Ferric Iron Method

ENVIRONMENTAL POLLUTION

Environmental Pollution 101 (1998) 12>130

Modelling of phosphorus removal from aqueous and wastewater samples using ferric iron

K. Fytianos a~*, E. Voudrias b, N. Raikos a Environmental Pollution Control Laboratory, Chemistry Department, University of Thessaloniki, 540 06 Thessaloniki. Greece

bDepartment of Environmental Engineering, Democritus University of Thrace, 67100 Xanthi, Greece

Received 24 June 1997; accepted 5 December 1997

Abstract

Batch laboratory scale experiments were conducted to investigate the removal of phosphate from aqueous and municipal wastewater samples by addition of FeCls.6HsO. The effect of pH, Fe-dose and initial phosphate concentration were assessed. Optimum phosphate removal, 63% for 1:l molar addition of Fe(II1) was observed at pH 4.5. However, a 155% excess of Fe-dose was necessary for complete phosphorus removal. Phosphorus removal from municipal wastewater was slightly higher than that observed for the aqueous solutions. A chemical precipitation mathematical model was developed and tested with the available experimental data. The model included a total of 15 chemical reactions and 4 solid phases with the option of single-phase precipitation or two-phase co-precipitation. The resulting system of non-linear algebraic equations was solved numerically, using the Wijngaarden-Dekker-Brent method. 0 1998 Elsevier Science Ltd. All rights reserved.

Keywords: Phosphorus removal; Iron addition; Mathematical modelling; Municipal wastewater

1. Introduction

Many municipal wastewater-treatment plants are required to remove phosphorus, in order to prevent eutrophication of the receiving surface water bodies, in which the plant effluents are discharged. Phosphorus removal can be accomplished either biologically or by addition of chemicals, such as alum (A12(S0&. 14H20), ferric ion salts (e.g. FeC13.6H20), ferrous iron salts (e.g. FeC12, FeS04.7H20) and lime.

Systems with metal salt (Al(III), Fe(II1)) addition can achieve W-95% total phosphorus removal. Effluent limitations of 1 mg litre- total phosphorus can be met with metal salt addition and efficient clarification to assure effluent total suspended solids of < 15 mg litre-i. To meet effluent discharge limitation of OSmg litre- total phosphorus, filtration of the secondary effluent will most likely be necessary. Even in systems employing biological phosphorus removal, metal salt addition may be necessary to meet special discharge requirements (Environmental Protection Agency, 1987). In this paper,

* Corresponding author. Fax: 00 3031 997747.

the removal of phosphate ion (PO:-) by precipitation with FeC13.6H20 was investigated.

The chemical reactions which take place between phosphate and ferric ions in wastewater are very complex and result in a much larger iron demand than that required by the precipitation reaction alone. The most important parameters affecting the extent of phosphate removal are iron dose, final pH and initial phosphate concentration.

Several studies have addressed the phosphate removal from municipal wastewater by addition of Fe(III), e.g. Hsu (1976), Kavanaugh et al. (1978) Environmental Protection Agency (1987) Luedecke et al. (1989), and references therein. Many of these studies were experimental in nature, whereas some presented the development and testing of theoretical models for phosphate precipitation by addition of ferric iron.

For example, Kavanaugh et al. (1978), presented a chemical precipitation model with only a limited number of Fe- and P- species and two solid precipitation phases, FePO,,,, and Fe(OH)s(,, (a total of six reactions). However, several more reactions need to be considered for a more accurate description of the system

0269-7491/98/$19.00 0 1998 Elsevier Science Ltd. All rights reserved. PII: SO269-7491(98)00007-4

124 K. Fytianos et al.lEnvironmental Pollution 101 (1998) 123-130

and determination of the required ferric iron dose for the desired degree of phosphate removal.

Luedecke et al. (1989) presented a chemical precipitation model, which included a total of 11 chemical reactions and a mechanism for phosphate removal by sorption onto the precipitates. The solid precipitation phases were ferric hydroxyphosphate (Fe2,5 P04(OH)4,s(,$ and ferric hydroxide (FeOOH,,,).

