Velocity, units conversion

ECC catalyst is subject to hydrothermal deactivation. This occurs when the A1 atom in the zeolitic cage is removed in the presence of water vapor and temperature. The result is a loss of activity and unit conversion. The effect of temperature on this process is nonlinear. The deactivation rate increases exponentially with temperature. Units that experience high afterburn have attributed high rates of catalyst deactivation on the higher dilute phase temperatures. This phenomenon is more apparent on units with high combustion air superficial velocities. The high velocity not only increases afterburn, but also increases catalyst entrainment to the cyclones and dilute area. COP is used to decrease afterburn and minimize catalyst deactivation. 

When the velocities of the two reactions are numerically equal, the system is in homeostasis, a dynamic equilibrium that does not modify the identity of the unit. Conversely, when the velocity of the building-up reaction Vp is larger than the opposite one, growth and eventually self-reproduction of the vesicles can be measured and if instead Vp is smaller than uj, there is destruction of the unit. 

Although individual line positions are given in velocity units, the quadrupole coupling constant is normally quoted in MHz. This facilitates comparison with NQR data. Moreover, data for 129I are usually converted into the value corresponding to 127I, again to assist comparisons. The conversion constants used are ... 

In the deduction from a kinetic basis equilibrium is regarded as the result of two opposite reactions proceeding with the same velocity. The velocity in question, or the amount of reaction in the unit of volume (cub. metre), is proportional to the mass of the substance present in that volume (expressed, say, in kilogram-molecules), i. e. to the concentration of the reacting substance if its molecules suffer conversion of themselves (unimolecular reaction). If, on the contrary, mutual action is necessary to bring about the reaction, the velocity of conversion, under given circumstances (of temperature, c.), is proportional to the number of collisions between the molecules involved in the reaction. The number is with sufficient dilution propor-... 

Radial density gradients in FCC and other large-diameter pneumatic transfer risers reflect gas—soHd maldistributions and reduce product yields. Cold-flow units are used to measure the transverse catalyst profiles as functions of gas velocity, catalyst flux, and inlet design. Impacts of measured flow distributions have been evaluated using a simple four lump kinetic model and assuming dispersed catalyst clusters where all the reactions are assumed to occur coupled with a continuous gas phase. A 3 wt % conversion advantage is determined for injection feed around the riser circumference as compared with an axial injection design (28). 

Gas Phase. The gas-phase methanol hydrochlorination process is used more in Europe and Japan than in the United States, though there is a considerable body of Hterature available. The process is typicaHy carried out as foHows vaporized methanol and hydrogen chloride, mixed in equimolar proportions, are preheated to 180—200°C. Reaction occurs on passage through a converter packed with 1.68—2.38 mm (8—12 mesh) alumina gel at ca 350°C. The product gas is cooled, water-scmbbed, and Hquefied. Conversions of over 95% of the methanol are commonly obtained. Garnma-alurnina has been used as a catalyst at 295—340°C to obtain 97.8% yields of methyl chloride (25). Other catalysts may be used, eg, cuprous or zinc chloride on active alumina, carbon, sHica, or pumice (26—30) sHica—aluminas (31,32) zeoHtes (33) attapulgus clay (34) or carbon (35,36). Space velocities of up to 300 h , with volumes of gas at STP per hour per volume catalyst space, are employed. 

Let us assume that A P is an elementary reaction and that it is spontaneous and essentially irreversible. Irreversibility is easily assumed if the rate of P conversion to A is very slow or the concentration of P (expressed as [P]) is negligible under the conditions chosen. The velocity, v, or rate, of the reaction A P is the amount of P formed or the amount of A consumed per unit time, t. That is. 

The first step in E-cat testing is to bum the carbon off the sample. The sample is then placed in a MAT unit (Figure 3-13), the heart of which is a fixed bed reactor. A certain amount of a standard gas oil feedstock is injected into the hot bed of catalyst. The activity i.s reported as the conversion to 430°F (221°C) material. The feedstock s quality, reactor temperature, catalyst-to-oil ratio, and space velocity are four variables affecting MAT results. Each catalyst vendor uses slightly different operating variables to conduct micro activity testing, as indicated in Table 3-2. 

