mathematical simulation of ionic equilibriums of water coolant using electrical conductivity and ph...

546

ISSN 0040-6015, Thermal Engineering, 2009, Vol. 56, No. 7, pp. 546–552. © Pleiades Publishing, Inc., 2009.Original Russian Text © E.N. Bushuev, 2009, published in Teploenergetika.

Reliable, economically efficient, and safe operationof power-generating units at thermal power stationsdepends to a considerable degree on the state of waterchemistry, which is standardized by the operationalregulations [1] and other normative documents.Increased inleakages of cooling water in steam-turbinecondensers or network water in delivery-water heaters,poor quality of makeup water, or inadequate meteringof chemical agents (e.g., ammonia or phosphates) maycause deviations from the required water chemistry;this generates a need to continuously monitor thesedeviations by means of automatic chemical monitoringinstruments over the entire water–steam path of apower unit.

Among the instruments that are able to reliablyrespond to these deviations at early stage of their devel-opment are conductivity meters and, partly, pH meters.It should be noted that different deviations from normalwater chemistry may give rise to the same response ofinstruments, e.g., an increase in the conductivity offeedwater. Individual kinds of deviations from normalwater chemistry can be distinguished on the basis ofreadings from conductivity meters and pH meters(which are the main instruments of an automatic chem-ical monitoring system) using an algorithm for calcu-lating the concentrations of ionic components of feed-water, boiler water, and their constituent flows. Such analgorithm is based on an analysis of mathematical mod-els describing ionic equilibriums in demineralizedwater, feedwater, and boiler water of power-generatingboilers [2–6].

A mathematical model for ionic equilibrium ofwater coolant contains the following equations:

—the equation of electrical neutrality for a directsample

(1)

where

C

k

and

C

j

are the molar concentrations of the

k

thcation and

j

th anion, mol/l, and

z

k

and

z

j

are the chargesof the

k

th cation and

j

th anion;

—equations describing a relation between the equi-librium concentrations of weak electrolyte dissociationforms. The number of these equations is determined bythe number of weak electrolytes contained in the con-cerned solution. The mathematical model for any aque-ous solution contains at least the equations describingdissociation of water and carbonic acid:

(2)

(3)

(4)

where

K

w

is the ionic product of water, the numericalvalue of which depends on the solution temperature

T

,(mol/l)

2

;

K

I

and

K

II

are the thermodynamic constantsfor dissociation of carbonic acid; and

and are the active concentrations of the

respective ions, mol/l; here and henceforth, the figuresin brackets correspond to concentrations of acids andions, mol/l;

Ckzkk Kt∈∑ C jz j,

j An∈∑=

Kw aH–aOH–;=

K1

aH+aHCO3

–

H2CO3[ ]----------------------;=

K II

aH+aCO3

2–

aHCO3

–

-------------------,=

aH+, a

OH–,

aHCO3

–, aCO3

2–

Mathematical Simulation of Ionic Equilibriumsof Water Coolant Using Electrical Conductivity

and pH Measurements

E. N. Bushuev

Lenin Ivanovo State Power Engineering University (IGEU), Rabfakovskaya ul. 34, Ivanovo, 153003 Russia

Abstract

—A generalized mathematical model for ionic equilibriums of water coolant is proposed. Particularcases of its solution for turbine condensate, demineralized water, feedwater, and boiler water are considered. Itis shown that, by using the proposed method, it is possible to indirectly determine the concentrations of stan-dardized ionic impurities from readings of conductivity meters and pH meters, instruments available in a regu-lar chemical monitoring system.

DOI:

10.1134/S0040601509070039

THERMAL ENGINEERING

Vol. 56

No. 7

2009

MATHEMATICAL SIMULATION OF IONIC EQUILIBRIUMS 547

—equations taking into account generation of ionic

pairs (e.g., NaS and Na

2

SiO

3

)

(5)

where

K

kj

is the thermodynamic constant for dissocia-tion of an ionic pair;

—the equation for the electrical conductivity of adirect sample

(6)

where

χ

is the specific electrical conductivity of a sam-ple, S/cm;

