$17.$ The $\_\_\_\_$ correlation provides a way to estimate the $\_\_$ between the actual and minimum number of stages required for a given $\_\_$ ratio in distillation columns, helping in the $\_\_\_\_$ design.

$18.$ Determining the $\_\_\_\_$ reflux ratio is crucial for economic operation, as it represents a balance between $\_\_$ and $\_\_$ costs, impacting the $\_\_$ and $\_\_\_\_$ of the distillation operation.

$19.\_\_\_\_$ and $\_\_$ equations are essential for calculating the $\_\_$ conditions necessary for achieving a desired separation, particularly in determining the $\_\_$ reflux ratio and the $\_\_\_\_$ flow rates in the column.

$20.$ The concept of $\_\_\_\_$ in a distillation column refers to operating at a condition where no $\_\_$ is produced, allowing for the calculation of the $\_\_$ number of stages and $\_\_\_\_$ analysis of the separation process.