Inferring pH from Conductivity and Cation Conductivity

Two common methods are used, but errors can occur if the sample and the model do not match.

By Joe Covey, Power Industry Product Engineer, Emerson Process Management, Rosemount Analytical

Inferred pH is a method of continuously calculating pH from straight and cation conductivity. The method is not widely used in the United States, but is popular in Europe. Inferred pH is attractive because under certain conditions it can eliminate the need for direct measurement of pH in feedwater and boiler water.

Measuring pH in condensate, feedwater and boiler water can be a challenge. Low conductivity and lack of buffer capacity make the measurement sensitive to contamination, electrical interference and sample flow changes. Although pH sensors having good accuracy and minimum flow sensitivity are available, many plant chemists still regard pH measurements with suspicion. pH sensors are also fragile—a reliable substitute for the thin, pH-sensitive glass bulb has yet to be found—and they need regular maintenance and recalibration.

Conductivity is different. The measurement is easy to make and the sensors are inexpensive, rugged and pre-calibrated at the factory. They need little maintenance and recalibration typically occurs once a year. And, as every plant chemist knows, if the cation conductivity is low, the pH of the condensate and feedwater can be estimated from the straight conductivity.

Inferring pH from conductivity is not new. However, analyzers that automatically perform the calculation are new. Inferred pH is based on certain assumptions about the sample. This article discusses the two models and the errors that result if the sample and model do not match.

Water Treatment Chemicals

In high pressure steam plants, small amounts of alkalizing agents are added to condensate, feedwater and boiler water to raise the pH to reduce corrosion. Boiler water chemicals also buffer the water against acid-forming contaminants. Treatment chemicals can be divided into two types: volatile chemicals and solids. Solid treatment chemicals are fed only to the boiler.

Ammonia is the most common volatile treatment chemical. It is injected into the condensate and becomes distributed throughout the water-steam system. Other pH adjustment chemicals, such as morpholine, are also used. Common boiler water treatment chemicals are sodium hydroxide and sodium phosphate salts. Except for trace amounts carried over with the steam, solid treatment chemicals remain in the boiler.

In addition to treatment chemicals, trace contaminants from condenser tube leaks, air in-leakage, breakdown of treatment chemicals and deterioration of polisher resins, are always present. These contaminants are primarily ionic or weakly ionic. They become distributed throughout the entire system, but accumulate in the boiler.

The two models for calculating inferred pH make assumptions about the alkalizing agent and the contaminant. The volatile model assumes the alkalizing agent is ammonia. The solids model assumes the alkalizing agent is sodium hydroxide. Both models assume the contaminant is sodium chloride.

Conductivity to Measure

Ammonia is a weak base. It undergoes the following reaction with water:

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Sodium hydroxide is a strong base. It dissociates completely in water:

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The equations show that adding either ammonia or sodium hydroxide to water changes both the pH and the conductivity. The graphs in Figures 1 and 2 show how pH, conductivity and concentration are related for dilute solutions of ammonia and sodium hydroxide at 25 C. Conductivity and pH depend on temperature, so the curves are different at different temperatures. The ranges are typical for a steam power plant. Two points are worth noting. First, only one measurement is needed to infer the other two. For example, if conductivity is measured, pH and concentration are automatically known. Second, the curves bend toward the x-axis. As conductivity increases, a given change in conductivity corresponds to a smaller change in pH.

Each point on the line corresponds to a different ammonia concentration.
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Each point on the line corresponds to a different sodium hydroxide concentration.
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The graphs can be used to infer pH only if the alkalizing agent (ammonia or sodium hydroxide) is the sole source of conductivity. If ionic contamination is present, the inferred pH will be inaccurate. For example, assume the conductivity of the feedwater is 0.80 uS/cm at 25 C, of which 0.10 uS/cm is from an ionic contaminant. Because the conductivity from ammonia is 0.70 uS/cm, the true pH is 8.40. However, the inferred pH (using 0.80 uS/cm) is 8.46.

