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Variable kinetic approach to modelling an industrial waste anaerobic digester
Accepted Manuscript Title: Variable kinetic approach to modelling an industrial waste anaerobic digester Author: Iv´an L´opez Mauricio Passeggi Liliana Borzacconi PII: DOI: Reference:
S1369-703X(14)00363-5 http://dx.doi.org/doi:10.1016/j.bej.2014.12.014 BEJ 6096
To appear in:
Biochemical Engineering Journal
Received date: Revised date: Accepted date:
4-8-2014 23-10-2014 24-12-2014
Please cite this article as: Iv´an L´opez, Mauricio Passeggi, Liliana Borzacconi, Variable kinetic approach to modelling an industrial waste anaerobic digester, Biochemical Engineering Journal http://dx.doi.org/10.1016/j.bej.2014.12.014 This is a PDF file of an unedited manuscript that has been accepted for publication. As a service to our customers we are providing this early version of the manuscript. The manuscript will undergo copyediting, typesetting, and review of the resulting proof before it is published in its final form. Please note that during the production process errors may be discovered which could affect the content, and all legal disclaimers that apply to the journal pertain.
Variable kinetic approach to modelling an industrial waste anaerobic digester
Iván López*, Mauricio Passeggi and Liliana Borzacconi Facultad de Ingeniería, Universidad de la República J.Herrera y Reissig 565, Montevideo, Uruguay
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(* [email protected])
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Variable kinetic coefficient is proposed in order to follow the acclimation of microorganisms. Batch test were used to obtain biodegradation potential. Monte Carlo methods were applied to obtain confidence interval of parameters. Continuous reactor was used to calibrate and validate the model.
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Highlights
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Abstract
Anaerobic co-digestion of agro-industrial wastes is a promising option for the
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stabilisation of residues with biogas production. A mixture of bovine ruminal
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content, tannery carving fat and activated sludge purge was considered for this
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study. Biodegradability tests for individual wastes and a mixture of wastes were performed in batch conditions. Additionally, a completely mixed reactor with an average residence time of 30 days and a loading rate of 3.0 gVS/L.d. was employed for the mixture of wastes. A Volatile Solids (VS) removal efficiency of 66% with a methane production of 0.38 LCH4/kgVSadded or 0.58 LCH4/kgVSremoved was attained. A first-order kinetic model with lag time was
employed to describe the behaviour of the batch tests. Parameter determination was performed using direct search methods. Monte Carlo methods were utilised to determine the range of parameters. An ultimate methanation of 90 ± 6% was obtained from the batch tests. For the continuous system, a simple model with a variable kinetic constant that reflects the microbiological activity was proposed. The model was calibrated by adjusting the stoichiometric coefficients using solids outlet data, and the kinetic constant was deduced using
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experimental methane flow data. The kinetic constant doubles for
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approximately four residence times, which demonstrates the acclimation of
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biomass.
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Keywords
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Anaerobic Processes, Biodegradation, Biogas, Modelling, Monte Carlo,
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Kinetic Parameters
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LIST OF SYMBOLS
first order kinetic constant [d-1]
km
first order kinetic constant in continuous model [L/gVS.d]
k1
stoichiometric coefficient from solids to methane conversion [LCH4/gVS]
k3
stoichiometric coefficient from solids to microorganisms conversion [-]
L
Laplace transform
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k
M
accumulated methane production [mL]
Mo
ultimate methane production [mL]
qCH4
methane flow [L/Lreactor.d]
rM
methane production rate [gCOD/L.d]
solid substrate degradation rate [gVS/L.d]
t
time [d]
X
solid substrate concentration [gVS/L]
Xb
biodegradable solid substrate concentration [gVS/L]
Xm
microorganisms concentration [gVS/L]
Xnb
non biodegradable volatile solid concentration [gVS/L]
Xt
total volatile suspended solids [gVS/L]
YX/M
yield coefficient, conversion of substrate into methane [gCOD methane/gVS]
θ
lag time for microbial activation[d]
Introduction
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rX
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At present, global changes in the world like minimization of greenhouse gases
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emissions, and the need of use renewable energy sources require a more efficient use of
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biotechnologies [1, 2]. The sustainability principles must be present in our technological decisions without detriment of other technical and economic considerations. In this
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sense, the anaerobic digestion of agro-industrial organic waste is an alternative
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treatment with significant advantages, such as low operating costs and power generation from biogas [3, 4]. Additionally, anaerobic technology has proven to be more favourable
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than the aerobic treatment of wastes from the point of view of greenhouse gas generation [5] and can even compete with other biofuels [6]. In this scenario, anaerobic digestion plays a key role because the products generated (e.g., hydrogen, methane) from the different metabolic steps can be used as energy sources in boilers, internal combustion engines or fuel cells [7] or as raw material for other processing options
(e.g., the production of biopolymers or other organic substances). For these reasons, anaerobic technology constitutes the core of organic waste treatment systems [8]. A constraint of the high-load operation is the presence of inhibitors, which are produced by the waste [9 - 11]. For instance, this constraint is found in the fat carving generated by tanneries, which contains a high concentration of fat that is abundant in triglycerides; the triglycerides degrade during digestion to glycerol and long-chain fatty acids. Additionally, long-chain fatty acids are potential inhibitors of methanogenesis
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[12, 13].
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Other wastes, such as ruminal content and secondary sludge from aerobic wastewater treatment plants, exhibit low methane generation potential due to their low
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biodegradability. With respect to the ruminal concentration, a high-fibre content hinders
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mixing if its size is not reduced by pretreatment [14]. This situation compels the
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digesters to operate with low-solid concentrations to limit the potential for high loads.
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Co-digestion is a widely used way in order to enhance the anaerobic degradations
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of solid substartes. The most reported experiences are related to agroindustrial or
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agricultural wastes and the organic fraction of municipal solid wastes, but also the
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sludgre from aerobic facilities is considered [15]. The mixture of wastes with different
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characteristics, enrich the substrate composition, dilutes the inhibitory components, prevents mixing problems and enhances methane generation [15 - 17].
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Despite increasing anaerobic applications, the comprehensive and practical
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modelling of these systems is still developing. An important milestone in this field was the development of the IWA (International Water Assotiation) ADM1 model (Anaerobic Digestion Model 1) [18]. This structured model included multiple steps describing the biochemical and physicochemical processes, which involved at least 26 dynamic state variables and many parameters. Although the complexity of anaerobic processes was
reflected in the ADM1 model, direct applications for modelling and control purposes are difficult to use. Additionally, the identification of model parameters under actual operational conditions is difficult. The ADM1 model also fails to depict all complex phenomena that occurs in an anaerobic system and must be expanded to include other phenomena [19]. Simpler models with reduced sets of state variables and parameters have been proposed [20 - 23]. Although simple models do not represent the complexity of real processes, the identification of parameters and model validations are more
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straightforward [24 - 26].
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As a rule, hydrolysis is the rate limiting step in the degradation of solid wastes. A first order kinetic rate with respect to the substrate is widely accepted for this step [27].
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The simplest kinetic model for the overall process is a first order kinetic expression.
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Several experimental procedures could be planned in order to obtain the model
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parameters, both in batch mode [28] or in continuous mode [29]. Specially, Biochemical
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order to obtain kinetics parameters.
