Experimental Investigation of Calcium Carbonate Precipitation and

Article pubs.acs.org/crystal

Experimental Investigation of Calcium Carbonate Precipitation and Crystal Growth in One- and Two-Dimensional Porous Media Sofia Jaho,†,‡ Georgia D. Athanasakou,†,‡ Varvara Sygouni,†,‡ Maria G. Lioliou,†,‡,§ Petros G. Koutsoukos,†,‡ and Christakis A. Paraskeva*,†,‡ †

Department of Chemical Engineering, University of Patras, Patras GR-26504, Greece Institute of Chemical Engineering Sciences, Foundation of Research and Technology, Hellas, Platani Achaias, Patras GR-26504, Greece

‡

ABSTRACT: Visualization experiments using one-dimensional (1-D) porous media made of Plexiglas and twodimensional glass porous networks were conducted to obtain qualitative and quantitative information concerning the precipitation and crystal growth of CaCO3 under varying flow and concentration conditions. Supersaturated solutions were prepared by mixing sodium bicarbonate and calcium chloride solutions before the pore networks. Nucleation and crystal growth were assumed to occur within the porous media. Changes in the initial and final solution composition were monitored. At low initial supersaturation values (SRinitial), a few crystals were observed within the flow channels and crystal growth took place exclusively on the newly formed crystals. As the SRinitial increased, more crystals were formed along the flow channels and new crystallites were continuously formed during the course of the experiments. Nucleation and crystal growth were not uniform. The crystal growth rates depended on the initial value of SR and flow path inside the medium. Porosity for the 2-D networks decreased when the SRinitial was high or when calcite-cemented sand was used as substrate.

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INTRODUCTION Many oil and gas reservoirs experience scale deposition, which causes loss of the permeability of the local rock formation and subsequently operational problems, especially in oil wells that are in their ripening period.1 Most scale found in oil fields forms either by direct precipitation when formation water breakthrough occurs2,3 or as a result of produced water becoming oversaturated with scale components when formation and injection water from special injection wells meet.4−9 Scale can develop in the formation pores near the wellbore, reducing formation porosity and permeability. Scale deposits can block flow by clogging perforations or by forming a thick layer of scale on the wall of the production tubing or in production equipment. In the majority of cases, scale deposits consist of calcium carbonate or calcium and/or barium or strontium sulfate salts.10−14 It should also be noted that often in oil fields radioactive barium is co-precipitated with barium sulfate scale.15 It is therefore important to gain a proper understanding of the kinetics of scale formation and its detrimental effects on porosity and permeability in the near wellbore region. The investigation of phenomena of this type in reservoirs is complex since reservoirs are usually mixed or fractionalwet,16,17 the pore surface topology is complex,18,19 fractures may exist,20 and, in most cases inside the pores, more than two phases (oil, gas, and brine) coexist.21−23 High temperature and pressure values during the operation conditions of a reservoir may result in gas release, and depending on gas saturation, bubbles may migrate or not.24 Moreover, reservoir mineralogy © XXXX American Chemical Society

also plays an important role on physicochemical processes. For example, the presence of Mg2+ inhibits the growth of calcite crystals.25 However, in most cases in order to obtain the fundamental principles of a process, a number of parameters such as pressure, pore topology, or multiphase flow are kept constant or they are simplified. From all possible scale types that may possibly form, calcium carbonate has been selected in this study, because of the high frequency with which it is encountered in oil fields.4 Calcium carbonate scale formation has been extensively discussed in the oil field scale literature, because of its contribution to dramatic losses in oil production. However, the overall mechanism of scale formation in oil fields is not yet fully understood. The rate of calcium carbonate nucleation and crystal growth depends on the supersaturation ratio, the temperature, the pressure, the flow conditions, and the nature of the reservoir rock.26−30 Once precipitation occurs in the near wellbore area, porosity and permeability of the formation decrease and consequently oil production is reduced. Permeability plays an important role in subsurface fluid flow, being one of the most important parameters, the knowledge of which is needed for the prediction of fluid flow patterns and the production of petroleum in oil fields.31−33 Several researchers have tested incompatible waters from oil fields in the Middle East,7,11,13 which produced calcium and barium sulfate precipitates. Received: September 11, 2015 Revised: October 27, 2015

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DOI: 10.1021/acs.cgd.5b01321 Cryst. Growth Des. XXXX, XXX, XXX−XXX

Crystal Growth & Design

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Figure 1. Experimental setup for the in situ monitoring of the crystal growth of CaCO3 (a) in 1-D Plexiglas porous media and (b) in 2-D glass porous networks. Magnification of the 2-D pore layout is shown.

saturation values, flow rates, temperature, pH and ionic strength of the solutions. Sand grains from different sources (embedded in the flow channel) were also used as an alternative substrate for the overgrowth of calcium carbonate. Calcium carbonate growth was related to crystal size evolution values obtained from the pore micromodel experiments. Precipitated crystals were distributed along the length of the types of porous media investigated, showing that scaling is not uniform and deposition occurs preferably close to the inlet point where supersaturation values are higher. Calcium concentrations and pH variation with time were recorded allowing for estimates of the growth rates. Calcium concentration changes as a function of time were also measured at various temperatures. Crystal growth rates, rate constants, and the activation energy for conditions of spontaneous precipitation of calcium carbonate were calculated from the calcium−time profiles obtained from the various experiments. Surface porosity measurements were also done in the glass pore networks, which showed loss of porosity depending on the nature of the substrate and on the initial supersaturation. Furthermore, the morphology of the precipitated crystals suggested a strong dependence on the supersaturation and temperature of the supersaturated solutions.

