A new project landed on my desk involving a tank, pump, agitator, heat exchanger and feed system for sodium thiosulfate (Na2S2O3). As usual, the vendor of the compound provided absolutely no physical properties. So, I had to scrounge for physical properties for this aqueous salt solution.
Unfortunately, a lack of such data isn’t unusual. I’m amazed at the dearth of available physical property data if your needs go beyond simple hydrocarbons.
When you face such a situation, your goal should be to find a property-versus-temperature regression equation or even one that includes concentration. That’s the only way you can optimize equipment without wasting a lot of time generating data on physical properties.
Like many engineers, I’ve got spreadsheets for physical properties of common pure organic compounds. Obviously, this didn’t help for the aqueous solution.
Here’s how I solved the problem. (If you have access to a corporate library with an extensive collection of journals and references, stop right here — I’m wasting your time.)
To size the tank, pump and heat exchanger, I needed density (specific gravity), viscosity, heat capacity and thermal conductivity. You likely will have to make a tradeoff between accuracy and consistency of the data. An engineering calculation within 10–15% generally is good enough; finding one accurate within 5% may be difficult and require a lot of time — and may not provide robust results in the target parameters you’re working with: temperature, pressure, concentration, etc.
The best approach is to spend some spare time scouring the Internet, text books, brochures, design guides and such for methods and then adapting them to spreadsheets. You’ll want to test the data again and again for limitations.
I found a 2007 article “Model for Calculation of Viscosity of Aqueous Solutions” by Marc Laliberte in the Journal of Chemical Engineering Data and a table of concentration versus specific gravity for Na2S2O3in the 8th edition of “Perry’s Chemical Engineers’ Handbook.” I discovered the 1992 book “Properties of Aqueous Solutions of Electrolytes” by Ivan Zaytsev and Georgiĭ Aseyev contains an equation for thermal conductivity of salt solutions as well as values for a parameter used in that equation for scores of salts.
The specific gravity (SG) was the greatest challenge. I had to hand-fit a curve to approximate the temperature effect. I was looking for an equation in the form SG = A (T, oF) + B (concentration, wt-%) + C. I had SG at a range of concentrations at 20°C (68°F) from Perry’s but only was interested in one concentration (30%) at a higher temperature. Fortunately, SG is a nearly linear equation; so, the approximation works if you can find a similar salt, in my case — Na2SO4. You can access some specific gravities here.
The viscosity method presented in the J. Chem. Eng. Data article provided a good starting point. I modified it because I had a better equation for water. This model worked well for the salts covered in that article. Again, as with density, if you can’t get an exact match, use a salt similar to the one you’re working with.
You can estimate heat capacity (Cp) by a method proposed by Vosseller in 1973: Cpmix = 1 – 0.7×Xi, where Xi is the fraction of salt. See: https://bit.ly/3fpwZsi.
If you need the Cp at a range of temperatures and concentrations, refer to the Dimoplan method described here. It’s a little complicated, involving a look-up table. For 30% Na2S2O3 with a molecular weight of 158.1, this method gives a Cp at 100°F of 0.764 BTU/lb.-°F. In comparison, the fixed Cp via the Vosseller method is 0.79 BTU/lb-°F.
For thermal conductivity of aqueous salt solutions, it’s best to refer to the Zaytsev and Aseyev book.
As with SG, you can approximate physical properties in the same solvent by finding data on a chemically similar compound. Avoid mixing cations, if possible; sodium is closer to potassium than calcium. In theory, charge affects the size of the cation or anion in a polar solvent like water.
Another useful technique is what I call a pseudo-spline curve fitting. This method involves matching the best curve for a property over a specified range. It works well with AND and OR gates nested in a spreadsheet. Try to avoid extended polynomials and multi-linear equations. If you must use them, be cautious.