Integration of photovoltaic panels and solar collectors into a plant producing biomethane for the transport sector: Dynamic simulation and case study

Abstract

In the current energy and environmental framework, the environmental impact of the road transport sector and the urban waste management and disposal are extremely important for highly crowded cities. This work assesses the energy, economic and environmental performance of an innovative paradigm for the full decarbonisation of the road transport sector. This problem is integrated with the management of the organic fraction of municipal solid waste. In particular, the proposed technology is based on an anaerobic digestion plant coupled with a biogas upgrading unit, for the production of biomethane. In addition, photovoltaic panels and solar thermal collectors are also considered for matching electrical and thermal demands, in order to achieve a fully-renewable system. To this scope, the system also includes suitable thermal and electric storages. The economic analysis also considers specific public funding policies, currently available for this technology. This system aims to be a novel paradigm in the energy scenario of waste disposal and road transport sector refurbishment. TRNSYS software was adopted to perform an accurate dynamic simulation for a one-year operation of the system. The anaerobic digestion model is developed by the authors in MatLab and integrated in TRNSYS, for dynamic simulation purpose. Results show that the plant is almost self-sufficient due to the integration of storage systems for both the thermal and electric energy. The photovoltaic system is able to reduce by 45% the energy dependence from the grid. Energy and environmental analyses show a Primary Energy Saving of 126% and a reduction of CO₂ equivalent emissions by 112%. The economic feasibility analysis shows a promising Simple Payback period of 6 years.

1. Introduction

The necessity of reducing the greenhouse gases (GHG) emissions and the energy dependence from fossil fuels in the main energy sectors is a critical point in the era of the energy transition [1]. Both the scientific researchers [2] and the policymakers [3] are moving in the same direction to achieve the decarbonisation goals, set for the forthcoming years [4]. Unfortunately, meeting the energy demand in an ever-changing society, such as the one we live in, is a highly especially in metropolitan urban areas [5]. The highly crowded environment of these areas implies a constant remarkable energy consumption, problems of waste disposal, and relevant air pollution [6]. In fact, the awful traffic conditions make the transport sector responsible for roughly 14% of the global GHG emissions in urban areas [7]. One of the most interesting and promising renewable sources to decarbonize the transport sector is represented by the biomethane, which can be obtained through biogas upgrading processes, also contributing to asses waste management issues [8]. The biogas can be produced from the anaerobic digestion of the organic matter, by means of chemical reactions taking place among a substrate and proper enzymes [9]. The biogas is a gaseous compound mainly composed of methane and carbon dioxide, obtained by means of the anaerobic digestion of the organic matter [10]. The operating temperature of the digestion process is one of the main parameters affecting th process and it must be controlled to avoid inhibition of biochemical species [11].

The produced biogas may be upgraded into biomethane, which is almost pure methane gas. Biomethane, complying with appropriate quality requirements may be injected into the national gas grid, or directly used for road transport purpose, by means of gas stations. Scarlat [12] showed that EU is leader in biogas and biomethane production, with more than 17´000 plants and a total installed capacity, in terms of primary energy production, greater than 10 GW, accounting for almost 70% of the overall worldwide capacity. The annual amount of biomethane injected to the national gas grid in 2015 was 1.5 million m³, provided by 340 plants; about 697 plants supplied 160 million m³ of biomethane in gas stations for vehicles. Germany is the leader in the production of biomethane, increasingly used for heat and electricity production. However, a recent study shows a great potential for electricity generation from biogas for integration into the national grid [13]. Sweden is the EU leader in the use of biomethane for the transport sector. Conversely, the biomethane production capacity is still poor in Italy. Here, the biogas market is predominant, but investments in renewable energies for the transport sector are mandatory to meet the goals of this Country in terms of GHG emissions [14]. D’Adamo et al. [15] proposed an assessment of the potential biomethane use in the city of Rome, in Italy. This solution could offer the possibility to solve two main issues highlighted for such town, namely: waste management and necessity of revamping the transport sector. Several public subsidies were considered in the evaluation of the economic profitability of the proposed solution. By considering several scenarios of biomethane plants size and alternative green solutions, the Net Present Value (NPV) varied from 0.49 M€ to 132.7 M€. The impact of local factors that influence the spreading of biogas technology was studied by Patrizio and Chinese [16]. The considered regions are Friuli Venezia Giulia and Emilia Romagna, both in Italy and both characterized by great potential of biogas production, despite different refueling infrastructures. Several pathways are considered including biogas production for electricity and upgrading to biomethane for road transport and grid injection. As a result, they found that the Italian incentives currently available for biomethane production even exceeds the real necessity, in some cases. Italian incentives for biomethane production are considered also in Ref. [17].

The upgrading process of biogas into biomethane is usually highly energy demanding expensive, limiting the use of such technology [18]. The most energy demanding upgrading solution is the cryogenic separation, producing liquefied biomethane (Bio-LNG) [19]. In spite of its high energy consumption, this solution is becoming more and more attractive for the possibility of an easy long-distance transportation and for the potential use in the maritime transport sector. However, cryogenic separation is still an expensive technology. Other technologies are currently considered more mature than cryogenic separation, such as water scrubbing [20]. The selection of the technology also depends on the end use of biomethane [21]. In many cases, high standards of the separation process are required for injection of the gas in the gas grid for use in the road transport, as in Tica [22]. In that work the authors compared the efficiency and the environmental impact of natural gas and diesel buses in the city of Belgrade. Both systems were tested in several driving conditions giving as a result that natural gas can be an efficient alternative to diesel. They found that the yearly demand of diesel is V_diesel = 678´900 L and the amount of biomethane needed to feed the new natural gas buses is V_bioCH4 = 333´282.19 Sm³.

To reduce the energy impact of the biogas upgrading processes, the cutting-edge studies are focused on the integration of renewable sources to meet this energy demand [23]. Despite this, many studies still evaluate the possibility to exploit the biogas production to produce renewable energy in some other ways, as for feeding fuel cells [24]. In most cases, the integration of a biomethane production plant with photovoltaic panels and wind turbines seems very promising [25]. However, many works focus on the coupling of these technologies both used to produce electricity [26]. In particular, biogas and solar source are studied for both off-grid [27] and rural grid [28] alternatives. The combined production of electricity and gas for the integration of renewables in both gas and electric consumption in residential users is also evaluated [29]. Recent studies consider the integration of renewable technologies integrated with the anaerobic digestion [30]. The majority of these studies include the exploitation of solar energy by means of solar thermal [31], photovoltaics [32], and combined photovoltaic/thermal units [33]. This is mainly due to the high thermal energy demand of the digester, and the huge amount of electricity required by the biogas upgrading unit, which could be vastly supplied by renewables.