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Methane Potential (BMP) tests [28] are standard tests that could be easily extended in
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Even though simple optimisation techniques, such as least squares methods, are
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widely used in order to obtain the model parameters, these methods do not provide
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information about the confidence interval of results. Standard deviations are obtained by repeated measures. This option increases the experimental work and consumes
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resources. Alternatively, simulation methods that only consume computational time,
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such as Monte Carlo, can be applied [30, 31]. The performance of the Monte Carlo confidence interval method is comparable to other widely accepted methods of interval construction, and it can be used when only summary data are available [32]. In chemical systems, kinetics parameters obtained from batch experiences are used without restrictions to design continuous systems. However systems that involves
microorganisms must take into account the acclimation phenomena. Then, kinetics parameters could change through time in order to reflect the acclimation or to reflect adverse microbiological conditions. In very simple models, lumping a complex behaviour in one single parameter, variation of this parameter could reflect the environmental conditions. The objective of this study is to evaluate the application of a simple kinetic model to describe the co-digestion of three agro-industrial wastes (ruminal content, tannery
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carving fat and biological sludge). The first order kinetic model is validated in batch
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using stardard experiences and the confidence range of parameters was determined using Monte Carlo techniques. The model is validated also in continuous conditions, but
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in this case a variable kinetic parameter is postulated describing the acclimation
Model
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capacity of microorganisms.
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Biodegradability tests are typically performed in batch conditions [28]. The solid
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substrate and anaerobic sludge (inoculum) are placed in batch reactors in anaerobic
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conditions. Cumulative methane production is monitored over time and the ultimate
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value is used to calculate the methane potential. The transformation of solid substrate into methane involves a complex series of subtransformations, whereas hydrolysis
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determines the total kinetics. Typically, a single first-order kinetic model is used to
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represent the hydrolysis of particulate matter [27]. Despite the complex phenomena involved, biodegradability curves can be fit to a simple first-order kinetic model.
(1)
where
(2)
where k is the first-order kinetic constant and X is the solid substrate concentration. The methane accumulative curve asymptotically approaches a value, which indicates the maximum fraction of substrate that can be transformed into methane. The stoichiometric
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coefficient YX/M relates the rate of substrate degradation to the rate of methane
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production. If both substances are expressed by the same units (e.g., grams of COD),
(3)
(4)
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The accumulated methane curve is
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this stoichiometric coefficient is the methanation yield of the solid substrate.
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where M is the accumulated methane, Mo is the maximum quantity of methane that can be obtained, and t is the time elapsed after the lag time θ. The lag phase that occurs at
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the beginning of the curves in batch tests is attributed to the microorganism
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requirements for acclimation or the need for activation of the biological activity. Thus, by fitting this model to the experimental data, the kinetic constant k and the asymptotic value Mo can be obtained (YX/M can be obtained if the initial amount of substrate is known). Continuous systems require another approach. First, a virtually complete mix can
be assumed due to the mechanical stirring device. The system can be considered to be a lumped parameter system, and the mass balance equations can be performed considering the entire reactor as a control volume. Second, the system is not truly a continuous reactor: the feed and the discharge are performed once a day as pulses of a few minutes; for the remainder of the day, the system behaves as a batch reactor. Due to the fact that the retention time is greater than one order of magnitude with respect to the feed period, which turns the system into a continuous operation mode.
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Dynamic mass balance equations produce ordinary differential equations with
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respect to time. Three variables are used as state variables: biomass concentration (Xm), biodegradable solid substrate concentration (Xb), and nonbiodegradable solid
(5)
(6)
(7)
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concentration (Xnb). The equations in the batch periods are expressed as
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where km is the kinetic first-order constant for the degradation of the biodegradable solids and k3 is the stoichiometric coefficient for the conversion of solids to
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microorganisms. In the feed and discharge events, the amount of fed solids must be added to the mass balance and the amount of discharged solids must be subtracted. Additionally, methane gas flow can be related to solid degradation. Due to the different time scales involved, an instantaneous release of gas can be assumed and the algebraic equation (8) can be written:
(8)
where k1 is the stoichiometric coefficient from the solids to methane conversion and qCH4 is the methane flow. Considering the model’s simplicity, all COD of the degraded solids is transformed into methane or microorganisms. The stoichiometric coefficients can be related as k1 + k3 = 1.
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The first-order kinetic constant km can be related to the microbial activity.
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Despite the simplicity of the model, this parameter reflects the complexity of the
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biochemical reactions that are involved in a complex net of microorganisms. This activity varies over time, which reflects the possible acclimation or inhibition of the
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microorganisms or variation in the biomass composition. To consider the variation in
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the microbial activity in the model, the kinetic constant km should be considered as a
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variable over time. Methods
3.1
Waste origin and characterisation
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The waste was collected weekly and maintained at less than 15°C prior to loading
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the reactors. Ruminal contents of bovine origin were obtained from a slaughterhouse
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after they were squeezed through a screw press. The tannery fleshing generated after the leather peeling process was processed through a meat grinder, which contained a disc with a 10 mm diameter holes, to obtain a suitable size to feed the reactors. The secondary biological sludge was obtained from an activated sludge plant that treats wastewater from an oil factory after it underwent a process of thickening by a
centrifugal decanter.
3.2
Analytical methods
Total and volatile solids were determined for each batch of waste. For the ruminal content, lignin was also determined. For the other two wastes, fats and oils and total Kjeldahl nitrogen were determined. At the outlet of the continuous reactor, total and
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volatile solids, soluble COD, pH, volatile fatty acids and bicarbonate alkalinity were
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determined.
All analyses were performed according to Standard Methods [33], with the
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exception of the lignin content that was determined by the Klason method [34]. The
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methane and carbon dioxide content in the biogas were determined by gas
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Batch assays
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chromatography.
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Batch biodegradability tests were performed for each waste type (rumen content,
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tannery fleshing and sludge from biological wastewater treatment) and for a mixture of these wastes. Batch tests were conducted in 150 mL flasks, which were filled with
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substrate and inoculum from an UASB reactor that receives malting wastewater. For the
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mixture biodegradability test, a ratio of inoculum/substrate of 2.84 was selected to ensure no limitations regarding the amount of microorganisms. The waste mixture presents a volumetric ratio of 4:2:1 for rumen contents, fleshing and sludge, which corresponds to generation rates in the country. The pH was adjusted and the flasks were gassed with nitrogen to achieve anaerobic conditions and subsequently sealed and
placed in a shaker at 30°C. Monitoring of the methane production was performed using a pressure transducer to measure the increase of pressure generated by biogas production, and the biogas composition was determined by gas chromatography.
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Continuous reactor
The continuous reactor has a usable volume of 3.0 L and a low-speed mechanical
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stirrer. It is placed in a heated cabinet to 35°C. The feed to the reactor was performed
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daily—Monday through Friday—after downloading the same volume. On Mondays and Fridays, it was fed double volume to compensate the lack of feed during the weekend.
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The produced biogas was measured by an MGC-1 MilliGascounter.
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Because the ruminal content contains a high concentration of fermentative
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bacteria but does not contain a significant concentration of methanogenic
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microorganisms, the reactor was inoculated with methanogenic sludge. This inoculum
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was obtained from a UASB reactor that was used to treat malting wastewater.
