## Abstract

Municipal solid waste (MSW) landfills now represent one of the most important issues related to the waste management cycle. Knowledge of biogas production is a key aspect for the proper exploitation of this energy source, even in the post-closure period. In the present study, a simple mathematical model was proposed for the simulation of biogas production. The model is based on first-order biodegradation kinetics and also takes into account the temperature variation in time and depth as well as landfill settlement. The model was applied to an operating landfill located in Sicily, in Italy, and the first results obtained are promising. Indeed, the results showed a good fit between measured and simulated data. Based on these promising results, the model can also be considered a useful tool for landfill operators for a reliable estimate of the duration of the post-closure period.

## INTRODUCTION

Since the 1970s, municipal solid waste (MSW) landfills have been used as large biological reactors where the organic fraction of MSW undergoes anaerobic digestion producing gas and liquid emissions (Owens & Chynoweth 1993; Lissens *et al.* 2001; Imhoff *et al.* 2007; Di Bella *et al.* 2012). The biodegradable portions of organic compounds are hydrolyzed and eventually methanized, producing landfill gas (LFG) composed by methane (CH_{4}), carbon dioxide (CO_{2}) and trace components. MSW landfills have been identified as one of the most important anthropogenic sources of CH_{4} emissions (Aronica *et al.* 2009; Di Bella *et al.* 2011; Di Trapani *et al.* 2013). This aspect is of particular concern, since CH_{4} is a greenhouse gas with a global warming potential 28 times that of CO_{2} (Kumar *et al.* 2016; IPCC 2007; El-Fadel *et al.* 2012). The utilization of the LFG would both prevent harmful atmosphere emissions and provide a source of green energy (Lee *et al.* 2017; Mboowa *et al.* 2017).

In order to optimize the sizing and the operation of the LFG extraction network in a sanitary landfill it is necessary to obtain reliable forecasts of LFG production from the beginning of a site's operation until its closure and even in the post-closure period. This challenge has been thoroughly addressed in the technical literature by Spokas *et al.* (2006) and Chen *et al.* (2009), for example. In this context, mathematical models can represent a suitable tool for obtaining reliable estimates of LFG production over time, showing the effects of different compositions of the disposed waste as well.

In the technical literature, many examples of mathematical models have been reported for the estimation of LFG production (Panepinto *et al.* 2013; Fei *et al.* 2016). Such models can be effectively applied for predictive purposes, but they must be validated for each specific case to properly evaluate the productivity and profitability of the energy systems that use waste from traditional landfills (Arena *et al.* 2003; Meima *et al.* 2008).

Although in principle organic matter degradation/gas production is a complex process characterized by different kinetic degradation rates, the most popular models are based on a simple first-order biodegradation kinetics model. This is a suitable approximation when one of the stages is definitely rate determining; moreover, such models have the merit of being easy to use and usually provide a good fit with field data.

Among the models based on first-order reaction kinetics, it is worth mentioning the one by Andreottola & Cossu (1988). In this model, the biodegradable organic carbon content in the solid phase is obviously considered the fundamental input parameter and different degradation rates were allowed. The model takes into account the influence of structural and operational features of the landfill, such as humidity, bulk density and size of waste, on the gas-generation process.

The model of El-Fadel *et al.* (1996) takes into account basic concepts from microbiology, chemistry and physics to simulate the production and transport of LFG and heat in a landfill body. This model shows the distribution of LFG and its diffusion through the landfill. Due to the complexity of this model, its application requires the knowledge of many parameters, which are often difficult to establish. Nevertheless, the ‘temperature’ parameter included in this model is one of the fundamental input parameters influencing on the intensity of processes.

The model of Hashemi *et al.* (2002) evaluates the gas flow split into two pathways: through the upper layer or cover and the extraction wells. This model is also very complex and difficult to apply because of the many local parameters required (more than 15).

The model of Manna *et al.* (1999) also considers the temperature as an input parameter for the calculation of the activation energy, necessary for starting the biodegradable processes. Another notable feature is that this model takes into account the waste layers density, which changes over time, so it represents the dynamics of the landfill processes from the beginning of the operation stage until the end of biogas production processes.

