Method of operative determination of the stability of circulating water with regard to the release of CaCO3

Sediments on the technological surfaces of the recirculating water supply system (RWSS) of enterprises are considered. The kinetic equation for the activity concentration of the main sediment component – Ca2+ ions in circulating water (CW) is discussed. Based on this equation, expressions were obtained for the rate of formation of CaCO3 from CW and the stability index of CW, which is expressed by the activity concentration of free Ca2+ ions not bound in CaCO3. These values are determined by measuring parameters of the quality of CW and the mode of operation of the recirculating system, which are provided for by the regulations for the operation of the RWSS Current information on the value of the stability index makes it possible to calculate the rate of CaCO3 precipitation and, if necessary, to develop quantitative parameters of operational measures to stabilize CW. The algorithm for calculating the stability index was applied to the RWSS of one of the HPPs, where softening of the feed water and bypass softening of CW are used. The calculated value of the index adequately reflects changes in the stability of the CW during variations in the operation mode of the RWSS. The stability index was used to calculate the parameters of CW acidification, which ensure the desired level of its stability.


Introduction
Today, the vast majority of large enterprises, thermal and nuclear power plants (HPPs, NPPs) are equipped with reversible water supply systems (RWSS).Almost 95% of water consumption there used for cooling of technological equipment.Considering the large consumption of cooling water (about 170,000 m 3 /hour per 1000 MW unit), natural, untreated water is used for cooling.Such water is capable of releasing solid sediments (mainly CaCO 3 on process surfaces, in particular, on pipe systems (PS) of turbine condensers (TC) [1,2].
The coefficient of thermal conductivity of sediments is ten times lower than that of the PS material, so that already at a thickness of (1.2-1.6)mm, the heat transfer coefficient of heat exchangers (HE) decreases by (30-40)%, and this leads to a decrease in the efficiency of power units by (0.5-1.2)% [3], excessive consumption of fuel by (1.5-3.5)% and the need to clean TCs, reducing the electrical load of the units.
Note that for a 1000 MW power unit, the corresponding annual electricity losses are (120÷245) million kWh, which roughly corresponds to the energy consumption of a city with a population of (40-80) thousand people.Excessive consumption of fuel at HPPs, along with economic losses, results in excessive emissions of heat, greenhouse gases, and harmful substances into the environment.To reduce the intensity of sediments partial or complete softening of the feed water, adding of mineral acids to the water and dosing of sediment inhibitors are used.The effect of the inhibitors is associated with blocking the growth centers of CaCO 3 crystal nuclei, providing them with an additional charge and thus stabilizing the CaCO 3 dispersion, which is expressed in a decrease in the intensity of deposits on the PS of heat exchangers [4,5].

Formulation of the problem
An important problem in the reagent stabilization of circulating waters of thermal power plants and nuclear power plants is the lack of reliable operational control of the ability of CW to form sediments.
The regulations [6] suggest using the Langelier index, LSI, or the CW supersaturation index with respect to CaCO 3 , SI [7,8].The mentioned indices are represented by expressions: • Langelier index: (H) s -activity concentration of hydrogen ions when the water system is in equilibrium with the environment; (H) -measured activity concentration.Today pH measuring is not difficult, but the calculation of pH s depends on the selected model of the bicarbonate system and does not always correspond to reality.
Because of this, pH s are recommended to be determined experimentally [9].It follows from formula (1) that if LSI < 0, there is an excess of hydrogen ions in the water system and it is corrosively active and capable of dissolving carbonate sediments.If LSI > 0, on the contrary, there is a lack of hydrogen ions in the system and it emits CaCO 3 .Of course, at LSI = 0, the hydrocarbonate system (HCS) is stable.
Unfortunately, knowing the LSI, we do not get a quantitative assessment of the degree of deviation of the HCS from the balance.That is, the LSI provides qualitative information about the state of the HCS and does not directly indicate the quantitative characteristics of measures to correct the stability of the CW.In addition, if we are talking about the RWSS, the LSI is not directly related to the operation mode of the RWSS.
• Index of CW supersaturation in relation to CaCO 3 : it is calculated by the formula, (Ca 2+ ), (CO 2− 3 ), L CaCO 3 − activity concentrations of calcium and carbonates ions and the solubility product of the CaCO 3 .
It follows from the physical content of formula (2) that with SI > 1, there is an excess of carbonate and calcium ions in the water system and it can release CaCO 3 .If SI < 1, on the contrary, there is a lack of ions in the system and it dissolves CaCO 3 .Of course, at SI = 1, the hydrocarbonate system is stable.However, as in the case of the Langelier index, the SI calculation gives only qualitative information about the state of the HCS, this information refers to the CW and does not reflect its status as an element of the RWSS.
At NPPs, the following ratio is used to characterize the stability of the CW ε is a given value, for example, 0.1÷ 0.3; Ht, Ht 0 is the total hardness of circulating water and feed water, the same for chloride concentrations C Cl , C Cl0 .
Therefore, today there is no generally accepted method for determining the quantitative degree of stability of CW, which could be directly used as a characteristic of the deviation of the state of CW from the equilibrium state, when a dynamic equilibrium is established in CW between the processes of CaCO 3 generation and its dissolution, and the rate of sediment growth is minimal (ideally, it goes to zero).
It is important that this method of determining the degree of stability of CW clearly depends on the regime parameters of RWSS and the quality of CW.Having such a parameter (by analogy with ( 1) and ( 2), we will call it the stability index), it would be possible to form an algorithm for calculating the doses of reagents or the level of softening of the feed water depending on the degree of deviation from the equilibrium state.It would be most convenient to obtain this value on the basis of operational information about the state of CW based on the data of regular measurements of RWSS regime parameters and CW quality parameters conducted at enterprises, in particular at HPPs and NPPs.
The formulation of the methodology for calculating the CW stability index in relation to the re-lease of CaCO 3 , and the application of the results of its determination in the real conditions of a specific TPP are considered in this work.