C

i

is the molar concentration of the

i

th ion,mol/l; and

λ

i

is the equivalent electrical conductivity ofthe

i

th ion, (S cm

2

)/g-equiv;—the equation correlating the activity of the

i

th ionwith its analytical concentration, mol/l,

(7)

—the equation for calculating the activity factor ofthe

i

th ion

(8)

where

I

= 0.5 is the ionic force of solution;

—the relation for calculating the equivalent electri-cal conductivity of the

i

th ion

(9)

λ

o, i

in infinitely diluted solution, (S cm

2

)/g-equiv, and is the relative dynamic viscosity of aqueous solution;

and

O4–

aka j Kkj,=

1000χ Ci zi λi( ),i

∑=

ai f iCi;=

f i f zi;I;T( ),=

Cizi2( )

i∑

χ f λ0 i, ;T ;η̃ C; i;…),(=

η̃

—the equation for the hydrogen ion exponent

(10)

Relations (8) and (9) for ultimately diluted solutionsare given by simple equations and become greatly compli-cated as the concentration of electrolytes increases [5].

An analysis of system of equations (1)–(10) showsthat its solution is generally a complicated problem,and this system becomes unsolvable if only a smallnumber of measured parameters are available.

Additional equations can be obtained using thewell-known method of subjecting a water sample toH-cation treatment [7, 8], during which part of the sam-ple being analyzed is passed through an H-column, andthe electrical conductivity of its filtrate is determined(see figure).

When the sample H-cation treatment method isused, system (1)–(9) is augmented with equations foran H-cationated sample, similar expressions (1) and (6)for a direct sample, and the balance (summary) equa-tion for the dissociation forms of carbonic acid (beforeand after an H-cation exchange filter)

(11)

and the equations describing the change in the concen-trations of strong acid anions during H-cation treatment

(12)

Equations (12) may become invalid only if theH-column being put in operation has been insuffi-ciently washed after regeneration.

System of equations (1)–(12) is written in generalform and becomes solvable if the number of unknownparameters (i.e., those to be determined) is equal to thenumber of equations.

The problem that has to be solved for automaticchemical monitoring systems used in thermal powerengineering is, as a rule, the inverse one: given the mea-sured values of electrical conductivity in the initialsample

χ

and in the filtrate after its H-cation treatment

χ

H

and the pH value in the initial sample, it is requiredto calculate the ionic composition of coolant, i.e.,

(13)

In this case, the temperature of a sample is addition-ally measured due to the fact that the temperature ofcooled water samples fluctuates in rather a wide range:from 15 to 35

°

C. This has considerable influence on thedissociation constants of weak electrolytes, as well ason the ionic mobility, and, ultimately, on the values ofthe quantities being calculated.

Solution of system of equations (1)–(12) for directand H-cationated samples is generally a complicated

pH aH+.log–=

H2CO3[ ] HCO3–[ ] CO3

2–[ ]+ +

= H2CO3[ ]H HCO3–[ ]H CO3

2–[ ]H+ +

= H2CO3[ ]sum

SO42–[ ]H SO4

2–[ ]; Cl–[ ]H Cl–[ ].= =

C1 C2 …Cn, ,{ } f χ χH pH T, , ,( ).=

System of sample

Medium

HR H-column

T

χ

pH χH

being

preparation devices

monitored

Instrumental diagram of automatic chemical monitoring.

548

THERMAL ENGINEERING Vol. 56 No. 7 2009

BUSHUEV

problem. However, it is possible to consider particularcases of solving this system of equations for individualflows of coolant.

DEMINERALIZED WATER

The mathematical model describing ionic equilibri-ums in demineralized water that is used for initial fillingof a power-generating boiler’s coolant circuit and mak-ing it up is the simplest case. This water contains in themain the following impurities: dissociation forms ofcarbonic acid, anions of strong acids (sulfates and chlo-rides), and cations (mainly sodium ions and to a smalldegree hardness ions). There is also a small quantity ofsilicic acid, which is in nondissociated state in deminer-alized water.

The following assumptions are used in the mathe-matical model for the conditions of demineralizedwater:

—The concentration of anions of strong acids isdetermined in recalculation for chlorine ion, which isthe prevailing anion,

(14)

—The concentration of hardness ions and sodiumions is calculated in recalculation for sodium ion,which is the prevailing cation,

(15)

—Demineralized water is a strongly diluted solu-tion; therefore, almost no ion pairs are generated in it.

