INTRODUCTION
Recent efforts to reduce the human impact on climate change, especially the reduction of CO_{2} emissions, include the replacement of fossil fuels, such as oil and coal, with renewable and less polluting energy sources. These efforts promoted increasing interest in the usage of biomass fuels to produce electricity. Biomass can be defined as any carbonaceous material, such as wood, straw, or sewage sludge, and is advantageous in that there is no net increase in CO_{2} emissions due to biomass combustion because CO_{2} produced from the combustion is consumed during plant growth (^{Roni et al., 2017}). The development and use of more advanced technologies involving biomass are important to reduce the dependence on fossil fuel resources, especially in rural areas, where biomass is readily available (^{Saidur et al., 2011}; ^{Demirbas, 2005}). Direct combustion of biomass is the most used thermochemical process to obtain heat from biomass.
However, for non-woody fuels in small-scale systems, direct combustion is hindered because of low energy efficiency and high pollutant emission (^{Verma et al., 2011}). Gasification is a process in which biomass is heated up to 800–1000 °C and is transformed by devolatilization and chemical reactions into syngas composed mainly of CO, CO_{2}, H_{2}, and CH_{4} (^{Saidur et al., 2011}). Mathematical modeling is a useful tool for the investigation of such thermal processes, as it can be used to study a given system without the need to run several experimental tests (^{Fournel et al., 2015}). The models can be built by studying the system behavior through equations that describe the physical and chemical phenomena involved in the process, such as Computational Fluid Dynamics or transient models (^{Silveira et al., 2017}; ^{Rajh et al., 2016}; ^{Siqueira et al., 2012}). Although these types of models can describe several phenomena, they require considerable detailed information about the system and computational resources. Thermodynamic equilibrium models have an advantage in this scenario, as they do not require a large database or detailed information about the chemical reactions occurring in the system. These types of models require the ultimate analysis of biomass (C, H, O, N, S, and moisture contents), mass flows of fuel and air, and system temperature and pressure as inputs (^{Baratieri et al., 2008}).
Although the equilibrium is not reached in real cases, these models can predict the composition of syngas produced through gasification processes with satisfactory accuracy (^{Gambarotta et al., 2017}). The models can be based on Gibbs Energy minimization (^{Fournel et al., 2015}; ^{Mendiburu et al., 2014}; ^{Jarungthammachote & Dutta, 2008}) or use of equilibrium constants (^{Aydin et al., 2017}; ^{Mozafari et al., 2017}; ^{Jarungthammachote & Dutta, 2007}). Altafini, Wander, and Barreto performed gasification tests using Pinus Elliotis sawdust as fuel (^{Altafini et al., 2003}). In order to model such experimental test, Fournel et al. and Jarungthammachote & Dutta developed computational models based on thermodynamic equilibrium to predict the formation of syngas. The predicted composition was compared to the experimental results (^{Fournel et al., 2015}; ^{Jarungthammachote & Dutta, 2008}). Because modeling involves the formation of gaseous compounds and thermochemical processes degrade the biomass components into simpler ones, the species of biomass does not significantly interfere in modeling; thus, the results vary according to the composition and moisture content of biomass.
This work aims to build and validate a thermodynamic model to predict the production of CO, CO_{2}, H_{2}, and CH_{4} based on Gibbs energy minimization, considering the formation of C_{(s)}, and to verify the role of the unburned carbon on the gasification yield, since the two cited models only took into account the gaseous products of the gasification.
MATERIAL AND METHODS
Biomass is defined as a material composed of four elements and is considered to have the chemical composition of CH_{a}O_{b}N_{c}. Because thermochemical conversion processes involve several different reactions and intermediate compounds, the gasification reaction can be simplified considering only the main compounds present in the media. The equilibrium media can be represented by [eq. (1)]:
Where:
a, b, and c are the number of atoms of hydrogen, oxygen, and nitrogen in biomass (kmol_{ELEMENT}/kmol C);
w is the wt% of moisture in biomass (kmol_{H2O}/kmol_{FEEDSTOCK});
r is the amount of air supplied to the process (kmol_{AIR}/kmol_{FEEDSTOCK}), and
n_{i} is the number of moles of species i in the system.