Recently, other models have been proposed, taking into account operation actions such as the installation of the covering cap and the recirculation of leachate (Berge *et al.* 2009; Sinan Bilgili *et al.* 2009). Indeed, it is worth noting that one must differentiate between the algorithms that enable the evaluation of LFG production and the commercial software that allow users to also take into account the different landfill management strategies (Sharff & Jacobs 2006; Wangyao *et al.* 2010). In this sense, the application results of several commercial software packages have been reported in the technical literature, such as, for instance, GasSim (Gregory *et al.* 1999, 2003), LandGEM (USEPA 2005) and IPCC (2006) models. Nevertheless, among the models summarized above and several others reported in the technical literature, only a few have been applied to real landfill sites. Indeed, the proper application of models is strongly site specific, depending in particular on the waste moisture content, the thermal profile inside the landfill body, the density profile with the landfill depth and the covering system features. This is a crucial aspect, since the need to consider site-specific landfill operational features requires the collection of a large amount of experimental data, which is not easy to acquire.

Bearing these considerations in mind, the present paper presents an application study of a mathematical model able to simulate the amount and rate of LFG production from an MSW landfill, inspired by one of the conceptual models cited above – Manna *et al.* (1999). The model consists of two parts: material balance and energy balance. The equations of material balance take into account the amount of biodegradable carbon fraction in the different waste layers involved in the anaerobic reactions, as well as the changes of density of the layers over time. Equations of energy balance calculate temperature changes over time, resulting from the anaerobic processes and thermal exchanges between layers and towards the landfill boundaries.

The model was first run and tested with fictitious data, then applied to an actual operating landfill located in Sicily, in Italy, as a case study. The main goal was to compare the model results with experimental data provided by the landfill operator in order to validate the model and to optimize the model parameters.

## MATERIALS AND METHODS

### Model description

As mentioned previously, the paper presents a mathematical model application aimed at simulating the LFG production in an MSW landfill. The model was inspired by the conceptual model proposed by Manna *et al.* (1999). Different aspects have been taken into account: the temperature profile, by applying a thermal balance within the landfill body, which influences the organic carbon that is available for the conversion process; the model also considers the material conversion for the gas generation process. The mathematical model is able to simulate landfill behavior under three different periods:

Period I : MSW is discharged into a cell and consequently the landfill depth increases as a function of time (L(t)). It is possible to distinguish two zones within the waste layer: an inhibition zone and a reaction zone. Briefly, in the inhibition zone, characterized by a residence time

*τ*<*t*and 0 <_{in}*z*<*L*no biochemical reactions will occur (as outlined in more detail below), whereas in the reaction zone_{in}(t),*L*_{in}(t)*<**z**<**L(t)*LFG production will occur (Figure 1(a)).Period II (

*t*_{cult}*<**t**<**t*_{cult}*+**t*): active landfilling has ended and the cell is covered with a clay layer. The whole depth is constant and the landfill can be divided into: clay layer, inhibition zone and reaction zone (Figure 1(b))._{in}Period III (

*t*>*t*_{cult}*+**t*): there is no inhibition zone (_{in}*L*= 0) since each layer is characterized by a residence time higher than inhibition time (Figure 1(c))._{in}

In particular, the inhibition zone has been evaluated according to the lag time *t _{in}*: the time from the placement of waste to the beginning of significant gas production. The absence of significant biochemical reactions could be due to different aspects (including initial microbial acclimation period, biodegradable substrate unavailability, etc.). In the present study, the lag time was set at 1 year, based on Cossu

*et al.*(1996).

### Mass balance equations

*ω*

_{i}is the biodegradable carbon fraction (kg kg

^{−1}

_{MSW}), A

_{k}is a dimensionless coefficient,

*t*is the simulation time (s),

*z*is the depth from the landfill top (m) and

*k*is the kinetic constant (s

^{−1}), expressed as: where E is the activation energy (J/(mol K)), R is the ideal gas constant (J/(mol K)), T

_{0}is the initial temperature value (K) and T

_{w}is the waste temperature (K).

*L*

_{in}(t)*<*

*z*

*≤*

*L(t)*) and depends on the variation of depth

*z*as a function of time according to:

The waste components that have been taken into account for gas production are: carbohydrates, fats and proteins. The first degradation process is the chemical/enzymatic hydrolysis of organic matter. Subsequently, the hydrolyzed compounds are subjected to biochemical transformations with volatile fatty acid (VFA) production and then metabolized with LFG production.

