Internal mass transfer limitations

A final, obvious but important, caution about catalyst film preparation Its thickness and surface area Ac must be low enough, so that the catalytic reaction under study is not subject to external or internal mass transfer limitations within the desired operating temperature range. Direct impingement of the reactant stream on the catalyst surface1,19 is advisable in order to diminish the external mass transfer resistance. 

A lot of work is currently carried out to extend this idea to fully dispersed two-dimensional (on a YSZ surface) or three-dimensional (in a porous YSZ structure) metal catalysts. The main problems to be overcome is current bypass and internal mass transfer limitations due to the high catalytic activity of such fully dispersed Pt/YSZ catalyst systems. 

Checking the absence of internal mass transfer limitations is a more difficult task. A procedure that can be applied in the case of catalyst electrode films is the measurement of the open circuit potential of the catalyst relative to a reference electrode under fixed gas phase atmosphere (e.g. oxygen in helium) and for different thickness of the catalyst film. Changing of the catalyst potential above a certain thickness of the catalyst film implies the onset of the appearance of internal mass transfer limitations. Such checking procedures applied in previous electrochemical promotion studies allow one to safely assume that porous catalyst films (porosity above 20-30%) with thickness not exceeding 10pm are not expected to exhibit internal mass transfer limitations. The absence of internal mass transfer limitations can also be checked by application of the Weisz-Prater criterion (see, for example ref. 33), provided that one has reliable values for the diffusion coefficient within the catalyst film. 

However, the pattern is complicated by several factors. The sugar molecules to be hydrogenated mutarotate in aqueous solutions thus coexisting as acyclic aldehydes and ketoses and as cyclic pyranoses and furanoses and reaction kinetics are complicated and involve side reactions, such as isomerization, hydrolysis, and oxidative dehydrogenation reactions. Moreover, catalysts deactivate and external and internal mass transfer limitations interfere with the kinetics, particularly under industrial circumstances. 

Kinetics of Free and Mao-osoib-Bound eaiymc. The results of the Lineweaver-Burk analysis of the initial rates for free and immobilized enzyme appear in Table I. The increase in the substrate affinity parameter due to some internal mass transfer limitations in the IME as no substrate-matrix interactions were present. The increase... 

First-order reactions without internal mass transfer limitations A number of reactions carried out at high temperatures are potentially mass-transfer limited. The surface reaction is so fast that the global rate is limited by the transfer of the reactants from the bulk to the exterior surface of the catalyst. Moreover, the reactants do not have the chance to travel within catalyst particles due to the use of nonporous catalysts or veiy fast reaction on the exterior surface of catalyst pellets. Consider a first-order reaction A - B or a general reaction of the form a A - bB - products, which is of first order with respect to A. For the following analysis, a zero expansion factor and an effectiveness factor equal to 1 are considered. 

First-order reactions with internal mass-transfer limitations Since the following equation is valid, under the assumption made earlier, we only have to replace the right form of the global rate as expressed in eq. (5.196) ... 

Tphe rate-limiting processes in catalytic reaction over zeolites remain A largely undefined, mainly because of the lack of information on counterdiffusion rates at reaction conditions. Thomas and Barmby (7), Chen et al. (2, 3), and Nace (4) speculate on possible diffusional limitations in catalytic cracking over zeolites, and Katzer (5) has shown that intracrystalline diffusional limitations do not exist in liquid-phase benzene alkylation with propene. Tan and Fuller (6) propose internal mass transfer limitations and rapid fouling in benzene alkylation with cyclohexene over Y zeolite, based on the occurrence of a maximum in the reaction rate at about 100 min in flow reaction studies. Venuto et al (7, 8, 9) report similar rate maxima for vapor- and liquid-phase alkylation of benzene and dehydro-... 

At catalytically active centers in the center of carrier particles, external mass transfer (film diffusion) and/or internal mass transfer (pore diffusion) can alter or even dominate the observed reaction rate. External mass transfer limitations occur if the rate of diffusive transport of relevant solutes through the stagnating layer at a macroscopic surface becomes rate-limiting. Internal mass transfer limitations in porous carriers indicate that transport of solutes from the surface of the particle towards the active site in the interior is the slowest step. 

Bernard, P. Barth, D. Internal Mass Transfer Limitation During Enzymatic Esterification in Supercritical Carbon Dioxide and Hexane. Biocatal. Biotransform. 1995, 12, 299-308. 

Bernard, P. Barth, D. Perrut, M. Internal Mass Transfer Limitation on Enzymatic Esterification in Supercritical Carbon Dioxide. In High Pressure and Biotechnology, Balny, C., Hayashi, R., Heremans, K., Masson, P., Eds. John Libbey U.K., 1992 pp. 451 155. 

Internal mass transfer limitations in industrial operation... 

For an immobilized enzyme it follows that a reduction in the rate of diffusion of a substrate to the active site of an enzyme will increase the apparent Km and reduce Fmax. The nature of the mass transfer effect depends on the fashion in which the enzyme is immobilized. Enzymes immobilized on the surface of a carrier will experience external mass transfer limitations between the bulk solution and the surface, whereas those entrapped within a porous matrix are also affected by internal mass transfer limitations due to the reduction in the rate of diffusion of substrate and products through the matrix. 

If, under experimental conditions internal mass transfer limitations are present then for an nth-order irreversible reaction the observed reaction rate can be written as ... 

Enzymatic Reaction in Supercritical Carbon Dioxide Internal Mass Transfer Limitation... 

