In the case that carrier and solvent are immiscible, the concentration of solute in extract and raffinate can be graphically depicted with the equilibrium curve in the loading diagram. Together with the volumes of feed and solvent, the mass balance for the solute leads to the amount of solute that can be recovered.
Whenever the miscibility of the two phases varies and is dependent on concentration, a triangular diagram is employed (Fig. 2.5). Here the three corners of the equilateral triangle stand for the pure components, the solvent S, the carrier T and the solute C. Each side of the triangle represents binary mixtures, each point within the triangle a ternary mixture. Since the sum of the perpendicular lines of any point in the triangle equals the height of the triangle, the length of these lines corresponds to the concentration of each component.
Cone. T
Fig. 2.5: Ostwald's triangle diagram
Cone. T
Fig. 2.5: Ostwald's triangle diagram
In liquid-liquid extraction at least one miscibility gap between solvent and feed is present. The binodal curve encloses the region of immiscibility (Fig. 2.6). In this area, a mixture with concentration M will separate into two equilibrium phases. The composition of the conjugate phases at equilibrium will lie on the binodal curve at either end of the tie line that passes through the average composition M of the total system. In a triangular diagram also the 'lever-arm rule' applies, where the lengths EM and MR correspond to the relative amounts of raffinate and extract. On the binodal curve, the plait point KP shows where the two conjugate phases disappear and approach each other in composition.
The tie lines and the miscibility gap are strongly influenced by changes in temperature.
A simplified representation of the phase equilibrium is the distribution diagram (Fig. 2.7). As demonstrated, the distribution equilibrium curve can be developed out of the triangular diagram. The slope of the equilibrium curve represents the distribution coefficient K. The position of the binodal curve and its tie lines in the liquid-liquid equilibrium is only determined by the activity coefficient.
Cone. T
Fig. 2.6: Triangle diagram for a system with two partly immiscible components
Cone. T
Fig. 2.6: Triangle diagram for a system with two partly immiscible components
Cone. T
Fig. 2.7: Construction of the distribution diagram from the triangle diagram
Cone. T
Fig. 2.7: Construction of the distribution diagram from the triangle diagram
For a single-stage extraction the following considerations can be made using the triangular diagram (Fig. 2.8). A binary mixture of carrier solvent T and solute C, denoted by the feed concentration F, is to be depleted in solute by an appropriate solvent S. The resulting heterogeneous mixture will separate at equilibrium into two coexisting phases E and R, the concentration of which is determined by the tie line through M.
The selectivity of the extraction can be determined graphically if the concentrations of extract D and raffinate phase G are converted on a solvent-free basis, the ratio of both concentrations represents the selectivity. If this distribution equilibrium is reached, a so-called theoretical stage is present. In reality, the achieved enrichment is far smaller than the theoretically possible one. When designing extractors, not only the theoretically required stages, but also a stage exchange degree, to be determined empirically, has to be taken into consideration. This is of special importance with multi-stage units.
Fig. 2.8: Depiction of a single-stage extraction in a triangle diagram 2.1.1.3.2 Multi-Stage Liquid-Liquid Extraction
On an industrial scale, emphasis is put on good solute depletion and liquid-liquid extraction is, therefore, carried out in several stages.
In discontinuous cross-current extraction, the solvent is mixed with the feed and subsequently separated; the leaving raffinate is again extracted with fresh solvent. An arbitrary number of extraction stages can follow. The result of a cross-current extraction is obviously determined by the distribution coefficient as well as the solvent ratio. In the case of a high distribution coefficient, the required number of extraction stages is low and the obtained solute therefore has a high concentration. By using large amounts of fresh solvent, a good solute depletion in the raffinate can be achieved. On the other hand, in case of a low distribution coefficient many extraction stages are necessary and the obtained solute concentration decreases rapidly. The graphical determination by employing the triangular diagram will lead to a tie line through M for every stage (Fig. 2.9). The corresponding concentration of solute in extract and raffinate will lie again on the binodal curve.