*i*has been assessed by the following equation, which takes into account its strict dependence on temperature values, according to Tabasaran (1982): where

*ω*is the total organic carbon fraction of biodegradable component

_{it}*i*(kg/kg

_{MSW}), while the other symbols have been already defined.

*z*: where

*ρ*

_{0}is the starting density value (kg/m

^{3})),

*ρ*

_{∞}the maximum density value corresponding to an infinite specific load (kg/m

^{3}) and

*β*a numeric coefficient obtained after a calibration procedure.

### Thermal balance equations

*L*

_{in}(t)*<*

*z*

*≤*

*L(t)*): where

*P*is the perimeter of the cell,

*n*is the gas volume producible per kilogram and per second (Nm

_{g}^{3}/kg

_{MSW}/s),

*–*Δ

*is the enthalpy of anaerobic reaction (J/Nm*

_{r}H^{3}),

*U(t)*is the overall heat transfer coefficient (W/m

^{2}/K) and

*C*is the specific heat (J/kg/K). The other symbols have been already defined.

_{pw}*z*<

_{0}*z*<

*L*, the energy balance can be expressed as: For the superficial zone (

_{in}(t))*0<z*

*≤*

*z*), characterized by the presence of the clay layer, the following equation can be applied: Figure 2 shows a flow chart of the model to enable better understanding of it.

_{0}### Model application

The boundary conditions that have been imposed are:

Tables 1 and 2 summarize the solutions of the equations for the energy balance by means of explicit finite difference equations, for the waste layer and the clay layer, respectively.

Interface . | Equation . | Validity on Δz . | Validity on Δt . |
---|---|---|---|

1 | z = 0 | ||

2 | z = z_{0} = 1.5 | ||

3a | |||

3b | |||

4 | & | ||

5 | |||

6 |

Interface . | Equation . | Validity on Δz . | Validity on Δt . |
---|---|---|---|

1 | z = 0 | ||

2 | z = z_{0} = 1.5 | ||

3a | |||

3b | |||

4 | & | ||

5 | |||

6 |

Interface . | Equation . | Validity on Δz . | Validity on Δt . |
---|---|---|---|

7 | z = 0 | ||

8 | |||

9 | |||

10 |

Interface . | Equation . | Validity on Δz . | Validity on Δt . |
---|---|---|---|

7 | z = 0 | ||

8 | |||

9 | |||

10 |

MSW fraction . | % . | C_{i} [kg_{C}/kg_{MSW}]
. | U_{i} [%]
. | f_{bi} [−]
. | ω_{it} [kg_{C}/kg_{MSW}]
. | k_{i} [year^{−1}]
. |
---|---|---|---|---|---|---|

Organic | 42.7 | 0.48 | 60 | 0.8 | 0.0656 | 0.693 |

Garden | 4.6 | 0.48 | 50 | 0.7 | 0.00773 | 0.2310 |

Paper | 24.8 | 0.44 | 8 | 0.5 | 0.0502 | 0.057 |

Wood | 1.3 | 0.5 | 20 | 0.5 | 0.00260 | 0.0347 |

Textiles and leather | 3.9 | 0.55 | 10 | 0.2 | 0.00386 | 0.0462 |

Plastic | 8.6 | 0.7 | 2 | – | – | – |

Metals, glass, inert waste | 14.1 | – | 3 | – | – | – |

MSW fraction . | % . | C_{i} [kg_{C}/kg_{MSW}]
. | U_{i} [%]
. | f_{bi} [−]
. | ω_{it} [kg_{C}/kg_{MSW}]
. | k_{i} [year^{−1}]
. |
---|---|---|---|---|---|---|

