Kinetics of Gypsum Precipitation for Designing Interstage Crystallizers

Sep 19, 2013 - Department of Chemical Engineering, Ben-Gurion University of the Negev, P.O. Box 653, Beer-sheva 84105, Israel. # Department of ...
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Kinetics of Gypsum Precipitation for Designing Interstage Crystallizers for Concentrate in High Recovery Reverse Osmosis Shuli Halevy,† Eli Korin,*,† and Jack Gilron# †

Department of Chemical Engineering, Ben-Gurion University of the Negev, P.O. Box 653, Beer-sheva 84105, Israel Department of Desalination and Water Treatment, Zuckerberg Institute for Water Research, Ben-Gurion University of the Negev, P.O. Box 653, Beer-sheva, 84105, Israel

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ABSTRACT: Treating desalination concentrates by precipitating sparingly soluble salts is a promising method for extending water recovery limits of such processes and thereby reducing concentrate volumes. One of more common technologies for carrying this out is the use of fluidized bed crystallizers, often with sand grains as the crystallizing surface. Most of the works done to date on such crystallizers for water treatment purposes have been on water softening, and little has been done on use of such crystallizers for precipitation of gypsum. This study was on the crystallization kinetics of gypsum at initial supersaturation levels typical of reverse osmosis (RO) concentrates, in the presence of silica sand grains or gypsum seeds, in a batch stirred tank crystallizer. The findings show that silica sand grains were efficient primary heterogeneous nucleators for gypsum. Crystallization kinetics increased with larger grain size or higher grain number concentration. Considering the different nucleation mechanisms, a central role for secondary nucleation is proposed to explain the present findings. Collisions between sand grains, on which initial crystals have formed, eject some or all of them into the solution to continue secondary nucleation and crystal growth. In seeded growth experiments with gypsum, it is confirmed that crystal growth rates were controlled by a surface reaction. For some of the experiments conducted in the presence of sand, the crystallization rate was higher than with gypsum seed crystals, over a significant range of concentrations. Moreover, the use of recycled sand decreased the induction period significantly compared to new sand.

1. INTRODUCTION 1.1. Technological Background. There is a growing need for more fresh water as populations grow, and water sources decline in quality and quantity. Desalinating waters from municipal wastewater, brackish and seawater sources by reverse osmosis (RO) has become the dominant technology for producing new water. Advances in RO technology have led to a significant reduction in the production cost of water desalination.1 A byproduct of desalination, RO concentrates contain high levels of dissolved salts and antiscalants. The concentrate streams in brackish and municipal wastewater desalination are typically 15−20% of the feedwater stream. Therefore, substantial volumes of saline wastewater are produced in the process, which must be managed in an environmentally acceptable manner. While the desalination concentrates from seawater RO can be discharged directly into the ocean, with appropriate environmental precautions, this is not a cost-effective option for inland desalination, due to high transportation costs. The commonly used options for concentrate disposal at inland locations, as surveyed by Mickley,2 include deep well injection, thermal desalination, and double-lined evaporation ponds. However, disposal costs for these options are high.3 Moreover, concentrates are already a high quality water following the strict pretreatment of RO feedwater. Therefore, minimization of concentrate volumes by increased recovery will reduce process costs. However, precipitation of scaling compounds is the main factor limiting recovery in RO. Scaling compounds commonly encountered in RO are gypsum (CaSO4·2H2O), calcium carbonate (CaCO3), barium sulfate (BaSO4), and silica. If the © 2013 American Chemical Society

retained stream becomes sufficiently supersaturated with respect to these salts, precipitation can occur on the membrane surface and lead to permeate flux decline and eventually the shortening of membrane useful life. In many of the feed waters, gypsum is the dominant sparingly soluble salt. Dosing the RO feed stream with antiscalants (such as phosphonates and polycarboxylic acids) is a commonly used approach for controlling precipitation fouling. These antiscalants act by inhibiting nucleation and crystal growth or by distorting the crystal habit to prevent scale adhesion to the membrane. However, even with the use of antiscalants, there are still maximum supersaturation ratios that cannot be exceeded, and this limits water recovery. Concentrate treatment has recently been shown to be a promising strategy for reducing concentrate volumes and extending water recovery limits. In this approach, mineral scales are removed from the concentrate to reduce its membrane scaling potential. This enables concentrate to be treated in a subsequent RO step to further reduce concentrate volume and increase water recovery.4 Several methods are proposed in the literature for scaling mineral removal from the concentrate. Precipitation softening of the RO concentrate with an alkaline chemical (e.g., Ca(OH)2, NaOH, or Na2CO3) is used to remove calcium ion as CaCO3 and thereby reduce supersaturation with respect Received: Revised: Accepted: Published: 14647

