# The monitoring of the water-chemical mode of low-pressure steam boilers using the pH value of boiler water

Ivan Tikhonov

*This article describes the technology of boiler water quality control with the control of the pH value of boiler water and the value of its electrical conductivity. Examples of this control are provided. The conditions under which this control is sufficiently effective are specified.*

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Is it possible to control the entire water-chemical mode** (**WCM) of a steam boiler by measuring only the pH and electrical conductivity of the boiler water?

Theoretically, Yes. In practice, the success of this control will be determined by the accuracy of pH and electrical conductivity measurements.

It should be noted that all of the following applies to low-pressure steam boilers that are not direct-flow, I.e. boilers in which the boiler water is formed by repeated evaporation of feed water.

The boiler water quality parameters are as follows:

– the alkalinity at phenolphthalein (P) and methylorange (M), mol/l;

– salinity (S), mg/l;

– the relative alkalinity of the boiler water (A), %.

All four indicators of boiler water quality are related, i.e. the value of each indicator depends on the values of other indicators.

The relative alkalinity of boiler water is just an indicator that connects the value of the alkalinity of boiler water and its salinity.

The relative alkalinity is determined by the formula:

The number 40 in the formula (1) indicates that it is assumed that only phenolphthalein alkalinity exists in the boiler, i.e. all sodium bicarbonate contained in the source water turns into sodium hydrate under the conditions of removing of carbon dioxide with steam in the boiler according to equation (2).

2NaHCO_{3}<-> Na_{2}CO_{3}+CO_{2}^{gas}+Н_{2}О<->2NaOH+CO_{2}^{gas } (2)

First, sodium bicarbonate turns into carbonate when removing carbon dioxide with steam and then sodium carbonate hydrolyzes in water to form sodium hydrate. Thus, the boiler water always has a fairly high pH.

When calculating the relative alkalinity, 2 assumptions are made. First, that the boiler contains only phenolphthalein alkalinity, i.e. sodium hydrate, and second, that the salinity of the boiler water is determined by the value of the electrical conductivity of the boiler water, taking into account the conversion coefficient. This leads to significant inaccuracies in determining the actual salinity of the boiler water. However, when calculating the relative alkalinity, this does not affect the resulting value of the relative alkalinity, since the permissible range of relative alkalinity is from 10 to 50 %.

In fact, the relative alkalinity only indicates that it is possible to occur in the boiler acidic (if A is less than 10 %) or alkaline (if A is more than 50 %) corrosion.

In fact, the relative alkalinity connects the alkalinity and salinity of the boiler water, but due to the assumptions used in its calculation, it does not allow us to judge whether the hardness salts pass into the boiler with feed water and (or) condensate, and whether there is scale and sludge formation in the boiler.

It is much more efficient to control the pH value of boiler water and the electrical conductivity value of boiler water for boiler water quality control purposes. An important advantage of this control is that the ratio of pH values and electrical conductivity of the boiler water can be used to determine whether the boiler is receiving hardness salts, and that it can be fully automated. In fact, chemical analyses will not be required (only at the stage of commissioning).

What is the essence of such control of the WCM of a steam boiler?

First, we need to understand clearly that the pH value in the boiler is determined by the number of hydroxide (OH-), which is formed as a result of decomposition of bicarbonates in the boiler (using the equation 2). Thus, the amount of hydrate will depend on the concentration of sodium bicarbonate in the feed water and the coefficient of evaporation of boiler water. It can be said that for the boiler water of a steam boiler of a certain pressure, at a certain concentration of bicarbonates in the feed water and a certain evaporation coefficient, **there is only one pH value.**

We can determine this value pH knowing the phenolphthalein (P) and methylorange (M) alkalinity. The method for calculating the pH value for f and M is presented in the article (I. Tikhonov, “The influence of various forms of carbon dioxide in water on its pH value” tiwater.info). This work contains theoretical justification, practical calculations and experimental results, and an algorithm for calculating the pH value from the values of P and M, taking into account the ionic strength of the solution.

