ph calculation by differential conductivity measurement in

Extended pH calculation model

PowerPlant Chemistry SPECIAL PRINT (2014) PowerPlant Chemistry 2014, 16(1)

SPEC

IAL

PRIN

T pH Calculation by Differential Conductivity Measurement in Mixtures of Alkalization Agents

Marco Lendi Dr. Heinz Wagner Dr. Peter Wuhrmann SWAN Analytische Instrumente AG, 8340 Hinwil/Switzerland

ANALYTICAL INSTRUMENTS

SWAN Analytische Instrumente AG · 8340 Hinwil/Switzerland

n Automatic and continuous measurement of total, cation and degassed cation conductivity

n Re-boiler according to Larson-Lane (ASTM D4519-94)

n Tightly controlled degassing temperature

n Calculation of sample pH and ammonia concentration.

Ask for technical documentation or check our homepage

Made in Switzerland

www.swan.ch

Analyzer AMI Deltacon DG Degassed Cation Conductivity

Water / Steam Analysis Equipment for Saudi Electric Company Power Plant PP10 manufactured by SWAN Systeme AG.

1PowerPlant Chemistry 2014, 16(1)

PPChem

INTRODUCTION

Proper measurement of pH is a key factor in corrosion risksurveillance in water-steam cycles. Many power plantchemists still consider the reliable and accurate on-linemeasurement of pH with ion selective glass electrodes incondensate or feedwater a difficult task. To guarantee areliable reading, high maintenance effort is required.

A pH calculation algorithm from differential conductivitymeasurement is a widely used alternative method for pHmeasurement in low conductivity water. The VGB guide-line (VGB-S-006-00-2012) describes a calculation modelwith two conductivity measurements before and after astrong acid ion exchanger. The calculation model is limitedto demineralized feedwater which contains only ammonia,sodium hydroxide or lithium hydroxide as an alkalizingagent [1].

State-of-the-art measuring equipment calculates the pHaccording to the VGB guidelines, but with a model tocover other alkalizing agents like morpholine andethanolamine. The performance and reliability of suchmeasuring systems have been demonstrated in severalfield-tests [2] as well as the precision, which has been discussed for various conditions. For example, the influ-ence of contaminants like sodium chloride or carbon diox-ide has been considered [3]. However all these studiesassume that only one alkalizing agent is present in thewater.

An increasing number of power plants are using mixturesof alkalizing agents like ammonia-ethanolamine or ammo-nia-morpholine. This not only raises the question ofwhether or not the existing calculation models can beused, but also of how far the calculated pH deviates fromreality.

In the following paper, the specific conductivity, acid con-ductivity and pH of high-purity water containing two acid-base pairs (representing the two alkalizing agents), an acidand a neutral contaminant as well as carbon dioxide atstandard temperature were simulated. The simulatedparameters were compared with the output of SWAN'sextended calculation model and the VGB model. The devi-ations and possible solutions are discussed as well.

pH CALCULATION MODELS

Basic Setup for pH Calculation by DifferentialConductivity

Two conductivity probes are required for simultaneousmeasurement before and after a strong acid cationexchanger. Figure 1 shows an example of a flow cell tomeasure differential conductivity.

The conductivity reading of the first probe (specific con-ductivity) is converted to 25 °C according to the modelchosen by the customer. For example, in a classic all-volatile treatment (AVT) program, the conversion model forammonia is set. But there are also compensation models

pH Calculation by Differential Conductivity Measurement inMixtures of Alkalization Agents

© 2014 by Waesseri GmbH. All rights reserved.

ABSTRACT

Proper measurement of pH is a key factor in corrosion risk surveillance in water-steam cycles. Since it still seems difficult to measure the sample pH directly with glass electrodes, pH calculation, using the difference between sampleconductivity before and after a strong acid ion exchanger, is a frequently used alternative. The precision and reliabilityof this measuring method is well known and proven in water-steam cycles containing one alkalization agent only.

For applications using mixtures of alkalization agents, the pH calculation model has never been verified. We investi-gated calculation models to predict the precision and limitations of pH calculation by differential conductivity measure-ment in morpholine-ammonia and ethanolamine-ammonia mixtures.