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During the first five months, the reactor was operated with an average load of 3
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gVS/L.d and 30 days of residence time. The waste was fed in a volumetric ratio of 4:2:1
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for rumen contents, tannery fleshing and secondary sludge, which corresponds to generation rates in the country, and the mixture was diluted with an equal volume of
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water. From day 165, the residence time was reduced to 20 days while maintaining the
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waste ratio, and the applied solids load was increased.
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Parameter identification To determine the parameters from the batch tests, Scilab software was employed
to perform an optimisation routine based on the Nelder and Mead Simplex method,
without regard to the points that correspond to the lag phase of the curve. To assess the confidence interval of the parameters, a Monte Carlo simulation was performed. This method has proved to be a useful for determining the probability distribution in biotechnological models [30, 31]. From the experimental values and the experimental standard deviation, new pseudo-experimental points were randomly generated considering a normal distribution. The procedure was repeated a thousand times and the frequency distribution was obtained. A normal distribution was verified using the Xi
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square criterion [35]. Considering a data confidence interval with 90% probability, the
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confidence intervals of the parameters were determined.
For the continuous reactor, equations (5) to (7) are solved jointly with the ode
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routine of Scilab between each fed interval. The final terms of each integration interval
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are adjusted by adding the fed mass and subtracting the discharged mass to obtain the
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(8) because the methane flow is known.
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initial point to the next integration. The activity constant km is deduced from equation
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However, the stoichiometric coefficients must be known to solve the system. A k3
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parameter tuning was performed using the Scilab software and an optimisation routine
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based on the Simplex method by Nelder and Mead, which considers the parameters in
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the batch test to be the initial value for iteration. The adjustment was performed considering the coincidence between the accumulated experimental values of solid exit
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with the model predictions. The accumulated values rather than the daily values were
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selected because they provide a better reflection of the essential trend of the process and minimise the influence of experimental errors. The objective function to be minimised is the sum of the squares of the differences between the value predicted by the model and the experimental value. For the parameter determination, the values of the first 120 days were considered and the next 70 days were reserved for the model validation.
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Results
4.1
Waste characterisation
Table 1 presents the waste characterisation used in the tests and lists the mean values and the corresponding standard deviations. The waste mixture yielded an average ratio of 1.56 gCOD/gVS.
Batch tests
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4.2
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[TABLE 1]
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Figure 1 shows the batch test curve for the mixture of wastes. Similar graphs are
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obtained for individual wastes (not shown). Experimental points were performed in
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triplicate and a blank performed in identical conditions without substrate addition was
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discounted. Ninety percent confidence ranges that consider the variance in the
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experimental values are shown.
[FIG.1] [FIG.2]
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Figure 2 shows the results of the Monte Carlo simulation for the batch test, which
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was performed with the mixture of wastes. Similar results for the individual wastes are not presented. The parameter distributions obtained from the Monte Carlo simulation are normal, which was statistically verified using a Xi square distribution. For the codigestion test, the adjustment of the first-order model with lag time yields the following results: k = 0.089 ± 0.013d-1, θ = 2.46 ± 0.50 d and Mo = 196 ± 11 mL (confidence
interval of 90%). According to this ultimate methane production, the biodegradation of the substrate is 487 ± 37 NmL of methane per gram of degraded VS, which corresponds to a 90 ± 6% of methanisation. Table 2 also presents the results of the test with only one substrate.
[TABLE 2] Continuous reactor
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During the first hundred days, the reactor was operated with an average residence time of 30 days and a volumetric organic load of 3.0 gVS/L.d. A mass balance in this
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period yields an inlet of 979 g of VS and an outlet of 331 g of VS. The net accumulation
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of volatile solids within the reactor was negligible. The VS removal efficiency was
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66%. Considering the experimental gCOD/gVS ratio of 1.56 for the feed and 1.40 for
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the outlet, the COD removal efficiency was 70%. This value corresponds with a
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methane production of 477 L, which corresponds to 1076 gCOD. The average methane
[FIG.3]
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production in this period was 0.38 NLCH4/gVSadded and 0.58 NLCH4/gVSremoved.
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Solids outlet accumulated values in the first 120 days was employed for the calibration. The model fit returns the following value for parameter: k3 = 0.316. Figure 3
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shows the results for the model validation and the estimated values of the various solid fractions. The results of the estimated outlet solids concentration (Xt) in the validation period (day 120 to day 190) show reasonable agreement with the experimental data.
[FIG.4]
Figure 5 shows the evolution of the first-order kinetic constant. A sustained increase in this parameter until days 120 – 140 shows the acclimation of the microorganisms to work in the reactor conditions. Disregarding the first ten days, in which the values may not be entirely representative, the activity doubles at
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approximately four mean solid residence times.
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[FIG 5]
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Experimental methane flow and model predictions are show in Figure 5. A
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relatively good agreement is observed in the general trend. The model prediction has a
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more oscillatory behaviour that the experimental measures. Biogas release from the
behaviour. Discussion
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solid mixture tend to be damped in practice, and this fact could explain the more gentle
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The experiments demonstrate the feasibility of co-digestion of the considered waste mixture. High biodegradability values can be attained, which results in acceptable
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stabilisation of waste and its transformation into biogas. These results are in agreement
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with the literature and confirm the benefits of the co-digestion with regard the single substrate digestion [15 – 17]. Despite its simplicity (first-order kinetics), the model fits the experimental data and can be applied to the batch biodegradability curves and a continuous stirred reactor. For batch curves, first-order with lag time employs the format that is shown in the
accumulated methane production vs. time graphs. For the batch tests, the asymptote of accumulated methane production is the ultimate value of methanation, i.e., the percentage of conversion in methane if infinite time has elapsed and the environmental conditions remain constant in the flask. The kinetic constant corresponds to the slope of the curve after a delay has elapsed. The results of the ultimate methanation potential found in literature show a great dispersion. As example, Sambusiti et al.[36] working with ensiled forghum forage at
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35ºC found 83% of methanation as ultimate value; Ferreira et al. [37] working with
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wheat straw at 35ºC found 51% of methanation as ultimate value; Jokela et al. [38] found values of 92% for paper and carboard and 96% for putrescibles at the same
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temperature. Temperature and source inoculum are other factors that have incidence in
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results [39, 40]. Is reasonable that ruminal content shown low methanation yield
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because in the rumen of the bovines some degradation of the organic substrate occurs.
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Similarly, the activated sludge purge can have some degree of stabilization and shown
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low anaerobic degradability in consequence.
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The first order kinetic constant values obtained in this paper are in agreement with
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literature. Sambusiti et al.[36] found values between
0.049 d-1 and 0.146 d-1 for
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sorghum degradation using different inoculum sources. Ferreira et al. [37] found a value of 0.069 d-1 for anaerobic degradation of wheat straw with no pretreatment. Jokela et al.
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[38] found values between 0.024 d-1 and 0.107 d-1 for different substrates. Borja et al.