Accordingly, we can calculate the pH value of the boiler water by performing preliminary analyses for f and M. At the same time, it is necessary to know the concentration of all salts in the boiler water to account for the ionic strength of boiler water in the calculation of pH. This is quite easy to determine by the value of the electrical conductivity of the boiler water.

The ionic composition of the boiler water will be determined by the composition of the feed water. The feed water contains sodium cations (Na) and anions of bicarbonate (HCO_{3}), sulfate (SO_{4}) and chloride (Cl). Accordingly, sodium bicarbonate will decompose in the boiler according to the equation (2), and sodium chloride and sulfate will be evaporated, and their concentration will be equal to their concentration in the source water multiplied by the evaporation coefficient.

The electrical conductivity of boiler water (λ) can be determined by the formula (3):

λ= ОН*40/0,17+НСО_{3}*84*n_{1}+СО_{3}*106/0,6+K_{у}* λ_{so}_{4}_{cl} , µS/cm, (3)

*where ОН, НСО _{3}, СО_{3 }– concentrations of hydrate, bicarbonate and sodium carbonate corresponding to the obtained pH value of boiler water according to the developed algorithm, mmol/l;*

*40 – molar mass of sodium hydrate, g/mol;*

*0,17 – conversion coefficient of specific electrical conductivity of sodium hydrate solution to salinity;*

*84 – molar mass of sodium bicarbonate, g/mol;*

*106 – molar mass of sodium carbonate, g/mol;*

*0,6 – conversion coefficient for the electrical conductivity of a sodium carbonate solution to salinity;*

*n _{1} – conversion coefficient of the electrical conductivity of the sodium bicarbonate solution to the salt content, n1 = 0.95-1.*

*λ _{so4cl} – electrical conductivity of sodium chloride and sulfate salts of feed water, µS/cm*

*λ _{so4cl} = λ_{feed} – A_{feed}*84/0,95 µS/cm , (4)*

*λ _{feed} – electrical conductivity of feed water, µS/cm;*

*84 – molar mass of sodium bicarbonate, g/mol;*

*0,95 – conversion coefficient of the electrical conductivity of a solution of sodium bicarbonate to salinity for electrical conductivity of the solution up to 700 µs/cm (if the conductivity of the solution more than 700 µs/cm, the conversion factor is taken equal to 1); *

*K _{у} – the coefficient of evaporation,*

*К _{у}=(P+М)/A_{feed} , (5)*

*A _{feed} – alkalinity of feed water, mol/l.*

By measuring the value of the electrical conductivity of feed water using the formula (4), you can determine the value of the electrical conductivity given by sodium sulfate and chloride (λ_{so4cl}). The evaporation coefficient is determined using the formula (5). Then the electrical conductivity of the boiler water is calculated using the formula (3).

The result is that knowing the value of f and M and also the value of electrical conductivity of the boiler water we can calculate the pH value of the boiler water (according to the method of I. Tikhonov, “The influence of various forms of carbon dioxide in water on its pH value” tiwater.info), and the pH value will be determined in the absence of boiler hardness and evaporation coefficient. If you measure the pH of the boiler water, the measured pH value will match the calculated value at the boiler water temperature of 25 ^{0}C.

If the sample temperature during the boiler operation differs from 25 ^{0}C, the measured pH value of the boiler water sample must be recalculated taking into account the sample temperature according to the equation

pH_{t}=k*(T_{samp}-25) +рН, (6)

*where, pH – measured (calculated) pH of boiler water at a temperature of 25 ^{0}С;*

*Т _{samp} – sample temperature at which the pH value is measured (рН_{t}), °С;*

*k – slope coefficient of the linear graph of the pH value dependence on the temperature of the boiler water sample k=(рН _{t }– рН)/(Т_{sump}-Т).*

The slope coefficient k must be determined individually for each boiler during commissioning.

As a result, using the above method, you can calculate the values of the function in the form of λ =f(pH).