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to calcium mineral scalants (e.g., CaSO4·2H2O and CaCO3). The high local supersaturation ratio generated by raising the pH with the alkaline addition generates the required driving force for accelerating CaCO3 nucleation and crystal growth.5 However, this method requires a large alkaline chemical dose. This is why some groups have already proposed and demonstrated relieving supersaturation by precipitating gypsum.6,7 Furthermore, it produces a fine suspension of crystals, which requires an additional stage of solid−liquid separation and an extensive dewatering of the resulting low solids content sludge.8 An alternative method relies on precipitating the sparingly soluble salt in the presence of solids, particularly crystalline seeds of the same mineral, for which the solution is already supersaturated, and on which the sparingly soluble salts can deposit. Addition of solids can also provide a surface area for heterogeneous nucleation and growth, thus enhancing the kinetics of mineral crystallization. In addition, the size of the final precipitates can be controlled by the initial parameters of the added solids (e.g., solid type, size and loading), in order to facilitate efficient solid−liquid separation.7,9,10 Examples of seed materials used are calcium carbonate, gypsum, and sand, the latter being common in fluidized bed crystallizers used in water softening.11 However, antiscalants present in RO concentrate can significantly inhibit crystallization rates due to the high stability it imparts to the supersaturated solution. Several pretreatment methods have been suggested for eliminating the antiscalant to allow higher crystallization rates of minerals salts during seeded precipitation from the concentrate. These include addition organic chelants, polymeric coagulants, surfactants, or base to the concentrate to scavenge the antiscalant, or using chemical/electrochemical oxidation to degrade it.12−14 The authors recently proposed a new RO process (flow reversal) based on periodic reversal of feed flow into the concentrate end of a membrane module at intervals less than the induction time of the precipitating salt. This process demonstrated increased recovery (85−90%) with elimination of antiscalant usage.15,16 Consequently, the supersaturation ratio of mineral salts in these concentrates is the same or higher than those present in conventional RO processes but with little or no antiscalant present. These concentrates can therefore be treated efficiently to crystallize supersaturated salts with reduced chemical consumption. One of the minerals commonly found at supersaturation in RO concentrates is CaSO4·2H2O (gypsum). Since the crystallization process has been shown to be advantageous for concentrate treatment, the present study investigated the crystallization kinetics of gypsum at supersaturation levels typical of flow reversal RO concentrates. According to the literature, the main possible crystallizers that can be considered for this process are stirred tank,17 fixed bed,18 and fluidized bed.19 Stirred tank crystallizers require an additional stage of solid−liquid separation, while fixed and fluidized bed crystallizers incorporate the solid−liquid separation within the crystallizer. When supersaturation is controlled such that crystallization occurs primarily by crystal growth onto the bed material, the treated effluent stream has minimal solid content. However, it has been reported that in fixed-bed crystallizers early breakthrough of the packed bed can occur due to deactivation of bed material by adsorption of natural organic matter.18 Therefore, fluidized bed is deemed to be the most economically effective crystallizer for treating concen-

trates.20,21 Furthermore, fluidized bed crystallizers (FBC) are successfully employed for municipal water softening by crystallization of CaCO3 on sand grains.11 However, a major manufacturer of such equipment raised problems in using it for gypsum (private communication), and we ourselves saw that gypsum was not retained on the sand in preliminary FBC experiments. Furthermore the published efforts in using interstage precipitation for gypsum6,7 focus on using sludge blanket reactors in which the gypsum served as its own seed and which were intermediate between a stirred tank and fluidized bed reactor. To our knowledge, no work on this system (i.e., a FBC for the crystallization of gypsum on sand grains) was found in the literature. Recent, preliminary FBC experimental results in this subject indicated the need for more intensive study.22 Therefore, this study focuses on the crystallization kinetics of gypsum, at supersaturation levels typical of RO concentrates in the presence of silica sand and gypsum seeds. To extract the kinetic data and study the mechanisms for nucleation on the surface of the sand media, it was found to be more convenient to carry out the experiments in a stirred tank reactor, even though as indicated above, an FBC or sludge blanket reactor would be preferred for actual implementation. 1.2. Theoretical Background. Supersaturation of a solution with respect to a certain mineral can be expressed in a number of different ways, among the most common expressions being the relative supersaturation, σ, and the supersaturation ratio, S. The relative supersaturation expresses the driving force for crystal growth and is defined by 1/ ν ⎛ IAP ⎞1/ ν ⎛ x y⎞ ⎟⎟ − 1 = ⎜⎜ {A} {B} ⎟⎟ − 1 σ = ⎜⎜ ⎝ K sp ⎠ ⎝ K sp ⎠

(1)

where IAP is the ion activity product of a solution, Ksp is the solubility product in terms of activity, ν is the total number of ions per formula unit of an electrolyte AxBy (i.e., ν = x + y). The driving force for primary nucleation (homogeneous and heterogeneous) is the supersaturation ratio, S, defined as23

S=

IAP {A}x {B} y = K sp K sp

(2)

According to classical theory of nucleation, the crystallization of a supersaturated sparingly soluble salt begins after an induction period, through primary nucleation process. On the basis of this theory the rate of nucleation, J, can be expressed as ⎛ βγ 3V 2 N f (θ ) ⎞ m A ⎟ J = A C exp⎜ − 3 2 ⎝ (RT ) ln (S) ⎠

(3)

where AC is a pre-exponential coefficient, β is a geometric factor, about 16π/3 for a spherical nucleus, γ is the interfacial tension, Vm is the molar volume (74.69 cm3 mol−1 for gypsum), and NA is Avogadro’s number, f(θ) is the correction factor for heterogeneous nucleation, T is the absolute temperature, and R is the gas constant. The induction time has frequently been used as a measure of the nucleation process, with the simplifying assumption that it is inversely proportional to the rate of nucleation,23,24, i.e., that t ind ∝ 14648

