I have come across a couple of instances recently where rheological measurements on cement slurries did not appear to follow the correct procedure. Surprisingly, one of these instances was in a peer reviewed journal article. The other was a technical data sheet available on a company website.
In both instances the rheological measurements included results at a viscometer rotational speed of 600 revolutions per minute (rpm). The highest recommended rotational speed in API RP 10B2 is 300 rpm, although readings at speeds > 300 rpm may be taken but after all other readings, including gel strength.
The limit on the maximum rotational speed while making rheological measurements on cement slurries is based on comparative testing between multiple laboratories (Beirute, R.M.: “API Revises Procedures to Measure Cement Slurry Rheology,” Oil & Gas Journal, (September 1, 1986) 84, No. 38, 36–38). The study found that there was better repeatability of measurements if the upper shear rate was limited to 511 s^{1}. Note, that at that time there was only one bob and rotor geometry (R1B1) generally used, so 511 s^{1} corresponded to 300 rpm.
In the documents there was also no indication that the results presented were an average of readings taken ramping up and ramping down in shear rate, as required by API RP10B2. Taking ramp up and ramp down readings can help indicate if the fluid has time dependent (thixotropic) properties or if the fluid is unstable.
A possible presentation of rheological measurements is shown below. It follows the guidelines in API RP10B2, 2^{nd} edition, April 2013.

Reading 

Rotational Speed (rpm) 
Rampup 
Rampdown 
Ratio 
Average 
3 
8 
5 
1.6 
6.5 
6 
9 
7 
1.29 
8 
30 
18 
16 
1.13 
17 
60 
27 
26 
1.04 
26.5 
100 
39 
39 
1 
39 
200 
69 
70 
0.99 
69.5 
300 
97 
– 
– 
97 
Rheometer configuration 
R1B1F1 

Conditioning 
Atmospheric pressure, 30 minutes at 50°C 

Initial slurry temperature 
50°C 

Final slurry temperature 
48°C 
In this example, the ramp up and ramp down readings are close (<5 units) so there is no indication of sedimentation or gelation. Note that these observations are not a substitute for static gel strength measurements or sedimentation tests.
The documents both fitted the data with the Bingham model:
τ = τ_{y }+ μ_{p}γ̇
Where τ is the shear stress at a shear rate γ̇, τ_{y} is the Bingham yield stress and μ_{p} is the plastic viscosity. When the shear stress, τ, is less than the Bingham yield stress there is no flow. Bingham plastic fluids are therefore shear thinning once the shear stress is greater than the yield stress.
Even though curve fitting is easy to do with spreadsheets there is still a tendency for people to use just two data points to fit the data, which was the case with the peer reviewed journal article (using 600 and 300 rpm data points). API RP 10B2 clearly states that 2point calculations should not be used.
As an example, I will use the average data points from the above table – I have converted the rpm and reading to shear rate (s^{1}) and shear stress (Pa) for the following analysis. Data fitting for the Bingham model has been done using the built in Excel linear regression functions.
The results for the fit are shown in Figure 1.
The curve fit using just the two data points at the highest shear rates does not match the data over the entire range and gives a yield stress value of 7.6 Pa. The curve fit using all the data points give a much better fit of the data over the entire range. The yield stress value is 3.7 Pa. The reading at 5.1 s^{1} (3 rpm) is 3.3 Pa.
In most cases fitting the data using all the data points will give a higher plastic viscosity and lower yield stress than using a twopoint data fit at high shear rates. Exceptions will be fluids exhibiting dilatancy (shear thickening).
The differences between the fits and the actual data can be seen more clearly on a loglog (Figure 2). The fit using all 7 data points overestimates the low shear rate viscosity but is much closer to the data than the twopoint fit.
Plotting the data on a loglog plot also shows that there are no signs of slippage at the wall, as the data points follow a smooth curve.
The HerschelBulkley model is a threeparameter model that combines power law and Bingham plastic behaviour.
τ = τ_{y }+ kγ̇^{n}
Where k is the consistency index, and n is the power law index.
The HerschelBulkley model simplifies to the Bingham model (if n=1) and to the power law model with τ_{y}=0.
Microsoft Excel can also be used to fit the HerschelBulkley model to a set of data as follows:
The best fit to the data above has:
τ_{y}=2.6 Pa, n=0.897, k=0.175 Pa.s^{n}
The fit is plotted in Figure 3:
There is a web application from Exovo that fits HerschelBulkley, Bingham and Power law models to rheological data using an accurate gap flow solution with end effect corrections. You may need to use the browser in full screen mode to activate the results button (observed with Edge and Chrome).
There is a more detailed discussion of fitting rheological models to data of drilling and cementing fluids in:
Hans Joakim Skadsem and Arild Saasen, “Concentric cylinder viscometer flows of HerschelBulkley fluids”, Appl. Rheol. 2019; 29 (1):173–181.
This is an open access paper available at: https://doi.org/10.1515/arh20190001