Permeability change is not always a linear function of the amount of precipitates formed. It also depends on the morphology of the deposits, of the substrate and of the preferred sites for scale formation.34−36 It is therefore of paramount importance to understand where and how precipitation of scale takes place within the porous medium and in which way this formation changes the porosity and permeability of the porous formation. Observations of scale evolution in glass micromodels have been extensively utilized for the investigation of multiphase flow phenomena in porous media,2,28,37,38 of their effects on colloids,39 and for the investigation of the mechanisms responsible for biomass plugging40,41 or scale formation in porous media.2,28,42,43 The latter works provided useful information for the kinetics of calcium carbonate and calcium sulfate precipitation using observations from glass micromodels. The model pore networks used in the present work included a 1-D flow medium made of Plexiglas and a transparent 2-D glass flow pore network. Both allowed observation and recording of the process of crystal growth at steady state conditions. An evaluation of the calcite scaling process in a particular case should be based on a multiphase equilibrium calculation where all equilibria for the produced water, oil, and gas system are involved. In the present work thermodynamic calculations were done with MultiScale which is a thermodynamic simulation tool to calculate the potential for salt precipitation (e.g., sulfates and carbonates) in systems containing water, oil, gas, and solids.44,45 From the input (temperature, pressure, and concentration of each compound) the composition of each phase, initial pH, and saturation ratios (SRs) for a range of salts and the maximum amount that may precipitate from these salts at equilibrium (i.e., SR = 1 at equilibrium) is calculated with MultiScale. The MultiScale software package used is owned by Statoil and has been licensed to Expro Fluids (Petrotech AS, Haugesund, Norway) for further development. The validity of the software was tested by running duplicate calculations with PHREEQC.46 In the present work, a more systematic study was attempted in order to reach conclusions concerning the precipitation and crystal growth of calcium carbonate in porous media under flow conditions. Crystal growth rates of CaCO3 were measured for micromodel substrates made of different materials (glass or Plexiglas) and of different geometry, varying initial super-

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EXPERIMENTAL SECTION

A. One-Dimensional Plexiglas Porous Medium. The flow channels made of Plexiglas were constructed with a length of 2, 6, 8, or 10 cm, width of 1 mm, and depth of 0.3 mm, as shown in Figure 1a. Calcium carbonate crystal growth was continuously monitored through an optical microscope (Zeiss) equipped with a digital programmed video camera (Axis 223 M network camera) connected to a computer. Snapshots were recorded within specific time intervals and were processed with imaging software (Adobe Photoshop). Calcium carbonate supersaturated solutions were prepared by in situ mixing of two soluble salt solutions, calcium chloride dehydrate (CaCl2·2H2O, Merck) and sodium bicarbonate (NaHCO3, Merck). Sodium chloride (NaCl, Merck) was added to maintain the solution ionic strength (IS) constant at the value of 0.15 mol/L. The two solutions were filtered through membrane filters (0.22 μm, Millipore) to remove heteronuclei and mixed just before the entrance point of the flow channel within a Teflon tube of 3 cm in length and 0.5 mm in diameter, with the aid of two syringe pumps which ensured constant flow rate (1 or 2 mL/h for each solution, or the equivalent superficial velocity is 0.55 up to 1.1 cm/min) and sufficient mixing. Technical B



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was designed to achieve different flow velocities of the reactant solution. The depth of the channels was about 0.3 mm. A scheme of the experimental setup is given in Figure 1b. The process of calcium carbonate crystal growth was monitored via a microscope (Zeiss), connected to a digital camera (Nikon F601s/N6006), or a video camera (Sony DXC-1821P Trinicon color video camera) and a TV (Sony PVM-2010 QM Trinitron color video monitor), and a PC equipped with imaging software (Sigma Scan Pro 5.0, SPSS Inc.). The pore network was prepared by filling it with the desired grains (silicate sand, carbonate-coated sand, calcite-cemented sand, or calcite seeds) and triple-distilled water, which was displaced by the supersaturated calcium carbonate solution during injection. The carbonate sand used in these experiments consisted of silicate grains covered with crystallized calcium carbonate. Surface Porosity Measurements. Surface porosity of the simulated capillary channels was measured from images captured at different time intervals using Sigma Scan Pro (Aspire Software International) software. The software labels all pores, grains, and growing crystals individually and computes their location, surface area, and perimeter (Figure 2). The sum of the areas from all recognized particles divided by the entire image area gave the total porosity of the image.

