By John W. Ryznar

Re

prin

t R

-20SM

An index for determiningthe amount of calciumcarbonate scale formedby a water

of which have been determined. K'2 is the second dis-sociation constant for carbonic acid, and K's is theactivity product of calcium carbonate. The term (K'2– K's) varies with ionic strength, dissolved solids, andtemperature. pCa is equal to the negative logarithmof the calcium ion concentration in moles per liter;pAlk is the negative logarithm of the total alkalinityof the water to methyl orange in terms of titratableequivalents per liter.

Larson and Buswell, using more recent data for evalu-ation of the constants and their variation with tem-perature and total dissolved solids, express theformula for the pH of CaCO3 as:

KspHs = log K2

– log (Ca+2)

– log (alk) + 9.30

2.5 √ u+ 1 + 5.3 √ u + 5.5

In this equation (Ca+2) and (alk) are expressed in partsper million as Ca and CaCO3, respectively.

The difference between the actual pH of a sample ofwater and its calculated pH is the measure of thedegree of calcium carbonate saturation and has beencalled the saturation index or:

Saturation Index = Actual pH – pHsA plus value for the saturation index indicates a ten-dency to deposit CaCO3; a minus value indicates atendency to dissolve CaCO3.

The saturation index is only qualitative, and, asLangelier emphasized, “the saturation index is anindication of directional tendency and of drivingforce, but it is in no way a measure of capacity.”The saturation index, however, is not alwaysreliable in predicting this because some wa-ters with a positive index may actuallybe quite corrosive.

The purpose of this investigation was to obtain aformula that will give a quantitative index of theamount of calcium carbonate scale that would beformed by a water at any temperature up to 200°Fand to predict, if possible, the corrosiveness of wa-ters that are non-scale forming. This information wasalso desired for waters in which inhibitors of thepolyphosphate or molecularly dehydrated phosphatetype were present.

Scale formation in distribution mains, domestic hot-water heaters, and various types of cooling equipmentis well known. Scale is also a problem in boilerfeedwater heaters and feedwater lines. In view ofthese and other problems caused by undesirabledeposits and incrustations, a formula having quanti-tative significance would be of great value in predict-ing the behavior of a water and in recommending thenecessary corrective treatment.

The molecularly dehydrated phosphates were studiedbecause of their ability to stabilize a water and thusprevent deposition of CaCO3. It was thought that thisquantitative index or formula could be best obtainedby using the values and corrections for the differentequilibria affecting calcium carbonate solubility.

The factors affecting CaCO3 solubility equilibria havebeen studied by many investigators. Larson andBuswell, in their paper “Calcium Carbonate Satura-tion Index and Alkalinity Interpretations,” give a goodbibliography on this phase of the problem. Prof. W. F.Langelier receives credit for first developing a gen-eral expression that takes into consideration thedifferent readily determined variables in a wateraffecting CaCO3 solution or precipitation.

For waters in a pH range of 6.5-9.5, Langelier’s for-mula for the pH at which a water is in equilibriumwith calcium carbonate is:

pHs = (pk'2 – pk's) + pCa + pAlk

K'2 and K's are apparent constants computed fromthe true thermodynamic constants K2 and Ks, values

The effect of a molecularly dehydrated phosphate onthe stability index of a water was studied. Thepolyphosphates have the ability of stabilizing an oth-erwise unstable water. In the presence of smallamounts of these phosphates, a water that would or-dinarily form a heavy deposit of CaCO3 remains stablefor extended periods of time.

EXPERIMENTAL WORK

In determining the pHs of a water, the constants andcorrections for salinity and temperature as given byLarson and Buswell were used. At higher dissolvedsolids and temperatures, the values were extrapolatedusing the same formulas as for obtaining pHs at thelower dissolved solids and temperatures. No attemptwas made to check experimentally, at the higher tem-peratures and salinity, the values thus obtained ofthe constants K'2 and K's.

Experimental tests to determine the amount of scaleformed by various waters were made on watershaving different 2pHs – pH values and on differentwaters having similar 2pHs – pH values.

The equipment for carrying out these tests is shownin Figure 1. In the tests reported, the water waspassed through the system only once.

Reasons for this are that the Langelier index doesnot indicate how much calcium carbonate will deposit,nor does it indicate whether a state of supersatura-tion will be present that will be great enough to pro-duce a precipitate, or whether it is great enough togive a protective film. This can be seen more clearlyby assuming that there are two waters with the fol-lowing characteristics:

Water A at 75°C; pHs = 6.0;actual pH = 6.5;Saturation Index = + 0.5

Water B at 75°C; pHs = 10.0;actual pH = 10.5Saturation Index = + 0.5

The saturation index would predict both waters to beequally scale forming. Actually, water A would be scaleforming, while water B would be quite corrosive.

To eliminate misinterpreting a positive saturationindex as being non-corrosive or scale forming, a newempirical expression, 2pHs – pH, is proposed.

The value obtained by the expression 2pHs – pH iscalled the stability index to differentiate it from thesaturation index. This stability index is not only anindex of CaCO3 saturation, but is also of quantitativesignificance. Using this expression, waters are muchmore accurately typed to determine whether scaleformation or corrosion is to be expected.

