# Summary

Tray efficiency measures the performance of a distillation tray or trays against the maximum theoretical performance. Similarly, a concept called Height Equivalent to Theoretical Plate (HETP) is used to measure the performance in a packed column. This article describes methods of quantifying tray efficiency in distillation tray analysis.

# Definitions

: | Height of packing | |

: | Height equivalent to theoretical plate | |

: | Actual number of trays | |

: | Theoretical minimum number of trays | |

: | Mole fraction | |

: | Mole fraction of vapor phase | |

: | Relative volatility | |

: | Tray efficiency, overall | |

: | Viscosity |

Subscripts and superscripts:

: | Actual | |

: | Baur efficiency | |

: | Feed | |

: | Component 'i' | |

: | Tray 'j' | |

: | Murphree efficiency | |

: | Overall | |

: | Theoretical | |

: | Theoretical or Equilibrium |

# Introduction

In a distillation column liquid and vapor are contacted while passing over and through trays (sometimes referred to as plates). In a theoretical analysis of the column performance such as the McCabe-Thiele method, the trays are assumed to operate at maximum efficiency. This means that the vapor and liquid phases are assumed to reach equilibrium as they interact over the plate. However, in practice there are many reasons why the vapor and liquid phases will not reach equilibrium as they pass.

The concept of tray efficiency quantifies the difference between the maximum theoretical or equilibrium performance and the actual performance achieved. There are many reasons while equilibrium performance is not achieved with the two common reasons being either insufficient contact time and/or insufficient mixing.

# Types of Tray Efficiency

There are several different measures of tray efficiency with each measure highlighting different performance issues. The three main tray efficiency metrics are overall tray efficiency, Murphree Vapor efficiency and Baur Efficiency which are described below.

## Overall Tray Efficiency

The overall tray efficiency describes the ratio of the number of theoretical trays to the actual number of trays required for an entire column:

Overall tray efficiency assumes that all trays have the same performance. This makes it a simple metric from which the total number of trays required can be determined for a a given distillation column. However in practice not all trays will share the same efficiency.

## Murphree Vapor Efficiency

The Murphree vapor efficiency measures performance of a single tray by considering the composition of the vapor phase as it enters and leaves a given tray. It is the ratio of the difference between the actual start and finish composition for a component, to the difference between the start and theoretical finish composition for the component as shown below.

## Baur Efficiency

The Baur efficiency provides a method of combining the Murphree efficiency for each component into a single efficiency measure for a tray. The Baur efficiency is also general enough that it may be used for packed beds.

# Estimation of Tray Efficiency

Estimation of tray efficiency is critical to ensuring that the performance of a column is adequate to perform its intended separation before it is built and commissioned. These days tray efficiency is mostly performed by specialist process modelling software provided by distillation equipment vendors (e.g. tray caps suppliers). However, there are a few empirical relationships that can be used to provide a rough estimate of tray efficiency in certain circumstances.

## Drickamer-Bradford Correlation

The Drickamaer-Bradford correlation is a simple empirical relationship that was developed for use with hydrocarbon mixtures and gives an estimation of the overall efficiency based on the mole fraction and viscosity of the liquid for each component.

Where,

is the mole fraction in the feed,

is the viscosity at the mean column temperature,

is the viscosity of water at 293K.

## O'Connel Correlation

The O'Connel correlation is another simple empirical relationship that was developed for bubble cap trays but can be conservatively applied to sieve and valve trays. The O'Connel correlation relates the overall tray efficiency of the column to the relative volatility of the key components and the feed viscosity. It was originally a graphical method based on a plot of data from operating columns, however relationships have been made based on the data and one is included here.

The feed viscosity (in cP) and relative volatility should be determined at the arithmetic mean of the top and bottom temperatures.

## Computation Methods

While the methods outlined above provide suitable methods for calculating 'ball park' tray efficiencies, vendor developed computational models should be utilised for detailed distillation column design. These models account for the gas-liquid phase contact dynamics deriving from the specific tray layout and design (sieve, bubble cap, valve etc).

# Packed Beds and Columns

For packed beds in distillation or absorption columns a similar concept exists called Height Equivalent to Theoretical Plate (HETP). The HETP is the height of packing material that is required to achieve the same separation as one theoretical tray as defined above. It can be used to calculate the amount of packing required to achieve the same separation as a known number of theoretical trays.

The HETP is a complex relationship between the physical properties of the fluids and the specifics of the separation being undertaken. General predicative correlations are not suitably accurate to be provided here. Accurate correlations are limited to specific applications, and it is best left to packing vendors to advise on performance.