reasons constrained the length between the mixing point and the inlet in the channel equal to 3 cm. This length was estimated to be adequate to allow sufficient time for the mixing of solutions. The use of dye solutions could give a degree of solution mixing; however, dyes were not used in order to facilitate the crystal visualization. The sodium bicarbonate solutions were freshly prepared for each day of the experiments. A scheme of the experimental setup is given in Figure 1a. The initial supersaturation values of calcium carbonate with respect to calcite was calculated using MultiScale: 10.5, 10.7, 20, and 21.28. Moreover, additional experiments for lower and higher SRinitial values were conducted. For SRinitial = 5.06 crystal nucleation was not observed during the experimental time period of this work (6 days). For SRinitial = 30, crystal growth resulted in channel clogging very fast but the experimental data were not sufficient to reach solid conclusions. The experiments were all accomplished under ambient conditions (θ = 25 °C). Due to technical reasons, the initial pH of the supersaturated solutions was not measured but it was estimated using MultiScale. The pH of the effluent was measured using a combination glass/Ag/AgCl electrode calibrated against four NBS buffer solutions (pH= 4.008, 6.864, 7.414, and 9.181). Samples of the effluent were collected for calcium analysis using atomic absorption spectroscopy (PerkinElmer Analyst 300). The morphology of the precipitated crystals within the porous medium was examined by scanning electron microscopy (SEM, FEI, Quanta FEG 250). B. Two-Dimensional Glass Pore Network. The transparent porous medium consisted of two mirror glass plates of the same dimensions treated using the photolithographic method.47,48 Initially the two mirrors were submerged in a NaOH solution (7.97 M) for 12 h and subsequently washed with water in order to remove the resin which covers the copper surface. When they were dried, in a dark room, using proper lighting, the copper surfaces were sprayed carefully using Electrolube RP50 positive photoresist, and they were put carefully in an oven for 15 min in order for the photoresist layer to be stabilized. When the two pieces were cold, a negative image (film) of the pore network was placed on each of the pieces, and they were put under UV lighting (at a distance of 40 cm) for 45 min. The two pieces were then submerged in a solution of NaOH (0.163 M) for not more than 30−60 s until the non-polymerized photoresist appeared, and they were shaken well until the photoresist was removed. Next, they were washed with tap water but not directly on the network. Using normal lighting the two parts were submerged in a solution of 200 mL of 65% HNO3 dissolved in 200 mL of water for 5−10 s in order to remove the copper surface which was not covered by photoresist and finally they were washed thoroughly with tap water. A quantity of wax (paraffin) was heated, and with the use of paintbrushes the glass surface was covered with wax except the surface which would be scribed. At the edges of the surface which would be scribed, a kind of moat was constructed in order to retain the solution inside. Then a solution of 90% HF was diluted in a volumetric tube of 500 mL at 75:25 (w/w), and the two parts were put in a plastic bowl. The surfaces to be scribed were covered by the solution of HF for exactly 5 min, and then they were washed several times with tap water. The wax was removed, and using a solution of 200 mL of 65% HNO3 in 230 mL of water, the copper was removed from the surfaces. For all stages and especially for the stage where HF was used, protective clothing was needed. Holes were opened on one of the glass plates with the use of a diamond drill, which served for fluid inlets and outlets, and the two plates were placed on each other carefully and finally were put in a programmed oven for sintering. The calcium carbonate supersaturated solutions were prepared by injecting two solutions from synchronized syringes, one solution containing twice the concentration of the required calcium ions and the other twice the carbonate alkalinity. The initial value of supersaturation with respect to calcite was calculated from MultiScale. The experiments were performed at initial supersaturation ratio values: 1.713, 3, 7, 8, 11.29, 13, and 30.27. The two solutions were filtered through membrane filters (0.22 μm, Millipore) to remove heteronuclei and mixed in a plastic tube 5 cm in length and 0.5 mm in diameter; at the desired temperature the inlet point of the porous medium (5 cm) is considered to provide sufficient time for solution mixing. The model

Figure 2. (a) Image captured during precipitation of CaCO3 from solutions supersaturated with respect to calcite, at 70 °C, SRinitial = 13, and ionic strength of 0.15 mol/L with NaCl. (b) Same image, analyzed with Sigma Scan Pro software. Blue areas represent the etched grains, while red areas are the growing crystals. Theoretical Background. Calcium carbonate forms a number polymorphs during its precipitation. There are three anhydrous crystalline forms including calcite, aragonite, and vaterite, and two hydrate forms, monohydrate and hexahydrate calcium carbonate (ikaite), which are reported to be less stable.49 The solubility products (Ks) for the different polymorphs of CaCO3 and their crystal structure are summarized in Table 1.50 Calcite is the most stable phase at