1 J

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Then, the induction time can be related to the supersaturation ratio by substituting J into eq 4: log t ind ∝

βγ 3Vm2NAf (θ ) 2.3(RT )3 log 2 S

(5)

Secondary nucleation occurs in the vicinity of the previously formed crystals present in the supersaturated system. One of the mechanisms for secondary nucleation is contact nucleation, which results from collisions between two crystals or between crystals and the crystallizer surfaces, mostly that of the agitator. According to this mechanism, secondary nuclei are produced by breakage or attrition processes, which result from collisions. Secondary nucleation in a stirred tank crystallizer can be affected by several factors: (1) The rotational speed of the agitator, since the probability of crystal−agitator contacts is directly proportional to the agitator speed. (2) Crystal size: large crystals generate more secondary nuclei than do small seeds because of their greater contact probability arising from their ability to cross streamlines and their larger collision energies. Very small crystals (smaller than about 5 μm) tend to follow the streamlines, behaving as if they were suspended in a stagnant fluid, rarely coming into contact with the agitator or other crystals. (3) Suspension density: secondary nucleation increased by increasing the number of crystals per unit volume of solution. (4) Supersaturation: increased supersaturation increased secondary nucleation. (5) The relative hardness of the contacting bodies.23,25 The relevance of these effects on secondary nucleation will become clear in our discussion of the results.

Figure 1. Schematic representation of the stirred tank crystallizer.

2. EXPERIMENTAL SECTION 2.1. Materials and Solution Preparation. Supersaturated solutions of calcium sulfate were prepared by mixing stoichiometric amounts of Na2SO4 (Sigma-Aldrich, ACS reagent grade) and CaCl2·2H2O (Sigma-Aldrich, ultra grade). The initial supersaturation ratios of these solutions were in the range between 2.4 and 2.8 (solution concentration ranged from 36 to 48 mM CaSO4), which are values intermediate between those of RO concentrates from Mashabe Sadeh Well water (Sgyp = 2) and from the flow reversal pilot plant operating at Mekorot’s “Sabha” site near Eilat (S = 3.5). In order to reach the ionic strength typically occurring in RO concentrates, an additional amount of NaCl (Sigma-Aldrich, ultra grade) was dissolved in the Na 2 SO 4 solution, so that the total concentration of NaCl in all of the experiments was 96 mM. Gypsum seeds and silica sand were used as the solid substrates in the crystallization experiments. Gypsum seeds (Sigma Aldrich, p.a. reagent) had an average diameter of 25 μm, which was estimated by particle size distribution (PSD) measurements (Analysette 22, Fritsch GmbH, Germany). The specific surface area of gypsum seeds attained from PSD measurements was 1.14 m2/g. Silica (quartz) sand (Negev industrial minerals Ltd.) of 99% purity had a measured density of 2.5162 g/cm3. Four fractions of sand particle sizes were used, with the following mean particle size for each fraction: 0.1, 0.35, 0.6, 0.7 mm, estimated by PSD measurements. 2.2. Experimental System. The crystallization kinetics experiments were carried out using a batch stirred tank crystallizer, in order to study in depth the crystallization kinetics of gypsum in the presence of sand and gypsum particles. A schematic representation of the apparatus is given in Figure 1, and a photo of the system is provided in Figure 2.

Figure 2. Picture of the stirred tank crystallizer (shown schematically in Figure 1).

The crystallizer consisted of a 1 L jacketed cylindrical glass vessel with a diameter of 10 cm, which was kept at a constant temperature of 25 °C ± 0.1 °C, by circulating water from a constant temperature water bath. The height of the solution in the vessel was 10 cm. The agitation in the crystallizer was performed by a mechanical agitator (Heidolph, model 50115) made of Teflon, with a speed range of 0−2000 rpm. In practice, the agitator was operated within the range 800−1300 rpm, since 800 rpm was the minimal speed, which enabled large particles (>0.1 mm) to be fluidized in the vessel. The impeller 14649

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calculated using OLI Stream Analyzer software (OLI Systems Inc., Morris Plains, NJ). Scanning electron microscope (SEM) micrographs were obtained on Quanta-200, SEM-EDAX, FEI Co. instrument. The samples were covered with gold to prevent surface charging. This measurement was used to characterize the sand surface and to estimate the morphology and size of gypsum crystals. The sand size distribution was determined by sieving through stainless steel sieves, 350 mm in diameter, ASTM mesh range of 25−150 (99−710 μm). The PSD of each fraction was also measured by laser particle size, Analysette 22 (Fritsch GmbH, Germany). Calculations of the specific surface area and average particle diameter of each fraction were performed in MaS control software (Fritsch GmbH, Germany), assuming a spherical shape. Samples of gypsum suspension were taken at the end of the experiment to PSD analysis in order to determine the particles size distribution of gypsum crystals that crystallized in the bulk of the solution. The analysis was performed on the same day of the crystal growth experiment in order to prevent particle agglomeration.

