External surface concentrations elimination

Let us now consider how the external surface concentrations can be eliminated when our reaction follows simple irreversible first-order kinetics. In this instance equation 12.4.20 becomes... 

For isothermal systems, it is occasionally possible to eliminate the external surface concentrations between equations 12.6.1 and 12.6.2 and arrive at a global rate expression involving only bulk fluid compositions (e.g., equation 12.4.28 was derived in this manlier). In general, however, closed form solutions cannot be achieved and an iterative trial and error procedure must be employed to determine thq global rate. One possible approach is summarized below. 

For low coke contents, the yield of olefins increased (Fig. 1) while the DME yield decreased with coke formation, even for the samples modified by external coking (Fig. 6a), where the effect of external surface was eliminated. The observed decrease in DME yield with coke formation for externally coked samples corresponds with a mechanism where DME is formed, diffuses and is converted in the catalyst pores. The diffusion of DME is expected to largely influence the olefin formation in the pores. The DME difflisivity decreased with coke formation, and the difference in activity with the amount of coke formed on SAPO-34 between MTO and DTO can then be explained by DME diffusion. Furthermore, the decrease in DME difflisivity has the opposite effect for DTO and MTO. Lower diffusivity decreases the DME concentration in Ae pores in DTO, hence reducing the olefin formation, while it increases the DME concentration in MTO, thereby promoting the formation of olefins. 

In the presence of intraparticle mass transfer limitations, the rate per particle is expressed in terms of the species concentrations prevailing at the exterior of the catalyst. However, when external mass transfer limitations are also present, these concentrations will differ from those prevailing in the bulk. Since bulk concentrations are what one measures in the laboratory, exterior surface concentrations must be eliminated to express the observed conversion rate in terms of measurable concentrations. In the paragraphs that follow, the manner in which one eliminates surface concentrations is indicated in some detail for a specific case. 

The net rate of reaction given Equation (12-46) is equal to the rate of mass transfer of A from the bulk fluid to the external pellet surface [Equation (12-47)]. We need to eliminate the surface concentration from any equation involving the rate of reaction or rate of mass transfer, because Cj cannot be measured standard techniques. To accomplish this elimination, first substitute Equation (12-48) into Equation (12-46) ... 

Here as is, for instance, the external particle surface area/volume of reactor. Eliminating the surface concentration C0 in terms of the observable bulk gas concentration C yields the overall specific rate of consumption of A ... 

The Weisz-Prater criterion makes use of observable quantities like -Ra)p, the measured global rate (kmol/kg-s) dp, the particle diameter (m) pp, the particle density (kg/m ) Dg, the effective mass diffusivity (m /s) and the surface concentration of reactant (kmol/m ). The intrinsic reaction rate constant ky need not be known in order to use the Weisz-Prater criterion. If external mass transfer effects are eliminated, CAb can be used, and the effective diffusivity can be estimated using catalyst and fluid physical properties. The criterion can be extended to other reaction orders and multiple reactions by using the generalized Thiele modulus, and various functional forms are quoted in the literature [17, 26, 28]. 

In Part 2 of the PCB story, we introduced the exchange between the water column and the surface sediments in exactly the same way as we describe air/water exchange. That is, we used an exchange velocity, vsedex, or the corresponding exchange rate, ksedex (Table 23.6). Since at this stage the sediment concentration was treated as an external parameter (like the concentration in the air, Ca), this model refinement is not meant to produce new concentrations. Rather we wanted to find out how much the sediment-water interaction would contribute to the total elimination rate of the PCBs from the lake and how it would affect the time to steady-state of the system. As shown in Table 23.6, the contribution of sedex to the total rate is about 20% for both congeners. Furthermore, it turned out that diffusion between the lake and the sediment pore water was much more important than sediment resuspension and reequilibration, at least for the specific assumptions made to describe the physics and sorption equilibria at the sediment surface. 

Positive deviations of it1/2 with increasing time can also be evidence for convection within an electrochemical cell. Convection can be caused by external vibrations or by density gradients created by the local concentration differences resulting from the electrochemical perturbation. While the influence of external vibrations can be largely eliminated by isolation of the cell with a damped table, the natural convection due to unequal densities of O and R is an unavoidable consequence of the experiment, the importance of which depends on the particular species involved. The effect of natural convection at planar electrodes is most serious when the surface is mounted vertically. It is therefore desirable to carry out electrochemical experiments at surfaces facing up or down whenever possible. 

Under some circumstances there will be a resistance to the transport of material from the bulk fluid stream to the exterior surface of a catalyst particle. When such a resistance to mass transfer exists, the concentration CA of a reactant in the bulk fluid will differ from its concentration CAi at the solid-gas interface. Because CAi is usually unknown it is necessary to eliminate it from the rate equation describing the external mass transfer process. Since, in the steady state, the rates of all of the steps in the process are equal, it is possible to obtain an overall rate expression in which CM does not appear explicitly. 

Next we can use Equations (12-45) through (12-48) to eliminate from Equation (12-47), so that the total molar transport of A from the bulk fluid to the external pellet surface can be expressed solely in terms of bulk concentration and other parameters of the system (e.g., the mass transfer coefficient, and the specific reaction rate, i). 

The therapeutic objectives in treating bacterial keratitis are the rapid elimination of the pathogen from the external eye and gaining control of the inflairunatory response. Optimally, broad-spectrum, antibacterial solutions should be used for topical antibiosis. The rapid elution of topical solutions from the ocular surface demands that high-concentration aqueous preparations of antibiotics be administered at 30-60 min intervals. The dmg selected should exhibit concentration-dependent, bactericidal activity that is, the rate... 

Here we will mention leftovers-lubricants that diminish the friction between polymer particles (internal) or with the walls of the fabricating machines (external). An internal lubricant affects mainly a reduction of viscosity while an external one affects the surface layer and augments the output (provided no slip occurs). Many lubricants serve simultaneously as internal and external agents, as a borderline is not that sharp. The polymer most demanding of lubrication is PVC for improving workability and elimination of degradation. However, other polymers are lubricated as well, like polystyrene, polyester and polyolefins. Among the common lubricants are fatty acids and their salts, paraffins, and low MW fractions of polyethylene. Only a small concentration should be used in order not to affect the ultimate properties. In the case of broadly distributed PE, self lubrication occurs. 

A toxic compound in air has to be eliminated by catalytic oxidation. The concentration of the toxic must be reduced from initially 1% to <1 ppm. At 100 °C the transformation rate is very high and in consequence limited by the external mass transfer between the bulk fluid and the catalytic surface. A small catalytic packed bed with spherical particles is used to treat a gas flow of 1.5 m h . ... 

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