—The equivalent electrical conductivity of an ioncorresponds to the value in infinitely diluted solutionλi ≈ λ0,i.

—Ignoring mutual influence of ions, i.e., consider-ing that fi ≈ 1, we can assume that ai ≈ Ci.

—Ionic forms of silicic acid dissociation are almostnot present at all and can be excluded from consider-ation.

Results of experimental investigations show that100% replacement of sodium cations by hydrogen cat-ions is not achieved as water passes through the H-cat-ion exchange column of a regular conductivity meter;therefore, an H-cationated sample must be taken intoaccount in the mathematical model.

With these assumptions and in view of (2)–(4),Eq. (1) for the electrical neutrality of water being ana-lyzed becomes

(16)

Cl–[ ]cond Cl–[ ] SO42–[ ];+=

Na+[ ]cond H0 Na+[ ];+=

Na+[ ]cond H+[ ]+

= Cl–[ ]cond 12K II

H+[ ]-----------+⎝ ⎠

⎛ ⎞ HCO3–[ ]

Kw

H+[ ]-----------.+ +

Electrical conductivity equation (6) for the samplebeing analyzed is written as follows:

(17)

The equation for electrical neutrality of an H-cation-ated sample is given by

(18)

The equation for electrical conductivity of an H-cat-ionated sample is written as

(19)

Analysis of Eqs. (16)–(19) shows that the number ofunknown variables exceeds the number of main equa-tions even for the simple case of demineralized water;therefore, additional relations must be introduced. Thebalance equation for dissociation forms of carbonicacid, which is obtained by transforming Eq. (11), or theassignment of a numerical value of the concentrationfraction of sodium ions exchanged by hydrogen cationin the H-column can be used as such additional rela-tions:

(20)

The numerical value of the coefficient a1 is stable; itis specified during adjustment of an automatic chemicalmonitoring system and usually lies in the range from0.95 to 0.99.

In the majority of cases, attempts to directly solvethis system of equations using software packages,including Mathcad, yield incorrect results. Negativeand complex values may be obtained. Neither changingthe values of initial approximations, nor increasing thecomputation accuracy, nor introducing limiting condi-tions help solve the problem. The problem can besolved by doing away with universal computation algo-rithms and developing an individual procedureintended for solving only this concrete calculationproblem [5, 8, 9].

The proposed mathematical model can be used inmonitoring the quality of makeup water, as well as con-densate and feedwater that does not contain ammonia,i.e., for neutral water chemistry.

As an example, Table 1 gives the results from mea-surements of the electrical conductivities χ and χH andthe pH value in feedwater and makeup (demineralized)

1000χ λNa+ Na+[ ]cond λ

H+ H+[ ] λCl– Cl–[ ]cond+ +=

+ λHCO3

–

2K II

H+[ ]-----------λ

CO32–+⎝ ⎠

⎛ ⎞ HCO3–[ ] λ

OH–

Kw

H+[ ]-----------.+

Na+[ ]H H+[ ]H+

= Cl–[ ]cond 12K II

H+[ ]H

--------------+⎝ ⎠⎛ ⎞ HCO3

–[ ]H

Kw

H+[ ]H

--------------.+ +

1000χ λNa+ Na+[ ]H λ

H+ H+[ ]H λCl– Cl–[ ]cond+ +=

+ λHCO3

–

2K II

H+[ ]H

--------------λCO3

2–+⎝ ⎠⎛ ⎞ HCO3

–[ ]H λOH–

Kw

H+[ ]H

--------------.+

a1Na+[ ]cond Na+[ ]H–

Na+[ ]cond

--------------------------------------------H+[ ]H

Na+[ ]cond

---------------------.= =



water in Unit 8 at the Konakovo district power station.In the same table we find the theoretical concentrationsof ion-generating impurities calculated using thedescribed mathematical model. It can be seen that, withclose values of electrical conductivity and pH, the con-centration of sodium ions is almost a factor of 3 and theconcentration of free carbonic acid is almost a factor of10 higher in demineralized water than they are in feed-water of the power unit. The possibility of obtainingsuch information in the online mode is an importanttask imposed on facilities for monitoring the chemistryof water coolant.