The objective of this work was to study the effect of pH, iron dose and initial phosphate concentration on phosphorus removal from aqueous phosphate solutions and municipal wastewater samples. A mathematical precipitation model was also developed in order to explain theoretically the experimental results. The model was tested using laboratory experimental data from precipitation in artificial systems and primary and secondary effluent of the municipal wastewater- treatment plant of the city of Thessaloniki, Macedonia, Greece. The model included a total of 15 chemical reactions and 4 solid phases with the option of single- phase precipitation or two-phase co-precipitation.

2. Model development

When ferric salts are added into water or wastewater for removal of phosphate ions, a large number of products, including complexes, polymers and precipitates are formed. The following reactions with their equilibrium constants were considered for the development of an equilibrium phosphate-precipitation model, using ferric iron addition:

Kl Fe3+ + Hz0 s Fe(OH)2+ + H +, log K, = -2.2 (1)

(Stumm and Morgan, 1970)

Fe3+ + 2H20 3 Fe(OH)l + 2H+, log& = -5.7 (2)


2Fe3+ + 2H20 2 Fez(O + 2H+, log K; = -2.9 (3)


Fe3+ + 3H20 $? Fe(OH )!$,, + 3H +, log K3 = - 12 (4)


Fe3+ + 4H20 2 Fe(OH ); + 4H+, log K4 = -22 (5)


3Fe3+ + 4HzO 2 Fes(OH )i+ + 4H +, log Ki = -6.3 (6)

(Amirtharajahh and OMelia, 1990)

H3P04 g HzPO, + H +, log &,I = -2.1 (7)

(Snoeyink and Jenkins, 1980)

H2P0,- 3 H2PO;- + H +, log Ka,2 = -7.2 (8)


HPO;- 3 H+P0T3, log Ka,3 = -12.3 (9)


Fe3- + HPOi- 2 FeHPO$, log Kr,p = 9 (10)

(Luedecke et al., 1989)

Fe3+ + HzPO; 2 FeHzPOi+, log &p = 1.8 (11)

log K2.p = 13.4 (this work)


Eqs. (l-6, 10 and 11) represent complex formation and Eqs. (7-9) represent the dissociation of phosphoric acid. A variation of K2,p by several orders of magnitude was reported in the literature, e.g. log K2,p = 1.8 (Stumm and Morgan, 1970) and log K2,p = 21.5 (Luedecke et al., 1989). This constant was used as a fitting parameter in the present work and its log value of 13.4 was determined by minimizing the sum of squares of deviations between experimental data and model calculated results.

In addition, four solid phases were considered in this model and their formation was tested with the experimental data. These phases were FeP04,+ Fe2.sP04 (OH)4.5(+ Fei.6H2P04(OH)3.s(s) and am-FeOOH(,). The first phase was considered in a chemical equilibrium model by Kavanaugh et al. (1978), the second and fourth in a similar model by Luedecke et al. (1989) and the third and fourth by Jenkins and Hermanowicz (1991).

The respective chemical equilibrium equations considered are as follows:

40.~

FeJW0H hr-3(s) T--, rFe 3+ + PO;-

+(3r - 3)OH - (12)

with: log Kso,p = -23 for r = 1, i.e. FePO+) and log KSQP = -97 for r = 2.5, i.e. Fe2.,P04(OH)4.sC,,

KS0.P Fet.&12P04(OH)3,gCs) ;--t 1.6Fe3+ + H2PO;

+3.80H -, log Kso,p = -67.2 (13)

K. Fytianss et al.lEnvirontnental Pollution 101 (1998) 123430 125

am - FeOOH + 3H + && Fe3+

+2H20, log &Fe = 2.5 (14)

The equilibrium constants of Eqs. (12-14) were obtained from Kavanaugh et al. (1978), Luedecke et al. (1989), Stumm and Morgan (1970) and Jenkins and Hermanowicz (1991).

