Catalyst phase mass balance

Cy Cy, and a quat balance giving, Cgy = qo Cqx- Bulk-phase concentrations are coupled to the conditions within the catalyst through the boundary conditions. Bulk-phase mass balances are required to keep track of changes in the bulk-phase organic and aqueous reagent concentrations... 

In the limit of small pressure perturbations, any kinetic equation modeling the response of a catalyst surface can be reduced to first order. Following Yasuda s derivation C, the system can be described by a set of functions which describe the dependence of pressure, coverage amplitude, and phase on T, P, and frequency. After a mass balance, the equations can be separated Into real and Imaginary terms to yield a real response function, RRF, and an Imaginary response function, IRF ... 

As will be shown later the equation above is identical to the mass balance equation for a continuous stirred-tank reactor. The recycle can be provided either by an external pump as shown in Fig. 5.4-18 or by an impeller installed within the reaction chamber. The latter design was proposed by Weychert and Trela (1968). A commercial and advantageously modified version of such a reactor has been developed by Berty (1974, 1979), see Fig. 5.4-19. In these reactors, the relative velocity between the catalyst particles and the fluid phases is incretised without increasing the overall feed and outlet flow rates. 

Although the Lewis cell was introduced over 50 years ago, and has several drawbacks, it is still used widely to study liquid-liquid interfacial kinetics, due to its simplicity and the adaptable nature of the experimental setup. For example, it was used recently to study the hydrolysis kinetics of -butyl acetate in the presence of a phase transfer catalyst [21]. Modeling of the system involved solving mass balance equations for coupled mass transfer and reactions for all of the species involved. Further recent applications of modified Lewis cells have focused on stripping-extraction kinetics [22-24], uncatalyzed hydrolysis [25,26], and partitioning kinetics [27]. 

A recent stndy (13,27) describes the use of Co-Si-TUD-1 for the liquid-phase oxidation of cyclohexane. Several other metals were tested as well. TBHP (tert-butyl hydroperoxide) was used as an oxidant and the reactions were carried out at 70°C. Oxidation of cyclohexane was carried out using 20 ml of a mixture of cyclohexane, 35mol% TBHP and 1 g of chlorobenzene as internal standard, in combination with the catalyst (0.1 mmol of active metal pretreated overnight at 180°C). Identification of the products was carried out using GC-MS. The concentration of carboxylic side products was determined by GC analysis from separate samples after conversion into the respective methyl esters. Evolution and consumption of molecular oxygen was monitored volumetrically with an attached gas burette. All mass balances were 92% or better. 

Depending on the temperature, there may be a carbon deficit in the mass balance upon individual pulses, i.e. CO consumption may be higher than C02 formation. A certain amount of carbon may be stored in the catalyst and released upon the following CO pulses or upon the first pulses of 02. In this case, some C02 appears in phase 2. A detailed investigation of C and O mass balance during OSC measurements has been made by Holmgren et al. [24],... 

In catalytic reactors we assume that there is no reaction in the fluid phase, and all reaction occurs on the surface of the catalyst. The surface reaction rate has the units of moles per unit area of catalyst per unit time, which we will call r". We need a homogeneous rate r to insert in the mass balances, and we can write this as... 

To repeat, we don t know and can t measure the gas-phase concentrations near the catalyst surface. We therefore have to eliminate them from any expressions and write the mass balances as functions of bulk concentrations alone. 

Consequently, while I jump into continuous reactors in Chapter 3, I have tried to cover essentially aU of conventional chemical kinetics in this book. I have tried to include aU the kinetics material in any of the chemical kinetics texts designed for undergraduates, but these are placed within and at the end of chapters throughout the book. The descriptions of reactions and kinetics in Chapter 2 do not assume any previous exposure to chemical kinetics. The simplification of complex reactions (pseudosteady-state and equilibrium step approximations) are covered in Chapter 4, as are theories of unimolecular and bimolecular reactions. I mention the need for statistical mechanics and quantum mechanics in interpreting reaction rates but do not go into state-to-state dynamics of reactions. The kinetics with catalysts (Chapter 7), solids (Chapter 9), combustion (Chapter 10), polymerization (Chapter 11), and reactions between phases (Chapter 12) are all given sufficient treatment that their rate expressions can be justified and used in the appropriate reactor mass balances. 

The algebraic equations for the orthogonal collocation model consist of the axial boundary conditions along with the continuity equation solved at the interior collocation points and at the end of the bed. This latter equation is algebraic since the time derivative for the gas temperature can be replaced with the algebraic expression obtained from the energy balance for the gas. Of these, the boundary conditions for the mass balances and for the energy equation for the thermal well can be solved explicitly for the concentrations and thermal well temperatures at the axial boundary points as linear expressions of the conditions at the interior collocation points. The set of four boundary conditions for the gas and catalyst temperatures are coupled and are nonlinear due to the convective term in the inlet boundary condition for the gas phase. After a Taylor series expansion of this term around the steady-state inlet gas temperature, gas velocity, and inlet concentrations, the system of four equations is solved for the gas and catalyst temperatures at the boundary points. 

Note that the gas-phase concentration CGz varies with the distance from the entrance z due to the plug-flow condition. If the gas phase is in complete mixed flow, then CG z - CG>0. Finally, the component mass balance around the catalyst is... 

