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Gypsum crystal growth kinetics under conditions relevant to CO2 geological storage
International Journal of Greenhouse Gas Control 91 (2019) 102829
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Gypsum crystal growth kinetics under conditions relevant to CO2 geological storage
T
Pedro M. Rendela,b, , Ittai Gavrielib, Nir Ben-Eliahua, Domenik Wolff-Boenischc, Jiwchar Ganora ⁎
a
Department of Geological and Environmental Sciences, Ben-Gurion University of the Negev, P. O. Box 653, Beer-Sheva, 84105, Israel Geological Survey of Israel, 32 Yesha'ayahu Leibowitz St., Jerusalem, 9692100, Israel c School of Earth and Planetary Sciences, Curtin University, GPO Box U1987, Perth, 6845, WA, Australia b
ARTICLE INFO
ABSTRACT
Keywords: CO2 Geological storage Gypsum Kinetics Pressure Precipitation
Deep saline aquifers are among the preferred potential repositories for carbon dioxide geological storage (CGS). Modeling the interaction of the injected CO2 with the brine is essential for proper planning of CGS, including avoidance of local precipitation of minerals such as sulfates, which may clog the injection borehole and decrease the injectivity of the surrounding rock mass. In the present study gypsum crystal growth kinetics at the pressure range of 1–100 bar and with the addition of different molal concentrations of dissolved CO2 was investigated. A series of flowthrough experiments were performed in a novel reactor system, designed to withstand high pressures, temperatures and corrosion. Gypsum growth rate was found to decrease with ascending pressure and increase with rising dissolved CO2 concentrations. Yet, separating the overall effect of these variables to their impact on the thermodynamics of the solution (i.e. super saturation) and on the reaction kinetics, reveal a very complex effect on the rate coefficient (khet). While due to the kinetic effect, the rate coefficient mostly decreases with rising dissolved CO2 concentrations, it has a second order polynomial behavior while pressure ascends. This implies that under the studied pressures and dissolved CO2 concentrations the thermodynamic is the main dominant parameter which governs the overall growth rate. It is suggested that both the thermodynamic and the kinetic effects arise from the respective dependence of the supersaturation of the solution and the rate coefficient (khet) on the solubility.
1. Introduction Carbon Capture and Storage (CCS) was confirmed both by The IEA (International Energy Agancy, 2017) and IPCC (Edenhofer et al., 2014) to be a critical component amongst all major global greenhouse gas reduction scenarios (Idem et al., 2006). Deep saline formations, depleted or depleting gas and oil fields, and enhanced oil recovery using CO2 are among the preferred potential repositories for CO2 due to their large storage capacity and their global abundance. Modeling the interaction of the injected CO2 with the brine in the reservoir is essential for proper planning of CGS operations. In an aqueous phase, dissolved CO2 reacts with water to produce carbonic acid. Dissociation of carbonic acid may then trigger the hydrolysis of the host rock, and consequently precipitation of secondary minerals such as carbonates (e.g., Carroll and Knauss, 2005; Hangx and Spiers, 2009; Kaszuba et al., 2005, 2003; Sorai and Sasaki, 2010; Sorai et al., 2005) and sulfates (Knauss et al., 2005; Pearce, 2018; Xu et al., 2007). These secondary minerals may decrease the porosity and permeability
of both the host rock and/or the cap rock, which may then affect the injectivity and/or sealing of the aquifer (e.g., Bacon et al., 2009; Pearce, 2018; Van Pham et al., 2012). One of the concerns in CGS is massive precipitation of sulfate minerals (e.g., gypsum and anhydrite) in the volume adjacent to the well bore (Singurindy and Berkowitz, 2003). Depending on the reaction kinetics, such precipitation may plug the bottom of the borehole and its close surroundings, producing a backpressure on the injection process. In order to predict the potential formation of sulfate minerals under CGS conditions, a deeper understanding of their precipitation kinetics is needed. Experimental data dealing with the kinetics of gypsum precipitation in natural brines and synthetic solutions are abundant (e.g., Christoffersen et al., 1982; He et al., 1994a, 1994b; Reznik et al., 2009, 2011; Witkamp et al., 1990), however, none of them deals with the effect of pressures or presence of CO2. Recently, Rendel et al. (2016) experimentally showed the influence of pressure and dissolved CO2 concentration on gypsum solubility at conditions relevant to CGS. While the solubility exponentially increases
⁎ Corresponding author. Currently address: Danish Hydrocarbon Research and Technology Centre, Technical University of Denmark, DTU, 2800 Kgs., Lyngby, Denmark. E-mail address: [email protected] (P.M. Rendel).
https://doi.org/10.1016/j.ijggc.2019.102829 Received 17 April 2019; Received in revised form 5 September 2019; Accepted 5 September 2019 1750-5836/ © 2019 Elsevier Ltd. All rights reserved.
International Journal of Greenhouse Gas Control 91 (2019) 102829
P.M. Rendel, et al.
as a function of pressure, it exponentially decreases as the CO2 molal concentration increases. The obtained results showed a good agreement to the latest Phreeqc v.3 (Appelo et al., 2014) thermodynamic geochemical model. In the present work, gypsum crystal growth kinetics was studied in pressurized solutions at 1, 50, 70 and 100 bar and with various molal concentrations of dissolved CO2 (0.20 ± 3.1%, 0.43 ± 3.4%, and 0.62 ± 2.7% (mol kg−1 solution)) at 70 bar. The growth rates at the different conditions were calculated in order to determine the effect of both pressure and CO2 on the precipitation kinetics.
Technologies), respectively. The separate inlet channels for the two under-saturated brines were designed to prevent precipitation of solid phases within the upstream tubing. Upon mixing in the reactor, these solutions form the super-saturated experimental solution. The overall confining hydraulic pressure in the system is controlled by a back pressure regulator (BPR) whose dome pressure is regulated with an inert gas (N2). The mixture is kept homogenized within the reactor vessel by an internal magnetic stirrer and a gas impeller. Process temperature is maintained stable by simultaneously heating and cooling the reactor through an external heating block and an internal cooling loop, respectively. At the outlet, the fluid is filtered through a 2 μm titanium frit. Temperature and pressure are monitored continuously throughout the experiment. The outlet solution is depressurized as it exits the BPR and collected for further analysis. The use of this flow-through system enables the injection of a CO2charged solution into the system without the need to separately inject liquid or gaseous CO2. This approach allows experimenting with different dissolved CO2 concentrations and sampling of the outflow solution during all experimental stages without disturbing the pressure conditions in the reactor.
2. Theoretical background Crystal growth is a process during which an existing crystal or nucleus continues to grow from a super-saturated solution. This process involves both a solid and a liquid phase and thus depends on the properties of both phases and the interface between them. Since crystal growth is a surface reaction, the heterogeneous growth rate is a function of the reactive surface area of the mineral. The supersaturation of the solution with respect to the growing crystal is another key parameter in determining the growth rate. Eq. (1) is a semi-empirical rate law describing the dependence of crystal growth rate on the deviation from equilibrium (Nielsen, 1981):
Ratehet = khet SA
(
1
1
)
3.2. CO2 introduction and analyses
n
The present study was conducted below CO2 supercritical conditions (at 25 °C). To avoid the development of two separate phases (gas and liquid) in the highly enriched CO2 environment within the vessel, the CO2 partial pressure was kept below the overall confining pressure of the system, attaining complete dissolution of the gas into the injected brine before reaching the reaction vessel. This was achieved by pumping small volumes of CO2 at constant flows of 50, 100 and 150 μL min−1 into the inlet brines through the static mixers to form two homogenous mixtures. While flowing through the long coil (jacketed tubes) the CO2 gradually dissolves, and carbonation occurs. The CO2 for the injection was kept at a temperature of approx. 8 °C in a liquid phase. The concentrations of CO2 in the experimental solutions were predetermined by running the experimental system with double deionized water under the planned experimental conditions. Multiple samples were collected over 2 weeks using a 1 mL precise sampling loop installed at the system (Fig. 1). Samples were unpressurized into 60 mL disposable plastic syringes containing approx. 30 mL of KOH solution (at ∼pH 11), and diluted (X100) using double deionized water. The diluted samples were then directly titrated for alkalinity using a 916 TiTouch Metrohm titrator with 0.01 N HCl using Gran functions (Stumm and Morgan, 1993). Assuming total alkalinity to be only carbonate alkalinity, and the injected CO2 to be the only source of carbon in the sample, dissolved CO2 concentrations could be calculated. Under the experimental conditions, CO2 flow rates of 50, 100 and 150 μL min−1 were found to yield solutions with dissolved CO2 concentrations of 0.20 ± 3.1%, 0.43 ± 3.4%, and 0.62 ± 2.7% (mol kg-1 solution), respectively.