Using Eqs. (l-11), the molar concentration of each soluble reaction product was determined as a function of [Fe3+], [PO:-], [Hf] and the respective activity coefficients:

[FeO-02+] = FH+l % [F$+]

[Fe(OH)t] = s [Fe3+]

(15)

(16)

[Fe2(0H)i+] = 3 [Fe3+12 (17)

[Fe(OH)!&G] = s [Fe3+l

[WOW;] = s [Fe3+]

[FeJ(OH)F] = m [H +l4 Fe3+13

[H3P041= K, Iz2K, 3 W + 12W:-1 . 1 I

[H2P0,] = & [H + 12W:-1

[HPO;-] = 2 [I-I + ]PO;-I

(18)

[FeHPOl] = K1&isp [H + ][Fe3+][POi-]

[FeH2POp] = $$:I [H+]2[Fe3+1[PO:-l

(19)

(20)

(21)

(22)

(23)

(24)

(25)

The constants Ii and Ai are functions of the activity coefficients yi and were computed according to the equations provided in the Appendix A.

In this paper, we will solve the problem of one-phase precipitation by considering the three solid phases, which are Fe,P04(OH),,_,,,, (i.e. FePO+, for r = 1 and Fe2.sP04(OH)4.5(s) for r = 2.5) and Fel.6H2PO4(OH),.s,), one at a time. This scenario is most likely to occur at stoichiometric ferric iron doses. Because at high iron doses, two-phase precipitation may be possible, we will solve the problem of co-precipitation of am-FeOOHc,, with each of the three phases mentioned, considering them one at a time.

3. Single-phase precipitation

For the case of precipitation of Fe,P04(OH)3,_3C,j as a single phase, the system is defined by Eqs. (1525), the solubility product (Eq. (26)), the mass balance for Fe and P (Eqs. (27) and (28)) and the stoichiometric ratio (Eq. (29)):

[PO;-] = &o+p . (M~+)(~*-~)[H +](3r-3)

(&)3-3 (&?+)* ypO:-

[Fed] = [Fe,1 + CT,F~

[po] = [ppl + cT,P

lFeIJ - ). PPI

with:

Kw = MI+ YOH- [H + IPH - 1

1 [Fe3+] (26)

(27)

(28)

(29

(30)

CT,F~ = [Fe3+] + [Fe(OH)2+] + Fe(OH)t]

+Wd0H)~l+ [WOH)&9)] + [Fe(OH)i]

+3[Fes(OH)F] + [FeHPOi] + [FeH2POi+]

(31)

cT,P = [H3P04] + [H,PO,] + [HPOZ-]

+[PO:-] + [FeHPOi] + [FeH2POi+] (32)

126 K. Fytianos et al./Environmental Pollution 101 (1998) 123430

where: [Fed] = dose of ferric iron, M [P,] = initial phosphorus concentration, M [Fe,] = concentration of Fe precipitated, M [Pr] = concentration of P precipitated, M

The system of eauations was reduced to a polynomial

Eq. (33) was solved numerically, using the Winjgaarden- Dekker-Brent method (Press et al., 1992).

_ equation for residual [Fe3] in solution:

@[Fe3+13 + P[Fe3+12 + A[Fe3+]

-(I - 1)BO[Fe3+]-(-) - rEO[Fe3+]-

+A=0

with a, P, A, B, E, 0 and A defined by:

@_3KbF& -- [H +I4

(33)

(34)

p _ =w; -- [H +I2

(35)

A=+%+$+$+$-$ (36)

B KLPALP = Ka,3 [H+]+z;z;;[H+]2

A3

E = &,~&,2&,3 H +I3 &,2&.3 A[H +I2

+++I+

@= Kso,p . (yH+)3-[H +](3r-3)

(jyw)3-3 h7e3+ 1 VPO-

A = r[Pol - [Fed]

(37)

(38)

(3%

(40)

For the case of precipation of Fei.6H2P04(0H)s.s(+ the coefficients @, P, A, B and E are defined as before, whereas 0 and A are:

o = &O,P&,2&,3 . (YH+)~.*W +I.*

Add.* (Ype~+)l%H*PO; (41)

h = 1.6[p,] - [Fed] (42)