Table 1. Crystal Structure and Solubility Products for the Different Polymorphs of Calcium Carbonate CaCO3 polymorph

crystal structure

− log Ks(25°C)

calcite aragonite vaterite ikaite amorphous

rhomboedric orthorhombic hexagonal monoclinic

8.4856 8.3456 7.9156 6.6257 6.4058

ambient conditions,51 while aragonite is a metastable phase and has been found to be formed at higher pressure and temperature values.52 Phase diagrams and data for the transformations between CaCO3 polymorphs as a function of temperature, pressure, and concentrations of calcium and carbonic ions have been reported in the literature.51−53 The metastable zone width of the calcium carbonate system, in which the labile and metastable regions were experimentally determined, have been extensively published in the literature.54 It was shown that the metastable zone width depends among others on the ions present and on the solution pH.55 The transformation of the initially precipitating unstable phases (vaterite and aragonite) to the thermodynamically most stable calcite depends to a large extent on C



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the initial solution supersaturation. The least stable phase was reported to be stabilized at high values of the supersaturation ratio and high pH values.55 In each experiment, the supersaturation ratio with respect to CaCO3 (calcite) was calculated by aCa 2 +aCO32 − SR = 0 K s,CaCO (1) 3 In eq 1 α denotes activities of the subscripted ions and K0s,CaCO3 is the thermodynamic solubility product of calcite. The most important equilibria of the carbonate species distribution in water solutions, which determine the relative amounts of the free Ca2+ and CO32− ions, may be described by the following reaction scheme:44

CO2 (g) ↔ CO2 (aq)

(2)

CO2 (aq) + H 2O ↔ HCO3− + H+

(3)

HCO3− ↔ CO32 − + H+

(4)

CO32 − + Ca 2 + ↔ CaCO3(s)

(5)

Figure 3. Sequence of images captured during precipitation of CaCO3 from solutions supersaturated with respect to calcite at different points of the porous medium: 2, 6, 8, and 10 cm from the inlet point (25 °C, SRinitial= 10.7, and ionic strength of 0.15 mol/L with NaCl).

According to eq 2 the total carbonate concentration in solution is dependent on the CO2 gas pressure. Equations 3 and 4 imply that the CO32− concentration in solution is a function of pH. An increase in pH shifts eqs 3 and 4 to the right and thereby increases the CO32− concentration and consequently the CaCO3 supersaturation. From eq 1, it follows that for SR > 1 there is a thermodynamic potential for precipitation of CaCO3 and the solution is supersaturated with respect to this salt. At SR = 1 the solution is saturated with respect to CaCO3, while at SR < 1 the solution is undersaturated and any solid CaCO3 present dissolves.

respectively, from the inlet point) the first crystals were observed after 2 days. Near the inlet point of the porous medium the precipitated amount and the crystal growth of calcium carbonate was higher, where calcite crystals of 0.15− 0.25 mm final size were formed. This gradient was attributed to the fact that SR values near the inlet were higher, so more crystals could be deposited and had enough time to grow in size, as it is also shown in Figure 4, where the evolution of the

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RESULTS AND DISCUSSION A. Experiments in One-Dimensional Plexiglas Porous Media. Crystal Growth and Distribution along the Porous Medium. A set of experiments was conducted to examine the distribution of the deposited crystals along the length of the porous medium. The deposition of calcium carbonate was not homogeneous along the length of the flow channel. The experimental data obtained from the visual observation of the experiments and more specifically the time of the first observed crystal and the number and the size of crystals are summarized in Table 2. Figure 3 shows a typical sequence of snapshots Table 2. Experimental Data for CaCO3 Precipitation in OneDimensional Porous Media at 25 °C for all SRinitial Values for Positions 2 and 4

a

SRinitial

flow rate (mL/h)

10.5 (position 2) 10.7 (position 2) 10.7 (position 4) 20 (position 2) 20 (position 4) 21.28 (position 2)

2 1 1 1 1 2

t (first formed crystals)

no. of crystals

crystal size (mm)

6.5 h 28 h 6d 3.5 h 6h 3h

5 1 2 3 13 12

0.06 0.17 0.02 n/aa 0.05 0.04

Figure 4. CaCO3 crystal size evolution during precipitation from solutions supersaturated with respect to calcite at different points of the porous medium as a function of time (positions 1−4: 2, 6, 8, and 10 cm from the inlet point, 25 °C, SRinitial= 10.7, ionic strength of 0.15 mol/L with NaCl).

n/a: not available.

size of a single crystal as a function of time is presented for all of the positions from the inlet of the porous medium at SRinitial = 10.7. The diagonal of a single face of the precipitated crystal as shown in the photographs obtained from the optical observation was used as a characteristic size to calculate linear growth rates of calcite. As may be seen, the growth of crystal’s

depicting the evolution of crystal growth at each position of the flow channel, for initial supersaturation value 10.7 at 25 °C. At position 1 (2 cm from the inlet point) the first crystal was observed after 6 h, while at position 4 (10 cm from the inlet point) the first crystals were observed only past 6 days from the onset of the experiment. At positions 2 and 3 (6 and 8 cm, D



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Table 3. Composition of solutions before and after the Mixing Point, Final Measured, and Calculated Composition Using MultiScale at 25 °C SRinitial

initial solution composition (mM)

total calcium concentration after mixing (mM)

equilibrium composition (M)a

total calcium concentration (mM)

10.50 21.28

13CaCl2·2H2O + 13NaHCO3 + 150NaCl 20CaCl2·2H2O + 20NaHCO3 + 150NaCl

6.5 10

5.2 × 10−6 5.2 × 10−6

5.4 7.4

a

Calculated.

size at positions 1 and 2 was more pronounced than the corresponding at positions 3 and 4, where only a few small crystals were precipitated for the same total time interval. In order to examine the effect of the initial SR value of the solution, a supplementary set of experiments was carried out (Table 3). Figure 5 shows the growth of a single crystal as a

Figure 6. Crystal size evolution during precipitation of CaCO3 from solutions supersaturated with respect to calcite at different initial supersaturation values as a function of time (position 4: 10 cm from the inlet point, 25 °C, SRinitial = 10.7 and 20, and ionic strength of 0.15 mol/L with NaCl).