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[41] reports a value of 0.054 ± 0.003 d-1 for the hydrolysis of olive pomace. Monte Carlo techniques are useful to assess the reliability of the results and enable
the identification of the valid range of parameters. Assuming a normal distribution in the experimental errors, the parameters in the batch tests also exhibit a normal distribution that is centred on the optimum value obtained from the experimental data (Figure 2).
Table 2 shows that co-digestion notably enhances the methanisation. Although the methanisation of individual wastes are 42, 87 and 29% for rumen contents, tannery fleshing and secondary sludge, respectively, the co-digestion of the mixture yields a methanisation of 90%. This value is greater than the simple combination of individual methanisation percentages, which confirms the results that are usually obtained in this type of test. Although the daily correlation between the experimental values and the model is
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not very high in the continuous reactor, a reasonable match is observed with the trend
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presented in the daily values (Figure 3). The result is validated because this trend continues in the last 70 days. Although Figure 3 shows some deviations within this
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validation period, they are not significant and can be attributed to observed deficiencies
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in gas and solid measurements.
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The value of the kinetic constant in the batch model (0.089 ± 0.010 d-1)
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corresponds to the product of km×Xm in the continuous model. In the initial condition of
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the continuous experiences, km = 5×10-3 g-1Ld-1, Xm = 17 gL-1, and km×Xm = 0.085 d-1.
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On day 130, the values are km = 3.5×10-2 g-1Ld-1, Xm = 22 gL-1, and km×Xm = 0.77 d-1,
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i.e., an increase of an order of magnitude. This fact is indicative of the adaptability of
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the continuous system, i.e., the evolution of biomass towards the species with greater ability to degrade the specific substrate. In addition, the continuous reactor was operated
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at 5ºC higher than the temperature of the batch experiences; this fact may explain a
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generally higher level of activity values beyond the general trend. 6
Conclusions
The results of the batch biodegradability tests and the continuous stirred reactor demonstrate that the co-digestion of a mix of rumen contents, fat carving and secondary
biological sludge is feasible with suitable results. A first-order kinetic model with lag time can adequately predict the results of batch experiences. A reasonable fit with experimental values is achieved. Monte Carlo methods are useful to determine the validity range of the parameters and have proven that the errors in the parameters exhibit normal distributions, assuming a normal distribution of the experimental errors. A simple model with a variable kinetic constant reasonably represents the
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experimental results in a continuous reactor. The variation in the first-order kinetic
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constant reflects the acclimation of the biomass to degrade the specific wastes fed to the reactor. The kinetic constant approximately doubles after four mean solid residence
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times.
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Acknowledgments: To Martín Benzo, who has collaborated in the experimental study. The study was
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supported by a grant from INIA – Uruguay (National Institute for Agricultural Research).
B.K. Ahring, P. Westermann, Redefining the role of anaerobic digestion, in
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organic fraction of municipal solid waste (OFMSW), Biochemical Engineering
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[18] D.J. Batstone, J. Keller, I. Angelidaki, S.V. Kalyuzhnyi, S.G. Pavlostathis, A. Rozzi, W.T.M. Sanders, H. Siegrist, V.A. Vavilin, The IWA Anaerobic, Digestión
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Model Nº 1 (ADM1), Wat. Sci. & Tech., 45 (10) (2002) 65-73.
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[19] D.J. Batstone, J. Keller, J.P. Steyer, A review of ADM1 extensions, applications, and analysis: 2002-2005. Wat. Sci. & Tech., 54 (4) (2006) 1-10.
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[21] C. Garía-Diéguez, O. Bernard, E. Roca, Reducing the Anaerobic Digestion Model Nº 1 for its application to an industrial wastewater treatment plant treating winery effluent wastewater, Bioresource Technology, 132 (2013) 244-253. [22] O.L. Yusuf Momoh, B.U. Anyata, D.P. Saroj, Development of simplified anaerobic digestion models 8SADM’s) for studying anaerobic biodegradability and kinetics of complex biomass, Biochemical Engineering Journal, 79 (2013) 84-93.
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[25] J.E. Haag, A. Vande Wouwer, I. Queinnec, Macroscopic modelling and
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optimization criterion selection, Bioprocess Biosyst. Eng., 36 (2013) 35-43. [27] J. Eastman, J.F. Ferguson, Solubilization of particulate organic carbon during the
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acid phase of anaerobic digestion, Journal WPCF 53(3) (1981) 352-366.
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[28] I. Angelidaki, M. Alves, D. Bolzonella, L. Borzacconi, J.L. Campos, A.J. Guwy, S. Kalyuzhnyi, P. Jenicek, J.B. van Lier, Defining the biomethane potential (BMP) of solid organic wastes and energy crops: a proposed protocol for batch assays, Water Science & Technology 59(5) (2009) 927-934.
[29] R.A. Labatut, L.T. Angenent, N.R. Scott, Biochemical methane potential and biodegradability of complex organic substrates, Bioresource Technology 102 (2011) 2255-2264. [30] T.G. Müller, N. Noykova, M. Gyllenberg, J. Timmer,.Parameter identification in dynamical models of anaerobic waste water treatment, Mathematical Biosciences, 177&178 (2002) 147-160. [31] I. López, L. Borzacconi, Modelling of slaughterhouse solid waste anaerobic
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[32] K.J. Preacher, J.P. Selig, Advantages of Monte Carlo Confidence Intervals for
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Indirect Effects, Communication Methods and Measures 6 (2012) 77-98.[33]
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APHA, AWWA, WEF, Standard Methods for the Examination of Water and
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Wastewater, 19th edition (1995) ISBN 0-87553-223-3.
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[34] D. Templeton, T. Ehrman, Laboratory Analytical Procedure #003 – Determination
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of Acid Insoluble Lignin in Biomass, Chemical Analysis and Testing Task
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Laboratory Analytical Procedure (1995). [35] D. Himmelblau, Process Analysis
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by Statistical Methods, Ed. J. Willey&Sons, 1970; ISBN 471 39985X.
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[37] L.C. Ferreira, A. Donoso-Bravo, P.J. Nilsen, F. Fdz-Polanco, S.I. Pérez-Elvira, Influence of thermal pretreatment on the biochemical methane potential of wheat straw, Bioresource Technology 143 (2013) 251-257.
[38] J.P.Y. Jokela, V.A. Vavilin, J.A. Rintala, Hydrolysis rates, methane production and nitrogen solubilisation of grey waste components during anaerobic degradation, Bioresource Technology 96 (2005) 501-508. [39] N. Ferreiro, M. Soto, Anaerobic hydroysis of primary sludge: influence of sludge concentration and temperature, Water Science and Technology 47 (12) (2003) 239-246. [40] F. Raposo, C.J. Banks, I. Siegert, S. Heaven, R. Borja, Influence of inoculum to
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Process Biochemistry 41 (2006) 1444-1450.
[41] R. Borja, A. Martín, E. Sánchez, B. Rincón, F. Raposo, Kinetic modelling of the
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phase olive pomace (TPOP), Process Biochemistry 40 (2005) 1841-1847.
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FIGURE LEGENDS: Fig. 1. Accumulated methane over time, measured in standard conditions; ◊ denotes
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experimental values, - denotes the model.
Fig. 2. Histogramme of the Monte Carlo simulations for k (first order kinetic constant),
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θ (lag time) and Mo (ultimate methane production) parameters for the batch test of the mixture of wastes.
