Equilibrium-curve design method

Classical Adiabatic Design Method The classical adiabatic method assumes that the heat of solution serves only to heat up the liquid stream and that there is no vaporization of solvent. This assumption makes it feasible to relate increases in the hquid-phase temperature to the solute concentration x by a simple eutnalpy balance. The equihbrium curve can then be adjusted to account For the corresponding temperature rise on an xy diagram. The adjusted equilibrium curve will become more concave upward as the concentration increases, tending to decrease the driving forces near the bottom of the tower, as illustrated in Fig. 14-8 in Example 6. 

The design of a distillation column is based on information derived from the VLE diagram describing the mixtures to be separated. The vapor-liquid equilibrium characteristics are indicated by the characteristic shapes of the equilibrium curves. This is what determines the number of stages, and hence the number of trays needed for a separation. Although column designs are often proprietary, the classical method of McCabe-Thiele for binary columns is instructive on the principles of design. 

SCALE-UP. The width of the mass-transfer zone depends on the mass-transfer rate, the flow rate, and the shape of the equilibrium curve. Methods of predicting the concentration profiles and zone width have been published, but lengthy computations are often required, and the results may be inaccurate because of uncertainties in the mass-transfer correlations. Usually adsorbers are scaled up from laboratory tests in a small-diameter bed, and the large unit is designed for the same particle size and superficial velocity. The bed length need not be the same, as shown in the next section. 

Operating Line and "Equilibrium" Curve. Both terms are of importance for the graphical solution of a separation problem, i.e., for the graphical determination of the number of stages of a cascade. This method has been developed for the design of distillation columns by MacCabe and Thiele and should be well known. For all cases, the operating line represents the mass and material balances. In distillation, the equilibrium curve represents the thermodynamical va-por/liquid equilibrium. For an ideal binary system, the equilibrium curve can be calculated from Raoult s law and the saturation-pressure curves of the pure components of the mixture. In all other cases, however, for example, for all membrane processes, the equilibrium curve does not represent a thermodynamical equilibrium at all but will represent the separation characteristics of the module or that of the stage. 

McCabe-Thiele method helps the identification of design troubles that could arrive with non-ideal mixtures when the equilibrium curve shows inflection points, as displayed in Fig. 16.2. 

To design such a process, the McCabe-Thiele method may be used to determine the number of theoretical separation stages, as examined in Sections 3.3.2-3.3.4 for distillation, absorption (gas scrubbing), and liquid-liquid-extraction. Thus, we obtain the number of theoretical extraction stages of a countercurrent extraction column based on the equilibrium curve (solubility of extract in the solvent for a given content in the solid) and the operating line. The latter depends on the extract content of the solid feed and residue, and on the in- and outlet extract concentration in the solvent The extract content of the feed is fixed, and the value of the residue is specified by the required degree of extraction. The inlet content of the extract in the solvent is also fixed, as either pure solvent is used or the value is specified by separation of the extract from the used solvent after the extraction. Therefore, the only parameter that is left is the outlet concentration of the extract in the solvent, which depends on the ratio of the solvent flow to the feed rate of the solid feedstock (mass balance). 

Jenny (Ref. 10) published a graphical method for multicomponent design calculation. A few plate-to-plate calculations are made at the top and bottom of the column and above and below the feed plate. For the section below the feed plate, a y,x diagram is made for the light key component using the calculated values to place the effective equilibrium curve for this component on the diagram. The operating line is drawn in the usual manner and the plates determined by the stepwise... 

If a gra cal method is used, the material balance establishes the operating line, and the required numbs of theoretical stages can be stepped oif b een the (iterating line and the equilibrium curve. If too many theoretical stages are indicated (i.e., more than about 3), a lower acid gas loading in the rich solution should be assumed and the design procedure repeated. 

The phase equilibrium of the binary system stearyl alcohol/C02 was measured in a high pressure view cell (own design) according to the synthetic method by Teipel et al. [6] and presented in Fig. 2. The curves represent the border between the homogeneous and two phase region above the curve a homogeneous solution is present, below two phases exist. The measurements were carried out for different concentrations of stearyl alcohol in CO2 represented by the different curves. It is seen that 2.1 wt.% of stearyl alcohol are complete soluble in SC-CO2 at 333 K and 20 MPa. 

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