(1)
Where Ω is the supersaturation of the solution, Ratehet is the observed heterogeneous crystal growth rate (mol s−1), SA is the mineral surface area (m2), khet is a heterogeneous rate coefficient (mol s−1 m-2), ν is the number of ions in the crystal formula unit other than the solvent (two in the case of gypsum) and n is the apparent reaction order with respect to the deviation from equilibrium (Ω1/ν-1). Several experimental studies have shown that the bulk growth rate of gypsum (the sum of growth on all crystallographic surfaces), may be described using a second order reaction (n = 2) (Amjad, 1985; Christoffersen et al., 1982; Liu and Nancollas, 1973; Nancollas and Liu, 1970; Reznik et al., 2011, 2009; Witkamp et al., 1990). The surface area following dissolution or precipitation may be empirically related to the initial surface area (SA(i)) (Christoffersen and Christoffersen, 1976; Shiliang He et al., 1994a, 1994b; Witkamp et al., 1990; Zhang and Nancollas, 1992) by:
SA = SA (i)
mt mi
p
(2)
where mi and mt are the masses of the initial and the growing crystals at time t (g), respectively, and p is a coefficient that depends on the crystal growth habit. p is equal to2 3 if the surface proportions of the growing crystal remain invariant during the growth process (Smith and Sweett, 1971). A p value of 0.5 indicates that growth occurs predominantly in two directions while a p value of 0 indicates one-dimensional growth with no increase in the surface area available for growth (e.g., Witkamp et al., 1990).
3.3. Experimental approach
3. Methods
Gypsum crystal growth rates were determined in two sets of flowthrough experiments performed at 25 °C in the presence of treated gypsum seeds (59 μm–149 μm):
3.1. Experimental system A novel experimental system (Rendel et al., 2018b), which allows interaction between CO2, brine and minerals under a range of temperatures (0–150 °C) and pressures (1–120 bar) was used. The system consists of a 300 mL flow-through continuously stirred reactor with two inlets and one outlet (Fig. 1). During experiments, two under-saturated brines containing pre-determined CO2 concentrations are injected through static mixers (Koflo Corp.) and temperature-controlled jacketed tubes under constant flow. Injection is via two piston pumps and a bench top syringe pump (VINCI
1 A first set of experiments to determine gypsum crystal growth rates only as a function of pressure without any CO2. The experiments were held under different confining pressures (1, 50, 70 and 100 bar), allowing the system to achieve a stable steady-state at each pressure. 2 A second set of experiments to determine gypsum crystal growth rates at a confining pressure of 70 bar in the presence of different molal concentrations of CO2 (0.20 ± 3.1%, 0.43 ± 3.4%, 2
International Journal of Greenhouse Gas Control 91 (2019) 102829
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Fig. 1. Schematic diagram of the flow-through experimental system.
0.62 ± 2.7% (mol kg−1 solution)). Here too, the system was allowed to achieve a stable steady- state at each dissolved CO2 concentration.
composition of the two solutions and the flow ratio. The solutions were prepared by weighing salts that make up the solutions with a precise balance and their dissolution in a known weight of de-ionized water. The activities of the individual ions and the supersaturation of the solution at the experimental conditions were calculated using the Pitzer specific-ion-interaction aqueous model (pitzer.dat database, with keyword PITZER) within the PHREEQC 3 code which is able to cope with high-salinity waters that are beyond the range of the Debye-Hückel theory (Appelo et al., 2014). CO2 was introduced into the model using the “REACTION” function, adding the number of moles of CO2(g) in a single step.
Periodically, approximately 1 mL solution was drawn from the sampling port using a syringe, filtered with a 0.22 μm filter disk and diluted by a factor of ∼1:100 (by weight), for SO42− analysis. SO42was analyzed using a Dionex DX500 high pressure liquid chromatography device following the method described by Reznik et al. (2009). Based on repeated analyses of SO42- standards, we estimate the precision to be ± 3% (one standard deviation). The gypsum seeds (pure CaSO4·2H2O) were prepared by crushing Satin-Spar crystals (precipitated from residual brines of a desalination plant; (Rosenberg et al., 2012) and sieving the powder to obtain a size fraction of 59 μm–149 μm using a matching set of sieves. The seeds were then pre-treated in a supersonic bath filled with a 99% methanol solution; the solution was sequentially replaced every 5 min with a fresh one, allowing the disposal of unwanted small suspended crystals (< 59 μm) which may have clung on the larger fragments. Finally the seeds where let to dry inside a fume hood at room temperature. The specific surface area of the gypsum seeds was measured using the BET method, with a NOVA 3000 (Micrometric) at IMI TAMI laboratories (Haifa, Israel), based on N2 adsorption, yielding a specific surface area of 3.4 m2 g−1. The accuracy and reproducibility of the surface area is ± 10%.
3.5. Determination of the kinetics of crystal growth In a well-mixed flow-through system, in which precipitation reactions occur, the change with time in the concentration of the reaction products (mol kg−1 solution s−1), is described by the following mass balance equation:
dCj, out dt
Precipitation of gypsum may be expressed by the reaction:
CaSO4 2H2 O
(3)
The deviation of a solution from equilibrium with respect to gypsum may be calculated in terms of the supersaturation of the solution (Ωgyp): gyp
=
Rate =
aCa2 + aSO42 a H2 2 O
IAP = K sp (aCa2+ aSO42 a H2 2 O)eq
Rate
j
SA V
q (Cj, out V
Cj, in)
(5)
where Cj,in and Cj,out are the concentrations of component j in the inflow and outflow solutions (mol kg−1 solution), respectively; νj - the stoichiometry coefficient of component j in the precipitation reaction; Rate - the growth rate (mol m−2 s−1); t stands for elapsed time (s); SA - the overall surface area of the growing mineral crystals/grains (m2); V - the volume of the reactor (m3), ρ - fluid density, and q - fluid flux through the system (kg s−1). Note that in this formulation, the growth rate is defined to be positive. Under steady-state conditions, when the composition of the outflow solution reaches a steady-state value, (i.e., dCj,out/dt = 0)) the growth rate may be described by:
3.4. Calculations
Ca2 + + SO42 + 2H2 O
=
q (Cj, out vj SA
Cj, in)
(6)
3.6. Gypsum solubility-definition
(4)
Solubility of a mineral is defined here as molal concentration of solutes in a solution saturated with respect to that mineral. In stoichiometric solutions, solubility is equal to the molal concentration of any of the lattice ions, divided by its coefficient in the mineral formula, while for non-stoichiometric solutions the solubility is equal to the lowest amongst these quotients. Thus, gypsum solubility in a stoichiometric solution is the molal concentration in saturation of either SO42− or Ca2+ while for a non-stoichiometric solution gypsum solubility is the
where IAP is the ion activity product, ai is the activity of species i, Ksp is the ion activity product at equilibrium (eq). Accordingly, Ω > 1 implies a supersaturated solution, whereas Ω < 1 is an undersaturated solution. In the present study, the concentration of SO42− was measured for each solution whereas Ca2+ concentration was calculated by subtracting the precipitated concentration from its initial concentration, assuming stoichiometric precipitation with the change in the measured SO42−. The concentrations of all other ions were calculated based on the initial 3
International Journal of Greenhouse Gas Control 91 (2019) 102829
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Table 1 Average chemical composition of the initial experimental solutions (mol kg−1 solution). Description
Na+
Ca2+
Cl−
SO42−
Ca2+/SO42−
I
Ω1bar
Ω50bar
Ω70bar
Ω100bar
Exp. 1 bar
0.0245
0.5437
1.0875
0.0122
44.37
1.778
1.78
1.66
1.62
1.55
Ω xxbar = Ωgyp at 25 °C and 1, 50, 70 and 100 bar without CO2, I = Ionic Strength. The uncertainty on the Na+, Ca2+, Cl− and SO42− concentrations is better than ± 3%.
different pressures at 25 °C was calculated with the PHREEQC v.3 geochemical model (Appelo et al., 2014), using the solution chemical composition as the input solution (Table 1). The high reliability of the PHREEQC code for these conditions was demonstrated experimentally by Rendel et al. (2016). 4. Results Figs. 3 and 4 present the change in SO 4 2− concentration with time for the first and second set of experiments, which lasted 20 and 28 h, respectively, enough time for all runs to attain a steadystate concentration. The steady-state concentrations tend to increase as pressure rises (Fig. 5; no CO 2 ); and to decrease as dissolved CO 2 concentration increases (Fig. 6; constant pressure). Note, that in the second set of experiments pressure was kept constant at 70 bar, and CO 2 was only injected after 15 h, allowing the system to approach an earlier steady-state concentration solely affected by the pressure. Examination of the precipitated gypsum at the end of the experiments showed that crystals tend to form stiff layers on the internal surfaces of the reactor cell as was previously described in Rendel et al. (2018a), (Fig. 2).
Fig. 2. Stiff layers of gypsum attached to the walls and to the internal parts of the reactor formed during the experiments.
Ca2+ molal concentration in saturation when Ca2+/SO42− < 1 and the SO42− molal concentration in saturation when Ca2+/SO42− > 1. 3.7. Experimental conditions
5. Discussion
Gypsum crystal growth rates were determined at 25 °C for a range of pressures and dissolved CO2 concentrations in seven flow-through experiments in the presence of ∼0.5 g of gypsum seeds. A single solution with an initial degree of supersaturation with respect to gypsum (Ωgyp) of 1.78 at 25 °C and 1 bar was used in all the experiments. CaCl2 and NaSO4 solutions were prepared separately by dissolving the corresponding salts with double deionized water. The final experimental solutions were formed in the reactor vessel upon the mixing of equal volumes of CaCl2 and NaSO4 solutions. Each solution was pumped into the reaction cell at a flow rate of 2.5 mL per minute. Ωgyp under the
5.1. Gypsum crystal growth as function of pressure and dissolved CO2 concentration Crystal growth rates (mol m−2 s−1) were calculated using Eq. (6), where the surface area of the growing mineral crystals (SA) was initially determined using Eq. (2), with p = 2/3. While most of the parameters in Eq. (2) are known at the onset of the experiment, the mass of the growing gypsum crystals at time t (mt) needs to be sequentially integrated for each time step (between each pair of sequential data points):
Fig. 3. SO42− concentration vs. time in pressurized experiments at 1, 50, 70 and 100 bar (no CO2). Dashed and solid black lines represent the inflow concentration and the average steady-state value at each pressure, respectively; doted gray lines represent one sigma uncertainty envelopes for each steady-state value. 4
International Journal of Greenhouse Gas Control 91 (2019) 102829
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Fig. 4. SO42− concentration vs. time in experiments at 70 bar with different dissolved CO2 concentrations. Injection of CO2 started after 15 h of experiments. Dashed and solid black lines represent the inflow concentration and the average steady-state values at the end of the experiments, respectively. Horizontal dotted gray lines represent one sigma uncertainty envelopes around each steady-state value.