Fig. 3.
Solids concentration in the feed and outlet and solids fractions concentration
estimates. (Xin, inlet solid concentration; Xb, biodegradable solid substrate; Xnb non
biodegradable solid substrate; Xm, microorganisms concentration; Xt cal, total solid concentration in the calibration period; Xt val, total solid concentration in the validation period; X exp, experimental outlet solid concentration).
Fig. 4.
Evolution of the variable first-order kinetic constant.
Fig. 5.
Methane flow in the continuous reactor. o experimental values;
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model results.
FOG (mg/gVS) 513 (125) 234 (133)
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TS VS (g/L) (g/L) 18 (4) 16 (4) 23 (6) 19 (6) 29 (12) 22 (10)
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Table 1. Waste characterization. The standard deviation is shown in parentheses
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Ruminal content Tannery carving fat Secondary sludge purge
KTN Lignine (mg/gVS) (mg/gVS) 18 (3) 28 (5) 74 (20) 17 (8) -
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Table 2 Parameters obtained from batch tests with a confidence range of 90%.
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Waste Ruminal content Tannery carving fat Secondary sludge purge Mixture of wastes
k (d-1) 0.056 ± 0.002 0.032 ± 0.011 0.098 ± 0.007 0.089 ± 0.013
Methanation (%) 42 ± 1 87 ± 22 29 ± 1 90 ± 6
̶ ,
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Accumulated methane over time, measured in standard conditions; ◊
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experimental values, - model.
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Fig.1
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Fig. 2 Histograme of the Monte Carlo simulations for k (first order kinetic constant), θ (lag time) and Mo (ultimate methane production) parameters for the batch test of the mixture of wastes.
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Solids concentration in the feed and outlet and solids fractions concentration estimates. (Xin, inlet solid concentration; Xb, biodegradable solid substrate; Xnb non biodegradable solid substrate; Xm, microorganisms concentration; Xt cal, total solid concentration in the calibration period; Xt val, total solid concentration in the validation period; X exp, experimental outlet solid concentration).
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Fig. 3
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Evolution of the variable first-order kinetic constant.
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Fig. 4
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Methane flow in the continuous reactor. experimental values; • , model results.
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Fig.5
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S1369-703X(14)00363-5 http://dx.doi.org/doi:10.1016/j.bej.2014.12.014 BEJ 6096
To appear in:
Biochemical Engineering Journal
Received date: Revised date: Accepted date:
4-8-2014 23-10-2014 24-12-2014
Please cite this article as: Iv´an L´opez, Mauricio Passeggi, Liliana Borzacconi, Variable kinetic approach to modelling an industrial waste anaerobic digester, Biochemical Engineering Journal http://dx.doi.org/10.1016/j.bej.2014.12.014 This is a PDF file of an unedited manuscript that has been accepted for publication. As a service to our customers we are providing this early version of the manuscript. The manuscript will undergo copyediting, typesetting, and review of the resulting proof before it is published in its final form. Please note that during the production process errors may be discovered which could affect the content, and all legal disclaimers that apply to the journal pertain.
Variable kinetic approach to modelling an industrial waste anaerobic digester
Iván López*, Mauricio Passeggi and Liliana Borzacconi Facultad de Ingeniería, Universidad de la República J.Herrera y Reissig 565, Montevideo, Uruguay
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(* [email protected])
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-
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Variable kinetic coefficient is proposed in order to follow the acclimation of microorganisms. Batch test were used to obtain biodegradation potential. Monte Carlo methods were applied to obtain confidence interval of parameters. Continuous reactor was used to calibrate and validate the model.
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-
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Highlights
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Abstract
Anaerobic co-digestion of agro-industrial wastes is a promising option for the
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stabilisation of residues with biogas production. A mixture of bovine ruminal
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content, tannery carving fat and activated sludge purge was considered for this
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study. Biodegradability tests for individual wastes and a mixture of wastes were performed in batch conditions. Additionally, a completely mixed reactor with an average residence time of 30 days and a loading rate of 3.0 gVS/L.d. was employed for the mixture of wastes. A Volatile Solids (VS) removal efficiency of 66% with a methane production of 0.38 LCH4/kgVSadded or 0.58 LCH4/kgVSremoved was attained. A first-order kinetic model with lag time was
employed to describe the behaviour of the batch tests. Parameter determination was performed using direct search methods. Monte Carlo methods were utilised to determine the range of parameters. An ultimate methanation of 90 ± 6% was obtained from the batch tests. For the continuous system, a simple model with a variable kinetic constant that reflects the microbiological activity was proposed. The model was calibrated by adjusting the stoichiometric coefficients using solids outlet data, and the kinetic constant was deduced using
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experimental methane flow data. The kinetic constant doubles for
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approximately four residence times, which demonstrates the acclimation of
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biomass.
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Keywords
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Anaerobic Processes, Biodegradation, Biogas, Modelling, Monte Carlo,
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Kinetic Parameters
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LIST OF SYMBOLS
first order kinetic constant [d-1]
km
first order kinetic constant in continuous model [L/gVS.d]
k1
stoichiometric coefficient from solids to methane conversion [LCH4/gVS]
k3
stoichiometric coefficient from solids to microorganisms conversion [-]
L
Laplace transform
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k
M
accumulated methane production [mL]
Mo
ultimate methane production [mL]
qCH4
methane flow [L/Lreactor.d]
rM
methane production rate [gCOD/L.d]
solid substrate degradation rate [gVS/L.d]
t
time [d]
X
solid substrate concentration [gVS/L]
Xb
biodegradable solid substrate concentration [gVS/L]
Xm
microorganisms concentration [gVS/L]
Xnb
non biodegradable volatile solid concentration [gVS/L]
Xt
total volatile suspended solids [gVS/L]
YX/M
yield coefficient, conversion of substrate into methane [gCOD methane/gVS]
θ
lag time for microbial activation[d]
Introduction
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1.
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rX
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At present, global changes in the world like minimization of greenhouse gases
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emissions, and the need of use renewable energy sources require a more efficient use of
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biotechnologies [1, 2]. The sustainability principles must be present in our technological decisions without detriment of other technical and economic considerations. In this
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sense, the anaerobic digestion of agro-industrial organic waste is an alternative
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treatment with significant advantages, such as low operating costs and power generation from biogas [3, 4]. Additionally, anaerobic technology has proven to be more favourable
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than the aerobic treatment of wastes from the point of view of greenhouse gas generation [5] and can even compete with other biofuels [6]. In this scenario, anaerobic digestion plays a key role because the products generated (e.g., hydrogen, methane) from the different metabolic steps can be used as energy sources in boilers, internal combustion engines or fuel cells [7] or as raw material for other processing options
(e.g., the production of biopolymers or other organic substances). For these reasons, anaerobic technology constitutes the core of organic waste treatment systems [8]. A constraint of the high-load operation is the presence of inhibitors, which are produced by the waste [9 - 11]. For instance, this constraint is found in the fat carving generated by tanneries, which contains a high concentration of fat that is abundant in triglycerides; the triglycerides degrade during digestion to glycerol and long-chain fatty acids. Additionally, long-chain fatty acids are potential inhibitors of methanogenesis
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[12, 13].
