Effect of mass-transfer limitations

In this section the effect of mass transfer limitation on the drop conversion rate and the order of drop conversion will be treated, and it will be shown that a process for which the real chemical reaction is of first order in the reactant A (which is dissolved in the dispersed phase) can still be influenced by the effect of segregation when the chemical conversion rate is limited by mass transfer of the reactants. 

Figure 8.7 Comparison of effects of mass transfer limitations in the desorption of alachlor from activated carbon using supercritical carbon dioxide tests with several flow rates and carbon mesh size. SLPM = Standard liters per minute.

The effect of mass transfer limitation on the overall process can also be expressed in terms of the effectiveness factor, relating the actual reaction rate to that observed if the catalyst surface were exposed to the same... 

However, reforming higher hydrocarbons needs much higher heat supply than methane, and other aspects that are often not well described are the effect of mass transfer limitations, carbon formation, by-products formation, etc. Additionally, as stated above, from a process point of view, higher hydrocarbons can be more effectively used to produce more valuable products than hydrogen. Here some examples ... 

Simulation of the effect of mass transfer limitations in complex gas-liquid reactions... 

Here, Rs is the solution resistance between the electrodes, which is typically much smaller than the other components. Ret is the charge transfer resistance, which accounts for the ability of the redox compound to interact with the electrode surface via electron transport. C is the capacitance between the electrode and the charged ions in solution. This capacitance is known as the double layer capacitance, which exists between any metal placed in an electrolyte solution. W is an element called the Warburg impedance, which accounts for the effects of mass-transfer limitations. The Warburg impedance itself has hoth a real and imaginary component and is frequency dependent. One can calculate... 

To further illustrate the points above, hypothetical current density-potential curves for reactions with different reaction rates (exchange current densities) and/or standard electrode potentials were calculated and plotted (Figure 3.5). These curves were calculated based on the Erdey-Graz-Volmer (Butler-Volmer) equation [Eq. (3.2)] describing the relation of current density and potential when the rate of reaction (current) is controlled solely by the rate of the electrochemical charge transfer process (activation kinetics) and the effect of mass transfer limitation on the current is not considered ... 

The effect of the cell density was studied in biodesulfurization of diesel oil by P. delafieldii R-8 [259], An optimum was reported to exist for this biocatalyst as well. Above 25g/L cell density, the specific desulfurization rate decreased. In this case a statistical analysis was not performed to identify the point of mass transfer limitation. 

In deriving eqn. (80), limitations due to mass transport at the interface were not considered. Strictly speaking, this is not realistic and as the reaction rate increases with overpotential in each direction a variation of the concentrations of reactant and product at the surface operates and concentration polarization becomes more important. Each exponential expression in eqn. (80) must be multiplied by the ratio of surface to bulk concentrations, ci s/ci b. The effect of mass transfer in electrode kinetics has been discussed in Sect. 2.4. 

Related Calculations. In this example, it was stated at the outset that mass-transfer effects were not limiting the process rate. In the general case, however, it is important to calculate the effect of mass-transfer resistance on the reaction rate. 

In many industrial reactions, the overall rate of reaction is limited by the rate of mass transfer of reactants and products between the bulk fluid and the catalytic surface. In the rate laws and cztalytic reaction steps (i.e., dilfusion, adsorption, surface reaction, desorption, and diffusion) presented in Chapter 10, we neglected the effects of mass transfer on the overall rate of reaction. In this chapter and the next we discuss the effects of diffusion (mass transfer) resistance on the overall reaction rate in processes that include both chemical reaction and mass transfer. The two types of diffusion resistance on which we focus attention are (1) external resistance diffusion of the reactants or products between the bulk fluid and the external smface of the catalyst, and (2) internal resistance diffusion of the reactants or products from the external pellet sm-face (pore mouth) to the interior of the pellet. In this chapter we focus on external resistance and in Chapter 12 we describe models for internal diffusional resistance with chemical reaction. After a brief presentation of the fundamentals of diffusion, including Pick s first law, we discuss representative correlations of mass transfer rates in terms of mass transfer coefficients for catalyst beds in which the external resistance is limiting. Qualitative observations will bd made about the effects of fluid flow rate, pellet size, and pressure drop on reactor performance. 

P12C-2 Use the references given in Ind. Eng. Chem. Prod. Res. Lev. /4, 226 (1975) to define the iodine value, saponification number, acid number, and experimental setup. Use the slurry reactor analysis to evaluate the effects of mass transfer and determine if there are any mass transfer limitations. 

From other experiments in which the effects of mass transfer have been analyzed, it appears that the following systems are mass transfer limited uranyl nitrate extraction by TBP, copper extraction by sodium-loaded DEHPA.19 and extraction of zinc and copperfll) chlorides by TIOA.20 Zinc extraction by dithizone in carbon tetrachloride is mass transfer limited at high zinc concentrations but kineticaily controlled at low zinc levels.21 Ferric ion extractions are repoted to be slow because of its sluggish llgand-excbenge kinetics.22 Extraction of ferric chloride by TIOA, for example, is controlled by a slow heterogeneous reaction.21... 

In order to evaluate the relative role of these two factors, the present results were compared with those obtained over powders in the absence of SO2 and H2O in the feed stream. Tests over powders were thus relative to the simplified case of negligible role of mass transfer limitations and absence of surface sulfates. A promoting effect of sintering on DeNOx activity was observed and it was interpreted as the effect of vanadium agglomeration, leading to the formation of V polymeric species with enhanced reactivity [5], The estimated values of specific intrinsic activity of the sulfates-ffee powders at the reaction temperature of 350°C are reported for comparison in Figure 3. The DeNOx activity of powders was always lower than that of the sulfate-containing monoliths, by a factor of 4 for the sample calcined at 500°C and a factor of 2.4 and 1.4 for the samples calcined at 750 and 800°C respectively. 

For liquids reacting in packed beds, the lower values of Pe might seem to make dispersion effects more important than for gases at the same Ljdp. However, even for very fast chemical reactions, high conversion of liquid cannot be obtained in short beds because of mass transfer limitations. Large values of Ljdp are needed at to get high conversion, and the effect of axial dispersion is small. 

Comparing Pi with Ej may give an insight of the incidence of mass transfer limitations and steric hindrances. If Yp is significantly higher than Ye, then those effects are probably relevant, but immobilization can have degree of selectivity (positive or negative) for the enzyme with respect to the whole protein that cannot be ruled out. 

The effect of mass transfer on electrode kinetics is shown in Fig. 3.12. Many useful kinetic rate expressions based on Tafel conditions, mass transport limitations can be developed from Eq. (3.59). Prediction of mass transfer effects may be useful in corrosion systems depending on the system s corrosion conditions. The mass transport limitations in corrosion systems may alter the mixed potential of a corroding system. Under Tafel conditions (anodic or cathodic), Eq. (3.59) can be written as ... 

Chapters 1 to 3 describe the theory of corrosion engineering and offer analyzed case studies and solved problems in the thermodynamics of corrosion processes, the relevance of electrochemical kinetics to corrosion, low field approximation theory, concentration polarization, the effects of polarization behavior on corrosion rate, the effect of mass transfer on electrode kinetics, and diffusion-limited corrosion rates. 

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