Mineral Precipitation Kinetics: Assessing the Effect of Hydrostatic

Article pubs.acs.org/crystal

Mineral Precipitation Kinetics: Assessing the Effect of Hydrostatic Pressure and Its Implication on the Nucleation Mechanism Narayan Bhandari,*,† Amy T. Kan,† Fangfu Zhang,† Zhaoyi Dai,† Fei Yan,† Gedeng Ruan,† Zhang Zhang,†,⊥ Ya Liu,† Rudi van Eldik,‡,§ and Mason B. Tomson†,⊥ †

Civil and Environmental Engineering, Rice University, 6100 Main Street, Houston, Texas 77005, United States Department of Chemistry and Pharmacy, University of Erlangen-Nuremberg, Egerlandstr. 1, 91058 Erlangen, Germany § Faculty of Chemistry, Jagiellonian University, Ingardena 3, 30-060 Krakow, Poland ⊥ Nanosystems Engineering Research Center for Nanotechnology-Enabled Water Treatment (NEWT), Rice University, Houston, Texas 77005, United States ‡

S Supporting Information *

ABSTRACT: Sulfate minerals (barite, anhydrite, and celestite) can be a technological hindrance as a result of scale formation especially for operations where seawater injection is involved. The effect of pH, temperature, and saturation index (SI) on sulfate mineral nucleation and growth are fairly wellknown, but the influence of pressure on the nucleation kinetics has attracted no attention. Here we show that nucleation kinetics of barite, anhydrite, and celestite is highly dependent on hydrostatic pressure applied even under constant thermodynamic driving force, that is, at the same supersaturation level. Activation parameters of barite nucleation kinetics were calculated, and measured values are in agreement with literature. The negative activation volume measured suggests that barite nucleation from hydrated Ba2+ and SO42− ions is coupled to an overall volume decrease, albeit a large volume increase due to dehydration is expected. The results indicate that nucleation is not controlled by desolvation of solvated precursor Ba2+ and SO42− ions but rather by an intrinsic volume collapse in the ratedetermining step of the nucleation and crystal growth processes. The activation parameters measured in this study indirectly support previous findings of formation of hydrated barite precursor before formation of crystalline barite particles.

1. INTRODUCTION Nucleation and growth of minerals from aqueous solution could be problematic in various industrial processes including oil and gas production due to scale formation.1,2 Of the many inorganic sulfate minerals, barium sulfate (barite), calcium sulfate (anhydrite), and strontium sulfate (celestite) are considered to be the most important minerals causing scaling problems in production tubing or formation damage leading to huge economic losses due to production shutdown and various other issues.2 Therefore, there is a great deal of interest in understanding the rate of scale formation and assessing the influence of various parameters on its nucleation and growth kinetics. Physicochemical parameters such as temperature, pressure, pH, ionic strength (IS), and degree of supersaturation are key determining factors that influence the tendency for mineral precipitation.3−7 Although, the effect of various chemical conditions such as pH, temperature, and saturation index (SI) on mineral nucleation and growth kinetics are fairly well-known,8 the effect of pressure on mineral nucleation, to our understanding, has never been studied. Classical nucleation theory (CNT) represents the main framework for the understanding of nucleation phenomena.9−11 Under the principles of classical nucleation theory, the transfer © 2016 American Chemical Society

of solute molecules from solution to the crystal is driven by the change in Gibbs free energy.12 In a supersaturated solution, crystal nucleation occurs when the chemical potential of the solute, μ, in the solution is greater than the one at equilibrium, μe.9 The driving force for nucleation is the difference in chemical potential (Δμ, eq 1), and nucleation begins as a consequence of the random collisions of the basic building blocks of crystals (atoms, ions, or molecules). aa Δμ = RT ln + − K sp (1) where a+ and a− are activities of cations and anions in supersaturated solution and Ksp is the thermodynamic solubility product of the solid. Therefore, Δμ is the critical factor for the nucleation process, and under similar supersaturation level, kinetics of mineral nucleation and growth are expected to be similar. However, the classical assembly of forming a nucleus by accretion of single atoms or molecules has been recently challenged.13,14 The mechanism of mineral precipitation is Received: January 24, 2016 Revised: July 10, 2016 Published: August 9, 2016 4846