Figure 5. Crystal size evolution during precipitation of CaCO3 from solutions supersaturated with respect to calcite at different initial supersaturation values as a function of time (position 2: 6 cm from the inlet point, 25 °C, SRinitial = 10.5 and 21.28, and ionic strength of 0.15 mol/L with NaCl).

chamber). In the case of SRinitial = 20 there was sufficient concentration of structural units of ions to form insoluble salts at that ultimate end of the flow chamber. The final size of the formed crystal was 0.05 mm at SRinitial = 20, while at SRinitial = 10.7 the final size was 0.02 mm, and the first visually observed crystals were precipitated after 6 h and 6 days, respectively. According to these experimental results shown in Figures 5 and 6 near the inlet point of the flow channel (position 2) more crystals of calcium carbonate are precipitated at high SRinitial values, but these crystals have smaller size than the limited (in number) crystals formed in the case of lower SRinitial values. On the contrary, near the outlet point of the flow channel (position 4) the concentration of ions to form crystals for low SRinitial values was not sufficient. Close to the exit of the flow chamber there were only a few small crystals for low SRinitial values while there were sufficiently large crystals of moderate size for high SRinitial values. In both positions the time interval for visual recording of the primarily formed crystals decreased with increasing SRinitial values. In principle, the higher the supersaturation, which is the driving force for spontaneous nucleation, the more crystals were expected to precipitate. A sequence of snapshots captured at position 4 for two different initial supersaturation values is presented in Figure 7a,b where the number of precipitated crystals is concerned. The first crystals were observed after 6 days from the onset of the experiment at SRinitial= 10.7, but for SRinitial= 20 the respective time lapse was 6 h. It may therefore be suggested that, at higher SRinitial values, the total number of the precipitated crystals is larger, as shown in Figure 7b. Sixteen crystals of calcium carbonate were finally precipitated at

function of time for SRinitial= 10.5 and 21.28 at position 2 (6 cm from the inlet of the medium). At higher SRinitial value (21.28), the rate of the crystal growth was lower and the final size of the formed crystal was 0.04 mm, while at SRinitial = 10.5 the final size of the crystal was 0.06 mm. This is not strange, and the observation is valid for a single crystal. In the case of low SRinitial values, only a few crystals were observed and these crystals were grown with time because of the continuous flow of new fresh solutions. In high SRinitial values, a large number of crystals were formed but their size was smaller in comparison with lower SRinitial values. Moreover, in high SRinitial values secondary nucleation and crystal growth was observed because of the abundance of ions that can form new crystals. Another important piece of information obtained from Figure 5 was that the first visually identified crystal was precipitated past 6.5 h for SRinitial= 10.5 while for SRinitial= 21.28 many crystals were observed after 3 h. The previously mentioned remarks are not valid for all positions within the flow chambers. Thus, the experiment was repeated for similar values of initial supersaturation (10.7 and 20 at 25 °C), and visualization was focused on a farther point from the entrance of the flow channel (position 4). The results are presented in Figure 6 which shows the crystal growth as a function of time at position 4 (10 cm from the inlet of the flow E



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Figure 7. (a) Number of CaCO3 crystals developed in the porous medium at position 4 (10 cm from the inlet point of the solutions supersaturated with respect to calcite) for SRinitial= 10.7 and 20 (25 °C, ionic strength of 0.15 mol/L with NaCl). (b) Sequence of images captured during precipitation of CaCO3 from solutions supersaturated with respect to calcite, taken at position 4 of the porous medium (10 cm from the inlet point) for SRinitial = 10.7 and 20 (25 °C, ionic strength of 0.15 mol/L with NaCl).

