Recovery of Phosphorus and Potassium from Source-Separated Urine

Mar 6, 2017 - Magnesium potassium phosphate hexahydrate (MgKPO4·6H2O, MPP) crystallization is a promising approach to recover phosphorus (P) and ...
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Recovery of Phosphorus and Potassium from Source-Separated Urine Using a Fluidized Bed Reactor: Optimization Operation and Mechanism Modeling Chi Zhang,† Kang-ning Xu,‡ Ji-yun Li,† Cheng-wen Wang,*,† and Min Zheng*,† †

School of Environment, Tsinghua University, Beijing 100084, P.R. China College of Environmental Science and Engineering, Beijing Forestry University, Beijing 100083, P.R. China

‡

ABSTRACT: Magnesium potassium phosphate hexahydrate (MgKPO4·6H2O, MPP) crystallization is a promising approach to recover phosphorus (P) and potassium (K). Achievement of large MPP crystal size is still critical for the MPP products utilization. We performed a pilot-scale fluidized bed reactor (FBR) with treatment of synthetic source-separated urine to capture the MPP crystallization. Using the optimized FBR operational parameters, as pH of 10.5, Mg:P molar ratio of 1:1, supersaturation ratio of 3.0, and superficial velocity of 350 cm/min, pellets of high purity (86 ± 2%) with a maximum size of 4 mm were achieved. The removal efficiencies of K and P reached 20−35% and 80−90%, respectively. Furthermore, we proposed a kinetic model to describe the pellet growth. The pellet growth rate was determined as G = 5.046 × 10−9SV0.88S1.96. The model combined with mass balance approach could predict P and K removal efficiencies of the FBR well. separation.17 Therefore, achievement of large MPP crystal size is still critical for the MPP products utilization. Crystallization using fluidized bed reactor (FBR) has been considered as an effective way to control the formation of fines. Previous studies on phosphate and ammonium removal from anaerobic digestion supernatant showed that MAP pellets over 3.0 mm could be produced in the FBR.18−20 Efficient FBR operation is heavily reliant on specialist knowledge of the key influencing factors.21 For example, there was increasing formation of MAP fines when supersaturation exceeded 2.8.19 The increasing superficial velocity of the FBR could greatly improve the MAP product size,22 and seeding procedure efficiently controlled nucleation and the MAP product size.23,24 However, effects of these operational parameters on the MPP crystallization for recovery of P and K in the FBR were still unclear. In this study, we performed a pilot-scale FBR to recover K and P by MPP crystallization from the source - separated urine. The objective was to optimize the operational parameters to obtain large-size MPP crystals and high recovery efficiencies of P and K. The stable FBR performances were investigated. Then, we developed a kinetic model to describe the pellet growth. The model combined with mass balance approach was further used to predict the removal efficiencies of P and K and pellet growth in the FBR.

1. INTRODUCTION Human urine contains high concentrations of nitrogen (N), phosphorus (P) and potassium (K), around 9000 mg/L, 700 mg/L and 2200 mg/L, respectively.1 Urine source-separation has been considered as a promising approach to recovering these nutrients from human urine and reducing the cost of wastewater treatment.2−4 Researchers have developed various nutrient recovery techniques for urine treatment among which struvite (MgNH4PO4·6H2O, MAP) crystallization received the most attention.5−10 Using the MAP crystallization, more than 90% of P and part of N could be recovered, whereas nearly all K would be lost. Currently, countries that utilize intense agricultural practices, such as China, the United States, India, and Brazil, are facing challenges in producing K fertilizers due to low potash reserves.11 Therefore, recovering K from the source-separated urine to yield fertilizer will be an attractive technique especially for these countries. Magnesium potassium phosphate hexahydrate (MgKPO4· 6H2O, MPP) crystallization is a promising approach to recovering P and K after removal of ammonium.9 MPP is a struvite-type compound, which could serve as a slow-release fertilizer similar to MAP.12 Thermodynamic modeling indicated that, by first removing most of ammonium via technologies such as stripping-adsorption13 and biochar adsorption,14 in theory up to 99% P and 33% K can be recovered as the MPP crystallization.15 Precipitates of MPP mainly formed ranging from 60 to 100 μm with negatively charged surface.16 As such, these fine MPP precipitates presented poor separation ability from the urine solution. This would lead to significant decrease in P and K recovery efficiencies and poor solid−liquid © XXXX American Chemical Society

