Stagnant regions

Suspensions of fine sohds may have pseudoplastic or plastic-flow properties. When they are in laminar flow in a stirred vessel, motion in remote parts of the vessel where shear rates are low may become negligible or cease completely. To compensate for this behavior of slurries, large-diameter impellers or paddles are used, with (D /Df) > 0.6, where Df is the tank diameter. In some cases, for example, with some anchors, > 0.95 Df. Two or more paddles may be used in deep tanks to avoid stagnant regions in slurries. 

Likewise, large-diameter impellers (D > Df/2) are useful for (1) avoiding stagnant regions in slurries, (2) short mixing times to obtain uniformity throughout a vessel, (3) promotion of heat transfer, and (4) laminar continuous averaging of slurries. 

For suspension of rapidly setthng particles, the impeller turbine diameter should be Df/3 to Dfl2. A clearance of less than one-seventh of the fluid depth in the vessel should be used between the lower edge of the turbine blade tips and the vessel bottom. As the viscosity of a suspension increases, the impeller diameter should be increased. This diameter may be increased to 0.6 Df and a second impeller added to avoid stagnant regions in pseudoplastic slurries. Moving the baffles halfway between the impeller periphery and the vessel wall will also help avoid stagnant fluid near the baffles. 

The stagnant region can be detected if the mean residence time is known independently, i.e., from Equation (1.41). Suppose we know that f=lh for this reactor and that we truncate the integration of Equation (15.13) after 5h. If the tank were well mixed (i.e., if W t) had an exponential distribution), the integration of Equation (15.13) out to 5f would give an observed t of... 

In the absence of diffusion, all hydrodynamic models show infinite variances. This is a consequence of the zero-slip condition of hydrodynamics that forces Vz = 0 at the walls of a vessel. In real systems, molecular diffusion will ultimately remove molecules from the stagnant regions near walls. For real systems, W t) will asymptotically approach an exponential distribution and will have finite moments of all orders. However, molecular diffusivities are low for liquids, and may be large indeed. This fact suggests the general inappropriateness of using to characterize the residence time distribution in a laminar flow system. Turbulent flow is less of a problem due to eddy diffusion that typically results in an exponentially decreasing tail at fairly low multiples of the mean residence time. 

When fluid velocities are high relative to the solid, mass transfer is rapid. However, in stagnant regions or in batch reactors where no provision is made for agitation, one may encounter cases where mass transfer limits the observed reaction rate. We should also note that in industrial practice pressure drop constraints may make it impractical to employ the exceedingly high velocities necessary to overcome the mass transfer resistance associated with highly active catalysts. 

The dispersion and stirred tank models of reactor behavior are in essence single parameter models. The literature contains an abundance of more complex multiparameter models. For an introduction to such models, consult the review article by Levenspiel and Bischoff (3) and the texts by these individuals (2, 4). The texts also contain discussions of the means by which residence time distribution curves may be used to diagnose the presence of flow maldistribution and stagnant region effects in operating equipment. 

Possible Disadvantages Expensive difficult to avoid stagnant regions more subject to immediate bubble merger difficult to clean difficult to modify not advisable for sticky solids requires peripheral seal ports not easily shrouded. 

In an otherwise ideal stirred tank it is estimated that 10% of the volume is occupied by stagnant fluid. If there were no stagnant region, the conversion would be 60%. What conversion is to be expected in the actual reactor. 

Figure 11.17 Photograph of the main flow and stagnant regions on a barrier screw running LDPE resin [22]. The white polymer is the main flow region, and the dark material is degraded resin in the stagnant region...

Stagnant regions with old black-colored resin... 

Thomas and Watson ( 9) of the Oak Ridge National Laboratory have shown that detached spiral wire turbulence promoters, positioned away from an RO membrane surface by small wire runners, markedly increased the rejection of salts and the permeation rate through the membrane. "Detached promoters" of this type may be designed to minimize stagnant regions in addition, they are relatively easy to install. 

---