Diffusion, internal

A part of reactants have been involved in reactions before they enter into the pores of catalysts from the external surface through the orifice of solid. Therefore, diffusion and reaction of reactant molecules take place simultaneously in pores. If the reaction rate of a reactant on the surface of catalyst is higher than diffusion rate, the reactant will be used up before it reaches to the deep sides of pores, indicating that only part of catalyst is utilized. In other words, the using ratio of catalyst internal surface is lower if there exists internal diffusion effect. The lower the diffusion rate and the bigger the catalyst particle, the lower the usage ratio of internal surface is. The concentration distribution of a reactant in a pore of catalyst is shown in Fig. 2.35. 

The diffusion processes in a catalyst can be classified as molecular diffusion, Knudsen diffusion and surface diffusion etc. 

It is known from theory of ideal gas molecular motion  

The expression above shows that DAm is proportional to t3/2 inversely proportional to total pressure of gas and independent of the radius of pore. 

In a small cylindrical pore, Knudsen diffusion coefficient Dak i s ) for component A can be calculated by expression as follows  

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Internal diffusion occurs during drying when Hquid or vapor flow obeys the fundamental diffusion laws. 

Internal diffusion may be defined as the movement of liquid or vapor through a sohd as the result of a concentration difference. 

A long heating cycle is necessaiy because the size of the solid objects or permissible heating temperature requires a long holdup for internal diffusion of heat or moisture. This case may apply when the cycle will exceed 12 to 24 h. 

Table 4-4 summarizes the ratings of the various reactors. The CFSTR and the recirculating transport reactor are the best choices because they are satisfactory in every category except for construction. The stirred batch and contained solid reactors are satisfactory if the catalyst under study does not decay. If the system is not limited by internal diffusion in the catalyst pellet, larger pellets could be used and the stirred-contained solids reactor is the better choice. However,... 

The flow and return connections will be designed to suit the flow rates and temperature differentials required. The water-return connection will be fitted with either an internal diffuser or a venturi nozzle to assist mixing of the water circulating within the shell and prevent water stratification. The flow connection will incorporate the... 

Chemical dosing. This is a connection into the tank with an internal diffuser for any corrective treatment required for the water. 

It is therefore important to examine under what conditions the above criterion is met (i.e. fast ion backspillover relative to its desorption or consumption) for otherwise the promotional process will be internally diffusion limited not due to slow diffusion of the reactants but due to slow diffusion (backspillover) of the promoting species. 

Adsorption equilibrium of CPA and 2,4-D onto GAC could be represented by Sips equation. Adsorption equilibrium capacity increased with decreasing pH of the solution. The internal diffusion coefficients were determined by comparing the experimental concentration curves with those predicted from the surface diffusion model (SDM) and pore diffusion model (PDM). The breakthrough curve for packed bed is steeper than that for the fluidized bed and the breakthrough curves obtained from semi-fluidized beds lie between those obtained from the packed and fluidized beds. Desorption rate of 2,4-D was about 90 % using distilled water. 

To check if this liquid-phase reaction is not controlled by diffusion, the reaction is repeated with different weights of catalysts. A linear correlation is found between the initial rate of reaction and the weight of catalyst, indicating that the rate is not controlled by external or internal diffusion. 

Unlike the earlier case, here decreases with increasing current not only at large but also at small values of polarization, since depends on polarization. For d >Ldiff (particularly when polarization is significant), the electrode will work under internal diffusion control. 

Inspection of Fig. 15.3 reveals that while for jo 0.1 nAcm , the effectiveness factor is expected to be close to 1, for a faster reaction with Jo 1 p,A cm , it will drop to about 0.2. This is the case of internal diffusion limitation, well known in heterogeneous catalysis, when the reagent concentration at the outer surface of the catalyst grains is equal to its volume concentration, but drops sharply inside the pores of the catalyst. In this context, it should be pointed out that when the pore size is decreased below about 50 nm, the predominant mechanism of mass transport is Knudsen diffusion [Malek and Coppens, 2003], with the diffusion coefficient being less than the Pick diffusion coefficient and dependent on the porosity and pore stmcture. Moreover, the discrete distribution of the catalytic particles in the CL may also affect the measured current owing to overlap of diffusion zones around closely positioned particles [Antoine et ah, 1998]. 

A mixture of decalin (bicyclo[4.4.0]decane) isomers (Fluka, >98%) with a cis-to-trans ratio of 2-to-3 was used as a starting material. The experiments were performed in an electrically heated 300-mL stainless steel autoclave (Parr Industries) at 523 K and 2 MPa. The stirring rate and the starting material-to-catalyst ratio were kept at constant values equal to 1500 rpm and 22 (w/w), respectively. The screened catalysts were crushed and the fraction bellow 63 pm was used in the experiments to suppress internal diffusion. 

Weisz-Prater criterion uses measured values of the rate of reaction to determine if internal diffusion is limiting the reaction. 

In order to include the internal diffusion, one has to start from... 

It ought to be verified, however, in all cases, that the experimental Q-9 curve truly represents the distribution of surface sites with respect to a given adsorbate under specified conditions. The definition of differential heats of adsorption [Eq. (39) 3 includes, in particular, the condition that the surface area of the adsorbent A remain unchanged during the experiment. The whole expanse of the catalyst surface must therefore be accessible to the gas molecules during the adsorption of all successive doses. The adsorption of the gas should not be limited by diffusion, either within the adsorbent layer (external diffusion) or in the pores (internal diffusion). Diffusion, in either case, restricts the accessibility to the adsorbent surface. 

The most reliable method for detecting the influence of internal diffusion upon the profile of Q-6 curves would be to determine calorimetrically and to compare the differential heats of adsorption of a given gas on the surface of similar samples with different porosities. But it would be very difficult... 

In our original column on this topic [1] we had only done a principal component analysis to compare with the MLR results. One of the comments made, and it was made by all the responders, was to ask why we did not also do a PLS analysis of the synthetic linearity data. There were a number of reasons, and we offered to send the data to any or all of the responders who would care to do the PLS analysis and report the results. Of the original responders, Paul Chabot took us up on our offer. In addition, at the 1998 International Diffuse Reflectance Conference (The Chambersburg meeting), Susan Foulk also offered to do the PLS analysis of this data. 

Importantly, the internal diffusion model for lectins binding to mucins is distinct from the classical lock and key model of ligand binding to a receptor. The internal... 

Modeling of Internal Diffusion Limitations in a Fischer-Tropsch Catalyst... 

Zhan, X., Davis, B. H. 2002. Assessment of internal diffusion limitation on Fischer-Tropsch product distribution. Applied Catalysis A General 236 149-61. 

The book focuses on three main themes catalyst preparation and activation, reaction mechanism, and process-related topics. A panel of expert contributors discusses synthesis of catalysts, carbon nanomaterials, nitric oxide calcinations, the influence of carbon, catalytic performance issues, chelating agents, and Cu and alkali promoters. They also explore Co/silica catalysts, thermodynamic control, the Two Alpha model, co-feeding experiments, internal diffusion limitations. Fe-LTFT selectivity, and the effect of co-fed water. Lastly, the book examines cross-flow filtration, kinetic studies, reduction of CO emissions, syncrude, and low-temperature water-gas shift. 

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