Received: Revised: Accepted: Published: A

December 13, 2016 March 2, 2017 March 6, 2017 March 6, 2017 DOI: 10.1021/acs.iecr.6b04819 Ind. Eng. Chem. Res. XXXX, XXX, XXX−XXX

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Figure 1. Schematic of the FBR setup (a) and model development of a perfectly classified FBR (b). (A) diameter: 30 mm, height: 250 mm; (B) diameter: 60 mm, height: 550 mm; (C) diameter: 80 mm, height: 600 mm; (D) diameter: 200 mm, height: 400 mm.

2. MATERIALS AND METHODS

the pellet settled in the harvesting zone, it was removed as product. As shown in Table 1, the first series of experiments was conducted to investigate the influence of various parameters so

2.1. Synthetic Urine. Synthetic urine is usually used instead of real urine for crystallization studies.9,15,25 The recipe should be determined carefully based on the composition of real urine. Generally, real urine contains both high concentrations of organic matters and ammonium.1,4 Feeding urine containing a concentration of ammonium above 700 mg N/L produced a precipitant of MAP instead of MPP. However, if the concentration of ammonium drops below 100 mg N/L, the forming MAP could be ignored.15 Therefore, pretreatment of urine for the ammonium removal, such as nitrificationdenitrification process, is strongly recommended before the MPP crystallization.9,15 Basically, the ammonium concentration in real urine could decrease to about 40 mg N/L, and 82 ± 5% of the dissolved COD in the urine could be eliminated after the nitrification-denitrification pretreatment in the literature.9 In addition, the organic matter had no significant influence on the precipitants forming.25 Therefore, the synthetic urine used in this study was prepared based on the following assumptions. First, urea is generally fully hydrolyzed into ammonium and bicarbonate in stored urine. Second, because of the precipitation of calcium and magnesium that occurs in the pipes and collection tank, a significant amount of calcium and almost all of the magnesium is removed from stored urine.4 Third, all the available bicarbonate and most of the organic substances can be removed from urine during biological nitrification.26,27 Finally, according to Wilsenach et al.9 after nitrification−denitrification the concentration of NH4+-N is about 40 mg N/L. The final composition of synthetic urine was 0.7 mM CaCl2·2H2O, 78.7 mM NaCl, 16.2 mM Na2SO4, 30.9 mM KH2PO4, 21 mM KCl, and 2.86 mM NH4Cl. 2.2. FBR Setup and Operation. The schematic of the FBR setup is shown in Figure 1a. During crystallization, the synthetic urine, inner recycle stream and the addition of MgCl2·6H2O and NaOH were all pumped into the crystallizer from the bottom. Seeds were added to the top section and move down toward the bottom while gradually growing larger. As soon as

Table 1. Experimental Conditions Used for Operational Parameters Optimization in the FBR

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19

pH

Mg:P molar ratio

dilution times

recycling ratio

superficial velocity (cm/min)

9.5 10 10.5 11 9.5 10 10.5 11 9.5 10 10.5 11 9.5 10 10.5 11 10.5 10.5 10.5

0.6 0.6 0.6 0.6 1.0 1.0 1.0 1.0 1.3 1.3 1.3 1.3 1.6 1.6 1.6 1.6 1.0 1.0 1.0

2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2

15 15 15 15 15 15 15 15 15 15 15 15 15 15 15 15 15 15 15

180 180 180 180 180 180 180 180 180 180 180 180 180 180 180 180 20 350 450

as to optimize the MPP crystallization process. Experiments 1− 16 examined the effects of pH, Mg dosage, and supersaturation; superficial velocity was kept the same. The superficial velocity is calculated by dividing the flow rate by the cross-sectional area. In this study, the superficial velocity was controlled by adjusting the total flow rate in the FBR. The total flow rate was adjusting by changing the inflow rate and recycling flow rate at the same time while keeping the recycling ratio consistent. Experiments 3, 17, 18, and 19 examined the effects of superficial velocity, Mg B

