Feedback Control of Multicomponent Salt Crystallization - Crystal

Article pubs.acs.org/crystal

Feedback Control of Multicomponent Salt Crystallization Daniel J. Griffin, Yoshiaki Kawajiri,* Martha A. Grover, and Ronald W. Rousseau School of Chemical & Biomolecular Engineering, Georgia Institute of Technology, Atlanta, Georgia 30332-0100, United States S Supporting Information *

ABSTRACT: A closed-loop strategy is developed for controlling batch cooling multicomponent crystallization. The strategy represents the sequential application of two established feedback control techniques: direct nucleation control followed by supersaturation control. Experimental results show that such a control scheme produces larger crystals (compared to linear cooling crystallization with the same batch time). In using this scheme to control the crystallization of a double salt from a solution containing sodium nitrate and sodium sulfate, we demonstrate the application of supersaturation control to a multicomponent salt crystallizationwhich requires knowledge of the solubility as a function of temperature, the ability to monitor concentrations in a multicomponent solution, and an appropriate expression for the driving force for crystallization of a salt. In this paper, a methodology for rapidly identifying the solubility of a solute in a multicomponent solution is presented and a new expression for supersaturationtermed the molar supersaturationis advanced as a measure of the driving force for crystallization of salts. lead to unacceptable radioactivity levels of the “clean” crystal product stream. In this study, we examine a batch cooling crystallization process for removing sulfate together with nitrate as a double salt from a multicomponent electrolytic solution. To achieve reliable separation, the crystallization must be controlled so that large crystals are produced. A number of open-loop and closedloop strategies have been developed for controlling crystallization operations to produce crystals with the desired characteristics.8−14 Here we examine a closed-loop strategy for cooling crystallization that uses measurement feedback to first guide an “internal seeding” operation and then moderate the thermodynamic driving force for crystallization. The control strategy for internal seeding follows from the socalled direct nucleation control (DNC) strategy, which uses feedback on the number of crystals in solution to guide crystallization−dissolution cycles and control the number of crystals produced.15−18 In the present work, only a single crystallization−dissolution loop is applied at the onset to generate a moderate number of seed crystals. This type of

1. INTRODUCTION Waste immobilization is an important part of the nuclear waste cleanup process at the Hanford site and elsewhere.1 That is, once the waste is removed from current storage tanks, it must be processed and converted to an immobile form. The current preferred method for waste immobilization is vitrification solidifying the waste in a glass matrix. However, the presence of many different components in the waste stream makes vitrification a challenging and expensive prospect. Sulfates are particularly problematic in waste solutions as they are hard to incorporate in glass and can disrupt the vitrification process.2,3 To avoid complications, the sulfate concentration in the waste stream fed to the vitrification operation must be kept below threshold levels. This can be achieved by diluting the feed stream or, preferably, by removing sulfate from the waste stream prior to vitrification. Sulfate can potentially be separated from nuclear waste via salt crystallization.4−7 In a crystallization−separation process, solid crystals are first formed and then filtered. Accordingly, the separation is dependent on the ability to partition the developed crystals from the mother solution, which, in turn, largely depends on the size and shape of the crystals. Effective solid−liquid partitioning is especially important for separation from nuclear waste, as small amounts of residual solution can © 2014 American Chemical Society

Received: September 11, 2014 Revised: October 28, 2014 Published: November 18, 2014 305