If the boiler with make-up water or condensate begins to receive hardness salts, there will be a deviation of the current measured values of λ and pH of the boiler water from the values determined by the initially constructed function λ =f (pH) for fully softened water.

This is what controls the WCM of steam boiler using the pH and electrical conductivity of the boiler water.

Thus, the proposed method can even control the operation of the water softening unit with a certain delay or the quality of the returned condensate.

It is necessary to say that the accuracy of pH and electrical conductivity measurements should be quite high. The higher the accuracy of pH and electrical conductivity measurements, the less hardness salts can be detected in the boiler water.

Let’s consider as an example the application of this method for controlling the WCM of a heat-tube steam boiler with a pressure of 8 bar.

Water of the following composition is used as the source water for the boiler room:

Total hardness | mg-eq/l | 0,02 |

Total alkalinity | mg-eq/l | 2,0 |

Chlorides | mg/l | 25 |

Sulfates | mg/l | 82 |

Sodium+potassium | mg/l | 18 |

Conductivity | µS/cm | 454 |

Condensate is returned to the boiler room. At the time of commissioning, the condensate return was about 70 %. The alkalinity of feed water in this case is 0.6 mmol/l. The concentration of sulfate is 0.284 mmol/l, and of chloride is 0.211 mmol/l.

The electrical conductivity value was set to 3000 µS/cm for boiler water. For this value of electrical conductivity in boiler water, the alkalinity values are P = 8 mmol/l and M = 0.5 mmol/l.

Accordingly, the evaporation coefficient is equal to

К_{у}=(P+М)/A_{feed} =(8+0.5)/0.6=14.16

According to the developed method for the values of P=8.0 and M=0.5, we calculate the pH value. The pH value is 11.69 (at 25 ^{0}C), which corresponds to the measured value of рН of boiler water with an error of 0.03 unit pH.

Then we determine the ratio of P to M for this steam boiler. The ratio will depend primarily on the coefficient of evaporation of boiler water. The higher the evaporation coefficient, the longer the boiler water is in the boiler and the longer the reaction takes according to the equation (2). I.e., the higher the evaporation coefficient is, the more P in the boiler relative to M is, while this ratio changes slightly in a wide range of the value of the evaporation coefficient. Under a certain assumption, you can use the data in figure 1 to calculate the pH. However, it is recommended to clarify the ratio of P to M for each specific boiler during commissioning.

**Figure 1 The dependence of methylorange (M) alkalinity of the boiler water on phenolphthalein (P).**

It is worth saying that if the boiler begins to receive hardness salts, there will be an increase in methylorange alkalinity in boiler water. This process is discussed in the article I. Tikhonov «On the issue of sludge and scale formation in a steam boiler» tiwater.info.

Then, using the formula (3), we calculate the value of the electrical conductivity of the boiler water, taking into account the sulphates and chlorides.

It turns out that each value of P and M corresponds to one pH value and one electrical conductivity value. Figure 2 shows a graph of the dependence of the conductivity value on the pH for boiler water calculated for the values P and M in the range P=1.0…25; M=0.2…2.5.

For example, P=8.0 mmol/l; M=0.5 mmol/l. The calculated pH value = 11.69; electrical conductivity λ =3109 µS/cm. And so the calculation is repeated for each P and M value P and M value in accordance with figure 1.

**Figure 2 The dependence of electrical conductivity on the pH of boiler water**

The pH (a) dependence graph is constructed when activities are being used in the calculation of the pH values. This graph is equal to the actual measured values of the boiler water pH at this value of electrical conductivity.

The pH (с) dependence graph is constructed when concentrations are being used in the calculation of the pH values. As a result, you can clearly see how with increasing ion concentrations (increasing the ionic strength of the boiler water), the measured pH value differs from the one calculated using concentrations. The higher the ion concentration (higher the electrical conductivity) is, the greater the difference between the pH values calculated using activities and concentrations is.

The graph of the dependence of the function λ =f(pH(a)) is the desired function.