DOI: 10.1021/acs.iecr.6b04819 Ind. Eng. Chem. Res. XXXX, XXX, XXX−XXX

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supersaturation ratio, j is growth order due to superficial velocity, and n is growth order due to supersaturation. Supersaturation ratio (S) for MPP is expressed by eq 2:29,30

dosage and pH were maintained at the same levels in these experiments. All experiments used two-time diluted synthetic urine. The dilution time was chosen to simulate the concentration of real source-separated urine, which is generally diluted between 1 and 5 times by flushing water. Magnesium potassium phosphate seed crystals were obtained by previous experiments in the FBR. The average size of the seeds was chosen as 0.47 mm. At the beginning of the experiments, seeds of 70 g were added to the FBR. Each of the experiments lasted 24 h. MPP products were removed from the bottom at different times and were measured to calculate the experimental growth rate. At the end of each experiment, all of the pellets were collected and classified by sieving. Then the pellets of different sizes were weighed to calculate the average size of all the MPP pellets in the FBR. The concentration of the outlet was measured at the end of each experiment. The second series of experiments was run for 25 days to investigate the stable FBR performances with different inflow concentrations using the optimized parameters determined by the first series of experiments. Synthetic urine of three different dilution times (dilution times = 5, 2, and 1) was used as inflow. The MPP products were collected after the reactor reached the stable condition. Seeds of 0.47 mm were added at 2 h intervals to the FBR, The desired weight of seeds was calculated by multiplying the average seeding rate desired (20 particles/s) by 2 h. The FBR was run for 10 h every day. The effluent was sampled daily for composition analysis. Product size was measured by sieving, and product composition was tested for purity analysis. The recycling ratio used in this study was experimentally determined. In the tests with six sets of recycling ratios of 2, 4, 8, 15, 20, and 25, the observation showed that the removal efficiencies of P and K increased with the dilution time decreased at relatively low recycling ratios of 2 and 4, while the removal efficiencies were basically unchanged with different dilution times at high recycling ratios above 8. Using low recycling ratio could easily cause locally high supersaturation at the bottom and even lead to blockage and total breakdown of the whole system. Therefore, a setup recycling ratio of 15 was used in the experiments. 2.3. Analytical Methods. Concentrations of Mg, K, and ortho-phosphate were measured for solution samples that were all filtered using 0.45 μm membranes. Characterization of pellet sample composition used two different techniques: analysis of crystalline forms via X-ray diffractometer (XRD, Rigaku TTRIII, Japan) and measuring Mg, K, Ca, Na, ammonium, and ortho-phosphate concentrations after dissolving the pellet in sulfuric acid. Concentrations of ammonium and orthophosphate were tested by a spectrophotometer (DR 5000, Hach, U.S.A.). Concentrations of Mg, K, Ca, and Na were measured with an inductively coupled plasma−atomic emission spectroscope (Thermo, U.S.A.). 2.4. Pellet Growth Model. Generally, the growth of pellet growth in a FBR can be described by an empirical model used in the literature22,28 which takes into account the key factors of the pellet growth process. According to the model, the pellet growth rate (G) is a function of superficial velocity, supersaturation ratio, etc. as shown in eq 1:

G=

dL = K SV jSn dt

⎛ IAP ⎞1/3 ⎟⎟ S = ⎜⎜ ⎝ K sp ⎠

(2)

where Ksp is the thermodynamic solubility product and IAP is the ionic activity product. Ksp is 10−12.2 for MPP was used.15 Supersaturation ratio was calculated by PHREEQC software.31

3. RESULTS AND DISCUSSION 3.1. Optimization Operational Parameters for the FBR. K and P removal efficiencies correlated strongly with Mg:P molar ratio and pH value in the FBR. As shown in Figure 2a, at every Mg:P molar ratio, P removal efficiency (maximum

Figure 2. P (a) and K (b) removal efficiencies at varying pH and Mg:P molar ratios. ◊, Mg:P = 0.6; ■, Mg:P = 1.0; ▲, Mg:P = 1.3; ●, Mg:P = 1.6.