CONDENSATE FROM A STEAM TURBINE AND DELIVERY-WATER HEATERS

AND FEEDWATER OF POWER-GENERATING BOILERS

Ammonium hydroxide NH4OH is usually meteredinto feedwater of power-generating boilers to maintainits pH value at a level of 9.1 ± 0.1 for reduction waterchemistry or at a level of 7.8–8.2 for oxidative waterchemistry. In this case, the concentration of NH4OHrecalculated for the concentration of ammonia isin the range 10–1000 µg/l, depending on the concentra-tion of carbonic acid and type of water chemistry.

When a power unit operates with all-volatile,ammonia, and ammonia-oxygenated water chemistries,condensate and feedwater contain mainly the followingadmixtures: dissociation forms of carbonic acid,ammonia, and anions of strong acids (sulfates and chlo-rides) and cations (mainly sodium ions and in a smalldegree hardness ions), as well as products from corro-sion of structural materials (oxides and hydroxides ofFe, Cu, Zn, Al, etc.), silicic acid, and oxygen. Silicicacid and oxygen are present mainly in molecular formand, therefore, are not taken into account in the equa-tions of ionic equilibriums.

The cation-exchange resin charged into the conduc-tivity meter’s H-column sorbs ammonium and sodiumions from the flow of the water sample. If steam turbinecondensate contains them in small concentrations and

CNH3

if the charge of cation-exchange resin has a smallheight, the sorption of ammonium and sodium ions isincomplete, which is illustrated by the data in Table 2(for ammonia). Thus, if a conductivity meter and pHmeter respond adequately to ammonia metered into theflow of direct sample, the readings of the conductivitymeter in the flow of H-cationated sample χH grow as theconcentration of ammonia in water increases, whichshould not be the case if ammonia undergoes full(100%) sorption in the H-column.

Incomplete sorption of ammonia is taken intoaccount in the mathematical model described above byintroducing the empirical factor m

where [NH3]tot and [NH3]tot, H are the total concentra-tions of ammonia dissociation forms in the direct andH-cationated samples, mol/l.

Investigations that were carried out have shown thatthe numerical value of this coefficient may be deter-mined from the expression

The mathematical model for ionic equilibriums ofcondensate and feedwater includes the following equa-tions:

NH3[ ]tot H, m NH3[ ]tot,=

m1.125

NH3[ ]1.293------------------------.=

Table 1. Results of measurements obtained using cooled samples of coolant from the APK-051 analyzer

Sample No. µS/cm µS/cm pH T, °C µg/l µg/l µg/l

Alkalinity (total),

µg-equiv/l

Feedwater

1 0.142 0.189 6.51 22.9 5.6 0.30 14.5 0.01

2 0.140 0.186 6.55 22.7 5.6 0.28 14.3 0.01

Demineralized water (after the mixed-bed filters of the chemical water treatment system)

3 0.250 0.360 6.42 27.4 14.3 7.44 15.7 0.2

4 0.250 0.345 6.44 26.9 13.1 3.55 15.0 0.1

* Electrical conductivity values recalculated for 25°C.

χ25*, χH25*, C

Na+, CCO2, C

Cl–,

Table 2. Measured electrical conductivity values obtainedwhen ammonia solution was metered in a condensate sample

NH3 concentration, µg/l χ, µS/cm χH, µS/cm pH

40 0.60 0.22 8.45

80 1.08 0.30 8.75

400 3.70 0.48 9.38

550


BUSHUEV

—electric neutrality equation (1) for water beinganalyzed, which takes the form

(21)

—electrical conductivity equation (6) for waterbeing analyzed

(22)

—Eqs. (2)–(4) describing dissociation of weak elec-trolytes in water being analyzed that are augmentedwith the equation for dissociation of ammoniumhydroxide

(23)

—the equation for the total concentration of ammo-nia dissociation forms

(24)