SRinitial= 20 at position 4, while only two crystals were formed at the same position at SRinitial= 10.7. Calcium Concentration Measurements and Rates. For the experiments performed in this work, initial supersaturation values of CaCO3 were calculated using MultiScale software whereas the supersaturation value at the effluent was estimated from the chemical analysis for total calcium concentration at the effluent stream using MultiScale. Despite the fact that the supersaturation inside the channel cannot be measured, an overall estimate was obtained from the integral concentration changes from the initial concentration to the final values. Supersaturation gradient within the porous media was the driving force for the nucleation and crystal growth of CaCO3 crystals. Calcium concentration of the effluent was measured in samples collected at the outlet of the flow channels and compared to the initial injected. In all of the experiments calcium concentration decreased as a function of time, since calcium carbonate crystals precipitated inside the porous media capturing calcium ions (Ca2+). In Figure 8 the total calcium concentration as a function of time for two different initial supersaturation values (SRinitial= 10.7 and 20) at position 4 is shown. As may be seen, the higher the SRinitial value, the larger the drop rate of calcium concentration was. This experimental observation may be attributed to the fact that the supersaturation gradient along the porous medium is higher for higher SRinitial values, as it has already been discussed. Experimentally and theoretically obtained pH values are summarized in Table 4 for the initial and equilibrium states for position 2. pH values experimentally obtained are close to the calculated values, and the pH decrease between the initial and final states is attributed to the CaCO3 precipitation. In order to examine the conditions at each position of the flow channel for the calcium concentration measurements for SRinitial = 10.7 the precipitation rate, R, was plotted as a function of the length of the supersaturated solution path in the porous medium, as shown in Figure 9. R was defined as the change of calcium concentration (ΔC) of the effluent as a function of

Figure 8. Plot of the total calcium concentration as a function of time measured at position 4 (10 cm from the inlet point of solutions supersaturated with respect to calcite) for SRinitial = 10.7 and 20 (25 °C, ionic strength of 0.15 mol/L with NaCl).

Table 4. pH Values Calculated from Multiscale and Experimentally Measured at the Start of the Experiments and at the Equilibrium for SRinitial = 10.50 and 21.28 SRinitial

calculated initial pH

measured initial pH

calculated equilibrium pH

measured final pH

10.50 21.28

7.91 7.86

8.27 8.00

7.03 6.77

7.42 7.37

time lapse, (Δt); i.e., it was equal to ΔC/Δt. As may be seen in Figure 9, the longer the flow channel the higher was the precipitation rate value at the respective distance from the entrance of the supersaturated solution, since more total time was available for the supersaturated solution within the flow medium resulting to higher consumption of calcium ions for F



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Figure 9. Rate of precipitation of CaCO3 at different positions from the inlet point of the solutions supersaturated with respect to calcite for SRinitial = 10.7 (25 °C, ionic strength of 0.15 mol/L with NaCl).

Figure 11. Images captured during precipitation of CaCO3 in Plexiglas porous media in the presence of (a) carbonate-coated sand, (b) calcite-cemented sand grains, and (c) synthetically prepared calcite seeds (25 °C, SRinitial = 13, and ionic strength of 0.15 mol/L with NaCl).

the formation of calcium carbonate and, therefore, to larger concentration gradients. Morphology of Precipitated Crystals. The main calcium carbonate polymorph formed in all experiments at 25 °C was calcite, as confirmed by SEM images. The presence of thermodynamically less stable polymorphs was identified by the morphological examination of the precipitates during the course of precipitation. However, these formations were not stabilized, and as a result they were not found at the end of the experiments, when significantly longer time had lapsed. In Figure 10a, a well-shaped calcite crystal is shown from a sample

case of precipitation on sand grains.35 This is the case of seeded crystal growth in which there is no nucleation barrier. This was verified in most of the cases when calcite was introduced in the porous medium (Figure 11c). In all cases presented in Figure 11, precipitation occurred both on the surface of the sand grains and in the pore space between them due to sufficiently high SR. B. Experiments in Two-Dimensional Glass Pore Networks. Distribution of Crystals along the Porous Network. The investigation of CaCO3 precipitation and crystal growth in 1-D flow channels provided useful information for understanding the mechanisms and the parameters that affect scaling under flow conditions. Oil and gas reservoirs may be simulated by networks consisting of spherical pores (chambers) and cylindrical pores (throats).18,59 In order to examine scaling under more realistic geometrical conditions compared to the conditions near the wellbore areas, 2-D glass networks were constructed for monitoring the CaCO3 crystal growth. At the end of each experiment the porous network was scanned across its length and width (x and y axis) to observe the distribution of the crystals in the porous medium. The profile of calcium carbonate precipitated was not homogeneous over the length of the porous medium. Figure 12 shows the precipitated calcite crystals along the channel for an experiment run at 70 °C with SRinitial = 8. A gradient was evident with relatively high amounts of calcium carbonate formed near the injection point, where the initial supersaturation was higher. The precipitated amount decreased toward the outlet of the porous medium. Near the injection point, calcite crystals of 0.06−0.1 mm final average size grew, while toward the outlet of the porous medium the crystals were not larger than 0.02 mm. Along the y axis, the distribution and the size of the crystals were found to be rather homogeneous while along the x axis it was found that a larger quantity of CaCO3 was formed mainly near the inlet of the network. Similar behavior was also observed during CaCO3 precipitation on Iceland spar calcite surfaces.60 In other studies61,62 it was found that when supersaturated fluids flowed through artificial fractures, most of the mineral deposition occurred within several centimeters from the supersaturated solution inlet. Furthermore, in the latter work it was reported

Figure 10. SEM pictures of precipitated calcite crystals at 25 °C and ionic strength of 0.15 mol/L with NaCl (a) at position 2 (6 cm from the inlet point of the solutions supersaturated with respect to calcite) for SRinitial = 10.5 and (b and c) at position 2 (6 cm from the inlet point of the solutions supersaturated with respect to calcite) for SRinitial = 21.28.