Сontinuous measurements of the pH and electrical conductivity (λ) of the boiler water must be made during the operation of the boiler. You need to recalculate the obtained pH and electrical conductivity values for 25 ^{0}C. Then compare whether the obtained values are on the graph of the function λ=f(pH(a)).

For our example. After a leak in the heat exchanger, the quality of condensate deteriorated. When the source water entered the condensate, the condensate hardness was up to 0.3 mg-eq/l from time to time. As a result of the ingress of hardness salts with condensate into the feed and boiler water, some of the carbonates of the boiler water began to precipitate, rather than hydrolyze with an increase in the pH of the boiler water. As a result, the electrical conductivity of the boiler water began to decrease and since its value was set at the level of 3000 µS/cm, more evaporation of the boiler water occurred (continuous purging of the boiler decreased) and, accordingly, the proportion of non-carbonate salts (sodium sulfate and sodium chloride) in the boiler water increased. As a result, the pH value is slightly lower with the same electrical conductivity value. In this example, the measured pH value was on average 11.55-11.6 when hardness salts entered boiler with condensate. At the same time, the electrical conductivity was maintained at the level of 3000 µS/cm. If you find the intersection point for pH=11.55 and λ =3000 µS/cm on the graph of the pH(a) in figure 2, you will find out that the intersection point lies above this graph. This will indicate that the boiler receives hardness salts.

The advantages of this method of control:

– Simplicity of applied technical solutions, as well as reliability and availability of the equipment used.

– Continuity of control. Monitoring of the water chemical mode (WCM) is carried out constantly and remotely, which allows you to immediately identify problems with the WCM and constantly maintain the optimal the WCM.

The disadvantages are that this control method is quite sensitive to the accuracy of measuring the pH value of boiler water. The required pH measurement accuracy is not more than 0.03 pH units. This control method is also sensitive to changes in the ratio of bicarbonates to chlorides and sulfates of the source water. Therefore, if it is assumed that the boiler room will work from several sources of water supply, then it is necessary to calculate its function λ =f(pH) for each source of water supply.

Figure 3 shows a schematic diagram of boiler water sampling from a continuous purge line for continuous measurement of pH and electrical conductivity (λ).

**Figure 3**

The method contains the following steps. Boiler water from the continuous purge line of the steam boiler 1, passing the shut-off valve 2, enters the water-water refrigerator of the sample 3, in which the boiler water is cooled to 10-30°C by supplying cooling water. Then the cooled boiler water sample passes the temperature sensor 4 with a cut-off valve. If the water sample exceeds 50°C, the valve closes automatically to prevent damage to the pH and λ flow sensors. Then the sample of boiler water passes through the fine filter 5 and simultaneously goes to the flow sensor pH 6 with the temperature sensor and the flow sensor λ 7. The measured values of the pH, λ and boiler water temperature are recorded by the automatic boiler purge controller 8 and compared with the values of the pH and λ of the boiler water, which are pre-set in the controller as a function of the dependence of λ of water on the pH, i.e. λ =f (pH), which is typical for boiler water, which does not get hardness salts with make-up water or condensate. The controller also maintains a constant value of the λ or pH of the boiler water by purging part of the boiler water using the automatic control valve 9 for continuous boiler purging. The supply of a sample of boiler water to the control and adjustment system of the WCM is carried out by means of a control valve 10. The sampling line is purged using the shut-off valves 11.

In conclusion I want to say that the use of this method of controlling for the WCM in conjunction with the conductivity control for installation of ion exchange water softening and electrical conductivity of return condensate will allow to get an instrument of remote control of the WCM of a steam boiler, which implemented the principle of cross-checking. In other words, if one parameter does not meet the standard and there is a change in other parameters, then this will definitely require finding out the reasons for this deviation. In this case the accuracy requirements for individual parameters can be significantly reduced. Probably, this will allow controlling the WCM with a lower requirement for accurate measurement of the pH value of the boiler water.

A patent application has been filed for this method of controlling the WCM.

Any constructive comments, feedback, or suggestions are highly welcome.