Cape Town 7530, South Africa. 16. 3Department of Mathematical Sciences, Harare Institute of Technology, P. O. Box BE 277, Belvedere,. 17. Harare, Zimbabwe.
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Original Research Article
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Journal of Applied Chemical Science International
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Journal of Applied Chemical Science International, ISSN No. : 2395-3705 (Print), 2395-3713 (Online), Vol.: 5,
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Issue.: 1
Original Research Article KINETIC MODELLING FOR BIO-METHANE GENERATION DURING ANAEROBIC DIGESTION OF MUNICIPAL SEWAGE SLUDGE UTILIZING ACTI-ZYME (BIO-CATALYST) AS A RESOURCE RECOVERY STRATEGY MUSAIDA M. MANYUCHI
1,2*
2
2
, DANIEL I. O. IKHU-OMOREGBE , OLUWASEUN O. OYEKOLA , WILLARD
3
3
ZVAREVASHE AND TREVOR N. MUTUSVA 1
Department of Chemical and Process Systems Engineering, Harare Institute of Technology, P. O. Box
BE 277, Belvedere, Harare, Zimbabwe. 2
Department of Chemical Engineering, Cape Peninsula University of Technology, Bellville, Western Cape,
Cape Town 7530, South Africa. 3
Department of Mathematical Sciences, Harare Institute of Technology, P. O. Box BE 277, Belvedere,
Harare, Zimbabwe
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Abstract
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This paper focuses on the kinetic modelling for simulation of bio-methane generation from
21
sewage sludge digestion utilizing Acti-zyme as a bio-catalyst. Sewage sludge was digested at
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37 °C and 55 °C for Acti-zyme loadings of 50 g/m3, sewage sludge loadings of 5-7.5 g/L.day
23
and retention time of up to 40 days. Optimal bio-methanation was achieved at 37 °C with
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78% composition. The bio-methane production experimental data was fitted to the linear,
25
exponential, logistics kinetic, exponential rise to a maximum and the modified Gompertz
26
kinetic models and the coefficients of determination (R2) obtained. A lag phase of 10 days
27
was observed during the bio-methanation process. The exponential rise to a maximum kinetic
28
model fully simulated the bio-methane generation with a R2 value of 0.999 and a rate
29
constant of 0.073 day-1. The logistics kinetic model can therefore be accurately applied for
30
modelling the experimental data for bio-methane production.
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Keywords: Acti-zyme, bio-methane, exponential rise to a maxima model, kinetic modelling
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1.
Introduction
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Sewage treatment results in unwanted and unutilized municipal sewage sludge which is send
34
off for landfilling resulting in the emissions of greenhouse gases.1 Of late there has been a
35
push for resources like biogas and bio-solids recovery from municipal sewage sludge as a
36
value addition strategy.1-4 Biogas, a form of green gas can be applied for cooking and heating
37
purposes whereas the bio-solids can be applied as bio-fertilisers. More recently, Acti-zyme,
38
an enzyme bio-catalyst has been applied for catalyzed sewage sludge digestion resulting in
39
enhanced biogas production.
40
process was done for Acti-zyme loadings of upto 70 g/m3, retention times of upto 40 days
41
and sewage sludge loadings of up to 10 g/L.day.4 Although, resource recovery from sewage
42
sludge utilizing Acti-zyme digestion is feasible there is still need to understand the kinetic
43
modelling that occur during the digestion process. Kinetic models for sewage sludge
44
digestion can be expressed as linear, exponential, logistics kinetic, exponential rise to a
45
maximum, first order exponential model and the modified Gompertz equation.5
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1.1
47
The linear model for biogas production can be expressed as shown in Eq. 1.1 for both the
48
ascending and descending stages.5
1-4
Furthermore, the impact of temperature on the digestion
Linear kinetic model
đŚ = đ + đđĄ ⌠⌠⌠⌠⌠⌠⌠⌠⌠⌠⌠⌠⌠⌠⌠⌠⌠⌠⌠⌠. . (1.1) 49
Where
50
Y = biogas production rate in mL/day
51
t = time in days
52
a and b = constants obtained from the intercept and slope of y vs. t in mL/day
53
1.2
54
In the exponential model it is assumed that the biogas production rate will increase with
55
increase in time and after a certain period, after reaching the highest point it will decrease to a
Exponential kinetic model
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zero exponentially with increase in time.5 The exponential kinetic model is represented by
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Eq. 1.2. đŚ = đ + đ exp(đđĄ) ⌠⌠⌠⌠⌠⌠⌠⌠⌠⌠⌠⌠⌠⌠⌠⌠⌠⌠⌠. (1.2)
58
Where
59
y = Biogas production rate in mL/day
60
t = time in days for sewage sludge digestion
61
a and b = constants in mL/day
62
c = constant in (per day)
63
1.3
64
The logistics kinetic model is represented by Eq. 1.3.
