Crystal Size Distribution and Aspect Ratio Control for Rodlike Urea

Article pubs.acs.org/IECR

Crystal Size Distribution and Aspect Ratio Control for Rodlike Urea Crystal via Two-Dimensional Growth Evaluation Pan Li, Gaohong He, Dapeng Lu, Xiaoyu Xu, Shuo Chen, and Xiaobin Jiang* State Key Laboratory of Fine Chemicals, R&D Center of Membrane Science and Technology, School of Chemical Engineering, Dalian University of Technology, Dalian, Liaoning 116024, China

ABSTRACT: Research on the evaluation of the two characteristic dimensional parameters (crystal length and width) of rodlike urea crystals is proposed. The two-dimensional crystal growth and the corresponding crystal aspect ratios (AR) are highlighted during the evaluation. Various particle size analysis methods are then introduced to investigate two-dimensional growth mechanisms. Improved crystal morphology (varied from rodlike to columnar), crystal size distribution (coefficient of variation = 31.4), and AR (4.97) are obtained by the proposed operation profile (increasing cooling rate from 0.05 to 0.40 °C min−1 and stable stirring rate of 300 rpm).

1. INTRODUCTION Crystallization is widely applied in solid−liquid separation processes with high separation efficiency and low operation cost.1−4 Because many finished chemical products exist in the form of crystalline solids, crystal particle properties [crystal size distribution (CSD) and morphology] have significant impact on the downstream process steps and final product quality.5−7 Thus, process control of crystallization which aims to obtain desired CSD and morphology is of importance.8−11 Model-based approaches involving morphological population balance applied to simulate CSD and predict the crystal morphology received a great amount of attention during the past two decades from both academic and industrial researchers.12,13 Briesen, Puel, and co-workers have made great contributions to the development of a morphological population balance model for predicting and controlling morphology of multidimensional crystals.14−16 With further understanding and development of the morphological population balance model,17 model identification of crystal facet growth kinetics in morphological population balance was then carried out using an integrated particle dispersion−imaging system, which aimed for the optimization of CSD and morphology.18 Thus, the development and identification of model-based approaches is also closely related to the particle size analysis instrument. At present, commercialized particle size technologies include focused beam reflective measurement (FBRM), particle vision © XXXX American Chemical Society

measurement (PVM), microscopy imaging analysis, etc. FBRM is generally used to measure the chord length distribution (CLD), which is a one-dimensional distribution. When facing multidimensional crystals, CLD obtained from FBRM is different from CSD and needs to be further handled before being applied to crystal kinetics,19,20 which limits the application of FBRM technology. PVM can provide real-time snapshots of crystals and can often be used to reflect morphology and estimate growth kinetics, applicable to both one-dimensional and two-dimensional crystal observation.12,16,21 Imaging techniques are able to reproduce both quantities and provide more detailed information on crystal morphology and shape.14,22 Crystal particles exhibiting needle-like or rodlike shapes have significant effects on the measured particles size distributions and should be focused on. The development of effective evaluation and controlling strategies based on particle size analysis and evaluation method for the CSD and morphology control is still a meaningful and challenging area of work.23,24 In this paper, urea crystal, a common chemical material, was investigated. The urea crystal which exhibits long rodlike shape belongs to the tetragonal crystal system which has two Received: Revised: Accepted: Published: A

November 7, 2016 February 15, 2017 February 20, 2017 February 20, 2017 DOI: 10.1021/acs.iecr.6b04310 Ind. Eng. Chem. Res. XXXX, XXX, XXX−XXX