The moisture and molar composition of biomass were obtained experimentally by proximate and ultimate analyses, and the air-to-fuel ratio (AFR) was obtained as a parameter of the experiment. Another proposed model considers the formation of char (C_{(s)}) as described by [eq. (2)]:
Input values | Altafini et al. (2003) |
---|---|
Carbon (wt%) | 52.05 |
Hydrogen (wt%) | 6.08 |
Oxygen (wt%) | 41.59 |
Nitrogen (wt%) | 0.28 |
Higher heating value (MJ/kg) | 20.4 |
Moisture content (wt%, waf) | 10.0 |
Biomass feed rate (kg/h) | 12.6 |
Air/biomass mass ratio (kg_{AIR}/kg_{BM}) | 1.96 |
Gasification temperature (K) | 1073 |
Note: waf = wet and ash-free basis.
The biomass and gasification data of the experimental system used by Altafini, Wander and Barreto are shown in Table 1 (^{Altafini et al., 2003}).
Gibbs energy minimization
When a closed system is in chemical equilibrium, its Gibbs energy (G) reaches a minimum value (^{Smith et al., 2017}). For a system with F and N_{j} species in phase j, the total Gibbs energy of the system is the sum of the contribution of each species-specific Gibbs energy. It is given by the chemical potential of each species i in phase j (μ_{i,j}) as follows:
Solving [eq. (3)] for a minimum G value implies determination of the number of each species in the equilibrium media (n_{i,j}) and prediction of the composition of the system (^{Sundman et al., 2015}). For a system composed of ideal gases at atmospheric pressure,
Where:
R is the universal gas constant (8.314 J/mol K), and
y_{i,j} is the mole fraction of gaseous species i in phase j. The equation for the Gibbs energy becomes:
Where:
n_{tot,j} is the total number of moles in phase j, and
Where:
Where:
C_{p} is the heat capacity at constant pressure of the compounds, and
T_{0} is the inlet temperature of the reactants (K).
The heat capacity is a function of the temperature, and its values can be given by a polynomial equation:
Where:
A, B, C, D, and E are empirical coefficients available in the literature.
In this study, the coefficients used were provided by NASA Technical Memorandum 4513 (^{Mcbride & Reno, 1993}). The calculation of the minimum Gibbs energy (Equation 10) consists of solving the equivalent optimization problem:
Subject to:
Where:
a_{k,i} is the number of atoms of the k-th element in a mole of species i, and
A_{k} is the total number of moles of the element in the reaction medium.
The first constraint (Equation 11) states the element mass conservation on the system, and the second constraint (Equation 12) denotes that the number of moles needs to be positive and less than the total number of moles of the species.
Model assumptions
In the development of G minimization, the following assumptions were made:
–. Thermodynamic equilibrium was reached;
–. Biomass and air enter the reaction media at 25 °C and 1 atm;
–. Average properties (temperature = 800 °C and pressure = 1 atm) and mass flow of the inputs and outputs are constant;
–. Only the species described by eqs (1) and (2) are formed during gasification;
–. All gases behave as ideal gases;
–. Ash in biomass is considered inert and is not present in the calculations.
–. The char behavior in the system was modeled in two ways: (i) considered to be in a distinct solid phase, and the calculation proceeds as [eq. (10)] states; and (ii) considered as a participant in the gas phase, in a way that only one phase was considered in the system. With this assumption, [eq. (10)] becomes:
Equilibrium Calculation
The optimization problem was implemented in MATLAB, a commercial computational software. The optimization problem was solved by the fmincon routine inside the software. The routine uses the sequential quadratic programming method (SQP), which is suitable for constrained optimization problems. The function applies an interior-point algorithm, obtaining Lagrange multipliers applying the Karush–Kuhn–Tucker (KKT) conditions (^{Singh et al., 2016}; ^{koukkari & Pajarre, 2006}).
Model validation
To validate the predicted syngas composition calculated by the developed model, the results were compared to the experimental data obtained by Altafini, Wander, and Barreto, who operated a downdraft gasifier using wood sawdust as fuel (^{Altafini et al., 2003}). The results were also compared to other similar models obtained by ^{Jarungthammachote & Dutta (2007)}, who developed a kinetic model considering species according to [eq. (1)], and ^{Fournel et al. (2015)}, who developed a Gibbs energy minimization model for the same system. A comparison was conducted between the two models described by eqs (1) and (2).
The modeling results were compared with the experimental values by determining the root-mean-square error (RMSE), defined by [eq. (14)]:
Where:
y is the value from the experimental result, and
ŷ is the predicted value from the model;
N_{T} is the total number of data points.
