Viscosity Conversion for temperature (re-visited)
Viscosity Conversion for temperature (re-visited)
I was searching for something else and found the above referenced thread in which the spreadsheet RMI ASTMN D341.xls was referred to and there were a couple of queries raised that, had I been aware at the time, I would have responded to so I apologise for not doing so at the time and take this opportunity to redress the situation.
The spreadsheet itself can be found at http://www.viscoanalyser.com/page8.html
The calculations apply to viscosity values above 2cst and is applicable as defined by the standard; that is, it means it is not just for fuel oils (as the data populating the spreadsheet might imply) but for any hydrocarbons within the scope of the ASTM D341 limitations and applicability.
The answers, from my own use of it, appear indistinguishable from some proprietary calculations such as a Castrol equation (blend 42?) used for lube oils but not others; some special calculations, such as the Shell V50 equation, are only applicable under specific circumstances.
Electric Pete commented:
"I looked at jmw's spreadsheet. I don't see any calculation for the values A and B in there (it looks like they were solved in some other program for specific oils and dumped into this spreadsheet). Also he mentioned he used celsius temperature and the equation does require Kelvin ( checked and that makes a big difference). "
Just to clarify:
The spreadsheet only uses the ASTM D341 equation of temperature Vs Viscosity:
where A and B are constants and T is the temperature in degrees kelvin, Log = logarithm to base 10.
Because most people have the viscosity data with temperatures in degrees C, the data is entered in degrees C format and converted to Kelvin in the calculations.
Z can be quite complex, worst case: Z = [v +0.7 + C - D + E -F + G -H] where C to H are all exponential functions of v) but for v>2cst, ASTM D341 allows that Z =(v+0.7) where v is the kinematic viscosity. This is the value of Z used in the spreadsheet.
A and B are constants unique to the fuel.
They are calculated in the hidden sheets and using the ASTM D341 equation, not some other program and not derived from some specific oil but from the oil in question.(anyone wants to delve deeper, email via the web site and I will reply with the password which is simply to protect against inadvertent changes).
So to use the ASTM D341 expression to find the viscosity at any temperature we need to solve the equation to find the relevant values of A and B.
This can be done if we know the viscosity of the hydrocarbon at two different temperatures. e.g. 128.58cst at 40degC and 15cst at 100degC.
log.log (v + 0.7) = A-BlogT........(i)
let v = 128.58cst at 40 OC
log.log (129.28) = A-Blog(313).............(ii)
let v = 15.00 cst at 100 OC
log.log (15.70) = A-Blog(373)...............(iii)
Note that 40degC has been converted to 313degreeK in (ii)
Now subtract one from the other [(ii) - (iii)] which eliminates A, and solve for B:
substitute B in (ii) and solve for A
log.log (15.70) = A-3.24log(373).............(iv)
A = 8.41
Now we have A and B for this oil, we can find the viscosity at any other temperature:
substitute A and B in (i)
log.log (v + 0.7) = 8.41-3.24logT........(v)
and now enter the temperature of interest, e.g. 50 OC, the base temperature is 323degK, and find v:
log.log (v + 0.7) = 8.41-3.24log(323)
v = 80.0cst at 50 OC
This calculation method is one I used when developing the dual viscometer method for process viscosity measurement of the viscosity at one or more reference temperatures.
It is used for everything from crude oil pipeline blending to asphalt blending and in practise requires two process viscometers in series (in a fast sample loop) and separated by a heat exchanger so they each measure the viscosity of the flowing oil stream at two different temperatures.
Of course, this is more sophisticated and expensive than some applications warrant so I also developed the Multi-curve Referral method where a single viscometer is used.
This uses reference curves to determine the ratio of the measured viscosity to the viscosities of the reference oils (fuels) at the same temperature and then applies the same ratios to the viscosities of the reference oils at the reference temperature to find the viscosity of the measured oil at the reference temperature.
This is very good with fuels oils but cannot be used with lubes because they have variable viscosity indicies.
The assumptions that allow it to work with fuel oils also are the foundation for some other single viscosity data solutions, most particularly, for fuel oil blending.
Virtually all the available fuel blend calculators need to make use of the temperature viscosity relationship and most make the same assumption; that with sufficient data on each grade of fuel there is a mean value for the viscosity index that will give good results each time.
Shell's BCALC.exe (which is downloadable from the web site, the link is in one of these threads somewhere) does exactly that. But you may find the DNV program BunkerMaster 2 is more useful since it also allows you to calculate the viscosity index.
That brings us back to the original thread; can you calculate the viscosity at any temperature if you know the viscosity index and the answer is yes, but only if you know the viscosity at one other temperature. Otherwise you need the viscosity at two temperatures.
Incidentally, in ASTM D341 it specifies that log = logarithm to base 10. It also includes the calculation of viscosity index in appendix XI.