The computer-reconstructed catalyst is represented by a discrete volume phase function in the form of 3D matrix containing information about the phase in each volume element. Another 3D matrix defines the distribution of active catalytic sites. Macroporosity, sizes of supporting articles and the correlation function describing the macropore size distribution are evaluated from the SEM images of porous catalyst (Koci et al., 2006 Kosek et al., 2005). Spatially 3D reaction-diffusion system with low concentrations of reactants and products can be described by mass balances in the form of the following partial differential equations (Koci et al., 2006, 2007a). For gaseous components ... 

Reaction only takes place in the dense phase since that is where the catalyst particles are. Since the exchange is with a uniform environment where the concentration is cp, we can see that by the time the bubble has reached the top of the bed, the concentration of reactant in it is cp + (co - cp).exp -Tr, where c0 is the entering concentration, H the height of the bed and Tr = QH/UaV is a dimensionless transfer number. By doing a mass balance on the dense phase as a whole14 we obtain a linear equation for cp in terms of the... 

In this section we develop a dynamic model from the same basis and assumptions as the steady-state model developed earlier. The model will include the necessarily unsteady-state dynamic terms, giving a set of initial value differential equations that describe the dynamic behavior of the system. Both the heat and coke capacitances are taken into consideration, while the vapor phase capacitances in both the dense and bubble phase are assumed negligible and therefore the corresponding mass-balance equations are assumed to be at pseudosteady state. This last assumption will be relaxed in the next subsection where the chemisorption capacities of gas oil and gasoline on the surface of the catalyst will be accounted for, albeit in a simple manner. In addition, the heat and mass capacities of the bubble phases are assumed to be negligible and thus the bubble phases of both the reactor and regenerator are assumed to be in a pseudosteady state. Based on these assumptions, the dynamics of the system are controlled by the thermal and coke dynamics in the dense phases of the reactor and of the regenerator. 

Catalyst mass balance in the dense emulsion phase Here the mass-balance equation is... 

The rate-based models usually use the two-film theory and comprise the material and energy balances of a differential element of the two-phase volume in the packing (148). The classical two-film model shown in Figure 13 is extended here to consider the catalyst phase (Figure 33). A pseudo-homogeneous approach is chosen for the catalyzed reaction (see also Section 2.1), and the corresponding overall reaction kinetics is determined by fixed-bed experiments (34). This macroscopic kinetics includes the influence of the liquid distribution and mass transfer resistances at the liquid-solid interface as well as dififusional transport phenomena inside the porous catalyst. 

The reactor was fed with 1.6 Nl/min of 1000, 2000 and 4000 ppm of methane in air. The mixtures were obtained by mixing N-50 synthetic air and 2.5 % (vol.) CH4 in N-50 synthetic air (Air Products). 40 ppm of SO2 (from a cylinder of 370 ppmV SO2 in N-50 synthetic air. Air Products) were added when the effect of sulphur on the catalysts activity was studied. Flow rates were controlled by calibrated mass flow controllers (Brooks 5850 TR). Exhaust gas was analysed by gas chromatography (Hewlett Packard HP 5890 Series II). Methane in the inlet and outlet streams was analysed using a 30 m fused silica capillary column with apolar stationary phase SE-30, and a FID detector. CO and CO2 were analysed using a HayeSep N 80/100 and a molecular sieve 45/60 columns connected in series, and a TCD detector. Neither CO, nor partial oxidation were detected in any experiment, the carbon mass balance fitting in all the cases within 2%. Methane conversions were calculated both from outlet methane and CO2 concentrations, being both values very close in all the cases. Methane (2000 ppmV) and SO2 (40 ppmV) concentrations have been selected because they are representative of industrial emissions, such as coke oven emissions. 

Aging and redispersion phenomena of electrocatalysts are currently little understood, and no models exist for their quantitative description. In analogy to supported catalysts for gas phase reactions (266), we can write a continuity (mass balance) equation for the change of surface concentration nj of a particle consisting of j atoms, by capture and emission of i atom particles (7>2).-... 

Note that the same mass-balance equations apply whether the reaction in the liquid phase is homogeneous or catalyzed by solid particles as in a slurry reactor. The difference between catalyzed and noncatalytic systems is accounted for in the global rate. If the reactants are introduced only in the gas phase, a mass balance is needed only for that phase. This situation exists for some slurry reactors where the liquid phase is inert and its purpose is simply to suspend the.catalyst particles. 

We consider the following physical situation. A first-order exothermic reaction runs on a smooth, nonporous catalytic element having a length L (thread, fiber, tube). Assume that there is no temperature distribution at the element cross-section, thus reducing the analysis to a one-dimensional case. Assume also that the reaction runs under conditions of transversal flow, and the heat and mass transfer between the catalyst surface and the bulk-flow are described by the effective coefficients a and respectively. Under these assumptions, the model can be written in the form of two equations, one describing the heat balance in the solid catalyst phase, and another the reactant balance in the gaseous phase of a certain characteristic layer adjacent to the catalyst surface ... 

For simplicity, assume fluid-phase mass transfer to be fast enough to maintain the bulk-fluid concentration of A up to the catalyst surface, the particle to be spherical, the reaction to be irreversible and first order, and mass transfer in the particle to obey Fick s law of diffusion. With the reaction as source-or-sink term, the differential material balance for A (change of content of a volume element = what enters minus what exits minus what reacts) is... 

For the heterogeneous models, mass and heat balance equations are formulated not only for the bulk of the fluid phase but also for the solid catalyst phase. 

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