was a propeller with a 44 mm diameter, 2 cm height, and a blade width of 1.5 mm. Online measurements of temperature were performed using a digital thermometer (Fluke 2937062). The solution conductivity was monitored using a conductivity probes connected to a conductivity meter (M.R.C., Q023725), with the probes inserted in the crystallizer lid and immersed to a constant depth in the solution. Data of conductivity and temperature versus time were recorded with a program based on Labview (ver. 6.1). 2.3. Experimental Procedure. All crystallization experiments were carried out in a batch stirred tank crystallizer described in section 2.2. Experiments with an initial CaSO4 concentration of 48 mM were initiated by taking equal volumes (400 mL) of 96 mM Na2SO4 and 96 mM CaCl2 prestabilized at the reaction temperature (25 °C) and mixing them together (the agitation speed was 1000 rpm) in the thermostatted batch crystallizer. The conductivity probe, thermocouple, and temperature controller (contact thermometer, MS D.B.P, model 27114) were immersed in the solution. Immediately after mixing the solutions, logging of the conductivity and temperature signals was initiated. After 10 min of mixing, the desired mass of the chosen solid substrate was then added to the supersaturated solution, and the crystallizer lid was covered with a plastic (parafilm) sheet to prevent evaporation. In order to follow the crystallization kinetics, samples of 3−7 mL were withdrawn from sample port located at the crystallizer lid, using a syringe fitted with a 0.45-μm filter and then diluted to 50 mL with tripled distilled water. The samples were retained for calcium analysis. Some measurements of the solution pH were conducted by pH meter (Metrohm, 744). At the completion of each experiment, which was performed in the presence of sand, the sand particles were filtered off using a suitable sieve. The filtered sand was washed in 23 mM (S = 1.1) solution to remove any residuals of fine crystals of gypsum or adhering supersaturated solution. The sand particles were finally filtered off using the vacuum filter system, dried at room temperature, and stored for subsequent study by SEM. In some experiments, the suspension of gypsum, which was attained after sand filtration, was retained for PSD analysis. 2.4. Analytical Methods. During the experiments samples were taken for direct analysis of calcium concentration by EDTA titration using hydroxynaphthol blue as the color indicator,26 with a standard deviation of 0.1−1% for replicate analyses. In addition, the online measurements of solution conductivity were used to determine calcium concentration indirectly via calibration curves previously prepared from conductivity measurements of various concentrations of calcium sulfate in the presence of 96 mM NaCl kept at 24 °C. The dependence was linear (R2 = 0.996) over the concentration range examined. Since conductivity is affected by the experimental system (flow patterns, bubbles), the conductivity measurements necessarily provides a less accurate estimation absolute calcium concentration. However, since this measurement is continuous, it allowed a more accurate determination of the induction time based on the point where the conductivity began to drop with time. The crystallization rate was estimated from the measured consumption rate of calcium. Assuming that total calcium concentration stayed equal to that of total sulfate, species composition in the solution and thermodynamic solubility product to obtain supersaturation of gypsum could be

3. RESULTS AND DISCUSSION 3.1. Crystallization of Gypsum in the Presence of Gypsum Seeds. To validate our system for studying the crystallization kinetics of gypsum in a batch stirred tank crystallizer, a seeded crystallization experiment was carried out to determine the rate controlling step of gypsum growth for the specific agitation condition in the crystallizer. In this experiment, the initial supersaturation ratio was 2.8, and the gypsum seed concentration was 5 g/L and had an average diameter of 25 μm, which was estimated by PSD measurements (Analysette 22, Fritsch GmbH, Germany). Figure 3 displays the change in

Figure 3. Seeded crystallization in a stirred tank crystallizer. Extent of crystallization vs time for 5 g/L gypsum seeds of ∼25 μm.

the extent of crystallization as a function of time for seeded crystallization. The extent of crystallization α is commonly defined as

α=

C0 − C C0 − Ceq

(6)

where C0, C, and Ceq are the initial, time-varying and equilibrium concentrations of calcium respectively.7 On the basis of the variation of calcium concentrations over time, the growth rate, Rg, was calculated according to eq 7: 14650

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Rg = −

dC dt

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3.2. Crystallization of Gypsum in the Presence of Silica Sand. In order to investigate the crystallization phenomenon of gypsum and its mechanisms in the presence of sand, it was first compared to an unseeded experiment. Figure 5 displays a typical curve of the crystallization kinetics of gypsum in the presence of sand compared with unseeded crystallization.

(7)

The dependence of rate on the relative supersaturation driving force, σ, was then fitted to the following equation: ⎛ m ⎞2/3 n R g = k gA 0 ⎜ ⎟ σ ⎝ m0 ⎠

(8)

This expression includes modification for the change in the surface area of crystals, which should not be neglected in this case. This modification assumes that the shape of the growing crystals remains invariant during the growth process (McCabe’s ΔL law).27 A plot of the logarithm of growth rate divided by the total crystals area against the logarithm of the relative supersaturation enables evaluation of the growth order from its slope and is displayed in Figure 4.

Figure 5. Crystallization in a stirred tank crystallizer. Calcium concentration vs time: a) unseeded b) in presence of 25 g/L silica sand, average grain size 0.35 μm.