The char formation was validated by char conversion data obtained experimentally by Altafini, Wander, and Barreto as well as by two correlations: one that predicts the C_{(s)} fraction among all the products in the system, given by (1-ϕ) in [eq. (15)] (^{Li et al., 2004}), and one that estimates the amount of the total C converted to the gas phase (β), as given by [eq. (16)] (^{Aydin et al., 2017}):
Where:
ER (equivalence ratio) is the ratio of the air supplied to the system and the stoichiometric air requirement for complete combustion.
RESULTS AND DISCUSSION
Predicted product distribution
The results of the mole number of the species described by eqs (1) and (2), using data from Table 1 as the input, and optimized by the objective functions composed by eqs (10) and (13) are shown in Table 2.
Species | n_{i} (Equations 1 and 10) | n_{i} (Equations 2 and 10) | n_{i} (Equations 1 and 13) | n_{i} (Equations 2 and 13) |
---|---|---|---|---|
CH_{4} | 0.3 | 0 | 0.11 | 0.04 |
CO | 106.26 | 5.8 | 106.58 | 77.26 |
CO_{2} | 32.11 | 44.03 | 31.98 | 40.32 |
H_{2} | 90.53 | 14.5 | 90.96 | 78.47 |
H_{2}O | 25.35 | 101.98 | 25.29 | 37.95 |
N_{2} | 165.52 | 165.52 | 165.52 | 165.52 |
C(s) | - | 88.84 | - | 21.07 |
n_{tot} | 420.07 | 420.67 | 420.44 | 420.63 |
The results show that the amount of char formation, although not very large, cannot be neglected, as the C_{(s)} accounts for the unburned carbon and indicates incomplete combustion, which lowers the energy efficiency of the process (^{Li et al., 2004}). When considering the char in a separate solid phase (objective function by Equation 10), there is a huge underestimation of the CO formation compared to the experimental value found by ^{Altafini et al., (2003)}, as shown in Table.
Prediction of syngas composition
The previous model and the experimental data were expressed in terms of syngas composition (CH_{4}, CO, CO_{2}, H_{2}, and N_{2} molar fractions). Therefore, since H_{2}O and C_{(s)} are products, the modified molar fraction (y_{i}) was calculated using [eq. (17)]:
Table 3 shows a comparison of the results of the experimental data obtained by ^{Altafini et al., (2003)} (first column), the gasification model made by other authors using the same experimental values (columns 2-4), and the models proposed in this study (columns 5-8). The results of columns 5 and 6 are the models developed without considering char formation, and columns 7 and 8 are the models developed considering char formation in the system.
In real gasification systems, some CH_{4} is formed (Table 3), although the equilibrium model does not predict significant amounts of it (^{Jarungthammachote & Dutta, 2007}). An explanation for this may be that the assumptions used in the model, such as ideal behavior of the gases and perfect mixture, and that the system reaches equilibrium are not totally satisfied, resulting in a difference between the experimental and predicted values. As stated by ^{Fournel et al. 2015}, the formation of CH_{4} is not thermodynamically favorable in equilibrium at higher temperatures, since the Gibbs energy of formation of CH_{4} is positive (
Experimental values | Models by other authors | Models developed in this study | ||||||
---|---|---|---|---|---|---|---|---|
1 (Altafini et al., 2003) | 2 (Altafini et al., 2003) | 3 (Jarungthammachote & Dutta, 2007)* | 4 (Fournel et al., 2015)* | 5 This study (No C(s) formed) | 6 This study (No C(s) formed)* | 7 This study (With C(s) formation) | 8 This study (With C(s) formation)* | |
CH_{4} | 2.31 | 0 | 1.66 | 1.66 | 0.03 | 1.66 | 0.01 | 1.66 |
CO | 20.14 | 19.7 | 23.34 | 21.47 | 27.11 | 25.32 | 21.16 | 20.16 |
CO_{2} | 12.06 | 10.15 | 9.82 | 11.14 | 7.43 | 8.87 | 11.5 | 12.56 |
H_{2} | 14.00 | 20.06 | 18.24 | 18.83 | 22.8 | 19.93 | 21.05 | 18.39 |
N_{2} | 50.79 | 50.1 | 46.93 | 46.9 | 42.63 | 44.21 | 46.28 | 47.23 |
RMSE | - | 3.05 | 3.12 | 2.88 | 6.62 | 5.46 | 3.92 | 2.55 |
Note:
^{*}CH_{4} amount fixed to the average experimental value obtained by ^{Jarungthammachote & Dutta (2007)}.