4. Two-phase co-precipitation

In the case of co-precipitation of am-FeOOHt,, and Fe,P04(0H)s,_3,+ the system is defined by Eqs. (15-25), the solubility products (Eqs. (26) and (43)) and the mass balance for Fe and P (Eqs. (27, 28, 31, 32, 44 and 45)):

[Fe3+] = Kso;;;3y)3 [H + 13 (43)

[Fe,1 = ~P9Q40H)~,-~~s~l +[am - FeOOH(,)] (4)

[p,,l = [FeJW0Hhr-3(,)l (45)

For the case of co-precipitation of am-FeOOH,,) and Fei,6H2P04(OH)3.8(,~, Eqs. (26, 44 and 45) need to be modified accordingly to account for the difference in stoichiometry.

Because of the co-precipitation, the residual [Fe3] and PO:-] in solution are fixed and were used to compute the molar concentrations of all soluble species of Fe and P (Eqs. (15-25)). In practice, regardless of which solid phase precipitates, we are interested in Cr,p and ([Fe$ + [Pr]) as a function of [P,] and [Fed]. The former provides an estimate of the percentage removal and the amount of P to be discharged daily. The latter is necessary for sizing the settling and thickening equipment, and managing solid disposal activities.

5. Materials and methods

De-ionized water was used for preparation of all synthetic solutions. Primary and secondary effluent was obtained from the municipal wastewater-treatment plant of the city of Thessaloniki, Macedonia, Greece. Dihydrogen potasium phosphate (KH2P04) and FeC13.6H20 of p.a. grade were reagent grade and pur- chased from Merck.

Precipitation experiments were conducted in laboratory scale batch reactors containing a known volume of aqueous KH2P04 solution, or primary or secondary effluent. The initial phosphate concentration in each experiment was determined before addition of a known volume of FeC13.6H20, according to Standard Methods (1975).

K. Fytianos et al./Environmental Pollution 101 (1998) 123430 127

6. Results and discussion

6.1. Comparison between theoretical and experimental results

A pC-pH diagram for the total P-species remaining in solution after removal of solid phases is presented in Fig. 1. In this figure, pC is defined as: pC = -log Cr,r, where Cr,p (mol litre-) is defined by Eq. (32). The three lines represent the model predictions for one at a time single phase precipitation of FeP04(,), Fe2.sP04 (OH&) and Fe1.6H2P04(OH)3.8 for the addition of Fe3+ at Fe:P= 1.1 molar ratio.

The only fitting parameter of the model for the com- putations in Fig. 1 was the equilibrium constant Kz,~ of Eq. (11). The model was calibrated for log K2,P= 13.35 for two of the three phases, Fe2.5P04(OH)4.s(s) and Fel.6H2P04(OH)3.s(s). It should be mentioned that the value of K2,P varies by several orders of magnitude in the literature. For example, Stumm and Morgan ( 1970) reported log K2,p = 1.8, and Luedecke et al. (1989) reported log K 2,P = 21.5. The latter investigators used the constant K2,p as a fitting parameter of their model as well. No adjustment was made for the FePO,,,, precipitation case, and the value of log Kz,p = 1.8 (Stumm and Morgan, 1970) was used in Fig. 1. Any other com- bination of K2,p values, resulted in poorer model fits.

Visual inspection of Fig. 1 shows that all three lines describe to some degree the experimental data, although the computation of sums of squares of deviations sug- gests that the best-fitting line is the one corresponding to single-phase precipitation of Fe2.5P04(OH)4.5(+ However, this line levels off and does not show the downward trend of the experimental data. On the other hand, the line corresponding to FePO,,,, exhibits larger deviations but follows closer the general trend of the experimental data.

Fig. 1 was constructed for 1: 1 molar addition of Fe3 + . Therefore, it was attempted to test the model perfomance for conditions of excess of Fe3+ addition and pH = 4.5. The experimental data and model predictions for one at a time single-phase precipitation are compared in Fig. 2. It appears that the line corresponding to precipitation of FePO,,,, describes the experimental data best, followed by the line corresponding to Fe2.5P04(OH)4.5(s). In contrast, the line corresponding to precipitation of Fei.6H2P04(OH)3.g(s) describes only some and exhibits very large deviations for the remainder of the data.