Logistics kinetic model
đś=
đ ⌠⌠⌠⌠⌠⌠⌠⌠⌠⌠⌠⌠⌠⌠⌠⌠⌠⌠(1.3) 1 + đđđĽđ(âđđĄ)
65
Where
66
C = cumulative biogas production (mL/day)
67
k = rate constant (per day)
68
t = hydraulic retention time (days)
69
a and b are constants
70
1.4
Exponential rise to a maxima kinetic model đś = đ´(1 â đđĽđ(âđđĄ)) ⌠⌠⌠⌠⌠⌠⌠⌠⌠⌠⌠⌠⌠⌠⌠⌠⌠(1.4)
71
Where
72
C = cumulative biogas production (mL/day)
73
A= Biogas production rate in mL/day
74
k = rate constant (per day)
75
t = hydraulic retention time (days)
76
a and b are constants
77
1.5
Modified Gompertz kinetic model
78
The kinetics of biogas production can be presented by the modified Gompertz equation.6,7
79
This model assumes biogas production is a function of time.5 đľđĄ = đľđđĽđ [â exp [
đ
đ đĽ đ (Ë â đĄ) + 1]] ⌠⌠⌠⌠⌠⌠⌠⌠⌠. . (1.5) đľ
80
Where
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Bt = Cumulative of biogas (mL/day) produced at any time (t)
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B â Biogas production potential
83
Rb = Maximum biogas production rate (mL/day)
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Ë = lag phase (days) which is the minimum time required to produce biogas after the Acti-
85
zyme has acclimatized
86
This study therefore focused on determining the potential kinematic model that can be used to
87
model the bio-methane production from sewage sludge utilizing Acti-zyme as bio-catalyst.
88
2.
Materials and Methods
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2.1
Materials
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Raw sewage sludge was obtained from a local used treatment plant which utilizes
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conventional sewage treatment methods. Acti-zyme was obtained from AusTech in Australia.
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An Inco Therm Labotec Incubator was used as for maintaining the temperature constant at 37
93
°C and 55 °C for the 500 mL Erlenmeyer flasks that were used as the digesters. The flasks
94
were plugged with cotton wool then covered with aluminum foil paper to ensure anaerobic
95
conditions were maintained.
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2.2
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2.2.1 Analysis of the raw sewage sludge
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The sewage sludge was filtered and dried to 60-80% moisture content. Moisture content and
99
volatile matter analyses were done using an AND moisture analyser. The %Moisture content
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(M) was determined by heating 5g of sample at 105âŚC for 30 minutes and then recording the
101
difference in weight. The %Volatile matter (VM) was determined by heating 5g of sample at
Methods
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105 âŚC for 3 minutes and then recording the difference in weight. The %Ash content (AC)
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was determined by completely incinerating the 5g sample using a burner. The total %fixed
104
carbon was determined as: 100% - %( M + VM + AC). pH and electrical conductivity
105
measurements were done using a Hanna HI 9810 instrument. The total Kjeldahl nitrogen
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(TKN), total phosphates (TP), biological oxygen demand (BOD 5) and the chemical oxygen
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demand (COD) where measured in milligrams per litre (mg/L) using the standard titrimetric
108
methods as indicated in Alpha9.
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2.2.2 Biogas production
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500 mL Erlenmeyer flasks representing the digesters were put in a controlled water bath set
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at 37 °C and 55 °C to create mesophillic conditions at atmospheric pressure. Outlets were
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created to facilitate the collection and sampling of the biogas produced. Optimum Acti-zyme
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loading of 0-70 g/m3 over retention period of 60 days batch wise were used in the digesters
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for biogas and bio-solids generation to ascertain the highest conditions that can be employed
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in sewage treatment using Acti-zyme.3 All experiments were replicated thrice and an average
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used. The pH in the digesters was between 6-7. Agitation in the digesters was fixed at 60 rpm
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using magnetic stirrers to ensure perfect mixing of sewage sludge and Acti-zyme.
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The quantity of biogas produced from the sewage sludge was measured through the
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displacement of water in millilitres per day (mL/day).3 The biogas generated was taken from
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the sampling points for composition analysis. A GC 5400 gas chromatography analysis was
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used to analyse the biogas content and the composition was expressed as a percentage.
