Product desorption limitation model

Three obvious models which could describe the observed reaction rate are (a) concentration equilibrium between all parts of the intracrystalline pore structure and the exterior gas phase (reaction rate limiting), (b) equilibrium between the gas phase and the surface of the zeolite crystallites but diffusional limitations within the intracrystalline pore structure, and (c) concentration uniformity within the intracrystalline pore structure but a large difference from equilibrium at the interface between the zeolite crystal (pore mouth) and the gas phase (product desorption limitation). Combinations of the above may occur, and all models must include catalyst deactivation. 

System Model. The equilibrium model (model a) did not properly represent the observed rate curve because the predicted peak maximum, using this model, always occurred at least an order of magnitude earlier in time than was actually observed when measured values for all parameters were substituted into the equilibrium model. Thus a mass transfer influence—e.g.j intracrystalline diffusional limitations or product desorption limitations—must be invoked to explain the data. The diffusional limitations model might fit the data qualitatively as Tan and Fuller (6) show for their system. However, this model contains three fitting constants and should be applied only when there is sufficient evidence of diffusional limitations. 

Figure 6. Simulation of ethylbenzene ethylation over SK-600 at 577°K and C8 C2 = 0.2 by product desorption limitation model...

Vapor-phase alkylation of benzene by ethene and propene over HY, LaY, and REHY has been studied in a tubular flow reactor. Transient data were obtained. The observed rate of reaction passes through a maximum with time, which results from build-up of product concentration in the zeolite pores coupled with catalyst deactivation. The rate decay is related to aromatic olefin ratio temperature, and olefin type. The observed rate fits a model involving desorption of product from the zeolite crystallites into the gas phase as a rate-limiting step. The activation energy for the desorption term is 16.5 heal/mole, approximately equivalent to the heat of adsorption of ethylbenzene. For low molecular weight alkylates intracrystalline diffusion limitations do not exist. 

Benzene alkylation over Y zeolites has been studied as a function of olefin, olefin aromatic ratio, temperature, and zeolite cation form. The rate has been modeled, and the rate-limiting process has been quantified as product desorption. 

For the model involving a desorption limitation (model c) a component mole balance is written over the gas phase and crystallite phase for product D (A + B - D). These are, respectively ... 

The same group has looked into the conversion of NO on palladium particles. The authors in that case started with a simple model involving only one type of reactive site, and used as many experimental parameters as possible [86], That proved sufficient to obtain qualitative agreement with the set of experiments on Pd/MgO discussed above [72], and with the conclusion that the rate-limiting step is NO decomposition at low temperatures and CO adsorption at high temperatures. Both the temperature and pressure dependences of the C02 production rate and the major features of the transient signals were correctly reproduced. In a more detailed simulation that included the contribution of different facets to the kinetics on Pd particles of different sizes, it was shown that the effects of CO and NO desorption are fundamental to the overall behavior... 

Hougen- Watson Models for Cases where Adsorption and Desorption Processes are the Rate Limiting Steps. When surface reaction processes are very rapid, the overall conversion rate may be limited by the rate at which adsorption of reactants or desorption of products takes place. Usually only one of the many species in a reaction mixture will not be in adsorptive equilibrium. This generalization will be taken as a basis for developing the expressions for overall conversion rates that apply when adsorption or desorption processes are rate limiting. In this treatment we will assume that chemical reaction equilibrium exists between various adsorbed species on the catalyst surface, even though reaction equilibrium will not prevail in the fluid phase. 

Carbon monoxide oxidation is a relatively simple reaction, and generally its structurally insensitive nature makes it an ideal model of heterogeneous catalytic reactions. Each of the important mechanistic steps of this reaction, such as reactant adsorption and desorption, surface reaction, and desorption of products, has been studied extensively using modem surface-science techniques.17 The structure insensitivity of this reaction is illustrated in Figure 10.4. Here, carbon dioxide turnover frequencies over Rh(l 11) and Rh(100) surfaces are compared with supported Rh catalysts.3 As with CO hydrogenation on nickel, it is readily apparent that, not only does the choice of surface plane matters, but also the size of the active species.18-21 Studies of this system also indicated that, under the reaction conditions of Figure 10.4, the rhodium surface was covered with CO. This means that the reaction is limited by the desorption of carbon monoxide and the adsorption of oxygen. 

