Intrinsic kinetics experimental measurement

Theoretical criteria normally contain an explicit expression of the intrinsic chemical rate, and optionally also a measured value of the observed reaction rate. Thus, these criteria are useful only when the intrinsic kinetics are available, and one is, for example, interested in whether or not transport effects are likely to influence the performance of the catalyst as the operating conditions are changed. If it is not possible to generate a numerical solution of the governing differential equations, either due to a lack of time or to other reasons, then the use of theoretical criteria will not only save experimental effort, but also provide a more reliable estimation of the net transport influence on the observable reaction rate than simple experimental criteria can give, which do not contain any explicit... 

Experimental Measurements of Reaction Kinetics. The reaction expressions discussed in the following model the intrinsic reaction on the catalyst surface, free of mass-transfer restrictions. Experimental measurements, usually made with very fine particles, are described by theoretically deduced formulas, the validity of which is tested experimentally by their possibility for extrapolation to other reaction conditions. Commonly the isothermal integral reactor is used with catalyst crushed to a size of 0.5-1.5 mm to avoid pore diffusion restriction and heat-transfer resistance in the catalyst particles. To exclude maldistribution effects and back mixing, a high ratio of... 

Thus by varying (by dilution or by changing Tq) and plotting a UITc) vs. l/Tc, the activation energy can be obtained readily. In this manner, the effective values of E have been measured for various SHS systems (cf Munir and Anselmi-Tamburini, 1989). However, it is not clear if these reported values correspond to actual elementary processes or whether they are the result of a complex interaction between transport and reaction phenomena. The simplifying assumptions made to derive Eq. (22) were stated earlier, and they all need to be satisfied under the experimental conditions in order to obtain intrinsic kinetic data. 

Many reports have shown that larger catalyst pellets lead to lower FT synthesis rates and to lighter products, particularly methane (32,52,56,57-63). Significant effort has been devoted to the measurement of intrinsic kinetics in diffusion-free pellets under differential reactor conditions (32,52,56, 57,59-65). These kinetic expressions are then combined with descriptions of diffusion through the liquid-filled catalyst pores to produce models that attempt to predict the effect of diffusional inhibition on synthesis rates. Most of these studies have concentrated on reactant diffusion effects and make use of standard effectiveness lactor and Thiele modulus treatments (52,56,59,65). These models describe many of the observed experimental trends, but several issues related to the processes that they describe remain... 

Stefuca et al. (1990) proposed an ET method offering a rapid, convenient, and general approach to determine kinetic constants of immobilized biocatalysts. Here, a differential reactor (DR) was used for the measurement of the initial reaction rate of sucrose hydrolysis (Vallat et al. 1986). The enzyme column of the ET has been considered as a differential packed-bed reactor, and with a mathematical model, intrinsic kinetic constants of immobilized invertase were calculated from experimental DR and ET data. 

Adsorption of molecules proceeds by successive steps (1) penetration inside a particle (2) diffusion inside the particle (3) adsorption (4) desorption and (5) diffusion out of the particle. In general, the rates of adsorption and desorption in porous adsorbents are controlled by the rate of transport within the pore network rather than by the intrinsic kinetics of sorption at the surface of the adsorbent. Pore diffusion may take place through several different mechanisms that usually coexist. The rates of these mechanisms depend on the pore size, the pore tortuosity and constriction, the cormectivity of the pore network, the solute concentration, and other conditions. Four main, distinct mechanisms have been identified molecular diffusion, Knudsen diffusion, Poiseiulle flow, and surface diffusion. The effective pore diffusivity measured experimentally often includes contributions for more than one mechanism. It is often difficult to predict accurately the effective diffusivity since it depends so strongly on the details of the pore structure. 