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Acti-zyme Biogas outlet Biogas collector
Sampling valve
Biodigester
Biogas quantity measuring jar
Bio-solids outlet
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Fig. 1. Municipal biogas collection system schematic
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The cumulative biogas production of the different media were then calculated in accordance
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to Eq. 2.1. đľđđđđđ đđđđđ˘đđĄđđđ đđđĄđđŁđđĄđŚ =
(đšđđđđ đđ˘đđ˘đđđĄđđŁđ đđđđđđ đđđđ˘đđĄ â đđđđđđ đđđđ˘đđĄ đđđđđ˘đđđ đđĄ đ đđđđĄđđđ đĄđđđ) ⌠⌠⌠⌠(2.1) đšđđđđ đđ˘đđ˘đđđĄđđŁđ đđđđđđ đđđđ˘đđĄ
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2.2.3 Bio-solids generation
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The cumulative bio-solids (digestate) generated per day were recorded for possible use as
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biofertilisers. The nitrogen, phosphorous, and trace elements content was determined using
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Labtronics double beam ultra violet visible spectrophotometer (uv-vis). The potassium
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content
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spectrophotometer.
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3.
Results & Discussion
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3.1
Characterization of the raw sewage sludge
was
determined
using
a
Thermo
Fisher
flame
atomization absorption
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The raw sewage sludge had a pH of 6.6-8.3, a moisture content of a maximum of 80% and a
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TS value of 1143 mg/L among other physico-chemical characteristics as indicated in Table 1.
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Table 1: Raw sewage sludge characteristics Parameter
Value
pH
6.3-8.3
COD
750Âą12.5 mg/L
TS
1143Âą14.35 mg/L
VS
2.5Âą0.05%
AC
15Âą5%
Moisture content
60Âą20%
TKN
245Âą5.1 mg/L
TP
52.5Âą2.7 mg/L
BOD5
557Âą2.5 mg/L
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3.2
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The amount of biogas produced is 100% higher in comparison to thermophilic conditions
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with a rich bio-methane of around 80% composition being produced (Table 2). 4 Therefore the
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data from the mesophillic conditions was only considered for kinetic modelling purposes.
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Biogas production from mesophillic and thermophilic conditions
Table 2: Comparison of biogas production from mesophillic and thermophilic conditions Parameter
Mesophillic
Thermophilic
conditions
conditions
Highest temperature (oC)
37
55
pH
6.3-7.8
6.3-8.3
Retention time (days)
40
40
Maximum biogas production rate
400
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(mL/day)
Bio-methane composition (%)
77.9
39.5
143
3.3
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catalyst
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Municipal sewage sludge digestion increased with increase in retention time for all media at
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the mesophillic and thermophilic conditions (Fig. 2). However, bio-methane quantity
147
produced was highest in a system containing 50 g/m3 of Acti-zyme and sewage sludge
148
loading of 7.5 g/L.day (Fig. 2). The bio-methane production went through the lag phase,
149
exponential phase, deceleration phase and stationary phase (Fig. 2). Lag time for biogas
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production is approximately 10 days for all systems digested at 37 oC and those digested at 55
151
o
152
days and the rate at which it was produced.
Biogas production from municipal sewage sludge utilizing Acti-zyme as digestion
C, the only major difference is the difference in gas quantity and composition after the 10
153 154
Fig. 2. Bio-methane production potential from municipal sewage sludge at different
155
conditions
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3.4
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The cumulative biogas production activity decreased significantly with increase in Acti-zyme
158
loading and also with decrease in sewage sludge loading at a retention time of 40 days which
Biogas production activity
159
was noted as the optimal retention time (Fig. 3). This can be attributed to all the active sites in
160
the sewage sludge being utilized by the Acti-zyme till saturation is achieved.
161 162
Fig. 3. Cumulative biogas production activity at different sewage sludge loadings and
163
different temperatures
164
3.4 Kinetic modelling of bio-methane production from sewage sludge
165
Five models were applied i.e. the linear, exponential, the logistics kinetic equation, the
166
exponential rise to a maximum equation and the modified Gompertz equation was not
167
considered. Experimental data at 37 âŚC, Acti-zyme loading of 50 g/m3 and sewage sludge
168
loading of 7.5 g/L.day was only considered since the bio-methane production was optimal at
169
these conditions. A lag time of 10 days was considered in relation to Fig. 2.
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3.4.1 Linear kinetic model analysis
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The linear model was fitted on the experimental data and coefficient of determination of R2 =
172
0.93 was found, which showed it is a good model for use on explaining the bio-methane
173
generation. The coefficient of determination indicates how well data fit a statistical model or
174
sometimes simply a line or curve. The linear model obtained is given by Eq. 7 and its fit to
175
the experimental data is shown in Fig. 4. đŚ = 14.19 + 1.229đĄ ⌠⌠⌠⌠⌠⌠⌠⌠. . (3.1)
176 177
Fig. 4. Comparison of the linear model and experimental data for bio-methane production
178
during sewage sludge digestion with Acti-zyme
179 180
3.4.2 Exponential kinetic model
181
The non-linear least squares method was used to find the exponential model that fitted the
182
bio-methane production during sewage sludge digestion. The linear model obtained is
183
represented by Eq. 3.2 and its relation to experimental data is shown in Fig. 5. The coefficient
184
of determination was R2 = 0.94 which showed that in terms of accuracy in representing the
185
experimental data, the exponential model was a better model than linear model.
