Kinetics and Mass Transfer

In this chapter, boundaries are calculated on maximum current densities achievable by bacteria in biofilms by examining the upper limits to biofilm kinetics and comparing these to limits imposed by substrate mass transfer to the biofilm. With this information, we can calculate maximum power densities (power per surface area). We have already seen in chapter 5 that there are limits on current and power densities imposed by internal resistance. Here, we examine the limits based on mass transfer calculations so that in a 

Microbial Fuel Cells. By Bruce E. Logan Copyright 2008 John Wiley Sons, Inc. 

To begin developing a simple biofilm model based on kinetics, we first assume that bacterial growth is proportional to the concentration of bacteria, or 

This result shows that the rate of substrate utilization is not a simple function of substrate concentration as this rate changes depending on the specific value of c (Fig. 7.1). We further assume that the cell density in the biofilm is constant. That means that as the cells grow the biofilm will become thicker, but the packing density of the cells in the biofilm 

We can examine two limits of the rate equation to make our calculations of biofilm kinetics easier very high and very low substrate concentrations. When the substrate concentration is high (r. e., non-limiting for growth), the bacteria grow at their maximum rate. Under these conditions, c X and cq. i-4 becomes equivalent to a zero-order rate constant, or 

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The rate of an electrochemical process can be limited by kinetics and mass transfer. Before considering electrode kinetics, however, an examination of the nature of the iaterface between the electrode and the electrolyte, where electron-transfer reactions occur, is ia order. 

This is a transitional region in which reaction kinetics and mass transfer resistance both affect the overall reaction rate. 

Mikkola, J.P., Salmi, T., and Sjoholm, R. (1999) Modelling of kinetics and mass transfer in the hydrogenation of xylose over Raney nickel catalyst. /. Chem. Technd. Biotechnol, 74, 655—662. 

Part I treats the fundamentals of modelling (mass balance ei ualions, involving reaction kinetics and mass-transfer rates), making them readily understandable to those new in the field. 

Merino, E., D. Nahon and Y. Wang, 1993, Kinetics and mass transfer of pseudo-morphic replacement, application to replacement of parent minerals and kaoli-nite by Al, Fe, and Mn oxides during weathering. American Journal of Science 293,135-155. 

Rieckmann and Volker fitted their kinetic and mass transport data with simultaneous evaluation of experiments under different reaction conditions according to the multivariate regression technique [116], The multivariate regression enforces the identity of kinetics and diffusivities for all experiments included in the evaluation. With this constraint, model selection is facilitated and the evaluation results in one set of parameters which are valid for all of the conditions investigated. Therefore, kinetic and mass transfer data determined by multivariate regression should provide a more reliable data basis for design and scale-up. 

Rieckmann, Th. and Volker, S Micro kinetics and mass transfer in poly(ethylene terephthalate) synthesis, Chem. Eng. Sci., 56, 945-953 (2001). 

Regimes 2 and 3 - moderate reactions in the bulk (2) or in thefdm (3) and fast reactions in the bulk (3) For higher reaction rates and/or lower mass transfer rates, the ozone concentration decreases considerably inside the film. Both chemical kinetics and mass transfer are rate controlling. The reaction takes place inside and outside the film at a comparatively low rate. The ozone consumption rate within the film is lower than the ozone transfer rate due to convection and diffusion, resulting in the presence of dissolved ozone in the bulk liquid. The enhancement factor E is approximately one. This situation is so intermediate that it may occur in almost any application, except those where the concentration of M is in the micropollutant range. No methods exist to determine kLa or kD in this regime. 

In Eqn. 5.3-1, rj is the effectiveness factor of the catalyst with respect to the dissolved gaseous reactant and the temperature of the outer surface. The rate of reaction within the catalyst pores is comprised in rj. R is the reaction rate expressed in moles of gaseous reactant, A, per unit of bubble-free liquid, per unit of time. Reaction is irreversible. In equation (1) it has not been assumed that the gas is pure gas A, its concentration in the bubbles being Cg. Also, Henry s law for the gas is assumed and written as in Eqn. 5,3-4. Using Henry s law, Eqn. 5.3-4, the intermediate concentrations (Cs, CL) can be eliminated using the above system of equations. This provides an expression of the global rate in terms of an apparent constant, ko, that contains the various kinetic and mass transfer steps. Therefore, the observed rate can be written as ... 

T. Kobayashi and M. Moo-Young, Kinetic and mass transfer behavior of immobilized invertase on ion-exchange resin beads, Biotechnol. Bioeng. 1973, 15, 47-67. 

Reactive extraction uses liquid ion exchangers that promote a selective reaction or separation. The solutes are very often ionic species (metal ions or organic/inorganic acids) or intermediates (furfural phenols, etc.), and the extraction chemistry is discussed elsewhere (11-13). Reactive extraction can be used for separation/ purification or enrichment or conversion of salts (14). A 2001 review on reactive phase equilibria, kinetics, and mass transfer and apparative techniques is given in Ref. 8. Reactive extraction equipment is discussed in detail in Ref. 15, and recent advances are given in Ref. 16. 

Kelkar VV, Ng KM. Design of reactive crystallization systems incorporating kinetics and mass-transfer effects. AIChE J 1999 45 69-81. 

V. V. Kelkar and K. M. Ng, Design of Reactive Crystallization Systems Incorporating Kinetics and Mass Transfer Effects, AIChE J.,... 

Lehtonen et al. (1998) considered polyesterification of maleic acid with propylene glycol in an experimental batch reactive distillation system. There were two side reactions in addition to the main esterification reaction. The equipment consists of a 4000 ml batch reactor with a one theoretical plate distillation column and a condenser. The reactions took place in the liquid phase of the reactor. By removing the water by distillation, the reaction equilibrium was shifted to the production of more esters. The reaction temperatures were 150-190° C and the catalyst concentrations were varied between 0.01 and 0.1 mol%. The kinetic and mass transfer parameters were estimated via the experiments. These were then used to develop a full-scale dynamic process model for the system. 

Kinetics and mass transfer were simulated for steady and non-steady state cocurrent or crosscurrent leaching of moving or stationary solids. 

The algorithm of the kinetics and mass transfer model is a system of algebraic equations that are developed in the following way. The key variable is AN, the change in the amount of a particular reactant or product component involved in a reaction step during an interval At. The material balance of a step is,... 

The author would like to acknowledge the help of Frank Zybert who did the detailed programing of the kinetics and mass transfer model. 

Kinetic and Mass-Transfer Barriers and Mediated Oxidation... 

Santacesaria, E., Tesser, R., Di Serio, M., Guida, M., Gaetano, D., Garcia Agreda, A. 2007. Kinetics and mass transfer of free fatty acids esterification with methanol in a tubular packed bed reactor a key pretreatment in biodiesel production. Ind. Eng. Chem. Res., 46, 5113-5121. 

Ahn et al. have developed fibre-based composite electrode structures suitable for oxygen reduction in fuel cell cathodes (containing high electrochemically active surface areas and high void volumes) [22], The impedance data obtained at -450 mV (vs. SCE), in the linear region of the polarization curves, are shown in Figure 6.22. Ohmic, kinetic, and mass transfer resistances were determined by fitting the impedance spectra with an appropriate equivalent circuit model. 

Polymerization frequently is performed in gas-phase reactors at intermediate pressures. The role of heterogeneous catalysts and the interaction between reaction kinetics and mass transfer can only be understood if sorption effects, solubilities of gases in solids, volume changes, and diffusivities at reactor conditions are known. 

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