dx.doi.org/10.1021/cg501368y | Cryst. Growth Des. 2015, 15, 305−317

Crystal Growth & Design

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Figure 1. (a) Optical microscope image of produced salt crystals. (b) Infrared absorbance spectrum for the salt crystals (dissolved in water). salt. In addition, quantitative analysis suggests that these anions exist in solution in a roughly 1:1 mol ratio, as expected for the salt Na3SO4NO3·H2O. Solutions were prepared by dissolving 99% ACS grade sodium sulfate and sodium nitrate from Alfa Aesar in DI water. The sodium sulfate contains, at a maximum, the following impurities: Insoluble matter 0.01%, Cl 0.001%, N 5 ppm, PO4 0.001%, heavy metals (as Pb) 5 ppm, Fe 0.001%, Ca 0.01%, Mg 0.005%, and K 0.01%. The sodium nitrate contains, at a maximum, the following impurities: Insoluble matter 0.005%, Cl 0.001%, IO3 5 ppm, NO2 0.001%, PO4 5 ppm, SO4 0.003%, Ca 0.005%, Mg 0.002%, heavy metals (as Pb) 5 ppm, and Fe 3 ppm. In nuclear waste mixtures, sodium, sulfur, nitrogen, hydrogen, and oxygen atoms exist as stable isotopesthe salts in question are therefore nonradioactive themselves. The radioactive components in Hanford waste are primarily the following: Sr-90/Y-90, Tc-99, Cs137/Ba-137m, Np-237, and Pu-239. However, radioactivity is not expected to effect the crystallization process, and no radioactive isotopes are present in the model solution. The primary means by which the salt product stream may be contaminated by radioactive components is through imperfect solid−liquid partitioning. In this work, we therefore examine methodologies for crystallizing the double salt from the model solution under the assumption that larger crystals will facilitate improved solid−liquid separation and that the operations developed for this system may be applied to more complicated radioactive solutions. 2.2. Crystallization System. Batch cooling crystallization experiments were run using an OptiMax workstation from Mettler Toledo. The system (shown in Figure 2) can be integrated with a number of

strategy, referred to as internal seeding, was proposed by Chew et al.19 to reduce process variation and used by Kim et al.20 to reduce inclusion and improve product quality. After internal seeding, attenuated total reflectance-Fourier transform infrared (ATR-FTIR) absorbance measurements are used to monitor the solution composition and inform temperature adjustments that keep operations at a set supersaturation level within the metastable zonewith the aim of promoting crystal growth over nucleation. This type of feedback strategy is referred to as supersaturation control (SSC) and has been successfully applied to a number of single-component crystallizations to produce larger crystals.21−28 The overall control scheme, internal seeding followed by supersaturation control, was suggested by Nagy and Braatz in a review on crystallization control,9 and a similar strategy was used by Simone et al.29 to control the polymorphic purity. In this article we review the basic concepts behind DNC and SSC, discuss extensions necessary to apply SSC to salt crystallization from a multicomponent solution, and finally present experimental results that show that internal seeding followed by SSC can be applied to the studied system to improve the crystal size.

2. MATERIALS AND EXPERIMENTAL SETUP 2.1. Model Multicomponent Electrolytic Solution. An aqueous solution containing sodium sulfate and sodium nitrate is used as a model multicomponent electrolytic solution. More specifically, this study focuses on the crystallization of the hydrated double salt, Na3SO4NO3·H2O, from aqueous solutions initially containing 7.25 g of dissociated Na2SO4 and 110 g of dissociated NaNO3 per 100 g of water. The initial composition is selected to be representative of the salt content in nuclear waste.4−6 The formation of the double salt, Na3SO4NO3·H2O, was identified by optical microscope images compared to images given by Herting et al.30 and confirmed by ex situ infrared measurements which probe the salt composition. The ex situ infrared measurement procedure was as follows: first, infrared spectra were recorded for pure water; next 5 g of the recovered salt was dissolved in 20 mL of water; finally, after the salt fully dissolved, the infrared spectra was recorded for the concentrated salt-water solution. Figure 1a shows an optical microscope image of the salt crystals, while Figure 1b shows a typical infrared absorbance spectrum measured for the concentrated salt-water solution obtained by the above-mentioned procedure. The infrared spectrum for the concentrated water-salt solution shows distinct peaks characteristic of both nitrate and sulfateindicating the presence of these anions in the

Figure 2. OptiMax workstation equipped with ATR-FTIR and FBRM probes. 306



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Figure 3. (a) Attenuated total reflectance Fourier transform infrared (ATR-FTIR) absorbance measurement. (b) Typical infrared absorbance spectra for nitrate and sulfate anions in water at concentration levels representative of nuclear waste solutions.

Figure 4. (a) Focused-beam reflectance measurement (FBRM). (b) Example chord length distribution measured by FBRM.

Figure 5. Direct nucleation control concept. (a) Illustration of typical time profiles for temperature and total chord counts under DNC. (b) Illustration of the crystallization trajectory on a phase diagram (temporal direction indicated by the arrow). Measurement points associated with a change in operation (from cooling to heating or visa-versa) are highlighted with a circle, square and triangle. advanced online measurement systems and provides the framework for feedback control. In addition to standard sensors for monitoring temperature and mixing intensity, the workstation was equipped with an ATR-FTIR measurement system and also with focused-beam reflectance measurement (FBRM) technology from Mettler Toledo. ATR-FTIR, FBRM, and temperature measurements are recorded by iC software and exported in real-time to MATLAB for processing and set-point determination. 2.2.1. Attenuated Total Reflectance Fourier Transform Infrared (ATR-FTIR) Absorbance. With ATR-FTIR the solution infrared absorbance can be measured rapidly in the presence of suspended solids (idea illustrated in Figure 3a).31 As sulfate and nitrate anions absorb infrared lighta typical spectra is given in Figure 3bthe composition of the studied multicomponent solution can be inferred from infrared absorbance measurements made in real-time. This