186
đŚ = â6786 + 6802đ 0.0001738đĄ ⌠⌠⌠⌠⌠⌠⌠. (3.2)
187 188
Fig. 5. Comparison of the exponential model and experimental data for bio-methane
189
production during sewage sludge digestion with Acti-zyme
190
3.4.3 Exponential rise to a maxima model
191
Non-linear least squares method was used to the fit exponential rise to a maximum model to
192
the bio-methane generation data. The exponential rise to a maximum model was found to
193
have a rate constant, k-value of 0.00031 day-1. The coefficient of determination, R2 = 0.96,
194
was quite high indicating that it is a good model. The exponential rise to a maximum model is
195
shown in Eq. 3.3 and its fit to the bio-methane experimental data is shown in Fig. 6. đś = 1.788đ104 [1 â exp(â0.0003048đĄ)] ⌠⌠⌠⌠⌠⌠⌠⌠⌠⌠⌠⌠⌠⌠⌠⌠⌠. (3.3)
196 197
Fig. 6. Comparison of the exponential rise to a maximum model and experimental data for
198
bio-methane production during sewage sludge digestion with Acti-zyme
199
3.4.4 Logistics kinetic model
200
The logistics kinetic model is used to represent biogas production rate related to microbial
201
activity. Non-linear least squares method was used to fit logistic kinetic model. The model
202
which represented the bio-methane production utilizing Acti-zyme is represented by Eq. 3.4.
203
The fit of the logistics kinetic model in relation to the bio-methane experimental data is
204
shown in Fig. 7. The coefficient of determination is R2 = 0.9977, this shows that it was a
205
better model than linear, exponential and exponential to a maximum models. đś=
458.2 ⌠⌠⌠⌠⌠. (3.4) 1 + 23.96exp(â0.0735đĄ)
206 207
Fig. 7. Logistics kinetic model and experimental data for bio-methane production during
208
sewage sludge digestion with Acti-zyme
209
3.4.4 Logistics kinetic model
210
The logistics kinetic model is used to represent biogas production rate related to microbial
211
activity. Non-linear least squares method was used to fit logistic kinetic model. The model
212
which represented the bio-methane production utilizing Acti-zyme is represented by Eq. 3.4.
213
The fit of the logistics kinetic model in relation to the bio-methane experimental data is
214
shown in Fig. 7. The coefficient of determination is R2 = 0.9977, this shows that it was a
215
better model than linear, exponential and exponential to a maximum models.
216
3.4.5 Modified Gompertz kinetic model
217
The modified Gompertz kinetic model was used to represent biogas production rate related to
218
microbial activity. Non-linear least squares method was used to fit the modified Gompertz
219
model. The fit of the logistics kinetic model in relation to the bio-methane experimental data
220
is shown in Fig. 8. The coefficient of determination is R2= 0.5479, this showed that the
221
modified Gompertz kinetic model cannot be used for approximation of bio-methane
222
production utilising Acti-zyme as bio-catalyst. An algorithm was run on the experimental
223
data to fit the modified Gompertz equation and the following values were obtained. A =
224
181.4, Rm = -15.46, e = -1.096 and lambda = 1.361.
225 226
Fig. 8. Modified Gompertz model and experimental data for bio-methane production during
227
sewage sludge digestion with Acti-zyme
228
3.4.5 Summary of the kinetic models
229
Based on the coefficients of determination indicated in Table 3, the logistic kinetic model had
230
the highest coefficient of determination of 0.999; therefore it is the best model of the five
231
models that can best explain the kinetics of bio-methane generation from sewage sludge
232
utilizing Acti-zyme as bio-catalyst. Furthermore, the logistics kinetic equation had the highest
233
k-value indicating the accuracy of the model.
234
Table 3: Summary of the kinetic models coefficients of determination and the rate constants Kinetic model
Coefficient of
Rate constants
determination
(k) (per day)
(R2) Linear
0.931
-
Exponential
0.941
-
Exponential rise to a maxima
0.956
0.00031
Logistic kinetic
0.999
0.073
Modified Gompertz
0.548
-
235
4. Conclusion
236
The logistics kinetic model can be accurately applied for modelling the experimental data for
237
bio-methane production from sewage sludge utilizing Acti-zyme as bio-catalyst at 50 g/m3 of
238
Acti-zyme and sewage sludge loading of 7.5 g/L.day.
239
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240
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