To accurately infer pH from conductivity, ionic contamination must be accounted for. That’s where cation conductivity comes in. Figure 3 explains how cation conductivity measures contamination in ammoniated feedwater. Figure 4 shows the relationship between cation conductivity and the concentration of sodium chloride entering the column.

The cation exchanger removes the background conductivity caused by ammonia. With no contamination, cation conductivity equals the conductivity of pure water. With salt contamination, conductivity increases as the column effluent is now a dilute mineral acid.
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The x-axis is the concentration of sodium chloride in the sample entering the cation column. The y-axis is the conductivity of the column effluent.
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Calculating inferred pH from straight and cation conductivity involves four steps:

  1. Convert the straight and cation conductivity to values at 25 C.
  2. Use Figure 4 to convert cation conductivity to sodium chloride concentration.
  3. Subtract the conductivity of sodium and chloride ions from the straight conductivity. The result is the conductivity of the ammonia or sodium hydroxide solution.
  4. Convert conductivity to pH using either Figure 1 or 2.

Figure 5 shows the influence of cation conductivity on inferred pH for ammonia solutions. Cation conductivity has the greatest influence when the conductivity (and ammonia level) is low. As conductivity increases, the cation conductivity correction becomes less important. A similar graph can be drawn for sodium hydroxide.

The cation conductivity from sodium chloride for each line is shown. As the ammonia concentration (conductivity) increases, the lines merge.
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Errors in Inferred pH

There are three sources of error in inferred pH. First, the straight conductivity, cation conductivity or temperature is wrong. Temperature is important because conductivity measurements are converted to values at 25 C before pH is calculated. Second, the temperature correction algorithm does not match the sample. Temperature corrections are based on certain assumptions about the composition of the sample. Errors result if the assumptions are wrong. Third, the sample does not match the model used to calculate inferred pH.

Although this article is primarily concerned with the third source of error, a brief discussion of the first two is worthwhile.

The worst case error for uncorrected conductivity is about 2 percent. Temperature error is no more than ±0.5 C. The error introduced by the temperature correction algorithm depends on how well the sample matches the assumptions made by the algorithm. For straight conductivity the error is small as long as ammonia (or sodium hydroxide) is the major alkalizing agent. For cation conductivity the error can be as much as 10 percent. The high error is caused by the correction algorithm not matching the actual sample. The typical cation algorithm assumes the cation conductivity is caused by hydrochloric acid. In real samples, significant amounts of carbon dioxide from air in-leakage can also be present, causing the corrected conductivity to be in error. Assuming a 2 percent error in straight conductivity and a 10 percent error in cation conductivity, the errors in inferred pH in ammoniated condensate are 0.04 at pH 8.2 (0.5 uS/cm) and 0.01 or less above pH 8.9 (2.5 uS/cm). An examination of Figure 5 makes it clear why the errors decrease as conductivity increases.

Next we examine the errors in inferred pH caused by failure of the model to match the sample. It is convenient to examine the errors in the all volatile treatment (AVT) and solids models separately.

AVT Model

The AVT model assumes the alkalizing agent is ammonia. If the alkalizing agent is morpholine or another amine, the model cannot be used. The pH-conductivity curves for organic amines are different from ammonia and the amine decomposition products add to the cation conductivity. Errors caused by applying the AVT model to amine-treated systems will not be discussed. Bases that are weaker than ammonia (like hydrazine) do not cause an error unless the ammonia level is low (pH<8.8) and the hydrazine level is high (>60 ppb).

The model assumes the contaminant is sodium chloride. More likely, contamination will be a mixture of mineral salts, including sodium chloride, from condenser leakage and atmospheric carbon dioxide from air in-leakage. Because mineral salts contribute about the same to the conductivity and cation conductivity as sodium chloride, they introduce little error. Carbon dioxide, however, can cause an error.