requires a calibration model to be constructed beforehand; the calibration strategy used here follows from previously reported work.32 Further details on the model accuracy can be found in the Supporting Information Section S.1. 2.2.2. Focused-Beam Reflectance Measurements (FBRM). Focused-beam reflectance measurements provide real-time insight on the number and size of crystals present in solution. As a focused light beam scans across a solution, suspended crystals cause reflections. From the duration of reflection, the chord lengthi.e. the distance scanned during continuous reflectionis calculated. This principle is illustrated in Figure 4a. The number of chord counts and the chord length distribution provide measures related to the number of crystals and the crystal size distribution, respectively. For the instrument used, the detection range is 1−1000 μm. 307



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3. METHODS: FEEDBACK SCHEMES FOR CONTROLLING CRYSTAL SIZE 3.1. Direct Nucleation Control (DNC). Direct nucleation control refers to an operational strategy that uses successive crystallization−dissolution cycles to control the number of crystals produced and ultimately yield larger crystals.16−18,33 The logic behind this control scheme is as follows. The total amount of mass that can be crystallized from a solution by cooling is dictated by the thermodynamics of that solution. For operations that start at the same solution composition and temperature and end in equilibrium at a given temperature, the crystal yield is fixed. That is, the total mass crystallized is independent of the specific process path. For such an operation, the average crystal size at the end of the run is determined by the number of crystals formed; i.e. large crystal numbers means small sizes and vice versa. The DNC strategy relies on feedback from measurements related to the number of crystals suspended in solution and requires little prior information about the crystallization system. One measure that reflects the number of crystals suspended in solution is the total number of chord counts recorded by FBRM.34,35 Figure 5 illustrates a simple DNC feedback strategy using this measure: the solution is first cooled at a constant rate until primary nucleation causes the total chord counts to increase above a selected high level; the solution temperature is then increased at a constant rate to drive dissolution until the chord count drops below a selected low level; this initiates cooling again and the operation is repeated until the solution temperature reaches the desired final temperature. The success of direct nucleation control in producing larger crystals relies on the dissolution of fines during heating and growth of existing crystals in successive cooling stages. As crystallization and dissolution kinetics are not known precisely, the specifics of the operational strategy (chord count levels, cooling and heating rates) must be selected empirically or heuristically. Lower selected count levels may produce larger crystal sizes;18 however, this likely comes at the cost of additional crystallization−dissolution cycles and longer batch times. 3.2. Supersaturation Control (SSC). The objective of supersaturation control is to moderate the thermodynamic driving force for crystallization and, in doing so, promote crystal growth over nucleation. This idea has frequently been applied to control the crystallization of nondissociated solutes from single-component solutions. For such systems, the relative supersaturation is often used as a measure of the driving force for crystallization: σ≡

C − C*(T ) C*(T )

Figure 6. Block diagram of the cascade feedback control scheme used to achieve a fixed relative supersaturation.

⎛ C − C*(T ) ⎞ TSP = arg⎜σSP = ⎟ C*(T ) ⎠ T ⎝

(2)

In this expression, σSP is the selected relative supersaturation set-point, C is the measured concentration of the (nondissociated) solute in solution, C*(T) is the solubility concentration as a function of temperature, and TSP is the determined temperature set-point. The inner loop then uses proportional-integral (PI) feedback control on temperature to manipulate the jacket temperature (TJ) such that the solution temperature moves toward the setpoint determined by eq 2 in the outer loop. The result of the SSC scheme is illustrated in Figure 7. As crystallization proceeds, underlying crystallization kinetics dictates the rate at which the concentration of solute in solution decreases. The controller simply responds to each new concentration measurement, decreasing the solution temperature if relative supersaturation is below the set-point and increasing the solution temperature if the relative supersaturation is above the set-point. 3.2.1. SSC for Salt Crystallization from a Multicomponent Solution. When a salt dissolves in solution it dissociates. Relative supersaturation, however, is a measure of the driving force for crystallization of a nondissociated solute. We therefore advance a newalbeit similarquantity termed molar supersaturation as a measure of the driving force for crystallization of a dissociated solute. For a generic salt with the following crystallization/dissolution expression A vA BvB ↔ vA A + vB B     ions in solution

solid salt

the molar supersaturation is defined as follows:

