Why does the diameter of distillation column vary at different location?

A distillation column has flows of materials going up and down the plates or packing. The flow across each plate or section of packing is an essential factor in the optimization calculations and design. Diameter is one of these considerations.

Since columns have "heavies" traveling down and "lights" moving up and the division between these components may not be even, the top and bottom flows may be quite different, and the optimal column diameter must be adjusted at different locations along the length. Add to this the introduction of a feed stream at some point in the mid-column and the flows are altered again.

But why be concerned about this? Columns are often constructed of expensive alloys, glass lined, or heat treated to avoid erosion, corrosion or stress problems. Minimizing the column size minimizes the cost. Along with quality of product, cost is an optimization factor.