3394
Ind. Eng. Chem. Res. 2004, 43, 3394-3402
SEPARATIONS Breakthrough and Elution Curves for Adsorption of Phosphates on an OH-Type Strongly Basic Ion Exchanger Hiroyuki Yoshida,* Hodaka Jitsukawa, and Wilmer A. Galinada Department of Chemical Engineering, College of Engineering, Osaka Prefecture University, 1-1 Gakuen-cho, Sakai 599-8531, Japan
The breakthrough and elution curves for adsorption of H3PO4, H2PO4- and HPO42-, PO43- ions on an OH-type strongly basic ion exchanger were investigated in a packed-bed column. The results appeared to be technically feasible. In all phosphate systems, sharp breakthrough curves were obtained, and they were affected by inlet concentrations. The breakthrough times decreased with an increase in the inlet concentration. The ion-exchange capacities of phosphates in the column decreased in the following order: H3PO4 aqueous solution > NaH2PO4 aqueous solution > Na2HPO4 aqueous solution > Na3PO4 aqueous solution. The values of the ratio between the ion-exchange capacity and the total ion-exchange capacity of the resin were in the range of 10030%. The experimental breakthrough data were correlated by neglecting the effect of axial dispersion and by using a linear driving force assumption in the intraparticle diffusion. At a separation factor of R g 0.0594, the theoretical breakthrough lines were calculated numerically for the Langmuir isotherm, while at 0.000 42 e R g 0.035 27, the theoretical breakthrough lines were all calculated using an analytical solution for the rectangular isotherm. The values of the intraparticle effective diffusivity increased with an increase in the influent concentration. In H3PO4 and NaH2PO4 systems, the contribution of surface and pore diffusions was significant, while in Na2HPO4 and Na3PO4 systems, the contribution of the pore diffusion was significant. The phosphate ions adsorbed in the column bed were completely eluted by using a NaOH aqueous solution. 1. Introduction Phosphates are very important basic materials to agriculture and fertilizer industries and chemical and metal-plating industries. They are largely used in the manufacture of various important phosphate-based products for household and industrial purposes.1-4 However, the large consumption of phosphate-bearing products is inevitably producing large amounts of phosphate-bearing wastes. Because phosphates eutrophicate environmental water, enormous efforts have been made to remove phosphates from wastes. On the other hand, there are many reports that deposits of high-grade phosphate ores would likely be depleted in the next few decades.3,5-9 Thus, it is very important to develop a production process of phosphates from phosphate-utilizing industrial processes and phosphate-containing wastewater systems to establish a new and alternative source of phosphates in order to prevent a global exhaustion of high-grade phosphate ores in the near future. Recently, we reported the results of the equilibria for adsorption of four different types of phosphate species (H3PO4, H2PO4-, HPO42-, and PO43-) on an OH-type strongly basic anion exchanger, DIAION SA10A, in aqueous media and at wide pH ranges by the batch method.10,11 The adsorption process was technically feasible for the recovery of phosphates. The amount of * To whom correspondence should be addressed. Tel./Fax: +81-72-2549298. E-mail:
[email protected].
phosphate adsorption on DIAION SA10A was relatively high for all phosphate systems considered. The proposed equilibrium models were able to correlate the experimental data well and explained the peculiarities in the experimental adsorption isotherms. We also reported the results of the parallel transport of phosphates by surface and pore diffusions in DIAION SA10A by the shallow bed method.12 The experimental data were successfully correlated by applying the homogeneous Fickian diffusion model and the parallel diffusion model for surface and pore diffusions. The experimental surface diffusivities of H2PO4- obtained in both H3PO4 and NaH2PO4 systems were 5-7 times larger than those in PO43- and HPO42-, which may be caused by the weaker affinity between the fixed cationic group and the adsorbate H2PO4- than in HPO42- and PO43-. In all phosphate systems, the values of pore diffusivities did not vary in the whole range of phosphate concentrations considered. The theoretical lines for the parallel diffusion model using the experimental values of both surface and pore diffusivities agreed reasonably well with the experimental data. Most ion-exchange operations are often carried out in columns. Therefore, it is important to conduct breakthrough curve experiments for the adsorption of phosphates on an OH-type strongly basic ion exchanger in a packed-bed column to establish an efficient separation and recovery of phosphates from various phosphatecontaining wastewater systems and phosphate-utilizing industrial processes. Packed-bed column operations
10.1021/ie030547x CCC: $27.50 © 2004 American Chemical Society Published on Web 05/20/2004
Ind. Eng. Chem. Res., Vol. 43, No. 13, 2004 3395
Figure 1. Experimental setup for breakthrough/elution curve measurement.
