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Apr 2, 2012 - C80 tetra-acid (also known as ARN) is a molecule present in crude oil that can precipitate during oil production in basic medium and in ...
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Reaction Between Tetrameric Acids and Ca2+ in Oil/Water System Sébastien Simon,* Christian Reisen, Anita Bersås, and Johan Sjöblom Ugelstad Laboratory, Department of Chemical Engineering, Norwegian University of Science and Technology (NTNU), N-7491 Trondheim, Norway ABSTRACT: C80 tetra-acid (also known as ARN) is a molecule present in crude oil that can precipitate during oil production in basic medium and in presence of calcium ions to form deposits. The formation of such deposits is detrimental in production because they can plug oil production facilities and may lead to costly production shutdowns due to deferment and clean up operations. To better understand this reaction, the solubility of a model molecule mimicking the properties of C80 tetra-acid (named BP-10) have been measured in an oil/water system, using chloroform as oil in presence of calcium to establish quantitative relationships between solubility and pH, calcium concentration, temperature, and other parameters. It has been determined that the maximum BP-10 concentration in oil phase (solubility limit) follows the following relationship: [BP-10]o = A × 10−4pH, with the fitting parameter A × [Ca2+]2 = 2.6 × 1018 mol−1·L+1. This relationship is valid at [Ca2+] ≥ 10 mM, with a slight overestimation of the solubility at lower calcium concentration from temperatures varying from 5 to 50 °C. This relationship holds at any ionic strength (up to 600 mM of NaCl) and total BP-10 concentration (up to 200 μM) in the system. In presence of Mg2+, the relation is still valid with a different prefactor. For all the studied systems, the concentration of BP-10 in water was very low, lower than 2 μM. The solubilities of C80 tetra-acid in oil phase with BP-10 one have been compared. Both molecules have a similar pH range for precipitation, but C80 tetra-acid has a different relationship between its concentration in oil phase and pH.

1. INTRODUCTION Crude oils are considered as acidic if their total acid number (TAN) exceeds a value of 0.5 mg KOH/g crude oil. This acidity is mainly, but not only,1 due to the presence of naphthenic acids (NA), which are complex mixtures of cylic, acyclic, and aromatic carboxylic acids.2−4 Their presence is associated with several problems in oil production, such as corrosion in refineries,5 pollution in refinery wastewaters and in oil sands extraction waters,6 formation of emulsion,7−11 and calcium naphthenate deposits.11−13 These deposits can severely plug oil/water surface separation installations. Some points of their formation mechanism are known: The increase of coproduced water pH upon field production, due to CO2 release, induces an increase of the dissociation degree of naphthenic acids. The formed naphthenates can then precipitate with calcium to form deposits.12 This process can be summarized with the following equations:

four carboxylic acid groups, are aliphatic, and have molecular weights in the 1230 g·mol−1 range (Figure 1).18,20−22 An ester of C80-TA was detected in one North Sea oilfield pipeline, but it could be the result of esterification of C80-TA with production chemicals.23 This structure led Lutnaes et al. to suggest an archaeal origin for the TA.20 TA is much more oil/water interfacially active than other NA, as shown by Brandal et al.18,24 It is now considered that the presence of TA is a prerequisite to the formation of calcium naphthenate deposits,16,26 but that does not necessary imply that deposits will be created. Indeed, Brocart et al.14 have shown that TA is present in a large number of crude oils, in 7 of the 9 crude oils they tested, but few of them present operational difficulties linked to the formation of calcium naphthenate deposits. As mentioned above, C80-TA is found in large proportion in calcium naphthenate deposits. Consequently, the easiest (and for now the only) way to obtain this molecule in order to study its properties is to isolate it from calcium deposits by a purification method such as the ion-exchange resin (IER) method.27 However, according to the experience of the authors, this method does not always give satisfactory purity of the tetraacids. Moreover, C80-TA is difficult to detect because it has no chromophore, and therefore, it is difficult to detect especially at the low concentrations similar to the ones found in petroleum crude oils. The lack of chromophore in the C80-TA and the purity issue brought forward a need for UV active model compounds with similar properties to gain more knowledge of the fundamental behavior of this category of molecules, both in