Organic | 42.7 | 0.48 | 60 | 0.8 | 0.0656 | 0.693 |

Garden | 4.6 | 0.48 | 50 | 0.7 | 0.00773 | 0.2310 |

Paper | 24.8 | 0.44 | 8 | 0.5 | 0.0502 | 0.057 |

Wood | 1.3 | 0.5 | 20 | 0.5 | 0.00260 | 0.0347 |

Textiles and leather | 3.9 | 0.55 | 10 | 0.2 | 0.00386 | 0.0462 |

Plastic | 8.6 | 0.7 | 2 | – | – | – |

Metals, glass, inert waste | 14.1 | – | 3 | – | – | – |

. | C_{p}[kJ/(kg K)]
. | λ [W/(m K)]
. |
---|---|---|

MSW | 2.17 | 0.0445 |

Clay | 3.35 | 0.00093 |

HDPE | – | 0.04 |

Ground | 0.73 | 0.1395 |

. | C_{p}[kJ/(Nm^{3} K)]
. | . |

Gas | 1.714 | – |

. | C_{p}[kJ/(kg K)]
. | λ [W/(m K)]
. |
---|---|---|

MSW | 2.17 | 0.0445 |

Clay | 3.35 | 0.00093 |

HDPE | – | 0.04 |

Ground | 0.73 | 0.1395 |

. | C_{p}[kJ/(Nm^{3} K)]
. | . |

Gas | 1.714 | – |

Δ_{r}H = −900 kJ/Nm^{3}; E = 12979 J/mol; T_{ground} = 284.15; T_{air} = 284.15.

. | Units . | Value . |
---|---|---|

Cultivation period | year | 8 |

Inhibition time (lag time) | year | 1 |

Clay layer depth | m | 1.5 |

Waste density (z = 0) | kg m^{−3} | 600 |

Waste density (bottom) | kg m^{−3} | 1190 |

β | m | 12.4^{a} |

Initial waste temperature | K | 308.15 |

. | Units . | Value . |
---|---|---|

Cultivation period | year | 8 |

Inhibition time (lag time) | year | 1 |

Clay layer depth | m | 1.5 |

Waste density (z = 0) | kg m^{−3} | 600 |

Waste density (bottom) | kg m^{−3} | 1190 |

β | m | 12.4^{a} |

Initial waste temperature | K | 308.15 |

^{a}Calibrated value.

### The landfill site

The case study landfill site is located in south-central Sicily at about 260 m above sea level (Figure 3). It covers an overall area of 18 ha. At present, it is composed of five disposal cells (named VE, V1, V2, V3, V4), only one of which (V4) is in the operational phase, whereas the remaining cells are in the post-operational phase and permanently covered with a multi-layered covering system. The mathematical model was applied to cell V3, characterized by a volume of 1.240.000 m^{3} and in operation from 2004 to 2011. The amounts of disposed waste (model input), the LFG emissions relating to 2012 and 2013, and the LFG recovery data have been provided by the owner of the landfill. Table 6 shows the waste quantities disposed of in cell V3. Moreover, direct measurements of methane flux have been carried out by the authors in cell V3 in two different field gathering campaigns, as outlined in the following section.

Year of disposal . | Units . | Value . |
---|---|---|

2004 | 10^{3} kg | 10,201 |

2005 | 10^{3} kg | 64,246 |

2006 | 10^{3} kg | 72,061 |

2007 | 10^{3} kg | 155,148 |

2008 | 10^{3} kg | 228,283 |

2009 | 10^{3} kg | 311,985 |

2010 | 10^{3} kg | 325,815 |

2011 | 10^{3} kg | 125,833 |

Year of disposal . | Units . | Value . |
---|---|---|

2004 | 10^{3} kg | 10,201 |

2005 | 10^{3} kg | 64,246 |

2006 | 10^{3} kg | 72,061 |

2007 | 10^{3} kg | 155,148 |

2008 | 10^{3} kg | 228,283 |

2009 | 10^{3} kg | 311,985 |

2010 | 10^{3} kg | 325,815 |

2011 | 10^{3} kg | 125,833 |

### Direct measurement of methane flux

The methane flux emission measurements were carried out by means of the flux chamber (static non-stationary) method. Briefly, a total of 191 and 126 sampling points were measured in the cell V3 during in the experimental campaigns carried out in September 2014 and November 2015, respectively. In order to increase the experimental dataset available for the present study, historical data have been retrieved by the landfill operator, referring to 2012 and 2013 (previous data would be not of interest, since the landfill was still in the operational period and only a portion of the waste would be active in the LFG production process).