Petrollese and Cocco [34] investigated the performance of a concentrated solar power (CSP) field integrated with a digester for biogas production for best start-up operation. The study also performs an economic analysis of the levelized cost of energy (LCOE) of the proposed system, based in the city of Ottana, in Italy. The biogas produced by fruit and vegetables is burned to heat a fluid up to the CSP output temperature. In fact, the same fluid is used in the CSP field. Both are mixed and stored in a hot tank which provides heat for an organic Rankine cycle (ORC). The digester is modeled by means of steady-state equations assuming that the AD always occurs in nominal conditions. The tank is instead modeled by means of mass and energy balance equations. In all the evaluated cases, the LCOE for the power produced is consistent with the literature, ranging between 120 and 150 €/MWh. Unfortunately their work lacks a dynamic analysis of the system and the biogas upgrading is not considered. Similarly, in Ref. [35] is shown a life cycle assessment (LCA) study of a coupled CSP-biomethane system. Recently, Singh et al. [36] evaluated the thermal performances of a digester coupled to a photovoltaic-thermal compound parabolic collector (PVT-CPC). Given the harsh climatic conditions of the analysed zone (the region of Sirinagar, India), the digester is supposed to be buried. The thermal model is based on the heat exchanger thermal balance inside the digester, simulating the heat transfer between the PVT-CPC fluid and the slurry. The electric model of the PVT-CPC is instead based on the Hottel-Whillier-Bliss equation, used to calculate the mean temperature of the panels. The electricity produced is a function of collectors efficiency, packing factor of cells, number of modules and aperture area. Six collectors resulted to be the optimal number, within a packing factor range of 0.2–0.4. However, no economic analyses were performed by the authors.

Hao [37] proposed a simulation model of a concentrating photovoltaic and thermal (CPVT) hybrid system coupled with a biomethane plant, based on energy balance equations for the CPVT module and supported by a multi-objective system optimization. The work shows that the CPVT module matches 7% of heat demand and 12% of electricity demand of the plant. Moreover, the proposed plant achieves a Simple Payback (SPB) of about 10 years. Sigarchian [38] used HOMER (Hybrid Optimization of Multiple Energy Resources) to study the combination of photovoltaic panels (PV), wind turbine (WT) and biogas engine, designed to supply the energy demand of a small village in Kenya. Such system was compared to an internal combustion diesel engine. A Levelized Cost of Energy (LCOE) 20% cheaper with respect to the reference system was estimated. A reduction of CO₂ emissions equal to 17 tons per year was also found. Biogas plant is fed with cattle manure, firstly, and sheep dropping, secondarily. The yield of biomethane from these biomasses is, respectively, about 60% and 70% [39]. Neither of them considers an accurate biological model for the biogas production.

Castley et al. [40] recently proposed an interesting work regarding a comparative analysis of several configurations of biomethane-fed cogeneration units. All the units are supposed to meet the cooling, heating, and power (CHP) demands of office buildings. The main interest is in comparing the effective benefits of using biogas as fuel for the combined CHP demand. In the optimal configuration, the CO₂ emissions were reduced by 93.7% and the primary energy saving was 32%. In addition, in this case no accurate dynamic analysis of the biogas production was considered. Li et al. [41] performed an experimental analysis of a biogas production system fed by an evacuated tube solar collectors. The work presents a relevant analysis on the effect of the temperature on the biogas production. Therefore, many control strategies are presented and discussed under different weather boundary conditions. Unfortunately, there is a lack of theoretical models of the anaerobic digestion process and no environmental or economic analyses are performed. Kamari et al. [42] investigated an innovative polygeneration system based on a biomass combustor, Rankine cycle, and biofuel production plant. The plant is developed to meet the energy demand of a district heating system. 33 MW heat transfer rate capacity, 76 MW biogas, and 161 MW bioethanol are generated by the biofuel production unit at the design operating conditions. The energy and thermodynamic analyses are carried out and the proposed polygeneration plant saves 15% of fuel energy when compared to the equivalent stand-alone production system.

1.1. Aim of the paper

The above presented literature review highlighted the most recent advancements and the main drawbacks in the research field of biogas and biomethane production. The management of the thermal condition in the anaerobic digester is crucial for maximizing the biogas production. At the same time, the upgrading of the biogas into biomethane requires electric energy which is generally relevant. To this purpose, it seems necessary to estimate the thermal and electric consumption of biogas and biomethane plants, especially under dynamic operating conditions. The aim of this paper is to analyse the coupling of solar photovoltaic and solar thermal technologies to meet these energy demands, in dynamic operating conditions of the systems. This represents a novelty in the field since there are no works studying the integration of solar thermal collectors and photovoltaic to meet the energy demand of a biomethane plant, analysing the dynamic operating conditions of the hybrid system. Moreover, this work performs a deep thermoeconomic analysis of this hybrid renewable biomethane plant proposed to decarbonize the transport sector. In addition, specific incentives are considered to assess the economic profitability for the specific case study proposed.

In particular, this study is proposed for a city in the region of Campania, in the south of Italy, where the issues of waste disposal and road transport sector pollution are predominant. Furthermore, the high solar radiation of this area makes the renewable technologies considered particularly appealing. In conclusion, this work proposes a novel paradigm for the green public transport, where a residential district is served by a fleet of buses fed by the biomethane produced by the organic urban wastes. The novelty is summarized in the following points.

• •A fully-renewable biomethane plant is proposed and analysed under dynamic operating conditions, based on the integration of Photovoltaics (PV) and Evacuated Tube Collectors (ETC) into the process.
• •A multiparametric analysis is carried out to investigate the profitability of the system by ranging the unit costs of the electricity and gas. Different scenarios are evaluated to understand how the market variability influences the economic return.
• •A sensitivity analysis is performed, to point out the best configuration of renewables integration and other components sizing. The optimal size of PV and ETC fields are evaluated, along with the optimal capacity of both thermal and electric energy storage systems.

• •A thermoeconomic analysis of the biomethane production plant is proposed to investigate the feasibility of a solution for the road transport sector decarbonisation. Advanced biomethane production, which means biomethane production from OFMSW, is strongly supported in Italy. The influence of such incentives on the feasibility of the system is analysed.

2. Layout

Fig. 1 shows the layout of the system proposed. Two main loops are detected in this plant, the solar loop (SL) and the digester loop (DL). The SL connects the evacuated tube collector (ETC) field to the thermal tank (TK). The water in the SL is pumped by the variable speed pump P2 from the tank to the ETC solar field. The ETC collector is used to provide heat transfer rate to the water by solar energy. The mismatch between solar radiation and the anaerobic digester (AD) thermal demand is mitigated by the TK. In the SL, solar energy is used to increase the fluid temperature up to the set point of 60 °C. A feedback controller manages P2 functioning. In particular, if the bottom temperature of the tank is greater than the temperature of the water outgoing the collector (T_b,tank > T_{out, coll}) or the solar radiation G < 10 W/m², the controller switches the pump off to prevent thermal energy dissipation.

Fig. 1.

Layout of the plant.

In addition, the SL is also equipped with the heat dissipator HE-2, in case the regulation with the P2 is not sufficient. In case T_{out, coll} > 60 °C, the surplus heat is dissipated by means of thermal exchange with a counterflow water at lower temperature. Conversely, when T_{out, coll} < 60 °C, no thermal dissipation occurs. That measure is proposed in order to avoid tank overheating, thus the inlet temperature set point is 60 °C.