(1)

where σ is the relative supersaturation, C is the solute concentration in solution, and C*(T) is the solubility concentration at the solution temperature, T. To regulate the relative supersaturation during cooling crystallizations, the temperature is adjusted with each new concentration measurement according to the cascade feedback loop shown schematically in Figure 6. In the outer loop, feedback on concentration is used to determine the temperature that would move the relative supersaturation to the desired level if the concentration remained fixed:

σA v

[X ]

B A vB

≡

XA vA XB vB − (X *A (T ))vA (X *B (T ))vB (X *A (T ))vA (X *B (T ))vB

(3)

where σAvABvB[X] is the molar supersaturation of the salt, XA and XB are the mole fractions of the dissociated salt components in solution, and X*i denotes the solubility mole fraction of each component. Theoretical development of molar supersaturation is presented in the Supporting Information Section S.2. The development assumes that the mole fraction of each solution component is close to the solubility mole fraction. This 308



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Figure 7. Supersaturation control concept. (a) Illustration of time profiles for temperature and relative supersaturation under SSC. (b) Illustration of the same operation on the phase diagram (temporal direction indicated by the arrow). Consecutive measurements used for feedback control are indicated with a circle, square, and triangle.

Figure 8. Cascade feedback scheme used to control the molar supersaturation of the double salt, Na3SO4NO3·H2O.

solution can be controlled during crystallization by manipulating temperature according to the same type of cascade feedback strategy outlined in the previous section. To apply this feedback scheme, the mole fraction (or equivalently, the concentration in mass solute per mass solvent units) of each salt component in solution must be measured simultaneously. The temperature set-point is then selected according the expression for molar supersaturation. For crystallization of the hydrated double salt, Na3SO4NO3·H2O, from the model multicomponent solution the cascade feedback scheme used is shown in Figure 8. 3.2.2. Initial Operations for Supersaturation Control. During supersaturation control, the controller adjusts the jacket temperature when the measured supersaturation deviates from the set-point. Accordingly, the temperature is successively varied to maintain a constant supersaturation when crystallization removes solute from solution. However, starting from a clear solution, the level of supersaturation selected as the setpoint may not be sufficient to drive primary nucleation, and thus the temperature will remain fixed and the crystallization will not proceed. To circumvent this issue, the temperature can first be decreased at a constant rate until nucleation is detected. Once nucleation initiates crystallization, the supersaturation controller is activated. However, the objective of supersaturation controlto mitigate nucleation and yield larger crystalscan be undermined by the initial linear cooling operation. As mentioned in Section 3.1, the total mass crystallized is dictated by the solution thermodynamics. Thus, applying linear cooling to drive primary nucleation may cause

assumption holds for the crystallizations given later in the paper. In order to implement supersaturation control, the solubilitytemperature relationship must be characterized a priori. For a simple solution containing only a single solute, the solubility function, C*(T), used to calculate the relative supersaturation can be found experimentally using the so-called polythermal method.36 When multiple solutes are present in solution, characterizing the solubility by the polythermal method becomes an experimentally arduous taskrequiring many experiments at varying concentration levels of each solute. In the Supporting Information Section S.3, a more efficient method for collecting the requisite solubility data for a multicomponent solution is proposed. This method, which we term the solubility trace method, exploits the closed mass balance in a batch cooling crystallization process and uses in situ monitoring to track the solution composition during temperature-driven dissolution of the solute of interest and thereby the solubility curve. In the present work, the solubility trace method is used to collect the solubility data required to implement supersaturation control prior to each run. In identifying a new solubility curve by this method prior to each new crystallization, the batch-to-batch variability in the solution thermodynamics (due to small compositional changes) as well as run-specific bias in the concentration measurements are accounted for. Given knowledge of the solubility-temperature relationship, the molar supersaturation of a salt in a multicomponent 309