Experimental data have been correlated with this ex-pression so that a semi-quantitative value can bederived for the amount of calcium carbonate scale thatwill be formed, and a qualitative estimate can be madeto indicate whether serious corrosion may be expected.

Using waters A and B, the following values would beobtained for the stability index:

Water A Water BSaturation Index +0.5 +0.5Stability Index +5.5 +9.5

Unlike the saturation indexes for these two waters,the stability indexes are quite different. The stabil-ity index will be positive for all waters. Experimen-tal results obtained on various waters indicate thatthe behavior of natural and treated waters having astability index of 5.5 will be similar and will give anappreciable amount of calcium carbonate scale.

Waters having a stability index of 9.5 will form onlya limited amount of calcium carbonate scale and may beseverely corrosive, especially at higher temperatures. Figure 1 — Apparatus for incrustation tests

Two tests were made simultaneously. The coils werecarefully cleaned, dried, and weighed before andafter each test to determine the amount of scale de-posited from the water.

The constant temperature baths could be adjusted togive an effluent temperature of the water from roomtemperature to the boiling point at any desired flowrate. The tests reported here were made at effluenttemperatures of 120, 160, and 200°F. All tests wereof two hours’ duration with a flow rate of 1 gallon.

This apparatus has been used in the laboratory forseveral years and gives results that can be easilyreproduced.

The incrustation obtained in these glass coils has beenchecked with field results. Good correlation has beenobtained in all cases, so that a water giving a certainnumber of milligrams deposit can be predicted eitheras giving trouble-free conditions or an objectionablescale in a certain length of time. This permits rapidrecommendation of the proper stabilizing or correc-tive treatment where necessary.

The results on incrustation on various waters are plot-ted against the stability index (Figure 2). Withoutstabilizing treatment, a water having a stability in-dex of approximately 6.0 or less is definitely scaleforming, while an index above 7.0 may not give a pro-tective coating of calcium carbonate scale. Corrosionwould become an increasingly greater problem as thestability index increased to above 7.5 or 8.0.

With polyphosphate, a water with a stability indexas low as 4.0 can be used at temperatures up to 200°Fwith little danger of scale formation. Inasmuch asthese phosphates also have definite corrosion inhibit-ing powers, a water with a stability index around 7.0 –8.5 may be profitably treated with these phosphates.

Although the points in the curves lie fairly close alongthe plotted lines, it is not claimed that any and allwaters will fit the curves as well. It is quite possiblein some cases that the stability index may be low,indicating a scaling tendency. Yet if the alkalinity isdue mainly to hydroxyl ion, there would be very littleCO3 present to give CaCO3. This would be especiallytrue of some lime-soda softened waters. However, itis felt that a water having a stability index of 7.5 ormore will not form a protective layer of CaCO3.

To determine how the laboratory results compare withfield results, a number of cases were taken at ran-dom, in which the analyses of the waters were com-

plete and the history of the behavior of the water wasknown. The values for pHs were calculated, using theformula of Larson and Buswell.

In most of the cases very little information was givenin the literature regarding the condition of the cold-water mains. The stability index, in most cases, indi-cated a corrosive tendency was present. The reactionsin the cold may have been slow and escaped notice,but it is felt that tuberculation due to corrosion hadin too many cases been taken in a matter-of-fact wayas something to be expected.

A New England Water Works Association (NEWWA)report shows that, based on tests of 473 pipelines in19 different systems, the average loss in capacity oftar-coated cast iron pipe, after 30 years of service,was 52%. Small mains carrying active water may loseover 60% of their capacity in this length of time. Thisrepresents a serious economic loss. Although tuber-culation due to corrosion is the most frequent causeof loss of flow due to increased friction, in certain casesthis could be due to incrustation formed by an un-stable water.

The data obtained by NEWWA indicated that therewas a marked correlation between the pH value ofwater carried and the rate of capacity loss in the

Figure 2 — Laboratory results showing relationshipbetween stability index and incrustation

N A L C O C H E M I C A L C O M P A N YONE NALCO CENTER NAPERVILLE, ILLINOIS 60563-1198

Registered Trademarks of Nalco Chemical Company Printed in U.S.A. 8-86

mains. Waters with a pH value of 6.5 gave twice theloss in capacity in a given length of time as thosehaving a pH value of 8.0.

Apparently, a water having a stability index of ap-proximately 6.0 at about 60°F, to which a stabilizingtreatment of polyphosphate has been added, shouldgive the best results in terms of minimum corrosionand/or scale in the whole system. Under these condi-tions, corrosiveness due to aggressive carbon dioxidewould be near the minimum in most cases.

On the whole, the field data correlate very well withthe laboratory results for the different stability in-dexes (Figure 3). Only those values are plotted wheredefinite information is given for a particular tempera-ture range. With a stability index of 7.5 or higher at140°F, corrosion is marked. At indexes of 9.0 or higher,corrosion is serious.

The stability index should implement the usefulnessof the saturation index, and should help to predictmore accurately how badly scaling or corrosive a par-ticular water supply may be.

Figure 3 — Field results superimposed on curve Aof Figure 2