Marco Lendi, Heinz Wagner, and Peter Wuhrmann

pH Calculation by Differential Conductivity Measurement in Mixtures of Alkalization Agents

Sonderdruck-Lendi aus Heft2014-01-0:Innenseiten 12.03.14 09:56 Seite 1

2


PowerPlant Chemistry 2014, 16(1)

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available for morpholine, ethanolamine, sodium hydroxideand strong acid. If the sample contains a mixture of alka-lizing agents, the model of the dominant species shouldbe chosen. Further reading shows that the temperatureconversion of the conductivity within the range of 25 °C to50 °C depends only little on the chemical composition ofthe sample [4].

The strong acid exchange resin should exchange a posi-tively charged ion for protons. Therefore the alkalizingagent is replaced with water, and a neutral salt like sodiumchloride is converted to hydrochloric acid. So, the tem-perature conversion model of the conductivity readingafter the strong acid exchange resin will be set to strongacid.

VGB Standard [1]

The VGB Standard uses the following equation (1) to cal-culate the pH of demineralized feedwater in the rangefrom 7.5 to 10.5:

(1)

where �SC defines the specific conductivity, �CC the cationconductivity (or acid conductivity), and CB is a factor thatdepends on the alkalizing agent.

SWAN pH Calculation Model

In the strong acid ion exchanger, every positively chargedion is exchanged for H+. So, every contamination leads toa pH decrease. In the model used for the calculation, weassume that the contamination is mainly sodium chloride(NaCl), therefore chloride is the main contaminationspecies after the cation exchanger. The acid conductivityis defined with equation (2):

(2)

where �H+, �OH– and �Cl– are the equivalent ionic conduc -tivities and [H+], [OH–] and [Cl–] the molar concentrations ofthe ions.

The electroneutrality after the cation exchanger is definedin equation (3):

(3)

Equations (2) and (3) are converted to equation (4) with thedissociation constant KW = [H

+] · [OH– ]. The pH after thecation exchange resin is defined as the negative logarithmof the [H+]CC concentration.

(4)

(5)

Assuming that sodium chloride is the only contaminant,the excess of [H+]CC after the cation exchanger must comefrom that source:

(6)

The specific (total) conductivity �SC is the sum of the ionsof the water, the alkalizing agent and the contaminantgiven by the equation (7):

(7)

Equation (7) is converted with equation (6) and withrespect to the electroneutrality of the alkalizing agent[B+]SC = [OH

–]SC – [H+]SC to obtain [H

+]SC as a function of�SC and �CC: To simplify equation (8), [H

+]CC is a placeholder for a term containing �CC (4).

(8)

The quadratic equation (8) is solved to [H+]CC to calculatethe pH before the cation exchanger from �SC and �CC. �B+is the equivalent ionic conductivity of the alkalizing agent.

Strong acid

exchange resin

Specific conductivity

measurementAcid conductivity

measurement

Figure 1:

Flow cell for differential conductivity measurement.

pH = logB

� �SC CC–13(

CB(+ 11

Alkalizing agent CB

Ammonia 273

Sodium hydroxide 243

Lithium hydroxide 228

� � �CC CC Cl· ·[ ] –= H + OH + Cl�H+

CC OH– –

+ –· [ ] [ ]

[ ]H+CC = OH + Cl[ ] [ ]–

CC–

[ ]H+CC =

� � � � � �CC CC2

W H Cl OH Cl+ ( ) – 4 K ( + ) ( – )· ·+ – – –

2 ( + )· � �H Cl+ –

pH = –log( )CC [ ]H+CC

[ ] [ ]NaCl H+CC= –

KW

[ ]H+CC

� � � �SC SC Cl Na· ·[ ] [ ]– ++ ) NaCl= H + OH + (�H+

SC OH–

+ –· [ ]

+ �B+

SC+· B[ ]

([ ] [ ]H ) ( – ) + H ( + )+SC

2H B

+SC Cl NH· ·� � � �+ + – +(

KW

[ ]H+CC

– – �SC + K ( + ) = 0W OH B· � �– +(H· [ ]+CC ))



PPChempH Calculation by Differential Conductivity Measurement in Mixtures of Alkalization Agents

Assumption for the Calculation Model

In part some assumptions were already mentioned toexplain the calculation models.

