1. Introduction
Thanks to advancements in technology, in recent decades, renewable energy has been deemed a very practical alternative to using conventional fossil fuels to supply cleaner sustainable energy systems [
1]. Biomass, a carbon-based renewable resource, is capable to replace fossil fuels with the least modification in conventional facilities compared to other renewable resources. Among all possible biomass conversion processes, yet direct combustion is the most commercialized one [
2,
3]. Other advancing technologies, such as anaerobic digestion (AD), hydrothermal carbonization (HTC), as well as hydrothermal gasification (HTG) are generally less commercialized, owing to poor infrastructure of raw fuel supply, high operational and capital cost, and mostly are in prototype-scale so far [
2,
3,
4,
5].
Moving bed, fluidized bed, and pulverized fuel combustors are identified as the commercialized combustion technologies to burning biomass fuels. Based on a certain application, each of the aforementioned systems can be a more fitting choice, as discussed elsewhere [
6]. In the course of small-scale purposes, moving grate furnaces are one of the most highly utilized approaches to burning raw and treated biomass waste. While, in addition, within the small to medium scale applications, the moving grate furnaces require less fuel preparation.
Currently, research has been conducted in order to modify the combustion system efficiency, as well as the contaminant emission issue that are associated with these systems [
7,
8,
9,
10,
11,
12]. Throughout the literature, the majority of the developed biomass combustion models were exercised in micro-scale system analyses in order to understand the biomass combustion properties more comprehensively [
13,
14,
15]. These models were rarely governed as a system analysis tool in order to evaluate the functional system outputs and required operation adaptation for more efficient combustion. For example, a numerical model was developed by Zhou et al. [
8] to study the effect of variant excess air ratio on combustion efficiency. The authors concluded that, under O
2 enriching combustion, which is defined as an increase in air flow rate from the stoichiometric condition to a higher fraction; the optimum combustion improvement is achieved when the O
2 volume fraction raises from 21% to 25%. Meanwhile, the maximum bed temperature is restricted to 1400 K. Similarly, bed and overbed zones were integrated on the same 3D grid, while the bed zone modeled through a porous medium [
16]. The model then characterized a flow pattern and a specific temperature, as well as, pollutant profiles in the combustion chamber. Flame temperature, species concentration, and ignition front velocity for a packed-bed biomass combustor under CO
2-rich condition was analyzed using an integrated 1D bed model into a 3D overbed model via Karim et al. [
17]. The CO
2-rich combustion indicates recycling flue gas as a fraction of primary air flowing into the fuel bed. The ignition front rate sped up to almost double the rate with CO
2-rich air feed conditions. A connected 1D bed model and 3D overbed model was developed to cope with how different quality fuel influenced operations [
18]. Larger high-temperature combustion zones were observed as a result of higher quality fuel, and, thus, consequently higher system efficiency. The effect of biomass fuel compositions variability on combustion properties in a moving grate combustor was studied through an independent bed model coupled with a simplified overbed combustion model [
19]. The results demonstrated a major impact of composition variability on ignition front rate, conversion time, and output heat flux, as well as a minor impact on the flame temperature. Existing models help engineers to design for a better biomass combustion, which is quite necessary for technology advancement. Meanwhile, system analysis using black-box model without paying attention to operational detail can be beneficial only for general decision making [
20]. However, for many of the domestic and industrial facility’s users, it is impractical to take advantage of such modeling applications. In other words, for example, it is crucially important for them to know how system operation should be readjusted when switching from variant feeding fuels for example from specific biomass pellets to wood chips. In addition, what the economic and ecosystem consequences of this fuel switching action are.
In this paper, functional thermal properties of a moving bed biomass boiler fed with three specific waste-based fuels: biomass pellets, wood waste, and refuse-derived fuel (RDF), are carefully determined through a routine of one-dimensional transient numerical bed model integrated with an overbed black-box model. In this study, instead of focusing on biomass combustion diagnosis and micro-scale combustion analyses, we propose the required adjustments to facilitate system operation settings when switching between the proposed fuels. Furthermore, to illustrate the long-term economic and environmental impacts of system operation with each fuel, life cycle costing (LCC) and life cycle analysis (LCA) are also conducted. It should be noted that moving grate boilers can concurrently burn different fuel types, such as those that are applied in this study. In consequence, the results of this article are highly informative for system users.
2. Modeling Procedure
The process of biomass combustion inside the packed bed deals with thermochemical reactions consisting of drying, devolatilization, and char combustion. To some degree, this is a complicated process that still has many unknown variables. The existing 1D, 2D, and 3D empirical models can predict the actual combustion process from an engineering standpoint.
