APPLICATION OF INTEGRATED CHEMICAL - PHYSICAL PROCESSES
MODELLING TO AERATION TREATMENT OF ANAEROBIC DIGESTER LIQUORS
M C Wentzel*, E V Musvoto and G A Ekama
Water Research Group, University of Cape Town, Department of Civil Engineering, Rondebosch,
7701, South Africa; *Corresponding author: e-mail: markw@eng.uct.ac.za.
ABSTRACT
A three phase (aqueous/solid/gas) mixed weak acid/base kinetic model developed by Musvoto et al.
(2000a,b) is applied to simulate the physical and chemical processes that occur on aeration of anaerobic
digester liquors. Included in the model are the kinetic reactions for (i) weak acid/base dissociations
(water, carbonate, ammonium, phosphate, and short-chain fatty acids), (ii) precipitation of struvite,
newberyite, amorphous calcium phosphate, calcium and magnesium carbonate, (iii) ion pair formation
and (iv) stripping of CO2 and NH3 gases. To generate data for model application, batch aeration tests
were conducted on two anaerobic digester liquors from (i) a spent wine upflow anaerobic sludge bed
(UASB) digester and (ii) a sewage sludge anaerobic digester. In the batch tests pH, Ca, Mg, PO 4-P, free
and saline ammonia (FSA) and H2CO3* Alkalinity (from which inorganic carbon is calculated) were
measured. After establishing from the literature values for (i) weak acid/base equilibrium constants
(pKa), (ii) weak acid/base kinetic rate constants (Kra), and (iii) ion pair stability constants (pKST), and trial
and error determination of (iv) mineral solubility products (pKSP) (within the range reported in the
literature), (v) ion pair kinetic rate constants (KrIP), (vi) mineral precipitation rate constants (Kppt) and (vii)
gas stripping rates (KrG), a good correlation between predicted and measured data was obtained for all the
parameters for both liquors. The solubility product values for the minerals that precipitated were the
same for both liquors and fall in the range of values quoted in the literature, but the specific precipitation
rate constants of the minerals differed for the two liquors.
KEY WORDS
anaerobic digester liquor, gas stripping, kinetic model, precipitation, solubility product, weak acid/base
INTRODUCTION
Loss of CO2 from anaerobic digestor liquor (ADL) through deliberate or inadvertent aeration causes an
increase in pH; at higher pH various calcium and magnesium phosphates (and possibly carbonates)
precipitate and NH3 stripping occurs. Loss of CO2 thus can be problematic, with magnesium phosphate
precipitants such as struvite causing pipe blockages (e.g. Borgerding, 1972; Mamais et al., 1994).
However, this process has been exploited as a treatment method for removal of the high concentrations of
N and/or P commonly found in ADL, particularly those from digestion of waste sludge from biological P
removal activated sludge systems (e.g. Pitman et al., 1989; Pitman 1999; Stratful et al., 1999). To
optimize this system, and to develop and evaluate alternative treatment methods for ADL, a model that
can conveniently handle three phase (aqueous/solid/gas) weak acid/base chemistry will be helpful.
Musvoto et al. (2000a) describe the development of a kinetic model for the single aqueous phase
behaviour of mixed weak acid/base systems and included precipitation of CaCO3, CO2 gas exchange and
ion-pairing effects. In the model, the weak acid/base equilibria have been formulated in terms of the
kinetics of the forward and reverse reactions for the dissociation of the weak acid/bases. The compound
H+ is explicitly included and pH is calculated from the H+ concentration via pH = -log fm [H+]. Similarly,
ion pairing equilibria have been formulated in terms of the kinetics of the forward and reverse reactions
for the ion pairs. This model was validated for the equilibrium (time independent) condition by
comparing predicted steady state results with predictions from well established equilibrium chemistry
based models in the literature, for (i) the three phase behaviour of the carbonate system in pure water, and
2
Wentzel, Musvoto and Ekama
(ii) the single aqueous phase behaviour of mixed weak/acid base systems (carbonate, ammonium and
phosphate). More extensive validation was not possible because suitable data were not available.
Musvoto et al. (2000b) extended the model to describe the three phase weak acid/base reactions that
occur when ADL are aerated. The resultant kinetic model was validated by comparing predictions with
(i) equilibrium (time independent) data available in the literature. In this paper, the model will be
described briefly and the validation extended to (ii) kinetic (time dependent) data obtained from aerated
batch tests on two ADL.
