$13.$ Side streams from a distillation column allow for the withdrawal of intermediate products at various points, which can affect the column's overall $\_\_\_\_\_\_,\_\_\_\_,$ and $\_\_\_\_\_\_.$

$14.$ The Gilliland correlation provides a relationship between the $\_\_\_\_\_\_$ and actual number of stages in a distillation column, aiding in the design by considering both the $\_\_\_\_$ and $\_\_\_\_\_\_$ of the separation.

$15.$ Optimum reflux ratio is a crucial design parameter that balances the capital and operating costs for a distillation column, affecting the $\_\_\_\_\_\_,\_\_\_\_,$ and overall $\_\_\_\_\_\_$ of the process.

$8.$ The Underwood equations are utilized to find the $\_\_\_\_\_\_$ for a given separation, taking into account the $\_\_\_\_$ of components and the $\_\_\_\_\_\_.$