Environmental Technology, Vol. 22. pp 1287-1293
© Selper Ltd, 2001
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
(Received 14 February 2001; Accepted 16 May 2001)
ABSTRACT
A three phase (aqueous/solid/gas) mixed weak acid/base kinetic model developed by Musvoto et al. 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 (K rIP), (vi) mineral precipitation rate constants (K ppt) 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.
Keywords.
Kinetic model, precipitation, weak acid/base, gas stripping, struvite.
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 [1, 2]. 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 [3-5]. 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. [6] describe the development of a kinetic
model for the single aqueous phase behaviour of mixed weak
acid/base systems and included precipitation of CaCO 3, 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 the three phase behaviour of the carbonate
system in pure water and 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. [7]
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 equilibrium (time independent) data
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available in the literature. In this paper, the model will be
described briefly and the validation extended to 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 CO 2
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. [6].
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. [8] for a detailed review). For
such processes, Koutsoukos et al. [9] have formulated a
general equation for the rate of mineral precipitation [8]. This
general precipitation equation can be modified by accepting
that no seed material has been added; for this case, the
precipitation rate no longer depends on the available growth
sites (s) so that the rate constants ks in the equation can be
replaced by a single precipitation rate constant Kppt [8]. This
precipitation rate equation can also be derived from the
hypothesis of Davies and Jones [10, 11] and, accordingly, was
accepted for use in the model to describe the kinetics of
mineral precipitation.
Mineral Precipitation from Anaerobic Digester Liquors
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. [8]. 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. [7]).
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 Debye-Hückel theory
for low and medium salinity waters (for details, see Musvoto
et al. [8]).
Ion Pairing
Ion pairing effects become significant at ionic strength
() > 0.025 [12]. The  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. [6], 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 [6]. The
stability constants for the ion pairs (pKST) were obtained from
the literature [13, 6] 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. [6, 7]. 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 [6] and process 46 [7] 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 the Computer Program Aquasim [14]. 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 a spent wine UASB digester
(UASBDL) and 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 ml and 10 ml samples were drawn
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from the batch reactor; the 10ml samples were immediately
analysed for free and saline ammonia (FSA), and the 100ml
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. [7].
Model Calibration
(i)
(ii)
(iii)
(iv)
(v)
(vi)
(vii)
In the model, values are required for:
weak acid/base equilibrium constants (pKa),
weak acid/base kinetic rate constants (Kra),
ion pair stability constants (pKST),
mineral solubility products (pKSP),
ion pair kinetic rate constants (KrIP),
mineral precipitation rate constants (Kppt) and
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 [6]. 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 calibration data
are reported (for details see Musvoto et al. [15]). 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 (K rIP) were adjusted
separately for each ion pair, but keeping the rates the same for
all batch tests. This meant 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, Figures 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. 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 [8] 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). MgCO3 was 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
[8].
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-1) 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); the rates for struvite and ACP
are much higher in the UASBDL than in the SSADL, while the
rate for CaCO3 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 kinetic model developed by Musvoto et al. [6, 7]
was applied to simulate the chemical and physical reactions
which occur on batch aeration of anaerobic digester liquors
(ADL) from a spent wine UASB digester (UASBDL) and an
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anaerobic digester treating a blend of primary and waste
activated sludges (SSADL). From a comparison of model
predictions with measured data, the following conclusions
can be drawn:
Figure 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
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(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.
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Figure 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.
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
Batch
Test 11
Batch
Test 12
Batch
Test 13
Batch
Test 14
Batch
Test 16
Batch
Test 17
Batch
Test 18
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
Rate of gas stripping (KrG1d-1)
O2
CO2
NH3
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
Solids precipitated (mg l-1)
Struvite
Newberyite
Amorphous Calcium phosphate (ACP)
CaCO3
MgCO3
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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
-Log Solubility product (pKSP)
Struvite
Newberyite
Amorphous Calcium phosphate (ACP)
CaCO3
MgCO3
Rate constant of precipitation (Kppt d-1)
Struvite
Newberyite
Amorphous Calcium phosphate (ACP)
CaCO3
MgCO3
1)
2)
3)
4)
5)
A good correlation between predicted and measured
data was obtained for all batch tests.
A single set of solubility product values for the five
minerals that precipitated (struvite, ACP, newberyite,
CaCO3 and MgCO3) applied to both liquor types.
Furthermore, the solubility product values all fall within
the range of values quoted in the literature.
A single set of precipitation rate constants was found for
all batch tests on a specific ADL type, but the constants
differed between the two ADL types. Most likely the
precipitation rates were influenced by particulate organic
concentrations; SSADL contained considerably more
particulate organics than UASBADL.
The types of minerals predicted to precipitate for the
conditions present are in agreement with information in
the literature.
The CO2 stripping rates were two orders of magnitude
higher than the NH3 stripping rates, in agreement with
the literature.
Literature
value
9.94 - 13.16
5.51 - 5.8
24 - 32.7
6.3 - 8.5
5 - 8.2
6)
The effect of ion pairing on model predictions requires
further investigation.
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 allows multi-mineral precipitation to be
investigated in an integrated and consistent manner. 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.
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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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