(125d) Impact of Surface Tension in Distillation. Part I: Introduction to Modern Surface Tension Models for Mixtures

Surface tension is critical in determining bubble and droplet dynamics in trayed and packed distillation columns. Fair’s well known correlation for flooding in tray columns employs a relative surface tension raised to the power of 0.2 with the reference value of the surface tension equal to 20 dynes/cm. The Billet and Schultes model for packed column performance sets a lower limit of 30 dynes/cm. The low (or non-existent) power dependency meant that engineers did not worry much about errors of a few dyne/cm.

In some high-pressure columns (demethanizers and nitrogen rejection units come to mind) the surface tension may become quite low, close to or even lower than 1 dyne/cm. When the surface tension is that low, errors of a few dynes/cm can easily alter the column diameter (or height) by a significant amount. Is the actual surface tension really that low? The answer could well be yes; we do know that the surface tension reaches zero at the critical point.

In simulation and design of these types of columns engineers almost inevitably resort to estimating the surface tension using a model that is available in the process simulation tool in use. Since surface tension is, arguably, the least well predicted physical property, often it is estimated by means of the simplest mixture methods available. In many cases the only choice of estimation model is a mole fraction weighted average of the pure component surface tensions. Sometimes, this is the worst possible model, but many of the alternatives are not much better (and can be worse in some circumstances). The mole fraction average is particularly problematic when one or more of the components is present at conditions above their own individual critical points (but the mixture as a whole is well below its own).

What is needed is a high fidelity model for mixture surface tensions that:

1. Retains accuracy at low surface tensions (close to mixture critical points),
2. Can handle mixtures in which some components are above their own critical points,
3. Does not cause column performance models (mass-transfer coefficients, interfacial areas, and pressure drop) to behave inappropriately when the surface tension is low (while not employing arbitrary cut-off values of the surface tension), and
4. Behaves reliably and efficiently when used in a column design simulation.

Models that claim to address at least some of these issues now exist; they come in three classes:

1. Density Gradient Theory (DGT)
2. Cubic models (analogous to cubic equations of state)
3. The Shardt-Elliot type of model

As far as we know, none of these models has yet been implemented in process design software.

Our purpose in Part I is to provide for the distillation community an introduction to these new classes of model and to provide an assessment, to the extent possible, of their respective abilities to handle the first two of the issues identified above (predict low surface tension with appropriate accuracy and to handle mixtures with supercritical components).