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DNC can be applied to control, qualitatively, the number of crystals produced and thereby yield large crystals; however, multiple crystallization−dissolution cycles are typically required, which could result in long batch times. SSC, on the other hand, can be used to moderate the driving force for crystallization to promote growth over nucleation and thereby efficiently yield large crystals; however, this control scheme is only expected to be successful when started from a solution already containing a moderate number of seed crystals. To efficiently produce large crystals without making material additions, we examine an alternative feedback control scheme which applies a DNC-like scheme for “internal seeding”19,20 followed by supersaturation control. This combined operation is expected to increase the average crystal sizefirst by the dissolution of fines to reduce the number of “seed” crystals and then by the promotion of growth over nucleation.33 The examined control scheme can be described in a stepwise manner as follows: (1) starting from a clear solution, the temperature is reduced at a constant rate until an increase in chord counts indicates primary nucleation; (2) on the detection of nucleation, the temperature is increased at a constant rate to dissolve most of the generated crystalsreturning the counts to near baseline levels; (3) finally, the cascade feedback strategy given in Section 3.2 is applied to the crystal-containing solution. The first two steps make up the “internal seeding” operation, while the third step listed represents the application of supersaturation control to a seeded solution. This control scheme is illustrated in Figure 10.

the formation of many nuclei and result in small crystals even if the supersaturation control algorithm is successful in promoting growth for the remainder of the run. Alternatively, the solution can be seeded to allow crystallization to occur by secondary nucleation or growth at lower supersaturation. The effect of the two different initial operations on the phase-diagram trajectory is illustrated in Figure 9.

Figure 9. Illustration of concentration−temperature profiles for crystallization under supersaturation control with different initial operations. The solid blue curve illustrates a typical phase diagram profile when linear cooling is initially applied past the supersaturation set-point to drive primary nucleation. The black dashed curve illustrates the typical phase diagram profile when seeds are used to initiate crystallization at the desired supersaturation level.

4. RESULTS AND DISCUSSION In this section, the proposed control scheme is compared against simple linear cooling. Dynamic measurements show significant differences in the crystallization kinetics under the two operating policies. Sieve and image analyses indicate that the control scheme produces larger crystals than simple linear cooling with the same batch time. To assess run-to-run variability, multiple controlled and linear cooling runs were implemented. A detailed analysis is presented for a single controlled and linear cooling run in Section 4.1. Key results are given for the replicate runs in Section 4.2. 4.1. Linear Cooling Crystallization vs Controlled Crystallization. 4.1.1. Time Profiles. Figure 11 shows the time profiles for temperature, chord counts, and the solution

While seed crystals can promote crystallization at lower supersaturation, the crystal product is now largely linked to the seeding strategy. Additionally, for nuclear-waste applications, we are motivated to explore operations that can be controlled remotely and do not require material additions. Therefore, we have examined an operation that uses “internal seeding” prior to supersaturation control. 3.3. Proposed Control Strategy: Internal Seeding Followed by SSC. In the previous two sections we discussed two established feedback control schemes for improving the crystal size, but noted drawbacks for the current application.

Figure 10. Internal seeding followed supersaturation control. (a) Illustration of the temperature and chord count time profiles under the proposed control scheme. (b) Illustration of the phase diagram trajectory under the proposed control scheme. The three procedural steps listed in the text are enumerated. Points on the trajectory that mark a switch from cooling to heating during internal seeding and then from internal seeding to supersaturation control are indicated with a circle and square, respectively. 310



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Figure 11. Measured time profiles for the temperature, total chord count and the solution composition for (a) Linear Cooling Run 1 and (b) Controlled Run 1. For the controlled run, the switch from cooling to heating during internal seeding is marked with a circle and the switch from internal seeding to supersaturation control is marked with a square. The three control steps listed in Section 3.3 are also enumerated next to the temperature profile.

to these thresholds, the cooling and heating rates during internal seeding as well as the supersaturation set point represent control parameters that must be selected by the operator prior to implementation. We selected a cooling rate of 0.5 °C/min, a heating rate of 2.0 °C/min, and a molar supersaturation set point of 0.10. As with the thresholds, the cooling and heating rates were selected somewhat arbitrarily. The supersaturation set point was chosen to be approximately one-third of the supersaturation levels that we observed just prior to primary nucleation events. The supersaturation profiles observed during each operation are shown in Figure 12. During linear cooling, the supersaturation builds at roughly a constant rate prior to nucleation.

