Thus, the addition of two phases A and B is shown on the diagram by point C on the straight line joining the two phases, whilst the difference (A — B) is found by a point C on the extension of the line AB. If, as shown in Figure 11.24, a phase represented by C in the region between the dew-point and boiling-point curves is considered, then this phase will divide into two phases A and B at the ends of a tie line through the point C, so that:
mA CB mB CA
The H — x chart, therefore, enables the effect of adding two phases, with or without the addition of heat, to be determined geometrically. The diagram may be drawn for unit mass or for one mole of material, although as a constant molar reflux does not now apply, it is more convenient to use unit mass as the basis. Thus, working with unit mass of product, the mass of the individual streams as proportions of the product are calculated.
Figure 11.26 represents a continuous distillation unit operating with a feed F of composition xf, and giving a top product D of composition xd and a bottom product W of composition xw. In this analysis, the quantities in the streams V of rising vapour and L of reflux are given in mass units, such as kg/s, and the composition of the streams as mass fractions, x referring to the liquid and y to the vapour streams as usual.
The plates are numbered from the bottom upwards, subscript n indicating the rectifying and m the stripping section.
HV and HL represent the enthalpy per unit mass of a vapour and liquid stream respectively.
Qc is the heat removed in the condenser. In this case no cooling of product is considered.
Qb is the heat added in the boiler.
The following relationships are then obtained by taking material and heat balances:
Vnjn = Ln+1Xn+1 + Dxd or: Vnyn - Ln+1Xn+1 = DXd (11.78)
VnHnV = Ln+1HL+1 + DH} + Qc or: VnHnV - Ln+1HL+1 = DHdL + Qc (11.79)
Putting Hd = HL + QC/D, then equation 11.79 may be written as:
From equations 11.77 and 11.78:
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