1. Temperature compensated viscosity
Viscosity, defined as the ratio of shear stress to shear rate, is an important fluid property that has an increasing presence in monitoring processes and control systems.
Viscosity is affected by temperature and pressure. For most liquids, the viscosity decreases with temperature, whereas it increases for gasses. An increase in pressure typically leads to an increase of viscosity, which is only relevant for high pressure applications.
In most cases, we want to monitor the fluid viscosity at a constant reference temperature. If the process temperature isn’t constant, an additional source of error to the control system is added. To avoid the temperature dependence on the fluid’s viscosity and truly monitor its consistency, the temperature compensated viscosity is introduced.
To compensate for temperature effects, we need a mathematical model that can be based on Exponential, Polynomial or Arrhenius functions.
2. Math model
The SRV and SME are together a powerful tool in the measurement of inline viscosity and temperature. With the use of mathematical models, temperature compensated measurements can be obtained.
Below is the mathematical formula for the viscosity polynomial model used in the RCP (Rheonics software).
Equation 1: Viscosity Polynomial Model.
ncomp - Compensated viscosity, calculated by the SME.
nL - Live viscosity, read by the SME.
X1 and X2 - Coefficients, added by user.
T - Temperature, read by the SME.
Tref - Reference temperature, is the temperature around which the SME will compensate the readings. This is defined and should be added by the user.
Along with the reference temperature, the reference viscosity (viscosity at Tref) is also of relevance for the calculations explained below.
3. Checking the data
User needs to take viscosity readings at normal operation temperature range, then go with higher and lower temperatures. Once enough data is obtained (to see the polynomial behavior), user should define the reference temperature.
For this example, the blue point (20°C) is used as typical set-temperature of the process line. The additional measurements should extend a bit beyond the expected temperature range.
The following steps outline the correct procedure for data analysis:
3.1. Select the reference temperature and viscosity from data obtained in tests. Here, reference temperature and viscosity are highlighted in blue in the next Table, we want to create a correlation at 20°C where we expect a viscosity of 1mPa.s.
|Temperature (°C)||Viscosity (mPa.s)|
3.2. Plot data points of Viscosity vs Temperature to study the behavior of the data. In this scenario, the data behavior can be represented by a second order polynomial curve.
3.3. Calculate the relation between compensated or reference viscosity and the measured viscosity by dividing the two.
Table 2. Compensated viscosity calculation table.
3.4. Calculate the difference between measured and reference temperature by subtracting them.
Table 3. Variation to the reference temperature.
3.5. Plot the V’ (Comp. Visco/Visco @20°) vs T' (T-Tref) and use a second order polynomial trendline to find X1 and X2 values or make a regression analysis to find the coefficients.
Table 4. Datapoints for viscosity and temperature referenced to known values
A graph tool is used to create a trendline with the points obtained, it can also show the trendline equation.
Figure 2: Plot chart V' vs T'.
Equation on Figure 2 is compared against Equation 1, accepting the value 1.0302 rounded as 1.
We have that:
X1=0.0274 and X2=0.0002.
Tref = 20°C
With all the input parameters set on the SME through the RCP software, the temperature compensated viscosity will look like next graph in Figure 3.
Figure 3. Expected results when applying the mathematical model.
4. How to load models into the SME?
The calculation tab on RCP allows configuring the SME to run mathematical models for viscosity, density, and concentration. Expert mode needs to be enabled for this.
Figure 4. Calculation tab for the exponential model of viscosity.
The following steps are needed to load the models into the SME:
In the dropdown list “Select Measurement to Apply Model” viscosity should be as default parameter. If not, select it from the options in the list.
In “Select Model from list” select the model you would like to use for the specific parameter. When you select the model, you will get more information about the specific equation used and the coefficients you will need to apply to that model. Select “Viscosity Polynomial model”
Input X1 calculated coefficient. For this example it has a value of 0.0247.
Input X2 calculated coefficient. For this example it has a value of 0.0002.
Input reference temperature used to find the coefficients models. In this example is 20°C.
Click “Upload Model” to load the model settings into SME. The button should turn GREEN for a couple of seconds if the action was successful or turn RED if the operation was unsuccesful. This action will refresh the values for the uncompensated and compensated indicators. Here you can verify if the model is calculating the expected values. If not, you can correct and repeat the process.
Click “Load Configuration” to update the display and channel configurations in SME.
4.1. LCD Display
For the SME-TRD, the compensated viscosity values can be shown on the display. Select the line to display the parameter:
Figure 5. Selecting read line for LCD display.
Changes can be verified on the “Communication” Tab.
Figure 6. The communication tab has loaded parameter.
Figure 7. Parameters loaded into the SMET-TRD.