composition during crystallization of the hydrated double salt, Na3SO4NO3·H2O, from the model solution under (a) linear cooling and (b) when the proposed control algorithm is applied. For convenience, these runs will be referred to as Linear Cooling Run 1 and Controlled Run 1. In Linear Cooling Run 1, supersaturation first builds without causing primary nucleation until the temperature is decreased to 68.5 °C. The onset of crystallization at this point is marked by a rapid increase in chord counts and a decrease in the concentration of sulfate in solution. While the concentration of nitrate in solution must also be decreasing slightly during crystallization of Na3SO4NO3·H2O, the fraction of nitrate removed from solution is small, and the change in concentration is therefore difficult to distinguish from measurement noise. Under the applied control scheme, the temperature is first decreased at a constant rate until a spike in the chord count is observed. The increase in chord count triggers heating and the solution temperature is increased at a constant rate until a temperature of about 79 °C is reached. At this point, the counts return to near baseline levels and supersaturation control is implemented. The temperature is then progressively decreased to maintain a constant molar supersaturation. In this experiment, a threshold of two times the baseline chord count was used to trigger the switch from cooling to heating, and a temperature of 79 °C (just under the solubility temperature for the total amount solute) was selected to trigger the switch from heating to supersaturation control. Although these thresholds were chosen somewhat arbitrarily, the intent was to heat shortly after primary nucleation without being too susceptible to noisy chord count measurements and to dissolve most of the crystal mass prior to implementing supersaturation control. In addition

Figure 12. Supersaturation profiles observed during Linear Cooling Run 1 and Controlled Run 1. The duration that SSC is applied is spanned by the bold line giving the supersaturation set point. 311



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Figure 13. Composition−temperature profiles measured for (a) Linear Cooling Run 1 and (b) Controlled Run 1. In (b) segments are labeled according to the stepwise proceedure given in Section 3.3.

Figure 14. Histograms of the squared-length-weighted chord counts measured by FBRM at end of the Linear Cooling Run 1 and Controlled Run 1.

After crystal nucleation, the supersaturation is depleted and near zero by the end of the run. During internal seeding, the supersaturation first builds while the solution is cooled; this supersaturation is then quickly depleted and eventually becomes negative when the solution is reheated. When SSC is applied, the relative supersaturation is maintained near the set point of 0.10. At the end of the run, a temperature plateau is instituted and the solution slowly de-supersaturates. Thus, under both operations the final solution appears to be close to saturation despite different sulfate concentration measurements at the end of the operation (Figure 11). This can be explained by run-specific measurement bias which is present in both the measured solubility curve and online composition measurements or by a true difference in the solution solubility due minor, unmeasured differences in the solute and impurity concentrations. 4.1.2. Trajectories on the Phase Diagram. Figure 13 shows the measured phase diagram profiles for Linear Cooling Run 1 and Controlled Run 1. Under linear cooling, rapid desupersaturation is observed at the onset of crystallization, and the composition−temperature profile closely follows the

measured solubility curve thereafter. On the other hand, the supersaturation control algorithm keeps the composition− temperature profile at a set distance from the solubility curve after the initial internal seeding loop. Note that a new solubility curve is experimentally determined using the solubility trace methodology prior to each run (Supporting Information Section S.3.2). Again, we attribute variation in the measured solubility curve from run-to-run to measurement bias and/or variation in the underlying solution thermodynamics due to slight changes in the impurity and solute concentration levels of the feed solutions. 4.1.3. Final Chord Length Distributions. The chord length distribution measured by FBRM provides some insight into the size of crystals. Figure 14 shows the squared-length-weighted chord count histograms measured at the end of Linear Cooling Run 1 and Controlled Run 1. Although the squared-lengthweighted chord count distribution is not interpreted as an exact measure of the crystal size distribution, this data suggest that crystals produced by the control scheme are larger than those produced by linear cooling.18,33 The effect of the control 312



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Figure 15. Optical microscope images of crystals recovered from (a.1−3) Linear Cooling Run 1 and (b.1−3) Controlled Run 1. Samples were taken from the first three sieve bins which contain the largest crystals: (1) 1000−2000 μm, (2) 850−1000 μm, and (3) 600−850 μm.

Figure 16. High-contrast images of a typical sample of crystals recovered from (a) Linear Cooling Run 1 and (b) Controlled Run 1. The scale bar is 1 cm in length.

Figure 17. (a) Mass-per-bin data gathered from sieve analysis for crystals from Linear Cooling Run 1 and Controlled Run 1. (b) Distribution of minimum Feret’s diameter of crystals according to high-contrast image analysis for crystal samples from Linear Cooling Run 1 and Controlled Run 1.

