Rate factors determining

The performance of adsorption processes results in general from the combined effects of thermodynamic and rate factors. It is convenient to consider first thermodynamic factors. These determine the process performance in a limit where the system behaves ideally i.e. without mass transfer and kinetic limitations and with the fluid phase in perfect piston flow. Rate factors determine the efficiency of the real process in relation to the ideal process performance. Rate factors include heat-and mass-transfer limitations, reaction kinetic limitations, and hydro-dynamic dispersion resulting from the velocity distribution across the bed and from mixing and diffusion in the interparticle void space. 

These relative rate data per position are experimentally determined and are known as partial rate factors They offer a convenient way to express substituent effects m elec trophilic aromatic substitution reactions... 

A key factor determining the performance of ultrafiltration membranes is concentration polarization due to macromolecules retained at the membrane surface. In ultrafiltration, both solvent and macromolecules are carried to the membrane surface by the solution permeating the membrane. Because only the solvent and small solutes permeate the membrane, macromolecular solutes accumulate at the membrane surface. The rate at which the rejected macromolecules can diffuse away from the membrane surface into the bulk solution is relatively low. This means that the concentration of macromolecules at the surface can increase to the point that a gel layer of rejected macromolecules forms on the membrane surface, becoming a secondary barrier to flow through the membrane. In most ultrafiltration appHcations this secondary barrier is the principal resistance to flow through the membrane and dominates the membrane performance. 

Determination of Controlling Rate Factor The most important physical variables determining the controlhng dispersion factor are particle size and structure, flow rate, fluid- and solid-phase diffu-sivities, partition ratio, and fluid viscosity. When multiple resistances and axial dispersion can potentially affect the rate, the spreading of a concentration wave in a fixed bed can be represented approximately... 

Overall Scale-Up Factor The final design filtration rate is determined by multiplying the bench-scale filtration rate by each of... 

Service conditions on all the ratings so determined, one may apply the applicable service factors as noted... 

Pipe diameters are rounded up to the next standard size, and proper wall thickness (schedule) is determined consistent with the operating pressure of that portion of the system. For the rate factor, see Figure 13-15. 

Extensive studies have been carried out by Giggins and Pettit and by Vasantasree and Hocking on a range of nickel chromium alloys with up to 50% alloying addition. Generally the principles outlined above can be used to interpret the experimental observations, where the thermodynamics of the reaction are a major factor determining the rate of attack, depending upon whether oxide or sulphide is the stable phase. 

The preexponential factor determines the rate of incidence of the gas particles onto the free surface at a unit pressure and has a dimension of (mole sec g-1 cm-1). 

For a long time, this finding was correlated with the observation that substituents at a radical center tend to enhance its stability (Section 1.1.2). This in turn led to the belief that the degree of stabilization conferred on the product radical by the substituents was the prime factor determining the orientation and rate of radical addition to olefins. That steric, polar, or other factors might favor the same outcome was either considered to be of secondary importance or simply ignored. ... 

The importance of the various factors determining the rate and regiospecifrcity of addition is illustrated by the data shown in Table 1.2 and Table 1.3. 

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