This paper presents a model for predicting the scaling tendenciesof barium, strontium, and calcium sulfates resulting from the mixing ofinjected and formation waters and from temperature and pressure effects. The model also predicts competitive simultaneous coprecipitation of BaSO4, CaSO4, and SrSO4, where sulfate is the common ion, reflecting theprecipitation of more than one sulfate mineral. The supersaturations andamounts of precipitation of the sulfates are calculated from their solubilities, which in turn are calculated by the Pitzer equation forelectrolyte ion activity coefficients.


In North Sea operations where seawater injection is a commondevelopment practice, barium, calcium, and strontium sulfate scaledeposition is a concern. Barium sulfate and related scale occurrenceis considered a serious potential problem that causes formationdamage near the production-well zone. Sulfate scales may resultfrom changes m temperature and/or pressure while water flows fromone location to another, but the major cause of sulfate scaling isthe chemical incompatibility between the injected seawater, whichis high in sulfate ions, and the formation water, which originallycontains high concentrations of barium, calcium, and/or strontiumions. An accurate, convenient, and fast model capable ofpredicting such scaling problems may be helpful in planning a waterfloodscheme. It may also aid in selection of an effective scaleprevention technique through the prediction of scaling tendency, type, andpotential severity. The model presented here is considered animprovement on the previous models.

Previous models neglected various aspects that affect scaling, and as a result, large errors may occur in scale prediction at certainconditions. Early prediction methods did not consider the pressureeffect on scaling. Another shortcoming of some of theprevious models lies in the assumption of salt solubility as the uniquefunction of sodium chloride concentration or ionic strength. Pucknell did consider the specific ion effect on solubility causedby the existence of Mg2+ and SO42-ions, but his solution israther empirical and not very reliable. Most of the models predictscale formation of only one mineral without considering the effectof the potential formation of other minerals in the samesolutions. This simplified treatment may lead to erratic conclusionswhen different scaling ions compete for a common ion componentto form scale. For example, in a solution containing Ba2 +, Ca2 +, and SO42 - ions, SO4 2 - ions are shared by Ba2 + and Ca2 + ions in forming BaSO4 and CaSO4 scales, and a separate scaleprediction for either BaSO4 or CaSO4 must give incorrect results byassuming that all the SO4 2 - ions in the solution are involved in the scaleformation of only one sulfate mineral. Vetter et al. reported a model forpredicting simultaneous precipitation of CaSO4, BaSO4, and SrSO4- Fig. 2 of Ref. 6 suggests that the effect of scaling of a less soluble sulfate, suchas BaSO4, on the precipitation of more soluble SrSO4 and CaSO4 wasconsidered, but the reverse effect (such as CaSO4 on BaSO4 and SrSO4) wasnot taken into account.

The model described in this paper was developed from asolubility-prediction model that generates sulfate solubilities atvarious solution compositions, temperatures, and pressures. Thesolubilities used in the scaling-tendency prediction are calculated fromthe Pitzer equation for electrolyte mean activity coefficients inaqueous solutions, which has been widely used since it was proposedby Pitzer and his coauthors. Solubilities of sparingly soluble salts (such as BaSO4, CaSO4, and SrSO4) over a-wide range ofion concentrations and compositions have been accuratelycalculated at 25 degrees C with the Pitzer equation. In the modelpresented in this paper, the Pitzer equation was successfully used incalculating CaSO4, BaSO4, and SrSO4 solubilities over wideranges of temperatures and solution compositions. The calculated solubilities agree reasonably well with the published data.

An iterative model based on the solubility prediction model wasdeveloped for predicting sulfate scaling tendency.

In the North Sea, it is common for two or three Ba +, Sr2 +, and Ca2+ ions to coexist in a formation water and to precipitate with SO4(2-)ions. In such a situation, the separate calculation of oneof scale without taking into account the effect of theconsumption of SO4(2-) ions by the other scale precipitation is unable toreflect the competition for SO4(2-)anions between the scalingcations. On the other hand, sequential calculation of the precivitationof the three sulfates starting from the least soluble BaSO4, then SrSO4, and finally the most soluble CaSO4 also ignores the effect of the more soluble scale formation (CaSO4) on the less solublescale formation (BaSO4). To avoid these deficiencies, the modelincludes an iteration method for calculating the simultaneousscaling problems of more than one sulfate mineral. The model predictssulfate scaling problems based on the thermodynamic solubilities. The influence of kinetic or dynamic factors is not taken into account.

A detailed description of the Pitzer equation, theparameterization of the virial coefficients in the equation, solubilityprediction, and the development of the scaling prediction model are givenhere. The predicted results for single solutions and mixed waters, thetemperature and pressure effects, and the scaling-tendency changewith the mixing ratio of two waters are discussed and comewith the results from previous models.

Pitzer's Approach

The general form of the Pitzer equation for electrolyte meanactivity coefficient is

In ymx = [zmzx]fy+(2vM/v) ma[BMa+(Emz)CMaa

+(vX/vM) Xa]+(2vX/v) Mc[BcX+(mz)CcXc

+(vM/vX) Mc]+ mcma[zMzX B'cac a+v-1(2vMzMCca+vM Mca+vX caX)]

+1/2 McMc'[(vX/v) cc'X+ zMzX 'cc']c c'+1/2 MaMa'[(vM/v) Maa'+zMzX 'aa'],.......(1)a a'

where mz= McZc= Ma Za .c a

Eq. 1 is composed of two parts. The first part is a modifiedDebye-Huckel term shown in Eq. 2 that accounts for the long-rangeelectrostatic interaction between ions:

fY = −A [I1/2 /(l+l.21 1/2)+(2/1.2)ln(1+1.21 1/2)].......... (2)


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