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Temperature Compensation Algorithms for Conductivity

Pete Anson here. In today’s blog, I’m discussing temperature correction in conductivity measurements. A few customers have inquired about this topic, so thought it might be a useful to discuss. Conductivity depends on both ion concentration and temperature. To reduce the influence of temperature on the measurement, common practice is to measure the raw conductivity and temperature and calculate what the conductivity would be at a reference temperature, typically 25°C. Clearly, the calculation requires making some assumption about the liquid being measured.

Below, I describe the temperature compensation algorithms commonly available in process conductivity analyzers. I also give examples where the correction is appropriate and some of the pitfalls associated with each algorithm.

  • Linear temperature correction . The linear temperature correction is an empirical correction used to convert the conductivity at the measured temperature to the conductivity at 25°C. It has the form: .  . .  . . C25 is the calculated conductivity at 25°C, Ct is the measured conductivity at t°C, and a is the linear temperature coefficient expressed as a decimal fraction. The linear temperature coefficient is user selectable between 0 and 5% per °C (a = 0.00 to 0.05). For dilute solutions of most salts the linear temperature coefficient is about 2% per °C. For acids the temperature coefficient is typically less, and for bases it is typically greater. The temperature coefficient is also a function of the concentration and temperature. Thus, a single temperature coefficient will rarely be suitable over a broad range of concentration or temperature. Common practice is to use an average temperature coefficient, but doing so is likely to introduce errors.
  • High purity water correction . The high purity water correction is also called the dilute sodium chloride correction. The model assumes the sample is pure water contaminated with a trace amount of sodium chloride. It also assumes (correctly) that the presence of the salt does not influence the conductivity of the water. This means that the conductivity of the solution is simply the sum of the conductivity of water and the conductivity of sodium and chloride ions. The correction can be best understood by reference to the graph below.

    .  .  .  .  .   . .   The pink line is the conductivity of pure water, and the blue line is the conductivity of sodium and chloride ions. The total conductivity of the solution, the green line, is the sum of the two. Point 1 on the green line is the raw conductivity at the measurement temperature. To perform the correction, the analyzer subtracts the conductivity of pure water at the measurement temperature from the raw conductivity. The result, Point 2, is the conductivity of sodium and chloride at the measurement temperature. Next, the analyzer converts the conductivity of sodium and chloride to the conductivity at 25°C, Point 3. Finally, the analyzer adds the conductivity of pure water at 25°C to the conductivity of sodium and chloride at 25°C to give the corrected conductivity

    of the solution at 25°C, Point 4.  . The basic assumption behind the model is that contribution of water and the contaminating salt to the total conductivity are independent of one another. Therefore, the model works very well when the contaminant is a neutral salt. However, if the contaminant is a slightly acidic or basic salt, like ammonium chloride or sodium acetate, small errors begin to creep in because the fundamental assumption is no longer met. Have you encountered these circumstances, and if so, did you see these errors? The presence of the acidic or basic salt suppresses the dissociation of water, so the contribution of water to the total conductivity is no longer independent of the salt. If the contaminant is a strong or weak acid or base, the suppression of the dissociation of water is even greater, and large errors result.  .  . Generally, the neutral salt correction should be used when the conductivity is less than about 5 uS/cm and there is reasonable expectation that the major contaminant in the sample is a neutral salt.  .  . . At higher conductivity, about 6 uS/cm at 25°C, the neutral salt correction behaves like the linear temperature correction model, albeit a correction in which the slope is temperature dependent. At 5°C the coefficient is 0.019, and at 90°C the coefficient is 0.025.

  • C ation conductivity correction . The cation conductivity temperature correction is also called the dilute hydrochloric acid correction. It is used exclusively in steam power plants where the cation conductivity measurement is used to detect contamination in steam condensate and boiler feedwater.  .  .  .  . The model assumes the sample is pure water contaminated with trace amounts of hydrochloric acid. It is considerably more complicated than the dilute sodium chloride model. Hydrochloric acid is a much stronger acid than water. It strongly suppresses the dissociation of water and thus has a profound effect on the contribution of water to the overall conductivity. The contribution of water also depends on the acid concentration. Increasing the acid concentration decreases the dissociation of water, and reduces its contribution to the total conductivity. The correction algorithm involves two steps. First, using the measured conductivity and temperature, the analyzer calculates the concentration of hydrochloric acid. Next, the analyzer calculates the conductivity produced by the same concentration of hydrochloric acid at 25°C. Although the algorithm is easy to describe, the algebra involved is extensive.  .  .  .  .  .   In the cation conductivity measurement, the typical contaminants are hydrochloric and sulfuric acids and carbonic acid. Hydrochloric and sulfuric acids are strong acids, and the correction algorithm works very well in samples where they are dominant. Carbonic acid is a weak acid, and, depending on its concentration relative to the strong acid, an error can result. Typically, the errors are small unless the sample is very cold (<10°C).
  • Using these guidelines, users can make reasonably accurate conductivity measurements in most applications. What have been your experiences with temperature compensation?

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