On the other side of the tank, the DL provides to the AD the thermal energy collected and stored in the TK. The hot water is delivered to the digester by means of a constant speed pump P1. This loop is equipped with an auxiliary biomass heater (AH), whose setpoint temperature (T_set,AH) is equal to 50 °C. A PID controller manages this loop, through the diverter DIV, based on the temperature inside the digester. If the fluid temperature (T_DL) is below the set point, equal to 50 °C, the water delivered to the digester is heated up to T_set,AH by the AH. When T_DL is greater than 50 °C, the PID controller proportionally diverts a suitable amount of water by means of D1, allowing such flow to bypass the digester. Therefore, only a limited share of hot water is provided to the digester, to avoid overheating and sharp temperature variations. When T_DL is higher than 52 °C, some heat is rejected to the environment by means of HE-1, reducing such temperature below the rated limit.

These controls are designed to keep the digester temperature to roughly 38 °C and to avoid digester overheating. In fact, the digester produces biomethane by means of mesophilic reaction. Sharp variations of its temperature may cause inhibition of biochemical processes, due to the death of mesophilic bacteria. A PV field is used to drive the auxiliary devices, such as the pumps, the mixing, and the biogas upgrading unit. The system is also equipped with a 1000 kWh lithium-ion battery storage, to maximize the self-consumption of electricity provided by the PV.

3. Model

To perform the dynamic simulation of the hybrid renewable energy system proposed in this work, several models were integrated. For simulating the anaerobic digestion process, the biological and thermal model of the reactor were developed in MatLab (R2021a), as well as the membrane separation for the biogas upgrading. Such models were integrated in TRNSYS (version 17), to exploit a large library of mathematical models for different components (“Types”) [43]. Yearly results of the simulated system are then used to perform the thermoeconomic analysis.

3.1. Biological model

The anaerobic digestion (AD) model developed in this work is the ADM1, widely adopted for the simulation of the biogas production from low total solid content biomass. In this work, the biogas production from OFMSW is investigated by means of a modified version of the ADM1, due to its reliability and robustness for this specific case. More specifically, this version of ADM1 just considers 13 out of the 19 components of the standard model, sufficient to provide accurate results for this application. Thus, this model is based on 13 differential equations, considering mass balances for each biological component. More details regarding this model can be found in Ref. [44]. The AD mechanism is a sequence of several biochemical processes which lead to the production of methane starting from complex organic matter [45]. To analyse the process is crucial to know the concentration of chemical species in the biomass; such concentrations are expressed as kg_COD/m³, where the chemical oxygen demand (COD) refers to the milligrams of oxygen required to chemically oxidize organic and inorganic substances in 1 L of H₂O. Thus, the model includes 10 processes and 13 components, including the Monod’s first-order kinetics for the extracellular processes and the Michaelis-Menten kinetics for the intracellular biochemical reactions. These assumptions lead to the equations system:

$$\frac{dSwaste,i}{dt}=\frac{qin}{Vwaste}{\mathrm{S}}_{waste,i,in}-\frac{qout}{Vwaste}{\mathrm{S}}_{waste,i}+\sum _{j=1}^{10}\phi j\alpha i,j$$ (1)

Eq. (1) represents a system of differential equations considered for a continuously stirred tank reactor (CSTR) [46] where the subscripts i and j refer, respectively, to the component and the process. S_waste,i,in is the input concentration of the substrate i in the liquid biomass, q_in and q_out are the input and output OFMSW flow rates, is the concentration of the substrate within the reactor, φ_i,j is the kinetic term and α_i,j is the biochemical coefficient of the substrate i during the process j.

3.2. Thermal model

The temperature of the digester T_dig dramatically affects the AD process. Steering the temperature inside the reactor is crucial to enhance bacteria operation. The dynamic calculation of T_dig can be performed considering the heat transfer occurring in the AD. Eq. (2) is the equation of thermal equilibrium applied to the control volume of the digester and eq. (3) is the project equation of the heat exchanger HE:

$${\dot{m}}_{OFMSW}{c}_{p,OFMSW}{T}_{in,OFMSW}+{\dot{m}}_W{c}_{p,W}{T}_{in,W}={\dot{m}}_{digestate}{c}_{p,digestate}{T}_{dig}+{\dot{m}}_{biogas}{c}_{p,biogas}{T}_{dig}+{\dot{m}}_W{c}_{p,W}{T}_{out,W}+U_{dig}{A}_{dig}\left(T_{dig}-T_{amb}\right)+U_f{A}_f\left(T_{dig}-T_{ground}\right)+U_{\mathrm{c}\mathrm{o}\mathrm{v}}{A}_{\mathrm{c}\mathrm{o}\mathrm{v}}\left(T_{dig}-T_{amb}\right)$$ (2)

$${\dot{m}}_{HW}{c}_{p,HW}\left(T_{in,HW}-T_{out,HW}\right)=n{U}_{HE,n}{A}_{HE,n}\Delta T_{lm}$$ (3)

m_digestate and m_biomass can be calculated by means of the biological model. Conversely, T_dig and the water outlet temperature, T_{out, water} are the unknown quantities to be calculated through the system of equations (2), (3). Once that T_dig is known, the biological model evaluates the microbial species evolution calculating the kinetic rates at that precise temperature level, predicting the biogas yield.

The model here proposed by the authors is an integration of already widely analysed and validated models proposed in literature. In fact, the ADM1 model is the most widespread model for the estimation of the biogas yield from the anaerobic digestion process applied to several biomasses. At the same time, the logarithmic-mean temperature model is largely used in almost all the heat transfer problems. Thus, the coupling of these models is considered to result in an intrinsically validated model. Unfortunately, the validation of the model as a whole is not presently possible, since the plant designed in this study is not available and the cost of the possible experimental setup is extremely high. Nevertheless, the models of all the components and processes included in the system were previously validated vs experimental or literature data. Therefore, according to the method widely used in literature, the model as a whole is considered validated too.

3.3. TRNSYS environment

Most of the models used in this work were taken from the TRNSYS library; some other models were specifically developed for the scope of the work and/or based on manufacturers’ data [59]. In particular, a suitable model was developed for the simulation of the anaerobic digester (AD), whose model was not available in the TRNSYS library.

3.3.1. Anaerobic digester

As previously mentioned, the anaerobic digestion biological model was developed in MatLab. Together with this model, thermal balance equation were integrated to calculate iteratively the value of the reactor temperature according to the different inlet water temperature and ambient temperature values. The model developed in MatLab was then integrated in TRNSYS environment by means of the type581a which allows one to recall the results of the MatLab file at each iteration. The strength of this integration is that the model can be recalled at each time step with different boundary conditions, preserving the evolution of the biochemical species. The main design parameters of the digester are summarized in Table 1.

Table 1.

Main parameters used for the design of the digester.

