Mass transfer-limited regions

In the mass-transfer limited region, conversion is most commonly increased by using more catalyst volume or by increasing cell density, which increases the catalytic wall area per volume of catalyst. When the temperature reaches a point where thermal oxidation begins to play a role, catalyst deactivation may become a concern. 

Notice that in the mass-transfer-limited region increasing or reducing the concentration of reactant B will make httle difference in the reaction rate (or the reactor productivity) because the concentration of A in the liquid is so small. Likewise, increasing the reactor temperature will not give an exponential increase in reaction rate. The reaction rate may actually decrease with increasing temperature because of a decrease in the equihbrium solubihty of A at the gas-liquid interface. 

Figure 5. Heptane to heptene ratio in intrinsic and mass transfer-limited regions at 248°C. Key is the same as in Figure 4.

The nonlinear current-voltage behavior associated with an electrochemical system is illustrated in Figiue 5.4(a). In the case shown here, the anodic (positive) current has an exponential dependence on potential whereas, the cathodic (negative) cvur-rent displays an influence of mass-transfer limitations. Regions are identified for which the current has a value equal to zero, the current is controlled by reaction kinetics, and the current is controlled by mass transfer. 

Suppose we now consider a series of step experiments in the anthracene solution discussed earlier. Between each experiment the solution is stirred, so that the initial conditions are always the same. Similarly, the initial potential (before the step) is chosen to be at a constant value where no faradaic processes occur. The change from experiment to experiment is in the step potential, as depicted in Figure 5.1.3a. Suppose, further, that experiment 1 involves a step to a potential at which anthracene is not yet electroactive that experiments 2 and 3 involve potentials where anthracene is reduced, but not so effectively that its surface concentration is zero and that experiments 4 and 5 have step potentials in the mass-transfer-limited region. Obviously experiment 1 yields no faradaic current, and experiments 4 and 5 yield the same current obtained in the chronoamperometric case above. In both 4 and 5, the surface concentration is zero hence anthracene arrives as fast as diffusion can bring it, and the current is limited by this factor. Once the electrode potential becomes so extreme that this condition applies, the potential no longer influences the electrolytic current. In experiments 2 and 3 the story is different because the reduction process is not so dominant that some anthracene cannot coexist with the electrode. Still, its concentration is less than the bulk value, so anthracene does diffuse to the surface where it must be eliminated by reduction. Since the difference between the bulk and surface concentrations is smaller than in the mass-transfer-limited case, less material arrives at the surface per unit time, and the currents for corresponding times are smaller than in experiments 4 and 5. Nonetheless, the depletion effect still applies, which means that the current still decays with time. 

Consider the case in which two reducible substances, O and O, are present in the same solution, so that the consecutive electrode reactions O -h ne R and O + n e R can occur. Suppose the first process takes place at less extreme potentials than the second and that the second does not commence until the mass-transfer-limited region has been reached for the first. The reduction of species O can then be studied without interference from O, but one must observe the current from O superimposed on that caused by the mass-transfer-limited flux of O. An example is the successive reduction of Cd(II) and Zn(II) in aqueous KCl, where Cd(II) is reduced with an E1/2 near —0.6 V v. SCE, but the Zn(II) remains inactive until the potential becomes more negative than about —0.9 V. 

Draw a rough quantitative graph of collection efficiency rotation rate for an RRDE at which the electrode reaction for the previous problem is carried out. Assume electrolysis occurs in the mass-transfer-limited region. The collection efficiency is 0.45 for Fe(II) Fe(III) + e. 

Prior to conducting the DOE (design of experiments) described in Table 3, it was established that no reaction took place in the absence of a catalyst and that the reactions were conducted in the region where chemical kinetics controlled the reaction rate. The results indicated that operating the reactor at 1000 rpm was sufficient to minimize the external mass-transfer limitations. Pore diffusion limitations were expected to be minimal as the median catalyst particle size is <25 pm. Further, experiments conducted under identical conditions to ensure repeatability and reproducibility in the two reactors yielded results that were within 5%. 

When fluid velocities are high relative to the solid, mass transfer is rapid. However, in stagnant regions or in batch reactors where no provision is made for agitation, one may encounter cases where mass transfer limits the observed reaction rate. We should also note that in industrial practice pressure drop constraints may make it impractical to employ the exceedingly high velocities necessary to overcome the mass transfer resistance associated with highly active catalysts. 

The chemical species were treated as passive scalar tracers in the unsteady LBM equations. The reaction was simulated as being mass-transfer limited at low Re — 166, with diffusivities in the ratios DA DB Dc— 1 3 2. The concentration fields shown in Fig. 16 are different for each species due to the different diffusivities. The slow-diffusing species A is transported mainly by convection and regions of high or low concentration correspond to features of the flow field. A more uniform field is seen for the concentration of faster... 

Chemical etching processes have similar mass-transfer-limited possibilities, with etching rates highest in regions of high flow velocities. In electrochemical etching of solids. 

For this work, a 9 1 volumetric flow ratio of liquid CO2 and methanol has been employed and this corresponds to a molar flow ratio of 8.5 1.5. From literatures [5], the critical parameters of such a mixture are about 50°C and 94 bar. From Figure 1, one can see that the two other isobars exhibit two maximas - one in the subcritical and the other in the supercritical region. It is a well-known fact that SFE processes are controlled either by solubility or mass transfer limitations [6]. As such, the shape of these isobars has to be explained in term of these two limitations too. 

This corresponds to mass-transfer limitation of the apparent surface reaction. Thus the combination of Eqs. p] and 2] is expected to give reasonable estimates of the rate of deposition for all particle-collector interaction profiles, provided the interactions are confined to a region which is thin compared to the diffusion boundary layer. 

To increase the efficiency of the electrochemical wastewater treatment process with conventional anodic materials, the mediated oxidation method has been proposed. This method avoids the production of oxygen, thanks to the generation of precursors that are successively transformed to active oxidants. When the BDD anodes are used, a positive contribution of the generated active oxidants can also be foreseen, but only in the previously defined region IV of the treatment. The production of strong oxidants in this region avoids the mass-transfer limitation and treatment efficiency is recovered. 

Figure 11-6 Regions of mass transfer-limited and reaction-limited reactions.

---