Stagnant zone model

Figure 3.4.1. Stagnant zone model for contacting efficiency in a trickle bed after Koros, R. M. [35]).

FIGURE 15.7 Effect of a stagnant zone in a stirred tank reactor according to the side capacity model. 

More complex situations can be imagined, for example, the combination of stirred-tanks, bypassing and stagnant zones. Care must be taken to establish the model parameters carefully however and not to merely fit the tracer response data. Experimental E-curve data is given in Fig. 3.27 and a possible model for this is shown in Fig. 3.28. 

Stirred tank performance often is nearly ideal CSTR or the model may need to take into account bypassing, stagnant zones or other parameters associated with the geometry and operation of the vessel and the agitator. Sometimes the vessel can be visualized as a zone of complete mixing in the vicinity of the impellers followed by a plug flow zone elsewhere, thus a CSTR followed by a PFR. 

DISCUSSION AND CONCLUSIONS In this study a general applicable model has been developed which can predict mass and heat transfer fluxes through a vapour/gas-liquid interface in case a chemical reaction occurs in the liquid phase. In this model the Maxwell-Stefan theory has been used to describe the transport of mass and heat. A film model has been adopted which postulates the existence of a well-mixed bulk and stagnant zones where the principal mass and heat transfer resistances are situated. Due to the mathematical complexity the equations have been solved numerically by a finite-difference technique. In this paper (Part I) the Maxwell-Stefan theory has been compared with the classical theory due to Pick for isothermal absorption of a pure gas A in a solvent containing component B. Component A is allowed to react by a unimolecular chemical reaction or by a bimolecular chemical reaction with... 

The mass balances [Eqs. (Al) and (A2)] assume plug-flow behavior for both the gas/vapor and liquid phases. However, real flow behavior is much more complex and constitutes a fundamental issue in multiphase reactor design. It has a strong influence on the reactor performance, for example, due to back-mixing of both phases, which is responsible for significant effects on the reaction rates and product selectivity. Possible development of stagnant zones results in secondary undesired reactions. To ensure an optimum model development for CD processes, experimental studies on the nonideal flow behavior in the catalytic packing MULTIPAK are performed (168). 

A number of investigators have modeled solute transport in soils assuming an equilibrium occurs between solution and solid phases. This assumption is often not valid in heterogeneous soil systems, and has been the impetus for the development of a number of nonequilibrium models. Some researchers have assumed that the nonequilibrium is caused by stagnant zones, which result in tortuous diffusional processes between solution and sorbed phases (Rao et al., 1979). Other researchers have attributed the nonequilibrium to kinetic effects. 

Figure 5.2 The most common kinetic model used to estimate rates of gas exchange across the atmosphere-water boundary is the Stagnant Film Model. This model essentially has the following three regions of importance (1) a well-mixed turbulent atmospheric zone (PG) (2) a well-mixed thin-film liquid zone (PG) and (3) a laminar zone (A-B) separating the two turbulent regions. The thin-film is considered permanent with a thickness defined as z- (From Broecker and Peng, 1974, with permission.)...

Vapor maldistribution. Most popular theoretical models (such as the AIChE and the Chan and Fair models, Sec. 7.2.1) postulate perfectly mixed vapor flow. In larga-diameter columns, vapor is more likely to rise in plug flow. Modeling work showed (143,179,180) that in the absence of stagnant zones on the tray, vapor flow pattern has generally little effect on tray efficiency. When column efficiency exceeds 30 percent (143), or when stagnant liquid zones exist (171,173,180), vapor plug flow reduces tray efficiency. 

The fracture system is modeled as a Id aquifer with high permeability (20 mobile cells with the numbers 1-20), each one connected to immobile cells (number 22-41, number 21 is reserved for the column s discharge). The content of the immobile cells can only be transferred to the mobile cells by diffusion. The value for a is calculated from Eq. 101 assuming De = 210"10 m2/s (range from 3-10"10 to 2-10"9 for ions in water, approximately one order of magnitude less for water in clays), 9im = 0.15, a = 0.1 m (thickness of the stagnant zone accompanying the fracture), and f,, i = 0.533 (Table 17)... 

An updated and expanded version of PHREEQC (version II) was published by Parkhurst and Appelo (1999). Version II has all of the capabilities of version I, and includes new routines for kinetically controlled reactions, solid-solution equilibria, fixed-volume gas-phase equilibria, variation of the number of exchange or surface sites in proportion to a mineral or kinetic reactant, diffusion or dispersion in one-dimensional (ID) transport, ID transport coupled with diffusion into stagnant zones, and isotope mole balance in inverse modeling. 

We probably don t have to, at this point, say that the overall model here, or even considerable simplifications of it, are best left to numerical solution. The axial dispersion model seems to work pretty well, at least for cases where the holdup/ wetting does not vary much with position in the reactor. For large changes in this factor, or for nonideal flows involving stagnant zones or liquid/gas bypassing, some version of one of the combined models will be required. It will be understood that these will be very specific to the particular design under consideration. 

When the reaction is fast enough so that diffusion of B toward the reaction zone is important, the penetration theory does not give the same results as the stagnant-film model. Numerical solutions of the equations for simultaneous diffusion and reaction of A and B based on the penetration theory have been reported [5] the enhancement factors are shown in Figure... 

The underlying idea for such a model is that only a fraction of the liquid flows in a more or less ordered way through the packing, while at each height there is a stagnant zone in which the liquid is well mixed and that exchanges mass with the flowing fraction. 

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