• The sample contains only one alkalizing agent.

• The contamination is sodium chloride.

• The calculation model works for sample pH within 7.5to 10.5.

In the next section, conditions are discussed which violatethe assumptions for the calculation model but representrealistic situations. The VGB and SWAN calculation mod-els have been tested with the following disturbances:

• Two alkalizing agents in the sample

• Carbon dioxide and sodium chloride as contaminants

The advantage of the expanded model used by SWAN isthe integration of sodium chloride as a contaminant andthe independent treatment of the specific and cation con-ductivities. Regarding this last point, �SC and �CC are notcoupled by a constant factor (1⁄3 in the VGB guideline). Thisis an important fact for the pH calculation below pH 8.5.

pH MODELING WITH FOUR VARIABLES

In Figure 2, the important steps for the pH modeling arelisted. In the first step, all possible variables are defined.The defined variables are:

• Two alkalizing agents and their concentration ranges

• Neutral salt (e.g. sodium chloride)

• Weak acid (e.g. carbon dioxide)

The system defined by these four variables is a polynomialof 5th degree which is solved to the proton concentration.So the pH of the defined system is known.

To calculate the total conductivity, one has to know theconcentration of all ions in the solution present at theknown pH. For example, carbon dioxide is a weak acidand will dissociate in water to form the bicarbonate ionHCO3

– and the carbonate ion CO32– . With respect to the

known pH value from step 2, the equilibrium concentrationof each ion is calculated. Therefore, the specific (or total)conductivity of the system is calculated.

In the last step, the system is modified to simulate theequilibria after a cation exchange resin. The followingchanges are made:

• The two alkalizing agents remain completely in thecation exchange resin.

• The neutral salt is converted to its corresponding acid.A contamination of sodium chloride leads to hydrochlo-ric acid after the cation exchange resin.

• Weak acids remain in the water.

With this new system, the pH and all ion equilibrium con-centrations are calculated. With the resulting ion concen-tration, the conductivity after a strong cation exchangeresin is calculated.

The calculated specific and cation conductivities are theinput parameter for the VGB and the SWAN calculationmodels (Figure 3). With respect to the calculated specific

Definition of

variables

pH calculation

of the system

Calculation of

the ion

equilibria

Calculation of

the cation

conductivity

Calculation of

the specific

conductivity

Concentration range of alkalizing

agent no. 1

Concentration range of alkalizing

agent no. 2

Define contaminants (CO , NaCl)2

Solution of a polynomial of 5 degreeth

Alkalizing agents

exchanged

Neutral salt turned into

its corresponding acid

CO passes the cation

exchange resin2

Figure 2:

Steps for correct pH modeling.

Definition of

variables

pH calculation

of the system

Calculation of

the ion

equilibria

Calculation of

the cation

conductivity

Calculation of

the specific

conductivity

Parameter to test the

calculation model

SWAN

model

VGB

model

Co

mp

ari

so

n

Figure 3:

The calculated specific and cation conductivities were put intothe VGB and SWAN calculation models.


4 PowerPlant Chemistry 2014, 16(1)

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and cation conductivities, the pH was calculated with theVGB and the SWAN calculation models. Additionally, thecalculated pH was compared with the calculated pH val-ues of the differential conductivity calculation systems toplot the deviations.

COMPARISON OF THE pH CALCULATIONMODELS

1. Mixture of ammonia and ethanolamine with sodiumchloride contamination

In the first example, three variables are used:

• Alkalizing agent no. 1: Ammonia with a concentration of0 mg · kg–1 to 2 mg · kg–1

• Alkalizing agent no. 2: Ethanolamine with a concentra-tion of 0 mg · kg–1 to 2 mg · kg–1

• Contamination with 50 µg · kg–1 sodium chloride

In Figures 4 and 5, the simulated pH and specific conduc-tivity before the cation exchange resin are shown withrespect to the ammonia and ethanolamine (ETA) concen-trations. The two figures summarize the results of steps 2and 3 of the modeling process shown in Figure 2.