MODEL DESCRIPTION
The three phase (aqueous/solid/gas) chemical processes that occur during aeration of ADL are the
forward and reverse dissociation processes of the weak acid/base species, precipitation of various
magnesium and calcium phosphates and carbonates, ion pairing and stripping of CO2 and NH3.
Weak acid/bases
For the carbonate, phosphate, free and saline ammonia (FSA) , short chain fatty acids (SCFA) and water
weak acid/base systems, there are 16 forward and reverse dissociation processes; 4 for the carbonate, 6 for
the phosphate, and 2 each for the water, SCFA and FSA systems. There are 13 compounds; 3 for the
carbonate, 4 for the phosphate and 2 each for the water, SCFA and FSA systems. These are processes 1
to 16 and compounds 1 to 13 in the model matrix of Musvoto et al. (2000a).
Precipitation of minerals
General formulation: In the precipitation of sparingly soluble salts from wastewaters, the crystal growth
process is almost invariably rate limiting, and the kinetics of this process is mostly surface controlled (see
Musvoto et al., 1998 for a detailed review). For such processes, the rate of mineral precipitation for many
sparingly soluble salts M + A - can be formulated by following the theory of Koutsoukos et al. (1980):
dM+A-/dt = -ks[([Mm+]+[Aa-]-)1/ - ([Mm+]0+[Aa-]0-)1/]n
(i)
where:
•
[Mm+], [Aa-] and [Mm+]0, [Aa-]0 are the concentrations in mole units of crystal lattice ions in
solution at time t and at equilibrium respectively. At equilibrium
[Mm+]0+ [Aa-]0- = KSP where KSP is the apparent solubility product of the salt.
•
k is the apparent precipitation rate constant.
•
s is proportional to the total number of available growth sites on the added seed material.
•
+ is the total number of cationic species.
•
- is the total number of anionic species.
•
 = + + •
n is determined experimentally and equals 2 for a number of divalent sparingly soluble salts.
In Eq. (i), accepting that no seed material has been added, the rate no longer depends on the available
growth sites (s) so that the rate constants ks can be replaced by a single precipitation rate constant Kppt.
This general equation can also be derived from the hypothesis of Davies and Jones (Benjamin et al.,
1976; Sturrock et al., 1977) and, accordingly, was accepted for use in the model to describe the kinetics of
mineral precipitation.
Mineral precipitation from ADL: Under aeration conditions of ADL, the solids most likely to precipitate
are various magnesium and calcium carbonates and phosphates. Domains for precipitation of the various
forms of these minerals have been delineated in the literature and are reviewed by Musvoto et al. (1998).
From these, struvite (MgNH4PO4), newberyite (MgHPO4), amorphous calcium phosphate (ACP,
Ca3(PO4)2.xH2O), calcite (CaCO3) and magnesite (MgCO3) were identified as the minerals most likely to
precipitate and precipitation processes for these were included in the model (processes 42 to 45; Musvoto
et al., 2000b).
3
Wentzel, Musvoto and Ekama
Solubility products: A range of solubility products (pKSP) for the five mineral salts identified above
(struvite, newberyite, ACP, calcite and magnesite) as likely to precipitate on ADL aeration were found in
the literature. These solubility products are at infinite dilution, i.e. for ideal solutions. To account for the
effect of ionic strength in non-ideal solutions, the solubility products were adjusted following the DebyeHückel theory for low and medium salinity waters (for details, see Musvoto et al., 1998).
Ion pairing
Ion pairing effects become significant at ionic strength (µ) > 0.025 (Loewenthal et al., 1986). The µ
values of the wastewaters where the model was to be applied, i.e. ADL, were anticipated to be greater
than 0.025 so ion pairing effects were included in the model. From Musvoto et al. (2000a), the ion
pairing equilibria were described in terms of the kinetics of the forward and reverse reactions and
included in the same manner followed for weak acid/bases. For solutions containing Ca, Mg, FSA and
PO4-P, from the literature eleven ion pairs were identified and included in the model as processes 20 to 41
(Musvoto et al., 2000a). The stability constants for the ion pairs (pKST) were obtained from the literature
(Ferguson and McCarty, 1971; Musvoto et al., 2000a) and adjusted for ionic strength effects with the
Debye-Hückel theory.
Gas stripping
Gases expected to be stripped are CO2 and NH3. The exchange of CO2 and NH3 between the liquid and
gas phases has been outlined by Musvoto et al. (2000a,b). For NH3 it was assumed that the atmosphere
acts as an infinite sink; thus the dissolution of NH3 from the atmosphere into solution was not included in
the model, only NH3 expulsion. Processes 18 and 19 (Musvoto et al., 2000a) and process 46 (Musvoto et
al., 2000b) describe CO2 liquid/gas exchange and NH3 stripping respectively.