H+[ ] Na+[ ]cond NH4+[ ]+ +

= Kw

H+[ ]----------- 1

2K II

H+[ ]-----------+⎝ ⎠

⎛ ⎞ HCO3–[ ] 2 CO3

2–[ ] Cl–[ ]cond;+ + +

1000χ λH+ H+[ ] λ

Na+ Na+[ ]cond+=

+ λNH4

+ NH4+[ ] λ

OH– OH–[ ]+

+ λHCO3

–

2K II

H+[ ]-----------λ

CO32–+⎝ ⎠

⎛ ⎞ HCO3–[ ] λ

Cl– Cl–[ ]cond;+

KNH4OH

aNH4

+aOH–

NH4OH[ ]------------------------;=

NH3[ ]tot NH4OH[ ] NH4+[ ];+=

—the equation for electric neutrality of the H-cat-ionated sample

(25)

and—the equation for electrical conductivity of the

H-cationated sample

(26)

This mathematical model differs from the model fordemineralized water in that it takes ammonia and prod-ucts of its dissociation into account. In this case, thesystem of equations remains solvable with the samecomposition of measured parameters, i.e., χ, χH, andpH, if we rigidly specify the ratio of chlorides andhydrocarbonates in the H-cationated sample; that is, if

we take = n. Study results indicate that this

ratio may vary in a wide range (0.01 ≤ n ≤ 5). The mostprobable values lie in the range n = 0.1–2.0; therefore,we can take n = 1 as a first approximation and then cor-

H+[ ]H Na+[ ]H m NH3[ ]tot+ +

= Kw

H+[ ]H

-------------- 12K II

H+[ ]H

--------------+⎝ ⎠⎛ ⎞ HCO3

–[ ]H Cl–[ ]cond;+ +

1000χ λH+ H+[ ] λ

Na+ Na+[ ]H+=

+ λNH4

+m NH3[ ]tot

+ λHCO3

–

2K II

H+[ ]H

--------------λCO3

2–+⎝ ⎠⎛ ⎞ HCO3

–[ ]H λCl– Cl–[ ]cond.+

HCO3–[ ]H

Cl–[ ]cond

----------------------

Table 3. Tuning of the APK-051 analyzer for monitoring the quality of turbine condensate and demineralized water

Sample No. χ25 pH25 n µg/l

(APK) µg/l

(LCA) µg/l

(APK) µg/l

(LCA) µg/l

(APK)

Turbine condensate

1 4.3 0.3 9.2 0.01 479 495 16.7 5 25.7

4.3 0.3 9.2 1.0 497 495 8.9 5 13.5

4.3 0.3 9.2 2.0 503 495 6.2 5 9.1

2 4.7 0.2 9.3 0.01 553 603 11.1 3 17.0

4.7 0.2 9.3 1.0 564 603 5.9 3 9.0

4.7 0.2 9.3 2.0 568 603 4.1 3 6.1

Demineralized water

3 5.4 0.13 9.5 0.01 687 743 7.0 12 10.7

5.4 0.13 9.5 1.0 693 743 3.7 12 5.9

5.4 0.13 9.5 2.0 696 743 2.5 12 3.8

Note: LCA denotes the results of a laboratory chemical analysis carried out by the operating personnel of the cogeneration station’s chemicaldepartment, and APK denotes the results obtained using the APK-051 analyzer operating in the automatic mode.

χH25 CNH3

, CNH3, C

Na+, CNa+, C

Cl–,



rect it if necessary. The value of n can be refined duringadjustment of a measurement system, depending on thekind of water chemistry used for a power unit and theflowrate of makeup water added to turbine condensate.In this case, by solving the system of equations relatingonly to an H-cationated sample for a concrete measure-

ment of electrical conductivity (recalculated for25°C) we can obtain fairly simple quantitative expres-sions for the concentrations of chlorides and hydrocar-bonates in the sample, µmol/l:

(27)

(28)

where is the electrical conductivity of the H-cation-ated sample, µS/cm.

Calculation of the other parameters of the system,including more exact determination of the measured pHvalue, which are required for the described mathemati-cal model, is fairly straightforward.

