#### 3.1. BIOLEACH Model

BIOLEACH [

77] is a mathematical model for the real-time management of urban solid waste landfills. The model allows for joint estimations of leachate and biogas production and incorporates the possibility of simulating leachate recirculation, both on the landfill surface and inside the waste mass, being therefore also suitable for simulating bioreactor landfills.

The BIOLEACH model has been conceived to be a decision support tool to ensure optimal landfill management. It can be used by the landfill operator avoiding the use of parameters that may be difficult to obtain.

The production of landfill gas and the generation of leachate are considered by the model as coupled processes. The biogas generation calculations are carried out at the same time as the leachate production calculations considering the physicochemical conditions actually existing inside the waste mass and the corresponding water balances.

BIOLEACH uses waste production data on a monthly scale, which gives it enough flexibility to adapt the model to possible variations arising from the real management needs of waste treatment facilities. Likewise, the model uses values of the climatological parameters on a monthly scale obtained from local meteorological stations, so that the simulations incorporate as much information as possible.

Figure 2 shows the conceptual model implemented in BIOLEACH.

The model serves as support for decision-making in the daily management of the landfill, responding to the real needs that the operator must face. The model considers that the landfill receives a known quantity of previously characterized waste under certain meteorological conditions and the availability of a limited volume of leachate storage in the pond.

Having a landfill management model that informs about the optimal operating rules, which guarantee that biogas production is maximum, is of paramount importance to meet the objectives set by current legislation on environmental protection.

#### 3.2. Optimal Monthly Biogas Production Calculation

In order to estimate the optimal monthly biogas production, it is necessary to know the characterization of the waste stored in the landfill. The characterization data include the total weight of each of the waste components, its moisture content and the masses of C, H, O and N included in the organic fraction of the waste. For the calculation of biogas production, the model considers both the rapidly decomposable (RDW) and the slowly decomposable (SDW) waste fractions, as well as the non-decomposable waste fraction (NDW) that usually results from process inefficiencies prior to separation in the event that the waste comes from a treatment plant.

Of all the stoichiometric formulations that describe the anaerobic degradation process of organic matter included in a MSW landfill, BIOLEACH has implemented the one shown in Equation (2), which enables the estimation of biogas production under optimal conditions (those that produce complete biodegradation of organic matter contained in the waste), depending on the chemical composition of the MSW and neglecting the effects of the presence of sulfur [

15]:

The term C_{a}H_{b}O_{c}N_{d} represents in molar base the organic matter composition at the beginning of the process. The coefficients a, b, c and d are the stoichiometric indexes of carbon, hydrogen, oxygen, and nitrogen, respectively. These coefficients are automatically calibrated by the model for a given mix of waste stored in the landfill. Their values depend on the proportions of the different components present in the waste mix. The above methodology assumes that the biodegradable organic fraction of the waste is completely stabilized and eventually degrades to form methane, carbon dioxide and ammonia. The speed of this conversion depends on the content of RDW and SDW within the waste mass and on the availability of water, which is a limiting factor as its absence can inhibit the biogas formation process.

Thus, BIOLEACH calculates the maximum biogas production independently for the rapidly biodegradable and for the slowly biodegradable fraction. The model considers that the kinetics of the organic matter degradation reaction follows a triangular pattern. The user must calibrate the percentage of MSW that is effectively available to be degraded and, in addition, must specify the parameters of the triangular model. These parameters are: (i) time used to reach the complete degradation of the RDW and SDW fractions, and (ii) time in which the maximum biodegradation rate is reached for the RDW and SDW fractions.

The model allows one to establish the percentage of the waste that is effectively available for its total degradation, distinguishing between the percentage corresponding to the RDW fraction and the SDW. According to [

15], these values are lower than 75% for RDW and 50% for SDW, which shows that, even after the completion of the biogas formation process, a high content of organic matter will still be stored inside the dump.

Figure 3 shows the flow diagram for calculating the maximum monthly biogas production based on the values of the three factors described above.

Next, the reaction kinetic model to establish the unit rate of biogas formation is described in greater detail. (m^{3} biogas/kg MSW every month) corresponding to each of the MSW fractions (RDW and SDW). Among the different existing reaction kinetic models for calculating biogas, due to its simplicity, the triangular decomposition model has been the one finally implemented in BIOLEACH. This triangular model has been independently defined to describe the degradation processes of the RDW and SDW fractions.

For the rapidly biodegradable fraction (

Figure 4): (i) total decomposition period = 5 years, and (ii) the maximum rate of biogas formation occurs 1 year after the discharge of the RDW into the landfill.

For the slowly biodegradable fraction (

Figure 5): (i) total decomposition period = 15 years, and (ii) the maximum biogas formation rate occurs 5 years after the discharge of the SDW into the landfill.

Therefore, to calculate biogas production at a certain moment, the age of the waste that has been previously deposited in the landfill must be taken into account, since the biogas production rates are different depending on the time elapsed from discharge to the instant of calculation. In accordance with all the aforementioned, the maximum biogas production at a given moment is obtained as a convolution of all the productions of both waste fractions (RDW and SDW) deposited in the landfill from its start-up to the calculation date.

Figure 6 illustrates this convolution process. BIOLEACH considers a temporary monthly discretization and keeps a strict control of these biogas production rates through the convolution process. This monthly temporal discretization is one of the main characteristics of the model, as it provides greater flexibility compared to the existing biogas and leachate calculation models at annual scale that are commonly used.

However, under real conditions, maximum biogas production will never be observed, as humidity conditions inside the landfill mass will not provide enough water to fully develop the organic matter decomposition process given by Equation (2). Therefore, a monthly biogas efficiency indicator (BEI) and an overall biogas efficiency indicator (OBEI) for the whole period analyzed (n months) can be defined as shown in Equations (3) and (4):

Evidently, ${\mathrm{BEI}}_{i}$ and $\mathrm{OBEI}$ values will vary between 0% (low efficiency) and 100% (high efficiency) in terms of biogas production. This index is useful to compare different simulation scenarios as shown below.