require optimum flow rate, bed height, influent concentration, and temperature to maximize the performance and efficiency of the column for the separation and recovery process. In industrial ion-exchange column operations, the effect of axial dispersion (0.10 e Re′ e 10) can be neglected.13,14 A general analytical solution, which includes film and intraparticle diffusion resistances, for the breakthrough curve of an ion-exchange system with irreversible equilibrium has been derived and presented.15 They adopted a different approach to solving the coupled differential mass balance equations in both fluid and solid phases, together with an equation for a rectangular isotherm. Both fluid and solid resistances were represented by linearized rate expressions, but the solution was obtained without recourse to the assumption of a constant pattern. In most ion-exchange operations, a regeneration or a recovery step of the column is usually conducted. The efficiency of an elution process largely depends on the kind of eluent and its eluting strength. A NaCl aqueous solution was used to recover 90% phosphate in a study on the selective removal and recovery of phosphate in a novel fixed-bed process.16 Several studies on the elution curves of pure amine and paints using NaOH and HCl aqueous solutions as eluents and in a cyclic operation were reported previously.17-19 In those reports, it was concluded that, because the experimental elution curves exhibited sharp peaks, pure amine and paints were completely and irreversibly recovered by the NaOH aqueous solution as the eluent. A NaOH aqueous solution was also used as the eluent to desorb phosphate from activated alumina, where more than 85% of phosphates was desorbed from the column.20 In this experimental study, the breakthrough and elution curves for adsorption of H3PO4, H2PO4-, HPO42-, and PO43- ions on an OH-type strongly basic ion exchanger, DIAION SA10A, are investigated in a packedbed column. The optimized packed-bed column operating conditions described previously13,14 are applied in this work. By neglect of the effect of axial dispersion and by use of a linear driving force assumption in the intraparticle diffusion, the experimental breakthrough data are analyzed and correlated. The values of the
Table 1. Experimental Physical Properties of DIAION SA10A
a
Average of 50 particles. b Average of 10 particles.
intraparticle effective diffusivity are determined by matching the theoretical breakthrough curves with the experimental ones to eludicate the contributions of both surface and pore diffusions in the intraparticle diffusion of phosphates. The phosphates in the column are eluted by using a NaOH aqueous solution as the eluent, and the effects of flow rates and of the feed solution concentration in the adsorption process on the elution curves of phosphates are discussed. 2. Experimental Section The phosphate compounds H3PO4 and Na3PO4‚12H2O were purchased from Nacalai Tesque Inc., Kyoto, Japan, and the compounds NaH2PO4‚2H2O and Na2HPO4‚ 12H2O were obtained from Kishida Reagents Chemicals, Kansai, Japan. The phosphate compounds and other chemicals used were all special grade and used as received. The strongly basic ion exchanger, DIAION SA10A, was obtained from Mitsubishi Chemical Corp., Tokyo, Japan. The polymer matrix is a styrene-divinylbenzene, and the functional group is a quaternary ammonium (type I). The experimental physical properties
3396 Ind. Eng. Chem. Res., Vol. 43, No. 13, 2004 Table 2. Experimental Systems and Conditions in Breakthrough/Elution Curve Measurements breakthrough resin
C0 [mol‚m-3]
adsorbate
DIAION SA10A (gel-type)
5 10 20 50 5 10 20 50 5 10 20 50 5 10 20 50
H3PO4
NaH2PO4
Na2HPO4
Na3PO4
uf × [m‚s-1]
Re′
eluting agent
C0 [mol‚m-3]
4.24
0.65
NaOHaq
1000
4.24
0.65
NaOHaq
1000
4.24
0.65
NaOHaq
1000
4.24
0.65
NaOHaq
1000