taken from flow medium of a length of 6 cm for SRinitial = 10.7. The final size of approximately 0.05 mm confirmed crystal size measurements obtained from the optical microscope in situ in combination with the image analysis software. At the same position but for higher initial supersaturation value (SRinitial = 21.28) calcite crystals were grown by a layer-by-layer mechanism and formed aggregates, as shown in Figure 10b,c, respectively. Effect of Substrates. When calcite seeds or carbonate sand was used, precipitation took place mainly on the surfaces of the introduced grains, as shown in Figure 11a,c and then grew out from the grains directing outward to the bulk solution. In experiments where calcite-cemented sand grains were used, precipitation was not selectively induced, as seen in Figure 11b. Calcite seeds were the most favorable substrate for the initiation of the precipitation process since the surface energy needed for precipitation to occur is much lower than that in the G



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growth, as may be seen in Figure 14. The calcite scale tended to form coherent deposits, not easily detachable by the fluid flow.

Figure 14. Calcite rhombohedra and aragonite agglomerates precipitated at 70 °C for SRinitial = 13 and ionic strength of 0.15 mol/L with NaCl.

Figure 12. CaCO3 distribution across the length of the porous medium for the experiment run in a 2-D glass network, at 70 °C, SRinitial = 8, and ionic strength of 0.15 mol/L with NaCl.

On the other hand, in many cases, aragonite clusters were partially removed due to flow, causing blockage of subsequent pore throats. Calcium and pH Measurements. Calcium concentration was measured in fractions of the pore fluid collected at the outlet of the porous medium. pH and total calcium concentration profiles (Figure 15a) followed the same trends. The values of total calcium allowed for the calculation of supersaturation−time profiles using MultiScale software. The independent SR values as a function of time are shown in Figure 15b, for SRinitial = 3 and 80 °C. Both calculations follow the same trend and agree with respect to calculated SR values. Thus, both total calcium and pH measurements can be used independently to measure precipitation rates during the experiment. Calcium Carbonate Growth Rates. The calcium carbonate crystal face growth rates over the temperature range 25−80 °C were determined by monitoring crystal size within the micromodel with time through successive snapshots, and the results are presented in Table 5. A plot of the crystal size as a function of time showed that calcium carbonate crystal growth was a linear function of time for the experimental conditions reported in the present work and that there was a significant increase in the growth rate with increasing temperature (Figure 16), and the data are summarized in Table 6. From the slope of this straight line, the calcium carbonate layer growth rate was

that, by the end of the experiment, the inlet was completely clogged with little deposition being recorded “downstream”. Surface Porosity Measurements. The measurements revealed significant porosity drop when calcite-cemented sand was introduced in the Plexiglas cell, compared to experiments made in glass porous media. An increase in the SRinitial resulted in a sharp porosity decrease, as may be seen in Figure 13a. Increasing SRinitial resulted in higher precipitation rates, and scale was formed nonselectively on the introduced grains and at the in between void space, resulting in the significant pοrosity and permeability changes measured. On the other hand, at lower SRinitial values, precipitation rates were significantly lower, resulting in the formation of a small number of crystals which grew preferably on the first nuclei formed. The type of the grains introduced in the porous medium plays a significant role. When carbonate-coated sand was used, the nuclei formed preferably on the sand grains and a slight reduction in porosity was measured. On the other hand, calcite-cemented sand also induced precipitation, mainly secondary nucleation, as already reported in a previous section (Effect of Substrates). It was evident that a strong correlation exists between the temperature and morphology of the scale formed. At relatively high temperatures (50−80 °C), calcite crystals and aragonite agglomerates were observed from the early stages of scale

Figure 13. (a) Effect of SRinitial on porosity change as a function of time. Experiments run at 25 °C and ionic strength of 0.15 mol/L with NaCl, with calcite-cemented sand. (b) Effect of the type of grains introduced in the porous medium on porosity changes for an experiment run at 25 °C, SRinitial = 11.29, and ionic strength of 0.15 mol/L with NaCl. H



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Figure 15. (a) pH and total calcium concentration values as a function of time obtained at the outlet of the pore network at 80 °C, SRinitial = 3, and ionic strength of 0.15 mol/L with NaCl. (b) Calculated values of SR based on the experimental data of Ca2+ and pH values presented in panel a.