Fig. 5. SO42− steady-state concentrations vs. pressure in pressurized experiments at 1, 50, 70 and 100 bar. SO42− steady-state concentrations increase with increasing pressure following a second order polynomial regression.
Fig. 7. Non-normalized gypsum crystal growth rate (mol s−1), (blue dots), and accumulated gypsum mass (g), (red dots) vs. time (h). Non-normalized crystal growth rates appears to reach a steady-state, while gypsum mass continues to growth, indicating a one-dimensional growth of gypsum layers on the inside surfaces of the reactor cell.
surface area of the mineral. Thus, keeping the crystals fully suspended in the solution maximizes the exposure of crystal surfaces to the solution. With this in mind, our experiments solutions were vigorously stirred. However, despite the stirring, the crystals formed layers of gypsum on the internal surfaces of the reactor cell (Fig. 2) and the available surface area for growth was therefore limited. In fact, after an initial stage of increase in surface area, we estimate that all the internal surfaces of the reactor were covered by gypsum. From this time on, the available surface area became constant, and the precipitation and growth continued as a one-dimensional growth. Under such condition, and as long as these do not change significantly, the non-normalized crystal growth rate (mol s−1) is expected to remain constant. Fig. 7 presents the non-normalized gypsum growth rate (mol s−1) and the accumulated gypsum mass mt (g) as a function of time (h), during a representative experiment (100 bar, no CO2). Initially, as the gypsum crystals grow and the available surface area increases, the non-normalized crystal growth rate also increases. However, after accumulation of approximately 2.7 g of gypsum in the reactor cell (including the initial ∼0.5 g of seeding), the non-normalized crystal growth rate became constant, indicating that the additional precipitation of gypsum continued as a one-dimensional growth with no increase in the available surface area (p in Eq. (2) is 0). In order to determine the normalized growth rate at steadystate, the surface area of the gypsum that fully covered the internal surfaces of the reactor must be known. This surface area (henceforth, final total reactive surface area) may be independently calculated for each experiment, by assuming that: (1) growth rate of gypsum is constant during
Fig. 6. SO42− steady-state concentrations vs. CO2 molal concentrations at 70 bar. SO42− steady-state concentrations decrease with increasing CO2 molal concentration following a second order polynomial regression. mt
mt = mini
t 1
mt
m=
Mwgyp q mini
(Cin t
Cout(t ) ) dt
(7)
where Cin and Cout are the SO42− concentrations in the inflow and outflow solutions (mol kg−1 solution), respectively; Mwgyp is the molar weight of gypsum (172.17 g mol−1), and q is the flow rate (kg solution s−1). As previously outlined, crystal growth is a surface reaction, with the heterogeneous growth rate being a function of the available reactive 5
International Journal of Greenhouse Gas Control 91 (2019) 102829
P.M. Rendel, et al.
1994b); and 8.36∙10−7 mol m−2 s−1, found by Zhang and Nancollas (1992)). This further supports the outlined methodology. The uncertainty in the calculated growth rates was estimated using the Gaussian error propagation method (Barrante, 1974), based on the measured SO42− concentrations vs. time within the time frame identified as being at steady-state concentration for each experiment (solid lines in Figs. 3 and 4). The propagated uncertainties in the rates range between 10.02% and 10.07% and are dominated by the uncertainty in the measurement of the surface area ( ± 10%). However, it should be noted that all our experiments were carried out using a single pretreated batch of gypsum seeds (see Section 3.3) that produced a homogenous powder. Since all experiments were conducted using a sub-sample from this powder, it can be assumed that the specific surface area of the initial gypsum seeds are identical in all and hence that the contribution of the surface area to the uncertainty in the growth rates is negligible when compared between the different experiments. This assertion is supported by the independent growth rates measured within the period prior to CO2 injection during our second set of experiments, in which the unpropogated gypsum growth rates differ by less than 1%. This small difference (< 1%) supports the suggestion that there is no significant difference in the surface area of the initial seeding material as well as in the surface area of the new gypsum formed during the experiments. In Table 2, we report the uncertainties that include the propagated uncertainty in surface area as well as uncertainties that do not include it. The former are used for comparison between our results and results from other studies that used different batches of gypsum, while the latter is used for comparison between experiments conducted in the present study using the same gypsum seeds batch. In order to evaluate the reliability of the obtained normalized growth rates, the normalized rate in the experiment performed at 1 bar, 25 °C and without CO2 was compared to rates reported by Zhang and Nancollas (1992) and Reznik et al. (2011), at similar conditions. Figs. 9 and 10 present the normalized growth rate (mol m−2 s-1) as a function of the initial Ca+/SO42- in solution and as a function of gypsum solubility, respectively, at 25 °C. The result from the present study (red dot), is in a good agreement with the previously reported rates. The growth rates vs. pressure and vs. dissolved CO2 concentration are plotted in Figs. 11 and 12, respectively, suggesting that the crystal growth rate decreases with the increasing pressure following a second order polynomial regression and increases linearly as dissolved CO2 concentration increases. It should be emphasized that due to the lack of a proper mechanistic explanation, the regressions presented in Figs. 11 and 12 are only based on the best data fitting.
Fig. 8. Calculated gypsum surface area vs. accumulated gypsum mass. The newly estimated surface area (blue dots) based on the initial normalized gypsum growth rate (see text) shows a shift towards a one-dimensional growth after the accumulation of approx. 1 g of gypsum in the reactor.
the entire experiment (the environmental conditions remain unchanged); and (2) initially, the surface area is linearly proportional to the mass, and the specific surface area (m2/g) is equal to the BET surface area of the gypsum seeding. The normalized growth rates during the first couple of hours of each experiment were used to obtain the change in total reactive surface area with time. This was achieved by dividing the growth rate (mol s−1) at time t with the initial normalized growth rate (mol m−2 s−1). Fig. 8 compares the total reactive surface area as estimated with this procedure and that calculated using Eq. (2), with p = 2/3, in a representative experiment (100 bar, no CO2). Initially, the surface area calculated by Eq. (2) is similar to that estimated by the normalized growth rate. Thereafter, while the surface area calculated using Eq. (2) increases continuously, it approaches a stable value when estimated by the normalized growth rate. In reality, at this stage, the newly precipitated gypsum grows on the gypsum coatings of the reaction vessel, and therefore the reactive surface area remains constant with time, i.e., crystal growth is one dimensional. The average surface area of all the experiments during the one- dimensional growth rate stage was 2.4 ± 0.2 m2. This average value represents the surface area of gypsum needed to cover the entire internal surfaces of the reactor and was used to derive a normalized steady-state growth rate (mol m−2 s−1) for each of the experiments. The normalized growth rates obtained during the second phase of the experiments are summarized in (Table 2). It should be noted that the rates obtained are all of the same order of magnitude as those found in previous works (1∙10−9–4∙10−8 mol m−2 s−1, found by Reznik et al. (2009); 1.7∙10−7–1.7∙10−8 mol m−2 s−1, found by He et al. (1994a,
5.2. Kinetic vs. Tthermodynamic effects on gypsum growth rate Gypsum crystal growth rate decreases as a function of pressure and increases with dissolved CO2 concentration. Eq. (1) suggests that these
Table 2 Experimental results. Experiment
1 bar 50 bar 70 bar 100 bar 70 bar, 0.2 M CO2 70 bar, 0.43 M CO2 70 bar, 0.62 M CO2
SO42−s.s
Rate
Uncertainties on Rates
(mmol kgs
−1
(mol m
8.3476 0.0086 8.8348 9.2191 8.0000 7.1964 6.6754
0.61% 0.43% 0.25% 0.39% 0.28% 0.74% 0.74%
1.560E-07 1.430E-07 1.310E-07 1.168E-07 1.529E-07 1.821E-07 2.011E-07
± ± ± ± ± ± ±
)
−2
−1
s
)
*
Ωs.s
**
± 1.18% ± 0.94% ± 0.66% ± 1.11% ± 0.53% ± 1.07% ± 0.90%
± 10.07% ± 10.04% ± 10.02% ± 10.06% ± 10.01% ± 10.06% ± 10.04%
1.20 1.15 1.15 1.17 1.16 1.18 1.21
log(khet)***
Solubility
(mol m
−2
−1
s
−4.77 −4.55 −4.60 −4.78 −4.59 −4.61 −4.70
± ± ± ± ± ± ±
0.37% 0.35% 0.33% 0.35% 0.33% 0.45% 0.33%
)
(mmol kgs−1) 6.9158 7.3814 7.5778 7.8854 6.7814 5.9489 5.3753
s.s at steady-state; Ωgyp was calculated with the PHREEQC v.3 geochemical model (Appelo et al., 2014) for the solution at steady-state at 25 °C and the appropriate experimental pressure of each experiment. * Uncertainties do not include the uncertainty in the surface area. ** Uncertainties include the uncertainty in the surface area. *** khet calculated using the rates that do not include the uncertainty in the surface area. 6
International Journal of Greenhouse Gas Control 91 (2019) 102829
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Fig. 11. Gypsum crystal growth rate vs. pressure. Crystal growth rates appear to decrease with increasing pressure following a second order polynomial regression. Fig. 9. Growth rate of gypsum (mol m−2 s−1) as a function of Ca+/SO42− ratio. All data are corrected to Ωgyp = 1.69. Results from Zhang and Nancollas (1992) in diamonds, Reznik et al. (2009) in squares and this research (experiment at 1 bar and without CO2) in red circles. The black line represents the linear regression as shown by Reznik et al. (2009).