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Industrial & Engineering Chemistry Research characteristic scale parameters (length and width direction) with a wide aspect ratio (AR).25−27 As is well-known, urea plays significant roles in fuel cell,28 selective catalytic reduction (SCR) for NOx abatement,29,30 etc. To maintain the high efficiency reaction in fuel cells or SCR systems,30,31 urea crystals with desired CSD and AR are of importance to improve effective separation of the included impurities. The stacked crystals with large AR are difficult to separate from impurityenriched liquid in the downstream washing, centrifugation, and drying processes. For the distinct two-dimensional size feature of urea crystal, the research of the growth process in both crystal length and width is beneficial for the overall CSD and aspect ratio control. Thus, in this paper, research on the evaluation of the two characteristic dimensional parameters (crystal length and width), aimed at obtaining reliable and reproducible crystal growth with desired size distribution and aspect ratio, was carried out. First, the solubility of the urea−water system and metastable zone width (MSZW) under different cooling rates and stirring speeds were measured and fitted as the basic data of the kinetic research. Various particle size analysis methods were then introduced and compared during the investigation of twodimensional growth mechanisms. Several modified operation curves based on MSZW measurement and two-dimensional kinetic evaluation were outlined and compared with the aim of acquiring urea crystals with improved CSD and AR.

Figure 1. Schematic diagram of the experimental apparatus for MSZW measurement.

cooling rate ranged from 0.05 to 0.6 °C min−1; the stirring speed ranged from 100 to 500 rpm. 2.3. Crystal Growth and Image Analysis. The experimental apparatus of kinetics research is shown in Figure 1. All kinetics experiments were also conducted in the same double-jacketed crystallizer. FBRM (Mettler Toledo Ltd., D600L) was used for collecting particle numbers and chord length distribution (CLD) data. PVM (Mettler Toledo Ltd., V19) was used for detecting crystal growth images. First, the prepared urea aqueous solution (saturation temperature is 35 °C) was added into the crystallizer. The initial temperature of the solution was kept at 5 °C above the saturated temperature for 30 min, accounting for the consistency of cooling. The solution temperature was recorded after the crystal nucleus was detected. The crystal slurry containing large amounts of crystals was taken out at a set time. The shape and morphology images of the crystals in the slurry were obtained by optical microscope [Motic (Xiamen) Electric Group Co., Ltd., Motic SMZ-168], and then the CSD was analyzed by Nano Measurer software. The concentration of the crystallization solution was analyzed by an Abbe refractometer. All kinetic experiments described in this work were carried out without seeding. To account for the stochastic character of primary nucleation, each experiment was repeated three times for the same cooling rate and stirring speed. The deviation in the temperature at the metastable limit was within 0.1 °C, and the reported CSD is the average over the three experiments. Stirring speed was set at 300 rpm during the research. Two classical cooling curves (fast cooling profile, 0.4 °C·min−1, and slow profile, 0.05 °C·min−1) were performed in the experiments to reveal the impact of supercooling degree on CSD and crystal morphology. Optimized experiments were launched with the modified operation profiles that involved the various cooling curves and stirring curves, which are listed in Results and Discussion. 2.4. Mass Balance and Determination of Particle Number N. To investigate the crystal nucleation without seeding, the mass balance of crystals and the determination of particles number, N, are needed. Total mass balance is given by

2. EXPERIMENTAL SECTION 2.1. Materials. The raw material urea was obtained from North Huajin Chemical Industries Group Corporation in China. Ion content of urea was analyzed by an inductive coupled plasma emission spectrometer (PerkinElmer Ltd., American, Optima2000DV). Hyperpure water, produced by alaboratory water purification system (Liaoning RIGHTLEDER Environmental Engineering Co. Ltd., China, LTLDP50), was of ultrapure grade with ion content less than 0.1 ppb. 2.2. Solubility and Metastable Zone Width Measurement. Urea was dissolved by stirring in 100 g of water at the respective temperature over 12 h. The solutions were filtrated to remove the dissolved solids. The concentration of the solution was measured by an Abbe refractometer (Shanghai Precision Instrument Co., Ltd., China, 2WAJ) through a concentration−refractive index standard curve to determine the solubility. The experimental apparatus for MSZW measurement and kinetics research is shown in Figure 1. All measurements were implemented in a 500 mL double-jacketed crystallizer. A program-controlled bath (Nanjing Fandilang Information Technology Co., Ltd., China, CKDC-2010) was used for temperature control. Laser transmitting and receiving devices (Thorlabs GmbH, PM100USB) were applied to determine the MSZW in the experiment based on observing the sudden change in the laser light transmission intensity. An adjustable stirring motor (Dragon Laboratory Instruments Limited, OS20Pro) was utilized for controlling the stirring speed. The MSZW (ΔTmax) was determined by the following equation: ΔTmax = Teq − T