Assuming that both alkalizing agents remain in the cationexchange resin and sodium chloride is exchanged forhydrochloric acid, the strong acidic solution has a simulated pH of 6.062 and a cation conductivity of0.369 µS · cm–1.

The simulated specific and cation conductivities wereused to re-calculate the pH of the solution with the VGB

and SWAN calculation models. The calculated pH wascompared with the simulated pH shown in Figure 4 to cal-culate the deviation, expressed as �pH.

In Figures 6 and 7, the VGB and SWAN pH calculationmodels are compared for one alkalizing agent only and acontamination of 50 µg · kg–1 sodium chloride. In Figure 6,the deviation of the VGB model becomes relevant atammonia concentrations lower than 1 mg · kg–1. For con-ditions with ethanolamine only, the VGB model's result is0.05 pH units higher than the simulated pH.

Figures 8 and 9 demonstrate that the VGB and SWAN calculation models perform well even in a mixture ofammonia and ethanolamine and with a simulated sodiumchloride contamination of 50 µg · kg–1. The only exclusionzones are the limits of the pH calculation models, whichmeans below a pH of 8 and in regions where one alkalizingagent is present.

2. Mixture of ammonia and morpholine with sodiumchloride contamination

This simulation follows the first example, but with morpho-line as the second alkalizing agent. Additionally, the con-centration ranges of the alkalizing agents have beenincreased to 4 mg · kg–1 to get closer to real dosing condi-tions in French nuclear plants [5].


• Alkalizing agent no. 2: Morpholine with a concentrationof 0 mg · kg–1 to 4 mg · kg–1

• Contamination with 50 µg · kg–1 sodium chloride

10

9

8

72.0

1.51.0

0.50 0

0.51.0

1.52.0

pH

NH [mg kg ]

3

–1

·ETA [mg kg ]

· –1

Figure 4:

pH before cation exchange resin.

00.5

1.01.5

2.0

NH [mg kg ]

3

–1

·

1.51.0

0.50

ETA [mg kg ]· –1

2.0

10.0

5.0

0

�[µ

Scm

]·

–1

Figure 5:

Specific conductivity in mixture of NH3 and ETA.





The pH and specific conductivity with respect to the alka-lizing agent mixture are simulated in Figures 10 and 11.After a cation exchange resin, the pH and cation conduc-tivity are the same as in the first example (pH = 6.062, � = 0.369 µS · cm–1).

In Figures 12 and 13, the VGB and SWAN pH calculationmodels are compared with the simulated pH value of thesystem. The VGB model does not include morpholine, thisexplains why the error increases at low ammonia concen-trations. The opposite behavior is shown with the SWANmodel, which gives the best results with low ammonia con-centrations. Even if the wrong alkalizing agent – morpho-

line instead of ammonia and vice versa – is run, SWAN'scalculation gives an error not higher than 0.04 pH units.

3. Mixture of ammonia and ethanolamine with carbondioxide contamination

In this model, the contamination source is a weak acid(carbon dioxide reacts with water to form carbonic acid).The concentration ranges of the alkalizing agents arecomparable with those from example no. 1.


0.04

0.02

0

–0.02

–0.04

�pH

0 0.5 1.0 1.5 2.0

NH [mg kg ]3–1·

VGB model

SWAN model

Figure 6:

Deviation with one alkalizing agent only (NH3).

0.04

0.02

0

–0.02

–0.04

�pH

0 0.5 1.0 1.5 2.0

ETA [mg kg ]· –1

VGB model

SWAN model

Figure 7:

Deviation with one alkalizing agent only (ETA).

0.05

0

–0.05

2.01.51.00.5

00

0.5

1.0

1.5

2.0

�pH

NH [mg kg ]3 –1·ETA

[mg

kg]

·–1

Figure 8:

pH deviation of VGB calculation model.

0.05

0

–0.05

2.01.51.00.5

0

0

0.5

1.0

1.5

2.0

�pH


[mg

kg]

·–1

Figure 9:

pH deviation of SWAN calculation model.