Parameter	Description	Value	Unit
${\dot{\mathit{m}}}_{\mathit{O}\mathit{F}\mathit{M}\mathit{S}\mathit{W}}$	mass flow rate of OFMSW	2016	kg/h
${\mathit{\rho }}_{\mathit{O}\mathit{F}\mathit{M}\mathit{S}\mathit{W}}$	Density of OFMSW	750	kg/m3
$\mathit{C}{\mathit{p}}_{\mathbf{,}\mathbf{O}\mathbf{F}\mathbf{M}\mathbf{S}\mathbf{W}}$	Specific heat of OFMSW	2.72	kJ/(kg K)
${\dot{\mathit{m}}}_{\mathbf{W}\mathbf{,}\mathbf{i}\mathbf{n}}$	mass flow rate of the inlet hot water range	1400 ÷ 9000	kg/h
${\mathit{T}}_{\mathbf{a}\mathbf{m}\mathbf{b}}$	ambient temperature range	−2 ÷ 35	°C
${\mathit{T}}_{\mathbf{W}\mathbf{,}\mathbf{i}\mathbf{n}}$	inlet hot water temperature range	40 ÷ 60	°C
HRT	Hydraulic Retention Time	30	d
${\mathit{T}}_{\mathbf{d}\mathbf{i}\mathbf{g}}$	digester temperature	38	°C
$\mathit{H}\mathit{r}\mathit{e}\mathit{a}\mathit{c}\mathit{t}$	height of digester	10	m
N	Number of heat exchanger coils	3	–

To couple the AD model with TRNSYS, a map of data obtained from the simulation in MatLab was integrated into the TRNSYS project. The combined biological-thermal model operated with different values of ambient temperature, flow rate and temperature of the water incoming the digester, and flow rate of biomass. The outputs are the operating temperature of the reactor, the temperature of the outgoing water, the heat transfer rate within the digester through the serpentine, and the mass flow rate of biogas. The results achieved for a set of input data were interpolated in TRNSYS to obtain the values for different operating conditions. In this way, it was possible to calculate the biogas production in dynamic conditions. More details about that model are available in Ref. [44].

3.3.2. Biogas upgrading

The upgrading unit consists of a three-stage selective membrane system (Fig. 2). It was simulated by an in-house model, since this component was not available in TRNSYS.

Fig. 2.

Three phases of the upgrading process.

For the other components of the plant, built-in models from TRNSYS libraries were adopted. Since there are no dedicated models for ETC in TRNSYS, the flat plate collector model was used. For adapting to the ETC model, the incident angle modifier (IAM) was managed. Type 71 is the one used in this TRNSYS version and the efficiency of both ETC and flat plate collectors (FPC) is calculated with the same equations.

3.3.3. Storage tank

The tank was modeled by the TRNSYS 4d type, considering a multi-layer system where each layer is perfectly mixed, and all the layers have the same dimensions. The equilibrium between adjacent layers is ruled by the energy balance equations eq. (4):

$$M_i{C}_p\frac{d{T}_i}{dt}={\alpha }_i{\dot{m}}_h{C}_p\left(T_h-T_i\right)+{\beta }_i{\dot{m}}_l{C}_p\left(T_l-T_i\right)+U{A}_i\left(T_{amb}-T_i\right)$$ (4)

Here, subscript “i” refers to the layer on which the energy balance is considered, whereas “h” and “l” refer to the higher and the lower layer, respectively. Further details are provided in [60]. The tank volume design value linearly depends on the ETC total area and on the volumetric flow rate of the pump, which is of 150 kg/(h m²), according to eq. (5):

$$V_{TANK}=Q_P\cdot A_{ETC}/1000$$ (5)

3.3.4. Thermoeconomic analysis

The performance of the proposed system (PS) was evaluated by comparison with a Reference System (RS), where it is assumed that a fleet of conventional buses, whose operating conditions will be explained later, are only fuelled by diesel.

The Primary Energy Saving (PES) is calculated according to eq. (6):

$$PES=\frac{P{E}_{RS}-P{E}_{PS}}{P{E}_{RS}}$$ (6)

Where PE_RS is related to the diesel used for road transport, whereas PE_PS is due to the difference between the primary energy related to the electricity withdrawn from the national electric grid and the primary energy saved thanks to the surplus biomethane, as reported in equations (7), (8) below:

$$PERS=\frac{V_{diesel}\cdot LH{V}_{diesel}}{3.6}$$ (7)

$$P{E}_{PS}=\frac{E_{el,fromgrid}-E_{el,togrid}}{{\eta }_{el,ref}}-V_{CH4,surplus}\cdot LH{V}_{NG}$$ (8)

Here, V_CH4,surplus is the difference between the volume of biomethane yearly produced by the digester and the annual demand of biomethane of the fleet of buses; this surplus is injected into the natural gas grid, allowing to save natural gas produced by fossil sources.

Similarly, the savings in terms CO₂ equivalent emissions are calculated according to eqs. (9), (10):

$$MCO{2}_{,RS}=f_{CO2,diesel}\cdot \delta \cdot 365$$ (9)

$$M_{CO2,PS}=E_{el,fromgrid}\cdot f_{CO2,EE}-V_{CH4,surplus}\cdot f_{CO2,CH4}$$ (10)

Where f_CO2,diesel is expressed in g/km and δ is the distance, in km/day, covered by the buses. Capital costs include expenditure for PV modules, auxiliary heater, solar collectors, storage systems, digester and biomethane plant, with corresponding auxiliary devices. In addition, it is assumed that a full refurbishment of the existing diesel buses is needed; therefore, assuming that the difference in costs between gas and diesel buses is negligible, no extra investments were considered for the replacement of the fleet. The feasibility analysis of the proposed system is assessed by calculating the Simple Payback (SPB) and Discounted Payback (DPB) period [47]. SPB can be expressed as:

$$SPB=\frac{IN{V}_{TOT}}{\Delta C}$$ (11)

Whereas the DPB is equal to

$$DPB=-\frac{\log \left(1-SPB\times a\right)}{\left(1+a\right)}$$ (12)

Where in eq. (11), $\Delta C$ is the difference between yearly costs for the Reference System (RS) and the Proposed System (PS), $IN{V}_{TOT}$ the total investment, or Capital Expenditure (CAPEX) and in eq. (12) a is the discount rate.

In the RS, buses run with diesel engines and all the costs are related to the cost of diesel. In the PS, the diesel is replaced by the biomethane; investment, maintenance and operating costs include the digester, the PV collectors, the tank, and the battery.

The operative costs are due to the energy and maintenance costs, M; this latter term was assumed equal to 1% of total investment costs. Therefore, the SPB is calculated as:

$$SPB=\frac{P_{p,PV}\cdot C_{u,PV}+E_{el,storage}\cdot C_{u,storage}+IN{V}_{AH}+A_{ETC}\cdot C_{u,ETC}+IN{V}_{DIG}}{V_{diesel}\cdot j_{diesel}-E_{el,fromGRID}*j_{EE}+\frac{Q_{th}}{{\eta }_{th,ref}}\cdot \frac{j_{wc}}{LH{V}_{wc}}-V_{C{H}_4,surplus}\cdot j_{NG}+M}$$ (13)

In Table 2, the data used for the thermoeconomic analysis are shown, for more details see Ref. [48].

Table 2.

Technical parameters of the thermoeconomic study.