The intrinsic catalytic properties of enzymes are modified either during immobilization or after they were immobilized [25-27], In heterogeneous catalysis such as is carried out by immobilized enzymes, the rate of reaction is determined not simply by pH, temperature and substrate solution, but by the rates of proton, heat and substrate transport, through the support matrix to the immobilized enzyme. In order to estimate this last phenomenon, we have studied the internal mass transfer limitation both in hexane and in SC C02, with different enzymatic support sizes. 

Concentration overpotential arises due to external or internal mass transfer limitations. For typical cross-flow monoliths, Debenedetti (19) has shown that concentration overpotential is not important under conditions similar to those explored here. 

To check for internal mass transfer limitation, it is possible to use the nondimensional Weisz modulus, Thiele modulus (Levenspiel, 1998) ... 

Intraparticle Diffusion and External Mass-Transfer Resistance For typical industrial conditions, external mass transfer is important only if there is substantial intraparticle diffusion resistance. This subject has been discussed by Luss, Diffusion-Reaction Interactions in Catalyst Pellets, in Carberry and Varma (eds.), Chemical Reaction and Reactor Engineering, Dekker, 1987. This, however, may not be the case for laboratory conditions, and care must be exerted in including the proper data interpretation. For instance, for a spherical particle with both external and internal mass-transfer limitations and first-order reaction, an overall effectiveness factor r, can be derived, indicating the series-of-resistances nature of external mass transfer followed by intraparticle diffusion-reaction ... 

About 30 mg of a Pt-Sn/AlaOs catalyst were used in each run. The particle size were chosen small enough to avoid internal mass transfer limitations. The catalyst was prepared by sequential impregnation of a commercial y-alumina support with aqueous solutions of SnCl2 and HaPtClfi [9]. Characterization data are summarized in Table 1. 

Many adsorbents, such as activated carbon and ion-exchange resins, can efficiently separate antibiotics and other small biologically active molecules from the fermentation broth. Unfortunately, these adsorbents also interact with the microbial cells and some of the dissolved nutrients. Thus, the use of ion-exchange resins and activated carbon to remove fermentation products is frequently associated with problems of simultaneous removal of nutrients and side products. Substantial volume reduction occurs but only limited purification can be achieved. Commercial adsorbents and ion-exchange resins are available in various matrices and sizes. Larger particles are preferred for easy separation from the broth but they can be internal mass transfer limited. 

In three-phase reactors, one of the main problems is often the mass transport limitations, which may reflect internal as well as external mass transfer resistances. The use of filamentous catalytic materials for multiphase reactions may help reduce or even avoid mass transfer limitations [63,132,133]. Filamentous woven cloths made of glass, composite mixed oxides, metallic alloys, or activated carbon (Figure 18) can be used as supports for active components such as platinum, palladium, or transition metal oxides. The diameters of the filaments are of the order of several micrometers and correspond to the typical diameters of catalysts that are suspended in the reaction medium. By using such small diameters, internal mass transfer limitations can be avoided. 

Advances in the technology of microstructured catalytic reactors depend crucially on the ability to generate appropriate catalyst layers. The activity of the catalyst determines the thickness of the layer that needs to be deposited on the structured support or the walls of the MSR. Relatively thick layers of up to several hundred micrometers are necessary for moderate reaction rates to achieve good reactor performance, whereas thin layers are desirable for very fast catalytic reactions to avoid internal mass transfer limitations (Section 3.2.3). 

The temperature dependency of the TOF is given in Figure 3. Since all the catalysts had the same platinum particle size (ca. 1.5 nm) the TOF appears to depend on the support morphology. The catalyst in which the fiber support was calcined at 1173 K exhibited the highest activity. This due to the lack of internal dif-fiisional limitations. The higher calcinations temperature results in closure of smaller pores and decreased pore volume (Figure 2), hence, less internal mass-transfer limitation is taking place. 

Phenyl-1,2-propanedione (Aldrich, 99%) was hydrogenated in a pressurized reactor (Parr 4560, V=300 cm ) in the absence of external and internal mass transfer limitation (verified experimentally). The reactor was equipped with an propeller type stirrer (four blades, propeller diameter 35 mm) operating at stirring rate of 1950 rpm. The hydrogen (AGA, 99.999%) pressure was 6.5 bar and teii ierature was 15 - 35°C. Pt/Al203 (Strem Chemicals, 78-1660) was used as a catalyst. The catalyst mass and liquid volume were 0.15 g and 150 cm, respectively The metal content was 5 wt.%, BET specific surface area 95 m / g, the mean metal particle size 8.3 nm (XRD), dispersion 40% (H2 chemisorption), the mean catalyst particle size 18.2 pm (Malvern). Catalysts were activated under hydrogen flow (100 cm / min) for 2 h at 400°C prior to the reaction. 

It is interesting to consider the effect of internal mass transfer limitations on the observed kinetics. Taking into account eq. (9.199) the reaction rate for n-th order kinetics at high values of Thiele modulus is given by r - k,C / Thiele modulus for n-th order kinetics is... 

Probably the most widely applied criterion is the one for internal mass transfer limitations in an isothermal catalyst particle, e.g. for pore diffusion. Due to Weisz and Prater (Advances in Catalysis 6 (1954) 143) no pore diffusion limitation occurs, if the Weisz modulus... 

The extent of external and internal mass transfer limitation can be estimated by the methods introduced by Carberry and by Wheeler-Weisz [12]. A Carberry number (Ca) smaller than 0.05 means that diffusional retardation by external mass transport may be neglected. A Wheeler-Weisz group (WW) smaller than 0.1 means that pore diffusion limitation is negligible [13,14]. 

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