It has been reported that the formed deposit hardens when exposed to ambient pressure and temperature, a phenomenon not understood yet but which could be linked to the glass transition temperature of deposits.14 It has been shown by Baugh et al.,15,16 and subsequently confirmed by other research groups,13,17,18 that calcium naphthenate deposits recovered on several sites contain massive proportions (as high as 40% w/w19) of acids, named ARN (meaning “eagle” in Norwegian) by their discoverers.16 In the following, these acids will be named C80-TA. These acids have © 2012 American Chemical Society

Received: Revised: Accepted: Published: 5669

January 8, 2012 March 8, 2012 April 2, 2012 April 2, 2012 dx.doi.org/10.1021/ie3000634 | Ind. Eng. Chem. Res. 2012, 51, 5669−5676

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Figure 1. (a) Formula of BP-10, molecule developed as model for C80-TA by Nordgård and Sjöblom.25 (b) Formula of the most abundant C80 6-ring tetra-acid after Lutnaes et al.20

acid-IER (ion exchange resin) method.27 The first step in that process is to wash the sample thoroughly in toluene to remove crude oil and oil-soluble fractions. The remaining solid was then exposed to a 2:1 volume mixture of toluene and 1 M HCl solution to dissolve the naphthenate. The naphthenic acids were then selectively isolated from other potentially occurring polar compounds by use of the ion-exchange resin QAE Sephadex A-25. The solvent was removed from the naphthenic acids by evaporation on a rotary evaporator at 60 °C and further by drying in an oven at the same temperature. The purity of the sample was determined to be 76% w/w by a NMR method previously developed by Simon et al.19 The chemicals used were of analytical grade and were used with no further purification. Water was from a Milli-Q system (Millipore). 2.2. Solubility Experiments. The solubility of tetra-acids (BP-10 and C80-TA) in the presence of calcium in an oil/water system was determined as follows: Tetra-acid was solubilized in chloroform, and 10 mL of this solution was put into contact with 10 mL of a NaCl- and CaCl2-containing buffer solution. The buffer molecules used, at a concentration of 10 mM, were acetic acid (pH < 5), 2-(N-morpholino) ethanesulfonic acid (MES, 5 < pH < 6.6),29 3-(N-morpholino) propanesulfonic acid (MOPS, 6.6 < pH < 7.8),29 and borax (pH > 7.8). It must be noted that it has been checked that MES and MOPS do not present any surface activity at the studied concentrations (no decrease of surface tension), and they do not precipitate in the presence of Ca2+. However, the presence of these buffers must be taken into account when the exact ionic strength must be calculated, because they are charged. The oil/water solutions were shaken at 250 rpm at room temperature (≈22 °C, unless stated) for 2 days. Then, the mixtures were centrifuged, and the phases were separated and filtered (oil phase, 0.2 μm PTFE filter; aqueous phase, 0.45 μm cellulose acetate filter). The pH of the aqueous phases were then measured with a Mettler Toledo Seveneasy pH meter S20 with an InLab electrode calibrated at the measurement temperature. For the BP-10 experiments, their UV−visible spectra were determined (Shimadzu, UV-2401PC, BP-10 experiments only). The concentrations of acid components in chloroform were determined as follows:

bulk and at interfaces. As a result, Nordgård and Sjöblom have developed model molecules with structure and properties close to C80-TA.25 These molecules are pure and easy to detect (as a result of the presence of a chromophore). An extensive comparison has been done showing that these molecules, in particular one named BP-10 (Figure 1), are able to satisfactorily mimic the properties of C80-TA.28 Indeed, BP-10 has a molecular weight (around 1000 g·mol−1) and a chemical structure (4 arms with COOH function at the tip) similar to those of C80-TA. Moreover, BP-10 forms the same cross-linked network at the oil/water interface as C80-TA.28 However, BP-10 is less soluble in apolar solvents such as xylene. In this article, the solubility of tetra-acid (both BP-10 and C80-TA) in presence of calcium in an oil/water system has been investigated. The goal is 2-fold: First, the effect of different parameters (calcium concentration, temperature, etc.) on the solubility of tetra-acid has been determined. This allows for the study of the effect of these operational parameters on the pH at which tetra-acid starts to precipitate. This is of practical importance when an operator is faced with a calcium naphthenate deposition problem. Second, experimental data have been compared with a simple thermodynamic model that allows the study of the precipitation mechanism of tetra-acid. In other words, we try to establish for the first time a phase envelop for BP-10 and fit the data with thermodynamic-based equations BP-10 has been considered in this article because this molecule is easier to detect (as a result of the presence of a chromophore) and purer than the indigenous C80-TA and is a good model molecule, as explained. Some solubility experiments were carried out with C80-TA extracted from a calcium naphthenate deposit the same way as with BP-10, for comparison purpose.

