10-4.3 Correlations for Solid-Liquid Mass Transfer 569 10-5 Selection, Scaling, and Design Issues for Solid-Liquid.
Bruce Nauman, Department of Chemical Engineering, Rensselaer Polytechnic Institute, Ricketts Building, 110 8th Street, Troy, NY
The reader will almost certainly benefit from the time invested in improved understanding of mixing equipment design. The characteristic time scale for a residence time distribution is the average residence time of the vessel. Another possibility is degradation caused by contact between the base and the product in the high pH liquid film around the particles.
A change in the mixing characteristics between the two reactors?” Marco remembers his fear during the development of this liquid-liquid reaction, as he was well aware of the potential problems. They both depend on location within a vessel and on very subtle changes in the composition of the liquids. One of these is a final reactive crystallization that will determine the physical properties of the product.
Figures I-1 through I-6 summarize some of the major symptoms and causes of plant mixing problems. If large particles have a very long dissolution time, there may be degradation of the product in the bulk.
Residence Time Distributions
The total time spent within the confines of the reactor is known as the exit age, or residence time, t. For single first-order reactions, knowledge of the RTD allows the yield to be accurately calculated, even in flow systems of arbitrary complexity. If the system is nonisothermal or heterogeneous, RTD cannot directly predict the reaction yield, but still provides a general description of the flow not easily obtained from rate measurements.
In theoretical studies, the experiments are mathematical and applied to a dynamic model of the system. The concentration of tracer at the reactor outlet will then decrease over time, eventually approaching zero as the tracer is washed out of the system. If moments of the highest possible accuracy are desired, the experiment should be a negative step change to obtain W(t) directly.
This means that the integrals of the different leaching functions all have a unit mean, so that the different flow systems can be compared independently of system size. Eddy diffusion in a turbulent system justifies exponential extrapolation of the integrals defining the moments in Table 1-2. To model bypass, the small tank would have a longer residence time than the large tank.
A CSTR acts as an exponential filter and provides good attenuation provided the period of the disturbance is less than t. The drawings show the working volume of. reactor, and you calculate that the liquid inventory should be about 12,500 lb. You achieve this by injecting the tracer on the suction side of the transfer pump that supplies the reactor.
You also dissolve a little polymer in the tracer stream to better match its viscosity to that of the reactor feed. Most of the concepts discussed in this chapter can be applied to unstable systems. For isothermal solid-catalyzed reactions, the contact time distribution is analogous to the residence time distribution.
Turbulence in Mixing Applications
It is the size of the packs of B that can be distinguished from the surrounding liquid A. Our estimate ignores that the packing of the molecules in the volume and on the surface may be different. Models reported in the literature have tended to focus on one of two parts of the problem.
The fluid far away from the particle is in laminar flow, but eddies form in the wake of the particle. Some droplet fragments can be much smaller than the Kolmogorov scale (Zhou and Kresta, 1998). This allows us to fingerprint the dominant frequencies in the current in terms of their energy content (E), or power spectral density (PSD), as a function of wavenumber (k, in m−1) or frequency (f, in Hz or s−1).
This is illustrated for the Intermig on the Visual Mixing CD attached to the back of the book. Over this range of eddy sizes, there remains no memory of the large-scale oriented motions (i.e., the trailing eddies), and there is no directional preference in the flow. At the time of writing, time-resolved simulations are still reserved for the expert user.
The effect of turbulence on scalars in the flow (c, T, reaction kinetics) is strong and is sensitive to the details of the velocity and turbulence fields.
Laminar Mixing: A Dynamical Systems Approach
In the case of an agitated tank operated at a constant speed, each passage of the impeller blades periodically disturbs the liquid. In (c), a chaotic flow grows exponentially, and the exponent characterizing the growth rate (, the Lyapunov exponent) can be calculated from the slope of the curve λ versus n. The time period is usually chosen to be the period of the driving force that creates motion in the system.
When measured with an array of electrodes, the H+ concentration is highly dependent on the placement of the electrodes in the tank. Some time later, a red stream was added to follow the time evolution of the mixing structure in the tank. After only 10 iterations of the flow, the lines in the center of the domain can no longer be distinguished (see Figure 3-11f).
One would expect the growth rate of the filament to be dictated by the Lyapunov exponent of the flow. The spatial distribution of the interface in a chaotic flow (whether it is globally chaotic or not) is highly non-uniform, and this inhomogeneity is a permanent feature of the flow. The spatial distribution of ρ exhibits strong fluctuations that are a permanent feature of the mixing process (i.e., the picture “looks the same” for the four flow periods).
The time invariance in the spatial distribution of ρ is another manifestation of the similarity of the structures generated by temporally and spatially periodic chaotic flows. Initially, half of the flow domain was filled with A and the other half contained only B. The concentrations of the reactants and the product are calculated from ϕ according to Eq. The landscape of the unreactive mixture (left side of Figure 3-27) looks almost identical to the reactive flow landscape (right side of Figure 3-27).
The four snapshots in the figure show four computational snapshots of the chaotic mixing process in successive time. The mechanism controlling the evolution of the reactive mixing process is essentially the same as in the sinus flow described earlier. We can go further than qualitative comparisons and measure the probability density function of the reactant and product concentrations in the reservoir.
The experimental distributions in the 3D chaotic flow are invariant after scaling and match the concentration distribution of the model system. The location of the reactive zones is practically identical to the structure of the mixture determined only by the chaotic stretching process.
Part A: Measuring Tools and Techniques for Mixing and Flow Visualization Studies