of DIAION SA10A are listed in Table 1. The procedures on the characterization and conditioning of the resin particles and the details on feed concentration determination are described elsewhere.10,11 Breakthrough/Elution Curve Measurement. The breakthrough and elution curve experiments were simultaneously conducted in a packed-bed column. Figure 1 shows the experimental setup used in both breakthrough and elution curve experiments. Table 2 summarizes the experimental systems and conditions. The ion-exchange column (4 in Figure 1; Amicon, 1.0 × 10-2 m i.d.) with a water jacket was packed with DIAION SA10A at a column height of 0.20 m. A known concentration of a phosphate solution from the feed tank (1 in Figure 1) was fed into the packed-bed column by using a tube pump (2 in Figure 1) passing through a circulating water bath. In all breakthrough runs, the flow rate was kept constant at 3.30 × 10-8 m3‚s-1 (Re′ ) 0.650). The water jacket of the column served to keep the experimental temperature at 298 K. The effluent solutions were successively collected by a fraction collector (5 in Figure 1; Eyela Fraction Collector DC-1200), and the corresponding pH of the solution was measured by a pH meter (6 in Figure 1; Horiba pH meter F-16 or F-23). The pH values were automatically registered into a computer. The concentration of phosphate in the effluent was analyzed by a high-performance liquid chromatograph (Shimadzu LC-10A). The phosphates adsorbed in the column were eluted using a 1000 mol‚m-3 NaOH aqueous solution as an eluting agent. In contrast to breakthrough curve experiments, elution flow rates were experimentally varied (Table 2). The eluates were also successively collected using a fraction collector, and the corresponding pH values were automatically recorded in a computer. 3. Theory When axial dispersion is neglected, a differential mass balance for a point in a column gives the familiar fixedbed equation
v
∂C ∂C 1 - ∂q j + + )0 ∂z ∂t ∂t
(
)
elution
104
(1)
where C (mol‚m-3) and q j (mol‚m-3) are the liquid-phase concentration and the adsorbent-phase mean concentration. Also, v [)uf/] (m‚s-1), , z (m), and t (s) denote the
uf × 104 [m‚s-1]
Re′
0.53 2.12 1.06 0.53 0.53 2.12 1.06 0.53 0.53 2.12 1.06 0.53 0.53 2.12 1.06 0.53
0.81 3.26 1.63 0.81 0.81 3.26 1.63 0.81 0.81 3.26 1.63 0.81 0.81 3.26 1.63 0.81
interstitial velocity, void fraction of the bed, space coordinate upstream (distance from the column inlet), and time, respectively. For simplicity, the mass-transfer rate is represented by a linear driving force expression
∂q j ) kfav(C - C*) ) kpav(q* - q j) ∂t
(2)
where kfav (s-1) and kpav (s-1) represent the volumetric mass-transfer coefficients in the liquid and adsorbent phases, respectively. C* (mol‚m-3) and q* (mol‚m-3) denote the equilibrium liquid-phase concentration and the equilibrium adsorbent-phase concentration at the liquid-solid-phase interface, respectively. In addition, the equilibrium isotherm is correlated by the Langmuir equation
q* )
q0KC* 1 + KC*
(3)
where K (m-3‚mol-1) and q0 (mol‚m-3) are the Langmuir equilibrium constant and the saturation capacity of the resin, respectively. The initial and boundary conditions are given by eqs 4 and 5, where C0 is the column inlet concentration.
(I.C.) q j ) 0 and C ) 0, at t ) 0
(4)
(B.C.) C ) C0, at z ) 0
(5)
Using dimensionless variables, eqs 1-5 may be transformed into eqs 6-10, respectively,
(Fixed-bed equation)
∂x ∂x ∂yj + +m )0 ∂ξ ∂τ ∂τ
(6)
(Linear driving force expression) y* - yj ∂yj ) x - x* ) (7) σ ∂τ δ (Langmuir isotherm) y* )
x* R + (1 - R)x*
(I.C.) yj ) 0 and x ) 0, at τ ) 0 where
(8) (9)
Ind. Eng. Chem. Res., Vol. 43, No. 13, 2004 3397
(B.C.) x ) 1, at ξ ) 0 x)
(10)
q0 1 - q j C* q* C , yj ) , x* ) , y* ) , m ) , C0 q0 C0 q0 C0 kfavz 1 ξ) , τ ) kfavt, R ) , v 1 + KC0 kfavC0 q0 σ) , δ) C0 kpavq0
(
)
For the equation at the solid-liquid interface, eq 11 is derived by substituting eq 8 into eq 7.