Fig. 12. Gypsum crystal growth rates vs. CO2 molal concentration in the experiments at 70 bar. Crystal growth rates appear to increase linearly with the increasing dissolved CO2 concentrations.
Fig. 10. Log k as a function of SO42− in equilibrium (for experiments with Ca+/SO42− > 1, SO42− represents the gypsum solubility); results from: Reznik et al. (2009 and 2011) in triangles, Zhang and Nancollas (1992) with NaCl or KCl additives in diamonds, He et al. (1994b) in squares and this research (experiment in 1 bar without CO2 at 25 °C) in red circles. The black curve represents the model developed by Reznik et al. (2011), for a Na+/Ca+ activity ratio < 7.
variables affect crystal growth rate by (1) changing the supersaturation of the solution (Ω), i.e. a “thermodynamic effect”, and/or (2) by changing the kinetic rate coefficient (khet), i.e., a “kinetic effect”. Figs. 13 and 14 present the calculated Ωgyp of the experimental solution as a function of SO42− concentrations, under various pressures and dissolved CO2 concentrations, respectively. Ωgyp was calculated with the PhreeqC v.3 geochemical software (Appelo et al., 2014), using the "Pitzer" specific-ion-interaction aqueous model, (Table 1) at 25 °C. Note that the interceptions of the lines with the x-axis (in both figures) represent the gypsum solubilities (i.e. SO42− concentration at equilibrium with gypsum) under the specific pressure or CO2 conditions. Initial Ωgyp of the experimental solutions and the steady-state Ωgyp (Ωs.s) are shown as symbols on the lines.
Fig. 13. Gypsum saturation degree in the experimental solution with changing SO42− concentrations (Ωgyp) vs. SO42− concentrations in the solution at various pressures. Ωgyp is calculated with PhreeqC v.3 geochemical model (Appelo et al., 2014) using the Pitzer specific-ion-interaction aqueous model at 25 °C. The black curve is the second order polynomial regression (R2 = 0.93) connecting the degree of gypsum saturation at steady-state in each experimental solution (circles). 7
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Fig. 14. Gypsum saturation degree in the experimental solution with changing SO42− concentrations (Ωgyp) vs. SO42− concentrations in the solution at various dissolved CO2 concentrations. Ωgyp is calculated with PhreeqC v.3 geochemical model (Appelo et al., 2014) using the Pitzer specific-ion-interaction aqueous model at 25 °C and 70 bar. The black curve is the second order polynomial regression (R2 = 0.99) connecting the degree of gypsum saturation at steadystate in each experimental solution (circles).
Fig. 16. Log rate coefficient (log(khet)) vs. CO2 molal concentration in the experiments at 70 bar; log(khet) follows a second order polynomial regression as pressure increases.
By calculating the rate coefficient (khet) with the appropriate Ωs.s for each experiment, the dependency of khet on the pressure and dissolved CO2 concentration was obtained (Figs. 15 and 16, respectively). While khet mostly decreases with CO2 concentration, it initially increases with pressure and then decreases. 6. Conclusions Gypsum crystal growth rates were determined in two sets of flowthrough experiments. Experimental results show that increasing pressure and CO2 concentrations have opposite effects on the growth rates of gypsum. The overall crystal growth was found to be controlled by two different effects; (1) a thermodynamic effect, which changes the degree of saturation with respect to gypsum (Ωgyp) through its effect on the solubility and (2) a kinetic effect, represented by the rate coefficient (khet). Accounting for all other effects while solely examining the kinetic effect reveals that under the studied pressure (70 bar) and dissolved CO2 concentrations gypsum crystal growth rate tends to decrease both when pressure (> 50 bar) and dissolved CO2 concentrations increase. An exception is observed at relatively low pressures where khet tends to increase. Fig. 17 summarizes the observed trends, implying that under the studied pressures and dissolved CO2 concentrations, the thermodynamic effect, is the dominant factor that governs the change in growth rates due to changes in pressure and dissolved CO2 concentrations. Our experimental results emphasize the important role that pressure and the presence of CO2 have on gypsum kinetics under conditions relevant to geological carbon storage. These effects need to be incorporated into all models of CO2-water-rock interactions under conditions relevant to CGS. Whereas the thermodynamic behavior during the injection of large quantities of supercritical CO2 into brines is well known and can be modeled, the kinetic nature of the reactions needs to be closely monitored during injection to avoid the potential precipitation of gypsum from the brine. Such precipitation may negatively affect the injectivity of the injection well and should be avoided.
Fig. 15. Log rate coefficient (log(khet)) vs. pressure; log(khet) follows a second order polynomial regression as pressure increases.
In order to determine if there is also a “kinetic effect” on the growth rate, the “thermodynamic effect” must be separated from the overall growth rate. Rearranging Eq. (1) and inserting the Ωgyp at steady state (Ωs.s), the number of ions in the crystal formula unit ν (two in the case of gypsum) and the apparent reaction order n (which was found to be two, according to the BCF crystal growth theory (Lasaga, 1998) and further experimental studies (Amjad, 1985; Christoffersen et al., 1982; Liu and Nancollas, 1973; Nancollas and Liu, 1970; Witkamp et al., 1990)), the rate coefficient khet, can be determined:
khet =
SA
(
Ratehet s.s
1
1
)
n
= 2.4
(
Ratehet 1 s.s 2
1
)
2
(8)
8
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Fig. 17. Schematic summary of the factors controlling the overall gypsum growth rates. The thermodynamic effect is represented by the change in the initial degree of saturation with respect to gypsum(Ωini). The kinetic effect is represented by the kinetic constant (khet, [mol m−2 s−1]). Solubility [mmol kgs−1], overall rate [mol m−2 s−1], pressure [bar] and CO2 concentration [mol kg−1 solution].
Declaration of Competing Interest
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The authors declare that they have no known competing financial interests or personal relationships that could have appeared to influence the work reported in this paper. Acknowledgements This research was supported by the Israeli Ministry of Water and Energy, (Grants #ES-32-2012 to JG and IG). P.M. Rendel is grateful to the Rieger Foundation of Santa Barbara California and the JNF in the United States for their generous support. We also wish to express our gratitude to I. Reznik for the fruitful discussion and Y. Keisar, T. Blank, P. Alster Har-Zion, L.B. Freitas and E. Shani for their technical assistance. We would like to express our gratitude and appreciation for the detailed and enlightening review carried out by the editor and anonymous reviewers. References Amjad, Z., 1985. Applications of antiscalants to control calcium sulfate scaling in reverse osmosis systems. Desalination 54, 263–276. https://doi.org/10.1016/0011-9164(85) 80022-9. Appelo, C.A.J., Parkhurst, D.L., Post, V.E.A., 2014. Equations for calculating hydrogeochemical reactions of minerals and gases such as CO2 at high pressures and temperatures. Geochim. Cosmochim. Acta 125, 49–67. https://doi.org/10.1016/j. gca.2013.10.003. Bacon, D.H., Sass, B.M., Bhargava, M., Sminchak, J., Gupta, N., 2009. Reactive transport modeling of CO2 and SO2 injection into deep saline formations and their effect on the hydraulic properties of host rocks. Energy Procedia 3283–3290. https://doi.org/10. 1016/j.egypro.2009.02.114. Barrante, J.R., 1974. Applied Mathematics for Physical Chemistry. Prentice-Hall Inc, New Jersey. Carroll, S.A., Knauss, K.G., 2005. Dependence of labradorite dissolution kinetics on CO2(aq), Al(aq), and temperature. Chem. Geol. 217, 213–225. https://doi.org/10. 1016/j.chemgeo.2004.12.008. Christoffersen, J., Christoffersen, M.R., 1976. The kinetics of dissolution of calcium sulphate dihydrate in water. J. Cryst. Growth 35, 79–88. https://doi.org/10.1016/00220248(76)90247-5. Christoffersen, M.R., Christoffersen, J., Weijnen, M.P.C., Van Rosmalen, G.M., 1982.