2. EXPERIMENTAL SECTION 2.1. Reagents. The BP-10 was prepared according to the method developed by Nordgård and Sjöblom25 and used as prepared. Briefly, the molecule was prepared by alkylation of 2,2′,4,4′-tetrahydroxybenzophenone with the ω-bromo ester using K2CO3 in dimethylformamide (DMF) at 80 °C and subsequent ester hydrolysis using KOH in MeOH. The C80-TA standard has been prepared from a calcium naphthenate deposit recovered from a North Sea field by the 5670

dx.doi.org/10.1021/ie3000634 | Ind. Eng. Chem. Res. 2012, 51, 5669−5676

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• BP-10 concentrations were determined by HPLC. The HPLC system utilized was built from the following modules: A degassing unit (Shimadzu DGU-20A HT), two pumps (Shimadzu LC-10ATvp), a gradient mixer (Shimadzu SUS), an autosampler/injector (Shimadzu SIL-20A HT, injection volume: 20 μL) a column cooler/ heater (Phenomenex ThermaSpheres TS-430), and a UV/vis detector (Shimadzu SPD-20A with a 10 mm path length cell). The column used was a Phenomenex (Luna 5 μ silica (2) 100 Å 250 × 4.6 mm), and the temperature was controlled at 25.0 °C. The data were collected and analyzed using the Shimadzu LC solution version 1.22 SP1 software. Elution was performed using a flow rate of 1 mL/min with 10% acetic acid in CHCl3 as mobile phase and detected by UV at 314 and 280 nm yielding the BP10 peak at approximately 6.8 min. • C80-TA concentration was determined according to a modified procedure based on Simon et al.19 1 mL of the solution to analyze was dried out under nitrogen. C80-TA was then derivatized into their 2-naphthacyl derivatives by adding 1 mL of dimethylformamide (DMF), 240 μmol of 2-bromo-2′-acetonaphthone, and 480 μmol of N,Ndiisopropylethylamine. The solution was stirred at room temperature for 15 min; then, 100 μL of an acetic acid solution (300 μmol in DMF) was added and stirred for additional 10 min to neutralize the excess of reagent. 20 μL of this reaction mixture was injected into the liquid chromatograph (same system as previously described) fitted with a Luna 5μ C18(2) 100A Column 250 × 4.6 mm. Elution was performed using a flow rate of 1 mL/min with 65% methanol and 35% CHCl3 as mobile phase and detected by UV at 247 and 282 nm.

with A=

Figure 2. Concentration of BP-10 in oil phase, [BP-10]o, after 2 days of shaking as a function of pH for different Ca2+ concentrations. Conditions: [BP-10]o,i = 200 μM, [NaCl] = 100 mM. The lines represents the equation [BP-10]o = A × 10−4pH with A × [Ca2+]2 = 2.6 × 1018 mol−1·L+1.

H4TA w ⇄ 4H + + TA4 − [H +]4 [TA4 −] [H4TA]W • Partition coefficient:

3.1.2.1. Influence of Calcium Concentration. Figure 2 presents the concentration of BP-10 in chloroform for [NaCl] = 100 mM, an initial BP-10 concentration in oil phase, [BP-10]o,i, of 200 μM, and different calcium concentrations. For information, 200 μM corresponds to 133 ppm. Every curve presents the same shape: At low pH, the BP-10 concentration is constant and equal to the initial BP-10 concentration. Then at a given pH, depending on the calcium concentration, there is a sudden decrease of the BP-10 concentration: The BP-10 precipitates, as will be proved by determining the BP-10 concentration in water in section 3.1.2.6. Then, the concentration of BP-10 decreases with pH until being nondetectable by HPLC. The simple thermodynamic model was tested with the obtained experimental data. As mentioned, it is only valid when a precipitate is in equilibrium with the water phase. Consequently, it was only tested with down parts of the different curves: for lower pH, the Ks equation is not valid. It can be noticed that the data can be successfully fitted by the presented simple model, with A × [Ca2+]2 = 2.6 × 1018 mol−1·L+1 for

(1)