δ(1 - R)x*2 {(1 - R)(δx + yj) - (Rδ + 1)}x* - R(δx + yj) ) 0 (11) When eq 11 is expressed in terms of x*, eq 12 is obtained.
x* ) [(1 - R)(δx + yj) - (Rδ + 1) ( ({(1 - R)(δx + yj) (Rδ + 1)}2 + 4R(δx + yj)δ(1 - R))]/2δ(1 - R) (12) By application of the finite difference technique, the solutions for the preceding nonlinear partial differential equations are obtained. According to Yoshida et al.,15 at R < 0.04, the isotherm can be considered as rectangular. They derived the analytical solutions for the breakthrough curve for eqs 1 and 2 for rectangular isotherm systems without using the constant pattern conditions. Numerical solutions were calculated using the following procedure. According to Yoshida et al.,21 the liquid-phase mass-transfer coefficient, kf, in a homogeneous packed-bed column with spherical resins can be calculated by using eq 13 and the liquid-phase masstransfer capacity, kfav, is obtained by eq 14, where Sh,
Sh )
kfdp 1 - 2/3 ) 1.85 (Sc × Re′)1/3 DL
(13)
6 k dp f
(14)
(
)
kfav )
dp (m), Sc [)µ(F/DL)], µ (kg‚m-1‚s-1), F (kg‚m-3), DL (m2‚s-1), and Re′ denote the Sherwood number, resin particle diameter, Schmidt number, viscosity, density, liquid-phase diffusivity, and adjusted Reynolds number, respectively. The liquid-phase diffusivity, DL, was determined by applying the Wilke-Chang equation22 given by eq 15. In addition, the volumetric resin-phase
DL ) 7.4 × 10-8
[
1/2
]
(xM) T ηV0.6
(15)
mass-transfer coefficient, kpav, was determined by matching the experimental breakthrough data with the calculated theoretical breakthrough lines. Then the effective particle diffusivity, Deff, was calculated by using eq 16.
kpav )
60 Deff dp2
(16)
4. Results and Discussion 4.1. Breakthrough Curves. Figures 2-5 show the effect of inlet concentrations on the breakthrough curves
Figure 2. Effect of concentration on breakthrough curves for the H3PO4 system on DIAION SA10A.
for adsorption of H3PO4, H2PO4-, HPO42-, and PO43ions on an OH-type strongly basic ion exchanger, DIAION SA10A, respectively. In all phosphate systems considered, the breakthrough times decreased with an increase in the inlet concentrations. The values of ionexchange capacities of phosphates in the column decreased in the following order: H3PO4 aqueous solution > NaH2PO4 aqueous solution > Na2HPO4 aqueous solution > Na3PO4 aqueous solution. Table 3 summarizes the calculated values for the breakthrough times, Langmuir isotherm coefficients, ion-exchange capacities, and separation factors. In all phosphate systems, the values of ion-exchange capacities have slight differences in the whole range of phosphate concentrations considered. The calculated values for the ratio between the ion-exchange capacity and the total ion-exchange capacity of the resin, q0/Q0, are also given in Table 3, with values ranging from 100 to 30%. The peculiar values in the ion-exchange ratio are explained by the following ion-exchange reactions between phosphate ions and the OH-type strongly basic ion exchanger:
H3PO4 system: R-OH- + H2PO4- a R-H2PO4- + OH[1:1] (17) NaH2PO4 system: R-OH- + H2PO4- a R-H2PO4- + OH[1:1] (18) Na2HPO4 system: 2R-OH- + HPO42- a R2-HPO42- + 2OH[2:1] (19) Na3PO4 system: 3R-OH- + PO43- a R3-PO43- + 3OH[3:1] (20) In the preceding equations of ion-exchange reactions,
3398 Ind. Eng. Chem. Res., Vol. 43, No. 13, 2004
Figure 3. Effect of concentration on breakthrough curves for the NaH2PO4 system on DIAION SA10A.