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Other wastes, such as ruminal content and secondary sludge from aerobic wastewater treatment plants, exhibit low methane generation potential due to their low
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biodegradability. With respect to the ruminal concentration, a high-fibre content hinders
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mixing if its size is not reduced by pretreatment [14]. This situation compels the
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digesters to operate with low-solid concentrations to limit the potential for high loads.
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Co-digestion is a widely used way in order to enhance the anaerobic degradations
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of solid substartes. The most reported experiences are related to agroindustrial or
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agricultural wastes and the organic fraction of municipal solid wastes, but also the
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sludgre from aerobic facilities is considered [15]. The mixture of wastes with different
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characteristics, enrich the substrate composition, dilutes the inhibitory components, prevents mixing problems and enhances methane generation [15 - 17].
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Despite increasing anaerobic applications, the comprehensive and practical
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modelling of these systems is still developing. An important milestone in this field was the development of the IWA (International Water Assotiation) ADM1 model (Anaerobic Digestion Model 1) [18]. This structured model included multiple steps describing the biochemical and physicochemical processes, which involved at least 26 dynamic state variables and many parameters. Although the complexity of anaerobic processes was
reflected in the ADM1 model, direct applications for modelling and control purposes are difficult to use. Additionally, the identification of model parameters under actual operational conditions is difficult. The ADM1 model also fails to depict all complex phenomena that occurs in an anaerobic system and must be expanded to include other phenomena [19]. Simpler models with reduced sets of state variables and parameters have been proposed [20 - 23]. Although simple models do not represent the complexity of real processes, the identification of parameters and model validations are more
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straightforward [24 - 26].
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As a rule, hydrolysis is the rate limiting step in the degradation of solid wastes. A first order kinetic rate with respect to the substrate is widely accepted for this step [27].
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The simplest kinetic model for the overall process is a first order kinetic expression.
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Several experimental procedures could be planned in order to obtain the model
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parameters, both in batch mode [28] or in continuous mode [29]. Specially, Biochemical
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order to obtain kinetics parameters.
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Methane Potential (BMP) tests [28] are standard tests that could be easily extended in
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Even though simple optimisation techniques, such as least squares methods, are
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widely used in order to obtain the model parameters, these methods do not provide
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information about the confidence interval of results. Standard deviations are obtained by repeated measures. This option increases the experimental work and consumes
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resources. Alternatively, simulation methods that only consume computational time,
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such as Monte Carlo, can be applied [30, 31]. The performance of the Monte Carlo confidence interval method is comparable to other widely accepted methods of interval construction, and it can be used when only summary data are available [32]. In chemical systems, kinetics parameters obtained from batch experiences are used without restrictions to design continuous systems. However systems that involves
microorganisms must take into account the acclimation phenomena. Then, kinetics parameters could change through time in order to reflect the acclimation or to reflect adverse microbiological conditions. In very simple models, lumping a complex behaviour in one single parameter, variation of this parameter could reflect the environmental conditions. The objective of this study is to evaluate the application of a simple kinetic model to describe the co-digestion of three agro-industrial wastes (ruminal content, tannery
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carving fat and biological sludge). The first order kinetic model is validated in batch
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using stardard experiences and the confidence range of parameters was determined using Monte Carlo techniques. The model is validated also in continuous conditions, but
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in this case a variable kinetic parameter is postulated describing the acclimation
Model
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2.
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capacity of microorganisms.
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Biodegradability tests are typically performed in batch conditions [28]. The solid
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substrate and anaerobic sludge (inoculum) are placed in batch reactors in anaerobic
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conditions. Cumulative methane production is monitored over time and the ultimate
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value is used to calculate the methane potential. The transformation of solid substrate into methane involves a complex series of subtransformations, whereas hydrolysis
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determines the total kinetics. Typically, a single first-order kinetic model is used to
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represent the hydrolysis of particulate matter [27]. Despite the complex phenomena involved, biodegradability curves can be fit to a simple first-order kinetic model.
(1)
where
(2)
where k is the first-order kinetic constant and X is the solid substrate concentration. The methane accumulative curve asymptotically approaches a value, which indicates the maximum fraction of substrate that can be transformed into methane. The stoichiometric
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coefficient YX/M relates the rate of substrate degradation to the rate of methane
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production. If both substances are expressed by the same units (e.g., grams of COD),
(3)
(4)
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The accumulated methane curve is
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this stoichiometric coefficient is the methanation yield of the solid substrate.
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where M is the accumulated methane, Mo is the maximum quantity of methane that can be obtained, and t is the time elapsed after the lag time θ. The lag phase that occurs at
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the beginning of the curves in batch tests is attributed to the microorganism
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requirements for acclimation or the need for activation of the biological activity. Thus, by fitting this model to the experimental data, the kinetic constant k and the asymptotic value Mo can be obtained (YX/M can be obtained if the initial amount of substrate is known). Continuous systems require another approach. First, a virtually complete mix can
be assumed due to the mechanical stirring device. The system can be considered to be a lumped parameter system, and the mass balance equations can be performed considering the entire reactor as a control volume. Second, the system is not truly a continuous reactor: the feed and the discharge are performed once a day as pulses of a few minutes; for the remainder of the day, the system behaves as a batch reactor. Due to the fact that the retention time is greater than one order of magnitude with respect to the feed period, which turns the system into a continuous operation mode.
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Dynamic mass balance equations produce ordinary differential equations with
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respect to time. Three variables are used as state variables: biomass concentration (Xm), biodegradable solid substrate concentration (Xb), and nonbiodegradable solid
(5)
(6)
(7)
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concentration (Xnb). The equations in the batch periods are expressed as
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where km is the kinetic first-order constant for the degradation of the biodegradable solids and k3 is the stoichiometric coefficient for the conversion of solids to
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microorganisms. In the feed and discharge events, the amount of fed solids must be added to the mass balance and the amount of discharged solids must be subtracted. Additionally, methane gas flow can be related to solid degradation. Due to the different time scales involved, an instantaneous release of gas can be assumed and the algebraic equation (8) can be written:
(8)
where k1 is the stoichiometric coefficient from the solids to methane conversion and qCH4 is the methane flow. Considering the model’s simplicity, all COD of the degraded solids is transformed into methane or microorganisms. The stoichiometric coefficients can be related as k1 + k3 = 1.
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The first-order kinetic constant km can be related to the microbial activity.
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Despite the simplicity of the model, this parameter reflects the complexity of the
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biochemical reactions that are involved in a complex net of microorganisms. This activity varies over time, which reflects the possible acclimation or inhibition of the
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microorganisms or variation in the biomass composition. To consider the variation in
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the microbial activity in the model, the kinetic constant km should be considered as a
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variable over time. Methods
3.1
Waste origin and characterisation
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The waste was collected weekly and maintained at less than 15°C prior to loading
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the reactors. Ruminal contents of bovine origin were obtained from a slaughterhouse
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after they were squeezed through a screw press. The tannery fleshing generated after the leather peeling process was processed through a meat grinder, which contained a disc with a 10 mm diameter holes, to obtain a suitable size to feed the reactors. The secondary biological sludge was obtained from an activated sludge plant that treats wastewater from an oil factory after it underwent a process of thickening by a
centrifugal decanter.
