(709b) Phase Separation Kinetics and Settler Design

Besides appropriate design of mass transfer equipment the successful design of phase separation equipment is an important issue in liquid-liquid extraction. Based on the balance of settling processes the design of batch settlers and the design of continuous settlers should be a simple task. Actually the rate of settling w is not constant but changes with height (w = w(h)).

Several investigations have focused on the development of design algorithms, addressing the phenomena which affect the rate of hindered settling of the dispersed phase. The review of Kamp et al [1] presents a very detailed discussion of the state of research, experimental techniques and modeling approaches. In this review a paper on the “Prediction of Steady State Dispersion Height from Batch Settling Data, published by Jeelani and Hartland in 1985 [2] is outlined. In the discussion of the theoretical background Jeelani and Hartland addressed proposals of Stonner and Wohler [3] for determining the rate of sedimentation of dispersed solvents from aqueous carrier phase. They mentioned that the settling height as well as coalescence height may show sigmoidal shape because of initial turbulences. Latter approach was used by Bol [4] and Rajcharak [5], who investigated several liquid-liquid dispersion systems. Bol [4] compared the monitoring of phase separation of liquid-liquid dispersions of MIBK dispersions in an optical cell and in an ultrasonic scanner. The system properties density, viscosity of the aqueous carrier phase and the interface tension were adjusted by adding PEG 4000 and sodium chloride to the aqueous carrier phase.

From a kinetics point of view droplet sedimentation of solvent dispersions in water may follow a zero order rate law for constant rate of sedimentation, a mixed order rate law (MOR), combining zero order and first order rate of sedimentation, or a consecutive step first order rate law (FOCR). As already suggested by Jeelani and Hartland [6] initial turbulences may induce pronounced retardation of phase separation, best modeled by a first order consecutive step rate law with sigmoidal shape of the sedimentation height versus sedimentation time.

The mixed order rate law and the consecutive step first order rate law were adapted to modeling droplet sedimentation from solvent dispersions in aqueous carrier, resulting in two easy to apply algorithms for highly accurate specification of the sedimentation rate (w(h)). Application of the mixed order approach results in a two parameter function (k₁ and k₂) of the dispersion height h and the maximum height of the clear liquid aqueous phase h_max, with either correlating the height with the independent variable time t for batch settling or the residence time for continuous settling. The advantage of this mixed order sedimentation rate model is the simple development of the height dependent settling rate w(h). When applying the consecutive step first order rate law the correlation of the height dependent rate of settling again follows a two parameter algorithm.

The rate models were compared with settling experiments. In both models the fit parameters k₁ and k₂ compare well with the physical properties of the systems and the preparation method of the corresponding dispersion.

Exemplarily the rate constants k₁ and k₂ of the FOCR model compare well with the physical properties viscosity and interfacial tension and the system property droplet size dp, as derived from the sedimentation rate for rigid spheres. For validation a series of 16 experiments with different PEG 4000 content and different NaCl concentration of the aqueous phase and the dispersed solvent MIBK was investigated.

From the MOR model the initial rate of settling can easily be determined, giving quick access to the initial mean drop size. The initial rate of settling was compared with the Henschke algorithm [7] and the proposal of Jeelani and Hartland [8]. While latter algorithm compares well with the data derived from experiments, the Henschke approach is about 25 % lower throughout.

From the comparison of the actual rate of sedimentation with the initial rate of sedimentation rate retardation can easily be determined, providing access to the volumetric amount of dispersed phase in the dense packed zone.

Conclusions

Rate based sedimentation models, as already suggested by Jeelani and Hartland [2] provide simple algorithms for quantifying the sedimentation process of droplets from solvent systems dispersed in aqueous carrier with simple and quick determination of the height dependent rate of sedimentation, as needed for successful settler design.

[1] Kamp, J., Vilwock, J., and Kraume, M., 2017: Drop coalescence in technical

liquid/liquid applications: a review on experimental techniques and modeling approaches,

Rev. Chem. Eng. 33, 1–47

[2] Jeelani, S.A.K., Hartland S., 1985: Prediction of steady state dispersion height from batch

settling data., AIChE J., 31: 711–720.

[3] Stonner, H. M., and Wohler, F., 1975: An Engineer’s Approach to a Solvent Extraction

Problem, Inst. Chem. Engrs. Symp. Ser., 42,14.1

[4] Bol, P., 2015: Investigation of drop dispersion in batch settling processes,

Dissertation, TU Graz.

[5] Rajcharak, B., 2016: Modeling of droplet sedimentation in liquid – liquid phase

separation, Master Thesis, TU Graz.

[6] Jeelani, S.A.K., Panoussopoulos, K., and Hartland, S., 1999: Effect of Turbulence on the

Separation of Liquid-Liquid Dispersions in Batch Settlers of Different Geometries, Ind.

Eng. Chem. Res., 38, 493-501.

[7] Henschke, M., Schlieper, L. H. and Pfennig, A., 2002: Determination of a coalescence

parameter from batch-settling experiments, Chemical Engineering Vol. 85. - pp. 369-378.

[8] Jeelani, S.A.K., and Hartland,S., 1998, Effect of Dispersion Properties on the Separation

of Batch Liquid-Liquid Dispersions, Ind. Eng. Chem. Res. 1998, 37, 547-554