In conclusion, as indicated by Figs 1 and 2, the experimental data were best modelled by single phase precipitation of FePO+), followed by precipitation of Fe2.5PO4(OH)4.s(+ as the second best choice. No fitting parameter was used in the case of FePO+,, whereas the equilibrium constant K2,p (Eq. (11)) was adjusted in Fig. 1 for the case of Fe2.5P04(OH)4.5(s). Any effort to

model the data using two-phase precipitation resulted in poor fits (Figs 3 and 4).

4.2. Chemical composition of the precipitates formed

The Fe:P ratio in the precipitate formed after addition of an equimolar amount of FeC13.6H20 to an aqueous KH2PO4 solution was determined by scanning

4.80 1 I es

Fig. 1. Comparison between theoretical and experimental results for single-phase precipitation. Effect of pH. Units of C are in mol Mm-. 0: experimental data from aqueous solutions; I: experimental data from primary effluent; E: experimental data from secondary effluent.

20.00

lo.00

; 12.00

0.00 I

I

I

I

I

I

,

,

__ _ I

,

I

I

I

,

I

I

I

I

I

I

0.0 40.0 96 & Feflll)

i20.0 160.0

Fig. 2. Comparison between theoretical and experimental results for single-phase precipitation. Effect of Fe-dose. Units of C are in mol litre-. 0: experimental data from aqueous solutions; IXI: experimental data from primary effluent; 8: experimental data from secondary effluent.

128 K. Fytianos et al./Environmental Pollution 101 (1998) 123-130

Fig. 3. Comparison between theoretical and experimental results for two-phase precipitation. Effect of PH. Units of C are in mol litre-. IXI: experimental data from primary effluent; 8: experimental data from secondary effluent.

m.00

7 1 ______________________

l2.00 -I t

-_-__----_--___

;; 8.00

0000 expabdd - lwoQ)+amaooH@J . - - - _ - FarpO~OH)&,@ + sm.FeoOH(., - - - - Fet&lO~OHhop + am-FeOO%o

B ti 0 C.)

4.00 I 00 O

0.00 , I I 1 I I I /

0.0 40.0 K ExcE2oF &?(lll)

120.0 160.0

Fig. 4. Comparison between theoretical and experimental results for two-phase precipitation. Effect of Fe-dose. Units of C are in mol litre-*. I: experimental data from primary effluent; EI: experimental data from secondary effluent.

electron microscopy (SEM). The analytical system attached to the SEM was an energy dispersive X-ray analytical system with a spot diameter of 1 Wm. The calibration element was cobalt. The calibration was performed once per day and a standard similar in composition with the analysed material was measured. The values of ratio obtained for three such measure- ments were 1.525, 1.820 and 1.666, with an average of 1.670. The theoretical stoichiometric Fe:P ratios for

the three precipitates FeP04(,), Fe2.5P04(OH)4.5(s) and Fe1.6H2P04(OH)3.8(sj under consideration in this study are 1.803,4.508 and 2.885, respectively.

It is obvious that, on the basis of Fe:P ratios alone, the precipitate formed in our experiments at Fe:P addition of 1:l can be neither Fe2.5P04(OH)4.5(sj nor Fer.6H2P04(OH)s.s(s) or mixtures of them with FeOOH,,. Therefore, the closest match is with FePO,,,,. The lower Fe:P ratio measured (1.670 < 1.803) is likely to. be due to experimental error. Otherwise, a solid phase with Fe:P < 1 (on molar basis) would have to be considered and such a compound could not be found in the relevant literature (Stumm and Morgan, 1970).

In experiments with addition of excess of Fe(II1) (Fig. 2), the solid phase precipitated can not be FePO,,,,. Since two-phase precipitation is not supported by experimental data (Figs 3 and 4), the iron excess has to be incorporated in precipitating solid phase, with a molar ratio Fe:P > 1. Based on Fig. 2, this solid phase is Fe2.sPO4(OH)4.5(,).

