Formation of Scales of Calcium Carbonate

Polymorphs: The Influence of Magnesium

Ion and Inhibitors
G.H. Nancollas, State U. of New York
K. Sawada, * Niigata U., Japan

Summary
The crystallization of calcium carbonate on calcite and crystallize from aqueous solution in at least three forms
aragonite at 70°C has been investigated by use of a - calcite, aragonite, and vaterite. Although calcite has
highly reproducible seeded growth technique. In both the greatest thermodynamic stability at ambient condi-
cases the rates of reaction are proportional to the square tions, the thermodynamically less stable aragonite and/or
of the relative supersaturations and are surface con- vaterite phases may be stabilized under certain condi-
trolled. The presence of low levels of magnesium ion in- tions of temperature or in the presence of other ions.
hibits calcite growth with the formation of magnesian Many surface waters contain appreciable quantities of
calcite, while at higher concentrations the spontaneous magnesium ion, and its influence on the mineralogy and
precipitation of aragonite takes place. Hydroxyethyl- morphology of calcium carbonate has been investigated
idene 1,1 diphosphonic acid (HEDP), a potential scale intensively. 2 Thus, it is well established that the
inhibitor, markedly reduces the growth rate of both magnesium ion favors the precipitation of aragonite
calcite and aragonite but has little effect on the rather than calcite. 3-5 In addition, this additive markedly
crystallization of vaterite, the least thermodynamically inhibits the nucleation and crystal growth of calcite and
stable calcium carbonate polymorph. The exclusive sometimes induces formation of needle-like magnesian
growth of vaterite on vaterite seed at 70°C under these calcites, MgCal. In contrast, the crystal growth of
conditions strikingly demonstrates the possibility of the aragonite is scarcely affected by the presence of
formation of intermediate metastable precursors during magnesium ion. 6,7
scale formation. The inhibition of calcite growth by magnesium ion has
been attributed to various factors. Reversible adsorption
Introduction at active growth sites on the calcite crystals may prevent
The precipitation and dissolution of calcium carbonate is crystallization; the magnesium ion therefore behaves as a
important in a wide variety of fields. 1 Most subsurface simple surface poison, 3,8 allowing the aragonite, which
waters produced with oil and gas contain relatively high precipitates more rapidly, to be stabilized kinetically. 4
concentrations of calcium ions. Moreover, since the con- Another view is that the incorporation of magnesium ion
centration of CO 2 in these waters is usually considerably into the growing crystalline phase during the formation
greater than that at the surface, calcium carbonate is one of magnesian calcite introduces strain into the lattice
of the more important scale-forming minerals in oil and with concomitant increase in solubility of the solid
gas production. In thermal flood operations, the reinjec- phase. 9,10 The resulting decrease in the degree of super-
tion of waste water into subsurface formations frequently saturation therefore leads to an apparent retardation of
introduces the problem of calcium carbonate scale for- calcite growth caused by the decrease in driving force.
mation. Although this often can be controlled by lower- The incorporation of magnesium ion having a smaller
ing the pH of the solution contacting the surfaces, the ionic radius compared with the calcium ion produces
problem is made more acute by a decreasing solubility appreciable lattice strain on the surface of the calcite, 2, 11
with increasing temperature and because the salt can inhibiting further crystal growth. This model also ac-
counts for the observed formation of needle-like crystals
'On leave with State U. of New York during the growth of calcite in the presence of mag-
0149-213618210003-8992$00.25
nesium by preferentially poisoning crystal growth
Copyright 1982 Society of Petroleum Engineers of AIME perpendicular to the c axis. 2
MARCH 1982 645
 Since the solubility of calcium carbonate decreases and filtered (0.22-lLm Millipore filter), and the concen-
with increasing temperature, the problem of scale forma- tration of calcium and magnesium ions was determined
tion is even more serious at the higher temperatures by atomic absorption spectroscopy. The crystallization
downhole. In addition, the temperature coefficients of cell also contained glass and calomel electrodes so that
the kinetic parameters for the formation of various poly- the pH change accompanying the crystal growth reaction
morphs may be quite different, and this is reflected by could be monitored. The electrode system was calibrated
the stability of the solid phases under specific conditions before and after each crystallization experiment with
of temperature and ionic strength. In view of the impor- potassium dihydrogen phosphate and borate buffer solu-
tance of these kinetic factors for the elucidation of the tions prepared by Bates' procedure. 12
mechanism of calcium carbonate precipitation and The seeded growth technique has the advantage that
dissolution, a highly reproducible seeded growth tech- crystal growth takes place on a well-defined surface of
nique.was used to study the growth of calcium carbonate known morphology. In the field, precipitation invariably
on calcite and aragonite seed material in the absence and takes place on a surface already present, either on the
presence of magnesium ion at a temperature of 70°C. In mineral itself or on a metal offering available sites for
addition, HEDP's influence on these reactions has been adsorption of lattice ions. The seeded crystal growth
investigated. Finally, the crystal growth of the thermo- methods therefore simulate field conditions much more
dynamically least stable form of calcium carbonate, closely than spontaneous precipitation studies. The dif-
vaterite, has been investigated at 70°C and in the ficulty of reproducing the results of spontaneous ex-
presence of HEDP. The resulting stabilization of vaterite periments is well known since the size and size distribu-
by scale inhibitor is striking. tion of the precipitated particles change continuously
during the reaction. In the case of calcium carbonate,
Experimental there is evidence that the initially formed phase rapidly
Reagent-grade calcium chloride and magnesium chloride undergoes transformation into calcite crystals. *
were recrystallized from triple-distilled water in the Results and Discussion
absence of CO 2 , Other solutions were prepared from the
analyzed analytical-grade reagents without further purifi- To analyze the kinetic data in terms of the free ionic
cation. Calcite seed crystals were prepared by addition of species, it is necessary to take into consideration the for-
5 L of 0.2 M calcium chloride solution to 5.5 L of 0.2 M mation of ion-pairs. For MgC0 3 and MgHC0 3 , the
sodium carbonate solution at 25°C at a rate of 250 thermodynamic equilibrium constants, K(MgCO 3) =
mLih - I. The calcite suspension was allowed to age (MgC0 3 )/(Mg2+)(CO}-) and K(MgHC0 3 ) =
with stirring for 1 day, the crystals were filtered (MgHCO 3+ )/(Mg2+ )(HCO 3-), where parentheses
(0.22-lLm Millipore'M filter), and resuspended in distilled enclose activities of ionic species, have been measured at
water for 1 week. This process was repeated until the temperatures from 10 to 90°C. 13 The values at 70°C,
crystals were free of chloride ions, and then they were 1.91 x 10 3 M- I and 17.0 M- I , respectively, are in
filtered and dried at 150°C. Aragonite crystals were good agreement with those calculated from the Fuoss
prepared in a similar precipitation experiment that was theory of ion-pair formation, which expresses the ion-
carried out within 1 hour at 90°C. The slurry was filtered pair dissociation constant in terms of the energy of
rapidly, washed in 90°C triple-distilled water, and dried electrostatic interaction between the ions. 14 For the cor-
at 150°C. Seed crystals ofvaterite were prepared by ad- responding calcium species, CaC0 3 and CaHC0 3 , the
dition of 200 mL of 0.2 M calcium chloride solution to only data covering a range of temperature are those of
250 mL of 0.2 M sodium carbonate solution at 25°C, Martynova et al., 15 who used a calcium ion selective
with stirring. The reaction was allowed to proceed for 1 electrode to measure the activity of free calcium ions.
hour and then the vaterite crystals were filtered and dried However, their data of 25°C led to dissociation con-
at 80°C for 30 minutes. The seed preparations were stants that are considerably higher than those reported by
characterized by X-ray powder diffraction. The results a number of other investigators. Although their data
confirmed the absence of mixed polymorphs in the agreed with those of Nakayama, 16 the latter work was
calcite and aragonite samples and less than 3 % calcite in criticized by Reardon and Langmuir 17 because there ap-
the vaterite. Typical scanning electron micrographs peared to be a serious inconsistency in the charge
(SEM's) of the seed materials are shown in Fig. 1. balance equation used by Nakayama. In a careful poten-
Specific surface areas (SSA) were measured by a single- tiometric investigation, using a glass electrode, Reardon
point BET method (Brunaur, Emmett, and Teller) (30/70 and Langmuir 17 measured the dissociation constant for
N 2 IHe gas mixture). SSA values of calcite and aragonite CaC0 3 and CaHC0 3 and presented a critical survey of
seed were 0.70 and 1.35 m 2 g- l , respectively. the literature data. They proposed values over the
Crystal growth experiments were made in a tightly temperature range 10 to 50°C that could be represented
covered Pyrex™ vessel thermostated at 70.0 ± O.I°C. by the equation
Calcium carbonate supersaturated solution was prepared logK(CaC0 3 ) = -27.393+4114IT+0.0561T.
by dropwise addition of sodium carbonate to 500 mL of
calcium chloride solution containing sodium chloride to For the dissociation constant of CaHC0 3 from 15 to
maintain the ionic strength at the required value. Follow- 45°C, the conductance measurements of Jacobson and
ing verification of the stability of the supersaturated solu- Langmuir l8 yielded values given by the equation
tions, crystal growth was initiated by addition of the seed
crystals in the form of a slurry that had been ultrasoni- -logK(CaHC0 3 ) = 2.95-0.0133T.
cated for about I minute to break up aggregates. Ali-
quots of the growth solution were removed periodically 'Mullin, JW.: private communication, University College, London (1978)

646 JOURNAL OF PETROLEUM TECHNOLOGY

 a. b.

c. d.

e.

Fig. 1-SEM's of calcium carbonate. a, calcite seed; b, aragonite seed; c, vaterite seed; d, Experiment 12 after 30 minutes of growth;
e, Experiment 12 after 3 hours of reaction; f, Experiment 24 exclusive growth of vaterite in presence of HEDP after 16 hours of
reaction.

MARCH 1982 647

 TABLE 1-THE CRYSTALLIZATION OF CALCIUM CARBONATE AT 70°C

Seed
C ca C C03 C Mg Concentration" I k
Experiment (10- 4 M) (10- 4 M) (10- 4 M) pH (mgL -1) (M) (M min -1 mg -1 L)
-
1 2.49 9.75 0 9.38 56(C) 0.102 189
2 2.52 9.44 0 9.38 113 (C) 0.102 193
3"" 2.66 9.66 b 9.38 116 (C) 0.102 191
4 2.65 46.9 ci 8.63 68(C) 0.100 210
5 1.20 5.76 0 9.39 38 (C) 0.112 203
6 2.56 9.59 0 9.24 39 (A) 0.002 865
7 2.66 46.9 0 8.62 38 (A) 0.100 770
8 1.38 5.80 0 9.47 40 (A) 0.012 830
9 2.50 9.45 0.63 9.38 75 (C) 0.103 147
10 2.36 9.39 1.26 9.38 76 (C) 0.103 94
11 2.46 9.40 2.53 9.38 77 (C) 0.103 50
12 2.59 9.19 6.13 9.39 73 (C) 0.103 - 6t
13 2.04 9.29 6.18 9.40 232 (C) 0.103 -7t
14 2.39 9.11 12.1 9.39 72 (C) 0.103 - 2t
15 2.52 9.43 2.52 9.24 37 (A) 0.102 854
·c = calcite seed; A = aragonite seed .
.. Stirring rate is 300 rpm. Normal stirring rate is 600 rpm.
tEstimated from initial growth curves before spontaneous precipitation of aragonite at these higher C Mg values.

For this paper, the appropriate ion association constants Fig. 3. The excellent linearity of the plots confirms the
at 70°C were calculated from those data by the Fuoss applicability of Eq. 1 for the growth of both calcite and
equation,14 yielding the values of7.41 X 10 3 M- 1 and aragonite at 70°C. The thermodynamic solubility prod-
40.7 M- 1 for K(CaC0 3) and K(CaHC0 3 ), respective- ucts, 1.29 x 10 -9 M2 and 1.68 X 10 -9 M2 for calcite
ly. Activity coefficients of z-valent ions, y z' were and aragonite, respectively, were determined by allow-
calculated from the extended form of the Debye-Hiickel ing crystal growth experiments to proceed to equilib-
equation proposed by Davies 19: rium. These values are in satisfactory agreement with the
values 0.955 X 10- 9 M2 and 1.38 X 10- 9 M2 ob-
tained by Christ et al. 22 and wit;1 the value for calcite,
1.102 X 10 -9 M2, calculated from the temperature
where I is the molar ionic strength and A, the constant of coefficient data reported by Jacobson and Langmuir. 18
the Debye-Hiickel equation, has the value 0.56 at 70°C. The rate constants for crystallization obtained from the
slope of the plots in Fig. 3 are given in Table 1. As can
Crystal Growth of Polymorphs be seen from the results of Experiments 4 and 7 in Table
in the Absence of Magnesium Ion 1, a change of pH had little effect on the rate constant in
Initial conditions of the crystal growth experiments of spite of the considerable increase in total concentration
calcium carbonate are summarized in Table 1. It can be of carbonate ion. The rate constant remained unaltered
seen in Fig. 2 that crystal growth began immediately even at low ionic strength (Experiments 6 and 8, Table
with the introduction of seed crystals, and thereafter the 1), despite an appreciable increase in growth rate. This
concentration of calcium ion decreased monotonically. provides a striking illustration of the need to express the
In these experiments, the supersaturation ratio 6 = driving force for crystal growth in Eq. 1 in terms of ac-
[(Ca2+ )(COl- )/Kso] of the initial solution was approx- tivities of the ionic species. If concentration terms were
imately five, Kso being the thermodynamic solubility used, the rate constants would vary markedly with ionic
product. Solid phases withdrawn during the experiments strength. In Experiment 2 (Table 1) it can be seen that a
were characterized by X-ray diffraction and SEM, and change in concentration of seed crystals, s, had a negligi-
no evidence was observed for epitaxial growth of one ble effect on the rate constant, which, therefore, is
polymorph on another or for secondary nucleation in the directly proportional to the concentration of seed as re-
supersaturated solutions. It is interesting to note that quired by Eq. 1. From rate data at 70 and 25°C, 21 the
highly supersaturated solutions (6 > 9) were unstable activation energies for crystallization were calculated as
and precipitated aragonite spontaneously at 70°C. 42 kJ mol -1 and 77 kJ mol -I for calcite and aragonite,
The crystal growth of a number of sparingly soluble respectively. The value for calcite is in excellent agree-
electrolytes has been investigated in some detail, and ment with that (42 kJ mol-I) calculated from seeded
various rate equations have been proposed. 20 In the case growth crystallization data at lower temperatures, 15 to
of calcite crystal growth,21 the rate was proportional to 35°C. 23 Table 1 (Experiment 3) shows that the rate con-
the square of the relative supersaturation expressed in stant for crystallization was affected little by change of
terms o(the activities of the lattice ions: stirring speed in tI1e reaction vessel. This evidence
-dec together with an activation energy that is appreciably
___ a =ksl[(Ca2+)(COl-)] 'I, _Ks~/'J2 ..... (1) larger than that expected for bulk diffusion control in-
dt l .
dicates that the mechanism of crystal growth for both
In Eq. 1, k is the rate constant for crystal growth and s is calcite and aragonite at 70°C is one of chemical control.
a function of the number of growth sites on the added It is interesting to note that the rate constant for aragonite
seed crystals. Plots of the rate of crystallization as a growth was lower than that of calcite at ambient
function of [[(Ca 2+)(COl-)] 'I, _Ks~/2J2 are shown in temperature,23 while the reverse was true at 70°C. Tak-

648 JOURNAL OF PETROLEUM TECHNOLOGY

ing into consideration the difference in specific surface
area of the calcite and aragonite seed crystals, it is
estimated that the rate constants for crystallization of two
polymorphs would be equal at a temperature of approx-
imately 50°C.
The influence of temperature on the nature of the
polymorph that precipitates during spontaneous
precipitation of calcium carbonate has been investigated
extensively. Wray and Daniels 24 showed that at lower
temperature « 30°C) vaterite was the dominant phase,
."()
()

o
with transformation taking place to the thermo-
dynamically stable calcite over a period of about 10
hours. At about 40°C calcite was formed, while at
higher temperatures (45 to 50°C) both calcite and
aragonite were formed. Pure aragonite was shown to 10 20 30 40
precipitate at temperatures above 70°C. In the study
Time / min
reported here, the initial precipitation of vaterite was
confirmed at 25°C and transformation to calcite was Fig. 2-Plots of total calcium concentration as a function of time
complete in 3 to 5 hours. It is interesting to note that the for calcium carbonate crystal growth in the absence of
temperature (approximately 50°C) at which the rate con- magnesium ion at 70°C. 0, Experiment 1; e, Experi-
ment 2; CD, Experiment 4; . , Experiment 6.
stants of aragonite and calcite were approximately the
same is close to that for which a change in the nature of
spontaneously precipitating phase takes place.

Influence of Magnesium Ion

Crystallization experiments made in the presence of
magnesium ion are summarized in Table 1. Growth
curves for calcite seeded growth are shown in Fig. 4. It
can be seen that the growth rate decreased with increas- ~ 04
ing magnesium concentration, and at relatively low " 0
()
values (e Mg < - 2.6 X 10 -4 M) the calcium concen- 0

tration decreased monotonically following the addition ... '0

~
of calcite seed crystals. SEM's showed no change in 0.2
morphology of the grown magnesiari calcite phase com-
pared with that of the calcite seed crystals. X-ray diffrac-
tion patterns of the grown product were also similar to
those for grown calcite, with the exception of a slight 2 3
broadening of the 29.3° peak toward larger 2() values,
indicating the formation of calcite containing a small
amount of magnesium carbonate. 25 ,26 In this region of
magnesium ion concentration, the growth rate again Fig. 3-Plot of - dCCa/dt as a function of [f(Ca 2 +)(CO:f2)J'12 -
Kso '12 J2. 0, Experiment 1; e, Experiment 2; CD, Experi-
followed Eq. 1. The rate constants are listed in Table 1. ment 4; . , Experiment 6.
At higher molar concentrations of magnesium ion,
e Mg' it can be seen (Fig. 4) that the crystallization took
place in two distinct steps. The marked inhibition during
approximately the first 60 minutes was followed by a 3
rapid and spontaneous precipitation of a phase confirmed
as aragonite by X-ray diffraction. Typical SEM's at the
beginning and end of this second step are shown in Figs.
Id and Ie. The radial crystals of aragonite in Fig. Id ap-
peared about 30 minutes after inoculation with calcite
seed, and these crystals grew larger during the reaction o
()
(Fig. Ie). It is interesting to note that the initial induction ()

period was almost independent of magnesium ion con- "2

centration (Experiment 13, Fig. 4) and of seed concen-
tration, again pointing to a spontaneous precipitation of
aragonite in the presence of high concentrations of
magnesium ion. In an additional experiment, in which 60 120 180
no calcite seed was added to the supersaturated solution,
Time / min
spontaneous precipitation of aragonite, confirmed by X-
ray diffraction, took place with a morphology identical Fig. 4-Plots of total calcium concentration as a function of time
for calcium carbonate crystal growth in the presence of
with that of Fig. Ie. The results suggest that at high magnesium ion at 70°C. 0, Experiment 1; . , Experi-
e Mg, the crystal growth of magnesian calcite, MgCal, ment 9; e, Experiment 10; CD, Experiment 11; e, Ex-
on calcite seed crystals was followed by the spontaneous periment 12; W, Experiment 13; EB, Experiment 14.

MARCH 1982 649

 TABLE 2-CRYST ALLIZATION OF CALCIUM CARBONATE POL YMORPHS
AT 70°C IN THE PRESENCE OF HEDP

Seed
CCa Cco 3 HEDP Concentration *
Experiment (10 -4 M) (10 -4 M) (10- 7 M) pH (mg L -1)
16 2.50 9.50 0 9.40 57(C)
17 2.50 9.50 0.374 9.40 57 (C)
18 2.50 9.50 0.732 9.40 57(C)
19 2.50 9.50 0 9.40 37 (A)
20 2.50 9.50 0.70 9.40 37 (A)
21 2.50 9.50 1.49 9.40 37 (A)
24 3.36 11.0 27.0 9.18 220 (V)* *
'C = calcite seed; A = aragonite seed.
"Vaterite seed crystals.

precipitation of aragonite, while at lower C Mg levels, the solubility, measured as a function of the mole fraction of
crystallization of MgCal was nearly completed within magnesium ion by a dissolution procedure,25,30 was
the induction period for aragonite nucleation so that the almost constant up to about 4 % MgCal and increased
precipitation of this phase did not take place. The rate gradually with increase in magnesium content until the
constants for initial MgCal formation at high magnesium value was almost twice that of pure calcite at 10%
concentrations were estimated from the initial slopes of MgCal. In our pure solutions, however, it can be seen in
the growth curves using the solubility of MgCal Fig. 4 that even at very low C Mg levels the effective
calculated from the calcium concentration at the end of solubility of the grown phase increased continuously as
this part of the reaction. The values are given in Table 1 the magnesium concentration in solution was increased.
and, as can be seen from Experiment 13, in which a large The resulting decrease in MgCal crystal growth was
amount of seed was used, the growth rate was propor- caused not only by the possible incorporation of
tional to the seed concentration. Thus, during the initial magnesium ion into the solid phase but also by the reduc-
stage of the growth of MgCal, the reaction rate is hardly tion in driving force resulting from the increased
influenced by subsequent aragonite formation. A plot of solubility product of the solid phases formed. In these
log k as a function of magnesium concentration in solu- experiments (even after 4 hours, during which the nor-
tion was linear, and a similar result was reported at 25°C mal crystal growth of calcite and aragonite in the absence
by Benjamin et at. 27 of magnesium was completed), the calcium concentra-
The mole fraction of magnesium ion incorporated into tion continued to decrease with time. This suggests that
the grown phase, MgCal, was estimated by dissolving the formation of an initial, more soluble, phase was
known amounts of solid phase in acid and analyzing for followed by transformation to a more stable phase.
magnesium. The data are subject to considerable error
because of the very small amount of magnesium released Influence of HEDP
for analysis, but the mole fraction of MgC0 3 increases Crystallization experiments of calcite, aragonite, and
from about 3 to 5 % for an increase in magnesium ion vaterite in the presence of HEDP are summarized in
concentration in the supersaturated solution from 0.6 to Table 2. It can be seen in Figs. 5 (calcite) and 6
2.6 X 10- 4 M. At C Mg = 6.2 X 10- 4 M, the value (aragonite) that HEDP at a concentration as low as
was about 10%. At the highest magnesium ion concen- 10 -7 M markedly inhibited the seeded crystal growth of
tration (12.1 X 10 -4 M), the incorporation showed a these phases at 70°C. This is similar to the results of a
marked increase to more than 15 %, and this has been at- study at 25°C in which HEDP was shown to reduce the
tributed to the substitution of surface calcium sites in the rate of crystallization of calcite seed crystals. 31 At low
calcite seed crystals by magnesium ion. 28 Following this concentrations of HEDP, following initial rapid rates of
initial growth of MgCal on calcite seed at higher C Mg , crystallization for both calcite and aragonite, the reac-
the amount of magnesium ion in the solid phase scarcely tions proceeded to equilibrium concentrations ap-
increased during the second stage of spontaneous preciably larger than the solubilities of the pure phases.
precipitation of aragonite. This suggests that magnesium The growth curves did not follow the second-order rate
ion does not incorporate into aragonite, in agreement equation, Eq. I, which holds in the pure systems. SEM's
with the results of previous workers. 2 ,9 As can be seen and X-ray powder diffractograrns of the grown phases
from Experiment 15 in Table 1, a level of magnesium confirmed that no polymorph transformation or sec-
ion comparable with that of calcium in the supersaturated ondary nucleation took place during the reactions. Since
solution had almost no effect on the rate of aragonite the concentrations of HEDP were much lower than that
growth or the solubility of this phase. SEM's and X-ray of calcium ion in the solution, the decrease in the latter
diffraction measurements also confirmed the absence of caused by complexation with phosphonate additive was
any other calcium carbonate polymorph. The exclusion negligible. At higher HEDP, 7 x 10- 8 M for calcite
of magnesium ion during the growth of aragonite has and 10- 7 M for aragonite, the growth of both calcium
been attributed to the inability of this ion to fit into the carbonate polymorphs was quenched completely after
aragonite lattice. 2 approximately 10 minutes of reaction. It is likely that
Berner and Morse 8 and Morse et al. 29 suggested that HEDP inhibits crystal growth by adsorption at growth
MgCal containing 2 to 7% mol fraction of MgC0 3 sites and at these concentrations, the surface area of seed
would be more stable than pure calcite in seawater. The crystals covered per molecule of HEDP, assuming the
650 JOURNAL OF PETROLEUM TECHNOLOGY
 0' 03

~
~ o,~

:o[~· :
.. "
U
U
cY" •
j
o •2

OO'OL--------~------~~------~------~l~
,0 6O 90 12O 0 30 6O 120180

Time/min Time/min

Fig. 5-Seeded growth of calcite in the presence of HEDP. 0, Fig. 6-The seeded growth of aragonite in the presence of
Experiment 16; e, Experiment 17; 0, Experiment 18. HEDP, 0, Experiment 19; e, Experiment 20; 0, Experi-
ment 21.

fonnation of a monolayer, was approximately 10 nm 2 therefore may be attributed not only to its adsorption at
for both calcite and aragonite. The relatively rapid initial active growth sites but also to a decrease in the ther-
rate of crystallization in the presence of HEDP indicates modynamic driving force for the fonnation of magnesian
either coprecipitation of HEDP as a calcium salt at the calcite scales.
crystal surface or an adsorption process that requires 5. The importance of kinetic factors in detennining the
several minutes for completion. The influence of HEDP nature of the scale that fonns is demonstrated strikingly
on the crystallization of vaterite is particularly in- by the results of the vaterite seeded growth experiments.
teresting. In Table 2, Experiment 24, an HEDP concen- Although vaterite is the least thennodynamically stable
tration of 2.7 X 10 -6 M had little effect on the of the calcium carbonate polymorphs and cannot be
crystallization of vaterite seed crystals. The crystalliza- precipitated from solutions above about 30°C, the phase
tion proceeded with the exclusive fonnation of vaterite grows exclusively on vaterite surfaces at 70°C in the
on the surface of the vaterite seed crystals even though at presence of traces of the scale inhibitor, HEDP.
70°C vaterite is the most thennodynamically unstable Moreover, vaterite is stabilized kinetically by a fonna-
polymorph. The possible stabilization of this phase by tion rate considerably greater than that for calcite or
the presence of scale inhibitors may be of particular aragonite, both of which are inhibited by HEDP.
significance in the field. By inhibiting the fonnation of 6. The results of this study suggest that the fonnation
aragonite and calcite, the crystallization of vaterite is of intennediate metastable precursors during scale for-
favored and the reaction takes place with a rate ( - 2 x mation may detennine the nature of the final deposit and
10 -4 M min -I mg -I L), which is appreciably more the behavior of added scale inhibitors. To control scal-
rapid than that of either calcite (l x 10 -6) or aragonite ing, it is important to characterize the mechanisms of
(2 x 10- 6 Mmin- I mg- I L). fonnation of all calcium carbonate polymorphs and the
factors governing their interconversion.
Conclusions
The results of this study indicate the following. Nomenclature
1. The fonnation of both calcite and aragonite scales
at 70°C, over a range of supersaturation and composition I = molar ionic strength of solution
of ionic medium, takes place by a surface-controlled k = rate constant for crystal growth
process. K = thennodynamic association constant for the
2. The rate is dependent on the square of the relative fonnation of species enclosed in
supersaturation and is independent of changes in fluid parentheses
dynamics of the liquid phases contacting the solids. Kso = thennodynamic solubility product
3. The nature of the solid that separates as scale M = molar concentration, mol L - 3
depends on the substrate surfaces already present.
T = temperature, °C
Calcite and aragonite surfaces induce the exclusive for-
mation of scales of calcite and aragonite, respectively. C Ca = total molar calcium concentration
4. The development of calcite scales is retarded by the C Mg = total molar magnesium concentration
presence of magnesium ion. Under such conditions, the s = parameter proportional to number of crystal
aragonite polymorph may be favored kinetically, and growth sites
this phase may fonn spontaneously even in the presence Yz = activity coefficient of z-valent ionic species
of the thennodynamically stable calcite. The incorpora-
() = supersaturation ratio
tion of magnesium ion during calcium carbonate scale
fonnation markedly influences the apparent solubility of
the magnesian calcite phase fonned. The effective in- Acknowledgments
hibition of scale fonnation by the magnesium ion We thank the donors of the Petroleum Research Fund,
MARCH 1982 651
administered by the American Chemical Soc., for a grant 20. Nancollas, G.H.: "The Growth of Crystals in Solution," Adv.
in partial support of this research. Coli. Interface Sci. (1979) 10, 215-252.
21. Nancollas, G.H. and Reddy, M.M.: "The Crystallization of
Calcium Carbonate: II - Calcite Growth Mechanism," J. Coli.
References Interface Sci. (1971) 37, 824-830.
1. Cowan, J.e. and Weintritt, D.J.: Water-Formed Scale Deposits, 22. Christ, C.L., Hostetler, P.B., and Siebert, R.M.: "Stabilities of