MODEL APPLICATION
The model was applied to describe the time dependent three phase weak acid/base reactions that occur
when ADL are aerated, using Aquasim (Reichert, 1994). No suitable data in the literature are available
on this process, so that an experimental investigation had to be undertaken to gather the appropriate data.
Experimental investigation
Aeration of ADL from (i) a spent wine UASB digester (UASBDL) and (ii) an anaerobic digester treating
sewage sludge (SSADL) were investigated. Five litre samples of each wastewater were placed in a batch
reactor and aerated for at least 24 hours. Temperature was controlled at 20C. The pH in the reactor was
recorded throughout the experiment. At frequent intervals, 100 m and 10 m samples were drawn from
the batch reactor; the 10m samples were immediately analysed for free and saline ammonia (FSA), and
the 100m samples 0.45µm filtered and analysed for Ca, Mg, total phosphate system species (PT), total
inorganic carbon species (CT) and short chain fatty acids (SCFA). Four batch tests were performed on
SSADL (Batch tests 11, 12, 13 and 14) and three on UASBDL (Batch tests 16, 17 and 18). Details of
methods are given in Musvoto et al. (2000b).
Model calibration
In the model, values are required for (i) weak acid/base equilibrium constants (pKa), (ii) weak acid/base
kinetic rate constants (Kra), (iii) ion pair stability constants (pKST), (iv) mineral solubility products (pKSP),
(v) ion pair kinetic rate constants (KrIP), (vi) mineral precipitation rate constants (Kppt) and (vii) gas
stripping rates (KrG). In the calibration, constants (i), (ii) and (iii) were regarded as model constants and
not changed; values for these constants were obtained from the literature (Musvoto et al., 2000a).
Constants (v), (vi) and (vii) were regarded as calibration constants and were changed to provide a close
correlation between theoretical model predictions and experimental results. Constants (iv) were
considered model constants, but a range of values are quoted in the literature so that the final values had
to be determined by calibration within the literature range. Changes to constants were made both by
visual trial and error fitting and the parameter estimation facility in Aquasim; visually there was little
discernable difference between results from the two calibration methods, and so only the visual fit
4
Wentzel, Musvoto and Ekama
calibration data are reported (for details see Musvoto et al., 2000c). In the calibration exercise, the
importance of ion pairing in the model predictions was not fully appreciated, and to improve the
correlation between predicted and measured results the values for the rates of ion pair formation (KrIP)
were adjusted separately for each ion pair, but keeping the rates the same for all batch tests. This caused
that the formation of the ion pairs was not effectively instantaneous as should be. In subsequent
modelling exercises it has become apparent that under some conditions ion pairing effects have a
significant influence on predicted results when the rates of ion pair formation are made effectively
instantaneous. A comprehensive study on this aspect will form the basis for a future paper.
Results and discussion
As examples, Figs 1 and 2 show measured and predicted results for batch test 12 on SSADL and batch
test 18 on UASBDL respectively. Good correlations were obtained between experimental and theoretical
model predictions for both liquors. Some of the constants and results obtained from the model
simulations for both SSADL and UASBDL are shown in Table 1.
