Diffusion mass-transfer-controlled reactions

Controlled by diffusive mass transfer Controlled by chemical factors A major distinction is between reactions that are ... 

The prospect of using enzymes as heterogeneous catalysts in scC02 media has created significant interest. Their low viscosity and high diffusion rates offer the possibility of increasing the rate of mass-transfer controlled reactions. Also, because enzymes are not soluble in supercritical fluids, dispersion of the free enzymes potentially allows simple separations without the need for immobilization. 

The role of mass transfer effects, whether occurring accidentally or by design, is ambivalent, causing Trevan to ask the question Diffusion limitation - friend or foe [115]. Lower activity as a result of low efficiency indicates that only a minor portion of enzyme is active during operation. The other unused portion may, in simple terms, replace the enzyme as it is inactivated step by step. In other words, mass transfer controlled reactions appear to be much less sensitive to decay of enzyme activity, thus falsely creating an impression of stabilization. Under harsh reaction conditions it may be advantageous to operate under these conditions to keep the reaction rate constant until the diffusion limitation disappears [82,115,116]. 

One of the expected benefits from using enzymes in supercritical fluids (SCFs) is that mass transfer resistance between the reaction mixture and the active sites in the solid enzyme should be greatly reduced if the reactants and products are dissolved in an SCF instead of running the reaction in a liquid phase. It is expected that the high diffusivity and low viscosity of SCFs will accelerate mass-transfer controlled reactions. 

Diffusion problems practically absent present (mass-transfer-controlled reaction)... 

Mass Transfer. The reaction rate of heterogeneous reactions may be controlled by the rates of diffusion of the reacting species, rather than the chemical kinetics. 

The performance of a reactor for a gas-solid reaction (A(g) + bB(s) -> products) is to be analyzed based on the following model solids in BMF, uniform gas composition, and no overhead loss of solid as a result of entrainment. Calculate the fractional conversion of B (fB) based on the following information and assumptions T = 800 K, pA = 2 bar the particles are cylindrical with a radius of 0.5 mm from a batch-reactor study, the time for 100% conversion of 2-mm particles is 40 min at 600 K and pA = 1 bar. Compare results for /b assuming (a) gas-film (mass-transfer) control (b) surface-reaction control and (c) ash-layer diffusion control. The solid flow rate is 1000 kg min-1, and the solid holdup (WB) in the reactor is 20,000 kg. Assume also that the SCM is valid, and the surface reaction is first-order with respect to A. 

For gas-film mass transfer control, we use equation 22.2-16a for reaction control, we use equation 22.2-18 and for ash-layer diffusion control, we integrate equation 22.2-13 numerically in conjunction with 22.2-19, as described in Example 22-3(c). The results generated by the E-Z Solve software (file ex22-4.msp) are shown in Figure 22.4. 

Kinetic experiments and rigorous modelling of the mass-transfer controlled polycondensation reaction have shown that even at low melt viscosities the diffusion of EG in the polymer melt and the mass transfer of EG into the gas phase are the rate-determining steps. Therefore, the generation of a large surface area is essential even in the prepolycondensation step. 

Flash Rusting (Bulk Paint and "Wet" Film Studies). The moderate conductivity (50-100 ohm-cm) of the water borne paint formulations allowed both dc potentiodynamic and ac impedance studies of mild steel in the bulk paints to be measured. (Table I). AC impedance measurements at the potentiostatically controlled corrosion potentials indicated depressed semi-circles with a Warburg diffusion low frequency tail in the Nyquist plots (Figure 2). These measurements at 10, 30 and 60 minute exposure times, showed the presence of a reaction involving both charge transfer and mass transfer controlling processes. The charge transfer impedance 0 was readily obtained from extrapolation of the semi-circle to the real axis at low frequencies. The transfer impedance increased with exposure time in all cases. 

In Fig. 42, the full-width at half maximum of the (narrower) exchange propagator provides an estimate of the effective diffusion coefficient of water molecules moving between the pore space of the catalyst and the inter-particle space of the bed. In this example, the value is 2 x lO- m s which gives a lower limit to the value for the mass transfer coefficient of 4x 10 ms This value was obtained by defining a mass transfer coefficient as Djd where d is a typical distance traveled to the surface of the catalyst that we estimate as half a typical bead dimension (approximately 500 pm). This value of the mass transfer coefficient is consistent with the reaction occurring under conditions of kinetic as opposed to mass transfer control. 

The removal of one of more selected components from a mixture of gases by absorption into a suitable solvent (Mass Separating Agent, MSA) is the second major operation of chemical engineering after distillation. Absorption is based on interface mass transfer controlled largely by rates of diffusion. It is worth noting that absorption followed by a chemical reaction in the liquid phase is often used to get more removal of a solute from a gas mixture. 