Parameter	Description	Value	Unit
ηel,grid	Rated efficiency of the power grid	0.46	-
ηAH	Rated efficiency of conventional boiler	0.95	–
LHVGN	Natural gas lower heating value	9.59	kWh/Sm3
LHVwc	Woodchip lower heating value	3.7	kWh/kg
LHVdiesel	diesel lower heating value	36	MJ/L
ρNG	Natural gas density	0.705	kg/m3
ρdiesel	Diesel density	480	kg/m3
fCO2, EE	Unit emission of CO2 per kWh,el	0.48	kgCO2,el/kWh,el
fCO2, NG	CO2 emissions per kWh of natural gas	0.20	kgCO2,NG/kWh,p
fCO2, NG	CO2 emissions per km driven by natural gas	1.23	kgCO2,eq/km
fCO2, diesel	CO2 emissions per km driven by Diesel fuel	1.57	kgCO2,eq/km
jEE	Unit cost of electric energy	0.18	€/kWh
jNG	Unit cost of natural gas	1.72	€/Sm3
jwc	Unit cost of woodchip	0.06	€/kg
jdiesel	Unit cost of diesel	1.26	€/L
Cu,PV	Unit cost of PV modules per peak power	1000	€/kWp
Cu,ETC	Unit cost of ETC	300	€/m2
Cu,storage	Unit cost of electric storage	200	€/kWh

Some specific incentives were also considered. In Italy, the use of biomethane in transports is subsidized by means of the “Certificates of release for consumption” (“CIC”), acknowledged to fuel companies who release biomethane to end users. A CIC corresponds to about 1231 m³ of CH₄ used in the transport sector; biomethane producers are acknowledged a public subsidy of 375 €/CIC; however, in case of “advanced biomethane production” (as in case of OFMSW used as feeding biomass), their value is doubled.

4. Case study

The case study refers to a plant under construction near Napoli, in the region of Campania, south of Italy. The selection of this region is due to the dual problem of the waste disposal and public transport sector underdevelopment. The plant was designed to receive 40´000 tons/year of OFMSW from nearby cities, operating 24/7 for 365 days/year. Given a volume of the digester V_dig = 2586.7 m³, a production of 7.46 tons/day of biogas is calculated. The total amount of biogas produced in one-year is V_biogas = 968´035.85 Sm³. The biomethane produced from this amount of biogas is used to match the natural gas demand of a fleet of buses, evaluated according to Ref. [22]. Table 2 resumes the main assumption regarding the fleet of bus considered in the case study. The optimal area of the ETC collectors was calculated as a result of a parametric analysis, considering both energy and economic objective functions. The ETC system is used to preheat the water up to 50 °C (set point value), before entering the digester. In case of scarce solar availability, the set point temperature is guaranteed by a 100-kW auxiliary biomass heater. Obviously, auxiliary heat will be required mainly during the winter season. As shown in Fig. 3, with a 200 m² solar field area, the auxiliary heat is strongly reduced in summer (less than 20%). The ETC field matches roughly 40% of total heat request on a yearly basis.

Fig. 3.

Auxiliary Heater and ETC fraction of heat demand.

The tank capacity was designed for storing the maximum heat produced by ETCs for 1 h. The corresponding volume of the tank is thus 30 m³. The plant is equipped with a lithium-ion battery (LIB) of 1800 kWh, calculated by assuming a ratio battery/PV rated capacity equal to 5 kWh/kW [49].

The PV capacity was selected ranging the PV field area from 2000 m² to 4000 m² and performing a parametric analysis; an optimal value of 2000 m² was found, corresponding to a LIB of 1800 kWh. The analysis is carried out by considering both the Profitability Index (PI) and energy saving (ΔPE) functions, depending on the PV field and the storage capacity. The solution adopted is a trade-off between these aspects, as shown in Fig. 4.

Fig. 4.

Energy savings (ΔPE) and Profitability Index (PI) of PV plant and Electric Storage solutions.

5. Results and discussion

In this section, the results provided by the simulation model for the case study proposed are shown and discussed, considering hourly, monthly, and yearly bases, in order to provide a comprehensive overview of the system performance. A parametric analysis is also shown, to investigate the most important factors who influence the feasibility of the system. Finally, an optimization of the layout is presented.

5.1. Daily analysis

The digester heat demand (Q_dig) mainly depends on the ambient temperature, which determines the heat loss toward the environment. Therefore, solar thermal systems are ineffective in reducing GHG emissions, especially during the summer period, in absence of a proper storage. In fact, during the winter period the tank provides heat constantly during the day, see Fig. 5 (a), with small oscillations. Conversely, in summer period, Fig. 5(b), the heat collected is sufficient to meet the thermal energy demand being activated until 11 a.m. ETCs provide greater heat production during the summer, when the heat demand of the digester is low. In fact, during the summer, the auxiliary heater is rarely turned on, and some heat dissipation is required during the hottest hours. In this period, the collector temperature rises almost up to 70 °C, keeping the T_tank at its set point of 60 °C (Fig. 6(b)). Conversely, the AH is often activated during the winter. In fact, in the winter period, the collector temperature (T_coll) and tank top temperature (T_tank) are constantly lower than 50 °C (Fig. 6(a)). The trend of the collector temperature is perfectly matched with the pattern of the thermal energy provided by the ETC field.

Fig. 5.

Dynamic results for thermal flow rates in typical winter day (a) and typical summer day (b) – Q_ETC = heat transfer rate from solar collectors; Q_TK = heat transfer rate provided by the tank; Q_AH = heat transfer rate provided by the boiler; Q_dig = heat transfer rate to the digester; Q_loss = thermal losses from the digester.

Fig. 6.

Temperature data for a typical winter day (a) and a typical summer day (b) – Tamb = ambient temperature; T_coll = collectors outlet temperature; T_tank = tank top temperature; T_dig = digester temperature; T_wat = water outlet temperature.

During the winter, the auxiliary heater is averagely turned off only from 12 p.m. to 4 PM.

A similar analysis can be performed for the results shown in Fig. 7. The electric power required by the plant (P_el,LOAD) is almost constant and equal to 120 kW, since the upgrading unit accounts for the major share of power demand and operates at full load for almost all day.

Fig. 7.

Dynamic results for electric powers in typical winter day (a) and typical summer day (b) – P_el,LOAD = power demand; P_el,toLIB = power sent to the battery; P_el,fromLIB = power withdrawn from battery; P_el,toGRID = power sent to grid; P_el,fromGRID = power withdrawn from grid; P_el,SELF = self-consumed power; P_el,PV = power produced by photovoltaic.

In winter, the power produced by PV (P_el,PV) matches the plant power demand only during the hours of high solar radiation, roughly from 10 a.m. to 15 p.m., see Fig. 7(a). Consequently, during the remaining parts of the day, the power demand of the plant is matched by the energy withdrawn from the public grid (P_el,fromGRID) and from the battery, (P_el,fromLIB).

For the typical summer day considered in Fig. 7(b), the PV peak power production (P_el,PV) is 238 kW. Here, the plant is not able to completely exploit the charge-discharge depth of the battery. In fact, the maximum SoC is roughly equal to 25%. However, the LIB allows the system to be self-sufficient for about 3 h after the PV power drops below the load. In the summer, the SoC rises up to 70%. Because of the higher PV production, auxiliary power is withdrawn from the grid only during the night hours. In fact, the PV, coupled to the LIB, is able to match the load for 16 h in a row. The LIB resulted quite oversized, since the charge/discharge depth of the batteries was not fully exploited, both during winter and summer periods: the maximum allowed SoC value of 95% is never reached.