The typical curve of gypsum crystallization process in the presence of sand can be divided into two sections: section a, where calcium concentration remains constant, represents the induction period. In section b, calcium concentration starts to decrease due to several processes: primary heterogeneous nucleation with nuclei spontaneously forming on the silica sand surface, secondary nucleation from the collision of pre-existing gypsum crystals with other solid surfaces, and the growth of gypsum crystals. In section b, the concentration change rate (the slope of the curve) initially increases and then begins to decrease. The initial increase in the slope of the curve is caused by the creation of new crystals (nucleation) and the increase of the area for crystal growth at a faster rate than the rate of decline of the driving force. As the relative supersaturation driving force is reduced, the slope of the curve starts to decrease as the nucleation process becomes less significant and crystal growth rate also slows down for the same reason. From a comparison between the two experiments (sand substrate vs unseeded), it can be seen that sand has a significant effect on the crystallization kinetics of gypsum. The induction time decreases from 120 to 33 min when sand substrate was present and the solution reaches equilibrium after 200 min, while in the absence of sand the system was still far from equilibrium after 200 min. These results suggest that the surface of the sand could be used as an efficient catalyst for gypsum nucleation, which induces the crystallization rates. In order to characterize the gypsum crystals that were obtained in the presence of sand, scanning electron microscope measurements were performed on samples of sand grains that were separated from the suspension at the end of the experiment. (It should be noted that a sufficient number of samples were taken from different experiments in order to ensure the results were representative.) The resulting images are shown in Figure 6. It can be seen that most of the sand surface remained clean (Figure 6A). EDS results of these samples showed that the concentration of gypsum on sand

Figure 4. Seeded crystallization in a stirred tank crystallizer with adding seeds. Logarithm of growth rate per total crystals area (y = ln(Rg/A)) vs logarithm of the relative supersaturation (x = ln(σ)) for 5 g/L gypsum seeds of ∼25 μm. (A) the first stages of the crystallization experiment, 0 < α < 0.3. (B) the later stages of the crystallization experiment, 0.37 < α < 0.95.

It can be seen from Figure 3 that seed introduction caused a rapid increase in the extent of CaSO4 crystallization until α reached 0.4, and then it increases moderately until crystallization approaches completion (i.e., α = 1) about 80 min after seeds were introduced. The initial fast crystallization can be attributed to a secondary nucleation process in the presence of the gypsum seeds, while the subsequent moderation in crystallization can be ascribe to growth of both gypsum crystals and nuclei. Moreover, it can be seen from Figure 4A that the first stage of the crystallization process has a growth order, which is higher (n = 2.6) than the growth order measured for the later stages of the crystallization experiment (n = 2.3). These trends were also observed in another study24 under similar conditions (5 m2/L of gypsum seeds, S = 1.8, T = 30 °C). In that study, the high reaction order for early stages of crystallization were ascribed to surface nucleation processes, which obscured second order crystal growth kinetics found when sufficient seeds were present. For the region that was ascribed to crystal growth (0.37 < α < 0.95), a linear relation was obtained for log(Rg/A) vs log(σ) with a slope of 2.3 (see Figure 4B). This result is in agreement with the early gypsum crystallization studies, in which the growth order was 2.27,28 A second order growth rate suggests that under the hydrodynamic conditions existing in this crystallizer (agitation speed of 1000 rpm) the growth rate of gypsum was surface reaction controlled. 14651

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Figure 6. Scanning electron microscope images of silica sand grain with gypsum crystals on its surface, taken at the end of the crystallization experiment (with sand mass concentration of 25 g/L, and d = 0.35 mm) from the stirred tank crystallizer: (A) the whole grain (B) enlargement of the area that is circled in image A.

those that grew on the sand surface indicates that the crystals appearing in the bulk were smaller. While this result could be ascribed to secondary nucleation injecting new crystals into the bulk, there is the possibility that the difference may also arise from the different measurement techniques used for assessing crystal size on the sand solids versus suspended crystals in the bulk. 3.3. Effect of the Initial Supersaturation on Gypsum Crystallization Kinetics with Sand. As was previously explained, the crystallization of gypsum in the presence of sand begins after an induction period, through a primary heterogeneous nucleation process. According to the classical theory of nucleation, the rate of nucleation is affected by the initial driving force. Therefore, the influence of the initial supersaturation on the crystallization of gypsum in the presence of sand was examined. A series of five batch crystallizer runs were carried out with gypsum S values ranging from 1.8 to 2.7, and the induction time was determined by when the initial plateau in calcium concentration ended with onset of decline in its concentration. These induction times were then plotted versus the initial supersaturation and the results are shown in Figure 8, which displays a linear relation between log(tind) and 1/log2(S) as was expected from the classical theory of primary heterogeneous nucleation (see eqs 3−5). On the basis of this relation, the interfacial tension between the developing crystalline surface and the supersaturated solution was calculated from the slope of the curve. A value of 7 mJ/m2 was obtained. The value of the interfacial tension obtained in the present system is lower than the value of 37 mJ/m2, reported in the literature, for relative supersaturations of 1−4 and temperatures between 25−90 °C.30 It can thus be concluded that the presence of sand could decrease the activation energy for heterogeneous nucleation by decreasing the interfacial tension and therefore increase the nucleation rate with respect to the unseeded crystallization as was shown previously (see section 3.2). 3.4. Effect of Sand Grain Number Concentration on the Crystallization Kinetics. In order to estimate the effect of number concentraion of sand grains, experiments were

surface is about 1%. Moreover, gypsum crystallized at certain locations of the sand surface, where primary heterogeneous nucleation is favored. These nucleation centers were located on the roughness feature of sand surface and on regions of pores, where the energetic barrier for heterogeneous nucleation is lower compared with the smooth regions of sand surface. Figure 6B displays an enlargement image of the circled region appears in Figure 6A. It can be seen that crystals display the morphologies of plates and needles, which are typical of gypsum,29 and that the crystal size is in the range of 5−20 μm. However, visual inspections revealed that most of the gypsum, which crystallized from the solution in the presence of sand, appeared in the bulk of the solution. Figure 7 shows the results