95%) increases with increasing pH value, but this effect levels off when pH exceeds 10.5. Similarly to the pH value, a higher Mg:P molar ratio was associated with increased P removal efficiency. When increasing Mg:P molar ratio from 0.6 (under dosage) to 1 (equal dosage), there is a significant increase in P removal. However, when the Mg:P ratio was raised from equal dosage to overdosage (Mg:P = 1.3 or 1.6), the increase in P removal was less significant. For example, at a pH value of 10.5, 91% P was removed with Mg:P = 1, which is 12% more than achieved with Mg:P = 0.6. Because of the high removal efficiency at Mg:P = 1, from a cost control perspective, equal dosage of Mg is preferable to over dosage for P removal. Similarly, higher pH led to higher K removal efficiency (maximum 37% at pH 11 and Mg:P = 1) (Figure 2b). Equal dosage performed better than the other two dosing conditions irrespective of pH value (e.g., at pH 11, equal dosage removed 8% more than Mg:P = 0.6; 4% more than Mg:P = 1.3; and 16%

(1)

where L is pellet size (m), t is time (s), K is the growth rate constant (m·s−1), SV is superficial velocity (m·s−1), S is C

DOI: 10.1021/acs.iecr.6b04819 Ind. Eng. Chem. Res. XXXX, XXX, XXX−XXX

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maximum average pellet size of 0.87 mm was achieved at superficial velocity of 450 cm/min. This is because, with increasing size, the settling velocities of the pellets are higher, such that the liquid−solid relative velocities increase. This accelerates the mass transfer ratio, thus enhancing pellet growth.21 Another key reason is that the increasing turbulence could lead to more frequent collisions between crystals, which reinforces crystal agglomeration.33 Agglomeration allows small crystals to bind together, which greatly contributes to product growth.22 However, it is also notable that the change in growth rate between 350 and 450 cm/min was much smaller compared to those below 350 cm/min. This is an indication of the formation of fines by breakage of the product, which was a result of the overly intensive turbulence inside the FBR (especially at the bottom section) when superficial velocity increased to 450 cm/min. Therefore, high superficial velocity is necessary to ensure all of the pellets are suspended and to reinforce product growth, whereas there should also be a maximum value (350 cm/min in this study) to ensure goodquality product and less fines formation. 3.2. Stable FBR Performance. Figure 4a shows that pellets as large as 4 mm were collected from the stable FBR. Previous studies on MAP crystallization in FBR also showed that it was possible to grow struvite-type pellets over 2 mm under suitable conditions. The MAP products produced by Shimamura et al.34 reached 3.5 mm. The grain size produced by a commercial FBR located in Japan ranged from 2.0 to 3.8 mm.19 Though the FBR demonstrated good control of fines there were small amount of fines flowing out from the top section during the stable operation of FBR. This might due to the attrition and breakage of pellets during the stable operation.20,35 The FBR is fully loaded during its stable operation process. A fully loaded FBR means that each section of the reactor is filled with fluidized pellets and the collisions among pellets could be significant in the reactor thus resulting in the attrition and breakage of pellets. Reducing the retention time of pellets could be one method to alleviate the formation of fines. The XRD profiles of the products (see Figure 4b) indicate that they mainly consist of MPP, and the pattern shows some background noise, indicating cocrystallization formation. Twenty random samples were taken from the collected MPP product. The composition was analyzed by dissolving in sulfuric acid. The results showed that the average purity of the pellets was 86 ± 2%, which was calculated from the K content. Based on the composition analysis, most of the impurities in the pellets were magnesium phosphate (13.00 ± 4.79 mg/g, estimated by the molar ratio of K:Mg:P in the pellets). Also a small amount of Ca (1.16 ± 0.83 mg/g), ammonium (2.53 ± 0.98 mg/g), and Na (3.89 ± 1.12 mg/g) were found in the pellets. The results confirmed that the influence of ammonium could be ignored when ammonium in urine was removed prior to the crystallization, which agrees with the assumptions for the synthetic urine in section 2.1. Figure 4c shows the nutrient removal efficiencies achieved during the stable operational experiments. The removal efficiencies of K and P were within the ranges 20−35% and 80−90%, respectively, for urine with different dilution times. There was no obvious changes in removal efficiencies for both K and P when the dilution times increased from 1 to 5 due to the dilution effect brought by the high recycling ratio. The K and P removed by FBR during the stable operation were a little bit lower than the results obtained by our optimization experiments (see section 3.1) and the estimated results by the thermodynamic model developed by Xu et al.15 that