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P.M. Rendel, et al. 90081-3. Nielsen, A.E., 1981. Theory of electrolyte crystal growth. The parabolic rate law. Pure Appl. Chem. 53, 2025–2039. Pearce, J.K., 2018. Experimental Determination of Impure CO 2 Alteration of Calcite Cemented Cap-Rock, and Long Term Predictions of Cap-Rock Reactivity. https://doi. org/10.3390/geosciences8070241. Rendel, P.M., Gavrieli, I., Wolff-Boenisch, D., Ganor, J., 2016. Gypsum solubility under pressure conditions relevant to CO 2 geological storage. Int. J. Greenh. Gas Control 55, 15–22. https://doi.org/10.1016/j.ijggc.2016.10.017. Rendel, P.M., Gavrieli, I., Wolff-Boenisch, D., Ganor, J., 2018a. Towards establishing a combined rate law of Nucleation and Crystal Growth – the case study of gypsum precipitation. J. Cryst. Growth 485, 28–40. https://doi.org/10.1016/j.jcrysgro.2017. 12.037. Rendel, P.M., Wolff-Boenisch, D., Gavrieli, I., Ganor, J., 2018b. A novel experimental system for the exploration of CO2-water-rock interactions under conditions relevant to CO2 geological storage. Chem. Eng. J. 334, 1206–1213. https://doi.org/10.1016/ J.CEJ.2017.11.067. Reznik, I.J., Ganor, J., Gal, A., Gavrieli, I., 2009. Gypsum saturation degrees and precipitation potentials from Dead Sea–seawater mixtures. Environ. Chem. Reznik, I.J., Gavrieli, I., Antler, G., Ganor, J., 2011. Kinetics of gypsum crystal growth from high ionic strength solutions: a case study of Dead Sea – seawater mixtures. Geochim. Cosmochim. Acta 75, 2187–2199. https://doi.org/10.1016/j.gca.2011.01. 034. Rosenberg, Y.O., Reznik, I.J., Zmora-Nahum, S., Ganor, J., 2012. The effect of pH on the formation of a gypsum scale in the presence of a phosphonate antiscalant. Desalination 284, 207–220. https://doi.org/10.1016/j.desal.2011.08.061.
Singurindy, O., Berkowitz, B., 2003. Evolution of hydraulic conductivity by precipitation and dissolution in carbonate rock. Water Resour. Res. 39, 1016. https://doi.org/10. 1029/2001WR001055. Smith, B.R., Sweett, F., 1971. The crystallization of calcium sulfate dihydrate. J. Colloid Interface Sci. 37, 612–618. https://doi.org/10.1016/0021-9797(71)90339-0. Sorai, M., Ohsumi, T., Ishikawa, M., 2005. Nanoscale surface observation of feldspar dissolved under supercritical CO2-water-mineral system. Energy 2334–2343. https:// doi.org/10.1016/j.energy.2003.10.024. Sorai, M., Sasaki, M., 2010. Dissolution kinetics of anorthite in a supercritical CO2-water system. Am. Mineral. 95, 853–862. https://doi.org/10.2138/am.2010.3202. Aquatic chemistry: chemical equilibria and rates. In: Stumm, W., Morgan, J.J. (Eds.), Natural Waters. Environmental science and technology. https://doi.org/10.1016/ S0016-7037(97)81133-81137. Van Pham, T.H., Aagaard, P., Hellevang, H., 2012. On the potential for CO2mineral storage in continental flood basalts – PHREEQC batch- and 1D diffusion–reaction simulations. Geochem. Trans. 13, 1–12. https://doi.org/10.1186/1467-4866-13-5. Witkamp, G.J., Van der Eerden, J.P., Van Rosmalen, G.M., 1990. Growth of gypsum. I. Kinetics. J. Cryst. Growth 102, 281–289. https://doi.org/10.1016/0022-0248(90) 90912-5. Xu, T., Apps, J., Pruess, K., Yamamoto, H., 2007. Numerical modeling of injection and mineral trapping of CO 2 with H 2 S and SO 2 in a sandstone formation. Chem. Geol. 1–70. https://doi.org/10.1016/j.chemgeo.2007.03.022. Zhang, J., Nancollas, G.H., 1992. Influence of calcium/sulfate molar ratio on the growth rate of calcium sulfate dihydrate at constant supersaturation. J. Cryst. Growth 118, 287–294. https://doi.org/10.1016/0022-0248(92)90073-R.
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Gypsum crystal growth kinetics under conditions relevant to CO2 geological storage
T
Pedro M. Rendela,b, , Ittai Gavrielib, Nir Ben-Eliahua, Domenik Wolff-Boenischc, Jiwchar Ganora ⁎
a
Department of Geological and Environmental Sciences, Ben-Gurion University of the Negev, P. O. Box 653, Beer-Sheva, 84105, Israel Geological Survey of Israel, 32 Yesha'ayahu Leibowitz St., Jerusalem, 9692100, Israel c School of Earth and Planetary Sciences, Curtin University, GPO Box U1987, Perth, 6845, WA, Australia b
ARTICLE INFO
ABSTRACT
Keywords: CO2 Geological storage Gypsum Kinetics Pressure Precipitation
Deep saline aquifers are among the preferred potential repositories for carbon dioxide geological storage (CGS). Modeling the interaction of the injected CO2 with the brine is essential for proper planning of CGS, including avoidance of local precipitation of minerals such as sulfates, which may clog the injection borehole and decrease the injectivity of the surrounding rock mass. In the present study gypsum crystal growth kinetics at the pressure range of 1–100 bar and with the addition of different molal concentrations of dissolved CO2 was investigated. A series of flowthrough experiments were performed in a novel reactor system, designed to withstand high pressures, temperatures and corrosion. Gypsum growth rate was found to decrease with ascending pressure and increase with rising dissolved CO2 concentrations. Yet, separating the overall effect of these variables to their impact on the thermodynamics of the solution (i.e. super saturation) and on the reaction kinetics, reveal a very complex effect on the rate coefficient (khet). While due to the kinetic effect, the rate coefficient mostly decreases with rising dissolved CO2 concentrations, it has a second order polynomial behavior while pressure ascends. This implies that under the studied pressures and dissolved CO2 concentrations the thermodynamic is the main dominant parameter which governs the overall growth rate. It is suggested that both the thermodynamic and the kinetic effects arise from the respective dependence of the supersaturation of the solution and the rate coefficient (khet) on the solubility.
1. Introduction Carbon Capture and Storage (CCS) was confirmed both by The IEA (International Energy Agancy, 2017) and IPCC (Edenhofer et al., 2014) to be a critical component amongst all major global greenhouse gas reduction scenarios (Idem et al., 2006). Deep saline formations, depleted or depleting gas and oil fields, and enhanced oil recovery using CO2 are among the preferred potential repositories for CO2 due to their large storage capacity and their global abundance. Modeling the interaction of the injected CO2 with the brine in the reservoir is essential for proper planning of CGS operations. In an aqueous phase, dissolved CO2 reacts with water to produce carbonic acid. Dissociation of carbonic acid may then trigger the hydrolysis of the host rock, and consequently precipitation of secondary minerals such as carbonates (e.g., Carroll and Knauss, 2005; Hangx and Spiers, 2009; Kaszuba et al., 2005, 2003; Sorai and Sasaki, 2010; Sorai et al., 2005) and sulfates (Knauss et al., 2005; Pearce, 2018; Xu et al., 2007). These secondary minerals may decrease the porosity and permeability
of both the host rock and/or the cap rock, which may then affect the injectivity and/or sealing of the aquifer (e.g., Bacon et al., 2009; Pearce, 2018; Van Pham et al., 2012). One of the concerns in CGS is massive precipitation of sulfate minerals (e.g., gypsum and anhydrite) in the volume adjacent to the well bore (Singurindy and Berkowitz, 2003). Depending on the reaction kinetics, such precipitation may plug the bottom of the borehole and its close surroundings, producing a backpressure on the injection process. In order to predict the potential formation of sulfate minerals under CGS conditions, a deeper understanding of their precipitation kinetics is needed. Experimental data dealing with the kinetics of gypsum precipitation in natural brines and synthetic solutions are abundant (e.g., Christoffersen et al., 1982; He et al., 1994a, 1994b; Reznik et al., 2009, 2011; Witkamp et al., 1990), however, none of them deals with the effect of pressures or presence of CO2. Recently, Rendel et al. (2016) experimentally showed the influence of pressure and dissolved CO2 concentration on gypsum solubility at conditions relevant to CGS. While the solubility exponentially increases
⁎ Corresponding author. Currently address: Danish Hydrocarbon Research and Technology Centre, Technical University of Denmark, DTU, 2800 Kgs., Lyngby, Denmark. E-mail address: [email protected] (P.M. Rendel).
https://doi.org/10.1016/j.ijggc.2019.102829 Received 17 April 2019; Received in revised form 5 September 2019; Accepted 5 September 2019 1750-5836/ © 2019 Elsevier Ltd. All rights reserved.
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as a function of pressure, it exponentially decreases as the CO2 molal concentration increases. The obtained results showed a good agreement to the latest Phreeqc v.3 (Appelo et al., 2014) thermodynamic geochemical model. In the present work, gypsum crystal growth kinetics was studied in pressurized solutions at 1, 50, 70 and 100 bar and with various molal concentrations of dissolved CO2 (0.20 ± 3.1%, 0.43 ± 3.4%, and 0.62 ± 2.7% (mol kg−1 solution)) at 70 bar. The growth rates at the different conditions were calculated in order to determine the effect of both pressure and CO2 on the precipitation kinetics.
Technologies), respectively. The separate inlet channels for the two under-saturated brines were designed to prevent precipitation of solid phases within the upstream tubing. Upon mixing in the reactor, these solutions form the super-saturated experimental solution. The overall confining hydraulic pressure in the system is controlled by a back pressure regulator (BPR) whose dome pressure is regulated with an inert gas (N2). The mixture is kept homogenized within the reactor vessel by an internal magnetic stirrer and a gas impeller. Process temperature is maintained stable by simultaneously heating and cooling the reactor through an external heating block and an internal cooling loop, respectively. At the outlet, the fluid is filtered through a 2 μm titanium frit. Temperature and pressure are monitored continuously throughout the experiment. The outlet solution is depressurized as it exits the BPR and collected for further analysis. The use of this flow-through system enables the injection of a CO2charged solution into the system without the need to separately inject liquid or gaseous CO2. This approach allows experimenting with different dissolved CO2 concentrations and sampling of the outflow solution during all experimental stages without disturbing the pressure conditions in the reactor.
