Convection-mass-transfer reaction

Convection-Mass-Transfer Reaction in the Bulk 12.4.3.1 Bulk Gas... 

Fig. 10. Numerical solutions of the forced-convection mass-transfer equation for the case of irreversible first-order chemical reaction [after Johnson et al. (J4)] (Solid lines— rigid spheres dashed lines—circulating gas bubbles).

The general mass balance for each phase at nonsteady state, considering convection, mass transfer and reaction (e. g. ozone decay), can be written ... 

Dan = timescale of pore diffusion/timescale of reaction = (L2 x kal)/De(( (5.46) Bi = external mass transfer/intemal mass transfer = (kfx RJ/Dgff (5.47) Bo = convective mass transfer/dispersive mass transfer = (u x k)/D L (5.48)... 

The mole fraction xA1 is the vapor pressure of A divided by the total pressure provided that A and B form an ideal gas mixture and that the solubility of gas B in liquid A is negligible. A stream of gas mixture A-B of concentration xA2 flows slowly past the top of the tube, to maintain the mole fraction of A at xA2. The entire system is kept at constant temperature and pressure. There is a net flow of gas upward from the gas-liquid interface. The transport process is in the i-direction and at steady state with no convective mass transfer, and the reaction source is... 

In this text, the conversion rate is used in relevant equations to avoid difficulties in applying the correct sign to the reaction rate in material balances. Note that the chemical conversion rate is not identical to the chemical reaction rate. The chemical reaction rate only reflects the chemical kinetics of the system, that is, the conversion rate measured under such conditions that it is not influenced by physical transport (diffusion and convective mass transfer) of reactants toward the reaction site or of product away from it. The reaction rate generally depends only on the composition of the reaction mixture, its temperature and pressure, and the properties of the catalyst. The conversion rate, in addition, can be influenced by the conditions of flow, mixing, and mass and heat transfer in the reaction system. For homogeneous reactions that proceed slowly with respect to potential physical transport, the conversion rate approximates the reaction rate. In contrast, for homogeneous reactions in poorly mixed fluids and for relatively rapid heterogeneous reactions, physical transport phenomena may reduce the conversion rate. In this case, the conversion rate is lower than the reaction rate. 

C = oxygen concentration at the reaction surface, kg = convective mass transfer coefficient, ks = intrinsic reaction rate constant,... 

Ash fouling appears to be initiated by the formation of a layer of sodium sulfate on the boiler tube. It is thought that thermal decomposition of sodium salts of carboxylic functional groups in the coal is the start of a sequence of reactions leading ultimately to the formation of sodium sulfate in the flame or flue gas. The convective mass transfer diffusion of the sodium-containing species through a boundary layer around the tube results in deposition of sodium sulfate on the tube surface. 

Gaiser and Kottke [S] have used a method similar to that developed by Marcinkowski and Zielinski [6] to visualize heat transfer and mass transfer improvements achieved by OCFS in comparison to parallel-channel devices. Their physicochemical method is based on convective mass transfer and produces colorization of the body wall as gas is passed through the support structures and reacting molecules are transferred from the gas bulk to the prepared wall material. The intensity of the colorization is a visual representation of the amount reacted and, since the surface reaction is very fast, of the mass transfer. Figure 7 shows the result of a typical such experiment. 

Next, a mathematical model that allows description of the separation and concentration of the components of a metallic mixture will be detailed the principal assumptions of the model are (1) convective mass transfer dominates diffusive mass transfer in the fluid flowing inside the HFs, (2) the resistance in the membrane dominates the overall mass transport resistance, therefore the overall mass transfer coefficient was set equal to the mass transfer coefficient across the membrane, and (3) chemical reactions between ionic species are sufficiently fast to ignore the contribution of the chemical reaction rates. Thus, the reacting species are present in equilibrium concentration at the interface everywhere [31,32,58,59]. For systems working under nonsteady state, it is also necessary to describe the change in the solute concentration with time both in the modules and in the reservoir tanks. The reservoir tanks will be modeled as ideal stirred tanks. 

Gas-to-liquid mass transfer can take place from a gas phase to a liquid phase (and vice versa) with or without chemical reactions. The concentration gradient of a transferred component in the bulk fluid and in the fluid at the interface is the driving force for mass transfer. When the mass transport occurs in a phase that is moving, the transport of the component is known as convective mass transfer. Convective mass transfer... 

Mixing has no impact on the intrinsic reaction kinetics, but it has a controlling effect on the temporal variation in species concentration and the mass transfer rate. This can be shown by examining the typical convective mass transfer rate equation ... 

Let us briefly consider convective mass transfer accompanied by a surface reaction in a circular tube. Laminar steady-state fluid flow in a circular tube of radius a with Poiseuille velocity profile is outlined in Subsection 1.5-3. For... 