DOI: 10.1021/acs.cgd.6b00126 Cryst. Growth Des. 2016, 16, 4846−4854

Crystal Growth & Design

Article

⎛ ∂ ln k ⎞ ⎟ ΔV ⧧ = −RT ⎜ ⎝ ∂P ⎠T

suggested to be a complex phenomenon that begins by forming prenucleation clusters well before a stable nucleus.15,16 Considering this ambiguity, it is our interest to add another dimension by including pressure variation to study the nucleation process, since much emphasis is usually placed on the temperature dependence of nucleation rates.17 The activation parameter obtained from pressure-dependent kinetics has been used as a valuable tool to aid in the understanding of chemical reaction mechanisms in solution,18−27 but application of high pressure (HP) to understand the details of nucleation processes, to our knowledge, has not been pursued yet. Therefore, the goals of this study are to understand the effect of pressure on mineral nucleation kinetics and obtain mechanistic insights on nucleation processes. The effect of hydrostatic pressure on sulfate mineral (barite, anhydrite, and celestite) nucleation under constant thermodynamic driving force was studied. Kinetics and activation volume profiles were quantified, and the observed results were interpreted. Our results indicate that the kinetics of mineral nucleation, even under constant thermodynamic driving force conditions, is a strong function of hydrostatic pressure. The marked differences in nucleation kinetics under high pressure may be due to intrinsic volume collapse associated with the encapsulation process of the hydrated Ba2+ and SO42− ions, and it is strongly accelerated by hydrostatic pressure. More importantly, the activation volume and entropy of activation of barite nucleation processes determined in this study suggest that dehydration of solvated Ba2+ and SO42− cannot play a dominant role during the nucleation process. It is conceivable that amorphous (hydrated) barite particulates may have been formed well before transferring to barite single crystals. 1.1. Physicochemical Background. Pressure is a fundamental physical property that influences the values of different thermodynamic and kinetic parameters. In the same way as temperature dependence studies reveal the energetics of the process, pressure-dependence studies reveal information on the volume profile of the process, which helps to quantify the effect of volume changes during the reaction and provides valuable insight into the intimate nature of the reaction mechanism. The kinetic effect induced by pressure can be directly related to the activation volume of the reaction that passes through a transition state as shown in eq 2. Experimentally, the effect of pressure on reaction kinetics can be expressed in terms of the activation volume (ΔV⧧), which is defined as the logarithmic pressure derivative of the rate constant.20,28

where R is the gas constant, T (K) is the absolute temperature, and k (s−1) is the overall rate constant of barite formation at a given pressure under constant temperature. Induction time of mineral nucleation (hereafter nucleation time, t0) and precipitation reaction rate are inversely proportional to each other;4,29 therefore, eq 4 can be modified to eq 5, ⎛ ∂ ln 1 ⎞ t0 ⎟ ΔV = −RT ⎜⎜ ∂P ⎟ ⎝ ⎠T ⧧

( )vs P at constant temperature according to eq

the plot of ln

1 t0

5 is used to quantify the activation volume under the given conditions. As shown above, the estimation of the activation volume of the mineral nucleation process requires the applicability of the transition state theory to the studied reaction which involves the formation of, for example, barite nuclei (solid particles) from supersaturated solutions containing dissolved precursor ions (i.e., Ba2+ and SO42−). Under such conditions, the validity of microscopic reversibility that involves the same transition state for both the forward and reverse reaction could be questionable. TST has been used previously to calculate the energetics [activation energy (Ea), entropy of activation (ΔS⧧) and enthalpy of activation (ΔH⧧)] of mineral nucleation and growth processes30−32 or water exchange reactions at the solid/ liquid interface.33 We propose that the formation of BaSO4 from supersaturated solutions containing hydrated Ba2+ and SO42− ions can still be described by TST for a homogeneous liquid phase process, at least to the point where nucleation and crystal growth occur and the system becomes heterogeneous.

2. EXPERIMENTAL DETAILS 2.1. Chemicals. All chemicals used, namely, sodium chloride (NaCl), calcium chloride dihydrate (CaCl2·2H2O), barium chloride dihydrate (BaCl2·2H2O), sodium sulfate (Na2SO4), strontium chloride hexahydrate (SrCl2·6H2O), and NaOH, were purchased from SigmaAldrich and are of high purity (>99% trace metals basis). PIPES (piperazine-1,4-bis(2-ethanesulfonic acid) sesquisodium salt (enzyme grade), a biological buffer reagent) was purchased from Fisher BioReagent. Stock solutions of cations, such as Ba2+, Sr2+, or Ca2+, and anion solutions (SO42−) were prepared using the respective salt solutions containing an appropriate amount of NaCl, CaCl2·2H2O (where applicable), and PIPES (7 mM) in DI water (18mΩ, Millipore). All solutions were prepared under ambient conditions; thus the reported concentrations and pH refer to room temperature and ambient pressure. 2.2. High Pressure (HP) Dynamic Flow Study. A schematic diagram of the dynamic flow apparatus is shown in the Supporting Information (Figure S1). The apparatus uses two high pressure syringe pumps (ISCO Teledyne 65 HP, up to 165 MPa) and an analytical UPLC dual piston pump (Scientific Systems, Inc., up to 124 MPa). Each of the syringe pumps is used for the injection of metal ions or “cation” and sulfate containing “anion” solutions, respectively. In each experiment, the cation and anion solutions were first pumped into separate heating coils where they can be heated and pressurized to the