Figure 4. Effect of concentration on breakthrough curves for the Na2HPO4 system on DIAION SA10A.
it is apparent that the number of functional groups occupied by various phosphate ions determines the total amount of phosphate adsorption (Table 3). Thus, in H3PO4 and NaH2PO4 systems, only one site of the resin is occupied by the H2PO4- ion per adsorption, while two and three sites are occupied by HPO42- and PO43- ions in the case of Na2HPO4 and Na3PO4 systems, respectively. In addition, the peculiar values of the ion-exchange ratio in Table 3 are explained by the following dissociation reactions of phosphates in the liquid phase: K1
H3PO4 {\} H+ + H2PO4K2
H2PO4- {\} H+ + HPO42K3
HPO42- {\} H+ + PO43-
pK1 ) 2.15
(21)
pK2 ) 7.20
(22)
pK3 ) 12.35
(23)
In Table 3, the values of the effluent pH after breakthrough in the H3PO4 system were in the range of 1.852.46 in the whole range of phosphate concentrations considered. In the batch experiment results reported previously,10,11 the ion-exchange ratio (q0/Q0) at pH < 4 was also equal to 1.0. At this particular pH range, only the H2PO4- ion exists, and the dissociation reaction was given by eq 21. Therefore, the ion-exchange ratio obtained in the breakthrough experiment for the H3PO4 system is consistent with the result in the batch experiment. In the NaH2PO4 system, the ion-exchange ratio is also equal to 1.0, with an effluent pH value from 5.5 to 6.03. In the batch experiment results, at 4 < pH < 8, the ion-exchange ratio was also equal to 1.0, which is consistent with the result obtained in this breakthrough study. The ion-exchange ratio was likewise explained by eq 21. In the Na2HPO4 system, the ionexchange ratio is approximately equal to 0.45, with an effluent pH value from 10.39 to 11.01. This particular pH range is also within the pH range presented in the batch experiment, which gave an ion-exchange ratio of
Figure 5. Effect of concentration on breakthrough curves for the Na3PO4 system on DIAION SA10A.
0.50. At 8 < pH < 12, both HPO42- and PO43- ions coexist, and the equation of the dissociation reaction was given by eq 23. In the Na3PO4 system, the ion-exchange ratio is equal to 0.34, with an effluent pH value from 11.67 to 12.06. This result is also consistent with the results obtained in the batch experiment, which gave an ion-exchange ratio of 0.33. The ion-exchange ratio was also explained by eq 23. The theoretical breakthrough curves in all phosphate systems, represented by solid lines, were all calculated according to the equations discussed in the preceding sections. Table 4 summarizes the various parameters used in theoretical calculations. When all theoretical breakthrough lines were calculated numerically for the Langmuir isotherm, the calculated theoretical lines were not able to correlate well with the breakthrough
Ind. Eng. Chem. Res., Vol. 43, No. 13, 2004 3399 Table 3. Calculated Parameters from Breakthrough Curves for All Phosphate Systems
resin
adsorbate
DIAION SA10A (gel-type) (Q2 ) 1932.4 mol‚m-3)
H3PO4
NaH2PO4
Na2HPO4
Na3PO4
C0 [mol‚m-3]
breakthrough time [min]
pH value of the eluate after breakthrough
5 10 20 50 5 10 20 50 5 10 20 50 5 10 20 50
1534 740 421 186 1096 592 301 116 696 331 154 59 614 291 152 58
2.46 2.26 2.05 1.85 6.03 6.02 5.90 5.50 10.72 10.98 11.01 10.39 11.67 11.72 11.89 12.06
Langmuir constants q0 [mol‚m-3] K [m3‚mol-1] 1795.26 2001.86 2118.60 2195.64 1628.38 1749.43 181.62 1854.55 846.28 856.52 861.10 864.58 651.65 652.92 653.62 654.02
0.781 25
1.242 85
8.223 68
56.689 34
separation factor, R
q0/Q0
0.202 96 0.111 23 0.059 40 0.025 203 0.136 19 0.071 97 0.035 27 0.016 21 0.023 84 0.012 04 0.006 75 0.002 73 0.004 04 0.002 09 0.001 03 0.000 42