H4TA 0 ⇄ H4TA w

[H4TA]W [H4TA]O • Solubility product: K wo =

(2)

Consequently, the concentration of BP-10 (or C80-TA) at the solubility limit in oil phase is given by the following equation: [H4TA]O =

Ks × 10−4·pH [Ca 2 +]2 K woKa 4

(5)

The subscripts o and w mean in the oil phase and in the water phase, respectively. TA4− is assumed to be completely insoluble in the oil phase. It should be noticed that this model is similar, but not identical, to the one presented by Mohammed et al.30,31 and that the possible self-aggregation (dimerization for instance) of BP-10 or C80-TA in oil phase has not been taken into account, as no data is available to assess this possible phenomenon. Moreover, this model is only valid when a precipitate is apparent; that is, the solubility product equation is valid. 3.1.2. Comparison with Experimental Data. In the following, the concentration of BP-10 remaining in the oil phase after 2 days of shaking has been measured as a function of pH for different conditions of ionic strength, calcium concentration, and so on. Chloroform was used as oil phase.

3. RESULTS AND DISCUSSION 3.1. Solubility of BP-10. 3.1.1. Simple Model. A simple thermodynamic model is proposed to link the solubility of BP10 (or C80-TA) in oil phase as a function of pH and calcium concentration in the water phase. H4TA and TA4− are written when BP-10 (or C80-TA) is fully protonated or ionized, respectively. This model is based on the following equilibria: • Acidity constant:

Ka 4 =

Ks [Ca 2 +]2 K woKa 4

= A × 10−4·pH (4) 5671

dx.doi.org/10.1021/ie3000634 | Ind. Eng. Chem. Res. 2012, 51, 5669−5676

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Figure 5 shows that the temperature has little influence (less than 0.15 pH units) on the solubility of BP-10 in an oil/water system in presence of calcium in the interval [5 °C−50 °C]. 3.1.2.5. Comparison between Calcium and Magnesium. In this part, the solubility of BP-10 in the presence of two different divalent cations: calcium and magnesium have been compared (Figure 6). The figure shows that the solubility of BP-10 in presence of calcium is lower than that in the presence of magnesium. This comparison between Ca2+ and Mg2+ is consistent with previously published data on the composition of deposits prepared under controlled conditions in aqueous solution.32 Indeed, it was shown that the precipitates formed in an equimolar solution of Ca2+ and Mg2+ with BP-10 contain a higher proportion of calcium ions. This difference was explained in terms of hydration state and size of the cations: Mg has a hydration number of 6, while Ca has one of 2; hence, small Mg2+ cations with a hydration state of 6 would experience the highest electrostatic shielding density from the coordinated H2O molecules, as compared to Ca2+ cations. The figure also shows that the simple model is able to fit the experimental data in presence of magnesium. According to eq 4, as Kwo and Ka must be the same for the two systems, it can be estimated that Ks (Mg2BP-10) is approximately 130 × Ks(Ca2BP-10). It has been reported that calcium is predominantly found in naphthenate deposits13 while magnesium is not, although both are present in production water. Even if the exact Ca2+/Mg2+ ratio for any specific field must be taken into account, the lower solubility constant for Ca2BP-10 explains why calcium should be predominant in naphthenate deposits over magnesium. 3.1.2.6. BP-10 Concentration in Aqueous Solution. For the moment, only BP-10 concentration determination results in oil phase have been presented. However, in order to have full mass balance of BP-10 in the investigated systems, the concentration of BP-10 in aqueous solution needs to be known. This knowledge would allow the determination of the mass of precipitate by difference between the initial BP-10 concentration in oil and the equilibrium concentration of BP-10 in oil and water at any pH. The first tests have indicated that the BP-10 concentrations in aqueous phase are very low, but how low? To determine a maximum aqueous concentration, the following set of experiments has been performed: • First, absorption spectra of BP-10 solution in water without calcium (NaCl 100 mM, borax buffer 10 mM, pH = 10) were determined, and a calibration curve of absorbance as a function of [BP-10]w at λmax = 325 nm was plotted. • Then, the UV spectra of all aqueous solutions recovered for all the experiments presented were systematically determined. It was noticed that these spectra are always close to the baseline and the absorbance at 325 nm varies from −0.006 and +0.021 with no apparent trend. • It can therefore be concluded that BP-10 concentration is always lower or equal to 2 μM (corresponding to an absorbance of 0.021) whatever the conditions (different calcium or sodium concentration, presence of magnesium, and so on). No trend as a function of water composition (salinity, calcium concentration, etc.) was found. More accurate values would require a more sensitive analytical method and/or a procedure to concentrate BP-10 samples in the aqueous phase. As the maximum concentration is very weak compared to the initial BP-10 concentration in