PPChem


• Carbon dioxide (CO2) contamination of 50 µg · kg–1

Sources of carbon dioxide intake are air leakages anddecomposition products of organic substances in thewater-steam cycle. Carbon dioxide is highly soluble inalkaline water because it reacts with water to form car-bonic acid ions. In Figure 14, it is shown that the pH of thewater decreases because of the weak acid. The carbonicacid ions will pass the cation exchange resin, giving a lowpH of 6.271 and an increased cation conductivity of0.214 µS · cm–1. In other words, the 50 µg · kg–1 CO2

increases the cation conductivity from 0.055 to0.214 µS · cm–1 after the cation exchange resin.

In Figure 15, the influence of CO2 on the pH calculation ofa system containing only ammonia is shown. The devia-tion is a consequence of the assumption that an increasedcation conductivity is treated as sodium chloride contami-nation. This error becomes more important with lowerammonia concentrations. Although the properties of CO2

are completely different from sodium chloride, the influ-ence on pH calculation based on differential conductivitymeasurement is negligible.

10

9

8

74.0

3.02.0

1.00 0

1.02.0

3.0

4.0

pH

NH [mg kg ]

3

–1

·Morpholine [mg kg ]

· –1

Figure 10:

pH before cation exchange resin.

01.0

2.03.0

4.0

NH [mg kg ]

3

–1

·

3.02.0

1.00

4.0

15.0

10.0

5.0

0

�[µ

Scm

]·

–1

Morpholine [mg kg ]· –1

Figure 11:

Specific conductivity in mixture of NH3 and morpholine.

0.04

0.02

0

–0.02

–0.04

�pH

0 1.0 2.0 3.0 4.0

NH [mg kg ]3–1·

VGB model

SWAN model

Figure 12:

pH deviation in water containing 4 mg · kg–1 morpholine and 50 µg · kg–1 NaCl.

0.04

0.02

0

–0.02

–0.04

�pH

0 1.0 2.0 3.0 4.0

Morpholine [mg kg ]· –1

VGB model

SWAN model

Figure 13:

pH deviation in water containing 0 mg · kg–1 NH3 and 50 µg · kg–1 NaCl.





Degassed cation conductivity (the sample after a strongacid ion exchanger is degassed to remove the carbondioxide) is a powerful tool to eliminate the influence of CO2

on the cation conductivity. In this example, 50 µg · kg–1

CO2 increased the cation conductivity from 0.055 to0.214 µS · cm–1. However the influence of the too highcation conductivity reading on the pH calculation is hardlymeasurable.

4. Mixture of ammonia and ethanolamine with carbondioxide and sodium chloride contamination

In this example, ammonia and ethanolamine are combinedwith two contaminations.



• Carbon dioxide (CO2) contamination of 50 µg · kg–1

• Contamination with sodium chloride of 50 µg · kg–1

With a contamination of 50 µg · kg–1 sodium chloride and50 µg · kg–1 CO2, the simulated pH after the strong acidion-exchange resin is 5.929 with a cation conductivity of0.491 µS · cm–1.

The simulated model represents conditions which areclose to or higher than the limitations of cation conductiv-ity in water-steam cycles. Figures 16 and 17 show the pHdeviation of the much simpler calculation model based ondifferential conductivity compared with that of the com-plex pH simulation model. The green color indicates

regions where the deviation is between 0.00 and 0.02 pHunits, yellow from +0.02 to 0.03, orange from 0.03 to 0.04and red is for deviations +0.04 and higher. The scale fornegative deviations uses bluish colors accordingly.

It is clear that the VGB calculation model gives slightlybetter values with high ethanolamine concentrations.However with lower alkalizing agent concentrations, thepH values are too low. Therefore, the SWAN calculationreturns better results with lower alkalizing agent concen-trations or if the sample pH is below 8. In summary, thedeviations from the VGB and SWAN models are lowerthan 0.05 pH units. In consideration of the conditions inthe water-steam cycle (pH between 8 and 10.5), the devi-ations are lower than 0.02 pH units.

