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.
Hi, I’m Michael Gaura from Rosemount Analytical and I’d like to share some interesting behind-the-scenes information with you.
Did you know that almost every Rosemount Analytical gas chromatograph goes into a 24-hour environmental chamber test? In the chamber, the GC must operate to spec while being effectively taken from the arctic to the desert. The temperatures in the chamber cycle between zero and 130 degrees F for a minimum of 24 hours. The data from the analyzer is then evaluated to ensure peak performance for each system. These product testing procedures are much stricter than the industry standard for analytical measurement products. As you can imagine, these tests cost Emerson time and money and the service is provided to customers absolutely free. Why do we do it?
Perhaps you can guess that these environmental tests are part of the secret behind making Emerson gas chromatographs unique in the market. Unlike most GCs, Rosemount Analytical systems don’t have to be placed in an environmentally-controlled shelter when they are used in the field. Also, if they are in a shelter and the environmental control system fails, the Emerson GC will just keep on ticking. This is because Emerson GCs have a robust, field-hardened, single casing design that allows them to operate to spec across the widest range of temperatures in the industry — from -20 to 60 degrees C (-4 to 140 degrees F). The environmental chamber test is designed to ensure this peak performance.
This capability is really significant because analyzer shelters can be one of the largest expenses associated with any analytical solution. Doing away with the need for a shelter can save customers hundreds-of-thousands of dollars upfront, by reducing the costs associated with engineering, shipping, construction, utilities, wiring, safety systems and much more. The ability of a GC to operate in a field environment without a shelter isn’t an industry standard, it’s an Emerson standard. We offer our customers the flexibility to place their GCs virtually anywhere they need them, easily and cost-effectively. We assure this capability with special environmental testing that challenges the product far beyond most applications.
Do you have a really tough environment for your GC? Our environmental testing engineers say “Bring it on.”