5.2. Monthly analysis

In Fig. 8(a), the monthly thermal energies are shown, to assess the effectiveness of integrating the ETCs into the biomethane plant. As expected, the major production of thermal energy from the ETC (E_t,ETC) field occurs in the summer; the maximum monthly production is equal to 18.6 MWh (August). In the same season, the thermal energy required from the digester (E_t,dig) is obviously minimum (14.25 MWh). In fact, the thermal demand of the AD consists of two main terms: i) the thermal losses to the environment, and ii) the thermal energy required for heating the waste entering the digester. Of course, the higher the ambient temperature, the lower these two terms.

Fig. 8.

Monthly thermal energy (a) and AH/DIG thermal ratio (b) – E_th,ETC = thermal energy provided by collectors; E_th,TK = thermal energy provided by the tank; E_th,dig = thermal energy supplied by the tank; E_th,AH = thermal energy supplied by the auxiliary heater.

The ratio of the thermal energy supplied form the auxiliary heater to the total heat demand of the digester is shown in the lower part of Fig. 8(b). It is clear that the ETC system is more efficient during the summer. However, the AH integration is always nonzero, even in the summer, since the tank is not able to store all the thermal energy produced by ETC. Therefore, the tank is not able to match the night-time digester thermal energy demand.

Fig. 9 (a) shows the monthly results for the electric energy flows.

Fig. 9.

Monthly electric energy (a) and electric energy ratios (b) – E_el,LOAD = electric energy demand; P_el,toLIB = electric energy sent to the battery; P_el,fromLIB = electric energy withdrawn from battery; P_el,toGRID = electric energy sent to grid; P_el,fromGRID = electric energy withdrawn from grid; P_el,SELF = electric energy self-consumed; P_el,PV = electric energy produced by photovoltaic.

The electric energy exported to the grid is always null, thanks to the LIB. The power demand of the plant is mainly due to the upgrading unit, which operates at full load during the whole year; therefore, the overall monthly consumption (E_el,LOAD) is almost constant during the year, with an average value of 87.5 MWh. The maximum value reached by the PV production is 61 MWh (July). The electricity withdrawn from the grid is remarkable, but the contribution of solar energy is significant. In fact, the ratio between the self-consumed electricity and the total load (E_el,SELF/E_el,LOAD) ranges from 23% (in winter) to 60% (in summer), see Fig. 9(b). This is also due to the presence of the LIB, which can meet up to almost 20% of the E_el,LOAD.

These results suggest that a greater PV capacity should be considered, to meet a larger share of the electric energy demand of the plant, better exploiting the battery charge-discharge depth. However, a too large PV field may introduce issues related with the area available for installing the modules.

5.3. Yearly analysis

The yearly results are summarized in Table 3 and Table 4.

Table 3.

Annual results: fuel consumptions.

Parameter	Description	Value	Unit
VbioCH4,r	Annual volume of biomethane required by the fleet of bus	333282.19	Sm3/y
VbioCH4,p	Annual volume of biomethane produced by the digester	651080.53	Sm3/y
VbioCH4,s	Annual volume of surplus biomethane	317798.33	Sm3/y
Vdiesel,r	Annual volume of diesel required by the fleet of bus	678900.00	L/y

Table 4.

Annual results: primary energy, CO_2, and costs.

Parameter	Description	Value		Unit
		Reference System	Proposed System
PEdiesel	Primary energy consumed by diesel vehicles	6789.00	–	MWh/year
PEgrid	Primary energy consumed by withdrawn from gird	–	577.37	MWh/year
PEAH	Primary energy consumed by the auxiliary heater	–	–	MWh/year
PEbioCH4,s	Primary energy saved by selling biomethane surplus	–	3565.20	MWh/year
MCO2,diesel	CO2 emissions produced by diesel fuelled vehicles	2288.55	–	tons/year
MCO2,grid	CO2 emissions produced by withdrawn from grid	–	278.86	tons/year
MCO2,AH	CO2 emissions produced by the auxiliary heater	–	47.21	tons/year
MCO2,bioCH4,s	CO2 emissions saved by selling biomethane surplus	–	713.04	tons/year
Fdiesel	Annual cost of diesel	856.37	–	k€/year
Fgrid	Annual cost of electric energy withdrawn from grid	–	103.93	k€/year
Fwc	Annual cost of woodchip	–	3.93	k€/year
FbioCH4	Annual economic return from surplus biomethane	–	544.88	k€/year
M	Total maintenance costs for the plant	–	131.28	k€/year
PEtot	Total primary energy consumed by the system	6789.00	−1792.19	MWh/year
Mtot	Total CO2 emissions produced by the system	2288.55	−283.39	tons/year
Ftot	Yearly operating cost of the system	856.37	−696.51	k€/year

Table 4 shows that the total amount of primary energy, produced CO₂ and operating costs for the proposed system have negative values, due to the savings in terms of avoided use of diesel for the buses, but also to the surplus biomethane exported to the gas grid. These results highlight the feasibility of the proposed solution. Table 5 shows the main performance indexes obtained from the yearly analysis.

Table 5.

Yearly performance indexes.

Parameter	Description	Value	Unit
ΔPE	Annual primary energy difference	8587.11	MWh/year
ΔCO2	Total amount of CO2 savings	2573.25	tons/year
ΔOC	Difference of total yearly operating costs	1.96	M€/year
PES	Primary Energy Saving	126	%
INVETC	ETC capital cost	0.06	M€
INVPV	PV capital cost	0.72	M€
INVDIG	Digester capital cost	12.50	M€
INVAH	Auxiliary heater capital cost	0.009	M€
INVTOT	Total capital cost	13.28	M€
SPB	Simple Payback period	11.40	years
DPB	Discounted Payback period	16.37	years
NPV	Net Present Value	3.03	M€
PI	Profitability Index	0.23	–
CIC	Incentives	0.79	M€
SPBCIC	Simple Payback period with incentives	6.82	years
DPBCIC	Discounted Payback period with incentives	8.51	years
NPVCIC	Net Present Value with incentives	14.13	M€
PICIC	Profitability Index with incentives	1.06	–

An overall PES equal to 126% was calculated, with a 112% reduction of CO₂ equivalent emissions Unfortunately, the overall capital cost of the plant is very high (INV_TOT = 13.28 M€), mainly due to the digester, involving a low profitability, in spite of high economic savings. A SPB of 11 years was calculated and a DPB of 16 years, leading to a NPV of 3.2 M€/year and a PI of 0.23. However, considering the incentives for the production of advanced biomethane, the economic indexes improve remarkably (SPB = 6.8 years, DPB = 8.5 years, NPV = 14.13 M€/year, PI = 1.06).

5.4. Sensitivity analysis

The unit costs assumed for the energy vectors in the case study are shown in Table 2. To analyse the profitability of the PS under different market conditions, several energy costs were considered. More specifically, the variables considered are: the unit cost of diesel, j_diesel, the unit price for the natural gas sold to the market, j_NG, and the unit cost of the electricity withdrawn from the grid, j_EE. Table 6 summarizes the range of variation assumed for the sensitivity analysis. The results are resumed in Fig. 10, in terms of SPB values.

Table 6.