0.9290 1.0359 1.0964 1.1362 0.8427 0.9053 0.9411 0.9597 0.4379 0.4432 0.4456 0.4474 0.3372 0.3379 0.3382 0.3384
Table 4. Parameters Used in Theoretical Breakthrough Calculations resin
uf × 104 H × 10 C0 [m] adsorbate [mol‚m-3] [m‚s-1]
DIAION SA10A H3PO4 (gel-type)
NaH2PO4
Na2HPO4
Na3PO4
5 10 20 50 5 10 20 50 5 10 20 50 5 10 20 50
4.24
2.00
4.24
2.00
4.24
2.00
4.24
2.00
0.393 0.400 0.400 0.400 0.420 0.430 0.410 0.410 0.425 0.410 0.410 0.420 0.400 0.410 0.400 0.410
q0 × 104 kfav × 10 kpav × 104 [mol‚m-3] [s-1] [s-1] 1795.26 2001.86 2118.60 2195.64 1628.38 1749.43 1818.62 1854.55 846.28 856.52 861.10 864.58 651.65 652.92 653.62 654.02
2.184 2.141 2.141 2.141 2.027 1.973 2.084 2.084 2.015 2.100 2.100 2.043 2.243 2.181 2.243 2.181
5.500 8.400 14.950 36.000 1.500 1.700 2.300 3.500 1.000 2.700 3.500 7.500 1.300 3.300 6.500 13.000
Deff [m2‚s-1] 5.87 × 10-12 8.96 × 10-12 1.59 × 10-11 3.84 × 10-11 1.63 × 10-12 1.85 × 10-12 2.50 × 10-12 3.80 × 10-12 1.10 × 10-12 2.97 × 10-12 3.85 × 10-12 8.24 × 10-12 1.46 × 10-12 3.71 × 10-12 7.30 × 10-12 1.46 × 10-11
DS [m2‚s-1]
DPa [m2‚s-1]
DL × 109 [m2‚s-1]
1.10 × 10-12 1.50 × 10-9
1.2008
1.30 × 10-12 2.36 × 10-10
1.2343
7.25 × 10-13 3.61 × 10-10
1.2705
6.84 × 10-13 5.53 × 10-10
1.3907
Figure 6. Effect of influent concentrations of phosphates on the intraparticle effective diffusivity.
Figure 7. Plots of intraparticle effective diffusivity based on eq 24.
data for the phosphate systems with a separation factor of R e 0.0594. According to Yoshida et al.,15 at R < 0.04, the isotherm can be considered as rectangular. Hence, the theoretical lines at R e 0.035 27 were calculated using the analytical solutions for the rectangular isotherm. The calculated theoretical lines agree well with the breakthrough data for these particular phosphate systems. Therefore, at a separation factor of R g 0.0594, the theoretical breakthrough lines were calculated numerically for the Langmuir isotherm, while at 0.000 42 e R e 0.035 27, the theoretical breakthrough lines were calculated using the analytical solutions for the rectangular isotherm. In all phosphate systems, the experimental breakthrough data were well correlated by the calculated theoretical breakthrough lines. Figure 6 shows the effect of influent concentrations of phosphates on the intraparticle effective diffusivity,
Deff, for all phosphate systems. First, the values of the volumetric resin-phase mass-transfer coefficient were determined by matching the experimental breakthrough data with the theoretical breakthrough lines. Then, the values for the intraparticle effective diffusivity, Deff, were calculated from eq 16 using the obtained kpav values. The values of Deff are likewise listed in Table 4. It is apparent that Deff increased with an increase in the influent concentration in the order H3PO4 aqueous solution > Na3PO4 aqueous solution > Na2HPO4 aqueous solution > NaH2PO4 aqueous solution. Because Deff values in all phosphate systems were affected by inlet concentrations, pore diffusion may contribute to the intraparticle mass transfer. In addition, Yoshida et al.23-25 presented a method to determine the surface diffusivity, DS, and the approximate pore diffusivity, DPa, using the values of Deff
3400 Ind. Eng. Chem. Res., Vol. 43, No. 13, 2004 Table 5. Comparison between the Amount of Phosphates Adsorbed and Recovered breakthrough resin
adsorbate
DIAION SA10A (gel-type)
H3PO4
NaH2PO4
Na2HPO4
Na3PO4
C0
[mol‚m-3] 5 10 20 50 5 10 20 50 5 10 20 50 5 10 20 50
time [min] 1534 740 421 186 1096 592 301 116 696 331 154 59 614 291 152 58
elution q0
[mol‚m-3] 1795.26 2001.86 2118.60 2195.64 1628.38 1749.43 1818.62 1854.55 846.28 856.52 861.10 964.58 651.65 652.92 653.62 654.02
Figure 8. Effect of flow rates on the elution curves for the H3PO4 system on DIAION SA10A.
