting interactions between the film and the substrate are described as a thickness-dependent surface energy of the film, j(h). This dependence is usually taken to be [26]... 

Physically, the effective wetting model seems to be the most appropriate one. This is supported by the fact that also hydrodesulphurization of vacuum and atmospheric residuals are better correlated by an effective catalyst wetting model than by the holdup model [60]. 

As described by the Wenzel wetting model, the increase of surface roughness should lead to a certain increase of contact angle (CA) values. To verify this statement, we investigated three different kinds of commonly used thin films known to be very different in grain size and, therefore, in surface roughness. Figure 3 shows the comparison of a 50 nm Au film, an 800 nm native oxidized titanium film (TiO") and an 800 nm wet chemically oxidized titanium film (TiO ) on a polished silicon substrate. 

From the data listed in the liquid taken off the oil-wet model, the polymer appears directly in the initial (injection) concentration thus, no adsorption can be observed. From this it... 

Nearly similar statements can be made for surface active agents. Petroleum sulfonates and alkyl aryl sulfonates were investigated in detail. In a water-wet porous system the amount of adsorbed polymer decreased considerably. In the oil-wet model, however, the polymer retention increased to a certain degree. 

In the water-wet model well-known trends may be observed. On the other hand, in the oil-wet system a substantial change takes place only in the case of pol)mier solution while the mobility of either the connate water or the distilled water does not exhibit any substantial difference as compared to the initial state. 

Disengagement of bitumen from solids wiU be favoured if their respective surfaces can be made more hydrophilic since a lowering of surface free energy will accompany the separation. The phase separation is enhanced by the effects of mechanical shear and disjoining pressure. Adopting the water-wet model for Athabasca oil sand, one has that a thin aqueous film already separates the bitumen from the sand. So this preexisting separation needs only to be enhanced. 

The Young equation cannot be used directly to explain the effect of surface roughness on the wettability of a material because it is valid only for ideal smooth solid surfaces. There are two wetting models that are proposed when a water droplet sits on rough surfaces, these are the Wenzel model and the Cassie-Baxter model. 

The models can be classified according to the basic hydro-dynamic premise underlying the model. The "holdup model" assumes that liquid-catalyst contacting is proportional to the amount of liquid that is held up in the bed. The "wetting model" presupposes that the key factor controlling catalyst utilization is the extent of wetting of the particles by liquid. The "partial... 

The "catalyst wetting" model assumes that the rate of reaction is proportional to the wetted surface of the catalyst and that this wetting can be described by correlations such as those given by Onda [52] for high liquid velocities and by Puranik and Vogelpohl [57] for low velocities. Mears [45] combined these expressions with a model for a first order reaction and obtained the relationships below for high liquid velocities ... 

The partial wetting model was adapted by Lee and Smith [40] to yield criteria for determining conditions under which negligible transport or partial wetting would obtain. To assure no pore diffusion limitations, it was found that the conventional criteria... 

Figure 3.3.1. Partial wetting model predictions for reaction by a...

Turek [80] using a simplified partial wetting model was able to reconcile measurements from a slurry, two stirred "basket reactors and a trickle bed. The reaction was glucose hydrogenation. 

By assuming that the contact efficiency = app/ v coincides with f and combining an expression for f with Eq. (52% Hears [48] suggested a semiempirical effective wetting" model to be used for scale up ... 

Fig. 1.7 The wetting model, based on a (p, g)-walk with q = 0.7. In (A) there is a typical delocalized trajectory (/ < / c) there are only a few retiu-ns, in fact 0(1) as N — oo, to the wall and all of them are close to the boundaries. In (C) instead there is a typical localized trajectory the returns are frequent, in fact there is a density of pinned (or contact) points. In the wetting language, the random line is the interface between a liquid phase (below) and a gas phase (above). So in (A) is the system is in the wet regime, in the sense that the wall is covered with liquid, while in (C) it is partly dry, so we speak of dry regime. We will see in Chapter 2 that an intermediate scenario appears at 13 = )3c (case (B)) there are o N) dry sites, but they may be found also in the bulk of the system.

The non-crossing constraint therefore becomes a hard wall constraint for the walk S and we are effectively dealing with the wetting model of Section 1.3 (with a particular choice of F(-)). In absence of constraint, the model falls of course in the class of models discussed in Section 1.2 and, as we have seen, the general models introduced in Section 1.2 include also the wetting models. In particular we have seen that the hard wall constraint induces simply a shift of the critical point. 

Brownian motion is essentially already present at microscopic level, that is at the level of random walks it is in fact rather easy to see, for example, that at criticality the wetting model based on the simple random walk is precisely the reflected simple random walk even at finite volume. This precise correspondence disappears beyond (p, g)-walks and the techniques of proof employed are substantially different and they are in fact based on two steps ... 

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