Range of values for the unit costs.

Parameter	Description	Value	Unit
jEE	Unit cost of electric energy	0.18 ÷ 0.30	€/kWh
jNG	Unit price of natural gas	0.80 ÷ 1.80	€/Sm3
jdiesel	Unit cost of diesel	1.25 ÷ 1.55	€/L

Fig. 10.

Sensitivity analysis: SPB – j_diesel= unit cost for diesel; j_NG= unit cost for natural gas; j_EE= unit cost for electricity; SPB = Simple Payback.

The SPB is strongly influenced by the cost of the diesel in the reference system. As expected, the greater the value of j_diesel, the greater the advantage with respect to the reference system and the lower the SPB. On the other hand, given a value of j_diesel, the SPB linearly increases with the cost of the electricity withdrawn from the grid. Similarly, the SPB decreases when the selling price of the natural gas increases. j_NG, exhibits a great influence, since his range of variation is wider than the one assumed for j_EE. As shown in Fig. 10, the SPB may decrease from about 8.5 years to 5 years.

The same comments apply to NPV (Fig. 11) and PI (Fig. 12).

Fig. 11.

Sensitivity analysis: NPV – j_diesel= unit cost for diesel; j_NG= unit cost for natural gas; j_EE= unit cost for electricity; NPV = Net Present Value.

Fig. 12.

Sensitivity analysis: PI – j_diesel= unit cost for diesel; j_NG= unit cost for natural gas; j_EE = unit cost for electricity; PI = Profit Index.

In the best case, the NPV could reach a value of about 18 M€, with a PI of 1.30.

Parametric analysis: PV and ETC areas, capacity of electric and thermal energy storage systems.

In this section, a multi-parametric analysis of the system under study is presented, aiming to investigate the optimal configuration of the system, by varying the following design parameters: i) area of the PV field (from 500 m² to 3000 m², corresponding to peak power between 90 kW and 540 kW) and capacity of the LIB (varying from 50 kWh to 2000 kWh, in this case also the kWh/kW ratio varies); ii) area of solar collectors size (from 50 m² to 500 m²) and tank volume (from 7.5 m³ to 75 m³), while PV and LIB capacities keep constant.

Fig. 13 shows some of the results provided by the parametric analysis in case the PV area and the LIB capacity vary.

Fig. 13.

Main energy parameters for the parametric analysis: electric energy – E_el,self = self-consumed electricity; E_el,toGRID = electricity sent to the grid; E_el,fromGRID = electricity withdrawn from the grid; PES = Primary Energy Saving; P_PV = photovoltaic field rated power; Cap_LIB = storage capacity.

The electricity sent to the grid (E_el,toGRID) is almost negligible for battery capacity greater than 500 kWh. This result is related with the remarkable power demand of the plant, which is able to instantly exploit the majority of renewable power produced by the PV field. The electricity withdrawn from the grid is not influenced by the storage until a value of 1500 m² of PV is reached, which corresponds to 270 kW of installed capacity. Below this value, the PV field gets largely undersized with respect to the plant demand. Hence, whatever is the size of the LIB, the electricity send to the LIB is always null or almost null. In fact, for PV field capacity lower than 270 kW the system is not able to exploit the LIB, because of the limited surplus of power compared to battery capacity, i.e. P_el,LOAD ≃ 120 kW vs P_el,PV,rated = 270 kW. Therefore, the system is not able to deliver a significant amount of electricity to LIB. The electric energy self-consumed (E_el,SELF) increases as PV field capacity and LIB capacity increase. However, for PV field capacity lower than 270 kW, the battery influence is almost negligible for the reasons above explained. As expected, the PES follows the same trend as E_el,SELF.

Fig. 14 shows the energy ratio values. The ratio E_el,SELF/E_el,LOAD highlights that for LIB capacity greater than 1000 kWh and PV peak power greater than 400 kW the E_el,SELF matches more than 50% of the plant electricity demand. This layout better exploits both the renewable power production and the battery discharge-charge depth. In fact, for such layout the LIB matches more than 15% of the overall electricity demand. This is also due to the fact that the power demand is almost constant (around 120 kW), while the PV power production overcomes P_el,LOAD only for a limited number of hours. Therefore, the higher the PV capacity, the higher the available power that may be delivered to the battery: P_el,available = P_el,LOAD - P_el,PV. The optimal PV-LIB configuration consists of a 540 kW PV plant equipped with a LIB with a capacity of at least 1000 kWh.

Fig. 14.

Self-consumption indicators from the parametric analysis: electric energy – ΔOC = operative costs difference; SPB = Simple Payback; NPV = Net Present Value; PI= Profit Index; P_PV = photovoltaic field rated power; Cap_LIB = storage capacity.

Fig. 15 shows the economic results of the sensitivity analysis. The best configuration is reached for a high capacity of the PV system and for low-mid capacity of the LIB, again. It is interesting to highlight that, for large capacities of the PV field, the economic savings are not influenced by the LIB capacity, until this decreases below 800 kWh. In this case, the NPV would be around 14 M€, which is the maximum value, for the cases evaluated; the corresponding PI is 1.06. The SPB does not vary significantly. This also means that the PV integration is always profitable, for the case under consideration. In any case, the sensitivity of the economic indices to the variables under evaluation is very low: the highest difference in the NPV is about 100 k€, and the maximum SPB variations are below 6 months. In fact, LIB and PV capital costs account for a limited share of the overall investment cost.

Fig. 15.

Economic indicators for the parametric analysis: electric energy – E_el,self/E_el,LOAD = self-consumption to total electric load ratio; E_el,self/E_el,PV = self-consumption to total photovoltaic production ratio; E_el,fromLIB/E_el,LOAD = electricity provided from battery to total electric load ratio; E_el,toLIB/E_el,PV = electricity sent to the battery to total photovoltaic production ratio; P_PV = photovoltaic field rated power; Cap_LIB = storage capacity.

As for the analysis regarding ETC area and volume of the storage tank, Fig. 16 shows the ratios of the thermal energy self-produced to the digester demand, E_th,SELF/E_th,DIG, and the thermal energy self-produced to the ETC overall production, E_th,SELF/E_th,ETC. As in the previous case, the tank volume influences the percentage of self-consumption only for ETC areas beyond 200 m²: for smaller ETC fields, the thermal energy provided by the solar source is just a small fraction of the load. For an ETC area of 500 m², and a storage volume greater than 50 m³, the self-consumption is higher than 50%.

Fig. 16.

Energy performance indicators from the parametric analysis: thermal energy – E_th,SELF/E_th,DIG = thermal energy self-consumed to thermal energy provided by the tank ratio; E_th,SELF/E_th,ETC = thermal energy self-consumed to thermal energy provided by the collectors ratio; E_th,AH = thermal energy provided by the auxiliary heater; Area_ETC = solar collector field area; V_TANK = tank volume.

Thus, as expected, larger tank capacity means greater availability of the thermal energy shared (see E_th,SELF/E_th,ETC). This parameter should then be exploited as much as possible, since the investment cost of the tank is very small, compared to the other costs.