more than Mg:P = 1.6). This might due to the cocrystallization formed with excess Mg dosage, which would reduce K removal efficiency.15 The results showed that the optimized parameters of the FBR for the P and K recovery via MPP crystallization were pH 10.5 and Mg:P = 1.0. This is consistent to the literature using batch experiments.15 Supersaturation is a key factor for crystal size,32 which in the present study varied with Mg dosage and pH. Figure 3a

Figure 3. Effect of supersaturation (S) (a) and superficial velocity (b) on average pellet size. ⧫, pH 9.5; ▲, pH 10.0; ◊, pH 10.5; ○, pH 11.0.

presents the effect of supersaturation on pellet size after 24 h. It is clear that pellet size initially increased with greater supersaturation and then declined at supersaturation above 3.0. This implies differing crystallization kinetics according to supersaturation range. Pellet growth within the FBR occurs in two ways. One is termed molecular growth: solute molecules are transported from the bulk to the crystal surface (mass transport); the solute molecules are then incorporated into the crystal lattice (surface reaction). The other is the agglomeration of crystals. Generally, increasing supersaturation can enhance both molecular growth22 and agglomeration.32 Therefore, increasing supersaturation could increase pellet growth rate if supersaturation remains below the critical level. However, when the supersaturation level is high enough to trigger significant primary nucleation, a large amount of fines are formed and compete mass with the growth process, resulting in smaller product size. Thus, in order to achieve the desired product size and better control of the fines effect, there should be an upper limit of supersaturation of 3.0 to avoid uncontrolled nucleation. Superficial velocity also had significant influence on pellet size (Figure 3b). Increasing superficial velocity from 20 cm/min to 450 cm/min enhanced average pellet size by 0.38 mm. The D

DOI: 10.1021/acs.iecr.6b04819 Ind. Eng. Chem. Res. XXXX, XXX, XXX−XXX

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Figure 4. Characterization of pellets and nutrients removal efficiencies of FBRs operation using the optimized operational parameters, as pH of 10.5, Mg:P molar ratio of 1:1, and superficial velocity of 350 cm/min. Pellets size (a), XRD analysis of pellets (b), and P and K removal efficiencies (c).▲, P removal efficiency when urine was not diluted; △, K removal efficiency when urine was not diluted; ⧫, P removal efficiency when urine was diluted 2 times; ◊, K removal efficiency when urine was diluted 2 times; ●, P removal efficiency when urine was diluted 5 times; ○, K removal efficiency when urine was diluted 5 times.

theoretically up to 99% of P and 33% of K could be recovered as MPP from urine. This was due to the small amount of fines flowing out with the effluent, which was caused by the attrition and breakage of pellets during the stable operation of FBR. Overall, the results indicated that the operational parameters obtained by the optimization experiments are reasonably effective for stable FBR operation to get desired product and K and P removal efficiencies. 3.3. Pellet Growth Model Calibration in the FBR. Data from six sets of experiments were selected to evaluate the pellet growth rate. These experiments were chosen according to the analysis in section 3.1 that supersaturation and superficial velocity should be controlled under the threshold to avoid the influence of uncontrolled nucleation and pronounced breakage. It was observed that the pellet growth rate increased when superficial velocity and supersaturation increased. The pellet growth rate varied from about 2.31 × 10−10 to 2.89 × 10−9 m/s as the superficial velocity increased from 20 to 350 cm/min, and it raised from 8.10 × 10−10 to 1.74 × 10−9 m/s when the supersaturation increased from 2.2 to 2.8. The data was fitted to eq 1 to calculate the pellet growth rate constant (K), growth order due to superficial velocity (j), and growth order due to supersaturation (n), which defined the pellet growth rate of MPP in a FBR as eq 3. G = 5.046 × 10−9SV 0.88S1.96

