Kinetics of Wastewater Treatment. Proceedings of a Post-Conference Seminar Held at the Technical University of Denmark, Copenhagen, 1978

176 Pages·1979·3.651 MB·English

by  S. H. Jenkins (Eds.)

KINETICS
OF
WASTEWATER
TREATMENT
Proceedings of a Post-Conference Seminar held at the Technical University of Denmark,
Copenhagen, 1978
Organized by Professor P. Harremoës
EXECUTIVE EDITOR
S. H. JENKINS
PERGAMON PRESS
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First edition 1979
Library of Congress Catalog Card No. 73-1162
ISBN 0 08 024855 1
Published as a supplement to
Progress in Water Technology
Volume 10 Numbers 5 and 6.
Printed in Great Britain by A. Wheat on & Co. Ltd., Exeter
Prog. Wat. Tech. 1979, Suppl. 1, pp. 1-17.
Pergamon Press. Printed in Great Britain.
CALCIUM PHOSPHATE PRECIPITATION IN A
DENITRIFYING BIOFILM —THE CONCEPTUAL
BASIS
Erik Arvin
Dept. of Sanitary Engineering, Bldg 115, Technical University of Denmark,
2800 Lyngby, Denmark
ABSTRACT
A kinetic model for calcium phosphate precipitation in a fixed denitrifying bio-
film is presented. The calcium phosphate precipitation is a result of the high
pH created in the biofilm by the denitrification reaction. According to the model
the phosphate removal is directly linked to the zero-order nitrate removal. In
addition the removal rate is predicted to be relatively high in areas with low
alkalinity wastewater. If calcium carbonate precipitates and exists in equilibrium
in the biofilm calcium phosphate will redissolve.
The theory presented may explain some of the observations often referred to as
luxury phosphate removal.
INTRODUCTION
It has been shown that calcium phosphate equilibria may control the soluble phos-
phate concentration in the effluent from biological wastewater treatment plants
in areas with medium-hard and hard water, Arvin (1978). Based on the phosphate
equilibrium theory it is possible to explain many of the observations often re-
ferred to as luxury phosphorus uptake and anaerobic phosphorus stripping.
In areas with soft water calcium phosphate precipitation may not occur due to the
composition of the bulk water. Nevertheless in soft water areas extensive phos-
phorus removal in activated sludge plants has been reported, Barnard (1976), Os-
borne & Nicholls (1977), Hoffmann & Marais (1977), Vogelzang & Marais (1977).
A theory is presented in the following which explains the extensive phosphorus re-
moval in soft water areas as calcium phosphate precipitation inside a denitrifying
biofilm. The theory combines the calcium phosphate equilibrium theory with the
theory of denitrification in biofilms.
1
E. Arvin
2
Riemer & Harremoés (1978) have shown that the diffusion of bicarbonate- and car-
bonate ions out of a denitrifying biofilm creates a surprisingly high pH in most
of the reaction zone, namely pH-values of 8.5-9.2. At such high pH values the
equilibrium phosphate concentration of some calcium phosphate compounds, for ex-
ample tricalcium phosphate, Ca (PO ) , is low, less than 1-4 mg P/ß, depending
2
of the calcium concentration. The low phosphate concentration in the biofilm
will establish a concentration gradient with the resultant flux of phosphate
from the bulk liquid into the biofilm.
According to this theory a high phosphate removal is not the result of usual mi-
crobial phosphate assimilation, but the microorganisms create an environment in-
side the denitrifying biofilm, which favors calcium phosphate precipitation.
GENERAL REACTION DELINEATION AND ASSUMPTIONS
A homogenous denitrifying biofilm is considered in the following. When methanol
acts as an electron donor the denitrification reaction is as follows.
f CH3OH + N0 - + \ N + I HC0 - + \ CO3- + § H 0 (1)
3 2 3 2
The consumption of the electrondonor and the production of bicarbonate and carbo-
nate per mole of nitrate will be called f , f and f in the following (stoi-
0
E i. Δ
chiometric coefficients).
The bicarbonate and carbonate ions increase the pH in the biofilm. The pH-profi-
les at various operating conditions, as calculated by Riemer & Harremoés (1978),
are shown in Figure 1.
Phosphate, which will not precipitate in the bulk liquid due to the low calcium
concentration, will precipitate as calcium phosphate at a certain distance from
the biofilm surface. Further into the biofilm calcium carbonate precipitation
will commence due to the increasing carbonate ion concentration. Figure 2
shows qualitatively the profiles of pH, calcium, and phosphate in the three zones
referred to above.
