CHAPTER
9
Following standard chemical engineering nomenclature, the concentration of the component of interest in the lighter stream, that is the stream with the lower density, is denoted by y. For example, in a gas absorption system, the light stream would be the gas; in a distillation column, it would be the vapour stream; in a liquidextraction system, it would be the liquid overflow. The concentration of the component in the heavier stream is denoted by x. Thus we have two streams; in one the concentration of the component is y and in the other, the heavier stream, it is x. For a given system, it is often convenient to plot corresponding (equilibrium) values of y against x, in an equilibrium diagram. 
In the simple case of multistage oil extraction with a solvent, equilibrium is generally attained in each stage. The concentration of the oil is the same in the liquid solution spilling over or draining off in the overflow as it is in the liquid in the underflow containing the solids, so that in this case y = x and the equilibrium/concentration diagram is a straight line. In gas absorption, such relationships as Henry's Law relate the concentration in the light gas phase to that in the heavy liquid phase and so enable the equilibrium diagram to be plotted. In crystallization, the equilibrium concentration corresponds to the solubility of the solute at the particular temperature. Across a membrane there is some equilibrium distribution of the particular component of interest. If the concentration in one stream is known, the equilibrium diagram allows us to read off the corresponding concentration in the other stream if equilibrium has been attained. The attainment of equilibrium takes time and this has to be taken into account when considering contact stages. The usual type of rate equation applies, in which the rate is given by the driving force divided by a resistance term. The driving force is the extent of the departure from equilibrium and generally is measured by concentration differences. Resistances have been classified in different ways but they are generally assumed to be concentrated at the phase boundary.
Stage contact systems in which equilibrium has not been attained are beyond
the scope of this book. In many practical cases, allowance can be made
for nonattained equilibrium by assuming an efficiency for each stage,
in effect a percentage of equilibrium actually attained.
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