Pore surface utilization ratio

It is seen from Fig. 8.18 that some of the curves of the change of reaction rate with particle size at different temperatures intersect. This indicates that when the reaction temperature varies, the effect of particle size on reaction rate will also vary. This phenomenon shows that the pore surface utilization ratio does not just vary with the size of particles, but also with the reaction temperature and the so-called catalyst efficiency as defined in equation (8.8). The pore surface utilization ratio (ISUR) for different sizes of particles at different temperatures is shown in Fig. 8.19. It can clearly be seen from Fig. 8.19 that particle size has the greatest effect on 77. The ISUR (77) is significantly lowered with increasing particle size. For example, when the reaction temperature (350°C) and other factors are the same, with the size increased from 0.6-0.9 mm to 4.0-6.7mm, 77 is decreased from 1 to 0.785 and 0.740 at 7.0 MPa and 15.0 MPa respectively. 

However, there is large difference between the conditions in industrial and in laboratory reactor. In addition to the size of catalyst particles for which the surface utilization ratio can be adjusted by Eq. (2.214), the catalyst amount used is much more for industrial reactor than laboratory one the reduction conditions and two-dimension distributions of gas flow and temperature caused by reactor structure are also different, as well as there is catalyst deactivation etc. Therefore, intrinsic rate constant k derived from activity data measured at laboratory cannot be used directly for the design calculation of industrial reactor. In order to simplify calculation, a concept of active coefficient is introduced, since it is too complicated to consider the process factors such as pore diffusion in large catalyst particles, industrial reduction and deactivation and two streams of gas flow and temperature distributions in industrial reactor etc, for which direct engineering applications are more difficult. That means that the intrinsic rate constant k obtained in laboratory or Eq. (2.214) is produced by the active coefficient. The magnitude of the active... 

The utilization of inner surface f is essentially the ratio of actual rate to the maximum possible reaction rate value of gas in the pore. The utilization ratio shows that the utilization of the inner surface is several times lower than the outer surface of particles. 

The pore size of the catalyst relates to the mass transfer process of catalytic reaction. When reactions proceed in an inner diffusion area, the mass transfer rate is relatively slow, and the pore size relates to the surface utilization ratio of the catalyst in the reaction. If the target product is an unstable intermediate, the pore size will affect the selectivity of reaction. Therefore, for a given reaction condition and composition of the catalyst, a catalyst should have the uniform pore size distribution in order to develop of a good catalyst. 

The author has studied the effect of particle size on the outlet ammonia concentration reaction rate and utilization ratio of the pore surface on the A301 catalyst at 7MPa, 10MPa and ISMPa respectively. Tables 8.16, 8.17 and 8.18 show the results. 

The support has an internal pore structure (i.e., pore volume and pore size distribution) that facilitates transport of reactants (products) into (out of) the particle. Low pore volume and small pores limit the accessibility of the internal surface because of increased diffusion resistance. Diffusion of products outward also is decreased, and this may cause product degradation or catalyst fouling within the catalyst particle. As discussed in Sec. 7, the effectiveness factor Tj is the ratio of the actual reaction rate to the rate in the absence of any diffusion limitations. When the rate of reaction greatly exceeds the rate of diffusion, the effectiveness factor is low and the internal volume of the catalyst pellet is not utilized for catalysis. In such cases, expensive catalytic metals are best placed as a shell around the pellet. The rate of diffusion may be increased by optimizing the pore structure to provide larger pores (or macropores) that transport the reactants (products) into (out of) the pellet and smaller pores (micropores) that provide the internal surface area needed for effective catalyst dispersion. Micropores typically have volume-averaged diameters of 50 to... 

A measure of the absence of internal (pore diffusion) mass transfer limitations is provided by the internal effectiveness factor, t, which is defined as the ratio of the actual overall rate of reaction to the rate that would be observed if the entire interior surface were exposed to the reactant concentration and temperature existing at the exterior of the catalyst pellet. A value of 1 for rj implies that all of the sites are being utilized to their potential, while a value below, say, 0.5, signals that mass transfer is limiting performance. The value of rj can be related to that of the Thiele modulus, 4>, which is an important dimensionless parameter that roughly expresses a ratio of surface reaction rate to diffusion rate. For the specific case of an nth order irreversible reaction occurring in a porous sphere,... 

Very high internal surface area zeolites (lO m /g) can be synthesized with controlled pore sizes of 8-20 A and controlled acidity [(Si/Al) ratio]. These find applications in the cracking and isomerization of hydrocarbons that occur in a shape-selective manner as a result of the uniform pore structure and are the largest-volume catalysts utilized in petroleum refining at present [20]. They are also the first of the high-technology catalysts where the chemical activity is tailored by atomic-scale study and control of the internal surface structure and composition. 

In the industrial applications of electrochemistiy, the use of smooth surfaces is impractical and the electrodes must possess a large real surface area in order to increase the total current per unit of geometric surface area. For that reason porous electrodes are usually used, for example, in industrial electrolysis, fuel cells, batteries, and supercapacitors [400]. Porous siufaces are different from rough surfaces in the depth, /, and diameter, r, of pores for porous electrodes the ratio Hr is very important. Characterization of porous electrodes can supply information about their real surface area and electrochemical utilization. These factors are important in their design, and it makes no sense to design pores that are too long and that are impenetrable by a current. Impedance studies provide simple tools to characterize such materials. Initially, an electrode model was developed by several authors for dc response of porous electrodes [401-406]. Such solutions must be known first to be able to develop the ac response. In what follows, porous electrode response for ideally polarizable electrodes will be presented, followed by a response in the presence of redox processes. Finally, more elaborate models involving pore size distribution and continuous porous models will be presented. 

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. 

Individual nanopores or nanopore arrays can be developed into a sensor to detect a species of interest. The transduction methods described earlier (e.g., I-V response or current-time (I-t) response) can be applied to sense/detect an analyte. For instance, changes in the observed rectification response of a nanoporous system can be used to indicate and identify the presence of an analyte. - Often, this change in ICR ratio can be attributed to a disruption in the surface charge of the nanopore as the analyte of interest binds to the pore. Direct sensing of electroactive molecules can be accomplished electrochemically with nanoporous electrodes chronoamperometry and voltammetry measurements are most often applied with these systems for detection. 3 2.i83 However, the most typical measurement utilized in the application of nanopores as sensors is that of resistive-pulse sensing in which current blockades occur as a molecule passes through a pore and alters the conductivity. " For a detailed list of analytes that have been detected via different nanoporous platforms and measurement techniques, please refer to Table 11.3. 

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