Rate of interphase transport

So, let s take a look at what this looks like, aside from trouble. In the steady state the rates of reaction and of heat generation (assuming exothermic reactions for the moment) are balanced first by the rates of interphase transport between the fluid phase and the catalyst. Thus,... 

Our analysis indicates that kinetic retardation of the interphase transport is essential for a well-balanced theory away from the critical point. The available simulations of the motion of a diffuse interface near a three-phase contact line, taking into account viscous retardation only and, in effect, assuming evaporation or condensation to be as easy as plain advection, may grossly overestimate the rate of interphase transport, but the latter remains essential even when its order of magnitude is reduced due to kinetic retardation. 

To determine the rate of interphase transport of any species being absorbed from the gas into the liquid (or desorbed from the liquid into the gas) through such a gas-liquid interface in a microporous/porous hydrophobic membrane, consider the concentration profile of species A shown in Figure 3.4.10. The flux of species A being absorbed at steady state may be written down for the three regions (gas film, membrane pore and liquid film) as follows ... 

Reformulation of the problems previously explained to account for interphase gradients essentially requires only the change of the surface boundary conditions. Assuming that we may see traditional mass- and heat-transfer coefficients as the rate constants characteristic of interphase transport, the boundary conditions for mass and energy conservation equations become... 

Answer Nniocai > 1 or 2, depending on the choice for the characteristic length (i.e., R or 2R). This lower limit for the Nusselt number corresponds to thermal energy transport exclusively by conduction, with no enhancement from convection parallel to the interface. In general, the Nnsselt number, which is a dimensionless heat transfer coefficient, represents a ratio of the total rate of interphase heat... 

Your experimental apparatus consists of a two-phase column in which mobile component A is transported from a stationary solid phase to a moving liquid phase that flows through the column. How should you quantify the average rate of interphase mass transfer, with units of moles per time, from very simple experimental measurements Your analytical device is not sophisticated enough to measure any concentrations within the column, but you do have experimental data that characterize the inlet stream at z = 0 and the outlet stream at z = L. 

Rate equations are used to describe interphase mass transfer in batch systems, packed beds, and other contacting devices for sorptive processes and are formulated in terms of fundamental transport properties of adsorbent and adsorbate. 

The effect of physical processes on reactor performance is more complex than for two-phase systems because both gas-liquid and liquid-solid interphase transport effects may be coupled with the intrinsic rate. The most common types of three-phase reactors are the slurry and trickle-bed reactors. These have found wide applications in the petroleum industry. A slurry reactor is a multi-phase flow reactor in which the reactant gas is bubbled through a solution containing solid catalyst particles. The reactor may operate continuously as a steady flow system with respect to both gas and liquid phases. Alternatively, a fixed charge of liquid is initially added to the stirred vessel, and the gas is continuously added such that the reactor is batch with respect to the liquid phase. This method is used in some hydrogenation reactions such as hydrogenation of oils in a slurry of nickel catalyst particles. Figure 4-15 shows a slurry-type reactor used for polymerization of ethylene in a sluiTy of solid catalyst particles in a solvent of cyclohexane. 

After phase separation, two sets of equations such as those in Table A-1 describe the polymerization but now the interphase transport terms I, must be included which couples the two sets of equations. We assume that an equilibrium partitioning of the monomers is always maintained. Under these conditions, it is possible, following some work of Kilkson (17) on a simpler interfacial nylon polymerization, to express the transfer rates I in terms of the monomer partition coefficients, and the iJolume fraction X. We assume that no interphase transport of any polymer occurs. Thus, from this coupled set of eighteen equations, we can compute the overall conversions in each phase vs. time. We can then go back to the statistical derived equations in Table 1 and predict the average values of the distribution. The overall average values are the sums of those in each phase. 

Reactions carried in aqueous multiphase catalysis are accompanied by mass transport steps at the L/L- as well as at the G/L-interface followed by chemical reaction, presumably within the bulk of the catalyst phase. Therefore an evaluation of mass transport rates in relation to the reaction rate is an essential task in order to gain a realistic mathematic expression for the overall reaction rate. Since the volume hold-ups of the liquid phases are the same and water exhibits a higher surface tension, it is obvious that the organic and gas phases are dispersed in the aqueous phase. In terms of the film model there are laminar boundary layers on both sides of an interphase where transport of the substrates takes place due to concentration gradients by diffusion. The overall transport coefficient /cl can then be calculated based on the resistances on both sides of the interphase (Eq. 1) ... 

The ratio of the rate of intrinsic kinetics to mass transport at the L/L-interphase is expressed by the Ha number (Eq. 9). According to Chaudhari et al. [ 14], the Ha numbers are smaller than 0.3 as long as the ratio of reaction rate to mass transport rate are not higher than 0.1. It is therefore concluded... 

Since the overall reaction rate in the loop reactor is limited by mass transport at the phase boundary, one would expect that the Ru concentration has a weaker influence on the rate of reaction than in the batch reactor. We have carried out experiments at a Ru concentration of 0.005 M as well as at 0.01 M and observed nearly a doubling of the overall reaction rate, giving rise to a reaction order of 0.96 with regard to Ru. The result is somehow surprising, since it can be explained only in terms of a kinetic control of the reaction, like in the batch reactor. On the other hand, previous experiments clearly indicate a mass transport limitation at the L/L-interphase. So the question which arises is how it can be possible that a multiphase reaction system is limited by both mass transport and kinetics ... 

In heterogeneous reactions, phase boundaries exist between phases and transport processes the intrinsic rate of reaction should be taken into account simultaneously in reactor design. The combination of mass transfer rates and reaction rates leads to the so-called overall rate. The goal is to express the global rate in terms of the bulk properties of the phases, eliminating the interphase properties. 

Table 4 summarizes a number of well-known theoretical diagnostic criteria for the estimation of intraparticle transport effects on the observable reaction rate. Tabic 5 gives a survey of the respective criteria for interphase transport effects. It is quite obvious that these are more difficult to use than the simple experimental criteria given in Tables 2 and 3. In general, the intrinsic rate expression has to be specified and, additionally, either the first derivative of the intrinsic rate with respect to concentration (and temperature) at surface... 

It is worth emphasizing that Eqs. (13-61) to (13-68) hold regardless of the models used to calculate the interphase transport rates and EJ. With a mechanistic model of sufficient complexity it is possible, at least in principle, to account for mass transfer from bubbles in the froth on a tray as well as to entrained droplets in a spray, as well as transport between the phases flowing over and through the elements of packing in a packed column. However, a completely comprehensive model for estimating mass-transfer rates in all the possible flow regimes does not exist at present, and simpler approaches are used. 

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