Figure 3 depicts the aerial view of the landfill and, as an example, the detail of the sampling points during the campaign of September 2014. The surface methane flow was determined by measuring the temporal change in methane concentration inside the chamber (LANDBOX HV30, LabService Analytica s.r.l.), using a portable flame ionization detector (Telegan Gas-Tec®), connected to a notebook for instantaneous data recording. The flux chamber had a volume of 0.026 m^{3} and covered a 0.08 m^{2} surface area on the ground; it was equipped with a small fan for gas mixing in the internal volume and it was properly sealed to the ground.

*Q*is the CH

_{4}flux (mg CH

_{4}m

^{−2}s

^{−1});

*V*(m

^{3}) and

*A*(m

^{2}) are the volume and footprint of the flux chamber respectively;

*c*is the CH

_{4}concentration (mg CH

_{4}m

^{−3}) and

*t*represents the time step (s). More specifically, the run time for each measurement was based on a flattening of the concentration/time curve. The temporal acquisition frequency was set to 1 s, since the expected fluxes were not so high. For further details on the procedure, the reader is referred to Di Trapani

*et al.*(2013).

*n*is the number of field measurements and

*Z*is the size of the investigated area, expressed in m

^{2}.

As mentioned previously, E was measured directly by means of the flux-chamber method, R data was provided by landfill operator, whilst O was set to the default value of 10%, according to Di Bella *et al.* (2011).

## RESULTS AND DISCUSSION

### Comparison between model result and experimental data

The model was applied to a real solid waste landfill to calibrate it by employing real data of methane gathered from the field campaigns. Specifically, a semi-automatic model calibration was carried out adopting a minimization of differences between measured and simulated values by means of the conjugate gradient.

Table 7 summarizes the field investigations, showing the resulting values of the most commonly used statistical indices. The CV (coefficient of variation) values confirmed the high spatial variability of the instantaneous emission rates for both campaigns.

Campaign . | Cell . | Field measur. . | Min [mg CH_{4} m^{−2} s^{−1}]
. | Average [mg CH_{4} m^{−2} s^{−1}]
. | Max [mg CH_{4} m^{−2} s^{−1}]
. | St.Dev. [mg CH_{4} m^{−2} s^{−1}]
. | CV [%] . |
---|---|---|---|---|---|---|---|

May 2012 | V3 | 44 | 0.001 | 1.238 | 12.67 | 2.89 | 459.94 |

March 2013 | V3 | 37 | 0.001 | 0.63 | 8.90 | 1.98 | 315.63 |

September 2014 | V3 | 191 | 0.001 | 0.52 | 17.17 | 2.21 | 426.01 |

November 2015 | V3 | 126 | 0.001 | 0.40 | 15.40 | 3.28 | 762.01 |

Campaign . | Cell . | Field measur. . | Min [mg CH_{4} m^{−2} s^{−1}]
. | Average [mg CH_{4} m^{−2} s^{−1}]
. | Max [mg CH_{4} m^{−2} s^{−1}]
. | St.Dev. [mg CH_{4} m^{−2} s^{−1}]
. | CV [%] . |
---|---|---|---|---|---|---|---|

May 2012 | V3 | 44 | 0.001 | 1.238 | 12.67 | 2.89 | 459.94 |

March 2013 | V3 | 37 | 0.001 | 0.63 | 8.90 | 1.98 | 315.63 |

September 2014 | V3 | 191 | 0.001 | 0.52 | 17.17 | 2.21 | 426.01 |

November 2015 | V3 | 126 | 0.001 | 0.40 | 15.40 | 3.28 | 762.01 |

In the different experimental campaigns, the highest emission zones were located in some sampling points close to LFG collection wells, which were characterized by faults between the liner and the well head, as previously mentioned.

Referring in particular to the field campaign carried out in 2014, starting from the instantaneous flux values, the overall methane emission from the investigated area was derived, with an average value as almost equal to 0.74 10^{4} Nm^{3}/month. Concerning the recovery data (measured values) provided by the landfill owner, it was 5.04 10^{6} Nm^{3}/month. Methane subjected to oxidation through the superficial cover soil (O) was 0.07 10^{4} Nm^{3}/month. Therefore, by applying a mass balance, it was possible to evaluate the net methane produced, which was 5.12 10^{6} Nm^{3}/month.