Figure 7. Particle size distribution of bulk gypsum crystals from batch crystallization experiment in the presence of sand (mass concentration of 25 g/L, d = 0.35 mm), taken at the end of the experiment.

of PSD measurement for these gypsum crystals, which were taken at the end of the crystallization experiment. As can be seen, the crystals size is in the range of 3−20 μm, where the average size is 9 μm. Moreover, a shoulder appeared in the distribution curve in the size range of 5−6 μm. As will be explained below, this indicates that in the present system a special nucleation mechanism is involved, which differs from that typical of crystallization from solutions. Comparison of the size distribution of crystals in the bulk of the solution with 14652

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size was also studied while controlling for total grain surface area (0.8 m2/L). This is shown in Figures 10 and 11.

Figure 8. Crystallization in the presence of sand in a stirred tank crystallizer. Logarithm of induction period vs the inverse of the square of the logarithm of the supersaturation ratio. Figure 10. Crystallization in a stirred tank crystallizer. Calcium concentration vs time for a constant sand grains surface area of 0.8 m2/ L (A) 6 g/L, d = 0.1 mm, (B) 25 g/L, d = 0.35 mm.

conducted with the same average grain size and different grain mass concentrations. The results for sand grains of a constant average grain size of 0.35 mm and 0.6 mm are displayed in Figure 9.

Figure 11. Crystallization in a stirred tank crystallizer. Calcium concentration vs time for a constant sand grains surface area of 0.8 m2/ L (A) 25 g/L, d = 0.35 mm, (B) 52 g/L, d = 0.6 mm.

Figure 9. Crystallization in a stirred tank crystallizer. Calcium concentration vs time for a sand grain size of 0.35 mm and sand mass concentration of (A) 5 g/L, (B) 25 g/L, and for a sand grain size of 0.6 mm and sand mass concentration of (C) 25 g/L, (D) 52 g/L.

It can be seen from Figures 10 and 11 that as the grain size increased, the crystallization kinetics became faster. The induction period became shorter, and the crystallization rate became higher. These results were obtained even though the number density of sand grains was smaller for the experiments, in which the grain size was larger. The number density for 25 g/L of 0.35 mm sand grains is 10 times lower than it is for 6 g/ L of 0.1 mm diameter sand grains, while the number density for 52 g/L of 0.6 mm diameter sand grains is 2.4 times lower than it is for 25 g/L of 0.35 mm diameter sand grains. Hence, this result showed that grain size was far more significant than number density in the range of parameters examined in these experiments. The strong effect of sand grain size on the gypsum precipitation kinetics can be explained in terms of the role of collisions as discussed in section 3.5. The larger the grain size, the larger the momentum per collision (or the intensity per collision) and therefore the higher the probability that enough energy is provided to effect the ejection of crystal from the sand surface into the bulk solution. Similarly, with greater momentum transfer per collision, the higher the probability that sand−crystal collisions will cause breakage of these bulk solution crystals. This in turn will enhance rates of both nucleation processes (primary heterogeneous and secondary nucleation) and crystal growth, as previously explained. 3.6. Effect of Grain Size at Constant Sand Mass Concentration. The effect of sand grain size was also

It could be argued that as the number density of sand grains is increased, the probability for sand−sand and sand−crystal collisions is also correspondingly increased. Increasing the frequency of sand−sand collisions could enhance the rate at which gypsum crystals that initially formed on the sand surface by primary heterogeneous nucleation are ejected into the solution. This ejection of crystals would clear the preferential site of heterogeneous nucleation and therefore enable the increase of the heterogeneous nucleation rate. At the same time, increasing the number of crystals ejected into the solution could increase the rates of secondary nucleation and crystal growth. Moreover, increasing the frequency of sand−crystal collisions can cause a breakage of crystals in the bulk of the solution. This breakage can increase the total surface area of crystals and thereby increasing the overall growth rate. It is also known that broken crystal surfaces “heal” rapidly by fast growth rate and then proceed to grow at a much slower rate.23 This phenomenon has indeed been reported for gypsum growth.31 This suggests that increasing the frequency of collisions may cause enhanced breakage and “healing” of gypsum crystals and by that allows relatively high crystallization rates. 3.5. Effect of Grain Size at Constant Sand Surface Area. Since volumetric crystal growth rates are proportional to the available crystal growth area (see eq 8), the effect of grain 14653

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change over time, as a result of nucleation and growth of gypsum on the sand surface, as was previously discussed. The effect of recycling of sand grains on the crystallization kinetics was therefore examined in a stirred tank crystallizer. Figure 13

examined for a wider range of grain sizes at a constant mass concentration of grains. Two values of mass concentration were examined. Figure 12 displays the influence of sand grain size for two values of mass concentration of 25 and 5 g/L.