The precipitation of phosphate ions will remove an equivalent amount of calcium
ions. Consequently the concentration of calcium in the biofilm will decrease
with the result that phosphate will precipitate with a lower rate compared to the
situation of constant calcium concentration throughout the biofilm.
The calcium carbonate precipitation may have a significent effect on both the pH
and the calcium concentration if a significant amount of the carbonate produced is
Precipitation in a Denitrifying Biofilm 3
removed as calcium carbonate. The pH increase will level off and the calcium
concentration will decrease with the total effect, that solid calcium phosphate
may dissolve.
Δ PH
0 0.1
Fig. 1. Distribution of pH in a denitrifying biofilm.
Plotted as a function of the location in the biofilm, expressed as a
fraction^ , of the active denitrifying part of the biofilm ζ = -— .
e
X : length in the biofilm
L : active length
Nitrate is assumed to be rate limiting, i.e. the nitrate concentration
determine the length L .
bulk liquid inert surface
Calcium carbonate and -phosphate precipitation
Calcium phosphate precipitation
Film with no precipitation : Transition zone
Fig. 2 Concentration profiles of pH, calcium and phosphate ions in a denitri-
fying biofilm. Shown qualitatively.
4 E. Arvin
To illustrate the general aspects of the biofilm reactions the development of a
kinetic model is based on ion concentrations, not ion activities, and in the
first place the Donnan distribution of ions between the bulk liquid and the bio-
film will be ignored. The errors introduced by this procedure will be discussed
later.
KINETICS OF CALCIUM PHOSPHATE PRECIPITATION IN A BIOFILM WITH NO CAL-
CITE PRESENT
The precipitated calcium phosphate compound is assumed to be in equilibrium
throughout the biofilm, i.e. the transition zone shown in Figure 2, is not consi-
dered. The length of this zone will be calculated in the following section.
In addition it is assumed that the carbondioxide concentration is negligible.
The equilibrium solubility of a calcium phosphate compound is a function of pH,
calciumactivity and the activity coefficients of hydrogenphosphate and dihydro-
genphosphate ions, Arvin (1978):
aH / K2,p 1 aCa \
(2)
Ρ'βςΐ aCaP V&H YRP04 V°4 &Η '
C : equilibrium concentration of soluble phosphate
K : a solubility constant specific for a specific calcium phosphate com-
pound
a : hydrogen ion activity
H
a : calcium ion activity
3 : a constant specific for a specific calcium phosphate compound. 3 >_ 1
p : a constant equal to: y (3 + 1)
ΎΗΡ0 : activity coefficient of HPO
4
ΎΗ2Ρ04: activity coefficient of H PO "
K : second dissociation constant of phosphoric acid
z9,p
K : complexation constant of the complex: CaHP0 (aq)
4
When the activity coefficients are put equal to 1, equation 2 is reduced to the
following equation at the alkaline pH level prevailing in the biofilm:
P*eq p \ C 2,p C CU /
r
Cca
Precipitation in a Denitrifying Biofilm 5
~ ß-1
H
PfSq K K2 /P P (1 + KC CCa) (3)
r
CCa
The flux of phosphate from the bulk liquid to the biofilm, N *, is equal to the
reaction rate of phosphate per unit area, r
a,p
dC
N * = -D -4^L
=
a,p p p dx
X = 0 (4)
dC
P'eq
concentration-gradient at the biofilm surface
dX
X = 0
D : diffusion coefficient of phosphate
X : depth in biofilm, refer to Figure 3.
By differentrating Eq. 3 with respect to X and rearranging, the result is:
3-2
dC C dC
H
P*eg _ H [(3-D (ΐ+κ^ c )
v K
dX - K K2,p — C Ca' dX
CCa
C dC
(5)
Ca H J
The term —^ K C is approximately equal to zero at the p and C values of
p c ca Ca
interest.
From this approximation and by inserting the expression for C (Eq. 3),
Equation 5 is changed to
dC: p,eq _ rΓ ,(A3 ,-,D d^CE„ dCC.a
dX p,eq [ C dX C„ (1+K^ C ) dX (6)
Ca C Ca
The calcium flux, N , is linked to the phosphate flux, N ,:
La P
N = f . N
C0a Ca p
which can also be written as:
dC„ / dC v
Ca
-D„ (- P^g) (7)
Ca dX f D
Ca V p dX y
f is the ratio of calcium to phosphorus in the solid calcium phosphate compound.