Conversely, the self-consumption with respect to the thermal energy provided by the ETC is the greatest possible when the lowest values for both the devices are selected. This happens independently from the load: this parameter must be compared with the values of E_t,SELF and E_th,ETC to be fully comprised. The PES of the system was not reported, since is not affected by these parameters. In fact, the AH is a biomass heater. Thus, the fossil primary energy consumed is the same, independently on the percentage of use of both alternatives.

Fig. 17 shows that the influence of the variables under evaluation is even lower when discussing economic feasibility. The maximum difference in the operative costs savings is lower than 20 k€; the same occurs to the NPV. On the one hand, the larger the sizes, the greater the savings on the operative costs; on the other hand, the smallest the sizes, the greater the NPV, but also the heat provided by the AH, as shown in Fig. 16. Therefore, a trade-off solution must consider that the energy performance results are more significantly influenced by the selected parameters. SPB and PI variations are almost negligible. This also depends on the fact that the thermal energy demand of the digester is by far lower than the electric one; furthermore, the cost of the biomass is by far lower than that of the electric energy. An optimal configuration should include an ETC field with an area of 500 m² and at least 60 m³ of thermal storage, to reduce the amount of biomass purchased.

Fig. 17.

Economic indicators for the parametric analysis: thermal energy – ΔOC = operative costs difference; SPB = Simple Payback; NPV = Net Present Value; PI= Profit Index; Area_ETC = solar collector field area; V_TANK = tank volume.

6. Conclusions

This work proposes a novel paradigm plant to address, at the same time, the issues of waste disposal and public road transport pollution. In particular an existing fleet of buses, covering a path of almost 4000 km/day. These buses are replaced by natural gas buses, fuelled by biomethane produced by means of a mesophilic digester, designed to operate at a constant temperature of 38 °C. The biogas is transformed into biomethane by means of an upgrading process. The model, developed in TRNSYS, was used to analyse a case study for a facility to be located near Caserta, south Italy. Here, the digester is fed by 48.3 tons/day of organic fraction of municipal solid waste and produces more than 650´000 Sm³/year of biomethane, mainly used to supply a fleet of public buses. A 360-kW photovoltaic plant equipped with a Lithium-Ion battery of 1800 kWh was integrated to the biomethane plant, along with 200 m² of evacuated tube collectors and a thermal storage of 30 m³; moreover, a biomass-fed auxiliary heater is included in the proposed layout.

The main findings are summarized below.

• •Using a 360-kW photovoltaic field, about 45% of the electric energy produced is self-consumed and the 1800 kWh storage allows one to meet large part of the electric energy demand with solar energy. The integration of a 200 m² evacuated tube collector solar field is useful to reduce the heat supplied by the auxiliary heater at 59% of the thermal energy required by the anaerobic digester.
• •The proposed biomethane plant achieves very promising results, producing 650´000 Sm³/year of methane and reducing the energy consumption of the bus fleet, in terms of fossil resources, by 126%, and CO₂ emissions by 112%.
• •Despite high capital costs, a promising Simple Payback period of 11 years was estimated, with a Profitability Index equal to 0.23, even without any public incentive. Considering public incentives, the profitably of the proposed plant furtherly improves, achieving a Simple Payback period of 6.8 years and a Profitability Index of 1.06.
• •A sensitivity analysis was performed, with special attention to the design variables represented by photovoltaics and electric energy storage capacities; the best values of such variables were 540 kW and 800 kWh, respectively, both from energy and economic viewpoints. The size of both the evacuated tube collectors and the corresponding storage tank have less influence on the performance of the system.

Future developments of this work will include a more detailed economic analysis including possible land costs of the solar systems. Furthermore, the integration of a more accurate thermal model will be considered, and different reactors were analysed.

Author contribution statement

Francesco Calise, Francesco Liberato Cappiello, Luca Cimmino, Massimo Dentice d’Accadia, Maria Vicidomini: Conceived and designed the experiments; Performed the experiments; Analysed and interpreted the data; Contributed reagents, materials, analysis tools or data; Wrote the paper.

Funding statement

This work was supported by Italian Ministry of University and Research (MUR) [Biofeed-stock—PON ARS01_00985].

Data availability statement

No data was used for the research described in the article.

Declaration of interest’s statement

The authors declare no conflict of interest.

Nomenclature

A

Area [m²]

AD

Anaerobic Digestion

AH

Auxiliary biomass-fired heater

ADM1

Anaerobic Digestion Model n°1

COD

Chemical oxygen demand [kg_COD/m³]

c

Specific heat [J/(kg K)]

CPVT

Concentrating photovoltaic-thermal collectors

CSTR

Continuously-stirred tank reactor

DIV

Diverter

DL

Digester Loop

DPB

Discounted Payback

Eel

Electric energy [kWh or MWh]

EES

Electric energy storage

Et

Thermal energy [kWh or MWh]

ETC

Evacuated Tube Collector

F

Cost [€]

GHG

Greenhouse Gas

HE

Heat exchanger

HRT

Hydraulic Retention Time

I

Radiation [W/m2]

INV

Capital cost [M€]

j

Unit cost [€/Sm3 or €/L or €/kWh]

k

First order rate

l

Membrane thickness [mm]

LIB

Lithium-Ion Battery

LHV

Lower heating value

$\stackrel{.}{m}$

Mass flow rate [kg/s]

MIX

Mixer

NPV

Net Present Value [M€]

OC

Operating Cost [M€/year]

OFMSW

Organic fraction of municipal solid waste

p

Pressure [bar]

P

Power [kW]

PE

Primary energy [MWh]

PES

Primary Energy Saving [%]

PI

Profitability Index [%]

PM

Molar mass [g/mol]

P1

Pump of digester loop

P2

Pump of solar loop

PS

Proposed system

PV

Photovoltaic

Q

Heat transfer rate [kW]

$\dot{Q}$

Volume flow rate [m³/s]

R

Ideal gas constant [kJ/(kg K)]

RS

Reference System

S

Concentration of soluble components

SL

Solar Loop

SPB

Simple Payback period [y]

T

Temperature [°C or K]

t

Time [s]

TK

Tank

TS

Total Solid

U

Heat transfer coefficient [W/(m² K)]

V

Volume [m³]

Greek symbols

α

Separation factor

β

Biochemical coefficient

δ

Distance [km/day]

φ

Kinetic equation

η

Efficiency

μ

Permeability

ν

Michaelis-Menten maximum specific uptake rate, d–1

ρ

Density [kg/m3]

Subscripts and superscripts

ac

Acetate

acet

Acetogenesis

acid

Acidogenesis

AC

Alternate electric current

amb

Ambient

COMPR

Compressor

COD

Chemical Oxygen Demand

coll

Collector

cov

Cover

DIG

Digester

el

Electric

F

Feed flow rate

f

Factor

GN

Natural gas

Grid

National electric grid

hot

Hot-side of a heat exchanger

HW

Hot water

i

About the component “i”

in

Inlet

j

About the process “j”

lm

Logarithmic mean

loss

Thermal losses

n

Heat Exchanger coils

OFMSW

Organic fraction of Municipal Solid Wastes

Out

Outlet

react

Reactor

s

Surplus

set

Set-point value

so

Soluble

th

Thermal

top

Top of the tank

tot

Total

v

Constant volume

w

Water

wc

Woodchip