Figure 12. Crystallization in a stirred tank crystallizer. Calcium concentration vs time for a constant sand mass concentration of 25 g/ L and grain size of (A) 0.1 mm, (B) 0.35 mm, (C) 0.6 mm, (D) 0.7 mm, and a constant sand mass concentration of about 5 g/L and grain size of (E) 0.35 mm (F) 0.1 mm.

Figure 13. Crystallization in a stirred tank crystallizer. Calcium concentration vs time for sand mass concentration of 25 g/L, and grain size of 0.35 mm (A) experiment 1, (B) experiment 2, (C) experiment 3.

As can be seen from Figure 12, for a constant mass concentration of 25 g/L, the crystallization kinetics was higher for the larger grain size even though the number density was lower for the larger grain sizes. However, the effect of grain size on the kinetics was less significant than for the experiment run at constant surface area of sand grains (see section 3.5 and Figures 10 and 11). This difference was due to the fact that for a constant mass concentration, the difference in the grain number was bigger than for a constant grain surface area. It can be seen that for the lower total mass concentration (5 g/L), the crystallization rate was higher for the larger grain sizes, but the induction time was shorter for the smaller grains. The longer induction time at lower mass concentration (5 g/L) for the larger grains indicated that the grain number effect was more significant than the grain size effect. This was so because the much larger number of collisions per unit time leads to a higher probability of generating the initial nuclei needed to promote crystal growth. The number of the larger grains (0.35 mm) was 43 times smaller than the smaller grains (0.1 mm). However, after the formation of nuclei, the suspension total number density (sand grains and bulk gypsum crystals) increased. Then the larger size grains again had an advantage over the smaller grain by enhancing the momentum of collisions between sand grains and bulk gypsum crystals promoting more rapid secondary nucleation. Thus the crystallization rate was eventually higher for the larger grain sizes. Moreover, SEM scans of sand samples taken at the end of these crystallization experiments revealed that the sand surface of the largest grains (d = 0.7 mm) was completely free of gypsum, while for all of the other sand grain sizes, gypsum was detected on the sand grain surfaces. This observation is consistent with the hypothesis that as the grain size increased, the intensity per unit collision increased leading to an increased rate of crystal ejection into the solution with resulting higher crystallization rates. 3.7. Recycling of Sand Grains. If the crystallization of gypsum in the presence of sand is carried out as a continuous process in a fluidized bed crystallizer (FBC), the sand substrate should in principle be maintained in the crystallizer until a desired crystal size is attained. Therefore, the sand surface will

presents a plot of calcium concentration against time for three experiments, in which the sand substrate was taken at the end of each experiment and reused in the subsequent experiment. The grain size was 0.35 mm, and the mass concentration was 25 g/L. The crystallization rate, expressed as the derivative of concentration by time (dC/dt), as a function of the relative supersaturation, σ, for the first and second experiments is shown in Figure 14.

Figure 14. Crystallization in a stirred tank crystallizer. Crystallization rate, dC/dt vs relative supersaturation, σ for sand mass concentration of 25 g/L, and grain size of 0.35 mm (A) experiment 1, (B) experiment 2.

It can be seen from Figure 13 that the use of recycled sand (Figure 13B,C) increased the crystallization kinetics compared with the first experiments (Figure 13A), in which the sand was “clean”. The induction time shortened from 32 min in the first experiment to 8 min in the second and the third experiments. Note that the kinetics for the second and the third experiments was almost unchanged. In Figure 14, it can also be seen that for a constant relative supersaturation the growth rate was higher for the recycled sand compared with the rates obtained for the “clean” sand. Eventually, the time to reach supersaturation ratio of 1.1 was 125 min for the first experiment compared with only 60 min for the second experiment. 14654

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Figure 15. Scanning electron microscope images of silica sand (sand mass concentration of 25 g/L, and d = 0.35 mm), taken before each crystallization experiment, performed in a stirred tank crystallizer: (1) the first experiment, (2) the second experiment, (3) the third experiment.

These results suggest that the pre-existing presence of gypsum crystals on the used sand surface accelerates the overall crystallization kinetics by providing initially available gypsum surface for crystal growth, and initial crystals population that can feed the secondary nucleation process, which proceeds due to the ejection of crystals into the bulk solution as a result of the collisions among the sand grains. This contrasts with the case of “clean sand”, in which gypsum must first nucleate in a primary heterogeneous process and only then can lead to secondary nucleation and crystal growth processes. Scanning electron microscope images of the sand surface before each crystallization experiment are shown in Figure 15. Examination of several samples of sand, which were taken prior to the second and the third experiment, revealed that while most of the sand surface remained clean, gypsum was crystallized at preferential nucleation sites. Comparing micrographs 2 and 3 in Figure 15, it seemed that there were no new crystallization sites but expansion of existing centers by crystal growth. Comparing these micrographs, we saw that the crystallization sites were expanded from 30 to 60 μm. It should also be noted that from examination of low magnification SEM micrographs (not shown), taken of sand samples before and after each subsequent run, it is clear by inspection that no noticeable attrition of sand particles occurred. These results seem to suggest that once an initial quantity of gypsum is present on the sand grains in the system at the beginning of the crystallization process, its absolute concentration has little influence on the crystallization kinetics. This observation could be explained by an autocatalytic process occurring when crystals are ejected from the sand surface into the solution. In