Figure 5. Comparison of pellet growth rate estimated by the pellet growth model (Gestimated) with the experimental data (Gexperimental).

mass balance approach similar to that adopted by Rahaman et al.36 to perform a modeling process for the FBR system. The approach is based on several simplifications: (1). The FBR is treated as a perfectly classified reactor and can be divided into layers (see Figure 1b). Each of these layers consists of pellets of the same size. Solution moves upward in plug flow. (2). Uncontrolled nucleation is neglected, and a consistent number of seeds is added from section D. When the FBR reaches the stable condition, the mass balance of MPP constituent species “i”, (K, Mg, and P) over an infinitesimal height (ΔH) can be expressed by eq 4:

(3)

where G corresponds to the analysis in section 3.1, according to which, increases both in supersaturation (below 3) and in superficial velocity could intensify pellet growth. The pellet growth rates of the other six sets of experiments were estimated using eq 3 and the estimated values were compared with the experimental ones in order to validate the obtained pellet growth rate parameters (Figure 5). The correlation coefficient of the fitting was 0.978, which showed a strong correlation between the experimental and estimated values of G. 3.4. Predictions of P and K Removal in the FBR. The P and K removal efficiencies during the stable FBR operation were further evaluated by combining the growth model with a

Qρl (C H − CH +ΔH ) (C Hin + 1)

=

(1 − ε)ΔHAβL2GρS αL3

(4)

where Q is flow rate (L/s), ρl is liquid density (kg/m ), CH is concentration of species “i” at height H (mol·L−1), CH+ΔH is concentration of species “i” at height H + ΔH (mol·L−1), CHin is concentration of species “i” in inlet (mol·L−1), ε is FBR voidage, A is cross-sectional area of the column (m2), β is 3

E

DOI: 10.1021/acs.iecr.6b04819 Ind. Eng. Chem. Res. XXXX, XXX, XXX−XXX

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Industrial & Engineering Chemistry Research surface factor, L is pellet size (m), G is pellet growth rate (m/ s), ρs is pellet density (kg/m3), and α is volume factor. Bed voidage (see eq 5) was calculated according to Rahaman et al.36 ⎡ 0.1 ⎡ ⎢ 2 2 ⎞1/3⎤ 2⎛ 4( ρ − ρ ) g ρ ( γ ) L 1 ⎢ l l ⎜⎜ S ⎟⎟ ⎥ ln⎢ ln ε = ⎢ 4.4 ⎢ μ ⎝ 225ρl μ ⎠ ⎥⎦ ⎣ ⎢ ⎣ ⎤ ⎥ Q /A ⎥ 2 2 1/3 ⎥ ⎛ ⎞ 4( ) ρ − ρ g S l ⎟ 10(−Lγ / D)⎜ 225 Lγ ⎥ ρl μ ⎠ ⎝ ⎦

Figure 6. Comparison of P (a) and K (b) removal efficiencies predicted results with the experimental data. The experimental data was obtained from the stable FBR operation using the optimized operational parameters, as pH of 10.5, Mg:P molar ratio of 1:1, and superficial velocity of 350 cm/min.

(5)

where γ is dimensionless diameter factor for a MPP pellet, μ is kinematic viscosity (m2·s−1), g is acceleration due to gravity (m· s−2), and D is diameter of the column (m). By rearranging eq 4, concentration of species “i” at height H + ΔH (CH+ΔH) can be expressed by eq 6: CH +ΔH = CH −

obtained in the stable FBR with treatment of urine of different dilutions. K and P removal efficiencies reached 20−35% and 80−90%, respectively. (3) A pellet growth model was proposed, expressed as the growth rate as G = 5.046 × 10−9SV0.88S1.96. The model fitted quite well to the pellet growth experimental data of the FBR. The growth model combined with mass balance approach can also predict the K and P removal efficiencies of the FBR, thereby helping to design the FBR system for the achievement of best MPP products.