Figure 9. Effect of flow rates on the elution curves for the NaH2PO4 system on DIAION SA10A.
based on the parallel transport model by pore and surface diffusions. The relationship of Deff, DS, and DPa is given by eq 24, where P is the void fraction of the
(
Deff 1 +
1 1 ) DS + DPa R R
)
(R ) q0/PC0)
(24)
resin particle. Figure 7 shows the plots of intraparticle effective diffusivity based on eq 24. The data are all well correlated by the straight lines. The values of DS and DPa were obtained from the intercepts and slopes of the straight lines, respectively, and they are listed in Table 4. Because the values of DPa/R are almost in the same order in all phosphate systems, pore diffusion in the particle is significant. The values of DS in H3PO4 and NaH2PO4 systems are larger than those in Na2HPO4 and Na3PO4 systems. It can be assumed that surface diffusion is significant in both H3PO4 and NaH2PO4 systems.
eluting agent
C0
[mol‚m-3]
NaOHaq
1000
NaOHaq
1000
NaOHaq
1000
NaOHaq
1000
V [mL‚min-1]
recovery ratio
0.25 1.00 0.50 0.25 0.25 1.00 0.50 0.25 0.25 1.00 0.50 0.25 0.25 1.00 0.50 0.25
185.0 90.2 60.8 12.4 186.9 75.2 44.9 16.4 93.7 50.5 26.7 12.1 82.1 40.8 21.1 8.3
Figure 10. Effect of flow rates on the elution curves for the Na2HPO4 system on DIAION SA10A.
Figure 11. Effect of flow rates on the elution curves for the Na3PO4 system on DIAION SA10A.
4.2. Elution Curves. Figures 8-11 show the elution curves for H3PO4, NaH2PO4, Na2HPO4, and Na3PO4 systems on an OH-type strongly basic ion exchanger, DIAION SA10A, respectively. The column bed, which was saturated by H2PO4-, HPO42-, and PO43- ions was eluted with a constant 1000 mol‚m-3 NaOH aqueous solution concentration at various flow rates. In all phosphate systems, the elution curves were affected by flow rates. The elution times increased with a decrease in flow rates. At a constant eluent concentration, high elution peaks were obtained at Re′ ) 0.1628 for all phosphate systems. Table 5 provides a comparison between the total amount of phosphate adsorbed in the column bed and the rate of phosphate recovery. For all phosphates systems, all column beds with the lowest and highest saturated phosphate concentrations were eluted at Re′ ) 0.0814, which gave maximum and minimum concentrations of elution curves of phosphates, respectively. In H3PO4, NaH2PO4, Na2HPO4,
Ind. Eng. Chem. Res., Vol. 43, No. 13, 2004 3401
and Na3PO4 systems, the maximum concentrations of elution curves of phosphates were 185, 187, 94, and 82 times larger than the original influent phosphate concentration, respectively. It is apparent that the rate of phosphate recovery increased with a decrease in the influent phosphate concentration. In Figures 8-11, the concentrations of elution curves of phosphates in H3PO4, NaH2PO4, Na2HPO4, and Na3PO4 systems in the whole range of phosphate concentrations considered were around 1000, 1000, 500, and 340 mol‚m-3, respectively. These peculiarities can be explained by the equilibrium reactions (reverse reactions) given in eqs 17-20. 5. Conclusions The breakthrough and elution curves for adsorption of phosphates on an OH-type strongly basic ion exchanger, DIAION SA10A, were investigated. In all phosphate systems, sharp breakthrough curves were obtained and the breakthrough curves were affected by inlet concentrations. The breakthrough times decreased with an increase in the inlet concentration. The ion-exchange capacities of phosphates in the column decreased in the following order: H3PO4 aqueous solution > NaH2PO4 aqueous solution > Na2HPO4 aqueous solution > Na3PO4 aqueous solution. The values of the ratio between the ion-exchange capacity and the total ion-exchange capacity of the resin were around 1.0 in H2PO4-, 0.40 in HPO42-, and 0.34 in PO43-. These differences in the ion-exchange ratios are well explained by the ion-exchange reactions between the OH- ion and phosphate ions. The experimental breakthrough data were all analyzed by neglecting the effect of axial dispersion and by using a linear driving force