Carbon dioxide affects the pH, conductivity and cation conductivity. When carbon dioxide dissolves in condensate, it neutralizes a portion of the ammonia, forming ammonium carbonate. The pH drops and, unless a large amount of carbon dioxide is present, the conductivity drops as well. Carbon dioxide also changes the cation conductivity. As the sample passes through the cation column, ammonium carbonate is converted to carbonic acid. Although carbonic acid is a weak electrolyte, it does contribute to the cation conductivity. In fact, in many plants, atmospheric carbon dioxide may be the major source of cation conductivity.

Figure 6 shows the error in inferred pH if carbon dioxide is present in concentrations between 0 and 50 ppb and sodium chloride is constant at 3.3 ppb. Each line corresponds to a different concentration (pH) of ammonia. An examination of the graph reveals several things. First, as the concentration of carbon dioxide increases, the cation conductivity increases. Second, as the concentration of carbon dioxide increases, the error in the inferred pH increases. And third, as the concentration of ammonia (that is, pH and straight conductivity) increases, the error in inferred pH caused by carbon dioxide decreases.

Each line refers to a different ammonia concentration; the approximate pH is shown next to the line. Numbers above the pH 8.5 line are the concentration of carbon dioxide (0 to 50 ppb). Sodium chloride concentration is 3.3 ppb.
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Solids Model

The solids model assumes sodium chloride is the boiler water contaminant. Again, this is unlikely. Other mineral salts will certainly be present, but they are likely to cause little error. Carbonates from air in-leakage are not likely to introduce error, either. In high-pressure boilers carbonates decompose, allowing carbon dioxide to escape with the steam. Ammonia, from feedwater treatment, may cause an error. Although ammonia is volatile and most escapes with the steam, some remains behind in the boiler. Ammonia does not affect the cation conductivity, but it does affect the pH and straight conductivity.

Figure 7 shows the error in inferred pH at two sodium hydroxide concentrations for different concentrations of ammonia. The sodium hydroxide levels are typical for caustic-only boilers. The error decreases as the concentration of sodium hydroxide increases. Sodium hydroxide is a strong base and suppresses the dissociation of ammonia. Therefore, the contribution of ammonia to the pH and conductivity decreases as the sodium hydroxide concentration increases.

Besides ammonia, the boiler water also contains 0.1 ppm chloride.
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The solids model for inferred pH is not applicable to boiler water treated with phosphates. Figure 8 shows the error if the solids model is applied to a boiler on equilibrium phosphate in which small amounts of free caustic are present. The figure shows that the error increases as the difference between the actual composition of the sample and the model becomes greater.

The boiler water also contains 0.2 ppm each of ammonia and sodium chloride. The phosphate is from trisodium phosphate (TSP).
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Figure 9 shows the error if the solids model is applied to a boiler on coordinated phosphate treatment. The errors are considerably higher than for equilibrium phosphate. In equilibrium phosphate, phosphate levels are typically low and a few parts per million of sodium hydroxide can be present. In coordinated control phosphate levels are generally higher and no free caustic is allowed. Because there is little similarity between the actual boiler water composition and the model, errors are high.

The boiler water also contains 0.2 ppm each of ammonia and sodium chloride.
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Presently, no consensus exists on how inferred pH should be used in cycle chemistry monitoring. Some plant chemists use nothing but inferred pH. Others find it useful only to check the accuracy of direct pH measurements. No matter which group one falls in, it is important to understand the limitations of inferred pH.

The closer the match between the sample and model, the more accurate will be the inferred pH. Because failure of the model to account for all forms of ionic contamination is a source of error, the most accurate inferred feedwater pH will be found in plants with full condensate polishing. Of course, as the pH increases, the contamination correction (cation conductivity) becomes less critical.

Error in the temperature-corrected straight and cation conductivity cannot be ignored, either. No temperature correction algorithm is perfect. Even if the uncorrected conductivity is error-free, the corrected conductivity will likely have an error, and the error generally increases the further the temperature is from 25 C. Because error in the measured conductivity affects the inferred pH, the best accuracy occurs when the temperature is close to 25C.


Joseph Covey is a product engineer for the Liquid Division of Emerson Process Management, Rosemount Analytical. He has over 25 years experience in industrial water treatment and testing, primarily in the electric power industry.

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