A drop population balance model for mass transfer in liquid-liquid dispersion. 1. Simulation and its results

Abstract

A simulation model was proposed to predict the trivariant drop distribution and mass-transfer rate for liquid-liquid dispersion systems, using the concept of drop population balance. The rates of changes in solute concentration and drop volume due to solute transfer were calculated by solving the moving boundary diffusion model in spherical coordinates. The diffusion equation was solved by both numerical and modified methods, and both results were found to be almost identical. The simulation results were compared with reported experimental data and calculated data for the systems without mass transfer, and good agreement was found between them. This agreement confirms that the simulation model can be extended to the systems with mass transfer.A new flow dynamic apparatus for measuring liquid-phase diffusion coefficients is shown to reproduce literature data. An important modification of the classic capillary diffusion tube is shown to give quick, reliable results using a minimum quantity of reagents. New data for the diffusion of m-xylene in o-xylene are also presented.

Simulation and experimental analysis of mass transfer in a liquid-liquid stirred tank extractor

“…As mentioned in the previous section, a drop must be defined by three independent variables, size ( ), age (a), and solute content (m) in a liquid-liquid extraction system. The trivariate DPBM was fully discussed by Jeon (1983) and Bapat (1982), and the DPBM for the system with mass transfer can be seen in Jeon and Lee's (1986) paper. In this study, Jeon and Lee's simulation method is used with Coulaloglou's (1975) drop interaction functions (breakage and coalescence functions).…”

“…with c = c0 at a = 0 and 0 < r < R( 0 De is the effective diffusivity and a is the age of the drop. Jeon (1983) and Jeon and Lee (1986) showed that the numerical result of the previous diffusion equation could be approximated by the following modified solution:…”

“…Hsia and Tavlarides (1983) was able to reduce the computing time by introducing the quiescence interval method with an event-oriented scheme. Bapat (1982) and Jeon (1983) fully discussed the trivariate DPBM and tried to develop improved algorithms for the simulation of a liquid-liquid stirred tank extractor. Jeon (1983) calculated the mass-transfer rate by the general diffusion equation and obtained a modified analytical solution by assuming a rigid spherical drop with no mass-transfer resistance in the continuous phase, while Bapat (1982) simulated a stirred tank extractor in which mass-transfer resistance was localized to the continuous phase.…”

“…Bapat (1982) and Jeon (1983) fully discussed the trivariate DPBM and tried to develop improved algorithms for the simulation of a liquid-liquid stirred tank extractor. Jeon (1983) calculated the mass-transfer rate by the general diffusion equation and obtained a modified analytical solution by assuming a rigid spherical drop with no mass-transfer resistance in the continuous phase, while Bapat (1982) simulated a stirred tank extractor in which mass-transfer resistance was localized to the continuous phase. A general rule that one of the resistances of the two phases can be ignored in a stirred tank extractor, however, has not been established yet.…”

Modeling interfacial area transport in multi-fluid systems

“…These methods are called population balance models. Curl (Curl, 1963), Hulbert and Katz (Hulbert, 1964), Eakman, Tsuchiya, and Fredickson (Eakman, 1965), Valentas and Amundson (Valentas, 1966a), Valentas, Bilous and Amundson (Valentas, 1966b), Bayens and Laurence (Bayens, 1969), Shah and Ramkrishna (Shah, 1973), Borwanker (Ramkrishna, 1973, 1974a), Park and Blair (Park, 1975), Coulaloglou and Tavlarides (Coulaloglou, 1977), Min and Ray (Min, 1978), Jeon and Lee (Jeon, 1986), Laso, Steiner, and Hartland (Laso, 1987), Guimares and Cruz-Pinto (Guimares, 1988), A1 Khani, Gourdon, and Casamatta (A1 Khani, 1989), Tsouris and Tavlarides (Tsouris, 1994), Jacob, (Jacob, I995), Ramkrishna, Sathyagal, and Narsimhan (Ramkrishna, 1995) and Lam, Sathyagal, Kumar, and Ramkrishna (Lam, 1996) have presented both theoretical approaches and experimental work validating various population balance models. Ramkrishna (Ramkrishna, 1974b) has examined the experimental work required to obtain information to apply a population balance model.…”