The latter was compared with the simulated value deriving from the mathematical model, referring to the specific month of investigation. The results obtained are summarized in Table 8.

. | Emission [m^{3}/month]
. | Recovery [m^{3}/month]
. | Oxidation [m^{3}/month]
. | Production [m^{3}/month]
. |
---|---|---|---|---|

Mathematical model (2012) | – | – | – | 1.35 10^{7} |

Experimental data (2012) | 3.86 10^{5} | 7.33 10^{6} | 2.31 10^{5} | 1.01 10^{7} |

Mathematical model (2013) | – | – | – | 7.39 10^{6} |

Experimental data (2013) | 1.83 10^{5} | 8.59 10^{6} | 2.74 10^{4} | 8.80 10^{6} |

Mathematical model (2014) | – | – | – | 5.39 10^{6} |

Experimental data (2014) | 0.74 10^{4} | 5.04 10^{6} | 0.07 10^{4} | 5.12 10^{6} |

Mathematical model (2015) | – | – | – | 3.20 10^{6} |

Experimental data (2015) | 0.62 10^{4} | 3.78 10^{6} | 0.06 10^{4} | 3.79 10^{6} |

. | Emission [m^{3}/month]
. | Recovery [m^{3}/month]
. | Oxidation [m^{3}/month]
. | Production [m^{3}/month]
. |
---|---|---|---|---|

Mathematical model (2012) | – | – | – | 1.35 10^{7} |

Experimental data (2012) | 3.86 10^{5} | 7.33 10^{6} | 2.31 10^{5} | 1.01 10^{7} |

Mathematical model (2013) | – | – | – | 7.39 10^{6} |

Experimental data (2013) | 1.83 10^{5} | 8.59 10^{6} | 2.74 10^{4} | 8.80 10^{6} |

Mathematical model (2014) | – | – | – | 5.39 10^{6} |

Experimental data (2014) | 0.74 10^{4} | 5.04 10^{6} | 0.07 10^{4} | 5.12 10^{6} |

Mathematical model (2015) | – | – | – | 3.20 10^{6} |

Experimental data (2015) | 0.62 10^{4} | 3.78 10^{6} | 0.06 10^{4} | 3.79 10^{6} |

Figure 4 shows the CH_{4} production curve, obtained using the model, as well as the CH_{4} production in the months of investigation, achieved through mass balance equation (Equation (19)), from measured data.

Figure 4 shows a good fit between simulation results and methane production evaluated with experimental data, even if the model result is slightly higher than the experimental data. This result is in agreement with previous data, which have highlighted that mathematical models usually give an overestimate of LFG production (Cossu *et al.* 1996). Nevertheless, the proposed model can be applied for reliable estimates of LFG production, thus representing a useful tool for landfill operators to evaluate a reliable duration of the post-closure period. The estimated LFG production increases until cell V3 is characterized by active landfilling, while afterwards there is a sudden production depletion; this behavior is consistent with previous findings. However, it has to be stressed that despite the good reliability of the model, further validation for a longer period (multi-year analysis) should be provided for future applications.

## CONCLUSIONS

This paper presents the results of a mathematical model application aimed at predicting LFG production from an MSW landfill. The model was applied to an actual operating landfill located in Sicily and its results were compared with experimental data. In particular, LFG recovery data were provided by landfill operator, whereas data of diffuse emission from the landfill surface were acquired directly by the authors. The results obtained showed a good fit between model simulation and experimental data, with only a slight deviation of model predictions compared with experimental data. This has highlighted the importance of direct measurements for the calibration/validation of the proposed model. Nevertheless, the proposed model can be applied for reliable estimates of LFG production, thus representing a useful tool for landfill operators to evaluate a reliable duration of the post-closure period.

## AKNOWLEDGEMENTS

Project SIGLOD – Sistema Intelligente per la Gestione e Localizzazione Ottimale delle Discariche – funded by European Community and Repubblica Italiana within **‘**PON04a2_F – SMART CITIES AND COMMUNITIES AND SOCIAL INNOVATION’ and managed by UniNetLab, Università degli Studi di Palermo – provided grants for the development of the model and the field measurements. The authors warmly thank Eng. Giovanni Contino for his precious help during model application.