For the extractive processes in the flavour industry, it is useful to determine an analytically identifiable constituent in the extract after each stage. Calculations then result in the number of actually employable stages.
In the laboratory, a multi-stage liquid-liquid extraction can be performed by a simultaneous distillation-extraction process according to Likens-Nickerson [29] (Fig. 2.10). Here, the liquid matrix with the solute in one flask is evaporated together with an immiscible solvent in a second flask. Extraction takes place in the vapour phase where an intensive distribution of both phases is ensured. The condensed vapours from the two phases are separated via a siphon using their different densities and their reintroduction into the original flasks. As the distillation process is continued, extraction is repeated until the solute is exhausted in the original matrix. This method is very useful when traces of non-volatile solutes are present, which are only partly miscible in the liquid matrix. Here carrier distillation lowers the boiling temperature of the solute considerably.
Fig. 2.10: Likens-Nickerson apparatus
Vacuum can be applied in order to reduce thermal exposure. The cooling funnel requires a deep-freezing mixture. This extraction method can easily be transferred onto an industrial scale. An important application is essential oils in water where steam distillation is carried out. For the distillative extraction process, different water-immiscible solvents are used. Thermal deterioration and retrieval ratio in the solvent have been studied intensively for fragrance materials [30].
In multi-stage continuous countercurrent extraction, it is characteristic that solvent and feed are continuously moving countercurrently towards each other in the extractor. The fresh solvent first comes into contact with the leaving raffinate and on the opposite side the leaving extract with the introduced feed. This leads to a large loading capacity for both sides and, therefore, to high enrichment of solute in the extract and high depletion in the raffinate. Therefore, the concentration of solute in the extract is much higher compared to cross-current extraction and less solvent is necessary for the depletion of solute in raffinate. Multi-stage extraction is achieved by the addition of the successive single stages with countercurrent flow of feed and solvent.
Depending on the technical construction of these extractors operating in the counter-current mode, two different classifications can be described: stage-wise or differential contacting of the two countercurrently flowing phases. In a stage-wise extractor, the concentration profile changes stepwise, since in each stage the separated layer of extract and raffinate are newly distributed in the following unit (e.g. mixer-settler battery, Robatel extractor).
In stage-wise liquid-liquid extraction, calculations can be performed from stage to stage. A convenient method for the determination of the necessary theoretical stages or minimum solvent ratio is again graphical depiction (Fig. 2.11). In the known loading diagram, the necessary stages can be determined by inserting the operating line. Together with the mass flow ratio of feed and solvent and the final concentration of solute in the raffinate, an operating line can be drawn into the loading diagram and the necessary steps to reach this value are counted.
Carrier Solvent
Solvent
Solute
Solute
Fig. 2.11: Loading diagram
Carrier Solvent
Solvent
Solute
Solute
(Extract)
(Raffinate)
Fig. 2.11: Loading diagram
The slope of the operating line is defined by the solvent ratio. The minimum solvent ratio depicts the operating line in the loading diagram with a common point on the equilibrium curve. Indefinite theoretical stages on the operating line would be neces sary to reach this position; therefore the solvent ratio is higher for operational use. Similar to distillation, extraction efficiency in stage-wise extraction units is expressed in HETS (height equivalent of a theoretical stage). The HETS is calculated from the theoretical stages and the total length of the extraction unit:
For the projection of an extraction unit, the practical theoretical plate number is determined by dividing the theoretical plate number by the plate efficiency value:
The height of a single plate in the unit is then defined by the total height of the mass transfer zone and the practical plate number.
