Mass transfer effects internal

To ensure the system is probing reactions in a kinetically controlled regime, the reaction conditions must be calculated to determine the value of the Wiesz-Prater criterion. This criterion uses measured values of the rate of reaction to determine if internal dififusion has an influence. Internal mass transfer effects can be neglected for values of the dimensionless number lower than 0.1. For example, taking a measured CPOX rate of 5.9 x 10 molcH4 s g results... 

This chapter describes the different types of batch and continuous bioreactors. The basic reactor concepts are described as well as the respective basic bioreactors design equations. The comparison of enzyme reactors is performed taking into account the enzyme kinetics. The modelhng and design of real reactors is discussed based on the several factors which influence their performance the immobilized biocatalyst kinetics, the external and internal mass transfer effects, the axial dispersion effects, and the operational stabihty of the immobilized biocatalyst. 

When a biocatalyst is immobihzed within a porons snpport, in addition to possible external mass-transfer effects there conld also exist resistance to internal diffusion of snbstrate, as this mnst dififnse throngh the pores in order to reach the biocatalyst. Conseqnently a snbstrate concentration gradient is established within the pores, resnlting in a concentration decreasing with increased distance (in depth) from the surface of immobihzed biocatalyst preparation. Similarly, a corresponding product concentration gradient is obtained in the opposite direction. 

The internal mass-transfer effects can be reduced, however, by decreasing the particle dimensions of the porous support containing the biocatalyst. Particle-diameter decrease results in a reduction of the distance from the outer support surface that the substrate must cross and, consequently, also results in a decrease of the substrate concentration gradient. 

The mass transfer effects cause, in general, a decrease of the measured reaction rate. The heat transfer effects may lead in the case of endothermic reactions also to a decrease of the equilibrium value and the resulting negative effect may be more pronounced. With exothermic reactions, an insufficient heat removal causes an increase of the reaction rate. In such a case, if both the heat and mass transfer effects are operating, they can either compensate each other or one of them prevails. In the case of internal transfer, mass transport effects are usually more important than heat transport, but in the case of external transfer the opposite prevails. Heat transport effects frequently play a more important role, especially in catalytic reactions of gases. The influence of heat and mass transfer effects should be evaluated before the determination of kinetics. These effects should preferably be completely eliminated. 

Internal recycle reactors are designed so that the relative velocity between the catalyst and the fluid phase is increased without increasing the overall feed and outlet flow rates. This facilitates the interphase heat and mass transfer rates. A typical internal flow recycle stirred reactor design proposed by Berty (1974, 1979) is shown in Fig. 18. This type of reactor is ideally suited for laboratory kinetic studies. The reactor, however, works better at higher pressure than at lower pressure. The other types of internal recycle reactors that can be effectively used for gas-liquid-solid reactions are those with a fixed bed of catalyst in a basket placed at the wall or at the center. Brown (1969) showed that imperfect mixing and heat and mass transfer effects are absent above a stirrer speed of about 2,000 rpm. Some important features of internal recycle reactors are listed in Table XII. The information on gas-liquid and liquid-solid mass transfer coefficients in these reactors is rather limited, and more work in this area is necessary. 

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. 

The rotating-basket reactor (often known as the Carberry reactor) has been widely used for gas-solid as well as gas-liquid-solid reactions (see Fig. 5-6). Its construction is not very difficult, but it is more complex and expensive to build than a batch or fixed-bed reactor. The catalyst baskets can either be attached to the stirrer [Fig. 5-7(6)] or they can, themselves, be used as the stirrer paddles [Fig. 5-7(a)]. Furthermore, a small variety of rotating catalyst baskets are available (see Fig. 5-8). Baskets must, in general, be small in diameter, so that internal mass-transfer effects are minimized. 

S. Mehdizadeh, J. Dudovic, P. C. Andricacos, L. T. Romankiw, and H. Y. Cheh, The Influence of Lithographic Patterning on Current Distribution in Electrochemical Microfabrication II. Experimental Study and Mass-Transfer Effects., in Proceedings of the First International Symposium on Electrochemical Microfabrication, M. Datta, K. Sheppard, and D. Snyder (eds.). The Electrochemical Society Inc., Pennington, NJ (1991), 91-3, pp. 40-51. 