4.1.4. Recovered Crystals. Produced crystals were filtered with a Buchner funnel and air-dried while shaking in a sieve

scheme on the crystal size is evaluated further in the following section. 313



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Figure 18. (a) Supersaturation profiles observed for linear cooling crystallizations. (b) Supersaturation profiles observed when the proposed control scheme (internal seeding, followed by supersaturation control) is applied.

The second size statistic used is the average minimum Feret’s diameter, calculated from image data:

stack. Once dried and weighed, representative samples were collected for imaging. To gain different perspectives, optical microscope images and high-contrast images were taken of the crystal samples. The experimental setup used to capture highcontrast images is given in the Supporting Information Section S.4. Microscope images of sample crystals from the Linear Cooling Run 1 and Controlled Run 1 are shown in Figure 15. Images on the left (a.1−3) are of crystals from Linear Cooling Run 1, while images on the right (b.1−3) are of crystals from Controlled Run 1. High-contrast images of crystal samples from these same runs are shown in Figure 16. Figure 16 provides qualitative evidence that the crystals produced under the proposed control scheme are larger than those produced with simple linear cooling. To quantify the effect of the control policy on crystal size, two sizing techniques are applied. The first is sieving and the second is image analysis (applied to the high-contrast images of sample crystals). Sieve analysis provides the mass of crystals in different sieve diameter ranges. Image analysis provides the size and shape statistics for each crystal object identified in the frame. We use the minimum Feret’s diameter to characterize the size of each crystal object this is the minimum distance between a pair of parallel lines tangent to the projected outline of the object, which is expected to be similar to the sieve diameter of a particle.37 Histogram representations of the sieve and image size data are displayed in Figure 17. Both sieve and image size analyses indicate that Controlled Run 1 produced fewer fines and more crystals in the larger size bins than Linear Cooling Run 1. Thus, the average crystal size is larger, while the coefficient of variance remains nearly the same. From this data, two quantitative average size measures are calculated. The first is the mass-weighted average crystal size provided by sieve analysis, calculated as follows: L̅ ≡

Nbins

Nbins

i=1

i=1

∑ miLimp/ ∑ mi

Nobj

dmF ̅ ≡

∑ dmF,i/Nobj i=1

(5)

where dmF, i denotes the minimum Feret’s diameter of the ith object, and Nobj is the number of objects in the frame. Additional details of the image analysis can be found in the Supporting Information Section S.4. The average size according to sieve analysis (L̅) was 459.5 μm for crystals recovered from Linear Cooling Run 1 and 607.3 μm for crystals recovered from Controlled run 1. The average minimum Feret’s diameter according to image analysis (d̅mF) was 453.4 and 685.7 μm for crystals recovered from Linear Cooling Run 1 and Controlled run 1, respectively. These size statistics suggest that the control scheme produces larger crystals than simple linear cooling. However, neither sieve analysis nor the applied image analysis differentiates between single crystals and agglomerates. Crystals that appear larger by these measures could instead just be more agglomerated. Therefore, to evaluate the validity of the size analysis presented, the extent of agglomeration must be examined. According to optical microscope images (e.g., Figure 15), crystals from the controlled run appear somewhat less agglomerated on average. To quantify the extent of agglomeration in a more systematic manner, we analyzed on the shape of crystal objects in the collected high-contrast macroscopic images. This analysis could only be reliably applied to crystals above 500 μm, but for these larger crystals the analysis suggest that 86.3% of the crystals recovered from Linear Cooling Run 1 were are agglomerates (two or more crystals combined), while for crystal samples from Controlled Run 1, 69.0% of the larger crystal objects were agglomerates (Supporting Information Section S.4). The optical microscope images and extent of agglomeration calculations together provide strong evidence that crystals recovered from the controlled run are no more agglomerated than the crystals recovered and sized from the linear cooling run. This gives credence to the conclusion that Controlled Run

(4)

where mi represents the mass of crystals in the ith sieve bin, Lmp i is the midpoint of the size range of that bin, and Nbins is the total number of bins. For this calculation, crystals with are sieved into 14 bins with the total size range from 20−2000 μm. 314



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Figure 19. Average squared-length-weighted chord count distributions measured at the end of the linear cooling and controlled crystallizations.

Figure 20. (a) Average sieve diameter distributions for recovered crystals. (b) Average minimum Feret’s diameter distributions for recovered crystals.