CONCLUSION

Two pH calculation models based on differential conduc-tivity measurement were compared with a simulated pH inmixtures of alkalizing agents. Additionally, contaminationswith sodium chloride and carbon dioxide were simulatedto model the conditions in a water-steam cycle as realisti-cally as possible.

On the basis of realistic simulated water-steam cycle con-ditions, the following conclusions can be drawn for mix-tures of alkalizing agents:

• In a pH range from 8 to 10.5, the deviation of both pHcalculation models was lower than 0.02 pH units.

10

9

8

72.0

1.51.0

0.50 0

0.51.0

1.52.0

pH

NH [mg kg ]

3

–1

·ETA [mg kg ]

· –1

Figure 14:

pH with 50 µg · kg–1 dissolved carbon dioxide.

0

–0.01

–0.02

–0.03

–0.04

–0.05

�pH

0 0.5 1.0 1.5 2.0

VGB model

SWAN model

NH [mg kg ]3–1·

Figure 15:

pH deviation from CO2 with 0 mg · kg–1 ETA.



PPChem

• In samples with a pH lower than 8.5 and a high con-tamination source, SWAN's expanded pH calculationmodel gives better results than the VGB calculation.

• Deviation in pH calculation due to carbon dioxide as acontaminant is insignificant.

pH calculation based on differential conductivity measure-ment is a reliable and low maintenance alternative to ionselective pH measurement even in samples containingmixtures of alkalizing agents.

REFERENCES

[1] Sampling and Physico-Chemical Monitoring of Waterand Steam Cycles, 2012, VGB PowerTech ServiceGmbH, Essen, Germany, VGB-006-00-2012-09-EN

[2] Maurer, H., On-Line pH-Measurement by DifferentialCation and Specific Conductivity, 1997. Presented atthe 1997 International Chemistry On-Line ProcessInstrumentation Seminar in Clearwater Beach, FL,U.S.A.

[3] Bursik, A., PowerPlant Chemistry, 2009, 11(4), 220.

[4] Wagner, H., PowerPlant Chemistry, 2012, 14(7), 455.

[5] Nordmann, F.; Aspects on Chemistry in FrenchNuclear Power Plants, 2004. Presented at the 14thInternational Conference on the Properties of Waterand Steam in Kyoto, Japan.

THE AUTHORS

Marco Lendi (B.S., Chemistry, University of AppliedScience, Zurich, Switzerland) joined SWAN AnalyticalInstruments in 2009 working first as a quality manager andstarting in 2010 in SWAN's customer support group. In2012 he was promoted to the R&D group.

Heinz Wagner (Ph.D., Physical Chemistry, University ofZurich, Switzerland) has a 35-year background in researchand development for optical systems for industrialprocess applications in gas and water analysis. He heldpositions as the head of R&D for photometric gas analysisfor Tecan AG (Switzerland) and in online spectrometry withOptan AG (Switzerland) before joining SWAN AnalyticalInstruments in 2003 as a research scientist for water qual-ity control applications.

Peter Wuhrmann (Ph.D., Analytical Chemistry, SwissFederal Institute of Technology ETHZ, Zurich, Switzerland)conducted several years of research work with ion-sensi-tive microelectrodes for intracellular ion measurements atthe Institute of Cell Biology at the Swiss Federal Instituteof Technology (ETHZ). He was a member of the foundinggroup of SWAN Analytical Instruments, where he has beenresponsible for R&D since 1991.

CONTACT

Marco LendiSWAN Analytical Instruments AGP.O. Box 3988340 HinwilSwitzerland

E-mail: [email protected]

0.04

0.02

0

–0.02

–0.04

�p

H

2.01.51.00.5

00

NH [mg kg ]3 –1·

0.5

1.0

1.5

2.0

ETA[m

gkg

]

·–1

Figure 16:

pH deviation of VGB calculation model.

0.04

0.02

0

–0.02

–0.04

2.01.51.00.5

0

0

0.5

1.0

1.5

2.0

�p

H


[mg

kg]

·–1

Figure 17:

pH deviation of SWAN calculation model.




n Battery-powered instrument for standalone operation

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