Ca
6 E. Arvin
L
water homogenous (inert support
biofilm material
N,^.
Cj#
H*l
Fig. 3. Geometry of biofilm with diffusion of component i.
The hydrogen ion gradient can be found from the following equilibrium equat-
dX
ion of the carbonate buffer system, which controls the pH:
CH C2
2,C (8)
: second dissociation constant of carbonic acid
2,C
: concentration of carbonate ions, CO^
: concentration of bicarbonate ions, HCC>
3
From Eq.8
dC
H
dX _ vc2 dx ci dX; (9)
The gradients of bicarbonate and carbonate ions are obtained from the concentrat-
ion profile equations.
The concentration profile of any component, i, involved in the denitrification
reaction can be calculated from a mass balance of a differential section, dx, of
the biofilm, Figure 3, refer to Harremoës (1978):
d2c.
ofN
1 = ± f. (10)
dX 1
C. concentration of component i
i
zero-order reaction rate of nitrate in the biofilm.
ofN
(Based on volume) (< 0)
D. diffusion coefficient of substance i
1
stoichiometric coefficient
positive sign used when substance i is produced and vice versa.
Precipitation in a Denitrifying Biofilm 7
The boundary conditions are
*
X=0 : C. = C.
1 1
dC.
X=L 1 = 0
dX
When substance i is produced the concentration profile is:
k k
* 1 ofN 2 ofN
ci - ci + 1 h H? x - fi -ΊΓ L x (11)
1 1
and the concentration gradient is:
dC. k
AT
1 dCH
Based on Eq. 9 and 12 -r— at the biofilm surface is:
dX
* *
dC H K2,C W(' C-~ Vf^ C^' f )
dX *2
X=0 C
2
(Concentrations with a star, C , indicate the concentration at the biofilm sur-
face) .
C *f
2 1
Considering that the term — is negligible, and (-k )«L is the zero-order
nitrate removal rate in the biofilm, r , Harremoës (1978), Equations 4, 6, 7
and 13 give:
r D (3-l)f C
a,p _ p 20 p,eq
ra,N r C * f„ D
Ί
|l + J2iS3 ÏÎ P I D c * (14)
I c" * (1+K C *) n J ϋ2 C2 U4J
L Ca C Ca' CaJ
It can be shown that the corresponding equation at constant calcium concentrat-
ion throughout the biofilm is:
r D (3-D fo C *
-5i£ . P 2 p,eq
ra,N V C 2
It is emphasized that C is not the actual phosphate concentration at the bio-
film surface, but the equilibrium phosphate concentration at the actual pH and
calcium concentration. A consequence of this is, that the relative phosphate re-
moval rate (relative to nitrate removal rate) is decreased by the increasing pH
because C * is decreased and vice versa. Figure 4 shows the relationship
P,eq
between C * and pH for dicalcium phosphate and tricalcium phosphate.
8 E. Arvin
. Cp mg P/1 Cp mg P/t
CaHPOA CQ3(P04Î2
20mgCa*4/l
50 - - —
70—·· —
20rrrçCa"/l
50mgCa**/l
70mgCa**/l
7.5 8 8.5 7.5 8 8.5
Fig. 4. Solubilities of CaHPO and Ca (P0 ) in relation to pH and calcium
4 2
activity, Arvin (1978).
Equation 13 also shows, that at a fixed pH in the bulk water the relative removal
rate is high at low carbonate concentration, i.e. at low alkalinity.
The magnitude of the parameters k and f depend of the carbon source. k
2 QfN
for methanol is 17-28 g m"3 min" (10°C), Riemer (1977). Values of k for
QfN
other carbon sources are not well established. Values of f in relation to the
2
type of carbon source is shown in Table 1.
Table 1. Stoichiometric Coefficients for Electron Donor (f )
Bicarbonate (f, ) and Carbonate (f ) in Denitrification
Reactions with Various Electron Donors
Electron donor fE fl f2
CH OH 5/6 2/3 1/6
HCOO~ 5/2 3/2 1
CH3C0O~ 5/8 7/8 3/8 1
C H5COO~ 5/14 11/14 4/14
CH4 5/8 1/4 3/8 1
Equation 14 shows that the phosphate removal is zero if 1, i.e. if dicalcium
phosphate, CaHPO , precipitates. This is a result of the approximation made in