Table 1
Values of model constants for simulation of physical and chemical processes for aerobic
batch tests on SSADL and UASBDL
Constant
Batch tests on SSADL
Batch tests on UASBDL Literature value
Batch Batch Batch Batch Batch Batch Batch
Test 11 Test 12 Test 13 Test 14 Test 16 Test 17 Test 18
-Log Solubility product (pKSP)
Struvite
Newberyite
Amorphous Calcium phosphate (ACP)
CaCO3
MgCO3
Rate constant of precipitation (Kppt /d)
Struvite
Newberyite
Amorphous Calcium phosphate (ACP)
CaCO3
MgCO3
Rate of gas stripping (KrG /d)
O2
CO2
NH3
Solids precipitated (mg/l)
Struvite
Newberyite
Amorphous Calcium phosphate (ACP)
CaCO3
MgCO3
13.16
5.8
25.46
6.45
7
13.16
5.8
25.46
6.45
7
13.16
5.8
25.46
6.45
7
13.16
5.8
25.46
6.45
7
13.16
5.8
25.46
6.45
7
13.16
5.8
25.46
6.45
7
13.16
5.8
25.46
6.45
7
300
0.05
150
50
50
300
0.05
150
50
50
300
0.05
150
2
50
300
0.05
150
50
50
3000
0.05
350
0.5
50
3000
0.05
350
0.5
50
3000
0.05
350
0.5
50
300
273
1.1
225
204
1.2
550
500
1.05
600
545
0.9
670
610
1.92
400
365
2.5
670
610
1.92
1236
3.8
140
58
0
1140
2.8
170
46
0
1250
2.8
160
43
0
1270
2.6
50
98
0
677
2.1
91
0
30
532
1.2
98
0
30
528
0
92
0
21
9.94 - 13.16
5.51 - 5.8
24 - 32.7
6.3 - 8.5
5 - 8.2
From a comparison of results on the two ADL, the following conclusions can be drawn (see Table 1):
Solids most likely to precipitate: The same solids, viz. struvite, ACP, newberyite, CaCO3 and MgCO3,
were identified from the literature as most likely to precipitate in both SSADL and UASBDL and on this
basis were included in the model (see above, and Musvoto et al., 1998 for details). With these
precipitants, the consistency between predicted and measured soluble species concentrations (Figs 1 and
2) indicates that no precipitants of importance have been omitted from the model. From the simulations,
in both liquors struvite formed the bulk of the precipitate followed by ACP (Table 1). MgCO 3 was
5
Wentzel, Musvoto and Ekama
predicted to precipitate in UASBDL, but not in SSADL. Conversely, CaCO3 was predicted to precipitate
in SSADL, but not in UASBDL. In both sets of experiments, newberyite was predicted not to precipitate
significantly. The predicted precipitants are in agreement with the domains of precipitation in the
literature (Musvoto et al., 1998).
Solubility products: For each precipitate formed, the values for the solubility products were the same for
both the SSADL and UASBDL, and all fall within the range of literature values (Table 1).
Specific rate constants for precipitation: For each type of wastewater, the same set of specific
precipitation rate constants was found for all the batch tests on that wastewater, except for batch test 13
for SSADL where a CaCO3 precipitation rate of 2 instead of the 50 (/d) for the other three batch tests was
required to give a good correlation. The specific precipitation rate constants found for struvite, ACP and
CaCO3 differ significantly between the SSADL and UASBDL (Table 1); (i) the rates for struvite and ACP
are much higher in the UASBDL than in the SSADL and (ii) the rate for CaCO 3 is lower for the
UASBDL than for SSADL.
Gas stripping: The specific rates for gas stripping for both CO2 and NH3 differed for each individual
batch test (Table 1). This is not unexpected as the aeration conditions (gas flow rates, mixing, solids, etc.)
differed in each batch test; in hindsight this is an omission as aeration rates in the batch tests should have
been controlled to be the same. Comparing the stripping rates for CO2 with those for NH3, the values for
CO2 were much higher, by two orders of magnitude. This is in agreement with the literature, where it is
evident that the volatility of CO2 is much higher than NH3.
CONCLUSIONS
The physical-chemical kinetic model developed by Musvoto et al. (2000a,b) is applied to simulate the
chemical reactions which occur in the aeration treatment of anaerobic digester liquors (ADL). The
processes operative in this system are the dissociation of the weak acid/bases, precipitation of solids
(struvite, newberyite, amorphous calcium phosphate, magnesium and calcium carbonate as identified
from the literature) and stripping of CO2 and NH3 gases. Ion pairing effects are also included in the
model, due to the ionic strength of the ADL being greater than 0.025. To validate the model, batch
experiments were conducted by aerating two ADL, viz. three batch tests on ADL from a spent wine
UASB digester (UASBDL) and four on ADL from an anaerobic digester treating a blend of primary
sludge and waste activated sludge (SSADL), and the results compared with model predictions. After
establishing from the literature values for (i) weak acid/base equilibrium constants (pKa), (ii) weak
acid/base kinetic rate constants (Kra), and (iii) ion pair stability constants (pKST), and trial and error
determination of (iv) mineral solubility products (pKSP) (within the range reported in the literature), (v)
ion pair kinetic rate constants (KrIP), (vi) mineral precipitation rate constants (Kppt) and (vii) gas stripping
rates (KrG), a good correlation between predicted and measured data was obtained for all batch tests. A
single set of solubility products and precipitation rate constants was found for all batch tests for each type
of waste. Further, as required the solubility product values all fall in the range of values quoted in the
literature. Also, the types of minerals that precipitated for the conditions present are in agreement with
information in the literature. However, the effect of ion pairing on model predictions requires further
investigation.