(2)

Within transition state (TS) theory, the activation volume of, for example, barite nucleation (eq 2), can be described as the difference in partial molar volumes between the TS (V⧧) and reactant species as indicated by eq 3. ΔV ⧧ = V̅ ⧧ − VR̅

(5)

where t0 is the nucleation time of mineral precipitation, for example, barite. Nucleation time is defined as the time period between the attainment of supersaturation and decrease of the concentrations of constituent ions from the aqueous phase due to nucleation/precipitation of the solid phase.14 The slope of

Ba 2 +(aq) + SO4 2 −(aq) ⇄ [Ba 2 +(aq)··· SO4 2 −(aq)]⧧ → BaSO4 (s) + nH 2O

(4)

(3)

However, because of the complexity to measure the partial molar volume of the activated complex, experimentally the activation volume of the reaction can be determined from kinetic data using eq 4. 4847



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desired pressure. After that, they were mixed by a T junction into the reaction coil. At the end of the reaction coil, an UPLC pump was used to pump in an inhibitor or chelating solution to prevent any further precipitation after this point. The chelator used in this study was a sulfonated poly(carboxylic acid) (SPCA). Our previous study suggested that SPCA can prevent precipitation of sulfate mineral efficiently at a given range of temperatures.34 After each experiment, the entire flow loop system was washed with DI water, followed by an EDTA solution (∼0.4 M, pH ≈ 10) for 10− 12 h and finally with DI water for ∼1−2 h. To avoid corrosion as well as carry over effects, the reaction coil used is made of Hastelloy C (HC) and a coaxial tubing made of fluorinated ethylene propylene (FEP) was threaded into the reaction coil (Figure S2).35,36 Additionally, reagent carrying tubing to and from the reaction coil was ma de of tita nium (T itanium Joe, product co de TU:CP2:0.125:0.055:0.035:SMLSS). The flow rates of the cation and anion solutions were designed such that the mixture has maximum residence time of 120 min (2 h) in the temperature/pressure controlled zone. The 2 h period was chosen because in most of the oil and gas production, the duration of the produced water traveling from the reservoir to the surface facility is usually less than 2 h.37 To determine the mineral nucleation kinetics in the dynamic flow experiments, effluents were periodically collected, filtered through 0.22 μm filter, diluted by 1% HNO3 to below the respective mineral supersaturation level and analyzed to determine the cation concentration (Ba2+, Ca2+, or Sr2+) by inductively coupled plasma optical emission spectrometry (ICP-OES). An illustration of nucleation time determination from a kinetic plot is given in the Supporting Information (Figure S3). To minimize the analytical errors in cation concentration measurements, an inert ion (potassium, K+) was also dosed in the reaction solution as a tracer or an internal standard. The analytical error was estimated to be below 5%. This dynamic flow loop test apparatus has been successfully applied to predict the scale formation and inhibition in previous investigations.34,36 In some case, nucleation kinetics at lower temperature/ pressure was evaluated using a laser light scattering method and the detailed experimentations of this method have been described previously.38 Despite the disagreement in the literature whether the mineral nucleation or crystal growth rate is a function of concentration or activities of constituents ions,7 we used the activity concepts to account for the nonideal behavior of the ions in solution as well as to maintain the constant thermodynamic driving force under various conditions. The amount of cation and anion needed to get the desired supersaturation level with respect to mineral phases under the given experimental conditions was calculated by using scale prediction software, ScaleSoftpitzer (SSP2015), developed by Rice University. This software has been tested rigorously with laboratory as well as field data and periodically updated to include the most recent available data in the literature. It has been commonly used in academia as well as in industries as a reliable tool for saturation index calculation in the laboratory or in field conditions.39−42 The saturation index (SI) was used to indicate the chemical potential (eq 6) level of brine with respect to mineral phase. SI of, for example, barite is defined as

SIbarite

2+ ⎧ ][SO4 2 −]γBa 2 +γSO 2 − ⎫ ⎪ [Ba ⎪ 4 ⎬ = log⎨ barite ⎪ ⎪ K sp ⎩ ⎭

was packed with barite−sand mixture and was connected to the backpressure control valve and high pressure pump. Ba2+ and SO42− containing brine solution at room temperature (at saturation index of barite 0.35 at given conditions) was pumped into the column, and the effluent was analyzed by ICP-OES to determine the concentration of Ba2+ remaining in the solution. In each case, the flow rate was adjusted in such a way that the reaction mixture has a contact time of 1, 10, 20, and 40 min, and data from the 20 min contact time were used to calculate the barite growth rate constant k (L mol−1 s−1).

