Coupled Transport Effects

Fourier s law. Pick s law, and Ohm s law all relate a flux to a transport coefficient times a gradient of some field. These three laws can be written in matrix form as 

---

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. 

There are two kinds of effects of the membrane on the enzyme behavior a specific interaction between the enzyme and the lipid membrane and a nonspecific interaction of the membrane structure by itself on the enzyme kinetics. In the case of ATPase, the enzyme in solution is working in homogeneous and isotropical conditions. At the opposite extreme, in the membrane the enzyme is working under asymmetrical boundary conditions. In the last case there is a coupling between a scalar process and the vectorial transport effect. In conclusion, the effect of the membrane on the enzyme behavior is not only a chemical effect, but also a geometrical one. 

In a voltammetric experiment conducted with an excess of electrolyte, the current in solution is carried by the electrolyte, not by the electroactive couple. Therefore, when solving the appropriate mass transport equations, it is appropriate to evaluate only diffusion of the electroactive species. The flux of electrolyte, which certainly occurs, is not manifested in the amplitude or position of the voltammetric signal. However, when the concentration of electrolyte is lower than that of the electroactive couple, the effect of the potential gradient... 

When a catalytic reaction takes place on a nonporous metal surface the coupling between the exothermic chemical reaction and the transport effects may also give rise to multiple steady states. Apparently, in the realm of chemical reaction engineering the first experimental observation of multiple steady states was done just for the catalytic wire problem [see Tamman (29), Davies (30), and Buben (5/)]. Catalytic gauzes consisting of wire screens or layers of metal pills (e.g., the silver crystals) are used for a number of industrially important catalytic reactions as, e.g., synthesis of... 

In coupled transport and solvent dehydration by pervaporation, concentration polarization effects are generally modest and controllable, with a concentration polarization modulus of 1.5 or less. In reverse osmosis, the Peclet number of 0.3-0.5 was calculated on the basis of typical fluxes of current reverse osmosis membrane modules, which are 30- to 50-gal/ft2 day. Concentration polarization modulus values in this range are between 1.0 and 1.5. 

Figure 11.13 The effect of replenishing a hollow fiber coupled transport module with fresh complexing agent. Membrane, polysulfone, hollow fiber/Kelex 100 feed, 0.2 % copper, pH 2.5 product, 2% copper, 100 g/L H2S04 [49]...

The contents of the present contribution may be outlined as follows. Section 6.2.2 introduces the basic principles of coupled heat and mass transfer and chemical reaction. Section 6.2.3 covers the classical mathematical treatment of the problem by example of simple reactions and some of the analytical solutions which can be derived for different experimental situations. Section 6.2.4 is devoted to the point that heat and mass transfer may alter the characteristic dependence of the overall reaction rate on the operating conditions. Section 6.2.S contains a collection of useful diagnostic criteria available to estimate the influence of transport effects on the apparent kinetics of single reactions. Section 6.2.6 deals with the effects of heat and mass transfer on the selectivity of basic types of multiple reactions. Finally, Section 6.2.7 focuses on a practical example, namely the control of selectivity by utilizing mass transfer effects in zeolite catalyzed reactions. 

Two important restrictions must be introduced to allow a general representation of the temperature and concentration dependence of the effective reaction rate in the diffusion controlled regime. The first concerns the restriction to simple reactions, i.e. which can be described by only one stoichiometric equation. Whenever several reactions occur simultaneously, it is obvious that the individual activation energies and reaction orders may be influenced quite differently by transport effects. Thus, how the coupled system in such a case finally will respond to a change of temperature or concentration cannot be specified in a generally valid form. 

The introduction of transport effects due to the formation of corrosion product deposits would not necessarily be confined to one half-reaction. It is likely that transport of the oxidant to the corrosion site would also be polarized. Such an effect, coupled possibly to a consumption of the oxidant in the bulk environment, would make the evolution in EC0RR with time much more difficult to inter-... 

The formulation of linear nonequilibrium thermodynamics is based on the combination of the first and second laws of thermodynamics with the balance equations including the entropy balance. These equations allow additional effects and processes to be taken into account. The linear nonequilibrium thermodynamics approach is widely recognized as a useful phenomenological theory that describes the coupled transport without the need for the examination of the detailed coupling mechanisms of complex processes. 

There is a variety of fundamental physical and chemical principles lhat can control the deposition rate and quality of a film resulting from a CVD process. We briefly introduce them here, but refer the reader to Chapter 2 and other books on CVD for more detailed discussions. The basic processes underlying CVD can be subdivided into mass transport effects and chemical effects, each of which can occur in both the gas and solid phases. Chemical effects can be further subdivided into thermodynamic effects and kinetic effects. In some cases, a particular effect can be separated out as rate limiting, and a CVD process can be said to be mass-transport controlled or surface-kinetics controlled. In reality, transport and chemical reactions are closely coupled, with their relative importance varying with the details of the operating conditions. 

Experiments were carried out with Ionac MC 3470 to determine the self-diffusion coefficient values for H+ and Al + in the coupled transport. Data points were used from the experiment involving 2N acid sweep solution in Figure 34.24b, presented later. These values formed the basis for aluminum transport rate or flux (7ai) calculation at different time intervals. The equilibrium data generated in Figure 34.20b were used in conjunction with Equation 34.25 to determine the interdiffusion coefficient values. Local equilibrium was assumed at the membrane-water interface. Eigure 34.24a shows computed Dai,h values for this membrane. When compared with Dai,h values for Nafion 117, it was noticed that the drop in interdiffusion coefficient values was not so steep, indicative of slow kinetics. The model discussed earlier was applied to determine the self-diffusion coefficient values of aluminum and hydrogen ions in Ionac MC 3470 membrane. A notable point was that the osmosis effect was not taken into account in this case, as no significant osmosis was observed in a separate experiment. 

In this chapter, general considerations are presented in an attempt to advance the understanding of the LM science at facilitated, coupled transport which allows the optimization of solutes separations. Factors that influence the effectiveness and selectivity of separation are analyzed. 

Figure 9.14 Effect of pH on copper coupled transport flux for three different complexing agents.20 (Membrane Celgard 2400. Feed 0.2% copper. Product 100 g/C H2S04).

Figure 9.16 The effect of small concentrations of copper in the feed on iron permeation through a coupled transport membrane.19 (Membrane Celgard2400/ LIX 64N. Feed pH 2.5. Product pH 1.0).

Figure 9.18 The effect of complexing agent concentration on the coupled transport flux of uranium.17 (Membrane Celgard 2400/Alamine 336 dissolved in Aromatic 150. Feed 0.2% uranium, pH 1.0. Product pH 4.5).

Figure 9.23 The effect of membrane thickness on flux through a coupled transport membrane.20 (Membrane Laminated Celgard 2400/various reagents. Feed 0.2% copper, pH 2.5. Product 100 g/C H2SO4).

Figure 9.24 The effect of membrane thickness on the coupled transport flux of nickel through reaction rate limited membrane.73 (Membrane Laminated Celgard 2400/30% Kelex 100 dissolved in Kermac 470B. Feed 0.2% nickel, pH 6.0. Product 100 g/fi HjSO. ...

Figure 9.39 Diagram illustrating spontaneous emulsification processes in a liquid membrane and the effect of the process on coupled transport flux.

Theoretical studies of catalytic conversion in a flow reactor reveal that a compensation effect will be observed under certain restrictive conditions. It appears that the compensation effect is observed when two or more coupled transport processes are involved and consequently may be a general law. Compensation effects have been observed in electronic conductivity in semiconductors, diffusion of atoms in solids, etc however, more work is needed to establish its generality. 

---