Bubble and Dew Point Methods

Introduction

Bubble and dew points are often of interest to process engineers for designing process equipment, and appear in some calculations of other thermodynamic properties. Whilst calculation of the saturation pressure for single components is relatively simple, calculating the bubble and dew points of mixtures is more challenging due to the non-linear nature of the equations.

The IDAES Generic Property Package Framework has a number of prebuilt methods for calculating the bubble and dew points of mixtures which are listed below.

Ideal Assumptions

In the case where ideal behavior can be assumed, i.e. Raoult’s Law holds, the bubble and dew points can be calculated directly from the saturation pressure using the following equations.

Ideal Bubble Pressure

This method is implemented as bubble_press_ideal.

\[P_{bub} = \sum_j{x_j \times P_{sat, j}(T)}\]
\[x_j(P_{bub}) \times P_{bub} = x_j \times P_{sat, j}(T)\]

where \(P_{bub}\) is the bubble pressure of the mixture, \(P_{sat, j}(T)\) is the saturation pressure of component \(j\) at the system temperature, \(T\), \(x_j\) is the overall mixture mole fraction and \(x_j(P_{bub})\) is the mole fraction of the vapor phase at the bubble pressure.

Ideal Bubble Temperature

This method is implemented as bubble_temp_ideal.

\[\sum_j{\left(x_j \times P_{sat, j}(T_{bub})\right)} - P = 0\]
\[x_j(T_{bub}) \times P = x_j \times P_{sat, j}(T_{bub})\]

where \(P\) is the system pressure, \(P_{sat, j}(T_{bub})\) is the saturation pressure of component \(j\) at the bubble temperature, \(T_{bub}\), \(x_j\) is the overall mixture mole fraction and \(x_j(T_{bub})\) is the mole fraction of the vapor phase at the bubble temperature.

Ideal Dew Pressure

This method is implemented as dew_press_ideal.

\[0 = 1 - P_{dew} \times \sum_j{x_j \times P_{sat, j}(T)}\]
\[x_j(P_{dew}) \times P_{sat, j}(T) = x_j \times P_{dew}\]

where \(P_{dew}\) is the dew pressure of the mixture, \(P_{sat, j}(T)\) is the saturation pressure of component \(j\) at the system temperature, \(T\), \(x_j\) is the overall mixture mole fraction and \(x_j(P_{dew})\) is the mole fraction of the liquid phase at the dew pressure.

Ideal Dew Temperature

This method is implemented as dew_temp_ideal.

\[P \times \sum_j{\left(x_j \times P_{sat, j}(T_{dew})\right)} - 1 = 0\]
\[x_j(T_{dew}) \times P_{sat, j}(T_{dew}) = x_j \times P\]

where \(P\) is the system pressure, \(P_{sat, j}(T_{dew})\) is the saturation pressure of component \(j\) at the dew temperature, \(T_{bub}\), \(x_j\) is the overall mixture mole fraction and \(y_j(T_{dew})\) is the mole fraction of the liquid phase at the dew temperature.