3. RESULTS 3.1. Effect of Pressure on Barite, Anhydrite and Celestite Nucleation. The effect of pressure on barite nucleation kinetics was evaluated by keeping all other parameters such as supersaturation conditions (e.g., SI), T, pH, IS, and molar ratios of cation to anion (R = 1) constant. Figure 1 shows the typical time-dependent cation (Ba2+)

Figure 1. Time-dependent Ba2+ concentrations at 103.42 (▲), 41.37 (×), and 0.10 MPa (■) at 25 °C under dynamic flow conditions. Experimental conditions: 1 M NaCl, 25 mM Ca2+, pH = 6.7, SIBaSO4 = 1.72.

concentration measured in the reaction mixture in dynamic flow experiments, and Table 1 summarizes the experimental conditions as well as measured induction time. As indicated in Table 1 and Figure 1, at 25 °C and SIBaSO4 = 1.72, there is no indication of barite nucleation (no decrease of the aqueous Ba2+ Table 1. Experimental Details and Estimated Barite Nucleation Time NaCl concn (M)

CaCl2 concn (mM)

SI

Ba2+ or SO42− concn (mM)

P (MPa)

t0a (s)

25 25 25 25 25 25 25 25 25 25 25 25 25 25

1 1 1 1 1 0.15 0.15 0.15 0.15 0.15 0.01 0.01 0.01 0.01

25 25 25 25 25 25 25 25 25 25 0 0 0 0

1.72 1.72 1.72 1.72 1.72 1.85 1.85 1.85 1.85 1.85 2.30 2.30 2.30 2.30

1.27 1.06 0.90 0.79 0.69 0.79 0.71 0.55 0.46 0.39 0.60 0.48 0.39 0.27

103.42 68.95 41.37 20.685 0.10 103.42 82.74 41.37 20.68 0.10 103.42 68.95 41.37 0.10

600 2070 3502 >7200 >7200 2103 2752 4963 >7200 >7200 600 1922 3129 4598

(6)

where [Ba ] and and γBa2+ and γSO42− refer to concentration (molality) and activity coefficients of barium and sulfate ions, respectively. 2.3. Barite Crystal Growth. Barite crystal growth studies were conducted in a plug flow reactor system, for which the principle and methodology were adopted from ref 43. Barite crystals from Ward Natural Sciences were grounded to fine powder, washed with dilute acetic acid to remove organic matter and then with water, and sieved, and particle size of 200−300 μm was mixed with similar sized (200− 300 μm) EDTA washed fine Ottawa sand (barite is 5% by wt). A HP stainless steel column (HiP, Erie, Pennsylvania) of total volume 2 cm3 2+

T (°C)

[SO42−]

a

4848

Nucleation time. DOI: 10.1021/acs.cgd.6b00126 Cryst. Growth Des. 2016, 16, 4846−4854


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particulates. Similarly, at 68.95 and 103.42 MPa, the measured nucleation times were found to be 62 and 37 min, respectively. Similar experiments were also conducted at lower ionic strength using 0.15 M NaCl at 150 °C (Table 2), and the results again showed a significantly shorter nucleation time of 26 min at a higher pressure of 103.42 MPa compared with more than 2 h at 3.44 MPa under similar experimental conditions. These observations again showed a significant influence of pressure on barite nucleation kinetics under similar thermodynamic driving force (Δμ, eq 1). To test the hypothesis whether such kinetic effect of pressure is exclusively related to barite nucleation, similar studies were also extended to other industrially important minerals, namely, anhydrite (CaSO4) and celestite (SrSO4). The anhydrite phase is unstable below 125 °C, and to avoid multiple phases of CaSO4 mineral precipitation,45 anhydrite nucleation experiments (at SICaSO4 = 0.57) were conducted at 150 °C (Table 3).

