Apr-2012

Comparison of ideal stage and mass transfer models for separation processes

The design and optimisation of separation processes is carried out using process simulators that utilise various calculation approaches. Two techniques that are widely used for modelling distillation are the ideal stage model and the mass transfer model.

Carl Fitz, S-Con Inc, Christopher Skowlund, Michael Hlavinka and Mauricio Lopez
Bryan Research & Engineering, Inc

Article Summary

The ideal stage model is relatively simple, but requires an overall efficiency for trays or a height equivalent of a theoretical stage for packing. The mass transfer model is significantly more computationally intensive and relies heavily on empirical equations for properties such as diffusivity, mass transfer coefficients and interfacial area.

The primary emphasis of this article will be on the application and comparison of the ideal stage and mass transfer models to systems with and without chemical reactions such as amine treating, glycol dehydration, reactive distillation and hydrocarbon separation columns. The advantages and disadvantages of each method will be discussed along with recommended guidelines for their application and use.

Introduction
Distillation plays an important role in many industrial chemical plants, but for most engineers the understanding of the complex phenomena occurring in a distillation column tends to be limited to the simplest of models. One reason for this is that most undergraduate and graduate programmes tend to gloss over these complexities due to the time it would require to thoroughly cover the topic. Another reason is that the simple models often tend to provide reasonably accurate results for relatively little work.

Over the past 30 years, advances in the computing power available to most engineers has allowed more complex distillation models to be implemented in commercial process simulation software. A similar increase in the utilisation of distillation columns to reliably perform separations that also incorporate ionic and molecular reactions has required the engineer to demand more of their simulation software. Although most engineers are not required to understand the intricacies of the mathematical models used to solve the most complex columns, it is important to understand the differences between the simpler ideal stage models and the more detailed mass transfer models or non-equilibrium stage models. Due to limitations inherent in the assumptions used to derive each model and the data required to accurately perform the calculations, neither model can be assumed to work best in all situations. But, with suitable experience and guidance, engineers can now be expected to provide reliable designs for a wider range of columns than in the past.

Obviously, the main disadvantage of the ideal stage approach is just that — the use of ideal stages to model real trays or packing depths. However, for most processes encountered in gas processing and other industries, the overall efficiencies are well established for properly operating conditions of the column. For systems that are unavailable, similar systems often exist to allow for efficiency estimation. If not, the mass transfer approach is available as an option.

The primary feature with the mass transfer approach to the end user is the ability to model a column with the actual number of trays in the unit or the actual depth of packing. However, as will be discussed later, there are still several assumptions that are made in this approach that can have a significant impact on results. Two that are worth mentioning at this point include the mixing model for trayed columns and the discretisation of the packing depth for packed towers. If the simulator allows the user to select from various alternatives for these parameters, knowing a priori the correct selection is problematic. If the values are fixed within the simulator, how does the user know for sure that proper values are selected for a given system? Further, the prediction of multicomponent mass transfer coefficients is of questionable accuracy. These facts lead us to recommend that columns modelled with the mass transfer approach be checked against an ideal stage model with an expected efficiency until you have sufficient experience with the particular application.

All simulation results presented in this article were made using the upcoming major release of BR&E ProMax1, which will be known as ProMax 4.0. ProMax offers the ability to use either the ideal stage or the mass transfer approach at the discretion of the user. These approaches can be applied to a wide variety of processes, with and without reactions, as will be seen in the examples that are presented later.

Model background
In this section, the basic concepts behind the ideal stage model and the mass transfer model are presented. In addition, some of the principal assumptions in each approach are given.

Ideal stage models
Chemical engineers have been modelling distillation columns using the ideal stage model for over a century.2 The ideal stage model is easy to use as a detailed equipment design is not required. The ideal stage model requires a minimum amount of data-only equilibrium relationships and enthalpy data for the heat balance. These are solved along with a material balance for each component and the requirement that the mole fractions in each phase sum to one. These are often referred to as the MESH (Mass, Equilibrium, Summation and Heat) equations. A graphical technique that solves the material and energy balance, assuming equilibrium is the Ponchon-Savarit3,4 diagram. If constant molar overflow is assumed, enthalpy data are not required. The popular McCabe-Thiele5 graphical method is an example of this approach. The ideal stage model is the fastest way to make stage-to-stage calculations. However, convergence becomes more difficult as the equilibrium and enthalpy data become more dependent on composition, temperature or pressure.

The assumptions of the ideal stage approach are that the vapour and liquid are both perfectly mixed so that the vapour and liquid leaving a stage are at the same composition as the material on the stage, and that thermodynamic equilibrium is obtained on each stage. Columns often do not operate under these conditions. The equilibrium assumption also means liquid and vapour leaving a stage are at the same temperature — a reasonable approximation for many industrial columns. The equilibrium assumption also means that the mole fractions of each component leaving a stage are related by the well-known expression: