Journal of Colloid and Interface Science 420 (2014) 57–64
Contents lists available at ScienceDirect
Journal of Colloid and Interface Science www.elsevier.com/locate/jcis
New methodology based on static light scattering measurements for evaluation of inhibitors for in bulk CaCO3 crystallization Maria F.B. Sousa ⇑, Celso A. Bertran Chemistry Institute, University of Campinas, P.O. Box-6154, Campinas 13.083-862, Brazil
a r t i c l e
i n f o
Article history: Received 29 September 2013 Accepted 3 January 2014 Available online 11 January 2014 Keywords: In bulk inhibition Homogeneous crystallization Calcium carbonate scale Particle size distribution
a b s t r a c t In the present work a new procedure for evaluation of scale inhibitor for calcium carbonate is proposed based on continuous measurement of particle size distribution by laser diffraction technique and simultaneous pH recording. From data obtained during real-time monitoring of the homogeneous nucleation and growth of CaCO3 particles formed in the bulk phase after the addition of carbonate ions to synthetic formation water (AF-W2), it was possible to evaluate the performance of four inhibitors classified in two groups: phosphonates (ethylenediamine tetramethylene phosphonic acid, EDTMP; diethylenetriamine pentamethylene phosphonic acid, DETPMP) and polymeric inhibitors (phosphino poly carboxylic acid, PPCA; polyvinyl sulfonate, PVS). The comparative bulk crystallization inhibition efficiency for the evaluated inhibitors, under the experimental conditions used in this work, increases in the following order: EDTMP < DETPMP < PVS ffi PPCA. Moreover, this methodology allowed the deduction of the main mechanism of their inhibiting action: nucleation inhibition or crystal growth retardation. Ó 2014 Elsevier Inc. All rights reserved.
1. Introduction Scaling occurs inside pipelines and other equipment reducing their effective diameter leading to obstruction problems and causing productivity loss. The oil and gas industry applies chemical treatments using formulations known as inhibitors in order to control, by preventing, reducing or delaying, the formation of inorganic scale. Typically these formulations contain phosphonate and carboxylate compounds or polymers based on polyacrylates and exhibit different performance as anti-scalants, depending on the conditions under which they are applied. Inhibitors can be continuously or periodically (squeeze) injected into the reservoir matrix. These species, a large number in sub-stoichiometric concentration ratio, are capable of controlling the processes of nucleation and/or crystal growth of sparingly soluble mineral salts either in bulk or on surfaces of pipes and other equipment, preventing the adhesion and/or blocking growth sites. Crystallization of calcium carbonate (CaCO3) is the most common source of mineral scale found in oilfield environments. Because of the abundant occurrence of this mineral it plays an important role in a broad range of industrial applications and has been intensively investigated [1–5]. The phenomenon of crystallization results from three processes: supersaturation, nucleation and growth of crystals. The supersaturation is the pre-condition
and the driving force for crystallization, affecting greatly the nucleation rate. The state of supersaturation, at a given temperature, is achieved when the concentration of a particular sparingly soluble salt exceeds its thermodynamic solubility product, Ksp, at that temperature. This unbalance can be originated by several factors, such as concentration of the ions involved in the equilibrium, fluctuations in temperature and/or pH variations. When the deviancy from the equilibrium is small, the supersaturated solution may exist in a metastable state. In this situation the solution returns to equilibrium only when pre-formed nuclei are introduced in the medium. On the other hand, if the degree of supersaturation is high enough to achieve the condition of supersolubility, precipitation occurs with or without an induction time [6]. For calcium carbonate the process of crystallization involves the reaction of aqueous calcium and carbonate ions, according to Eq. (1): 2 Ca2þ ðaqÞ þ CO3ðaqÞ ! CaCO3ðsÞ
So, the supersaturation ratio, SR, is defined by the expression (2):
SR ¼ ⇑ Corresponding author. E-mail addresses: [email protected] unicamp.br (C.A. Bertran).
(M.F.B.
Sousa),
bertran@iqm.
0021-9797/$ - see front matter Ó 2014 Elsevier Inc. All rights reserved. http://dx.doi.org/10.1016/j.jcis.2014.01.001
ð1Þ
fCa2þ ½Ca2þ fCO2 ½CO2 3 3
K sp
ð2Þ
2þ where fCa and fCO2 are the activity coefficient while [Ca2+] and 3 ½CO2 stands for the concentration of calcium and carbonate ions 3
58
M.F.B. Sousa, C.A. Bertran / Journal of Colloid and Interface Science 420 (2014) 57–64
respectively, and the ksp is the thermodynamic solubility product of CaCO3. Crystallization tendency can also be represented by the supersaturation index SI, which is related to the supersaturation ratio (SR) according to Eq. (3).
SI ¼ logðSRÞ
ð3Þ
The crystal growth process starts when stable nuclei of critical size have been formed at the nucleation stage. Many theories have been proposed to explain the mechanisms that cause crystal growth [6–9], among them, the diffusion theories and adsorption-layer theories are the most relevant. Crystallization processes are still in need to be better understood and then controlled to guarantee that the desired purpose will be achieved, whether it is to promote crystal production or to suppress scale formation by the use of anti-scaling formulations. However, it is known that both nucleation and growth processes interact and contribute to the crystal size distribution. In general, nucleation requires a higher degree of supersaturation than growth [9]. The ability of controlling these phenomena, at substoichiometric concentrations, is the property required for an effective scale inhibitor performance. Although precipitation and scaling are resulting from crystallization they are different processes. Recent studies show that the kinetics involved in the precipitation process is not compatible with the kinetics observed in the formation of fouling deposits [10–12]. It was also observed that both processes show different mechanisms and do not respond in the same way to the concentration of inhibitor [10] and to supersaturation ratio [13]. Therefore, regarding the performance of scale inhibitors, it is important to evaluate these phenomena separately and when possible in parallel, then characterizing the whole process. This approach will facilitate the choice of the appropriate inhibitor for a particular purpose, given that all aspects of a crystallization process are strongly interrelated and interdependent [14]. Several authors have applied different methods and techniques to study kinetic parameters of both homogeneous and heterogeneous [10–15,16], just homogeneous [17–19] or only heterogeneous [20–22] calcium carbonate crystallization and to evaluate the performance of scale inhibitors [10–15,18,20,21,23]. For instance, Neville and Morizot [10] used an electrochemical technique to quantify scale formation at the surface of a rotating disk electrode. The method was based on changes in the rate of oxygen reduction at the electrode surface, caused by the nucleation and growth of calcium carbonate. Chen and co-workers [15] applied synchrotron radiation wide angle X-ray scattering (WAXS) in order to better understand the processes of formation and inhibition of scale by following, for the first time, crystallization in situ. A study of CaCO3 adhesion mechanism was conducted by Abdel-Aal et al. [16] using a combined bulk chemistry/QCM technique. Kazmierczak and co-workers [17] developed a method in which the activities of ionic species were maintained constant during crystal growth, aiming to study the kinetics of calcium carbonate in a wide range of supersaturation index. Gabrielli et al. [20] used chronoelectrogravimetry, chronoamperometry and impedance measurements for determination of several parameters such as CaCO3 nucleation induction time and instantaneous growth rate, as well as to investigate the efficiency of anti-scale treatments. A new evaluation method for CaCO3 inhibitors based on pH measurements was reported by Zhang et al. [18]. According to the authors, the pH of the brine was the only measured parameter used to calculate the supersaturation value at which the
precipitation of calcium carbonate started in the presence of each evaluated inhibitor. In a recent paper Boerkamp and co-workers [21] related that continuous measurement of guided light attenuation is capable of monitoring the dynamics of heterogeneous crystal growth of calcium carbonate deposits on the surface of an optical fiber sensor. The studies were carried out in the presence or absence of a scale inhibitor. Some authors have used turbidity measurements to study the inhibition of calcium carbonate [14] and barium sulfate crystallization [24,25]. In the study conducted by Tantayakom et al. [24], these authors state that turbidity measurements alone cannot differentiate between nucleation inhibition or growth inhibition mechanism. Baugh et al. [25], however, developed a methodology for scale inhibitor screening that is able to distinguish the inhibition mechanism. In other words, according to the authors, the method provides information on how the anti-scaling formulation acts, if it is affecting mainly the nucleation rate or the growth rate of the precipitate. Even though it is well known that the adherence and growth of scale on metal surfaces are more complex processes than precipitation within the bulk, and the minimal inhibitory concentration (MIC) for heterogeneous and homogeneous crystallization may be different [26], yet the performance of scale inhibitors to prevent nucleation and crystal growth in the bulk phase is a good indication of their effectiveness as anti-scalants. In this work a new procedure for evaluation of scale inhibitor for calcium carbonate is proposed based on continuous measurement of particle size distribution by laser diffraction technique and simultaneous pH recording. Real-time monitoring of the homogeneous nucleation and growth of CaCO3 particles formed in the bulk phase after the addition of carbonate ions to synthetic formation water (AF-W2) allows performance evaluation of scaling inhibitors and enables deduction of the main mechanism of their inhibiting action: nucleation inhibition or crystal growth retardation. The process of crystal growth was followed in the presence of four inhibitors presented in Fig. 1, classified in two groups: phosphonate inhibitors (ethylenediamine tetramethylene phosphonic acid, EDTMP; diethylenetriamine pentamethylene phosphonic acid, DETPMP) and polymeric inhibitors (phosphino polycarboxylic acid, PPCA; polyvinyl sulfonate, PVS).
Fig. 1. Schematic structures of commercial scale inhibitors used in this work: EDTMP (ethylenediamine tetramethylene phosphonic acid) DETPMP (diethylenetriamine pentamethylene phosphonic acid); PPCA (phosphinopolycarboxylic acid); PVS (polyvinyl sulfonate).
59
M.F.B. Sousa, C.A. Bertran / Journal of Colloid and Interface Science 420 (2014) 57–64 Table 1 Composition of synthetic brine AF-W2. Ion +
Na K+ Mg++ Ca++ Sr++ Ba++ Cl
Concentration (mg L1)
Concentration (mol L1)
52,552 1794 2361 14,194 2246 138 116,556
2.286 0.046 0.097 0.354 0.026 0.001 3.288
Table 2 Supersaturation ratio and pH values related to the added volume of carbonate solution. Condition
0.038 mol L1 Na2CO3 mL
SR
SI
pHc
pHf
Uninhibited 5 ppm EDTMP 5 ppm DETPMP 5 ppm PPCA 5 ppm PVS
6.86 10.40 15.19 16.65 17.07
182 398 562 692 776
2.26 2.60 2.75 2.84 2.89
8.01 8.33 8.38 8.49 8.61
6.79 7.29 7.39 7.66 7.46
SR – supersaturation ratio; SI – supersaturation index; pHc – critical pH value; pHf – final pH value.
2. Experimental 3. Results and discussion In all assays conducted in this study, synthetic formation water of high salinity called AF-W2, whose composition is shown in Table 1 and 0.038 M sodium carbonate solution were used. Analytical grade reagents (anhydrous Na2CO3 and chloride salts of sodium, potassium, magnesium, calcium, barium and strontium) were obtained from Synth-Brazil. Solutions were prepared using de-ionized water (Milli-Q Plus Water System, Millipore). The artificial brine, with high ionic strength (3.8 mol L1), simulates the composition of the formation water found in some production areas in Brazil.
2.1. Particle size distribution measurements Particle size measurements were performed using a particle size analyzer (Mastersizer 2000) coupled to a sample dispersion unit (Hydro 2000S), both from Malvern Instruments. A blank uninhibited test and experiments with 5 ppm of each inhibitor separately (PVS, PPCA, DETPMP and EDTMP) were conducted at 25 °C and proceeded for at least five-and-a-half hours. The background was measured prior to each test. Particle size distribution measurements started directly after the reagent solutions were gradually mixed. An automatic injector (Titrino plus 848, Metrohm) was used to deliver at a rate of 0.5 mL min1 the precipitating solution (0.038 M Na2CO3), into the dispersing unit containing 140 mL of the synthetic formation water (AF-W2). For all cases, the mixing of the solutions and the measurements were carried out under forced convection condition (1750 rpm) and ultrasonication intensity of 30%, to prevent particles to agglomerate and to remove bubbles from the flow path. Throughout the experiment, the pH was measured and recorded by means of a combined glass-calomel electrode (Metrohm) connected to the Titrino plus unit. The precipitating solution was added until the laser obscuration attained a pre-established maximum value and simultaneously the rising pH reached its maximum. During the first hour the measurements were recorded at intervals of 36 s and after that at each 66 s all over the experiment. The synthetic formation water and the precipitating solution of sodium carbonate were mixed slowly to avoid batch condition where supersaturation is immediately achieved upon abrupt addition of the reagent solutions. Therefore the AFW2 solution was undersaturated at the outset of the experiment and progressive and slowly reached critical supersaturation.
2.2. SEM characterization of calcium carbonate particles Suspended CaCO3 particles were separated from solution by centrifugation, washed three times with deionized water, spread out over sample holders and dried at 70 °C for 6 h. Samples were imaged by SEM secondary electrons, using a scanning electron microscope (SEM), model JEOL SM-6360LV (JEOL Ltd., Tokyo, Japan) applying an accelerating voltage of 5 kV.
3.1. Inhibitors performance from supersaturation ratio (SR) The precipitation of calcium carbonate or any other salt results from three mutual processes: supersaturation, nucleation and crystal growth. Understanding how scale inhibitors act in these processes is important to define the best inhibitor for a particular situation. Therefore, assessing in real time, in bulk nucleation and growth processes of calcium carbonate particles, in the presence and absence of inhibiting formulations, is an approach that enables performance evaluation of scale inhibitors. Although other earth alkali metal ions (Mg2+, Ba2+ and Sr2+) are present in the synthetic formation water, AF-W2, taking into account Ksp values, ion concentration and SEM–EDS (scanning electron microscopy with energy dispersive spectroscopy) analysis of the crystallized material, it is assumed that almost only CaCO3 is precipitated under the applied conditions. The supersaturation index (SI) for calcium carbonate as calcite, defined by Eq. (2), was quantified for each experimental condition (Table 2), by using the program PHREEQC Interactive, version 3.1.1.8288 [28]. Concentration (mol L1) of all initial species present in the solutions (with known densities), as well the pH value at which the precipitation began were inputted in the program and the Ptizer database was applied. Table 2 shows the supersaturation ratio that the system AF-W2 plus sodium carbonate, in the presence of each of the four inhibitors, was able to reach up to the point of calcium carbonate precipitation. As expected, the SR observed in the presence of scale inhibitors is higher than the obtained in their absence. Theoretically, nuclei formation event is possible at any supersaturation ratio value exceeding the concentration of saturation (SR > 1). However, in practice, the nucleation rate is almost zero until SR achieves a certain value, the so-called critical supersaturation ratio (SRc) [24]. For the majority of species crystallizing from aqueous systems the critical degree of supersaturation can be as high as 102–103 [27]. This phenomenon was also observed in the present work with SRC ranging from 102.26 (uninhibited system) to 102.89 (inhibition with 5 ppm PVS), and the inhibitory ability increased in the following sequence: EDTMP < DETPMP < PPCA < PVS. 3.2. Inhibitors performance from D[4,3] data Applying the concept of equivalent spheres the particle size is defined by the diameter of a sphere having the same volume as the real particle. This diameter is designate as D[4,3] and its variation over time reflects the variation of the total volume of the particles formed during the experiment. The growth process was followed by registering the variation of D[4,3] as a function of time. As the added volume of carbonate solution was different for each situation, normalization was made for better comparison of the results, using the added volume in the experiment without inhibitor as the unit. Normalized D[4,3] values were then plotted against
60
M.F.B. Sousa, C.A. Bertran / Journal of Colloid and Interface Science 420 (2014) 57–64
Fig. 2. Variation of the particle volume weighted mean, D[4,3] (normalized by the volume of Na2CO3 added) as a function of time, after the slow addition of Na2CO3 solution in uninhibited brine and in the presence of inhibitors (5 ppm). Inset shows curves without normalization.
time, producing the curves shown in Fig. 2, enabling evaluation of inhibitors performance for in bulk homogeneous precipitation. The more effective the inhibitor the less substantial is the particle growth and faster the plateau of the curve is reached. This plateau is in fact a ‘‘pseudo steady state’’ and actually corresponds to a very slow growth kinetics as also observed by other authors [14,29]. The comparative inhibitory efficiency for in bulk crystallization, based on the D[4,3] parameter, increased in the almost same order as observed from SRc values, with exception for PVS that changes place with PPCA, nevertheless, the difference in the performances of these two inhibitors is minimal. Although, each of these species will be classified in the present work accordingly to the mechanism it predominately follows in the beginning of the crystallization process, it is important to notice that they have the ability of acting through both inhibition mechanisms: nucleation and crystal growth. As it can be seen in Figs. 2 and 3, PVS and PPCA, belonging to the class of nucleation inhibitors for calcium carbonate, presented also the capacity for preventing further growth: after a short initial period particle diameter increases very slowly in comparison with the other cases, despite greater amounts of carbonate were added resulting in higher SI (Table 2). Nucleation inhibition involves the disruption or redissolution of scale nuclei by inhibitor molecules. For homogenous crystallization, this disruption affects the thermodynamic stability of the growing nuclei. As a result, the critical radius required for crystallization increases [30]. Nucleation inhibitors evaluated in this work were able to prevent the development of nucleating particles until the supersaturation reaches a value which is approximately 4.0 times the supersaturation for crystallization to occur in the blank experiment. However, once nucleation occurs, as the supersaturation level is too high the formed nuclei grow and reach maximum size very quickly. In the case of growth inhibitors, the main nucleation stage is very distinct of the growing period: D[4,3] increases slowly at first, and then the growth rate raises dramatically before reaching a condition of slow growth kinetic. This behavior is shown in the 3D graphs presented in Fig. 3. In experiments with the inhibitor EDTMP it is observed the formation of a first pseudo plateau, i.e. a decline in growth rate soon after the initial measurements. But the growth kinetics increases again after a certain elapsed time. This behavior may be an indication that at higher supersaturation the inhibitor can prevent the growth of calcium carbonate crystals for a limited time, but after a while the high supersaturation effect
will prevail. When the inhibitor DETPMP is used, in the very beginning of the measurements, occurs the formation of larger particles, which soon decrease in size before the continuous process of growth restarts. These former particles are probably agglomerated of amorphous calcium carbonate (ACC), the most unstable of CaCO3 polymorphous, which converts to vaterite or calcite. This assumption is based on studies carried out by Abdel-Aal et al. [16]. These authors present a diagram showing the change in the polymorphic abundance of calcium carbonate precipitated in bulk phase. There, is possible to see that the transformation of calcium carbonate polymorphous occurs by a mechanism involving dissolution of the less stable and growth of the more stable form. They also demonstrate that the dissolution of ACC is much faster than the growth rate of vaterite and calcite. The three-dimensional graphs presented in Fig. 3 show the variation of two quantities over time: the volume weighted D[4,3], and the total scattered light (integration of the scattering curves provided by the 52 detectors in the equipment). These graphs are important because they show very clearly the different behavior of the two groups of inhibitors. One of them shows a period in which the variation of D[4,3] is very slow at the beginning of the experiment while in the other group the initial variation of D[4,3] is very sharp. In the first group, including the experiment without inhibitor, and the inhibitors DETPMP and EDTMP, after the nucleation period, D[4,3] increases following a parabolic pattern as predicted by Nielsen and Toft [31] for the growth kinetics of calcium carbonate, and even though the growing rate slows down, this group does not reach a real plateau during the elapsed time. The second group of inhibitors, consisting of PVS and PPCA, allows the supersaturation to reach an excessive rise until some nuclei formation occurs and this event is instantaneously followed by fast crystal growth. However, a plateau growth appears soon after D[4,3] reaches a value of approximately 17 and 15 micrometers respectively for PVS and PPCA, indicating that they also act as growth inhibitors. Chemical composition and the degree of dissociation of each compound have to be taken into account in order to understand the inhibitor performance. In the case of the uninhibited experiment, there is a clear period where D[4,3] growth is very slow. The same behavior is observed in experiments with DETPMP and EDTMP, both are phosphonates and therefore mainly classified as crystal growth inhibitors or growth retarding additives. In crystal growth inhibition the aim is to prevent the growth of the crystal. This mechanism involves blockage of active growth sites by the adsorption of the inhibitor molecules. In doing so, efficient crystal growth inhibitors, such as phosphonates, stop those most active sites (kinks) from taking part in the crystal growth process. As proposed by Zieba et al. [32] concerning phosphonate adsorption on hydroxyapatite crystals, the inhibition action on calcium carbonate growth is probably also due to the binding of phosphonate anions to superficial calcium ions. The way the total light scattering varies with time also differs according to the group of inhibitor used. When a nucleation inhibitor is added, the scattered energy decreases over time after reaching a maximum. In the case of growth inhibitors, the change of energy with time is constantly increasing, even though the inhibitor EDTMP shows a minimum that matches with the end of the first plateau in the beginning of the experiment. Blickle et al. [33] carried out a study relating crystal growth kinetics and particle size distribution based on statements in the literature, and proposed a new relation between them. The authors claim that this mathematic relation can be applied to determine the characteristics of crystallization caused by any of the following methods: cooling, evaporation or precipitation. From the derived equations several kinetic constants (rate constants of nucleation k1, k2, k3, and growth K0, K1, K2) can be determined,
M.F.B. Sousa, C.A. Bertran / Journal of Colloid and Interface Science 420 (2014) 57–64
61
Fig. 3. Variation of D[4,3] and total scattered energy versus time for uninhibited and inhibited experiments. According to Malvern Instruments the unit (uls) stands for ‘‘units of light scattering’’ and it is a conversion from the collected light energy and has no correspondent SI unit.
and from them, theoretical particle size distribution curves can be obtained. Concerning the growth stage, the authors summarize as follows the effect of kinetics characteristics on particle size distribution: if K2 increases both the scattering and the particle size also increase; however if K1 is increased the particle size increases while the scattering decreases. The results obtained in the present work indicate that the presence of nucleation inhibitors increases K1, which is a rate constant dependent of several parameters, such as the rate constant of the surface reaction (K0), mass transfer coefficient and the density of the solid phase. Considering that K2, according to the authors, is the rate constant of crystal growth due to the lattice defect it is reasonable to expect that in the presence of growth inhibitors, there will be an increase of K2, since the mechanism of action of this type of inhibitor involves their adsorption on active growth sites, resulting in crystal lattice defects. These assumptions could explain the different trends in scattering during the calcium carbonate growth in the presence of different types of inhibitors.
3.3. Inhibitors performance from obscuration curves Another parameter measured by the granulometer is the obscuration caused by suspended particles in the light path (Fig. 4). For all inhibitors, following an initial increase in the laser obscuration, a maximum value is reached after a few measurements and then there is an exponential decrease leading to an almost constant value. As the obscuration is determined by the number of particles per unit of volume rather than the volume of particles, this decrease is an indication of Ostwald-ripening mechanism [19], where the increase in average particle size occurs by the annihilation of small particles through diffusion [34]. In the case of nucleation inhibitors, even in high supersaturation condition the maximum obscuration of the laser does not reach values as higher as those obtained in the experiments with crystal growth inhibitors and in the uninhibited situation. Again, considering that obscuration is related to amount of particles, when nucleation inhibitors are added to the brine a fewer number of nuclei is formed explaining the lower interference in the intensity of the laser.
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M.F.B. Sousa, C.A. Bertran / Journal of Colloid and Interface Science 420 (2014) 57–64
However when comparing the results between themselves, it is seen that, at the same inhibitor concentration, DETPMP is able to keep the supersaturation up to the point of CaCO3calcium carbonate precipitation of at a much higher level than EDTMP. The supersaturation for the experiment with DETPMP is about 1.4 times higher than that for the experiment with EDTMP (Table 2). 3.5. Particle size distribution diagrams
Fig. 4. Laser obscuration versus time for uninhibited and inhibited (5 ppm) experiments. Data not normalized for relative supersaturation ratio.
Particle size distribution diagrams provide a clear indication of the inhibitor performance as time elapses, as can be seen in Fig. 6. It is evident that in the presence of the inhibitors PVS and PPCA there is only one growing population, whereas with DETPMP and EDTMP at least two distinct populations can be observed and there is a sharp displacement over time to larger diameters. It can be also observed the presence of small particles even in the final measurement (dotted lines) in the condition without inhibitor and in the presence DETPMP and EDTMP. This is an indicative that secondary nucleation is probably occurring.
16 14 12 10 8 6 4 2 0
Fig. 5. Variation of pH as a function of time during (until the peak) and after de addition of Na2CO3 solution to uninhibited and inhibited brines.
3.4. pH monitoring The pH was monitored during and after the continuous and slow addition of carbonate solution to AF-W2 brine containing or not inhibitor, starting from an initial pH value of 6.2 (Fig. 5). Following the initial increase, the pH reached a maximal value, the critical pH (pHc) [18,35], then decreased promptly signalizing the onset of CaCO3 precipitation. The beginning of calcium carbonate formation was also indicated by the relative laser obscuration in the paticle size analyzer. At this point the addition of carbonate was stopped. As the addition rate in all experiments was the same (0.5 mL min1) the volume of titrant used in each case (Table 2) is proportional to time and increases in the following order: without inhibitor
Contents lists available at ScienceDirect
Journal of Colloid and Interface Science www.elsevier.com/locate/jcis
New methodology based on static light scattering measurements for evaluation of inhibitors for in bulk CaCO3 crystallization Maria F.B. Sousa ⇑, Celso A. Bertran Chemistry Institute, University of Campinas, P.O. Box-6154, Campinas 13.083-862, Brazil
a r t i c l e
i n f o
Article history: Received 29 September 2013 Accepted 3 January 2014 Available online 11 January 2014 Keywords: In bulk inhibition Homogeneous crystallization Calcium carbonate scale Particle size distribution
a b s t r a c t In the present work a new procedure for evaluation of scale inhibitor for calcium carbonate is proposed based on continuous measurement of particle size distribution by laser diffraction technique and simultaneous pH recording. From data obtained during real-time monitoring of the homogeneous nucleation and growth of CaCO3 particles formed in the bulk phase after the addition of carbonate ions to synthetic formation water (AF-W2), it was possible to evaluate the performance of four inhibitors classified in two groups: phosphonates (ethylenediamine tetramethylene phosphonic acid, EDTMP; diethylenetriamine pentamethylene phosphonic acid, DETPMP) and polymeric inhibitors (phosphino poly carboxylic acid, PPCA; polyvinyl sulfonate, PVS). The comparative bulk crystallization inhibition efficiency for the evaluated inhibitors, under the experimental conditions used in this work, increases in the following order: EDTMP < DETPMP < PVS ffi PPCA. Moreover, this methodology allowed the deduction of the main mechanism of their inhibiting action: nucleation inhibition or crystal growth retardation. Ó 2014 Elsevier Inc. All rights reserved.
1. Introduction Scaling occurs inside pipelines and other equipment reducing their effective diameter leading to obstruction problems and causing productivity loss. The oil and gas industry applies chemical treatments using formulations known as inhibitors in order to control, by preventing, reducing or delaying, the formation of inorganic scale. Typically these formulations contain phosphonate and carboxylate compounds or polymers based on polyacrylates and exhibit different performance as anti-scalants, depending on the conditions under which they are applied. Inhibitors can be continuously or periodically (squeeze) injected into the reservoir matrix. These species, a large number in sub-stoichiometric concentration ratio, are capable of controlling the processes of nucleation and/or crystal growth of sparingly soluble mineral salts either in bulk or on surfaces of pipes and other equipment, preventing the adhesion and/or blocking growth sites. Crystallization of calcium carbonate (CaCO3) is the most common source of mineral scale found in oilfield environments. Because of the abundant occurrence of this mineral it plays an important role in a broad range of industrial applications and has been intensively investigated [1–5]. The phenomenon of crystallization results from three processes: supersaturation, nucleation and growth of crystals. The supersaturation is the pre-condition
and the driving force for crystallization, affecting greatly the nucleation rate. The state of supersaturation, at a given temperature, is achieved when the concentration of a particular sparingly soluble salt exceeds its thermodynamic solubility product, Ksp, at that temperature. This unbalance can be originated by several factors, such as concentration of the ions involved in the equilibrium, fluctuations in temperature and/or pH variations. When the deviancy from the equilibrium is small, the supersaturated solution may exist in a metastable state. In this situation the solution returns to equilibrium only when pre-formed nuclei are introduced in the medium. On the other hand, if the degree of supersaturation is high enough to achieve the condition of supersolubility, precipitation occurs with or without an induction time [6]. For calcium carbonate the process of crystallization involves the reaction of aqueous calcium and carbonate ions, according to Eq. (1): 2 Ca2þ ðaqÞ þ CO3ðaqÞ ! CaCO3ðsÞ
So, the supersaturation ratio, SR, is defined by the expression (2):
SR ¼ ⇑ Corresponding author. E-mail addresses: [email protected] unicamp.br (C.A. Bertran).
(M.F.B.
Sousa),
bertran@iqm.
0021-9797/$ - see front matter Ó 2014 Elsevier Inc. All rights reserved. http://dx.doi.org/10.1016/j.jcis.2014.01.001
ð1Þ
fCa2þ ½Ca2þ fCO2 ½CO2 3 3
K sp
ð2Þ
2þ where fCa and fCO2 are the activity coefficient while [Ca2+] and 3 ½CO2 stands for the concentration of calcium and carbonate ions 3
58
M.F.B. Sousa, C.A. Bertran / Journal of Colloid and Interface Science 420 (2014) 57–64
respectively, and the ksp is the thermodynamic solubility product of CaCO3. Crystallization tendency can also be represented by the supersaturation index SI, which is related to the supersaturation ratio (SR) according to Eq. (3).
SI ¼ logðSRÞ
ð3Þ
The crystal growth process starts when stable nuclei of critical size have been formed at the nucleation stage. Many theories have been proposed to explain the mechanisms that cause crystal growth [6–9], among them, the diffusion theories and adsorption-layer theories are the most relevant. Crystallization processes are still in need to be better understood and then controlled to guarantee that the desired purpose will be achieved, whether it is to promote crystal production or to suppress scale formation by the use of anti-scaling formulations. However, it is known that both nucleation and growth processes interact and contribute to the crystal size distribution. In general, nucleation requires a higher degree of supersaturation than growth [9]. The ability of controlling these phenomena, at substoichiometric concentrations, is the property required for an effective scale inhibitor performance. Although precipitation and scaling are resulting from crystallization they are different processes. Recent studies show that the kinetics involved in the precipitation process is not compatible with the kinetics observed in the formation of fouling deposits [10–12]. It was also observed that both processes show different mechanisms and do not respond in the same way to the concentration of inhibitor [10] and to supersaturation ratio [13]. Therefore, regarding the performance of scale inhibitors, it is important to evaluate these phenomena separately and when possible in parallel, then characterizing the whole process. This approach will facilitate the choice of the appropriate inhibitor for a particular purpose, given that all aspects of a crystallization process are strongly interrelated and interdependent [14]. Several authors have applied different methods and techniques to study kinetic parameters of both homogeneous and heterogeneous [10–15,16], just homogeneous [17–19] or only heterogeneous [20–22] calcium carbonate crystallization and to evaluate the performance of scale inhibitors [10–15,18,20,21,23]. For instance, Neville and Morizot [10] used an electrochemical technique to quantify scale formation at the surface of a rotating disk electrode. The method was based on changes in the rate of oxygen reduction at the electrode surface, caused by the nucleation and growth of calcium carbonate. Chen and co-workers [15] applied synchrotron radiation wide angle X-ray scattering (WAXS) in order to better understand the processes of formation and inhibition of scale by following, for the first time, crystallization in situ. A study of CaCO3 adhesion mechanism was conducted by Abdel-Aal et al. [16] using a combined bulk chemistry/QCM technique. Kazmierczak and co-workers [17] developed a method in which the activities of ionic species were maintained constant during crystal growth, aiming to study the kinetics of calcium carbonate in a wide range of supersaturation index. Gabrielli et al. [20] used chronoelectrogravimetry, chronoamperometry and impedance measurements for determination of several parameters such as CaCO3 nucleation induction time and instantaneous growth rate, as well as to investigate the efficiency of anti-scale treatments. A new evaluation method for CaCO3 inhibitors based on pH measurements was reported by Zhang et al. [18]. According to the authors, the pH of the brine was the only measured parameter used to calculate the supersaturation value at which the
precipitation of calcium carbonate started in the presence of each evaluated inhibitor. In a recent paper Boerkamp and co-workers [21] related that continuous measurement of guided light attenuation is capable of monitoring the dynamics of heterogeneous crystal growth of calcium carbonate deposits on the surface of an optical fiber sensor. The studies were carried out in the presence or absence of a scale inhibitor. Some authors have used turbidity measurements to study the inhibition of calcium carbonate [14] and barium sulfate crystallization [24,25]. In the study conducted by Tantayakom et al. [24], these authors state that turbidity measurements alone cannot differentiate between nucleation inhibition or growth inhibition mechanism. Baugh et al. [25], however, developed a methodology for scale inhibitor screening that is able to distinguish the inhibition mechanism. In other words, according to the authors, the method provides information on how the anti-scaling formulation acts, if it is affecting mainly the nucleation rate or the growth rate of the precipitate. Even though it is well known that the adherence and growth of scale on metal surfaces are more complex processes than precipitation within the bulk, and the minimal inhibitory concentration (MIC) for heterogeneous and homogeneous crystallization may be different [26], yet the performance of scale inhibitors to prevent nucleation and crystal growth in the bulk phase is a good indication of their effectiveness as anti-scalants. In this work a new procedure for evaluation of scale inhibitor for calcium carbonate is proposed based on continuous measurement of particle size distribution by laser diffraction technique and simultaneous pH recording. Real-time monitoring of the homogeneous nucleation and growth of CaCO3 particles formed in the bulk phase after the addition of carbonate ions to synthetic formation water (AF-W2) allows performance evaluation of scaling inhibitors and enables deduction of the main mechanism of their inhibiting action: nucleation inhibition or crystal growth retardation. The process of crystal growth was followed in the presence of four inhibitors presented in Fig. 1, classified in two groups: phosphonate inhibitors (ethylenediamine tetramethylene phosphonic acid, EDTMP; diethylenetriamine pentamethylene phosphonic acid, DETPMP) and polymeric inhibitors (phosphino polycarboxylic acid, PPCA; polyvinyl sulfonate, PVS).
Fig. 1. Schematic structures of commercial scale inhibitors used in this work: EDTMP (ethylenediamine tetramethylene phosphonic acid) DETPMP (diethylenetriamine pentamethylene phosphonic acid); PPCA (phosphinopolycarboxylic acid); PVS (polyvinyl sulfonate).
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M.F.B. Sousa, C.A. Bertran / Journal of Colloid and Interface Science 420 (2014) 57–64 Table 1 Composition of synthetic brine AF-W2. Ion +
Na K+ Mg++ Ca++ Sr++ Ba++ Cl
Concentration (mg L1)
Concentration (mol L1)
52,552 1794 2361 14,194 2246 138 116,556
2.286 0.046 0.097 0.354 0.026 0.001 3.288
Table 2 Supersaturation ratio and pH values related to the added volume of carbonate solution. Condition
0.038 mol L1 Na2CO3 mL
SR
SI
pHc
pHf
Uninhibited 5 ppm EDTMP 5 ppm DETPMP 5 ppm PPCA 5 ppm PVS
6.86 10.40 15.19 16.65 17.07
182 398 562 692 776
2.26 2.60 2.75 2.84 2.89
8.01 8.33 8.38 8.49 8.61
6.79 7.29 7.39 7.66 7.46
SR – supersaturation ratio; SI – supersaturation index; pHc – critical pH value; pHf – final pH value.
2. Experimental 3. Results and discussion In all assays conducted in this study, synthetic formation water of high salinity called AF-W2, whose composition is shown in Table 1 and 0.038 M sodium carbonate solution were used. Analytical grade reagents (anhydrous Na2CO3 and chloride salts of sodium, potassium, magnesium, calcium, barium and strontium) were obtained from Synth-Brazil. Solutions were prepared using de-ionized water (Milli-Q Plus Water System, Millipore). The artificial brine, with high ionic strength (3.8 mol L1), simulates the composition of the formation water found in some production areas in Brazil.
2.1. Particle size distribution measurements Particle size measurements were performed using a particle size analyzer (Mastersizer 2000) coupled to a sample dispersion unit (Hydro 2000S), both from Malvern Instruments. A blank uninhibited test and experiments with 5 ppm of each inhibitor separately (PVS, PPCA, DETPMP and EDTMP) were conducted at 25 °C and proceeded for at least five-and-a-half hours. The background was measured prior to each test. Particle size distribution measurements started directly after the reagent solutions were gradually mixed. An automatic injector (Titrino plus 848, Metrohm) was used to deliver at a rate of 0.5 mL min1 the precipitating solution (0.038 M Na2CO3), into the dispersing unit containing 140 mL of the synthetic formation water (AF-W2). For all cases, the mixing of the solutions and the measurements were carried out under forced convection condition (1750 rpm) and ultrasonication intensity of 30%, to prevent particles to agglomerate and to remove bubbles from the flow path. Throughout the experiment, the pH was measured and recorded by means of a combined glass-calomel electrode (Metrohm) connected to the Titrino plus unit. The precipitating solution was added until the laser obscuration attained a pre-established maximum value and simultaneously the rising pH reached its maximum. During the first hour the measurements were recorded at intervals of 36 s and after that at each 66 s all over the experiment. The synthetic formation water and the precipitating solution of sodium carbonate were mixed slowly to avoid batch condition where supersaturation is immediately achieved upon abrupt addition of the reagent solutions. Therefore the AFW2 solution was undersaturated at the outset of the experiment and progressive and slowly reached critical supersaturation.