concentration from the mixture) within 2 h at a pressure of 0.10 and 20.68 MPa or nucleation time, t0, is more than 2 h. However, at a similar supersaturation level [SIBaSO4 = 1.72] and a higher pressure of 41.37 MPa, the Ba2+ concentration started to decrease from the reaction mixture after 58 min of reaction time, indicating nucleation of barite particulates. Therefore, we assigned 58 min to be the nucleation time of barite formation under the given conditions. Similarly at 68.95 and 103.42 MPa, the measured nucleation times were found to be 34 and 10 min, respectively. Note that because of the nonideal nature of ions in the mixed electrolyte system at given conditions, the concentrations of barium and sulfate ions needed to achieve the same supersaturation level at elevated pressure were considerably higher than those at lower pressure (see tables). As mentioned in the Experimental Details section, our HP dynamic flow apparatus does not allow us to monitor the nucleation time for longer than 2 h. To determine the nucleation time at ambient pressure (i.e., at 0.10 MPa), a laser light scattering detection method44 was used, and it was estimated to be 4.2 h. A comparison of the measured nucleation time indicates a significant effect of pressure on barite nucleation kinetics. For instance, barite nucleation time decreased from 4.2 h to 10 min when the pressure was increased to 103.42 MPa. Additionally, barite nucleation experiments at various pressures were also conducted at moderate ionic strength using mixed electrolytes (0.15 M NaCl and 25 mM CaCl2), as well as at low ionic strength using 0.01 M NaCl. The measured nucleation time of barite nucleation under those conditions are also summarized in Table 1. Regardless of the ionic strength, the measured barite nucleation time still showed a considerable pressure effect (see Table 1). Considering its importance to geothermal as well as oil and gas recovery (especially relevant to deepwater production), the effect of pressure on barite nucleation kinetics at elevated temperature was also investigated at high and moderate ionic strengths, and the results are summarized in Table 2. As

Table 3. Experimental Details and Estimated Nucleation Time for Celestite and Anhydritea

NaCl concn (M)

CaCl2 concn(mM)

150 150 150 150 150 150 150 150 150

1.00 1.00 1.00 1.00 1.00 0.15 0.15 0.15 0.15

25 25 25 25 25 25 25 25 25

SI

Ba2+ or SO42− concn (mM)

P (MPa)

t0 (s)

0.55 0.55 0.55 0.55 0.55 0.90 0.90 0.90 0.90

0.75 0.64 0.60 0.50 0.45 0.55 0.45 0.38 0.29

103.42 68.95 51.71 20.68 3.44 103.42 68.95 41.37 3.44

2235 3720 4510 >7200 >7200 1588 4412 5274 >7200

125 125 125 150 150 150

mineral

NaCl concn (M)

SI

Ca2+ or Sr2+ concn (mM)

P (MPa)

t0 (s)

celestite celestite celestite anhydrite anhydrite anhydrite

1 1 1 1 1 1

0.50 0.50 0.50 0.57 0.57 0.57

9.24 7.25 5.46 50.15 35.20 25.34

103.42 51.71 3.44 103.42 51.71 3.44

1488 3308 5772 600 1769 3840

a

In celestite nucleation experiments, 25 mM CaCl2 along with 1 M NaCl was also used as background electrolytes.

Celestite nucleation was conducted at 125 °C [SISrSO4 = 0.50]. As shown in Table 3, the influence of pressure on anhydrite and celestite nucleation was also comparable to that of the barite system, suggesting a similarity in the pressure dependence of the nucleation processes for all three sulfate minerals. 3.2. Effect of Pressure on Barite Crystal Growth. Mineral nucleation is a rather complex process.13,16,46 To avoid any uncertainties, the effect of pressure on the reaction rate was measured in a well-known seeded growth system using a HP plug flow reactor at 0.20, 51.71, and 103.42 MPa. The general experimental procedures are similar to that of ref 43, and the underlying principle of a plug flow reactor is briefly described in the Supporting Information. Table 4 summarizes the Ba2+

Table 2. Experimental Details and Estimated Barite Nucleation Time (t0) at 150 °Ca T (°C)

T (°C)

Table 4. C0, Ce, and C of Ba2+ Ion during Seeded Growth at 20 min of Contact Time at Various Pressuresa

a

See Supporting Information for the description of the estimation of t0 .

a

indicated in Table 2 at 150 °C and SIBaSO4 = 0.55, there was no indication of barite nucleation within 2 h at a pressure of 3.44 and 20.68 MPa or the nucleation time, t0, is more than 2 h. However, at a similar supersaturation level [SIBaSO4 = 0.55] and at a higher pressure of 51.71 MPa, the Ba2+ concentration showed a progressive decrease from the reaction mixture after 76 min of reaction time, indicating nucleation of barite

P (MPa)

Ce (mM)

C0 (mM)

C (mM)

0.20 51.71 103.42

0.093 0.131 0.174

0.131 0.201 0.271

0.107 0.145 0.186

Ce was estimated using SSP2015.

concentration measured in the effluent at a contact time of 20 min in each case. The rate constants (k, L mol−1 s−1) of barite growth in contact with Ba2+ and SO42− at SI of 0.35 were calculated at 0.20, 51.71, and 103.42 MPa at 25 °C. Figure 2 shows a plot of ln k vs P and indicates that pressure has a considerable effect on barite growth kinetics under the given experimental conditions. 4849



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Figure 2. Plot of ln k vs P in barite seeded growth experiments (Table 5). Experimental conditions: SIBaSO4 = 0.35, 1 M NaCl, 25 mM CaCl2, and pH 6.7.