Mass-transfer Effects. - Zeolites possess a large internal surface area and are necessarily subject to mass-transfer effects, although there have been relatively few studies of these. Swabb and Gates observed that for H-mordenite at low temperatures (155°C), rate was independent of crystallite size for methanol dehydration, but at higher temperature rate variation was consistent with a Thiele model. 

Because of their tunable properties, supercritical solvents provide a useful medium for enzyme-catalyzed reactions.f The mechanism of enzyme-catalyzed reactions is similar to the mechanism described for solid-catalyzed reactions. External as well as internal transport effects may limit the reaction rate. Utilizing supercritical fluids enhances external transport rate due to increase in the diffusivity and therefore mass transfer coefficient. Internal transport rate depends on the fluid medium as well as the morphology of the enzyme. Supercritical fluids can alter both. 

Prior to the systematic kinetic e q)eriments a screening of the mass transfer effect was carried out. A conparison of erqjeriments performed widi a catalyst particle mean diameter of 760-960 pm and of 250-500 pm showed quite similar results which indicate the absence of internal mass transfer resistances. Moreover, ejq)eriments performed with different agitation velocities (800 and 200 rpm) gave similar results, suggesting the absence of macro-mixing effects and external mass transfer resistances around the catalyst particles. 

When the reaction rates in the monolith channels are sufficiently high, a significant gradient will develop between the concentration at the channel center and that at the catalyst surfaces. This external mass transfer effect must be considered in addition to internal diffusion effects. The rate of external mass transfer at a given value of z is equal to the reaction rate inside the catalyst at steady state ... 

Diffusion, partition, and enzyme,reactions influence the sensor characteristics in a complex manner. The effect of enzyme immobilization on the reaction rate is described by the following terminology. Apparent or effective kinetics are observed when internal or external diffusion affects the overall rate. Inherent kinetics prevail when only partitioning (and not mass transfer) effects are present. Intrinsic kinetics describe the enzyme-catalyzed reaction when no partitioning effects or diffusion limitation are present. 

The Thiele modulus, calculated from reaction rate data, diffusion length, and diffusion coefficient, can be used to evaluate internal mass transfer effects. Expressed with the Michaelis constant and maximum reaction velocity, the Thiele modulus is given by... 

Baddour [26] retained the above model equations after checking for the influence of heat and mass transfer effects. The maximum temperature difference between gas and catalyst was computed to be 2.3°C at the top of the reactor, where the rate is a maximum. The difference at the outlet is 0.4°C. This confirms previous calculations by Kjaer [120]. The inclusion of axial dispersion, which will be discussed in a later section, altered the steady-state temperature profile by less than O.S°C. Internal transport effects would only have to be accounted for with particles having a diameter larger than 6 mm, which are used in some high-capacity modern converters to keep the pressure drop low. Dyson and Simon [121] have published expressions for the effectiveness factor as a function of the pressure, temperature and conversion, using Nielsen s experimental data for the true rate of reaction [119]. At 300 atm and 480°C the effectiveness factor would be 0.44 at a conversion of 10 percent and 0.80 at a conversion of 50 percent. 

The rates at which chemical transformations take place are in some circumstances strongly influenced by mass and heat transfer processes (see Sections 12.3 to 12.5). In the design of heterogeneous catalytic reactors, it is essential to utilize a rate expression that takes into account the influence of physical transport processes on the rate at which reactants are converted to products. Smith (94) has popularized the use of the term global reaction rate to characterize the overall rate of transformation of reactants to products in the presence of heat and mass transfer limitations. We shall find this term convenient for use throughout the remainder of the chapter. Global rate expressions then include both external heat and mass transfer effects on the reaction rate and the efficiency with which the internal... 

An appreciation of the relative magnitudes of heat and mass transfer effects in internal and external diffusion is useful. A measure of the relative magnitudes is the ratio of the mass to heat Biot numbers ... 

Note that fem,e F or rra,eS re the effective (measured) values of the rate constant and rate, respectively, which includes all internal and external mass transfer effects. 

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