2.2. SEM characterization of calcium carbonate particles Suspended CaCO3 particles were separated from solution by centrifugation, washed three times with deionized water, spread out over sample holders and dried at 70 °C for 6 h. Samples were imaged by SEM secondary electrons, using a scanning electron microscope (SEM), model JEOL SM-6360LV (JEOL Ltd., Tokyo, Japan) applying an accelerating voltage of 5 kV.
3.1. Inhibitors performance from supersaturation ratio (SR) The precipitation of calcium carbonate or any other salt results from three mutual processes: supersaturation, nucleation and crystal growth. Understanding how scale inhibitors act in these processes is important to define the best inhibitor for a particular situation. Therefore, assessing in real time, in bulk nucleation and growth processes of calcium carbonate particles, in the presence and absence of inhibiting formulations, is an approach that enables performance evaluation of scale inhibitors. Although other earth alkali metal ions (Mg2+, Ba2+ and Sr2+) are present in the synthetic formation water, AF-W2, taking into account Ksp values, ion concentration and SEM–EDS (scanning electron microscopy with energy dispersive spectroscopy) analysis of the crystallized material, it is assumed that almost only CaCO3 is precipitated under the applied conditions. The supersaturation index (SI) for calcium carbonate as calcite, defined by Eq. (2), was quantified for each experimental condition (Table 2), by using the program PHREEQC Interactive, version 3.1.1.8288 [28]. Concentration (mol L1) of all initial species present in the solutions (with known densities), as well the pH value at which the precipitation began were inputted in the program and the Ptizer database was applied. Table 2 shows the supersaturation ratio that the system AF-W2 plus sodium carbonate, in the presence of each of the four inhibitors, was able to reach up to the point of calcium carbonate precipitation. As expected, the SR observed in the presence of scale inhibitors is higher than the obtained in their absence. Theoretically, nuclei formation event is possible at any supersaturation ratio value exceeding the concentration of saturation (SR > 1). However, in practice, the nucleation rate is almost zero until SR achieves a certain value, the so-called critical supersaturation ratio (SRc) [24]. For the majority of species crystallizing from aqueous systems the critical degree of supersaturation can be as high as 102–103 [27]. This phenomenon was also observed in the present work with SRC ranging from 102.26 (uninhibited system) to 102.89 (inhibition with 5 ppm PVS), and the inhibitory ability increased in the following sequence: EDTMP < DETPMP < PPCA < PVS. 3.2. Inhibitors performance from D[4,3] data Applying the concept of equivalent spheres the particle size is defined by the diameter of a sphere having the same volume as the real particle. This diameter is designate as D[4,3] and its variation over time reflects the variation of the total volume of the particles formed during the experiment. The growth process was followed by registering the variation of D[4,3] as a function of time. As the added volume of carbonate solution was different for each situation, normalization was made for better comparison of the results, using the added volume in the experiment without inhibitor as the unit. Normalized D[4,3] values were then plotted against
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Fig. 2. Variation of the particle volume weighted mean, D[4,3] (normalized by the volume of Na2CO3 added) as a function of time, after the slow addition of Na2CO3 solution in uninhibited brine and in the presence of inhibitors (5 ppm). Inset shows curves without normalization.
time, producing the curves shown in Fig. 2, enabling evaluation of inhibitors performance for in bulk homogeneous precipitation. The more effective the inhibitor the less substantial is the particle growth and faster the plateau of the curve is reached. This plateau is in fact a ‘‘pseudo steady state’’ and actually corresponds to a very slow growth kinetics as also observed by other authors [14,29]. The comparative inhibitory efficiency for in bulk crystallization, based on the D[4,3] parameter, increased in the almost same order as observed from SRc values, with exception for PVS that changes place with PPCA, nevertheless, the difference in the performances of these two inhibitors is minimal. Although, each of these species will be classified in the present work accordingly to the mechanism it predominately follows in the beginning of the crystallization process, it is important to notice that they have the ability of acting through both inhibition mechanisms: nucleation and crystal growth. As it can be seen in Figs. 2 and 3, PVS and PPCA, belonging to the class of nucleation inhibitors for calcium carbonate, presented also the capacity for preventing further growth: after a short initial period particle diameter increases very slowly in comparison with the other cases, despite greater amounts of carbonate were added resulting in higher SI (Table 2). Nucleation inhibition involves the disruption or redissolution of scale nuclei by inhibitor molecules. For homogenous crystallization, this disruption affects the thermodynamic stability of the growing nuclei. As a result, the critical radius required for crystallization increases [30]. Nucleation inhibitors evaluated in this work were able to prevent the development of nucleating particles until the supersaturation reaches a value which is approximately 4.0 times the supersaturation for crystallization to occur in the blank experiment. However, once nucleation occurs, as the supersaturation level is too high the formed nuclei grow and reach maximum size very quickly. In the case of growth inhibitors, the main nucleation stage is very distinct of the growing period: D[4,3] increases slowly at first, and then the growth rate raises dramatically before reaching a condition of slow growth kinetic. This behavior is shown in the 3D graphs presented in Fig. 3. In experiments with the inhibitor EDTMP it is observed the formation of a first pseudo plateau, i.e. a decline in growth rate soon after the initial measurements. But the growth kinetics increases again after a certain elapsed time. This behavior may be an indication that at higher supersaturation the inhibitor can prevent the growth of calcium carbonate crystals for a limited time, but after a while the high supersaturation effect
will prevail. When the inhibitor DETPMP is used, in the very beginning of the measurements, occurs the formation of larger particles, which soon decrease in size before the continuous process of growth restarts. These former particles are probably agglomerated of amorphous calcium carbonate (ACC), the most unstable of CaCO3 polymorphous, which converts to vaterite or calcite. This assumption is based on studies carried out by Abdel-Aal et al. [16]. These authors present a diagram showing the change in the polymorphic abundance of calcium carbonate precipitated in bulk phase. There, is possible to see that the transformation of calcium carbonate polymorphous occurs by a mechanism involving dissolution of the less stable and growth of the more stable form. They also demonstrate that the dissolution of ACC is much faster than the growth rate of vaterite and calcite. The three-dimensional graphs presented in Fig. 3 show the variation of two quantities over time: the volume weighted D[4,3], and the total scattered light (integration of the scattering curves provided by the 52 detectors in the equipment). These graphs are important because they show very clearly the different behavior of the two groups of