This app accompanies the paper in The Journal of Physical Chemistry B, Seishi Shimizu and Steven Abbott, How Entrainers Enhance Solubility in Supercritical Carbon Dioxide, J. Phys. Chem. B, 2016, 120, 3713–3723
The aim of the app is to show, from real-world data, that entrainers work in scCO2 by interacting with the solute. This might sound obvious, but there have been decades of confusing ideas based on the entrainer affecting the scCO2 density and/or on the entrainer self-associating. With KB it is easy to show that both alternative explanations are wrong. So if you want a good entrainer, just make sure that it likes to associate with the solute. It's as easy as that.
Because the app uses experimental datasets, you don't have to "do" anything. Just look at the data, the graphs, and the calculated values to start making sense of a complex system, using the Example combobox to choose your system.
There has been much confusion as to the true mechanism of how relatively low levels of small molecules such as methanol or acetone ("entrainers") can give a large increase of solubility in scCO2. Some have said that it is due to formation of entrainer clusters. Others have said that it is due to an increase in density of the scCO2 produced by the entrainer. Others have said that it is due to entrainer/solute interactions.
This app takes real experimental data and, via KB, shows unambiguously that the effect is due to entrainer/solute interactions, indicated by a large Gu2 where u is solute and 2 is entrainer. Close examination shows that entrainer self-association decreases solubilization. The density hypothesis is easily dismissed simply by looking at the data columns. For example at 350 Bar the density of the system without entrainer is 0.929 and the solubility is 0.31% but at 120Bar the density with entrainer is 0.789 yet the solubility is 0.73%.
Given some basic experimental inputs of densities and solubilities at a given temperature with different pressures (the combobox allows you to load datasets from a variety of solutes and entrainers and there is an option to load your own datasets) it is possible to calculate the key KB parameters for the scCO2 (1), the entrainer (2) and the solute (u). Unless you have accurate experimental data, some assumptions have to be made about partial molar volumes V1, V2 and the NRTL parameters τ12, τ21 and σ (usually assumed to be 0.3) but you will find that any reasonable assumption for these values does not alter the overall conclusion. The partial molar volume of the solute, Vu is calculated from the experimental data. The f value in the table is the "enhancement ratio" of solubility with and without the entrainer.
As noted above, the numbering convention is 1=CO2, 2=Entrainer, u=Solute.
The Inputs are the working pressure (covering a range from above Pc), temperature (covering a range from above Tc), the mole fraction of entrainer expressed (for convenience) as %, your estimate of the partial MVols of CO2 (see below) and the entrainer, the MWt of the entrainer and the solute, and the NRTL inputs described above. Some suggested NRTL values are provided in the combobox, but NRTL values pairs vary considerably between different data sources so you may choose to use different values.
The Outputs are the key KB ratio that describes the solubilisation (SolGrad), along with the top term (SoluteGs) on its own and the bottom term (EntrainerGs) on its own:
SolGrad = (Gu2-Gu1)/(1+c2(G22-G12)) = SoluteGs/EntrainerGs
Here c2 is the molar concentration of the entrainer. For convenience both c1 and c2 are calculated from the input x2.
The entrainer effect is mostly about Gu2 which, for all reasonable inputs stands out as the only large value. Gu1 describes the solute's interaction with the CO2. If this were large then there would be no need for an entrainer. So we want big Gu1, but to get a boost from the entrainer requires an even larger Gu2.
We have insufficient information from these inputs to calculate G22 and G12 separately, but it is clear that any self-aggregation of the entrainer (a large G22) leads to a reduction in the entrainer effect (because it causes a larger EntrainerGs value), for the obvious reason that self-associating molecules are not associating with the solute.
Finally, the Span and Wagner EoS is used to calculate the density of CO2 at the given P and T from which the MVol is calculated which can be a good approximation for V1. An approximation is good enough because errors in V1 make no significant difference to the overall picture. Similarly, errors in the estimate of the entrainer's MVol, V2, make very little difference. The partial MVol of the solute, Vu is required for the calculation of the Gij values and in turn calculated from the input data.
Purists will know of the RTkτ isothermal compressibility term which is generally neglected in KB calculations. The values shown are calculated from the EoS and clearly justify this assumption. The code used is translated (with kind permission) from the Fortran code downloaded from the Supplementary Information to Brian J.O.L. McPherson, Weon Shik Han, Barret S. Cole, Two equations of state assembled for basic analysis of multiphase CO2 flow and in deep sedimentary basin conditions, Computers & Geosciences 34 (2008) 427–444.
For those who would prefer to load/edit their own datasets, a number of data files can be downloaded as scCO2DataFiles.zip, unzipped into a convenient folder then loaded using the file button. Each file contains the reference to the source of the data. Users can create their own data files as simple tab- or comma-separated files containing rows with the 5 inputs for the table: Pressure, Density, Solubility, Density, Solubility where the first pair are pure CO2 and the second pair are with the entrainer. An optional line has the mole fraction %, MWt of entrainer and solute and the temperature. Blank lines, header text etc. are ignored.
This methodology for understanding the effects of scCO2 entrainers was devised by Dr Seishi Shimizu at U. York.