calcium concentrations of 100, 30, and 10 mM. Especially, the equation well-represents the sharp decrease of the BP-10 concentration in the oil phase. For lower concentrations of 4 and 2 mM, the simple model underestimates the precipitation pH by approximately 0.2 pH units. One explanation can be given to this discrepancy. Sundman et al. have prepared precipitates in bulk by putting into contact BP-10 and calcium and sodiumcontaining salt solution in basic medium. They have shown that, at low [Ca2+]/[BP-10] ratio (close to 1), Na+ can be incorporated in the formed precipitates.32 This phenomenon is not taken into account by the simple model and could explain the differences existing between the simple model and the experimental data. 3.1.2.2. Influence of Sodium Chloride Concentration. Another parameter studied is the influence of the sodium chloride concentration (or ionic strength) on the solubility of BP-10. Figure 3 presents the concentration of BP-10 in chloroform as a function of pH at three different sodium chloride concentrations of 20, 100, and 600 mM.

Figure 3. Concentration of BP-10 in oil phase ([BP-10]o) after 2 days of shaking as a function of pH for different NaCl concentrations. Conditions: [BP-10]o,i = 200 μM, [CaCl2] = 10 mM. The lines represents the equation [BP-10]o = A × 10−4pH with A × [Ca2+]2 = 2.6 × 1018 mol−1·L+1.

Figure 3 shows that increasing the NaCl concentration from 20 to 600 mM has no or very little influence (less than 0.15 pH units) on the solubility of BP-10. This observation has consequences in the calculation of the BP-10 solubility product, as shown in section 3.1.2.6. 3.1.2.3. Influence of Initial BP-10 Concentration. The third parameter investigated is the influence of the initial BP-10 concentration onto its solubility properties. Figure 4 shows that the initial BP-10 concentration has no influence on its solubility because all the points at concentrations lower than the initial concentration (i.e., when there is formation of precipitate) superimpose onto a “master curve”. This shows that the results presented in this article are valid, whatever the total concentration of BP-10 in the system is. 3.1.2.4. Influence of Temperature. The fourth parameter investigated is the influence of temperature, (Figure 5). Four temperatures were considered: 5 °C, room temperature (approximately 22 °C), 40 °C, and 50 °C. The oil/water systems were kept shaking for 2 days in double sleeve beakers. Then, a sample of every phase was taken at the considered temperature before being filtered. The centrifugation step was discarded to prevent any temperature variation for the sample during the experiment. 5672

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Figure 4. Concentration of BP-10 in oil phase ([BP-10]o) after 2 days of shaking as a function of pH for different BP-10 initial concentrations (the right curve is a zoom of the left curve). Conditions: [NaCl] = 100 mM, [CaCl2] = 10 mM. The lines represents the equation [BP-10]o = A × 10−4pH with A × [Ca2+]2 = 2.6 × 1018 mol−1·L+1.

Figure 5. Concentration of BP-10 in oil phase ([BP-10]o) after 2 days of shaking as a function of pH for different temperatures. Conditions: [BP-10]o,i = 200 μM, [NaCl] = 100 mM, [CaCl2] = 10 mM. The lines represents the equation [BP-10]o = A × 10−4pH with A × [Ca2+]2 = 2.6 × 1018 mol−1·L+1.

Figure 6. Concentration of BP-10 in oil phase ([BP-10]o) after 2 days of shaking as a function of pH for different BP-10 initial concentrations. Conditions: [BP-10]o,i = 200 μM, [CaCl2] = 10 mM. The lines represents the equation [BP-10]o= A × 10−4pH with A × [Ca2+]2 = 2.6 × 1018 mol−1·L+1 for the calcium case and A × [Mg2+]2 = 3.5 × 1020 mol−1·L+1 for the magnesium case.