this autocatalytic process, every formed crystal produces many other additional crystals; thus, the initial surface concentration of crystals on the sand grains does not significantly affect the kinetics after a threshold is past. 3.8. Proposed Mechanism for Crystallization of Gypsum in the Presence of Sand. In light of the above experimental results, we can now propose a reasonable scheme of autocatalytic mechanisms driving the crystallization of gypsum in the presence of sand. The mechanism is based on the nature of the collisions among the bulk macroscopic particles (sand grains and gypsum crystals) suspended in the crystallizer. The crystallization process is initiated after the induction period by primary heterogeneous nucleation, which occurs on energetically favored regions of the silica surface (kinks, corners, and other roughness features). As a result of collisions among the sand particles, the nuclei are then ejected from the surface into the solution. This enables secondary nucleation and crystal growth processes to proceed simultaneously with the ongoing heterogeneous nucleation. The secondary nuclei are produced by collisions among particles (sand−sand, sand− gypsum, or gypsum−gypsum collisions), particle−agitator contacts, and shear forces in the solution (see Figure 16). These processes qualitatively explain how overall crystallization kinetics of gypsum in the presence of sand was affected by the sand properties: the kinetics increased with increasing sand grain size or sand grain number concentration (see Figures 9−12). Moreover, a unique PSD of the crystallizing gypsum, with a shoulder in size ranges of 5−6 μm, was obtained (see Figure 7). The shoulder suggests that different mechanisms 14655

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(22 mM < CCa < 37 mM) comparable rates to those measured in the gypsum seeded experiment. It is appropriate that future work should extend the present research to study the effects of varying scaling ions and other ions typically presented in RO brines.

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AUTHOR INFORMATION

Corresponding Author

*E-mail: [email protected]. Notes

The authors declare no competing financial interest.

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ACKNOWLEDGMENTS NATO Science for Peace SfP Contract: 982481, Chief Scientist of the Ministry of Israeli Trade and Industry - High Tech Incubator Program, and Rotec Ltd., provided financial support. Dr. Yitzhak Ladizhansky provided invaluable technical assistance.

Figure 16. Illustration of the mechanism for the crystallization of gypsum in the presence of sand.

were involved in the formation of the particles throughout the experiment. The most obvious explanation is that the large particle size reflects crystal nuclei with a longer age, which have already had time to grow, whereas the smaller shoulder reflects those crystal grains that were most recently formed and ejected. This hypothesis is supported by the micrograph in Figure 6b wherein larger crystals with a size of ∼20 μm are seen next to isolated smaller crystals (see at right of this micrograph) with size of approximately 5 μm. The alternative explanation would be that the shoulder reflects breakage processes that occurred simultaneously with crystal growth of the nuclei ejected from the sand grains. This latter explanation would be plausible if groups of crystals (such as the cluster in Figure 6b, are ejected as a unit from the sand grain and some are broken apart in subsequent collisions.

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4. CONCLUSIONS Extensive investigation of the kinetics of gypsum precipitation in the presence of sand substrate was performed in a batch stirred tank crystallizer. In a preliminary gypsum seeded experiment, a second order growth rate was obtained. This result suggests that for the hydrodynamic conditions existing in the crystallizer (agitation speed of 1000 rpm), the growth rate of gypsum is surface reaction controlled. Silica sand had a significant effect on the crystallization kinetics of gypsum. In the presence of sand, both nucleation and crystal growth are much faster than in the unseeded experiment. Hence, the sand can be used as an efficient catalyst for gypsum precipitation from supersaturated solutions such as RO concentrates. A PSD of the bulk gypsum crystals, with a shoulder in size ranges of 5−6 μm was characteristic of gypsum crystallization in the presence of sand. Under the examined range of sand parameters, the kinetics can be improved by increasing the grain size or grain number concentration with grain size having a dominant effect. To explain these results, a primary heterogeneous-secondary nucleation sequence was proposed to describe the crystallization of gypsum in the presence of sand: after initial small size crystals formed on the sand grain surface by primary heterogeneous nucleation process, collisions among the sand particles eject nuclei from the surface into the solution. This enables secondary nucleation (due both to crystal−crystal collisions and shear forces between crystals-bulk solution) and crystal growth processes to proceed simultaneously with the ongoing heterogeneous nucleation. The sand experiments with the fastest overall rates of gypsum precipitation showed over a significant range of concentrations

NOMENCLATURE A = crystals surface area (m2) AC = pre-exponential coefficient in eq 3 (nuclei m−3 s−1) C = solute concentration (mol L−1) f = correction factor in eq 3 J = primary nucleation rate (nuclei m−3 s−1) Ksp = solubility product (molν L−ν) kg = overall growth rate (mol(1−n) L(n−1) m−2 s−1) m = mass of crystals (kg) NA = Avogadro’s number (6.02214 × 1023 mol−1) n = growth order R = gas constant (8.314472 J mol−1 K−1) Rg = growth rate (mol L−1 s−1) S = supersaturation ratio T = temperature (K, °C) t = time (s) Vm = molar volume (m3 mol−1)

Greek Letters

α - extent of crystallization in eq 6 β - geometric factor in eq 3 γ - interfacial tension (J/m2) θ - contact angle (°) ν - total number of ions per formula unit of the electrolyte σ - relative supersaturation

Subscripts

eq - at equilibrium gyp - gypsum ind - induction 0 - at time t = 0 Superscripts

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x - number of cations y - number of anions

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