The results obtained using [eq. (10)] as the objective function were omitted from the table because they showed RMSE values of 19.13 (using species described in Equation 1) and 12.82 (using species described in Equation 2). It can be concluded that [eq. (13)] is the objective function that shows better results for the gasification syngas prediction.
There was an overestimation of H_{2} formation and an underestimation of CH_{4} formation by the equilibrium model. Fixing the value of CH_{4} reduces the estimated amount of H_{2} and increases the CO_{2}, making the estimation closer to the experimental values, as shown by the RMSE values.
The model in column 8 (using Equation 2 as input) has the lowest root-mean-square error in the prediction of syngas composition. The models developed by ^{Jarungthammachote & Dutta (2007)} and ^{Fournel et al. (2015)} are based on Equation 1 (which does not consider char formation). Although the models show similar root-mean-square errors, it can be seen from the results in Table 1 that the char is present in significant amounts, and the slightly better accuracy of the model can be attributed to the formation of C_{(s)} (^{Gambarotta et al., 2017}).
The results show that the equilibrium model is a good approximation of the gasification system, with good accuracy in predicting the syngas composition. Gasification systems are typically at high temperatures and good mixture rates, which favor the system to achieve the equilibrium state.
Prediction of char formation
After validating the syngas prediction, an analysis of the prediction of char formation was performed on models obtained by using eqs ((2) and (() (with fixed and unfixed CH_{4} amount), which showed better agreement with experimental results.
Table 4 shows a comparison between the results for the char conversion calculated by this study and that calculated by the correlations given by eqs (15) and (16). The conversions Φ and β given by the model were calculated by the C_{(s)} fractions given by the estimated equilibrium composition, and the correlations were estimated by the ER value, which was ER = 0.31355 for the experimental run by ^{Altafini et al., (2003)}.
Correlations | This study Eq. 2 and 13 | This study Eq. 2 and 13 * |
---|---|---|
0.054 (Eq. 15) | 0.0477 | 0.040 |
0.821 (Eq. 16) | 0.855 | 0.881 |
Note:
^{*}Model with CH_{4} amount fixed to the average experimental value obtained by ^{Jarungthammachote & Dutta (2007)}.
The results show that, although the modified model with a fixed amount of CH_{4} showed better accuracy for the prediction of syngas composition, the unmodified model showed a better prediction of char formation. In order to investigate the effect of the moisture content of biomass on the carbon conversion, ^{Altafini et al., (2003)} conducted an experimental study of the effect, with biomass moisture ranging from 0% to 30%. The results obtained experimentally were compared with those simulated by this model using Equations (2) and (13), which showed better prediction of the syngas. The results are shown in Figure 1.
*Model with CH_{4} amount fixed to the average experimental value obtained by ^{Jarungthammachote and Dutta (2007)}.
The model shows a satisfactory prediction of the carbon conversion, especially for intermediate values of moisture content (5-20%). The unmodified model (without fixing the CH_{4} amount) showed better prediction of the char conversion than the modified model. Thus, both equilibrium models can be used for the gasification modeling: the unmodified model for a better prediction of carbon conversion and the modified model for the prediction of syngas composition.
CONCLUSIONS
The present study demonstrated the applicability of Gibbs energy minimization to predict gaseous emissions from biomass gasification. The model does not require much detailed information about reactions and other conditions and can predict the composition of the system with good accuracy. From the comparison of the results for the two reaction equations, it can be stated that the formation of solid carbon cannot be neglected (molar fraction of 4-5%, for this study), since even in ideal cases, there is C_{(s)} in the equilibrium products. The model showed better prediction accuracy when compared to the other models that did not account for char formation, leading to the conclusion that the C_{(s)} formation can be taken into account in equilibrium models with a reasonably good prediction of the carbon conversion.
This type of model can help to evaluate the suitability of gasification of any biomass with known composition and moisture content, reducing the need for experimental tests. The model could be used to simulate other thermochemical processes, such as combustion and pyrolysis (^{Li et al., 2004}; ^{Mozafari et al., 2017}), but the results could be less accurate since these processes have poorer mixing than gasification, making it more difficult for the system to achieve the equilibrium state.