1 produced larger crystals on average than Linear Cooling Run 1. 4.2. Supersaturation Profiles and Crystal Size Data from Multiple Linear Cooling and Controlled Runs. Agglomeration and crystal breakage were observed to occur during the drying and shaking process. To verify that the crystal size differences reported in Section 4.1 resulted from the crystallization operation and not random effects of the postcrystallization operations, the same operations were repeated two additional timesresulting in three controlled runs and three linear cooling runs in total. For the controlled runs, the temperature profile changes slightly from run to run, as the controller adapts to measurement feedback on the runspecific crystallization kinetics. This results in different batch times. The first run (Controlled Run 1) had a batch time of 105 min, while the second and third applications of the control algorithm resulted in batch times of 120 and 101 min, respectively. The supersaturation profiles for each of the three linear cooling and controlled runs are shown in Figure 18. Although

there are minor differences in the curves from run to run, the operational strategy dictates the shape in a consistent way. Linear cooling always results in a profile characterized by the gradual build up and depletion of supersaturation. The internal seeding operation (at the start of each controlled run) results in a “sped-up” and exaggerated version of this profilein which supersaturation quickly builds, is depleted, and is eventually negative. Once supersaturation control is instituted, the relative supersaturation is maintained near the set point of 0.10 in each case. This supersaturation is depleted during the temperature plateau instituted at the end of each controlled run. Although each operation starts from the same conditions (within measurement error) and ends at the same temperature, the different supersaturation profiles achieved by the two different operating strategies has a significant effect on the size of the crystals produced. This can be seen in the average chord length distributions recorded by FBRM at the end of each run as well as the size measurements for the recovered crystals. The average chord length distributions recorded by FBRM at the end the runs are shown in Figure 19, while the average size 315



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Table 1. Crystal Size, Extent of Agglomeration, and Recovered Mass Data for Each Run average crystal size by sieve analysis L̅ (μm)

average crystal size by image analysis d̅mF (μm)

average extent of agglomeration (%)

mass recovered (g)

459.5 483.3 432.4 458.4 607.3 540.1 630.7 592.7

453.4 414.7 305.9 391.3 685.7 542.8 720.1 649.5

86.3 67.6 84.8 79.6 69.0 68.5 55.7 64.4

12.19 14.14 15.11 13.81 14.04 12.22 14.60 13.62

linear cooling run 1a linear cooling run 2 linear cooling run 3 linear cooling average controlled run 1 (105 min.) controlled run 2 (120 min.) controlled run 3 (101 min.) controlled average (108.7 min) a

Each linear cooling run has a batch time of 105 min.

and the Cecil J. “Pete” Silas Endowment is gratefully acknowledged. Thanks to Kathryn Green for collection of infrared spectra for calibration as well as Rupa Ramamurthi for crystal sieving/weighing.

distributions for the recovered crystals measured by sieve analysis and image analysis are shown in Figure 20. The data displayed in Figures 19 and 20 are calculated from the aggregate FBRM, sieve, and image data for crystals generated by all three linear cooling runs and three controlled runs. Additional size data are provided in Table 1. This table gives the calculated average size statistics, the calculated extents of agglomeration, and the total recovered crystal mass for each run. From this data we see that the control algorithm does not affect the mass of crystals produced, but does consistently produce larger crystals.

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5. CONCLUSIONS We have examined a feedback control strategy that varies the solution temperature during crystallization according to the sequential application of direct nucleation control and supersaturation control. This control algorithm was applied to salt crystallization, demonstrating the ability to apply supersaturation control to a multicomponent crystallization. For the model two-component electrolytic solution, the control scheme resulted in crystals that were approximately 150% larger on average than those produced by linear cooling. The examined feedback control strategy and techniques given (e.g., multicomponent concentration monitoring from ATRFTIR and the solubility trace methodology) do not rely on kinetic or thermodynamic models and are expected to be of general use for understanding and controlling multicomponent crystallizations.

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ASSOCIATED CONTENT

S Supporting Information *

Details on the following four topics: (1) infrared measurement calibration model error, (2) supersaturation of a dissociated salt, (3) the solubility trace methodology, and (4) high-contrast image analysis. This material is available free of charge via the Internet at http://pubs.acs.org.

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REFERENCES

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AUTHOR INFORMATION

Corresponding Author

*Phone: (404) 894-2856. Fax: (404) 894-2866. E-mail: [email protected]. Notes

The authors declare no competing financial interest.

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ACKNOWLEDGMENTS Financial support from the Consortium for Risk Evaluation with Stakeholder Participation (CRESP), the Nuclear Energy University Program (NEUP), the Georgia Research Alliance, 316



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Feedback Control of Multicomponent Salt Crystallization - Crystal

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