Effect of Tray Pressure Drop on the Trade-off between Trays and Energy

The classical trade-off between number of trays and energy consumption in distillation design is one of the fundamental concepts in chemical engineering. Conventional wisdom states that the use of more stages results in lower reflux ratios and lower reboiler duties for a specified separation. A hyperbolic relationship is expected in a plot of stages versus energy. More stages increase capital cost but reduce energy cost, so an economic optimum exists. Total annual cost, which balances capital and energy costs, is frequently used as the objective function to be minimized. This paper points out that the expected hyperbolic relationship does not apply in low-to-moderate pressure columns when the effect of tray pressure drop is included in the vapor-liquid and design equations. For a given reflux-drum pressure, adding more trays increases pressures in the lower part of the column. If the separation is favored by lower pressure, as is the case in many chemical systems, adding more trays can result in higher energy consumption because the higher pressures in the lower section of the column adversely affect relative volatilities. Two examples are presented that defy the conventional distillation wisdom of selecting a pressure that still permits the use of cooling water in the condenser in systems where decreasing temperatures increase relative volatility.