2. Theoretical background Crystal growth is a process during which an existing crystal or nucleus continues to grow from a super-saturated solution. This process involves both a solid and a liquid phase and thus depends on the properties of both phases and the interface between them. Since crystal growth is a surface reaction, the heterogeneous growth rate is a function of the reactive surface area of the mineral. The supersaturation of the solution with respect to the growing crystal is another key parameter in determining the growth rate. Eq. (1) is a semi-empirical rate law describing the dependence of crystal growth rate on the deviation from equilibrium (Nielsen, 1981):
Ratehet = khet SA
(
1
1
)
3.2. CO2 introduction and analyses
n
The present study was conducted below CO2 supercritical conditions (at 25 °C). To avoid the development of two separate phases (gas and liquid) in the highly enriched CO2 environment within the vessel, the CO2 partial pressure was kept below the overall confining pressure of the system, attaining complete dissolution of the gas into the injected brine before reaching the reaction vessel. This was achieved by pumping small volumes of CO2 at constant flows of 50, 100 and 150 μL min−1 into the inlet brines through the static mixers to form two homogenous mixtures. While flowing through the long coil (jacketed tubes) the CO2 gradually dissolves, and carbonation occurs. The CO2 for the injection was kept at a temperature of approx. 8 °C in a liquid phase. The concentrations of CO2 in the experimental solutions were predetermined by running the experimental system with double deionized water under the planned experimental conditions. Multiple samples were collected over 2 weeks using a 1 mL precise sampling loop installed at the system (Fig. 1). Samples were unpressurized into 60 mL disposable plastic syringes containing approx. 30 mL of KOH solution (at ∼pH 11), and diluted (X100) using double deionized water. The diluted samples were then directly titrated for alkalinity using a 916 TiTouch Metrohm titrator with 0.01 N HCl using Gran functions (Stumm and Morgan, 1993). Assuming total alkalinity to be only carbonate alkalinity, and the injected CO2 to be the only source of carbon in the sample, dissolved CO2 concentrations could be calculated. Under the experimental conditions, CO2 flow rates of 50, 100 and 150 μL min−1 were found to yield solutions with dissolved CO2 concentrations of 0.20 ± 3.1%, 0.43 ± 3.4%, and 0.62 ± 2.7% (mol kg-1 solution), respectively.
(1)
Where Ω is the supersaturation of the solution, Ratehet is the observed heterogeneous crystal growth rate (mol s−1), SA is the mineral surface area (m2), khet is a heterogeneous rate coefficient (mol s−1 m-2), ν is the number of ions in the crystal formula unit other than the solvent (two in the case of gypsum) and n is the apparent reaction order with respect to the deviation from equilibrium (Ω1/ν-1). Several experimental studies have shown that the bulk growth rate of gypsum (the sum of growth on all crystallographic surfaces), may be described using a second order reaction (n = 2) (Amjad, 1985; Christoffersen et al., 1982; Liu and Nancollas, 1973; Nancollas and Liu, 1970; Reznik et al., 2011, 2009; Witkamp et al., 1990). The surface area following dissolution or precipitation may be empirically related to the initial surface area (SA(i)) (Christoffersen and Christoffersen, 1976; Shiliang He et al., 1994a, 1994b; Witkamp et al., 1990; Zhang and Nancollas, 1992) by:
SA = SA (i)
mt mi
p
(2)
where mi and mt are the masses of the initial and the growing crystals at time t (g), respectively, and p is a coefficient that depends on the crystal growth habit. p is equal to2 3 if the surface proportions of the growing crystal remain invariant during the growth process (Smith and Sweett, 1971). A p value of 0.5 indicates that growth occurs predominantly in two directions while a p value of 0 indicates one-dimensional growth with no increase in the surface area available for growth (e.g., Witkamp et al., 1990).
3.3. Experimental approach
3. Methods
Gypsum crystal growth rates were determined in two sets of flowthrough experiments performed at 25 °C in the presence of treated gypsum seeds (59 μm–149 μm):
3.1. Experimental system A novel experimental system (Rendel et al., 2018b), which allows interaction between CO2, brine and minerals under a range of temperatures (0–150 °C) and pressures (1–120 bar) was used. The system consists of a 300 mL flow-through continuously stirred reactor with two inlets and one outlet (Fig. 1). During experiments, two under-saturated brines containing pre-determined CO2 concentrations are injected through static mixers (Koflo Corp.) and temperature-controlled jacketed tubes under constant flow. Injection is via two piston pumps and a bench top syringe pump (VINCI
1 A first set of experiments to determine gypsum crystal growth rates only as a function of pressure without any CO2. The experiments were held under different confining pressures (1, 50, 70 and 100 bar), allowing the system to achieve a stable steady-state at each pressure. 2 A second set of experiments to determine gypsum crystal growth rates at a confining pressure of 70 bar in the presence of different molal concentrations of CO2 (0.20 ± 3.1%, 0.43 ± 3.4%, 2
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Fig. 1. Schematic diagram of the flow-through experimental system.
0.62 ± 2.7% (mol kg−1 solution)). Here too, the system was allowed to achieve a stable steady- state at each dissolved CO2 concentration.
composition of the two solutions and the flow ratio. The solutions were prepared by weighing salts that make up the solutions with a precise balance and their dissolution in a known weight of de-ionized water. The activities of the individual ions and the supersaturation of the solution at the experimental conditions were calculated using the Pitzer specific-ion-interaction aqueous model (pitzer.dat database, with keyword PITZER) within the PHREEQC 3 code which is able to cope with high-salinity waters that are beyond the range of the Debye-Hückel theory (Appelo et al., 2014). CO2 was introduced into the model using the “REACTION” function, adding the number of moles of CO2(g) in a single step.
Periodically, approximately 1 mL solution was drawn from the sampling port using a syringe, filtered with a 0.22 μm filter disk and diluted by a factor of ∼1:100 (by weight), for SO42− analysis. SO42was analyzed using a Dionex DX500 high pressure liquid chromatography device following the method described by Reznik et al. (2009). Based on repeated analyses of SO42- standards, we estimate the precision to be ± 3% (one standard deviation). The gypsum seeds (pure CaSO4·2H2O) were prepared by crushing Satin-Spar crystals (precipitated from residual brines of a desalination plant; (Rosenberg et al., 2012) and sieving the powder to obtain a size fraction of 59 μm–149 μm using a matching set of sieves. The seeds were then pre-treated in a supersonic bath filled with a 99% methanol solution; the solution was sequentially replaced every 5 min with a fresh one, allowing the disposal of unwanted small suspended crystals (< 59 μm) which may have clung on the larger fragments. Finally the seeds where let to dry inside a fume hood at room temperature. The specific surface area of the gypsum seeds was measured using the BET method, with a NOVA 3000 (Micrometric) at IMI TAMI laboratories (Haifa, Israel), based on N2 adsorption, yielding a specific surface area of 3.4 m2 g−1. The accuracy and reproducibility of the surface area is ± 10%.
3.5. Determination of the kinetics of crystal growth In a well-mixed flow-through system, in which precipitation reactions occur, the change with time in the concentration of the reaction products (mol kg−1 solution s−1), is described by the following mass balance equation:
dCj, out dt
Precipitation of gypsum may be expressed by the reaction:
CaSO4 2H2 O
(3)
The deviation of a solution from equilibrium with respect to gypsum may be calculated in terms of the supersaturation of the solution (Ωgyp): gyp
=
Rate =
aCa2 + aSO42 a H2 2 O
IAP = K sp (aCa2+ aSO42 a H2 2 O)eq
Rate
j
SA V
q (Cj, out V
Cj, in)
(5)
where Cj,in and Cj,out are the concentrations of component j in the inflow and outflow solutions (mol kg−1 solution), respectively; νj - the stoichiometry coefficient of component j in the precipitation reaction; Rate - the growth rate (mol m−2 s−1); t stands for elapsed time (s); SA - the overall surface area of the growing mineral crystals/grains (m2); V - the volume of the reactor (m3), ρ - fluid density, and q - fluid flux through the system (kg s−1). Note that in this formulation, the growth rate is defined to be positive. Under steady-state conditions, when the composition of the outflow solution reaches a steady-state value, (i.e., dCj,out/dt = 0)) the growth rate may be described by:
3.4. Calculations
Ca2 + + SO42 + 2H2 O
=
q (Cj, out vj SA
Cj, in)
(6)
3.6. Gypsum solubility-definition
(4)
Solubility of a mineral is defined here as molal concentration of solutes in a solution saturated with respect to that mineral. In stoichiometric solutions, solubility is equal to the molal concentration of any of the lattice ions, divided by its coefficient in the mineral formula, while for non-stoichiometric solutions the solubility is equal to the lowest amongst these quotients. Thus, gypsum solubility in a stoichiometric solution is the molal concentration in saturation of either SO42− or Ca2+ while for a non-stoichiometric solution gypsum solubility is the
where IAP is the ion activity product, ai is the activity of species i, Ksp is the ion activity product at equilibrium (eq). Accordingly, Ω > 1 implies a supersaturated solution, whereas Ω < 1 is an undersaturated solution. In the present study, the concentration of SO42− was measured for each solution whereas Ca2+ concentration was calculated by subtracting the precipitated concentration from its initial concentration, assuming stoichiometric precipitation with the change in the measured SO42−. The concentrations of all other ions were calculated based on the initial 3
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Table 1 Average chemical composition of the initial experimental solutions (mol kg−1 solution). Description
Na+
Ca2+
Cl−
SO42−
Ca2+/SO42−
I
Ω1bar
Ω50bar
Ω70bar
Ω100bar
Exp. 1 bar
0.0245
0.5437
1.0875
0.0122
44.37
1.778
1.78
1.66
1.62
1.55
Ω xxbar = Ωgyp at 25 °C and 1, 50, 70 and 100 bar without CO2, I = Ionic Strength. The uncertainty on the Na+, Ca2+, Cl− and SO42− concentrations is better than ± 3%.