approximation in the intraparticle diffusion. For all phosphate systems, at a separation factor of R g 0.0594, the theoretical breakthrough lines were calculated numerically for the Langmuir isotherm, while at 0.000 42 e R e 0.035 27, the theoretical breakthrough lines were all calculated using an analytical solution for the rectangular isotherm. The values of the intraparticle effective diffusivity, Deff, increased with an increase in the influent concentration in the order H3PO4 aqueous solution > NaH2PO4 aqueous solution > Na2HPO4 aqueous solution > Na3PO4 aqueous solution. The values of both surface and pore diffusivities were determined using Deff based on the parallel transport by surface and pore diffusions. In H3PO4 and NaH2PO4 systems, the contribution of surface and pore diffusions was significant, while in Na2HPO4 and Na3PO4 systems, the contribution of pore diffusion was significant. At a constant 1000 mol‚m-3 NaOH aqueous solution concentration, sharp elution peaks were obtained. Phosphates were completely and irreversibly desorbed, and highly concentrated phosphates were recovered. In all phosphate systems, all elution curves were affected by flow rates. The elution times increased with a decrease in flow rates. It is apparent that the rate of phosphate recovery increased with a decrease in the influent concentration. Acknowledgment This research was partly supported by the Ministry of Education, Culture, Sports, Science and Technology of Japan under the 21st Century Center of Excellence (COE-21) Program, 24403, E-1, entitled “Water-Assisted Evolution of Valuable Resources and Energy from Organic Wastes”.
Nomenclature C ) equilibrated concentration of phosphate; effluent concentration (mol‚m-3) C0 ) initial concentration of phosphate; influent concentration (mol‚m-3) C* ) equilibrium liquid-phase concentration at the liquidsolid-phase interface (mol‚m-3) Deff ) intraparticle effective diffusivity (m2‚s-1) DL ) liquid-phase diffusivity (m2‚s-1) DPa ) approximate pore diffusivity determined from the slope of the plots according to eq 24 (m2‚s-1) DS ) solid-phase diffusivity based on the parallel diffusion model (m2‚s-1) dp ) resin particle diameter (m) H ) height of the ion-exchange bed (m) K ) Langmuir equilibrium constant (m3‚mol-1) k′f ) liquid-phase mass-transfer coefficient (m‚s-1) kfav ) liquid-phase mass-transfer capacity (s-1) kpav ) resin-phase mass-transfer capacity (s-1) M ) molecular weight of the solvent (g‚mol-1) Q0 ) total ion-exchange capacity of the resin [mol‚(kg of dry resin)-1 or mol‚m-3] q ) resin-phase concentration of phosphates [mol‚(kg of dry resin)-1 or mol‚m-3] q0 ) saturation capacity of the resin or the resin-phase concentration of phosphates in equilibrium with C0 [mol‚ (kg of dry resin)-1 or mol‚m-3] q j ) resin-phase mean concentration of phosphates [mol‚ (kg of dry resin)-1 or mol‚m-3] q* ) equilibrium resin-phase concentration at the liquidsolid-phase interface (mol‚m-3) R ) separation factor Re ) Reynolds number Re′ ) Re/(1 - ) ) adjusted Reynolds number Sc ) µ/FDL ) Schmidt number Sh ) Sherwood number T ) temperature (K) t ) time (s) uf ) linear velocity (m‚s-1) V ) solution volume (m3); volumetric flow rate (mL‚min-1); molal volume of solute at the normal boiling point [mL‚(g‚mol)-1] v ) interstitial velocity (m‚s-1) W ) weight of the resin (kg of dry resin) x ) dimensionless liquid-phase concentration; association parameter multiple of nominal molecular weight of a solvent y ) dimensionless resin-phase concentration yj ) dimensionless resin-phase mean concentration z ) space coordinate upstream (distance from the column inlet) [m] R ) q0/PC0 ) void fraction of the bed (0.40) P ) void of fraction of the resin particle η ) viscosity of the solution (cP) µ ) viscosity [kg‚(m‚s)-1] F ) density (kg‚m-3) ξ ) dimensionless height of the bed τ ) dimensionless time
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Received for review July 1, 2003 Revised manuscript received January 21, 2004 Accepted March 3, 2004 IE030547X