Toft63 and 1.06 × 10−10 reported by Dawe and Zhang28 for SR ≈ 2.4 with 0.2 mol/kg NaCl. The plot of the calculated rate constants as a function of temperature is described by an Arrhenius equation of the form

Table 5. CaCO3 Growth Rates at Different Temperatures expt

model network

θ (°C)

SRinitial

4 5 6 7 8

glass glass glass glass glass

25 35 60 70 80

7 7 7 7 7

r (m/s) 4.90 6.05 2.45 3.71 4.71

× × × × ×

10−10 10−10 10−9 10−9 10−9

kp (s/m) 1.81 2.23 9.05 1.37 1.74

× × × × ×

10−10 10−10 10−10 10−9 10−9

k p = A exp( −Eact /R gasT )

where A is a constant, Rgas is the gas constant, and Eact is the activation energy for precipitation to occur. Plots of log(kp) as a function of 1/T were linear, as shown in Figure 17. From the slope of the straight line a value for the activation energy equal to 39 kJ/mol was calculated, in good agreements with literature reported values from experiments of calcium carbonate spontaneous precipitation.64,65 Effect of Gas Bubbles. As already mentioned, the temperature and pressure were constant during the injection of supersaturated solutions in the porous medium but in some cases a gas phase was released from the solution, when the solutions were heated to the desired temperature. Whenever air was trapped, a number of calcite rhombohedral crystals were formed just below and in contact with the gas bubbles (Figure 18). A possible explanation for this phenomenon is that, besides the local pH increase around the gas bubbles, the gas bubbles may act as heterogeneous nucleation catalysts since, due to the small gas bubble size, their surface energy is high.28

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Figure 16. Crystal size evolution during precipitation of CaCO3 from solutions supersaturated with respect to calcite at 25, 60, and 80 °C for SRinitial = 7.

CONCLUSIONS The precipitation and crystal growth of CaCO3 along the length of 1-D porous media was not homogeneous. Near the inlet point of the flow channels more crystals precipitated but their growth rate was lower compared to the growth rate calculated near the outlet of the media. Crystal growth rates were higher for experiments performed at higher SRinitial values. In all experiments performed in this work, it was observed that the final size of the grown crystals, near the inlet point of the porous media, was smaller in comparison with the outlet. The size differences of the crystallites formed may be attributed to the relatively higher values of the supersaturation at the entrance point, which favored the formation of a larger number of smaller size crystallites. The deposition of CaCO3 crystals was more intense for high initial SR values in all positions of the flow channel. These remarks may be attributed to the gradient of supersaturation that was developed inside the porous media. The time necessary for nucleation and subsequent growth of CaCO3 crystals to a size to be visually observed was shorter as the initial

Table 6. Crystal Size of CaCO3 for SRinitial = 7 at Different Temperature Values for Two-Dimensional Networks θ (°C) crystal size (mm)

25 0.09

60 0.18

80 0.24

calculated. The calculation of the crystal growth rate constant was done from plots of the growth rate as a function of the solution saturation ratio using the Davies−Jones rate equation: r = k p(SR0.5 − 1)2

(7)

(6)

The calculated rate constants, kp, at different temperatures and supersaturation values are listed in Table 5. The value 1.81 × 10−10 sm−1 calculated for experiment at 25 °C and SRinitial = 7 with 0.6 mol/kg NaCl can be compared with the reported calcite growth rate constant of 4.6 × 10−11 sm−1 at 25 °C and atmospheric pressure reported by Nielsen and I



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Figure 17. Rate constants against 1/T at different temperatures and SRinitial = 7.

Notes

The authors declare no competing financial interest.

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ACKNOWLEDGMENTS This research was partially funded by the European Union (European Social Fund-ESF) and Greek National Funds through the Operational program “Education and Lifelong Learning” under the action Aristeia II (Code No. 4420). We also thank Professor Terje Østvold from the Norwegian University of Science and Technology (NTNU), for the good cooperation and the private communications we had on issues related to precipitation of sparingly insoluble salts within porous media. The assistance of Dr. S.G. Rokidi with SEM imaging and suggestions is acknowledged.

Figure 18. Formation of CaCO3 crystals at the gas−liquid interface in glass porous networks.

SR was higher in all positions of the channel. The drop rate of the total calcium concentration at the effluent was higher when the initial SR value increased. At 25 °C mainly calcite was identified. Concerning the deposition of CaCO3 crystals in 2-D porous networks it may be concluded that it was not homogeneous over the length of the media. Near the inlet point the amount of the precipitated crystals was higher as the initial SR value increased. This finding is consistent with the results obtained in 1-D porous media and with similar data for 2-D porous media given in the literature.2,28,37,38,42,43 The crystal growth rates were found to depend on the temperature. Increasing temperature of the supersaturated solutions resulted in higher CaCO3 growth rates. The concentration of calcium ions and the pH of the effluent reduced over time, and they both followed the same trend, allowing the measurement of the precipitation rates independently. At a range of temperature between 50 and 80 °C calcite and aragonite clusters were observed. Regarding the surface porosity measurements, an intense drop was revealed when calcite-cemented sand was used as substrate in the 1-D Plexiglas channels compared to the experiments conducted in glass porous networks. At higher initial SR values the porosity drop was more rapid and the scale was formed nonselectively.

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AUTHOR INFORMATION

Corresponding Author

*E-mail: [email protected]; [email protected]. Tel.: +30 2610 997252. Fax: +30 2610 997574. URL: http:// www.chemeng.upatras.gr/el/personel/faculty/el/takisp. Present Address §

Statoil ASA, Arkitekt Ebbells veg 10, NO-4035 Trondheim, Norway. J



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Experimental Investigation of Calcium Carbonate Precipitation and

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