Gulf Publishing Co., Houston (1976). Calcite and Aragonite," J. Res. USGS (1974) 2, 175-184.
2. Folk, R.L.: "The Natural History of Crystalline Calcium Car- 23. Kazmierczak, T.: "Kinetics of Precipitation of Calcium Car-
bonate: Effect of Magnesium Content and Salinity," J. Sed. Pet. bonate," PhD dissertation, State U. of New York-Buffalo (1978).
(1974) 44, 40-49. 24. Wray, J.L. and Daniels, F.: "Precipitation of Calcite and
3. Lippmann, F.: Sedimentary Carbonate Minerals, Springer- Aragonite," J. Am. Chem. Soc. (1957) 79,2031-2034.
Verlag, Germany (1973). 25. Plummer, L.N. and MacKenzie, F.T.: "Predicting Mineral
4. Bischoff, J.L.: "Kinetics of Calcite Nucleation: Magnesium Ion Solubility from Rate Data: Application to the Dissolution of
Inhibition and Ionic-Strength Catalysis," J. Geophys. Res. (1968) Magnesium Calcites," Am. J. Sci. (1974) 274, 61-83.
73,3315-3322. 26. Goldsmith, J.R., Graf, D.L., and Heard, H.C.: "Lattice Con-
5. Kitano, Y.: "The Behavior of Various Inorganic Ions in the stants of the Calcium-Magnesium Carbonates," Amer.
Separation of Calcium Carbonate from a Bicarbonate Solution," Mineralogist (1961) 46, 453-457.
Bull., Chern. Soc. Japan (1962) 35, 1973-1980. 27. Benjamin, L., Lowenthal, R.E., and Marais, G.: "Calcium Car-
6. Pytkowicz, R.M.: "Rates of Inorganic Calcium Carbonate bonate Precipitation Kinetics, Part 2, Effects of Magnesium,"
Nucleation," J. Geol. (1965) 73, 196-199. Water South Africa (1977) 3, 155-165.
7. Pytkowicz, R.M.: "Calcium Carbonate Retention in Super- 28. M'oller, P.: "Determination of the Composition of Surface Layers
saturated Sea-Water," Am. J. Sci. (1973) 273,515-522. of Calcite in Solutions Containing Mg," J. Inorg. Nuc!. Chem.
8. Berner, R.A. and Morse, J.W.: "Dissolution Kinetics of Calcium (1973) 35, 395-401.
Carbonate in Sea Water: IV - Theory of Calcite Dissolution," 29. Morse, J.W., Mucci, A., and Walter, L.M.: "Magnesium In-
Am. J. Sci. (1974) 274, 108-134. teraction with the Surface of Calcite in Sea Water," Science
9. Berner, R.A.: "The Role of Magnesium in the Crystal Growth of (1979) 205, 904-905
Calcite and Aragonite from Sea Water," Geochim. Cosmochim. 30. Chave, K.E., Deffeyes, K.S., Weyl, P.K., Garrels, R.M., and
Acta (1975) 39, 489-504. Thompson, M.E.: "Observations on the Solubility of Skeletal
10. Winland, H.D.: "Stability of Calcium Carbonate Polymorphs in Carbonates in Aqueous Solutions," Science (1962) 137, 33-34.
Warm, Shallow Sea Water," J. Sed. Pet. (1969) 39,1579-1587. 31. Reddy, M.M. and Nancollas, G.H.: "The Crystallization of
11. Lahann, R. W.: "A Chemical Model for Calcite Crystal Growth Calcium Carbonate. Part III, Calcite Crystal Growth Inhibition by
and Morphology Control," J. Sed. Pet. (1978) 48, 337-344. Phosphonates," Desalination (1973) 12, 61-73.
12. Bates, R.G.: Determination of pH: Theory and Practice, John
Wiley & Sons Inc., New York City (1964) 62-64.
13. Siebert, R.M. and Hostetler, P.B.: "The Stability of the SI Metric Conversion Factors
Magnesium Bicarbonate Ion Pair from 10° to 90°C," Am. J. Sci.
(1977) 277,697-715. A x 1.0* E-Ol nm
14. Fuoss, R.M.: "Ionic Association: III - The Equilibrium Between Btu x 1.055056 E+OO kJ
Ion Pair and Free Ions," J. Am. Chem. Soc. (1958) 80, 5059. cal x 4.184* E-03 kJ
15. Martynova, 0.1., Vasina, L.G., and Pozdniakova, S.A.:
"Dissociation Constants of Certain Scale Forming Salts,"
cu ft x 2.831 685 E-02 m3
Desalination (1974) 15, 259-265. OF (OF-32)/1.8 °C
16. Nakayama, F.S.: "Magnesium Complex and Ion Pair in micron X 1.0* E+OO 11 m
MgCOrCO z Solution System," J. Chem. Eng. Data (1971) 16,
178-181.
mL X 1.0* E+OO cm 3
17. Reardon, E.J. and Langmuir, D.: "Thermodynamic Properties of sq ft x 9.290 304* E-02 m2
the Ion Pairs MgC0 3 and CaC0 3 from 10 to 50°C," Am. J. Sci.
*Convcrsion factor is exact.
:1974) 274, 599-612. JPT
18. Jacobson, R.L. and Langmuir, D.: "Dissociation Constants of
Original manuscript received in SOCiety of Petroleum Engineers office April 11 ,1980.
Calcite and CaHC0 3 from 0 to 50°C," Geochim. Cosmochim.
Paper accepted for publication Sept. 2, 1981. Revised manuscript received Jan. 14,
Acta (1974) 38,301-318. 1982. Paper (SPE 8992) first presented at the SPE Fifth Inti. Symposium on Oilfield
19. Davies, e.W.: Ion Association, Butterworths, London (1964). and Geothermal Chemistry held in Stanford, CA, May 28-30, 1980.

652 JOURNAL OF PETROLEUM TECHNOLOGY