Figure 5. Plots of log 1/t0 vs P of anhydrite and celestite precipitation reaction (Table 4). Dark gray and black lines represent corresponding linear fit.

3.3. Measurement of Activation Volume for Barite, Anhydrite, and Celestite Precipitation. From the experimentally determined nucleation time (Tables 1 and 2) at various pressures under similar supersaturation levels and other physicochemical conditions, log(1/t0) vs P curves of barite nucleation at 25 and 150 °C at high ionic strengths were plotted (see Figure 3). Figure 4 shows log(1/t0) vs P plots for

Table 5. Experimental Conditions and Estimated Activation Volumes for Various Minerals T (°C)

mineral

IS (M)

25 25 25 150 150 125

barite barite barite barite anhydrite celestite

0.01 0.16 1.15 1.15 1.1 1.15

activation volume, ΔV⧧ (cm3/mol) −46 −40 −61 −47 −61 −47

± ± ± ± ± ±

8 3 9 2 7 8

estimated activation volumes for barite, anhydrite, and celestite nucleation are large negative values within −40 to −60 cm3/ mol. The closely similar activation volumes for nucleation of these sulfate minerals suggest a similarity in the precipitation processes. However, large negative activation volumes suggest that pressure has a positive effect on the nucleation kinetics and are indicative of a decrease in the overall partial molar volume during the formation of the transition state.18,20 Similarly, from Figure 2, the activation volume for barite seeded growth was estimated to be −12 ± 2 cm3/mol. The negative activation volume that resulted in this case is in agreement with that of a nucleation process, suggesting that bond formation between Ba2+ and SO42− is coupled to an overall volume collapse under supersaturated conditions. The considerably larger negative activation volume found during nucleation compared with that of the growth process further indicates that the former process requires more energy to overcome the activation barrier.

Figure 3. Plots of log 1/t0 vs P at 25 and 150 °C as indicated in the figure. Conditions: 1 M NaCl, 25 mM CaCl2, and pH 6.7.

4. DISCUSSION As demonstrated in Tables 1−5 and Figures 1 and 2, we observed a significant (as high as 2 orders of magnitude) influence of hydrostatic pressure on barite and other sulfate mineral nucleation kinetics under similar thermodynamic driving force conditions (Δμ, eq 1). The saturation index (SI, eq 6) is the expression for supersaturation or chemical potential of the system (eqs 1 and 6), and activity coefficients were used to account for the deviations from ideal behavior in mixed electrolytes at various pressures.47,48 Therefore, the 2 orders of magnitude faster barite nucleation kinetics (at 25 °C) observed when the pressure was increased from 0.10 to 103.42 MPa at moderate ionic strength conditions was not expected especially under similar supersaturation levels. Based on the principles of classical nucleation theory and activity concepts, the hypothesis here was that at constant supersaturation level (at similar chemical potential), mineral nucleation kinetics is expected to

Figure 4. Plots of log 1/t0 vs P at ionic strengths of 0.01 M (■) and 0.16 M (▼) at 25 °C. Dotted and dashed lines represent corresponding linear fit.

barite nucleation at 25 °C at moderate and low ionic strengths. Figure 5 displays log(1/t0) vs P plots for anhydrite and celestite as indicated. Table 5 summarizes the measured activation volumes for barite, anhydrite, and celestite nucleation. The 4850