Drying as an endothermic reaction has a significant impact on combustion. Many studies have proved that higher moisture content of biomass particles can diminish thermal performance and increase contaminant emissions [
15,
21,
22,
23]. By analyzing the literature, where different drying models can be identified, Arrhenius and heat sink models have been applied in recent studies. The influence of moisture content of different particle shapes on drying behavior was examined using the Arrhenius and heat sink models by Khodaei et al. [
24]. Through a lack of experimental data regarding particle de-moisturization, the heat sink model exhibited more compatible results that was opted for in this work. Pyrolysis occurs after the evaporation of the initial moisture content. This includes several interrelated parallel reactions that initiate at disparate temperatures and begin at a higher rate than drying. Here, the fuel mass of the bed profoundly diminishes while volumetric fuel bed reduction is insignificant. Varied pyrolysis models have been listed in Reference [
25], although only a few of them have been recently applied in the biomass conversion models due to their relative complexity and inaccuracy. Among all, the model with three parallel reaction-terms has been dominantly utilized, as it has a trade-off between computational cost and precision, and, therefore, simulates the devolatilization process in this article. The most complex reactions occur during char combustion, in which both diffusion and thermal mechanisms compete to overtake the reaction. It is imagined that char reaction consists of four overlapping reactions [
25], while, in most of the research, the fourth reaction, the reaction of carbon with hydrogen, is overlooked, due to its negligible effect on the whole process. For a detailed description of each subprocess and the corresponding models, Reference [
26] is recommended.
Fuel bed simulation has been conducted through varying techniques in the publications. They can be categorized as empirical bed models, separate bed models, discrete particle models (DPM), and porous medium bed models. A more thorough explanation of each technique can be found through further research beyond the scope of this article [
27]. The separation of fuel bed and overbed zone modeling is the most preferred strategy in biomass furnace modeling, in which it facilitates the sensitive and in-depth analysis of solid particle conversion. Instead of 3D modeling of fuel beds, 2D models (or 1D transient models) are usually governed, because fields gradient in the z-direction of bed zones are insignificant. According to the literature, this strategy can be implemented by utilizing variant approaches, including the single-particle model, the continuous medium model, and the particle-resolved model. The single-particle model delivers proper results for a fluidized bed system, because the proposed particles have uniform boundary conditions, while in the moving grate combustors, particles have non-uniform boundary conditions. The particle-resolved modeling has modified the problems with single-particle molding, however, the computational cost of this is quite high. In this article, the continuous medium model is governed to simulate fuel conversion, where it has a fair trade-off between accuracy and computational cost. It should be mentioned that this method could raise dispersion in results when large-size particles are deployed.
Figure 1 visualizes the fuel particles arrangement under the actual condition and continuous medium modeling approach along with heat transfer mechanisms inside the fuel bed. From this figure, the main limitation of the continuous medium model is to neglect radiation between particles inside the fuel bed. The furnaces side walls are assumed to be insulated so that no heat leakage can occur from the fuel bed zone to the outside of the walls. Reactions happen in the vertical direction inside the fuel bed, whereby the horizontal gradient is insignificant. The one-dimensional transient model is executed, in order to eliminate the complexity of two-dimensional modeling. This method, the so-called walking column, tracks changes in a tiny column of the fuel bed from the opening of the grate until all fuel in the column is consumed [
28]. The column is split into small cells, as each cell consists of the solid and gas phase and is updated during the conversion process. The solid phase initially includes a predefined amount of moisture, volatile, and char, which are gradually depleted during the process until all solid parts convert to gaseous elements. A one-dimensional walking column strategy which models a 2D steady-state fuel bed geometry, coupled with overbed black-box modeling, is visualized in
Figure 2. Heat flux is then obtained from oxidation of combustible gases in the overbed zone.
The solid and gas phase governing equations used in this work are demonstrated in
Table 1. Other information related to the modeling, such as kinetic formula of subprocesses, coefficients of specific heat, conductivity, source terms of governing equations, and so on, are presented in
Table 2. Gas pressure drop for laminar flow in the packed fuel bed is also introduced in
Table 2, where L is the fuel bed height,
is the gravitational constant,
is effective porosity,
air is absolute viscosity,
is air velocity,
is effective particle diameter, and
is air density [
29].
During the conversion of fuels, volumetric shrinkage of single biomass particles causes the fuel bed to decay, which is referred to as fuel bed porosity [
36]. An explicit approach is used in this article, so that the particle mass consumption inside the grid is continuously observed until the all grid mass is depleted. In each iteration, each grid is filled by its upper grid mass. In this way, bed shrinkage is fairly traceable while biomass conversion proceeds [
37].
,
, and
imply a shrinkage factor of drying, pyrolysis and char oxidation, at which values 0.1, 0.15, and 0.75 are assigned, respectively.
