Hi, I’m Joe Covey, and I’m a product manager at Emerson Process Management, Rosemount Analytical. In this Analytic Expert post I’d like to discuss some pitfalls in linear slope temperature correction.
Electrolytic conductivity is widely used by industry to measure the total concentration of ions in a sample. Conductivity also depends on temperature, so an increase or decrease in temperature can cause a significant change in conductivity even though the ion concentration stays constant. Compensating for temperature is an important part of measuring conductivity, and all process conductivity analyzers feature user-selectable temperature correction algorithms that automatically convert measured conductivity to the value at a reference temperature, typically 25°C.
The most common temperature correction – probably suitable for about 80% of applications – is the linear slope model. This model assumes the percent difference between the conductivity at a given temperature relative to the conductivity at 25°C divided by the temperature difference is a constant. For most neutral electrolyte solutions the increase is roughly 2% per °C. Typically, the temperature coefficient is user-programmable.
The problem is that in real solutions the slope is not constant. It depends on the electrolyte, the concentration and the temperature. Thus, using a single slope under varying conditions can lead to errors. Some numbers should help illustrate the problem. This table gives the percent change in conductivity per °C for different concentrations of potassium chloride at different temperatures.
As the table shows, the temperature coefficient changes quite a bit as the temperature changes. For example, for 75 ppm potassium chloride, the temperature coefficient between 0 and 25°C is 1.81% per °C, but between 100 and 25°C, it is 2.27% per °C. The temperature coefficient also depends on concentration. Although in the present example the difference is fairly small, it would be wrong to conclude that the variability with respect to concentration is always less than the variability with respect to temperature.
Because the temperature coefficient is not constant, the typical approach is to use an average coefficient over the range of concentration and temperature the sensor will be used. One way to calculate the average is to use the least squares method to fit a straight line to the data. For potassium chloride solutions between 75 and 7500 ppm and 0 and 100°C, the least squares average temperature coefficient is 2.13% per °C. Using this value to calculate the corrected conductivity at 25°C gives the following results for 750 ppm KCl. The percent errors for the other concentrations are similar.
If the temperature correction were perfect, the corrected conductivity would be 1413 uS/cm for measurements made at all temperatures, and the percent error would be zero. Obviously, this is not the case, particularly for 0°C. At other temperatures the errors are at most a few percent, which, depending on the application, may be completely acceptable. But, the important thing to understand is that the simple linear slope correction is not perfect.