In conclusion, at Fe:P = 1:l molar ratios, the precipitating phase is FePO,,,. At Fe:P > 1:l molar ratios, the precipitating phase supported by the data, is Fe2.5PO4(OH)4.5(,).

6.3. E#ect of pH on phosphate removal

Fig. 5 presents the percentage removal of phosphorus species in the pH range 3-8, for equimolar addition (1: 1) of Fe(II1). The experimental data show that the removal is optimum (5363%) in the pH range 4-5.5. The highest value of 63% removal was observed at pH 4.5. These results are in qualitative agreement with the line corresponding to FePO,, precipitation in Fig. 1. The excellent quantitative agreement between model prediction for Fe2.5P04(OH),,5,, precipitation and the highest pC value (at pH 4.5) was considered circum- stantial, since the precipitating phase at 1:l Fe:P addi- tional is FePO,,, as was explained before. Clearly, the trend in the observed phosphorus removal as a function of pH was best simulated with the FeP04(,) line (Fig. 1).

6.4. ESfect of Fe(III) dose excess on phosphate removal

Fig. 6 indicates that P-removal increased with increasing Fe(II1) dose. The increase ranged from 63% for equimolar Fe(II1) addition (0% excess) to 100% for Fe:P=2.55:1 (155% excess), all determined at pH 4.5. This trend was also predicted by the mathematical model (Fig. 2).

4.5. Eflect of initial phosphate concentration

The percentage removal of phosphate increased as its initial concentration increased from 1 to Sppm. Above 5ppm the percentage removal levelled-off, as shown in

K. Fythos et al./Environmental Poilution 101 (1998) 123-130 129

1 2 3 4 5 6 7 6

PH

Fig. 5. Effect of pH on removal of PO:- by FeCls.6HaO. +: aqueous solutions; IXI: experimental data from primary effluent; EI: experimental data from secondary effluent.

100

95

90

t 65 : B 60

= 8 75

E 2 70

' 65

60 ki

55

50 1 0 30 60 So 120 150 160

% Excess of FeCI,.GH,O

Fig. 6. Effect of excess of FeC13.6H20 on the removal of PO:-. Values in parentheses are Fe:P molar ratios. Excess of 0% corresponds to stoichiometry. I: experimental data from primary effluent; EI: experimental data from secondary effluent.

70

65

60 .

:! 55 B

: 50

g I$ 45 ae

40

35

__ 0 5 10 15 20 25 30

Initial PO, concentration (ppm)

Fig. 7. Effect of initial PO:- concentration on its removal by FeCls.6HrO.

Table 1 Removal of phosphate from municipal wastewater

Primary treatment

Secondary treatment

Fe:P Removal (%)

1.1 70.6 2.71 97.6 1.0 60.7 2.52 93.6

Fig. 7. To assess the effect of initial phosphate concentration, equimolar Fe(II1) doses at pH 4.5 were used.

6.6. Phosphorus removal from municipal wastewater

Primary and secondary wastewater samples were col- lected from the biological wastewater-treatment plant of the city of Thessaloniki, Macedonia, Greece. The plant has a capacity of 40 000 m3 day- and removes BODs and suspended solids by more than 90/o. The treatment train includes grit and fat and oil removal, primary treatment with addition of FeClS04, primary clarification, secondary activated sludge treatment, secondary classification and disinfection with chlorine dioxide. The addition of FeClS04 in the treatment plant did not affect our results, because our experiments were conducted several hours after addition of FeClSO+

The initial phosphate concentration in the wastewater was 22.7 ppm for the primary and 10.5 ppm for the secondary effluent. These samples were treated by addition of FeC13.6H20 in the same way as the respective aqueous samples. The molar Fe:P ratios used were 1.1 and 2.71 for the primary and 1.0 and 2.52 for the secondary effluent. At pH 4.5, the respective phosphorus removals were 70.6 and 97.6% for the primary effluent and 60.7 and 93.6 for the secondary effluent. These results are presented in Table 1.