Ozone contactors supplied with diffusers are usually divided into stages (see Fig. 7) whose number depends on the major objectives of ozonation. Thus, for instantaneous or mass transfer controlled ozonations, two stages are sufficient, whereas for slow ozonation reactions a higher number is required. In order to reach plug flow behavior in the water, these... 

Exploitation of liquid-liquid microreactor in organic synthesis offers attractive advantages, including the reduction of diffusion path lengths to maximize the rate of mass transfer and reaction rates. Despite the advantages, interest in liquid-liquid micro reactors did not take off until recently, perhaps because of the complication of flow pattern manipulation combined with the limited numbers of liquid-liquid reactions. Initial interest focused on the control of parameters responsible for variation in flow patterns to engineer microemulsions or droplets. However, it was soon realized that liquid-liquid microdevices are more than just a tool for controlling flow patterns and further interest developed. 

The various steps in the removal of a gas from air by a porous adsorbent may be confined broadly to the following processes (a) mass transfer or diffusion of the gas to the gross surface (b) diffusion of the gas into or along the surface of the pores of granular adsorbent (c) adsorption on the interior surface of the granules (d) chemical reaction between the adsorbed gas and adsorbent (e) desorption of the product and (/) transfer of the products from the surface to the gas phase. Whether surface reaction or diffusion (mass transfer) to the surface becomes the rate-controlling step will become evident in the analysis of the experimental data with respect to the rate constant. 

The mass transfer coefficient, K, is defined as the ratio of the mass transport controlled reaction rate to the concentration driving force. The concentration driving force will depend on both turbulent and bulk convection. Bulk convection depends on molecular diffusivity, while the turbulent component depends on eddy diffusivity (4). The mass transfer coefficient considers the combination of the two transport mechanisms, empirically. 

The kinetics of the process was considered as oxidative reactions in series with each other, but in parallel with respect to the OH, so that the concentration of OH radicals in the reaction zone was determined by the fastest reaction step. As a consequence, if the value of the imposed current was sufficiently high to complete the first oxidative step of phenol to hydroquinone (i = 2FkmCo which corresponded to y > 0.07) which involves two electrons, the disappearance of phenol was mass-transfer controlled but the total mineralization was not achieved. In these conditions, the concentration of OH was too low to provoke an appreciable reaction rate of the less oxidisable intermediates. Thus, the products of the first oxidative step accumulated in the laminar film, from which they diffused to the bulk solution where they were identified. 

The mechanisms described above similarly apply to the case of desorption with reaction (i.e., where the product of a liquid-phase reaction is volatile and desorbs in the gas phase). The word absorption in the above discussion will be replaced by the word desorption for this case. In most practical situations, more than one reaction occurs simultaneously. Under these situations, the terms "slow, fast, and instantaneous are applied to each reaction individually. Although the terms slow, fast, and "instantaneous reactions (or diffusion-controlled and mass-transfer-controlled regimes) are discussed with respect to gas-liquid reactions, they can also be applied to gas liquid-solid reactions, where the solid is either a catalyst or a reactant. 

The diffusion and chemical reaction rates depend only on the concentration of gaseous reactants at the working electrode surface, and by definition, are independent of electrode potential. When concentration overpotentiai dominates the total overpotentiai at the working electrode, a limiting current exists. This limiting current is the maximum current obtained when the electrochemical reaction is completely mass-transfer controlled. ... 

Many homogeneous reactions occur in the liquid phase, but consume reactants that must be supplied by mass transfer from a gas phase (or occasionally from another liquid phase). This is a typical problem of reaction engineering and is treated in some detail in most modem texts of that field [1,3,4,9,16,17]. Customarily, a power law is assumed for the rate of the chemical reaction and is then combined with a standard linear-driving force or Fickian diffusion treatment of mass transfer. A mass-transfer limitation lowers the rate, which in some extreme situations can become entirely mass transfer-controlled. Certain types of multistep reactions, however, can produce a totally different and very interesting behavior that may involve instability. 

Mass-transfer overpotential results from a finite mass-transfer rate from bulk electrolyte to electrode or vice versa. If the system is mass-transfer controlled, a limiting current density exists. The limiting current density is the maximum reaction rate under mass-transfer control. It increases as the concentration of the reacting species, their diffusion rate, temperature, or flow rate increase. In a system with limiting current density, the overpotential follows Eq. (12). The overpotential increases very rapidly when approaching the limiting current density. 

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