(1)

where Teq was the equilibrium temperature and T denoted the detected nucleation temperature. A single-factor experiment was carried out to investigate the effect of operation conditions on MSZW, including cooling rate and stirring speed; the

M T = M S + Ml

(2)

M TC i = MSCS + MlC l

(3)

where MT, MS, and Ml are the mass of the total system, crystal phase, and liquid phase, respectively. Ci, CS, and Cl are the mass B

DOI: 10.1021/acs.iecr.6b04310 Ind. Eng. Chem. Res. XXXX, XXX, XXX−XXX

Article

Industrial & Engineering Chemistry Research Table 1. MSZW Data for Urea−Water System ΔTmax (°C) stirring speed (rpm)

0.05 °C·min−1

0.10 °C·min−1

0.20 °C·min−1

0.40 °C·min−1

0.60 °C·min−1

100 200 300 400 500

2.2 2.0 1.4 1.2 1.0

3.2 2.6 2.2 1.6 1.4

4.7 4.0 2.6 2.3 2.1

6.9 5.2 3.6 3.4 3.0

8.6 7.7 5.4 4.4 4.0

fraction of urea in the initial solution, crystal phase, and liquid phase, respectively. When eqs 2 and 3 are combined, the mass of crystals at different times can be expressed as

MS =

M T (C i − C l ) 1 − Cl

When eqs 7−9 are combined, the following equation resulted when the supercooling reached the MSZW limitation ΔTmax 1 n ln ΔTmax = K + ln v − ln Nr (10) m m The mathematical model for MSZW of urea aqueous solution based on the measured MSZW data was calibrated using the least-squares method, which was given as

(4)

Then, the number of particles, N, in different times can be estimated by

N=

MS V̅ ρ

ΔTmax = 129.64v 0.5304Nr −0.5207 ,

R2 = 0.97

(11)

Comparison of experimental MSZW data and calculated MSZW values is shown in Figure 2. The deviation of calculated

(5)

where V̅ is mean volume of crystals and ρ is the density of urea crystal.

3. RESULTS AND DISCUSSION 3.1. Solubility and MSZW. The solubility, x (g/100 g water), has a significant dependence on temperature. The Apelblat simplified empirical equation was used to fit solubility data,32 leading to a good agreement. The correlation coefficient (R2) is 0.9985. ln(x) = −112.56 + 3617.57/(T + 273.15) + 18.46ln(T + 273.15)

(6)

The MSZW was measured under various cooling rates (ranging from 0.05 to 0.60 °C·min−1) and stirring speeds (ranging from 100 to 500 rpm). The measured MSZW data are listed in Table 1. Many researchers have applied Nyvlt’s mathematical model for relating the nucleation rate to the MSZW33−36 B0 = K 0ΔCmax mNr n

(7)

B0 = qv

(8)

Figure 2. Comparison of experimental MSZW data and calculated MSZW values.