As an example, in Table 3 we find the results of tun-ing a type APK-051 automatic analyzer for detectingimpurities in condensate, an instrument using which thedescribed algorithm is implemented in a cogenerationstation’s power unit equipped with a drum boiler(pdr = 13.8 MPa). It can be seen that a laboratory chem-ical analysis frequently gives contradictory results.Thus, the values of ammonia concentrations have largescatter and show higher concentrations of ammonia atlower values of χ, which is impossible. The results of achemical analysis on determining the content ofsodium ions give rise to doubts, as a lower content ofsodium ions than that in demineralized water isobserved in turbine condensate at higher values of χH.

The results obtained using the APK-051 instrumentcorrelate well with the data obtained from a chemicallaboratory analysis of ammonia at n = 2. In addition, ananalysis of data given in Table 3 shows that, by tuningthe parameter n, it is possible to obtain the calculatedconcentration of sodium ions at the level of their mea-sured values.

BOILER WATER

The mathematical model of ionic equilibriums thatwas considered above can also be extended for theboiler water of drum boilers operating with phosphatewater chemistry. In this case, however, we have the fol-lowing peculiarities as compared with the model forfeedwater: a buildup of salt concentration occurs in aboiler, and a solution of sodium phosphate is added toprevent scale from occurring.

χH25

Cl–[ ]cond

= 1000χH

25

426.2a1 1 n+( ) 126.5 1 n+( ) 1 a1–( ) 31.9n–+----------------------------------------------------------------------------------------------------------------;

HCO3–[ ]

0.45 2.346a1χH25+

0.45 10–pH 6++------------------------------------------- Cl–[ ]condn,=

χH25

Addition of phosphoric acid salts to boiler watercauses them to undergo hydrolysis in accordance withthe equations

(29)

(30)

(31)

Reaction (29) proceeds almost completely in thedirect cooled sample of boiler water that arrives to thesensors of chemical monitoring instruments, and sodoes reaction (30) in the H-cationated sample, a cir-cumstance that has a considerable effect on the mea-sured values of χ, χH, and pH.

The presented mathematical model is even morecomplicated than that for feedwater, because it takesinto account the addition of phosphates into the system.The system of equations lying at the heart of this math-ematical model is solved by sequentially calculatingionic equilibrium first for feedwater, then for boilerwater in the salt compartment, and then for boiler waterin the pure compartment.

The ratio of chloride concentrations in feedwaterand boiler water serves as an equation for making thetransition from feedwater to boiler water,

where Kc is the ratio of feedwater concentration to thestate of boiler water in the salt compartment.

Experimental results show that it is possible to takeKc = 10 as a first approximation. A further refinement ofthe concentration ratio is carried out automatically dur-ing the operation of a program for a personal computer.The mathematical model for calculating admixtures inboiler water was developed with participation of theauthor of this paper and was described in [3].

As an example, Table 4 gives the results from mea-surements of the electrical conductivities χ and χH, thepH value, and the concentration of phosphates in boilerwater of Boiler 3 at Mosenergo’s TETs-23 cogenera-tion station (the boiler’s salt compartment). In the same

PO43– H2O OH– HPO4

2–;++

HPO42– H2O OH– H2PO4

–;++

H2PO4– H2O OH– H3PO4.++

Cl–[ ]bw

Cl–[ ]fw

----------------- Kc,=

Table 4. Measured and calculated values of indicators char-acterizing the quality of boiler water

SampleNo.

χ25,µS/cm µS/cm

pHmg/l mg/l

(calculation)

1 53.0 39.0 10.0 – 8.2

2 53.2 41.1 10.1 9.0 9.1

3 11.4 9.2 9.3 1.6 0.6

4 49.7 46.3 9.9 7.9 7.4

5 58.2 42.9 10.0 9.9 8.9

χH25, PO4

3–[ ], PO43–[ ],

552


BUSHUEV

table, we find the theoretical concentrations of phos-phates calculated using the described mathematicalmodel.

The presented generalized mathematical model forionic equilibriums of water coolant circulating in powerunit technological circuits can also be used to evaluatethe concentrations of acid products resulted from ther-molysis of organic impurities in feedwater recalculatedfor the concentration of acetic acid (from the electricalconductivity of an H-cationated sample of feedwaterand live steam taken in a once-through power-generat-ing boiler) [4, 10].