Calculation method
It was shown in [1] that the main component of the sediments is calcium carbonate CaCO 3 .Accordingly, the procedure for determining the stability of CW should be based on monitoring the dynamics of the concentration of Ca 2+ ions in CW.To obtain the kinetic equation for the concentration of Ca 2+ , we use the balance of the number of moles of calcium in the circulating water of the RWSS and take into account that the concentration of calcium changes in the CW due to water exchange, water evaporation, and the formation of CaCO 3 .Other channels of changes in the concentration of Ca 2+ ions in CW are neglected.
Let us denote the rate of CaCO 3 formation by R(t), mole/(dm 3 • s), then for a simple RWSS we can write an expression for the rate of change of the activity concentration of Ca C 0 (t), C(t) -activity concentrations of calcium ions in feed and circulating waters; Q f (t), V (t)− feed water flow rate and water volume of the RWSS; T f (t) is the time of filling the RWSS with feed water.The parameter φ(t) in formula ( 4) is called the dynamic factor.As it follows from (5), for the stationary mode of operation of the RWSS, when d dt ln [C Cl (t)] ≈ 0, this value approaches the concentration coefficient k = C Cl C Cl0 of circulating water and is determined by the standard method by measuring the concentration of chloride ions.
Let's transform (4) to the form that shows how Ca 2+ ions are distributed in CW, The left part (6) is the activity concentration of calcium ions, what it would be in CW in the absence of CaCO 3 formation.The first term on the right is part of the concentration of calcium ions that have changed to the state of CaCO 3 during the time T f -the stay of the feed water in the RWSS.The third term is the excess (that exists at the moment of time t) activity concentration of free calcium ions in CW, which can be determined by any available method.
After dividing both sides of (6) by C 0 (t) • φ(t), let's convert it to the form The first expression (8) is the fraction of calcium ions of the feed water, which during its stay in the RWSS passes into the state of CaCO 3 .Let's call this value the factor of instability of water with respect to the precipitate of CaCO 3 .
The second expression ( 8) is the fraction of calcium ions from the feed water that does not change to the CaCO 3 state during its stay in the RWSS.It is natural to consider this value as an index of the stability of circulating water in relation to the release of CaCO 3 .For a stationary state, when dC(t)/dt = 0, the stability index takes the form it is equal to the fraction of the concentration of free Ca 2+ ions remaining in the CW relative to the amount of Ca 2+ ions that would be in the CW in the absence of CaCO 3 formation.For transient processes controlled by external conditions, provided that the value of the second term in square brackets ( 8) is proportional to unity the value of the stability index will depend on the sign (10) and will reflect the influence of external factors unrelated to the formation of CaCO 3 .That is, the stability index introduced by us adequately describes the process of carbonate release for the operating mode of RWSS close to stationary.By the way, having determined the stability index, we can use (8) to calculate the rate of formation of CaCO 3 from circulating water, Note that in the case of the use of bypass softening of CW such that a part of CW is removed from the circulation flow, softened in a special bypass clarifier and returned to the circulation flow again, the expression for calculating the stability index changes, C(t) , Q bp (t) -water consumption through the bypass clarifier, C bp (t) -activity concentration of calcium ions at the outlet of the bypass clarifier.
The characteristic feature of bypass clarifier that is important when using sediment inhibitors is the absorption of a part of the inhibitors from CW.Moreover, the concentration of inhibitors can decrease in the CW stream by (30-40)%.Therefore, the loss of inhibitors must be compensated for by a corresponding increase in their dosage in circulating water.