different pressures at 25 °C was calculated with the PHREEQC v.3 geochemical model (Appelo et al., 2014), using the solution chemical composition as the input solution (Table 1). The high reliability of the PHREEQC code for these conditions was demonstrated experimentally by Rendel et al. (2016). 4. Results Figs. 3 and 4 present the change in SO 4 2− concentration with time for the first and second set of experiments, which lasted 20 and 28 h, respectively, enough time for all runs to attain a steadystate concentration. The steady-state concentrations tend to increase as pressure rises (Fig. 5; no CO 2 ); and to decrease as dissolved CO 2 concentration increases (Fig. 6; constant pressure). Note, that in the second set of experiments pressure was kept constant at 70 bar, and CO 2 was only injected after 15 h, allowing the system to approach an earlier steady-state concentration solely affected by the pressure. Examination of the precipitated gypsum at the end of the experiments showed that crystals tend to form stiff layers on the internal surfaces of the reactor cell as was previously described in Rendel et al. (2018a), (Fig. 2).
Fig. 2. Stiff layers of gypsum attached to the walls and to the internal parts of the reactor formed during the experiments.
Ca2+ molal concentration in saturation when Ca2+/SO42− < 1 and the SO42− molal concentration in saturation when Ca2+/SO42− > 1. 3.7. Experimental conditions
5. Discussion
Gypsum crystal growth rates were determined at 25 °C for a range of pressures and dissolved CO2 concentrations in seven flow-through experiments in the presence of ∼0.5 g of gypsum seeds. A single solution with an initial degree of supersaturation with respect to gypsum (Ωgyp) of 1.78 at 25 °C and 1 bar was used in all the experiments. CaCl2 and NaSO4 solutions were prepared separately by dissolving the corresponding salts with double deionized water. The final experimental solutions were formed in the reactor vessel upon the mixing of equal volumes of CaCl2 and NaSO4 solutions. Each solution was pumped into the reaction cell at a flow rate of 2.5 mL per minute. Ωgyp under the
5.1. Gypsum crystal growth as function of pressure and dissolved CO2 concentration Crystal growth rates (mol m−2 s−1) were calculated using Eq. (6), where the surface area of the growing mineral crystals (SA) was initially determined using Eq. (2), with p = 2/3. While most of the parameters in Eq. (2) are known at the onset of the experiment, the mass of the growing gypsum crystals at time t (mt) needs to be sequentially integrated for each time step (between each pair of sequential data points):
Fig. 3. SO42− concentration vs. time in pressurized experiments at 1, 50, 70 and 100 bar (no CO2). Dashed and solid black lines represent the inflow concentration and the average steady-state value at each pressure, respectively; doted gray lines represent one sigma uncertainty envelopes for each steady-state value. 4
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Fig. 4. SO42− concentration vs. time in experiments at 70 bar with different dissolved CO2 concentrations. Injection of CO2 started after 15 h of experiments. Dashed and solid black lines represent the inflow concentration and the average steady-state values at the end of the experiments, respectively. Horizontal dotted gray lines represent one sigma uncertainty envelopes around each steady-state value.
Fig. 5. SO42− steady-state concentrations vs. pressure in pressurized experiments at 1, 50, 70 and 100 bar. SO42− steady-state concentrations increase with increasing pressure following a second order polynomial regression.
Fig. 7. Non-normalized gypsum crystal growth rate (mol s−1), (blue dots), and accumulated gypsum mass (g), (red dots) vs. time (h). Non-normalized crystal growth rates appears to reach a steady-state, while gypsum mass continues to growth, indicating a one-dimensional growth of gypsum layers on the inside surfaces of the reactor cell.
surface area of the mineral. Thus, keeping the crystals fully suspended in the solution maximizes the exposure of crystal surfaces to the solution. With this in mind, our experiments solutions were vigorously stirred. However, despite the stirring, the crystals formed layers of gypsum on the internal surfaces of the reactor cell (Fig. 2) and the available surface area for growth was therefore limited. In fact, after an initial stage of increase in surface area, we estimate that all the internal surfaces of the reactor were covered by gypsum. From this time on, the available surface area became constant, and the precipitation and growth continued as a one-dimensional growth. Under such condition, and as long as these do not change significantly, the non-normalized crystal growth rate (mol s−1) is expected to remain constant. Fig. 7 presents the non-normalized gypsum growth rate (mol s−1) and the accumulated gypsum mass mt (g) as a function of time (h), during a representative experiment (100 bar, no CO2). Initially, as the gypsum crystals grow and the available surface area increases, the non-normalized crystal growth rate also increases. However, after accumulation of approximately 2.7 g of gypsum in the reactor cell (including the initial ∼0.5 g of seeding), the non-normalized crystal growth rate became constant, indicating that the additional precipitation of gypsum continued as a one-dimensional growth with no increase in the available surface area (p in Eq. (2) is 0). In order to determine the normalized growth rate at steadystate, the surface area of the gypsum that fully covered the internal surfaces of the reactor must be known. This surface area (henceforth, final total reactive surface area) may be independently calculated for each experiment, by assuming that: (1) growth rate of gypsum is constant during
Fig. 6. SO42− steady-state concentrations vs. CO2 molal concentrations at 70 bar. SO42− steady-state concentrations decrease with increasing CO2 molal concentration following a second order polynomial regression. mt
mt = mini
t 1
mt
m=
Mwgyp q mini
(Cin t
Cout(t ) ) dt
(7)
where Cin and Cout are the SO42− concentrations in the inflow and outflow solutions (mol kg−1 solution), respectively; Mwgyp is the molar weight of gypsum (172.17 g mol−1), and q is the flow rate (kg solution s−1). As previously outlined, crystal growth is a surface reaction, with the heterogeneous growth rate being a function of the available reactive 5
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1994b); and 8.36∙10−7 mol m−2 s−1, found by Zhang and Nancollas (1992)). This further supports the outlined methodology. The uncertainty in the calculated growth rates was estimated using the Gaussian error propagation method (Barrante, 1974), based on the measured SO42− concentrations vs. time within the time frame identified as being at steady-state concentration for each experiment (solid lines in Figs. 3 and 4). The propagated uncertainties in the rates range between 10.02% and 10.07% and are dominated by the uncertainty in the measurement of the surface area ( ± 10%). However, it should be noted that all our experiments were carried out using a single pretreated batch of gypsum seeds (see Section 3.3) that produced a homogenous powder. Since all experiments were conducted using a sub-sample from this powder, it can be assumed that the specific surface area of the initial gypsum seeds are identical in all and hence that the contribution of the surface area to the uncertainty in the growth rates is negligible when compared between the different experiments. This assertion is supported by the independent growth rates measured within the period prior to CO2 injection during our second set of experiments, in which the unpropogated gypsum growth rates differ by less than 1%. This small difference (< 1%) supports the suggestion that there is no significant difference in the surface area of the initial seeding material as well as in the surface area of the new gypsum formed during the experiments. In Table 2, we report the uncertainties that include the propagated uncertainty in surface area as well as uncertainties that do not include it. The former are used for comparison between our results and results from other studies that used different batches of gypsum, while the latter is used for comparison between experiments conducted in the present study using the same gypsum seeds batch. In order to evaluate the reliability of the obtained normalized growth rates, the normalized rate in the experiment performed at 1 bar, 25 °C and without CO2 was compared to rates reported by Zhang and Nancollas (1992) and Reznik et al. (2011), at similar conditions. Figs. 9 and 10 present the normalized growth rate (mol m−2 s-1) as a function of the initial Ca+/SO42- in solution and as a function of gypsum solubility, respectively, at 25 °C. The result from the present study (red dot), is in a good agreement with the previously reported rates. The growth rates vs. pressure and vs. dissolved CO2 concentration are plotted in Figs. 11 and 12, respectively, suggesting that the crystal growth rate decreases with the increasing pressure following a second order polynomial regression and increases linearly as dissolved CO2 concentration increases. It should be emphasized that due to the lack of a proper mechanistic explanation, the regressions presented in Figs. 11 and 12 are only based on the best data fitting.