Thus, the developed mathematical models describ-ing the ionic equilibriums of a power unit’s water cool-ant and methods for solving them make it possible touse the minimal number of reliable measurements (theelectrical conductivities of an initial and H-cationatedsamples, pH value, and temperature of a sample) as abasis for determining the content of standardizedadmixtures (ammonia, sodium ions, chlorides, and totalalkalinity) in feedwater, as well as phosphates and otherion admixtures in boiler water that are used as indica-tors for diagnosing deviations from normal waterchemistry of power units at thermal power stations.

Individual fragments of the mathematical model andmethods of using them were reflected in reports andhave been met with approval at international confer-ences that were held in Russia (Moscow, 2006), Swit-zerland (Zurich, 2006), and Germany (Berlin, 2008).

The developed mathematical models can be used aspart of the mathematical support of systems for chemi-cal–technological monitoring and will allow deviationsfrom normal water chemistry to be detected at an earlystage of their development.

The described method and the APK-051 analyzerhave been checked under field conditions at Russianthermal power stations.

The proposed mathematical model and fragmentsthereof were used in development of electronic educa-tional aids: a computer-based training simulator for theKostroma district power station and a computerizededucational system for the Kalinin nuclear power sta-tion. They have also been laid down as the basis of [5],a book that won an award in the all-Russia competitionof manuscripts of educational, scientific-technical, andreference literature for power engineering that wasorganized by RAO Unified Energy Systems of Russia

and the Moscow Power Engineering Institute (Techni-cal University) in 2007.

REFERENCES1. SO (Industry Branch Standard) 153-34.20.501-2003

(RD 34.20.501-59): Operational Regulations for Elec-tric and Thermal Power Stations of the Russian Federa-tion (SPO ORGRES, Moscow, 2003) [in Russian].

2. B. M. Larin, E. N. Bushuev, E. V. Kozyulina, andYu. Yu. Tikhomirov, “A Practical Approach for Monitoringthe Water Chemistry of Drum Boilers,” Teploenergetika,No. 10, 11–17 (2005) [Therm. Eng., No. 10 (2005)].

3. B. M. Larin, E. N. Bushuev, Yu. Yu. Tikhomirova, andS. V. Kiet, “Determination of Phosphate Concentrationin Boiler Water Using Conductivity Measurements,”Teploenergetika, No. 7, 21–27 (2008) [Therm. Eng.,No. 7 (2008)].

4. B. M. Larin, E. N. Bushuev, A. B. Larin, et al., “A Cal-culation Method for Determining the Concentration ofPotentially Acid Substances in Feedwater of Once-Through Boilers,” Teploenergetika, No. 4, 38–41 (2008)[Therm. Eng., No. 4 (2008)].

5. B. M. Larin and E. N. Bushuev, Principles for Mathe-matically Simulating Chemical-Technology ProcessesUsed for Treatment of Coolant at Thermal and NuclearPower Stations (MEI, Moscow, 2009) [in Russian].

6. B. M. Larin, E. N. Bushuev, E. V. Kozyulina, et al., “Cal-culating the Concentrations of Ion-Producing Admix-tures in Water Coolant Used in a Power Unit of a Ther-mal Power Station from Electrical Conductivity and pHMeasurements,” Certificate of Official Registration of aComputer Program No. 2006614194.

7. A. A. Mostofin, “Correction of Readings from Conduc-tivity Meters with Preinserted H-Cation Exchange Fil-ters,” Elektr. Stn., No. 1, 79–81 (1974).

8. B. S. Rogatskin, A. V. Otchenashenko, V. F. Gvozdev,et al., MU (Methodical Guidelines) 34-70-114-85:Methodical Guidelines on Application of ConductivityMeasurement Monitoring for Maintaining Water Chem-istry at Power Stations (SPO ORGRES, Moscow, 1986)[in Russian].

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10. B. M. Larin, E. N. Bushuev, A. B. Larin, andM. K. L. Bhatti, “A Calculation Method for Determiningthe Concentration of Potentially Acid Substances inFeedwater of Once-Through Boilers,” in Proceedings of15th International Conference on the Properties ofWater and Steam, Berlin, Germany, 2008.

mathematical simulation of ionic equilibriums of water coolant using electrical conductivity and ph...

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