Application example
The proposed methodology for calculating the CW stability index for the formation of CaCO 3 will be applied to characterize the CW condition and minimize the growth rate of CW precipitation at one of Ukraine's HPPs.For this purpose, we use the CW parameters that were measured in accordance with the operating regulations of the RWSS, namely: Taking into account the high hardness of natural water (9.5 − 14.5) mg−eq dm 3 before feeding into the RWSS, approximately 85% of the feed water is softened so that its calcium hardness at the entrance to the RWSS was ≈ 2.1 mg−eq dm 3 , and in the CW reached ≈ (4.0 − 4.4) mg−eq dm 3 , with a concentration factor of k = 3.0 − 3.5.
During the 300-day RWSS studies, see figure 1 it worked in standard mode (without bypass) with an inhibitor concentration of C i = 3.5 mg dm 3 .The stability index before turning on the bypass calculated according to formula (9) was in the range of Ψ st ≈ (0.60 − 0.63), which was clearly insufficient for the normal operation of power units.The turbine condensers had to be cleaned every 3 months, and due to the need to reduce the electrical load during cleaning, the station suffered significant losses.To increase the current stability, starting from the 300th day of observation, the bypass clarification of the CW with the following parameters was included: The results of the calculation of the stability index according to formula (12) is shown in figure 1.We see that the use of bypass clarification of the CW increases the stability of CS up to 87% while maintaining the same inhibitor concentration in CW of 3.5 mg dm 3 .Note that the expression for the stability index in the bypass mode, formula (12), allows us to calculate the amount of CW consumption for bypass required to ensure the desired level of stability.
After reaching Ψ st ≈ 0.82 − 0.88, the precipitation rate decreased by almost three times, which made it possible to clean TCs during scheduled preventive repairs.
In order to make sure of the effectiveness of choosing the right dose of the inhibitor and the adequacy of the algorithm for calculating the degree of stability, starting from the 540th day, the dose of the inhibitor was reduced by 30%.Accordingly, the calculated stability of CW also decreased by ≈ 30%.This indicates that the method of calculating the stability of CW adequately reflects the processes in CW.The results presented here indicate the possibility of operational control of the stability of CW based on the data of regular measurements of its quality parameters and parameters of the operating mode of the RWSS.
5. An example of application for correcting the stability of CW with acid Let's consider an alternative option of stabilizing CW by acidifying it, for example, with sulfuric acid.Assume that the CW stability after softening was 60%.Considering it insufficient, we calculate the amount of sulfuric acid dose that must be added to the feed water to achieve the desired level of stabilization max Ψ st = 0.87.
To do this, we take into account that each gram mole of the acid binds an equivalent number of calcium ions, that is, the expression for the desired value of the stability index is presented as ∆C is the part of the concentration of Ca 2+ ions that is bound by the acid, it is equal to the added concentration of the acid C A in the CW; Ψ st is the existing stability of CW before acidification.
From expression (14), we determine the concentration of the acid that must be added to CW, Considering that the amount of acid in CW due to concentration is φ times higher than in feed water, we get the acid concentration for feed water, According to (15), we find the mass concentration of sulfuric acid (100%), which must be added to the feed water, We compare it with the consumption of the inhibitor during simultaneous bypass (take into account the increase in the dose of the inhibitor by 1.4 times due to its absorption by the bypass clarifier), We obtain that the mass concentration of the inhibitor is 17.6 times lower than that of the acid.That is, in this case, it might be more expedient to limit, after softening the feed water, its acidification instead of two procedures of adding an inhibitor and bypass softening.
The calculations presented here are intended to show how useful the concept of the stability index is, as it allows obtaining a quantitative level of stability of CW and simplifies the estimation of the number of reagents needed to achieve the desired level of stabilization of CW and makes it possible to compare stabilization options without much difficulty.

Conclusions
• To quantitatively characterize the degree of stability of CW, we suggest using the stability index.It has a clear physical meaning -it is equal to the relative part of the concentration of Ca 2+ ions that remains free in the CW, not bound in calcium carbonate.The calculation procedure is also simple and clear.
• It should be kept in mind that the stability index adequately describes the process of CaCO 3 formation in the case when there are no sharp changes in the concentration of Ca 2+ ions in the RWSS, see (10), caused by external conditions (the established mode of operation of the RWSS).• For operational control and determination of the level of stability of CW, it is necessary to measure the parameters of water quality and mode of operation of the RWSS in the established mode of operation of the RWSS: Ca 2+ 0 , Ca 2+ , (Cl − ) 0 , (Cl − ) , Q f , V. • It follows from expression (12) that the rate of formation of CaCO 3 is proportional to the concentration of calcium ions in the feed water, its consumption, and is inversely proportional to the water volume of the RWSS.In other words, RWSS with a larger water volume are less sensitive to contamination of heat exchangers than with a smaller one.In particular, this concerns to RWSS with cooling ponds.

Figure 1 .
Figure 1.Dependence of CW stability index Ψ st on the number of the measurement day.Vertical lines 300 and 540 indicate the moments of CW clarification switching on and the reduction of inhibitor dose.