In more complicated ternary mixtures, the triangular diagram is again suitable for graphical description (Fig. 2.12). The mass balance for the determination of the point M, depicted previously for the single stage, is now required along the entire unit. The difference between mass flow of extract and raffinate in every cross-section is equal and corresponds to the net mass flow at either end of the apparatus. Since the sum of two amounts in a triangular diagram is represented by a point on a line between them, the difference may be represented by a point on an extended line through them. The corresponding lines for each cross-section originate from one single point which represents the net mass flow at one end. This point P is designated as difference point or pole. The location of this point P can be determined graphically if the inlet phase, the required purity of the raffinate phase and the ratio of raffinate and extract flow are known. Originating from the inlet feed F and solvent S, the point M is determined. As this mixture is also considered to be a mixture of raffinate and extract, outlet extract Em can be found as the intersection between the binodal curve and the line through point M and outlet raffinate Rm. The location of the difference point is found at the intersection of both lines EmF and RmS.
The position of the difference point can also be situated on the other side of the triangular diagram. There are also some restrictions with respect to the necessary minimum solvent/feed ratio. Further details can be found elsewhere [20, 21].
After determination of the difference point, it is possible to determine the necessary number of theoretical stages. Starting from the extract Em the raffinate Rj for the first stage is found by using the tie line through Em. A line through P and Rj intersects with the binodal curve and results in E2. This procedure is repeated until the final raffinate point Rm is reached.
The example results in three theoretical stages. By modifying the solvent/feed ratio, it is possible to change the number of theoretical stages. A larger number of stages means less solvent flow in relation to feed flow and consequently reduced cost of solvent recovery. Opposite results will be received for increased solvent flow.
In the differential extraction mode, the concentration profile changes continuously as the two phases have no exact stepwise phase separation and a continuous movement towards each other is present. Here, an ideal contacting pattern for the two phases corresponds to a perfect countercurrent plug flow (e.g. extraction towers, Podbielniak extractor). For the determination of extraction efficiency in these kinetic systems, the HTU-NTU (height of a transfer unit and number of a transfer unit) models were developed. The mass transfer model is based on a differential volume element in the column where a thin-film contact for the two phases results in the solute transfer into the extract. The HTU is again defined over the column length H:
Fig. 2.12: Determination of the number of theoretical plates in a triangle diagram s Cone. T-► Rœ T
Fig. 2.12: Determination of the number of theoretical plates in a triangle diagram
The HTU values for the solute transfer of the releasing (raffinate) and receiving (extract) phase are calculated with the two following equations, where the integrals describe the NTU from the loading difference of the two respective phases:
F/S : flowrate of feed and solvent K: mass transfer coefficient X - X': loading difference of the raffinate phase a: interfacial area per unit volume A: cross-section area
AKgS Y Y
Y' - Y: loading difference of the receiving phase
The first HTU term contains the physical and fluid-dynamic parameter and the second NTU term expresses the number of theoretical stages as function of the solute concentration difference. The extractor-specific HTU value is, on the one hand, described by the quotient of flow rate and cross-sectional area of the column, and, on the other hand, it is characterised by the interfacial area per unit volume and the mass transfer coefficient. The former is mainly influenced by drop size and phase hold-up, the latter by the relative movement of the dispersed phase. These characteristic HTU values can be experimentally measured for a certain extractor type and are used for comparison with other extractors or for the projection of larger units.
The NTU values that characterise the concentration profile can be graphically determined if the operation line is parallel to the equilibrium curve in the loading diagram. In this case NTUR = NTUE and reflects the theoretical stage number nth. A deviation of the ideal plug flow in the continuous and dispersed phase occurs for the following reasons:
- eddy diffusion in axial and radial direction in the continuous phase
- different velocity spectrum over column cross-section
- carry along of small dispersed droplets in axial direction
- broad velocity spectrum of ascending droplets due to the different droplet size.
These phenomena are defined as axial dispersion which reduces the mass transfer. Therefore, additionally a term called HDU (height of diffusion rate) has to be taken into account for the measured HTU':
The HDU can also be experimentally determined by measuring the residence time distribution of the two phases in the extractor unit.
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