Fig. 8. Calculated gypsum surface area vs. accumulated gypsum mass. The newly estimated surface area (blue dots) based on the initial normalized gypsum growth rate (see text) shows a shift towards a one-dimensional growth after the accumulation of approx. 1 g of gypsum in the reactor.
the entire experiment (the environmental conditions remain unchanged); and (2) initially, the surface area is linearly proportional to the mass, and the specific surface area (m2/g) is equal to the BET surface area of the gypsum seeding. The normalized growth rates during the first couple of hours of each experiment were used to obtain the change in total reactive surface area with time. This was achieved by dividing the growth rate (mol s−1) at time t with the initial normalized growth rate (mol m−2 s−1). Fig. 8 compares the total reactive surface area as estimated with this procedure and that calculated using Eq. (2), with p = 2/3, in a representative experiment (100 bar, no CO2). Initially, the surface area calculated by Eq. (2) is similar to that estimated by the normalized growth rate. Thereafter, while the surface area calculated using Eq. (2) increases continuously, it approaches a stable value when estimated by the normalized growth rate. In reality, at this stage, the newly precipitated gypsum grows on the gypsum coatings of the reaction vessel, and therefore the reactive surface area remains constant with time, i.e., crystal growth is one dimensional. The average surface area of all the experiments during the one- dimensional growth rate stage was 2.4 ± 0.2 m2. This average value represents the surface area of gypsum needed to cover the entire internal surfaces of the reactor and was used to derive a normalized steady-state growth rate (mol m−2 s−1) for each of the experiments. The normalized growth rates obtained during the second phase of the experiments are summarized in (Table 2). It should be noted that the rates obtained are all of the same order of magnitude as those found in previous works (1∙10−9–4∙10−8 mol m−2 s−1, found by Reznik et al. (2009); 1.7∙10−7–1.7∙10−8 mol m−2 s−1, found by He et al. (1994a,
5.2. Kinetic vs. Tthermodynamic effects on gypsum growth rate Gypsum crystal growth rate decreases as a function of pressure and increases with dissolved CO2 concentration. Eq. (1) suggests that these
Table 2 Experimental results. Experiment
1 bar 50 bar 70 bar 100 bar 70 bar, 0.2 M CO2 70 bar, 0.43 M CO2 70 bar, 0.62 M CO2
SO42−s.s
Rate
Uncertainties on Rates
(mmol kgs
−1
(mol m
8.3476 0.0086 8.8348 9.2191 8.0000 7.1964 6.6754
0.61% 0.43% 0.25% 0.39% 0.28% 0.74% 0.74%
1.560E-07 1.430E-07 1.310E-07 1.168E-07 1.529E-07 1.821E-07 2.011E-07
± ± ± ± ± ± ±
)
−2
−1
s
)
*
Ωs.s
**
± 1.18% ± 0.94% ± 0.66% ± 1.11% ± 0.53% ± 1.07% ± 0.90%
± 10.07% ± 10.04% ± 10.02% ± 10.06% ± 10.01% ± 10.06% ± 10.04%
1.20 1.15 1.15 1.17 1.16 1.18 1.21
log(khet)***
Solubility
(mol m
−2
−1
s
−4.77 −4.55 −4.60 −4.78 −4.59 −4.61 −4.70
± ± ± ± ± ± ±
0.37% 0.35% 0.33% 0.35% 0.33% 0.45% 0.33%
)
(mmol kgs−1) 6.9158 7.3814 7.5778 7.8854 6.7814 5.9489 5.3753
s.s at steady-state; Ωgyp was calculated with the PHREEQC v.3 geochemical model (Appelo et al., 2014) for the solution at steady-state at 25 °C and the appropriate experimental pressure of each experiment. * Uncertainties do not include the uncertainty in the surface area. ** Uncertainties include the uncertainty in the surface area. *** khet calculated using the rates that do not include the uncertainty in the surface area. 6
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Fig. 11. Gypsum crystal growth rate vs. pressure. Crystal growth rates appear to decrease with increasing pressure following a second order polynomial regression. Fig. 9. Growth rate of gypsum (mol m−2 s−1) as a function of Ca+/SO42− ratio. All data are corrected to Ωgyp = 1.69. Results from Zhang and Nancollas (1992) in diamonds, Reznik et al. (2009) in squares and this research (experiment at 1 bar and without CO2) in red circles. The black line represents the linear regression as shown by Reznik et al. (2009).
Fig. 12. Gypsum crystal growth rates vs. CO2 molal concentration in the experiments at 70 bar. Crystal growth rates appear to increase linearly with the increasing dissolved CO2 concentrations.
Fig. 10. Log k as a function of SO42− in equilibrium (for experiments with Ca+/SO42− > 1, SO42− represents the gypsum solubility); results from: Reznik et al. (2009 and 2011) in triangles, Zhang and Nancollas (1992) with NaCl or KCl additives in diamonds, He et al. (1994b) in squares and this research (experiment in 1 bar without CO2 at 25 °C) in red circles. The black curve represents the model developed by Reznik et al. (2011), for a Na+/Ca+ activity ratio < 7.
variables affect crystal growth rate by (1) changing the supersaturation of the solution (Ω), i.e. a “thermodynamic effect”, and/or (2) by changing the kinetic rate coefficient (khet), i.e., a “kinetic effect”. Figs. 13 and 14 present the calculated Ωgyp of the experimental solution as a function of SO42− concentrations, under various pressures and dissolved CO2 concentrations, respectively. Ωgyp was calculated with the PhreeqC v.3 geochemical software (Appelo et al., 2014), using the "Pitzer" specific-ion-interaction aqueous model, (Table 1) at 25 °C. Note that the interceptions of the lines with the x-axis (in both figures) represent the gypsum solubilities (i.e. SO42− concentration at equilibrium with gypsum) under the specific pressure or CO2 conditions. Initial Ωgyp of the experimental solutions and the steady-state Ωgyp (Ωs.s) are shown as symbols on the lines.
Fig. 13. Gypsum saturation degree in the experimental solution with changing SO42− concentrations (Ωgyp) vs. SO42− concentrations in the solution at various pressures. Ωgyp is calculated with PhreeqC v.3 geochemical model (Appelo et al., 2014) using the Pitzer specific-ion-interaction aqueous model at 25 °C. The black curve is the second order polynomial regression (R2 = 0.93) connecting the degree of gypsum saturation at steady-state in each experimental solution (circles). 7
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Fig. 14. Gypsum saturation degree in the experimental solution with changing SO42− concentrations (Ωgyp) vs. SO42− concentrations in the solution at various dissolved CO2 concentrations. Ωgyp is calculated with PhreeqC v.3 geochemical model (Appelo et al., 2014) using the Pitzer specific-ion-interaction aqueous model at 25 °C and 70 bar. The black curve is the second order polynomial regression (R2 = 0.99) connecting the degree of gypsum saturation at steadystate in each experimental solution (circles).
Fig. 16. Log rate coefficient (log(khet)) vs. CO2 molal concentration in the experiments at 70 bar; log(khet) follows a second order polynomial regression as pressure increases.
By calculating the rate coefficient (khet) with the appropriate Ωs.s for each experiment, the dependency of khet on the pressure and dissolved CO2 concentration was obtained (Figs. 15 and 16, respectively). While khet mostly decreases with CO2 concentration, it initially increases with pressure and then decreases. 6. Conclusions Gypsum crystal growth rates were determined in two sets of flowthrough experiments. Experimental results show that increasing pressure and CO2 concentrations have opposite effects on the growth rates of gypsum. The overall crystal growth was found to be controlled by two different effects; (1) a thermodynamic effect, which changes the degree of saturation with respect to gypsum (Ωgyp) through its effect on the solubility and (2) a kinetic effect, represented by the rate coefficient (khet). Accounting for all other effects while solely examining the kinetic effect reveals that under the studied pressure (70 bar) and dissolved CO2 concentrations gypsum crystal growth rate tends to decrease both when pressure (> 50 bar) and dissolved CO2 concentrations increase. An exception is observed at relatively low pressures where khet tends to increase. Fig. 17 summarizes the observed trends, implying that under the studied pressures and dissolved CO2 concentrations, the thermodynamic effect, is the dominant factor that governs the change in growth rates due to changes in pressure and dissolved CO2 concentrations. Our experimental results emphasize the important role that pressure and the presence of CO2 have on gypsum kinetics under conditions relevant to geological carbon storage. These effects need to be incorporated into all models of CO2-water-rock interactions under conditions relevant to CGS. Whereas the thermodynamic behavior during the injection of large quantities of supercritical CO2 into brines is well known and can be modeled, the kinetic nature of the reactions needs to be closely monitored during injection to avoid the potential precipitation of gypsum from the brine. Such precipitation may negatively affect the injectivity of the injection well and should be avoided.
Fig. 15. Log rate coefficient (log(khet)) vs. pressure; log(khet) follows a second order polynomial regression as pressure increases.
In order to determine if there is also a “kinetic effect” on the growth rate, the “thermodynamic effect” must be separated from the overall growth rate. Rearranging Eq. (1) and inserting the Ωgyp at steady state (Ωs.s), the number of ions in the crystal formula unit ν (two in the case of gypsum) and the apparent reaction order n (which was found to be two, according to the BCF crystal growth theory (Lasaga, 1998) and further experimental studies (Amjad, 1985; Christoffersen et al., 1982; Liu and Nancollas, 1973; Nancollas and Liu, 1970; Witkamp et al., 1990)), the rate coefficient khet, can be determined:
khet =
SA
(
Ratehet s.s
1
1
)
n
= 2.4
(
Ratehet 1 s.s 2
1
)
2
(8)
8
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Fig. 17. Schematic summary of the factors controlling the overall gypsum growth rates. The thermodynamic effect is represented by the change in the initial degree of saturation with respect to gypsum(Ωini). The kinetic effect is represented by the kinetic constant (khet, [mol m−2 s−1]). Solubility [mmol kgs−1], overall rate [mol m−2 s−1], pressure [bar] and CO2 concentration [mol kg−1 solution].
Declaration of Competing Interest
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