For large rate constants kv of the volume chemical reaction, a thin diffusion boundary layer is produced near the drop surface its thickness is of the order of ky1//2 at low and moderate Peclet numbers, and the solute in this layer has time to react completely. As the Peclet number is increased further, because of the intensive liquid circulation within the drop, there is not enough time to complete the reaction in the boundary layer. The nonreacted solute begins to get out of the boundary layer and penetrate into the depth of the drop along the streamlines near the flow axis. If the circulation within the drop is well developed, a complete diffusion wake is produced with essentially nonuniform concentration distribution that pierces the entire drop and joins the endpoint and the origin of the diffusion boundary layer. In case of a first-order volume chemical reaction, an appropriate analysis of convective mass transfer within the drop for Pe > 1 and kv > 1 was carried out in [150,151]. It should be said that in this case, in view of the estimate (5.4.8), which is uniform with respect to the Peclet number, the mass transfer intensity within the drop is bounded by the rate of volume chemical reaction. 

The solution to this problem requires an analysis of multiple gas-phase reactions in a differential plug-flow tubular reactor. Two different solution strategies are described here. In both cases, it is important to write mass balances in terms of molar flow rates and reactor volume. Molar densities and residence time are not appropriate for the convective mass-transfer-rate process because one cannot assume that the total volumetric flow rate is constant in the gas phase, particularly when the total number of moles is not conserved. In each reaction, 2 mol of reactants generates 1 mol of product. Furthermore, an overall mass balance suggests that the volumetric flow rate is constant only when the overall mass density does not change. This is a reasonable assumption for liquid-phase reactors but not for gas-phase problems when the total volume is not restricted. The exception is a constant-volume batch reactor. 

This analysis begins with the unsteady-state mass balance for component i in the well-mixed reactor. At high-mass-transfer Peclet numbers, which are primarily a function of volumetric flow rate q, the rate processes of interest are accumulation, convective mass transfer, and multiple chemical reactions. Generic subscripts are... 

Consider a train of five CSTRs in series that have the same volume and operate at the same temperature. One first-order irreversible chemical reaction occurs in each CSTR where reactant A decomposes to products. Two mass-transfer-rate processes are operative in each reactor. The time constant for convective mass transfer across the inlet and outlet planes of each CSTR is designated by the residence time x = Vjq. The time constant for a first-order irreversible chemical reaction is given >y X = l/k. The ratio of these two time constants,... 

Now, the coupled mass and thermal energy balances can be combined and integrated analytically to obtain a linear relation between temperature and conversion under nonequilibrium (i.e., kinetic) conditions because it is not necessary to consider the temperature and conversion dependence of (Cp mixture)- At high-mass-transfer Peclet numbers, axial diffusion can be neglected relative to convective mass transfer, and the mass balance is expressed in terms of molar flow rate F, and differential volume dV for a gas-phase tubular reactor with one chemical reaction ... 

The product of the Reynolds and Schmidt numbers, which counts as one dimensionless number, is equivalent to the Peclet number for mass transfer, PeMx- The Peclet number represents the ratio of the convective mass transfer rate process to the diffusion rate process of component, and it appears on the left-hand side of the dimensionless mass transfer equation for component i. The remaining r dimensionless transport numbers can be treated simultaneously because they represent ratios of scaling factors for the reactant-product conversion rate due to the jth independent chemical reaction relative to the rate of diffusion of component I. Hence,... 

Hence, the dimensional scaling factor for convective mass transfer is the same in each mass balance. Similarly, dimensional scaling factors for all of the independent chemical reactions do not change from one mass balance to the next. However, when the r - - 2 dimensional scaling factors in the mass balance for component i are divided by the dimensional scaling factor for component i s rate of diffusion (i.e., i.mixCAo/L ), one obtains r - -1 dimensionless numbers... 

Now that one has obtained the basic information for the molar density of reactant A within the liquid-phase mass transfer boundary layer, it is necessary to calculate the molar flux of species A normal to the gas-liquid interface at r = l bubbie, and define the mass transfer coefficient via this flux. Since convective mass transfer normal to the interface was not included in the mass transfer equation with liquid-phase chemical reaction, it is not necessary to consider the convective mechanism at this stage of the development. Pick s first law of diffusion is sufficient to calculate the flux of A in the r direction at r = /fbubbie- Hence,... 

In Chapter 10, the dimensionless scaling factor in the mass transfer equation with diffusion and chemical reaction was written with subscript j for the jth chemical reaction in a multiple-reaction sequence (see equation 10-10). In the absence of convective mass transfer, the number of dimensionless scaling factors in the mass transfer equation for component i is equal to the number of chemical reactions. Hence, corresponds to the Damkohler number for reaction j. The only distinguishing factor between aU of these Damkohler numbers for multiple reactions is that the nth-order kinetic rate constant in the jth reaction (i.e., kj), for a volumetric rate law based on molar densities, changes from one reaction to another. The characteristic length L, the molar density of key-limiting reactant A on the external surface of the catalyst CA.sur ce, and the effective diffusion coefficient of reactant A, a. effective, are the same in aU Damkohler numbers that appear in the dimensionless mass balance for reactant A. In other words. 

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