Outflowing gas species from solid fuel conversion are presumed to be CO, CO
2, CH
4, H
2, H
2O, and C
6H
6, whereby some react with oxygen mainly in the overbed zone. To quantify the fraction of volatile gases during combustion, the experimental results of another publication were employed [
38]. Homogeneous gas-phase reactions [
39], together with the corresponding enthalpy of reaction, are presented in Equations (2)–(5). The overbed gas-phase reactions along with the in-bed char combustion eventually form the source of heat generation in the combustion chamber. The accumulation of all the previously mentioned reactions are then accounted for in heat flux calculation.
3. Solution and Validation
The finite difference method (FDM) is employed to discretize the conservation equations based on the given solution algorithm in
Figure 3. FDM is a well-documented method suits the simple geometries. A fully implicit scheme backward difference in time and the central difference in space (BTCS) is opted for, in order to resolve the energy equation for the solid phase (heat equation), an upwind scheme for the gas-phase mass and momentum equations (advection equation), by using a BTCS scheme. Finally, an upwind scheme for the gas-phase energy and species equations (advection-diffusion equation) using the backward difference in time, the forward difference in first-order derivative term, and central difference for the second-order derivative term. Although the selected schemes are unconditionally stable, the accuracy of the solution will be protected by choosing the proper step size. Varied time step (10
−2 to 10
−3 s) has opted for the solution along with 100 grid cells for the walking column. As most elements of the time-space matrix were zero, a sparse matrix method was used to speed up the solution procedure. The Python software was applied to code the solution algorithm.
Bed temperature and mass loss profiles concerning the developed model were validated versus two separate experiments implemented on packed-bed biomass combustors [
40,
41]. From
Figure 4, there is a satisfactory agreement between the model and experiments, unless there is a reasonable deviation, caused by inherent modeling error, model assumption, measuring error, etc.
The dispersion between the temperature profile in terms of the experiments and model predictions within the drying stage can be interpreted in this way: the fuel moisture resided inside the particle pores absorbs a high proportion of the heat flowing from the overbed zone. In other words, most of the absorbed heat by particle in beginning step of conversion is used to increase moisture temperature, therefore, the particle surface temperature change is much slower. In doing so, the inside particle temperature rises, while the outer surface temperature, which the thermocouple measures, does not rise at the same rate as inside. This is deemed a limitation of the fuel bed experiment. Additionally, the predicted fuel bed conversion obtained by current simulation is in line with an earlier experiment, based on a study by Yin et al. [
42], showing the contribution of drying, devolatilization, and char burnout in different lengths of a moving grate.
5. Conclusions
In this article, a thermo-economic and environmental analysis was conducted for a moving grate biomass boiler to compare the utilization of three variant waste fuels, including biomass pellets, wood waste, and RDF in the proposed system. Fuel conversion inside the fuel bed was delicately modeled using an in-house routine numerical model. The useful heat flux from the boiler was calculated through an overbed black-box model based upon each feeding fuel, and the required time of complete fuel combustion was determined. It was concluded that biomass pellets deliver the highest system thermal efficiency so that the pellet-fueled system provides 548 GJ heat annually, opposite to 282 GJ utilizing wood waste, and 355 GJ utilizing RDF. Furthermore, the maximum solid bed temperature for biomass pellets is about 11% higher than the estimation in the RDF scenario. This is mainly because of the higher fixed-carbon content of biomass pellets. Moreover, a separate comprehensive economic analysis was practiced for the proposed biomass boiler with respect to each alternative fuel, and, again, the results revealed the privilege of using biomass pellets among all other waste fuels. Although the COH of RDF scenario was lowest by 7.63 ¢/kWh, which was 7% and 22% less than biomass pellets and wood waste respectively, the IRR of the pellet-fueled system was highest by 36%, because of its higher heating capacity compared to all others. Regardless of the scenario, the fuel cost reserved the most contribution to the total life cycle cost of heat production. In the last section of the article, a comparative LCA ratified the importance of employing fuels with no carbon footprint. The CO2 emission from the RDF combustion was obtained far higher than other plant-based fuels, which were counted as CO2 neutral emission.
Biomass boilers should be considered to be promising facilities for heating supply in remote areas [
59]. In future studies, it is recommended to investigate the deployment of combustible waste from cargo ships for heating purposes from thermo-economic and environmental viewpoints. Carrying waste is problematic for shipping companies. On the other hand, the randomness of fuel arrangements inside the fuel bed, along with fuel constituents, and size uncertainty, are some challenges encountering biomass combustor operation and modeling in the present day. Quantifying the relevant effects on the system operation is recommended. Lastly, the LCA system boundary of this study was limited to some degree, which can be extended up to the very beginning and very end for future works.