oil, 20 to 200 μM, most of the difference between the actual [BP-10]o and [BP-10]o,i presented in Figures 2−6 are due to the formation of precipitates and not solubilization of BP-10 in the aqueous phase. Consequently, in the following, the solubility of BP-10 in oil phase has been likened to the solubility in the entire oil/water system. 3.1.2.7. Significance of the Fitting Parameter A. The A term depends on the Kwo, Ka, and Ks defined in section 3.1.1. As these parameters can be determined independently, a review of them is a good way to test the simple model and check its consistency. • Kwo, the partition coefficient: This value has been determined for BP-10 for the system chloroform/water at different ionic strengths.33 This value depends on the ionic strength (salting-out effect) but is close to 5.10−4 for all the systems. This value is consistent with previously reported data for mononaphthenic acids.34,35 • Ka: A recent study has determined the pKa of BP-10 by potentiometry.36 The titration has been carried out at a concentration of 1 mM (above the critical micellar

concentration (CMC)) at different salinity (20, 100, and 600 mM of NaCl). The results show that the apparent pKa values of BP-10 are high (7−8) and depend on the ionic strength. These results were confirmed from the data obtained by measuring the oil/water partition coefficient of BP-10 in absence of calcium.33 These high values are due to the formation of micelles and do not correspond to the pKa of BP-10 monomers. This trend has also been observed for fatty acids.37 However, the solubility of BP-10 in oil phase for the system in presence of calcium does not depend on the ionic strength, as noticed on Figure 3, perhaps because the BP10 concentration in water is low, below the CMC. Indeed, the CMC values of BP-10 determined by Sundman et al.36 are equal to 22, 5.1, and 0.6 μM in respectively 20, 100, and 600 mM of NaCl, that is, higher than the measured BP-10 concentrations in water, except perhaps in 600 mM NaCl medium. In this case, there is most likely the presence of only BP-10 monomers in the aqueous phase. Consequently, a Ka value of 10−5.4, 5673

dx.doi.org/10.1021/ie3000634 | Ind. Eng. Chem. Res. 2012, 51, 5669−5676

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Table 2. Summary of Experiments Realized Using the Model System: BP-10 in a Chloroform/Water System with Calcium, Sodium Chloride, and Buffer in the Aqueous Solution

intrinsic acid constant of a molecule named BP-5 (BP-10 with pentyl alkyl chain instead of decyl for BP-10), has been chosen, a value already used to model the potentiometric titration curves of BP-10.36 • From these values, Ks(Mg2BP-10) and Ks(Ca2BP-10) can be calculated (Table 1). Table 1. Solubility Product of Ca2BP-10 and Mg2BP-10a

param.

range investigated

NaCl concn temp. CaCl2 concn

20−600 mM 5−50 °C 4−100 mM

initial BP-10 concn comparison Ca/Mg

20−200 μM

divalent cation Ca2+ A × [Ca ] Ks 2+ 2

a

Mg2+

2.6 × 10 3.3 × 10−7 18

3.5 × 1020 4.4 × 10−5

See section 3.1.2.7 for the details of the calculation.

However, it can be seen that [BP-10]w ≤ 2 μM, that means Ks must be lower or equal to 2.10−10, even in presence of magnesium. This discrepancy shows that the simple model can successfully fit the solubility of BP-10 in oil phase, but the theoretical considerations behind it are not completely consistent. As noticed in section 3.1.1, the possible self-association properties of BP-10 in oil phase have not, for instance, been taken into account. Dimerization has been shown to be an important phenomenon for fatty acids, for instance.38,39 3.2. Solubility of C80-TA. In this part, the solubility properties of BP-10 with the real C80-TA found in calcium naphthenate deposit have been compared. This comparison acts as a new test bench for the validity of BP-10 as model molecules for C80-TA in addition to the previous studies.25,28 Figure 7 compares the solubility of C80-TA and BP-10 in oil. It can be noticed that the two molecules precipitate in a similar pH range, but they have different kinds of relationships between the solubility in oil and pH. Indeed it can be noticed that [C80TA]o does not follow a 10−4pH relationship as BP-10 does. This difference is not due to bad accuracy of the measurements because they are reproducible, as proved by the comparison of two sets of independent measurements displayed in Figure 7.

effect of param. on precip. negligible: less than 0.15 pH unit negligible: less than 0.15 pH unit 0.9 pH unit variation, follows [BP-10]o = A × 10−4pH with A × [Ca2+]2 = 2.6 × 1018 mol−1·L+1 with a slight overestimation of BP-10 solubility at low calcium concentration (