These removals are slightly higher than those observed for the aqueous laboratory solutions and agree reasonably well with the theoretical model predictions (Figs 1 and 2).

7. Conclusions

The removal of phosphate from aqueous and municipal wastewater samples by addition of ferric iron is pH-dependent. The optimal removal was 63% at pH 4.5 for equimolar Fe-dose. Excess addition of Fe-dose increased the percentage phosphate removal of 63% at 0% excess to 100% for 155% excess. For equimolar Fe- dose, the phosphate removal was a function of its initial concentration in the 0-5ppm range. Above Sppm, the removal was unaffected by the initial phosphate concentration. Phosphate removal from municipal wastewater was slightly higher than that observed for the aqueous solutions. A mathematical chemical precipitation model

130 K. Fytianos et al./Environmental Pollution 101 (1998) 123-130

was developed and tested with the experimental data. Based on the model calculations and the SEM analysis of the formed precipitate, it was concluded that: at Fe:P 1:1 molar ratios the precipitating phase was FePO,,,,. At Fe:P > 1:l molar ratios, the precipitating phase was Fe2.5PWGH)4.5(s).

References

Amirtharajah, A., OMelia, C.R., 1990. Coagulation processes: destabil- ization mixing and flocculation. In: Water Quality and Treatment, American Water Works Association, 4th Edition. McGraw-Hill, New York, NY 10020-1095 pp. 269-365.

Environmental Protection Agency, 1987. Design Manual, Phosphorus Removal, EPA/625/i-87/001, Cincinnati, Ohio.

Hsu, P.H., 1976. Comparison of iron (III) and alumninum in precipitation of phosphate from solution. Water Research 10,903907.

Jenkins, D., Hermanowicz, S.W., 1991. Principles of chemical phosphate removal. In: Sedlak, R. (Ed.). Phosphorus and nitrogen removal from municipal wastewater. Principles and practice, 2nd Edition. Lewis Publishers, CRC Press, LLC. Raton, FL, USA 33431 pp. 91-110.

Kavanaugh, M.C., Krejci, V., Weber, T., Eugster, J., Roberts, P.V., 1978. Phosphorus removal by post-precipitation with Fe(II1). Jour- nal Water Pollution Control Federation 50,216234.

Luedecke, C., Hermanowicx, S.W., Jenkins, D., 1989. Precipitation of ferric phosphate in activated sludge: a chemical model and its ver- ification. Water Science and Technology 21, 325337.

Press, W.H., Tenkolsky, S.A., Vetterling, W.T., Flannery, B.P., 1992. Numerical Recipes in Fortran. The Art of Scientific Computing, 2nd Edition. Cambridge University Press, Cambridge.

Snoeyink, V.L., Jenkins, D., 1980. Water Chemistry. Wiley, New York. Standard Methods, 1975. Standard Methods for the Examination of

Water and Wastewater, 14th Edition. APHA, AWWA, WPCF. American Public Health Association, Washington, DC 20036.

Stumm, W., Morgan, J.J., 1970. Aquatic Chemistry. Wiley, Inter- science, New York.

Appendix A

The following equations were used to compute the constants Pi and hi as functions of activity coefficients yi:

ri = YFe+ YH+ YFe(OH)+

(AI)

r2 = YFe3+

(YH+?YF~(oH); WI

r; = (YFe3+j2

(YH+ j2 YF~oI-I)~

r3 = YFe+ (YH+ I3 YF~(oH)!&

r4 = YFe+ (YI-I+)~YF~(OH),-

r& = (?+e3+ I3 oH+ )4Y~e,(~~)F

A1 = YF@- YH +

YHPq-

A 3

= YIc$(YH+)~

Y&p04

A~ p = YE+ YFe+ YFO:-

YFeHFO:

643)

644)

645)

W)

(A71

648)

(A9

(AlO)

(Al 1)

In all cases, the activity coefficients, yi, were calculated from the Guntelberg approximation (Snoeyink and Jenkins, 1980):

& log fl= -Aw$ - 1 +

Ferric Iron Method

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