The results for the SSADL were compared with those on the UASBDL. From the simulation results it
was found that (i) a single set of solubility product values for the five minerals that precipitated (struvite,
ACP, newberyite, CaCO3 and MgCO3) applied to both liquor types, but that the specific precipitation
rates were different for each liquor, (ii) the rates of struvite and ACP precipitation were increasingly
slower with increasing particulate organic concentrations; SSADL contained considerably more
particulate organics than SSADL, (iii) gas stripping/dissolution rates of CO2 and NH3 were different in
each batch test; the CO2 stripping rates were two orders of magnitude higher than the NH3 stripping rates.
6
Magnesium
Calcium
150
150
(a)
(b)
Ca pred.
100
M g (g /m 3 )
C a (g /m 3 )
Wentzel, Musvoto and Ekama
Ca meas
50
M g pred.
100
0
M g meas.
50
0
0
0.5
1
1.5
Time (d)
2
2.5
0
0.5
2
2.5
Total Carbonate
Total Phosphate
800
200
(c)
(d)
PT pred.
150
C T (g C /m 3 )
PT (g P/m 3 )
1
1.5
Time (d)
PT meas.
100
CT pred.
600
CT meas.
400
200
50
0
0
0
0.5
1
1.5
Time (d)
2
0
2.5
0.5
2
2.5
pH
Free and Saline Ammonia
800
1
1.5
Time (d)
9
600
8.5
500
pH
F SA (g N /m 3 )
700
400
8
300
FSA pred.
200
100
pH pred.
7.5
FSA meas.
(e)
(f)
0
pH meas.
7
0
0.5
1
1.5
Time (d)
2
2.5
0
0.5
1
1.5
Time (d)
2
2.5
Fig 1: Predicted and measured soluble concentrations for calcium (Ca, Fig 1a, top left), magnesium (Mg, Fig 1b, top right),
total phosphate (PT, Fig 1c, middle left), total carbonate (CT, Fig 1d, middle right), free and saline ammonia (FSA, Fig 1e
bottom left) and pH (Fig 1f, bottom right) for aerobic batch test 12 on anaerobic digester liquor from Cape Flats sewage
treatment (Cape Town, South Africa) digester treating primary and waste activated sludge.
7
Calcium
(a)
50
Ca meas
30
30
10
10
0
0
0.4
0.6
0.8
Time (d)
1
0
1.2
Total Phosphate
(c)
80
0.4
0.6
0.8
Time (d)
1
1.2
Total Carbonate
(d)
PT pred.
C T (g C /m 3 )
100
0.2
800
120
PT (g P/m 3 )
M g meas.
40
20
0.2
M g pred.
50
20
0
(b)
60
Ca pred.
40
Magnesium
70
M g (g /m 3 )
60
C a (g /m 3 )
Wentzel, Musvoto and Ekama
PT meas.
60
40
600
400
CT pred.
200
20
CT meas.
0
0
0
0.2
0.4
0.6
0.8
Time (d)
0
1.2
Free and Saline Ammonia
140
120
0.6
0.8
Time (d)
1
1.2
pH
9
FSA meas.
80
8.5
60
8
40
7.5
20
0.4
9.5
FSA pred.
100
0.2
10
pH
F SA (g N /m 3 )
1
pH pred.
7
(e)
pH meas.
(f)
6.5
0
0
0.2
0.4
0.6
0.8
Time (d)
1
1.2
0
0.2
0.4
0.6
0.8
Time (d)
1
1.2
Fig 2: Predicted and measured soluble concentrations for calcium (Ca, Fig 2a, top left), magnesium (Mg, Fig 2b, top right),
total phosphate (PT, Fig 2c, middle left), total carbonate (CT, Fig 2d, middle right), free and saline ammonia (FSA, Fig 2e
bottom left) and pH (Fig 2f, bottom right) for aerobic batch test 18 on anaerobic digester liquor from Stellenbosch Farmers=
Winery (Wellington, South Africa) spent wine UASB digester.
8
Wentzel, Musvoto and Ekama
The three phase kinetic based weak acid/base chemistry model and the approach on which it is based is
proving to be a useful tool for research into and design of wastewater treatment systems. For research,
the model helps to focus attention on issues not obvious from direct experiment and from a single batch
test allows determination of solids precipitation data in an integrated and consistent manner for a number
of minerals simultaneously. For design, by conducting a number of tests on a particular wastewater, the
model can be calibrated for the particular wastewater and treatment process. Once calibrated, this kind of
model can be used for predicting the outcome of different treatment processes to identify for investigation
those that hold promise.
ACKNOWLEDGEMENTS
This research was supported financially by the Water Research Commission, National Research
Foundation and University of Cape Town and is published with their permission.
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