They used this model to predict the effective diffusivity in the partially impervious deposit (zone 4). They developed and solved the coupled mass balance equations for spherical pellets in a fixed bed reactor. To compare the model with experimental data, they measured the conversion of propane and propylene over partially poisoned pellets in a small isothermal packed bed reactor. For intrinsic kinetic rates of propane and propylene they employed the empirical rate equations proposed by Volts et al. and Hiam et al. The Hegedus model is briefly described below ... 

Substrate limitations have been documented and quantitatively described ( U, 2, 17 ). Dooley et al. (11) present an excellent description of modeling a reaction in macroreticular resin under conditions where diffusion coefficients are not constant. Their study was complicated by the fact that not all the intrinsic variables could be measured independently several intrinsic parameters were found by fitting the substrate transport with reaction model to the experimental data. Roucls and Ekerdt (16) studied olefin hydrogenation in a gel-form resin. They were able to measure the intrinsic kinetic parameters and the diffusion coefficient independently and demonstrate that the substrate transport with reaction model presented earlier is applicable to polymer-immobilized catalysts. Finally, Marconi and Ford (17) employed the same formalism discussed here to an immobilized phase transfer catalyst. The reaction was first-order and their study presents a very readable application of the principles as well as presents techniques for interpreting substrate limitations in trlphase systems. 

Implications of the Effectiveness Factor Concept for Kinetic Parameters Measured in the Laboratory It is useful at this point to discuss the effects of intraparticle diffusion on the kinetic parameters that are observed experimentally. Unless one is aware that intraparticle diffusion may obscure or disguise the true intrinsic chemical kinetics, he or she may draw incorrect conclusions regarding the reaction order and the... 

Descriptions of pore development and stracture require microscopic models of the particle. These models include intrinsic kinetics and pore stractural changes during bumoff. Three of the most popular mieroscopic models are a random eapillaiy pore model, one in which the pores are considered spherical vesicles connected by cyhndri-cal micropores, and one in which the pores have a treelike structure. These models allow for pore growth and coalescence in their respective fashions and provide estimates of reactive smface area. Parameters required for these models are obtained from experimental measurements of the various chars. 

In general, the intrinsic kinetic parameters of a catalytic reaction under study are unknown. Therefore, the relationships based on the Thiele modulus cannot be used to estimate the influence of inner mass transfer on the measured overall reaction rate. Observed is the experimentally accessible efficient reaction rate, In... 

In this case, since the diffusion factor no longer masks the kinetics of the reaction (Tp experimentally measured values of can be used in conjunction with known values of A and to obtain the intrinsic reaction rate constant k. The values of p and q can be obtained by the usual technique of varying one variable at a time (constant at different values of A, and vice versa). However, it has to be ensured that... 

Aiming to obtain an intrinsic kinetic expression, experimental data for inlet temperatures between 310-420°C were used. 99 experimental points, the axial solid temperature profiles (measured for each experiment), the mass balances of model B and a numerical nonlinear regression code were simultaneously employed to estimate the kinetic parameters. A power law type expression was used to model the reaction rate behavior ... 

Experimental evaluation of the effective diffusivity Dg is possible, if intrinsic kinetics of the reaction is known, and requires a comparison of the measured and predicted global rates which may also involve an iterative procedure. 

A new development may be the use of transient techniques in slurry model reactors. Weng and Smith [l33] recently presented a model for the reactant concentration in the gas outlet if a pulse of reactant was introduced in the gas feed. Mathematically they showed the possibility of distinguishing between the adsorption rate and the true surface reaction rate. A slightly different mathematical treatment is presented by Datta and Rinker [64]. We do not know of experimental work on measuring intrinsic kinetics using such transient techniques. 

Laboratory data collected over honeycomb catalyst samples of various lengths and under a variety of experimental conditions were described satisfactorily by the model on a purely predictive basis. Indeed, the effective diffusivities of NO and NH3 were estimated from the pore size distribution measurements and the intrinsic rate parameters were obtained from independent kinetic data collected over the same catalyst ground to very fine particles [27], so that the model did not include any adaptive parameters. 

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