Laser desorption Fourier transform mass spectrometry (LD-FTMS) results from a series of peptides and polymers are presented. Successful production of molecular ions of peptides with masses up to 2000 amu is demonstrated. The amount of structurally useful fragmentation diminishes rapidly with increasing mass. Preliminary results of laser photodissociation experiments in an attempt to increase the available structural information are also presented. The synthetic biopolymer poly(phenylalanine) is used as a model for higher molecular weight peptides and produces ions approaching m/z 4000. Current instrument resolution limits are demonstrated utilizing a polyethylene-glycol) polymer, with unit mass resolution obtainable to almost 4000 amu. 

Later on, Iribarne and Thomson proposed a different mechanism for the production of gas-phase ions from charged droplets [27,28]. Interestingly, the motivation for their studies was far removed from a concern for the needs of mass spectrometry. Instead, it stemmed from their interest in charged droplets as a possible source of ions in the atmosphere. They proposed a model for such ion formation based on the idea that, on charged droplets that were small enough, evaporation could make the surface field sufficiently intense to lift solute ions from the droplet into the ambient gas before the Rayleigh limit is reached. This model is nowadays usually referred to as ion desorption model (IDM). 

In many industrial reactions, the overall rate of reaction is limited by the rate of mass transfer of reactants and products between the bulk fluid and the catalytic surface. In the rate laws and cztalytic reaction steps (i.e., dilfusion, adsorption, surface reaction, desorption, and diffusion) presented in Chapter 10, we neglected the effects of mass transfer on the overall rate of reaction. In this chapter and the next we discuss the effects of diffusion (mass transfer) resistance on the overall reaction rate in processes that include both chemical reaction and mass transfer. The two types of diffusion resistance on which we focus attention are (1) external resistance diffusion of the reactants or products between the bulk fluid and the external smface of the catalyst, and (2) internal resistance diffusion of the reactants or products from the external pellet sm-face (pore mouth) to the interior of the pellet. In this chapter we focus on external resistance and in Chapter 12 we describe models for internal diffusional resistance with chemical reaction. After a brief presentation of the fundamentals of diffusion, including Pick s first law, we discuss representative correlations of mass transfer rates in terms of mass transfer coefficients for catalyst beds in which the external resistance is limiting. Qualitative observations will bd made about the effects of fluid flow rate, pellet size, and pressure drop on reactor performance. 

The reaction mechanism is based on the Langmuir-Hinshelwood model for heterogeneous catalysis. This represents sorption and desorption of reactants and products as equilibria the ligand-exchange reaction is considered rate limiting. By... 

This picture of a substantial phosphorus constraint is drastically altered when the presence of the inorganic labile (i.e., sorbed) phosphorus pool is taken into account (Scenario C). Desorption of phosphate occurs in response to increased rates of removal from the soil solution. Consequently, the reduction in soil solution phosphorus concentration over 1730 levels is only 9% for 1981-1990. This contrasts with the 25% reduction in Scenario B. Consequently, the enhancements of Gp and Np are more similar to the no-P-constraint case, though a full expression of the COi-in-duced growth response is still not possible. Accordingly, the rate of net carbon accumulation by the ecosystem is 6.5 mol m - year", substantially more than Scenario B, but about 20% less than what is modeled to be the case if no phosphorus limitations to plant production occurred. 

Figure 15-1 Total pressure dependence of the best pseudo-first-order kinetic rate constant when a first-order rate law approximates a Hougen-Watson model for dissociative adsorption of diatomic A2 on active catalytic sites. Irreversible triple-site chemical reaction between atomic A and reactant B (i.e., 2Acr - - Bcr -> products) on the catalytic surface is the rate-limiting step. The adsorption/desorption equilibrium constant for each adsorbed species is 0.25 atm. ...

Since there is no capillary moisture conduction to the product surface in the frozen product, no first drying stage exists. It starts with the second drying stage. The ice or sublimation front continuously moves inside the product. The required heat for sublimation is transferred to the product by conduction or radiation, or with a combination of both. Moisture vapor diffusion in the dried product follows the Knudsen molecular flow model (see Table 5-2). In the third drying stage residual liquid moisture desorbs to the inner and outer product surface from its bonded state. Since desorption occurs only after complete sublimation of ice, the heat transfer has to be reduced to avoid heating the product over the permissible limit. 

Building a mathematical model for a chemical engineering system depends to a large extent on the knowledge of the physical and chemical laws governing the processes taking place within the boundaries of the system. This includes the different rates of mass, heat, and momentum transfer, rates of reactions and rates of adsorption-desorption, and so forth. It also includes the thermodynamic limitations that decide the feasibility of the process to start with, as well as heat production and absorption. 

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