MSZW values and experimental MSZW data was acceptable. With eqs 6 and 11, the solubility and MSZW under set operating conditions can be obtained for further evaluation of the crystallization process under various operating conditions. 3.2. Evaluation of the Two-Dimensional Growth Kinetics. The experimental cooling curves (slow profile, 0.05 °C·min−1; rapid profile, 0.40 °C·min−1), crystal images ,and crystal size properties are shown in Figure 3. The length of urea crystals reached more than 800 μm at the initial stage of crystal growth. The explosive growth on length direction indicated the dominating role of the length direction growth at the initial stage. With the AR changed from 8.90 to 6.50 even at the slowing cooling curves (0.05 °C·min−1), the obtained crystals were still rodlike with large AR, which should be improved. The yield and the corresponding suspension density were used to represent the crystallization process directly. Crystal numbers (N) and supersaturation against crystallization process are shown in Figure 4. To imply the driving force of nucleation and growth, supersaturation was defined as the difference with the actual concentration and the equilibrium concentration. Particle number, N, was calculated by eq 5, and mean volume of crystals, V̅ , was the statistical average value of V (V = LW2) analyzed by Nano Measurer software. Under the slow cooling

where K0 is the nucleation rate constant, ΔCmax the metastable supersaturation in the solution, and Nr the stirring speed (rpm); m and n are kinetic parameters. v = dT/dt, which was cooling rate, °C/min. q = ε(dCeq/dT), where ε = O/[1−c(O− 1)], and O is the ratio of molecular weights of hydrate. Because there was no solvate of urea, ε equaled 1 in this study. As in past studies,4,35,36 eqs 7 and 8 are used to characterize MSZW rather than estimating the true nucleation rate expression. For cooling crystallization, in the concentration range that nucleation occurred, the metastable supersaturation was related to the metastable zone width of approximately linear dependence.32,37 Thus, the metastable supersaturation ΔCmax was assumed to be proportional to the supercooling ΔTmax: ⎛ dCeq ⎞ ΔCmax = ⎜ ⎟ΔTmax ⎝ dT ⎠

(9) C


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Industrial & Engineering Chemistry Research

Figure 3. Cooling curves, average crystal size in length and width, and AR.

cooling rate was 0.05 °C·min−1, the experimental metastable zone was 1.4 °C. Hence, after initial nucleation, the supersaturation decreases gradually along with crystallization because of crystal nucleation and growth. When the cooling rate was 0.40 °C·min−1, MSZW reached 3.6 °C, which resulted in the high nucleation rate. When excess supersaturation was consumed by vast nucleation and crystal growth, the supersaturation decreased gradually. Further investigation of the changes of two characteristic dimensional crystal sizes and AR during the crystallization process are shown in Figure 5. With the relatively faster width growth rate of the slow cooling curve (0.88 μm min−1 in width compared to 5.72 μm min−1 in length, 0.05 °C·min−1), the average AR varied from 9.0 to 6.5 during the whole crystallization; whereas, because of the relatively fast length direction growth under the rapid cooling curve, the corresponding average AR varied only from 8.5 to 7.0, respectively. It can be found that both cooling curves presented insufficient modification of the average AR; the optimization of the AR should introduce more complicated operation curves to adjust the nucleation and crystal growth kinetics. In addition, the changes of the measured size distribution of FBRM, two characteristic dimension size distributions, and aspect ratio distribution of crystals (obtained by image analysis) during the crystallization process are shown in Figure 6. Figure

Figure 4. Calculated particle number (N) and supersaturation during the crystallization process.

curve, N increased quickly at the initial stage and then became stable. Different from the slow cooling curve, persistent increasing of N indicated that the nucleation had a continuous impact on the whole crystallization procedure under the rapid cooling curve. Online measured supersaturation also revealed the distinct trends of the different cooling curves. When the

Figure 5. Crystal size of two characteristic dimensions and aspect ratio during the crystallization process. D


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Figure 6. Size distribution of FBRM, two characteristic dimension size distillations, and aspect ratio distribution of crystals during the crystallization process.