(C Hin + 1)(1 − ε)ΔHAβGρS Qρl αL

(6)

In order to calculate C, another mass balance should be introduced to eliminate other variables in eq 6. This mass balance describes pellet growth over the infinitesimal height (ΔH; eq 7): ρS Nα(L H3

−

L H3 +ΔH)

=

■

(1 − ε)ΔHAβL2GρS α L3

(7)

Corresponding Authors

where N = number of seed crystals added per unit time, LH = pellet size at height H (m), and LH+ΔH = pellet size at height H + ΔH (m). By rearranging eq 7, LH+ΔH can be expressed by eq 8: LH3 +ΔH = LH3 −

(1 − ε)ΔHAβG Nα 2L

AUTHOR INFORMATION

*Tel.: +86 10 62771551. Fax: +86 10 62788148. E-mail: [email protected]. *E-mail: [email protected]. ORCID

Min Zheng: 0000-0001-9148-7544

(8)

Notes

The authors declare no competing financial interest.

Effluent concentration was predicted by solving eqs 1−6 and 8) for the experimentally measured boundary conditions (H = 0, C = CHin, LHi is pellet product size and H = He (bed height), LHe is crystal seed size). Data of nine independent runs of the stable operations were chosen and compared with the stimulated results (Figure 6). The estimated values for K and P removal efficiencies correlated well with the experimental data (maximum deviation 8%). Thus, the growth model could be used to design and optimize the MPP crystallization process in a FBR, and assist in achieving better product and effluent quality. Operators can calculate the effluent quality or pellet size by adjusting the parameters included in the model (e.g., diameter or height of the FBR, operational parameters, etc.) with no need to conduct pilot testing with different FBR designs and operational parameters.

■

ACKNOWLEDGMENTS This study was supported by National Natural Science Foundation of China (No. 21277079) and the Major Science and Technology Program for Water Pollution Control and Treatment (No. 2014ZX07305-003)

■

4. CONCLUSIONS (1) Optimization operational parameters for pellet growth and P and K removal in the FBR were determined as pH of 10.5, Mg:P molar ratio of 1:1, supersaturation of 3.0, and superficial velocity of 350 cm/min. (2) Using the optimized operational parameters, pellets as large as 4 mm with average purity of 86 ± 2% were F

NOMENCLATURENOMENCLATURE A = cross-sectional area of the column (m2) CH = concentration of species “i” at height H (mol/L) CH+ΔH = concentration of species “i” at height H+ΔH (mol/ L) CHin = concentration of species “i” in inlet (mol/L) D = diameter of the column (m) FBR = fluidized bed reactor g = acceleration due to gravity (m/s2) G = pellet growth rate (m/s) He = bed height i = species IAP = the ionic activity product j = growth order due to superficial velocity K = growth rate constant (m/s) Ksp = the thermodynamic solubility product DOI: 10.1021/acs.iecr.6b04819 Ind. Eng. Chem. Res. XXXX, XXX, XXX−XXX

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Industrial & Engineering Chemistry Research

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L = pellet size (m) LH = pellet size at height H (m) LH+ΔH = pellet size at height H (m) LHe = crystal seed size LHi = pellet product size MAP = magnesium ammonium phosphate hexahydrate MPP = magnesium potassium phosphate hexahydrate n = growth order due to supersaturation N = number of seed crystals added per unit time Q = flow rate (L/s) S = supersaturation ratio SV = superficial velocity (m/s) t = time (s) α = volume factor β = surface factor γ = dimensionless diameter factor for a MPP pellet ΔH = infinitesimal height ε = FBR voidage ρl = liquid density (kg/m3) ρs = pellet density (kg/m3) μ = kinematic viscosity (m2/s)

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DOI: 10.1021/acs.iecr.6b04819 Ind. Eng. Chem. Res. XXXX, XXX, XXX−XXX