Coalescence-redispersion

The coalescence-redispersion (CRD) model was originally proposed by Curl (1963). It is based on imagining a chemical reactor as a number population of droplets that behave as individual batch reactors. These droplets coalesce (mix) in pairs at random, homogenize their concentration and redisperse. The mixing parameter in this model is the average number of collisions that a droplet undergoes. 

Figure 1.6. Four micromixing models that have appeared in the literature. From top to bottom maximum-mixedness model minimum-mixedness model coalescence-redispersion model three-environment model.

Luss and Amundson (LI 3) employed this model to analyze reactor stability and control for segregated two-phase systems. The Monte Carlo simulation was employed to model the age distribution of segregated drops in the vessel. Conditions of operation under which heat-transfer effects may control the design of the reactor were given. It was shown that some steady states may be obtained in which the temperature of some drops greatly exceeds the average dispersed-phase temperature. The coalescence-redispersion problem was not considered here because of unreasonable computation times. 

The drops behave as segregated entities between flow and coalescence-redispersion simulation. The coalescence and breakage frequencies can be varied with vessel position. The computational time was related to coalescence frequency data available in the literature. Figure 15 shows the steady-state dimensionless droplet number size distribution as a function of rotational speed for continuous-flow operation. As expected the model predicts smaller droplet sizes and less variation of the size distribution with increase in rotational speed. Figure 16 is a comparison of the droplet number size distribution with drop size data of Schindler and Treybal (Sll). 

The model can be employed to predict the effects of droplet size distribution and droplet coalescence-redispersion on conversion and selectivity for reacting dispersions. The reactions can occur in either phase simultaneously with interphase heat and mass transfer. 

Harada and co-workers (HI) developed two coalescence-redispersion models to describe micromixing in a continuous-flow reactor. In the first model, the incoming dispersed-phase fluid is assumed to consist of uniformly sized droplets. These droplets undergo 0 to n coalescences and redispersions with surrounding droplets of a constant average concentra-... 

Mass transfer involves establishing a transfer between the elementary regions of the reactor and between individual phases (interfacial mass transfer coefficients gas phase mass transfer, liquid phase mass transfer, mass transfer with reaction, liquid-solid mass transfer), as well as other elementary phenomena and processes connected with mass transfer gas phase phenomena and processes (gas hold-up, bubble size, interfacial area and bubble coalescence/redispersion), volumetric mass transfer and power consumption during mass transfer (2). 

A generalization of these population balance methods to reactions with arbitrary RTD was given by Rattan and Adler [126]. They expanded the phase space of the distribution functions to include the life expectation as well as concentration of the individual fluid elements i/ (C, A, 0- The population balance then reduces to all of the previous developments for the various special cases of segregated or micromixed flow, the perfect macromixing coalescence-redispersion model, and can be solved as continuous functions or by discrete Monte Carlo techniques. Goto and Matsubara [127] have combined the coalescence and two-environment models into a general, but very complex, approach that incorporates much of the earlier work. 

Stagewise contact with controlled coalescence redispersion cycles Tray column Pulsed sieve column. Pulsed Mixer-Settler-cascade, Extraction tower with controlled cycle Scheibel column, ARD-Extractor, Leisibach column, Mixer-Settler cascade ... 

Pojman, J. A. Epstein, I. R. Kami, Y. Bar-Ziv, E. 1991a. Stochastic Coalescence-Redispersion Model for Molecular Diffusion and Chemical Reactions. 2. Chemical Waves, J. Phys. Chem. 95, 3017-3021. 

FIGURE 3.3.3 Integration zone (shown in the shaded region) for calculating total number of droplets in coalescence-redispersion process. Transformation to u, v coordinates by m = c — c, v = c H- c. ... 

In the foregoing example, the deterministic event is the chemical reaction in the drops while the random events are those of drop entry into and exit from the reactor, and coalescence-redispersion within the reactor. The interval of quiescence, therefore, represents the period in which none of the following processes occur (i) addition of drops with the feed, (ii) loss of... 

In this section, we are concerned with simulation algorithms based on the approach of a fixed discrete time step for the quiescence interval. The concentrations in each drop can be updated using their initial values and reaction rates without interruption by drop entry, exit, or coalescence-redispersion. At the end of the interval, however, by generating a suitably calculated random number (to be presented subsequently), the process which disturbed the quiescence may be identified. The state of the population is now readily updated for further continuation of the simulation. 

Describe the coalescence/redispersion model in less than three sentences. 

Bajpai, R. K., D. Ramkrishna, and A. Prokop (1976). Coalescence redispersion model for drop-size distributions in an agitated vessel, Chem. Eng. ScL, 31(10), 913-920. 

---