Transport effects negligible

Salt flux across a membrane is due to effects coupled to water transport, usually negligible, and diffusion across the membrane. Eq. (22-60) describes the basic diffusion equation for solute passage. It is independent of pressure, so as AP — AH 0, rejection 0. This important factor is due to the kinetic nature of the separation. Salt passage through the membrane is concentration dependent. Water passage is dependent on P — H. Therefore, when the membrane is operating near the osmotic pressure of the feed, the salt passage is not diluted by much permeate water. 

When the potential step is small and the system is chemically reversible three cases of interest are analyzed. First, when the reaction is kinetically sluggish (electrochemi-cally -> irreversible or quasireversible) and the -> mass transport effects are negligible. 

After Dekker et al. (1995), criteria for negligible transport effects in steady-state kinetics are as follows. The criterion for negligible external mass transport resistance in steady-state kinetics is... 

The intraparticle transport effects, both isothermal and nonisothermal, have been analyzed for a multitude of kinetic rate equations and particle geometries. It has been shown that the concentration gradients within the porous particle are usually much more serious than the temperature gradients. Hudgins [17] points out that intraparticle heat effects may not always be negligible in hydrogen-rich reaction systems. The classical experimental test to check for internal resistances in a porous particle is to measure the dependence of the reaction rate on the particle size. Intraparticle effects are absent if no dependence exists. In most cases a porous particle can be considered isothermal, but the absence of internal concentration gradients has to be proven experimentally or by calculation (Chapter 6). 

One simple example of an experiment in which transport effects are considered to be negligible is illustrated in Figure 4.1 and is described in detail in [3]. An oxidizing stream at an elevated temperature and traveling with... 

Let us now consider the unsteady, three-dimensional flow of a homogeneous reacting fluid with negligible transport properties. In view of the simplifications that arise when transport effects are absent (see Section 4.2.1), equations (l-l)-(l-4) become... 

Since transport effects are neglected in equation (19), the equation does not depend on assumptions 8 and 10 of Section 5.2. Clearly, equation (19) can also be made to apply to a system involving any one-step reaction by suitably modifying the definition of F (x, cp). In fact, since transport effects are negligible, the problem of computing the structure of the downstream portion of the detonation wave for any reaction mechanism merely involves a forward integration of a set of equations of the form... 

Let us consider a steady flow for which a Cartesian coordinate system (x, y, z) can be established such that -h x is the principal flow direction and all flow properties are independent of z. In this two-dimensional (x, y) flow, it will further be assumed that except in a layer extending parallel to the principal flow direction, all flow properties vary so slowly that transport effects are negligibly small. For convenience, the viscous, diffusive, and heat-conducting layer will be placed in the vicinity of the plane y = 0 (which, for example, may represent a stationary flat plate, or may divide two parallel... 

Another characteristic of the fluidized bed is the small size and density of catalyst particles necessary to maintain proper fluidization. The particles provide a much larger external surface per unit mass of catalyst than those, in a fixed-bed unit. This results in a higher rate of reaction (per unit mass) for a nonporous catalyst. Also, internal transport effects are negligible. 

Case 3 Reaction Occurring Within fluid Film. As a third example consider die silantion when species A disappears by homogeneous reaction in Ihe fluid film. Such a model has been used to predict die effect of chemical reaction on gas absorption rales (Chapter 6) or on canier-faciliimed transport in membranes (Chapter 19). For simplicity, assume die reection to be first order and irreversible and the solution to be dilute so that bulk flow transport is negligible and Ihe total molar concentration constant. The standy-state belsuce for A is obtained from simplification of Eq, (2.3-14) ... 

The analysis we have been working with has considered the case where the areas involved are the external surfaee, a, and internal area, s, for transport and reaction, respectively. Consider now the ease [W. Goldstein and J.J. Carberry, J. Catal., 28, 33 (1973)] where the contribution of the external surface (which is also catalytic) to the overall reaction is not negligible compared to the internal surface, s. This can be quite possible when the catalyst supplied is very active and is finely divided to minimize transport effects. We would like to know what the isothermal effectiveness and the point selectivity of intermediate for Type III reaction in such a situation is. Recall that the point or differential selectivity is defined as (rate of production of y)/(rate of reaction of i). 

Normally the phenomena of external and internal mass transport cannot be treated as completely separate. Theoretically, separation of these two effects may be difficult, but experimentally it is quite possible to create conditions in which (a) the effect of external transport is negligible (by increasing the relative fluid velocity) or (b) the effect of internal limitation is minimal (by reducing particle size). Generally, however, both phenomena must be taken into con-... 

The first set of preliminary experiments in a kinetic study carried out in laboratory PBRs should establish the flow conditions at which external transport effects are negligible. The second set of diagnostic experiments conducted should verify the particle size requirements under which intraparticle transport effects are eliminated. A study of intrinsic kinetics must make use of the flow rates and particle sizes that exclude both external and internal transport limitations, respectively. 

---