Monte-Carlo coalescence-dispersion

Table 13-12 summarizes the main simnlation methods that have been or are in use. In the discussion that follows, Enlerian methods based on time-averaged (or Reynolds-averaged) balance equations for the component concentrations and segregation will be emphasized, but the Lagrangian-oriented engulfment model and Monte Carlo coalescence-dispersion models are also presented. 

Monte Carlo Coalescence-Dispersion Simulation of Mixing... 

Canon et al. (1977) simulated the flow, mixing, and reaction in the Paul and Treybal stirred reactor using a Monte Carlo coalescence and dispersion (C-D) method. In this method elements of the fluid are simulated by points that move according to the flow pattern in the vessel. These points have mass and composition representing some fraction of the fluid in the vessel. The points are caused to mix (coalesce), react, then disperse. The number of points undergoing C-D during each time increment is proportional to a C-D frequency. The local C-D frequency (coalescences/time/site) was found to be related to local turbulence as follows ... 

Tavlarides presents a sophisticated model for representing coalescence and breakage of droplets in liquid-liquid dispersions. The model relies on the population balance equation and still requires the adjustment of 6 parameters. The solution of such equations is difficult and requires the use of Monte-Carlo methods... 

Spielman, L. A., and Levenspiel, O., A Monte-Carlo treatment for reacting and coalescing dispersed phase systems. Chem. Eng. Sci. 20, 247 (1965). 

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. 

Spielman and Levenspiel (1965) appear to have been the earliest to propose a Monte Carlo technique, which comes under the purview of this section, for the simulation of a population balance model. They simulated the model due to Curl on the effect of drop mixing on chemical reaction conversion in a liquid-liquid dispersion that is discussed in Section 3.3.6. The drops, all of identical size and distributed with respect to reactant concentration, coalesce in pairs and instantly redisperse into the original pairs (after mixing of their contents) within the domain of a perfectly stirred continuous reactor. Feed droplets enter the reactor at a constant rate and concentration density, while the resident drops wash out at the same constant rate. Reaction occurs in individual droplets in accord with nth-order kinetics. 

Spielman LA, Levenspiel O. A Monte Carlo treatment for reaction and coalescing dispersed systems. Chem Eng Sci 1965 20 247. 

Tavlarides (1981) 1981 Monte Carlo methods Direct Used phenomenological models describing coalescence and dispersion to predict DSD, with results compared with experiments. A review. 

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