To improve the mixing quality in the tubular reactor, Kenics type in-line static mixer reactor was employed. The in-line static mixers were designed to mix two or more fluids efficiently since an improved treinsport process such as flow division, radial eddying, flow constriction, and shear reversal eliminated the gradients in concentration, velocity and temperature. However, only 70 % conversion was achieved with one Kenics mixer unit. As shown in Table 2, five mixer units were required to achieve the maximum conversion. 

Flow Flux, Permeability, Conversion The productivity of a membrane module is described by its flux J = volumetric permeate flow rate/membrane area with units of volume per area per time. Relatively high flux rates imply that relatively small membrane areas are required. The permeate volume is usually greater than the feed volume for a given process. Flux is also the magnitude of the normal flow velocity with units of distance per time. 

Fig. 3.19 Schematic illustration of the measurement geometry for Mossbauer spectrometers. In transmission geometry, the absorber (sample) is between the nuclear source of 14.4 keV y-rays (normally Co/Rh) and the detector. The peaks are negative features and the absorber should be thin with respect to absorption of the y-rays to minimize nonlinear effects. In emission (backscatter) Mossbauer spectroscopy, the radiation source and detector are on the same side of the sample. The peaks are positive features, corresponding to recoilless emission of 14.4 keV y-rays and conversion X-rays and electrons. For both measurement geometries Mossbauer spectra are counts per channel as a function of the Doppler velocity (normally in units of mm s relative to the mid-point of the spectrum of a-Fe in the case of Fe Mossbauer spectroscopy). MIMOS II operates in backscattering geometry circle), but the internal reference channel works in transmission mode...

Routh and Russel [10] proposed a dimensionless Peclet number to gauge the balance between the two dominant processes controlling the uniformity of drying of a colloidal dispersion layer evaporation of solvent from the air interface, which serves to concentrate particles at the surface, and particle diffusion which serves to equilibrate the concentration across the depth of the layer. The Peclet number, Pe is defined for a film of initial thickness H with an evaporation rate E (units of velocity) as HE/D0, where D0 = kBT/6jT ir- the Stokes-Einstein diffusion coefficient for the particles in the colloid. Here, r is the particle radius, p is the viscosity of the continuous phase, T is the absolute temperature and kB is the Boltzmann constant. When Pe 1, evaporation dominates and particles concentrate near the surface and a skin forms, Figure 2.3.5, lower left. Conversely, when Pe l, diffusion dominates and a more uniform distribution of particles is expected, Figure 2.3.5, upper left. 

The conclusion that dimensionless numerical values are universal is valid only if a consistent system of units is used for all quantities in a given equation. If such is not the case, then the numerical quantities may include conversion factors relating the different units. For example, the velocity (F) of a fluid flowing in a pipe can be related to the volumetric flow rate (Q) and the internal pipe diameter (D) by any of the following equations ... 

Figure 9.13 Temperature profile along the catalytic bed (a) and CH4 conversion, H2 concentration and H2 throughput per unit catalyst volume (b) in CH4 ATR catalytic activity tests carried out at high space velocity.

Using the SI units, the velocity of the EOF is expressed in meters/second (m s ) and the electric held in volts/meter (V m ). Consequently, the electroosmotic mobility has the dimension of m V s. Since electroosmotic and electrophoretic mobility are converse manifestations of the same underlying phenomena, the Helmholtz-von Smoluchowski equation applies to electroosmosis, as well as to electrophoresis (see below). In fact, it describes the motion of a solution in contact with a charged surface or the motion of ions relative to a solution, both under the action of an electric held, in the case of electroosmosis and electrophoresis, respectively. 

Gliksman s approach The result of the conversion of equations into nondimensional ones is a set of dimensionless parameters (Froude number, velocity, particle size, diameter ratios, etc.) that should be matched in both small and large systems. It is not necessary for the values of the parameters to be equal in each system. Instead, the dimensionless number ratios have to remain the same. To achieve this, the particle size and/or the particle density of the solids have to be changed appropriately in the small unit. It usually results in a smaller particle size in the small unit compared to the large one. 

---