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large positive activation volume, is expected in nucleation of barite from highly solvated Ba2+ and SO42− ions. Thus, a large negative activation volume found in this case was at first sight rather surprising since the reaction volume for the dissolution of barite is about-40 cm3/mol, which would suggest a reaction volume of +40 cm3/mol for the reverse process (precipitation of BaSO4). The latter positive number suggests that volume changes due to a decrease in electrostriction of the hydrated reactant ions Ba2+(aq) and SO42−(aq) and totally overrules the intrinsic volume changes associated with the nucleation of BaSO4. On the basis of these results, it would be reasonable to expect a positive activation volume for the nucleation process in contrast to the very negative values found in the present study. This suggests that nucleation is not controlled by desolvation (in the present case dehydration) but rather by an intrinsic volume collapse in the rate-determining step of the nucleation and crystal growth processes. To understand the details of the mineral precipitation process, Petrou and Terzidaki32 applied transition state theory to calculate the activation parameters [activation energy (Ea), entropy of activation (ΔS⧧), and enthalpy of activation (ΔH⧧)] for calcium carbonate and calcium sulfate nucleation and growth processes. Their results also indicate that desolvation of hydrated cations and anions is not the rate-determining step during nucleation and growth based on significantly negative activation entropies obtained for these processes.32 In order to provide further evidence, we also studied the temperature dependence of the nucleation process under identical conditions selected for the pressure dependence studies on barite nucleation (see Supporting Information). The obtained results, ΔH⧧ = 22 ± 3 kJ mol−1 and ΔS⧧ = −209 ± 8 J K−1 mol−1, show that the nucleation process is characterized by a low activation enthalpy barrier and a very negative activation entropy with an overall ΔG⧧ = 84 ± 7 kJ mol−1 at 298 K. These values are well in the range of values of energetic parameters reported for similar sulfate mineral nucleation processes.32 The thermal activation parameters clearly show that the nucleation process is an entropy-controlled process. A strong correlation between activation volume and activation entropy for a variety of reactions has been found.27 The very negative activation entropy value also correlates well with the very negative activation volume found for the barite nucleation process. Therefore, from both the activation entropy and activation volume parameters, we conclude that the intrinsic volume and entropy changes must be part of the rate-determining nucleation process. Thus, dehydration cannot play a dominant role during the nucleation process, at least under the given experimental conditions. Our experimental design did not allow us to quench the reaction mixture at desired experimental conditions to characterize the barite particles as they formed. Prior study has suggested that barium sulfate crystal formed via formation of a dense liquid precursor phase, nucleation of primary nanoparticles, and two levels of oriented aggregation resulting in micrometer-sized barite single crystals.13 A recent report claims that prenucleation ion associates must form prior to solid BaSO4 nucleation,54 and it further suggests the existence of an amorphous (hydrated) BaSO4 solid phase, then transformation to crystalline barite after dehydration.54 Based on this literature finding of hydrated BaSO4 formation early on and the large negative activation volume measured in this study, it appears reasonable to propose that during the nucleation process, hydrated Ba2+ is encapsulated by the negatively

be comparable regardless of the hydrostatic pressure. One can argue that changes in environmental conditions due to increase in pressure may have affected the nucleation mechanism and hence overall rate of nucleation. We assume that there is no impact on the mechanism of nucleation due to pressure alone since the pressure range used is well within the ranges of most thermodynamic and kinetic experiments performed (0−200 MPa) and it is small in terms of influencing the reaction mechanism. Much higher pressures and temperatures may be required to influence mechanistic changes as a result of changes in bond lengths and bond angles. The mild temperatures and pressures used in the present study are, however, large enough to have an impact on the kinetics of nucleation. Therefore, we suggest that the observed differences in sulfate mineral nucleation kinetics are due to inherent kinetic effects of pressure similar to that of temperature or ionic strength.49 We will discuss the possibility of how the sulfate mineral precipitation kinetics may have been influenced by elevated pressure under the same supersaturation level in more detail later. One of the aims of this work is to understand mineral nucleation processes in terms of activation volume data determined using the application of HP techniques, which has in the past been successfully applied to the understanding of organic and inorganic reaction mechanisms in solution.26,27,50,51 To gain insight into the mechanism of mineral precipitation, we determined the activation volumes for barite, anhydrite, and celestite nucleation, as well as barite growth processes (Table 5). In general, the measured activation volume is the sum of two components: an intrinsic part (ΔV⧧intr), which represents changes in partial molar volume due to changes in bond lengths and angles, and a solvational part (ΔV⧧sol) that accounts for partial molar volume changes due to changes in electrostriction and other effects associated with the reorganization of the surrounding solvent molecules during the activation process.20 In principle, the intrinsic contribution is the mechanistic indicator for the chemical process. In the case of barite nucleation from aqueous phase Ba2+ and SO42− ions, the process involves an intrinsic volume decrease (negative ΔV⧧intr) due to bond formation and a solvational volume increase (positive ΔV⧧sol) due to desolvation of the hydrated Ba2+ and SO42− ions in the supersaturated solution. The large negative ΔV⧧ value obtained in this study indicates that the intrinsic volume changes are significantly larger than the volume increase due to desolvation of the hydrated Ba2+ and SO42− ions. Unfortunately, there is no directly comparable volume data in the literature, but some studies have reported reaction volumes for the dissolution of barite and celestite. The reaction volume (ΔV) is the overall partial molar volume change between reactants (solid) and produced ions.20 Blount estimated the reaction volume for barium sulfate dissolution at 25 °C to be −40 ± 4 cm3/mol at 100 MPa and at infinite dilution.52 Macdonald and North reported that the reaction volume for celestite (SrSO4) dissolution in distilled water (up to 100 MPa) at 22 °C to be −49 ± 11 cm3/mol.53 The reaction volume of −40 cm3/mol for barite (BaSO4) dissolution also involves two contributions: an intrinsic volume increase due to bond cleavage (positive volume) and a solvation volume decrease (negative volume) due to hydration of the produced ions. The large negative reaction volume for barite dissolution52 indicates that the solvation volume decrease is much larger than the intrinsic volume increase during dissolution. Therefore, a large solvation volume change (positive contribution), that is, 4851