6A−C exhibit CLD (obtained from FBRM) and the two characteristic dimensional size distribution (obtained from image analysis) at three different crystallization stages: 50 min (initial stage), 130 min (medium stage), and 250 min (terminal stage) for the slow cooling curve. The corresponding product yields were 0.1, 0.17, and 0.27; in the 5 min (initial stage), 15 min (medium stage), and 30 min (terminal stage) stages for the rapid cooling curve, the corresponding product yields were 0.11, 0.19, and 0.28. As can be seen, product yields of the two cooling operations at each stage were kept similar for comparison purposes. CLD results of FBRM were greatly different from that of image analysis. Hence, for some crystals without symmetry,

geometry cannot be described by a single size parameter. For needle- or rodlike crystals of large AR such as urea crystals, the CLD results obtained by FBRM cannot be directly used to accurately characterize the multidimensional CSD. The probability of the FBRM laser crossing a crystal of large AR in the length dimension is orders of magnitude lower than the width direction; therefore, FBRM technology is incapable of obtaining enough statistics along the length direction to accurately track its size evolution. As comparison, Figure 6B,C provided more detailed kinetic crystal growth data: as to both cooling curves, the crystal width sizes grew faster and obtained wider size distribution than that of the crystal length size. The impacts and the advantages of E


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Figure 7. Crystal growth rate and images of the growth frontier under various cooling curves.

Figure 8. Modified operation profiles and the images of the obtained crystal products.

morphologies of the two cooling curves are compared, uneven and sunken crystal planes can be detected because of the rapid growth on the length direction at the 0.40 °C min−1 curve (as shown in Figure 7). These distinct morphological defects will definitely cause impurity inclusions and adhesion. Moreover, besides the impact on the MSZW, proper stirring rate was beneficial to maintaining the original crystal morphology by decreasing the shear force on the crystal growth frontier, which will be modified and revealed in section 3.3. 3.3. Modified Process and AR Evaluation. Considering the combined impact of cooling rate and stirring rate on MSZW, CSD, crystal morphology, and AR, modified operation profiles for potential industrial applications are proposed. The CSD, AR of the obtained crystals, the relevant engineering aspect, process duration, and manufacture efficiency of the modified operations are compared. Five modified operation profiles (A−E in Figure 8) were applied under the same cooling interval, from 35 to 15 °C; thus, similar theoretical yield and suspension density were obtained. Cooling profiles were accomplished with setting multistage cooling processes. Stirring profiles were reached through an adjustable motor. The theoretical MSZW of A−E (calculated by eq 11 were 1.96, 1.96, 1.36, 1.36, and 7.25 °C, respectively. The diverse crystal morphology, AR, and CV of the crystal products can be found in Figures 8 and 9. It can be seen that profile D was the only operation profile that can improve the AR of the crystals to smaller than 5.0

various cooling curves can be confirmed by the calculated AR distribution (shown in Figure 6D). It was interesting to find that the AR distribution under the slow cooling curve became narrow and that the average AR decreased from 8.2 to 6.4. However, the AR distribution under rapid cooling curve had shown no obvious variations during the investigated duration. A further comparison on the crystal growth rate of the two characteristic dimensions and images of the growth frontier under various cooling curves is shown in Figure 7. Compared with Figure 5, GL of two cooling conditions exhibited a trend similar to that of supersaturation, indicating GL was more sensitive to the change of supersaturation. The growth rates in the length and width directions are quite distinct. For the slow cooling curves (0.05 °C/min), the average growth rate in the length direction surpasses the width direction by 4.2 times, whereas under the fast cooling curves (0.40 °C/min), the average growth rate in the length direction surpasses the width direction by 7.5 times. As such, it is not surprising that the temporal evolution and the final value of the AR varied significantly for the two cooling rates (Figure 6). As the secondary growth direction, the width growth was relatively stable during the whole crystallization process. Images of PVM were captured online and can reveal the crystal morphology in detail. Because of the layer-by-layer growth mechanism of urea, the growth paths from outside to inside on the length direction can be clearly observed by PVM, similar to the one reported in the literature.35 When the crystal F


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Figure 9. Average aspect ratio and CV (the colored numbers in the figure) evaluation of the modified operation profiles.