3.2
Analytical methods
Total and volatile solids were determined for each batch of waste. For the ruminal content, lignin was also determined. For the other two wastes, fats and oils and total Kjeldahl nitrogen were determined. At the outlet of the continuous reactor, total and
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volatile solids, soluble COD, pH, volatile fatty acids and bicarbonate alkalinity were
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determined.
All analyses were performed according to Standard Methods [33], with the
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exception of the lignin content that was determined by the Klason method [34]. The
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methane and carbon dioxide content in the biogas were determined by gas
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Batch assays
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3.3
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chromatography.
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Batch biodegradability tests were performed for each waste type (rumen content,
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tannery fleshing and sludge from biological wastewater treatment) and for a mixture of these wastes. Batch tests were conducted in 150 mL flasks, which were filled with
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substrate and inoculum from an UASB reactor that receives malting wastewater. For the
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mixture biodegradability test, a ratio of inoculum/substrate of 2.84 was selected to ensure no limitations regarding the amount of microorganisms. The waste mixture presents a volumetric ratio of 4:2:1 for rumen contents, fleshing and sludge, which corresponds to generation rates in the country. The pH was adjusted and the flasks were gassed with nitrogen to achieve anaerobic conditions and subsequently sealed and
placed in a shaker at 30°C. Monitoring of the methane production was performed using a pressure transducer to measure the increase of pressure generated by biogas production, and the biogas composition was determined by gas chromatography.
3.4
Continuous reactor
The continuous reactor has a usable volume of 3.0 L and a low-speed mechanical
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stirrer. It is placed in a heated cabinet to 35°C. The feed to the reactor was performed
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daily—Monday through Friday—after downloading the same volume. On Mondays and Fridays, it was fed double volume to compensate the lack of feed during the weekend.
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The produced biogas was measured by an MGC-1 MilliGascounter.
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Because the ruminal content contains a high concentration of fermentative
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bacteria but does not contain a significant concentration of methanogenic
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microorganisms, the reactor was inoculated with methanogenic sludge. This inoculum
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was obtained from a UASB reactor that was used to treat malting wastewater.
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During the first five months, the reactor was operated with an average load of 3
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gVS/L.d and 30 days of residence time. The waste was fed in a volumetric ratio of 4:2:1
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for rumen contents, tannery fleshing and secondary sludge, which corresponds to generation rates in the country, and the mixture was diluted with an equal volume of
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water. From day 165, the residence time was reduced to 20 days while maintaining the
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waste ratio, and the applied solids load was increased.
3.5
Parameter identification To determine the parameters from the batch tests, Scilab software was employed
to perform an optimisation routine based on the Nelder and Mead Simplex method,
without regard to the points that correspond to the lag phase of the curve. To assess the confidence interval of the parameters, a Monte Carlo simulation was performed. This method has proved to be a useful for determining the probability distribution in biotechnological models [30, 31]. From the experimental values and the experimental standard deviation, new pseudo-experimental points were randomly generated considering a normal distribution. The procedure was repeated a thousand times and the frequency distribution was obtained. A normal distribution was verified using the Xi
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square criterion [35]. Considering a data confidence interval with 90% probability, the
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confidence intervals of the parameters were determined.
For the continuous reactor, equations (5) to (7) are solved jointly with the ode
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routine of Scilab between each fed interval. The final terms of each integration interval
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are adjusted by adding the fed mass and subtracting the discharged mass to obtain the
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(8) because the methane flow is known.
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initial point to the next integration. The activity constant km is deduced from equation
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However, the stoichiometric coefficients must be known to solve the system. A k3
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parameter tuning was performed using the Scilab software and an optimisation routine
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based on the Simplex method by Nelder and Mead, which considers the parameters in
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the batch test to be the initial value for iteration. The adjustment was performed considering the coincidence between the accumulated experimental values of solid exit
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with the model predictions. The accumulated values rather than the daily values were
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selected because they provide a better reflection of the essential trend of the process and minimise the influence of experimental errors. The objective function to be minimised is the sum of the squares of the differences between the value predicted by the model and the experimental value. For the parameter determination, the values of the first 120 days were considered and the next 70 days were reserved for the model validation.
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Results
4.1
Waste characterisation
Table 1 presents the waste characterisation used in the tests and lists the mean values and the corresponding standard deviations. The waste mixture yielded an average ratio of 1.56 gCOD/gVS.
Batch tests
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4.2
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[TABLE 1]
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Figure 1 shows the batch test curve for the mixture of wastes. Similar graphs are
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obtained for individual wastes (not shown). Experimental points were performed in
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triplicate and a blank performed in identical conditions without substrate addition was
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discounted. Ninety percent confidence ranges that consider the variance in the
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experimental values are shown.
[FIG.1] [FIG.2]
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Figure 2 shows the results of the Monte Carlo simulation for the batch test, which
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was performed with the mixture of wastes. Similar results for the individual wastes are not presented. The parameter distributions obtained from the Monte Carlo simulation are normal, which was statistically verified using a Xi square distribution. For the codigestion test, the adjustment of the first-order model with lag time yields the following results: k = 0.089 ± 0.013d-1, θ = 2.46 ± 0.50 d and Mo = 196 ± 11 mL (confidence
interval of 90%). According to this ultimate methane production, the biodegradation of the substrate is 487 ± 37 NmL of methane per gram of degraded VS, which corresponds to a 90 ± 6% of methanisation. Table 2 also presents the results of the test with only one substrate.
[TABLE 2] Continuous reactor
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4.3
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During the first hundred days, the reactor was operated with an average residence time of 30 days and a volumetric organic load of 3.0 gVS/L.d. A mass balance in this
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period yields an inlet of 979 g of VS and an outlet of 331 g of VS. The net accumulation
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of volatile solids within the reactor was negligible. The VS removal efficiency was
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66%. Considering the experimental gCOD/gVS ratio of 1.56 for the feed and 1.40 for
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the outlet, the COD removal efficiency was 70%. This value corresponds with a
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methane production of 477 L, which corresponds to 1076 gCOD. The average methane
[FIG.3]
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production in this period was 0.38 NLCH4/gVSadded and 0.58 NLCH4/gVSremoved.
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Solids outlet accumulated values in the first 120 days was employed for the calibration. The model fit returns the following value for parameter: k3 = 0.316. Figure 3
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shows the results for the model validation and the estimated values of the various solid fractions. The results of the estimated outlet solids concentration (Xt) in the validation period (day 120 to day 190) show reasonable agreement with the experimental data.
[FIG.4]
Figure 5 shows the evolution of the first-order kinetic constant. A sustained increase in this parameter until days 120 – 140 shows the acclimation of the microorganisms to work in the reactor conditions. Disregarding the first ten days, in which the values may not be entirely representative, the activity doubles at
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approximately four mean solid residence times.
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[FIG 5]
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Experimental methane flow and model predictions are show in Figure 5. A
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relatively good agreement is observed in the general trend. The model prediction has a
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more oscillatory behaviour that the experimental measures. Biogas release from the
behaviour. Discussion
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5.