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finding of the significant acceleration of the barite scaling kinetics by pressure suggests that accurate estimation of the influence of these physicochemical conditions on scaling kinetics is needed before making a scale mitigation plan, especially in such harsh production environments.

charged oxo groups on the tetrahedral SO42− ion. This is probably followed by the dehydration of the amorphous BaSO4 (transformation to crystalline form)54 that may account for the large volume increase of ca. +80 cm3/mol following the transition state as shown schematically in the constructed volume profile in Figure 6. Therefore, the negative activation

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ASSOCIATED CONTENT

S Supporting Information *

The Supporting Information is available free of charge on the ACS Publications website at DOI: 10.1021/acs.cgd.6b00126. Schematic of experimental design, methodology of determination of the nucleation (induction) time, experimental details and results of the barite seeded growth, and estimation of entropy and enthalpy of activation of barite nucleation (PDF)

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AUTHOR INFORMATION

Corresponding Author

*Phone: +1-713-348-2149. E-mail: Narayan.Bhandari@rice. edu.

Figure 6. Schematic volume profile for the formation of BaSO4 from Ba2+ and SO42−. All partial molar volume data (V) are given in cm3/ mol.

Notes

The authors declare no competing financial interest.

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ACKNOWLEDGMENTS The authors acknowledge the financial support by a consortium of companies including Baker Hughes, Tomson Technologies, BWA, CARBO, Chevron, ConocoPhillips, Dow, Halliburton, Hess, Kemira, Kinder Morgan, Marathon Oil, NALCO Champion, Occidental, Petrobras, Saudi Aramco, Schlumberger, Shell, Southwestern Energy, SNF, StatOil, Total, EOG, Italmatch, Cenovus, and Weatherford. This work was also supported by the NSF Nanosystems Engineering Research Center for Nanotechnology-Enabled Water Treatment (ERC1449500).

volume measured in this study may indirectly support previous finding of formation of hydrated barite precursor before formation of crystalline barite particles as proposed by recent studies.13,54 More importantly, negative activation volume resulted due to intrinsic volume collapse associated with the encapsulation process of the hydrated Ba2+ and SO42− ions is suggested to play a key role during the nucleation reaction and is strongly accelerated by hydrostatic pressure.

5. CONCLUSIONS Although the understanding of the influence of extreme conditions on mineral precipitation is crucial for geochemistry and efficient recovery of oil and gas, there is no literature data on the kinetic effect of pressure on nucleation processes. The results presented here indicate a strong influence of hydrostatic pressure on sulfate mineral nucleation kinetics even under a similar supersaturation level. The large negative activation volume measured correlates very well with the large negative entropy of activation and suggests a highly ordered transition state structure, indicating that desolvation does not occur during the formation of the activated complex. These observations are in agreement with literature that hydrated amorphous barite precursors may have been formed before formation of barite crystals. In oil and gas production, injection of seawater into reservoirs to maintain reservoir pressure as well as to improve secondary recovery are well-established. Sulfate mineral, especially barite, scaling risk during seawater injection in offshore or a similar production scenario has been a persistent flow assurance problem.55 The efficient method to control scale deposits is to prevent their formation by chemical inhibition using scale inhibitors. However, in harsh production environments such as in deep water production [pressure >100 MPa, temperature >150 °C, and total dissolved solids (TDS) ≈ 300 000 mg/L], the application of chemical treatment could be cumbersome and expensive. Thus, to avoid potential scaling problems, injection of safe levels of sulfate containing seawater in those production wells has been suggested.37,56,57 The

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REFERENCES

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Mineral Precipitation Kinetics: Assessing the Effect of Hydrostatic

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