(4.97). Moreover, the obtained crystal morphology changed from long rodlike to the columnar one, which was much more favorable for the downstream separation. Crystal product of profile C also exhibited good morphology with small aspect ratio (5.92). The overall operation duration of profile C (controlling slow cooling process) was two times that of profiles A, B, D, and E, which was less efficient than other profiles. In addition, it should be noted that with the similar theoretical yield and suspension density of each operation, the larger average crystal size (the data point located in the right top corner of Figure 9) meant less crystal numbers, which indicated a better control on the secondary nucleation of the corresponding operation profiles. Thus, profile E had obtained the smallest average crystal size and a large AR. The terminal AR of profile E (8.66) was similar to the initial one of the rapid cooling curve (8.60), which meant that slowing the cooling curve at the medium and terminal stages of profile E had no effect on the improvement of AR. Besides the average aspect ratio and coefficient of variation (CV), to quantitatively evaluate the control effect of the five operation profiles, CSD in two characteristic dimensions (length and width) and AR distribution should be emphasized, which are shown in Figure 10. Clear distinction of the terminal length and width distribution among the five operation profiles indicated the modified cooling curves and stirring curve had a significant impact on the two-dimensional growth. The slow cooling rate at the initial stage (inhibition of nucleation) and the increasing cooling rate at the medium and terminal stages (acceleration of secondary direction growth) in profile D maintained the high growth rate of the width direction. Thus, crystal products of profile D acquired the largest average width (245 μm), which was beneficial for the smallest average AR (4.97) among the five operation profiles. The gradually varied stirring rate (profile B) lead to wider AR distribution and smaller average width (174 μm); moreover, the length direction growth was promoted with the increasing stirring energy input. These combined effects led to the largest average AR (8.84) and wider AR distribution among the five operation profiles, which meant the crystal shape tended to be rodlike rather than columnar with wide size distribution. With these additional crystal size and shape data, more meaningful information for the feedforward control and operation profile design can be revealed.

Figure 10. Crystal size distribution in two characteristic dimensions (length and width) and aspect ratio distribution of the modified operation profiles (average aspect ratio, the colored numbers in the panels).

5. CONCLUSIONS Research on the evaluation of the two characteristics dimensional growth (crystal length and width), aimed at obtaining urea crystals with desired CSD and AR, was carried out. Modified operation curves based on MSZW measurement and two-dimensional kinetic evaluation were then proposed. The improved crystal morphology, CSD (CV = 31.4) and AR (4.97) were obtained by the operation profile D (increasing cooling rate from 0.05 to 0.40 °C min−1 and stable stirring rate of 300 rpm). It should be noted that AR is a relative scale parameter that can be utilized to evaluate how the operation profile impacts the crystal growth on the length and width characteristic dimensions. It will provide more information for the operation profile optimization. Still, the accurate CSD and growth rate are also the critical data for the crystallization kinetic research and process design. To obtain the accurate data above, the development of the particle size analysis technology and instrument (online and offline) should be emphasized also. Moreover, a quantitative evaluation system should be established that involves CSD (average size distribution, size distribution on the characteristic dimensions, etc.) and AR to provide a comprehensive analysis of the experimental results obtained from the various particle size analysis technologyies and other process analysis instruments. G


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AUTHOR INFORMATION

Corresponding Author

*E-mail: [email protected]. Phone: +86-411-84986291. Fax: +86-411-84986291. ORCID

Xiaobin Jiang: 0000-0003-0262-4354 Notes

The authors declare no competing financial interest.

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ACKNOWLEDGMENTS This work is supported by National Natural Science Foundation of China (Grants 21527812, 21676043, U1663223, 21306017), Changjiang Scholars Program (T2012049), the Fundamental Research Funds for the Central Universities (DUT16TD19), and Education Department of the Liaoning Province of China (LT2015007).

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Crystal Size Distribution and Aspect Ratio Control for Rodlike Urea

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