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solid mixture tend to be damped in practice, and this fact could explain the more gentle
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The experiments demonstrate the feasibility of co-digestion of the considered waste mixture. High biodegradability values can be attained, which results in acceptable
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stabilisation of waste and its transformation into biogas. These results are in agreement
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with the literature and confirm the benefits of the co-digestion with regard the single substrate digestion [15 – 17]. Despite its simplicity (first-order kinetics), the model fits the experimental data and can be applied to the batch biodegradability curves and a continuous stirred reactor. For batch curves, first-order with lag time employs the format that is shown in the
accumulated methane production vs. time graphs. For the batch tests, the asymptote of accumulated methane production is the ultimate value of methanation, i.e., the percentage of conversion in methane if infinite time has elapsed and the environmental conditions remain constant in the flask. The kinetic constant corresponds to the slope of the curve after a delay has elapsed. The results of the ultimate methanation potential found in literature show a great dispersion. As example, Sambusiti et al.[36] working with ensiled forghum forage at
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35ºC found 83% of methanation as ultimate value; Ferreira et al. [37] working with
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wheat straw at 35ºC found 51% of methanation as ultimate value; Jokela et al. [38] found values of 92% for paper and carboard and 96% for putrescibles at the same
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temperature. Temperature and source inoculum are other factors that have incidence in
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results [39, 40]. Is reasonable that ruminal content shown low methanation yield
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because in the rumen of the bovines some degradation of the organic substrate occurs.
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Similarly, the activated sludge purge can have some degree of stabilization and shown
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low anaerobic degradability in consequence.
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The first order kinetic constant values obtained in this paper are in agreement with
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literature. Sambusiti et al.[36] found values between
0.049 d-1 and 0.146 d-1 for
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sorghum degradation using different inoculum sources. Ferreira et al. [37] found a value of 0.069 d-1 for anaerobic degradation of wheat straw with no pretreatment. Jokela et al.
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[38] found values between 0.024 d-1 and 0.107 d-1 for different substrates. Borja et al.
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[41] reports a value of 0.054 ± 0.003 d-1 for the hydrolysis of olive pomace. Monte Carlo techniques are useful to assess the reliability of the results and enable
the identification of the valid range of parameters. Assuming a normal distribution in the experimental errors, the parameters in the batch tests also exhibit a normal distribution that is centred on the optimum value obtained from the experimental data (Figure 2).
Table 2 shows that co-digestion notably enhances the methanisation. Although the methanisation of individual wastes are 42, 87 and 29% for rumen contents, tannery fleshing and secondary sludge, respectively, the co-digestion of the mixture yields a methanisation of 90%. This value is greater than the simple combination of individual methanisation percentages, which confirms the results that are usually obtained in this type of test. Although the daily correlation between the experimental values and the model is
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not very high in the continuous reactor, a reasonable match is observed with the trend
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presented in the daily values (Figure 3). The result is validated because this trend continues in the last 70 days. Although Figure 3 shows some deviations within this
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validation period, they are not significant and can be attributed to observed deficiencies
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in gas and solid measurements.
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The value of the kinetic constant in the batch model (0.089 ± 0.010 d-1)
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corresponds to the product of km×Xm in the continuous model. In the initial condition of
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the continuous experiences, km = 5×10-3 g-1Ld-1, Xm = 17 gL-1, and km×Xm = 0.085 d-1.
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On day 130, the values are km = 3.5×10-2 g-1Ld-1, Xm = 22 gL-1, and km×Xm = 0.77 d-1,
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i.e., an increase of an order of magnitude. This fact is indicative of the adaptability of
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the continuous system, i.e., the evolution of biomass towards the species with greater ability to degrade the specific substrate. In addition, the continuous reactor was operated
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at 5ºC higher than the temperature of the batch experiences; this fact may explain a
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generally higher level of activity values beyond the general trend. 6
Conclusions
The results of the batch biodegradability tests and the continuous stirred reactor demonstrate that the co-digestion of a mix of rumen contents, fat carving and secondary
biological sludge is feasible with suitable results. A first-order kinetic model with lag time can adequately predict the results of batch experiences. A reasonable fit with experimental values is achieved. Monte Carlo methods are useful to determine the validity range of the parameters and have proven that the errors in the parameters exhibit normal distributions, assuming a normal distribution of the experimental errors. A simple model with a variable kinetic constant reasonably represents the
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experimental results in a continuous reactor. The variation in the first-order kinetic
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constant reflects the acclimation of the biomass to degrade the specific wastes fed to the reactor. The kinetic constant approximately doubles after four mean solid residence
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times.
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Acknowledgments: To Martín Benzo, who has collaborated in the experimental study. The study was
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supported by a grant from INIA – Uruguay (National Institute for Agricultural Research).
B.K. Ahring, P. Westermann, Redefining the role of anaerobic digestion, in
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[1]
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FIGURE LEGENDS: Fig. 1. Accumulated methane over time, measured in standard conditions; ◊ denotes
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experimental values, - denotes the model.
Fig. 2. Histogramme of the Monte Carlo simulations for k (first order kinetic constant),
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θ (lag time) and Mo (ultimate methane production) parameters for the batch test of the mixture of wastes.
Fig. 3.
Solids concentration in the feed and outlet and solids fractions concentration
estimates. (Xin, inlet solid concentration; Xb, biodegradable solid substrate; Xnb non
biodegradable solid substrate; Xm, microorganisms concentration; Xt cal, total solid concentration in the calibration period; Xt val, total solid concentration in the validation period; X exp, experimental outlet solid concentration).
Fig. 4.
Evolution of the variable first-order kinetic constant.
Fig. 5.
Methane flow in the continuous reactor. o experimental values;
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model results.
FOG (mg/gVS) 513 (125) 234 (133)
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TS VS (g/L) (g/L) 18 (4) 16 (4) 23 (6) 19 (6) 29 (12) 22 (10)
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Table 1. Waste characterization. The standard deviation is shown in parentheses
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Ruminal content Tannery carving fat Secondary sludge purge
KTN Lignine (mg/gVS) (mg/gVS) 18 (3) 28 (5) 74 (20) 17 (8) -
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Table 2 Parameters obtained from batch tests with a confidence range of 90%.
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Waste Ruminal content Tannery carving fat Secondary sludge purge Mixture of wastes
k (d-1) 0.056 ± 0.002 0.032 ± 0.011 0.098 ± 0.007 0.089 ± 0.013
Methanation (%) 42 ± 1 87 ± 22 29 ± 1 90 ± 6
̶ ,
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Accumulated methane over time, measured in standard conditions; ◊
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experimental values, - model.
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Fig.1
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Fig. 2 Histograme of the Monte Carlo simulations for k (first order kinetic constant), θ (lag time) and Mo (ultimate methane production) parameters for the batch test of the mixture of wastes.
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Solids concentration in the feed and outlet and solids fractions concentration estimates. (Xin, inlet solid concentration; Xb, biodegradable solid substrate; Xnb non biodegradable solid substrate; Xm, microorganisms concentration; Xt cal, total solid concentration in the calibration period; Xt val, total solid concentration in the validation period; X exp, experimental outlet solid concentration).
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Fig. 3
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Evolution of the variable first-order kinetic constant.
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Fig. 4
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Methane flow in the continuous reactor. experimental values; • , model results.
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Fig.5
o