inhibitors. One of them shows a period in which the variation of D[4,3] is very slow at the beginning of the experiment while in the other group the initial variation of D[4,3] is very sharp. In the first group, including the experiment without inhibitor, and the inhibitors DETPMP and EDTMP, after the nucleation period, D[4,3] increases following a parabolic pattern as predicted by Nielsen and Toft [31] for the growth kinetics of calcium carbonate, and even though the growing rate slows down, this group does not reach a real plateau during the elapsed time. The second group of inhibitors, consisting of PVS and PPCA, allows the supersaturation to reach an excessive rise until some nuclei formation occurs and this event is instantaneously followed by fast crystal growth. However, a plateau growth appears soon after D[4,3] reaches a value of approximately 17 and 15 micrometers respectively for PVS and PPCA, indicating that they also act as growth inhibitors. Chemical composition and the degree of dissociation of each compound have to be taken into account in order to understand the inhibitor performance. In the case of the uninhibited experiment, there is a clear period where D[4,3] growth is very slow. The same behavior is observed in experiments with DETPMP and EDTMP, both are phosphonates and therefore mainly classified as crystal growth inhibitors or growth retarding additives. In crystal growth inhibition the aim is to prevent the growth of the crystal. This mechanism involves blockage of active growth sites by the adsorption of the inhibitor molecules. In doing so, efficient crystal growth inhibitors, such as phosphonates, stop those most active sites (kinks) from taking part in the crystal growth process. As proposed by Zieba et al. [32] concerning phosphonate adsorption on hydroxyapatite crystals, the inhibition action on calcium carbonate growth is probably also due to the binding of phosphonate anions to superficial calcium ions. The way the total light scattering varies with time also differs according to the group of inhibitor used. When a nucleation inhibitor is added, the scattered energy decreases over time after reaching a maximum. In the case of growth inhibitors, the change of energy with time is constantly increasing, even though the inhibitor EDTMP shows a minimum that matches with the end of the first plateau in the beginning of the experiment. Blickle et al. [33] carried out a study relating crystal growth kinetics and particle size distribution based on statements in the literature, and proposed a new relation between them. The authors claim that this mathematic relation can be applied to determine the characteristics of crystallization caused by any of the following methods: cooling, evaporation or precipitation. From the derived equations several kinetic constants (rate constants of nucleation k1, k2, k3, and growth K0, K1, K2) can be determined,
M.F.B. Sousa, C.A. Bertran / Journal of Colloid and Interface Science 420 (2014) 57–64
61
Fig. 3. Variation of D[4,3] and total scattered energy versus time for uninhibited and inhibited experiments. According to Malvern Instruments the unit (uls) stands for ‘‘units of light scattering’’ and it is a conversion from the collected light energy and has no correspondent SI unit.
and from them, theoretical particle size distribution curves can be obtained. Concerning the growth stage, the authors summarize as follows the effect of kinetics characteristics on particle size distribution: if K2 increases both the scattering and the particle size also increase; however if K1 is increased the particle size increases while the scattering decreases. The results obtained in the present work indicate that the presence of nucleation inhibitors increases K1, which is a rate constant dependent of several parameters, such as the rate constant of the surface reaction (K0), mass transfer coefficient and the density of the solid phase. Considering that K2, according to the authors, is the rate constant of crystal growth due to the lattice defect it is reasonable to expect that in the presence of growth inhibitors, there will be an increase of K2, since the mechanism of action of this type of inhibitor involves their adsorption on active growth sites, resulting in crystal lattice defects. These assumptions could explain the different trends in scattering during the calcium carbonate growth in the presence of different types of inhibitors.
3.3. Inhibitors performance from obscuration curves Another parameter measured by the granulometer is the obscuration caused by suspended particles in the light path (Fig. 4). For all inhibitors, following an initial increase in the laser obscuration, a maximum value is reached after a few measurements and then there is an exponential decrease leading to an almost constant value. As the obscuration is determined by the number of particles per unit of volume rather than the volume of particles, this decrease is an indication of Ostwald-ripening mechanism [19], where the increase in average particle size occurs by the annihilation of small particles through diffusion [34]. In the case of nucleation inhibitors, even in high supersaturation condition the maximum obscuration of the laser does not reach values as higher as those obtained in the experiments with crystal growth inhibitors and in the uninhibited situation. Again, considering that obscuration is related to amount of particles, when nucleation inhibitors are added to the brine a fewer number of nuclei is formed explaining the lower interference in the intensity of the laser.
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However when comparing the results between themselves, it is seen that, at the same inhibitor concentration, DETPMP is able to keep the supersaturation up to the point of CaCO3calcium carbonate precipitation of at a much higher level than EDTMP. The supersaturation for the experiment with DETPMP is about 1.4 times higher than that for the experiment with EDTMP (Table 2). 3.5. Particle size distribution diagrams
Fig. 4. Laser obscuration versus time for uninhibited and inhibited (5 ppm) experiments. Data not normalized for relative supersaturation ratio.
Particle size distribution diagrams provide a clear indication of the inhibitor performance as time elapses, as can be seen in Fig. 6. It is evident that in the presence of the inhibitors PVS and PPCA there is only one growing population, whereas with DETPMP and EDTMP at least two distinct populations can be observed and there is a sharp displacement over time to larger diameters. It can be also observed the presence of small particles even in the final measurement (dotted lines) in the condition without inhibitor and in the presence DETPMP and EDTMP. This is an indicative that secondary nucleation is probably occurring.
16 14 12 10 8 6 4 2 0
Fig. 5. Variation of pH as a function of time during (until the peak) and after de addition of Na2CO3 solution to uninhibited and inhibited brines.
3.4. pH monitoring The pH was monitored during and after the continuous and slow addition of carbonate solution to AF-W2 brine containing or not inhibitor, starting from an initial pH value of 6.2 (Fig. 5). Following the initial increase, the pH reached a maximal value, the critical pH (pHc) [18,35], then decreased promptly signalizing the onset of CaCO3 precipitation. The beginning of calcium carbonate formation was also indicated by the relative laser obscuration in the paticle size analyzer. At this point the addition of carbonate was stopped. As the addition rate in all experiments was the same (0.5 mL min1) the volume of titrant used in each case (Table 2) is proportional to time and increases in the following order: without inhibitor
