Ultimate analysis of RDF (dry basis, weight Percentage) 
The management of refused derived fuel (RDF) is one of the most significant problems especially for developing countries. Technologies to convert biomass energy already exist as well. Gasification through a bubbling fluidized bed gasifier (BFBG) is discussed in this context. A BFBG is able to deal with wide variety of fuels due to the presence of inert bed material, in which bubbles mix turbulently under buoyancy force from a fluidizing agent like air or oxygen . Under such violent bed conditions biomass waste particles are able to react fully to release volatiles as a result from high solids contact rate. Gases are released from the biomass particles and can then be used for producing electricity. In the literature there are several investigations on gasification processes from the thermodynamic point of view. Altafini and Mirandola  presented a coal gasification model by means of chemical equilibrium, minimizing the Gibbs free energy. The authors studied the effect of the ultimate analysis and the gasifying agents/fuel ratio on the equilibrium temperature (adiabatic case) in order to obtain the producer gas composition and the conversion efficiency. They concluded that the equilibrium model fits the real process well. Similar conclusions for biomass gasification are presented by the same authors , simulating the gasifying process in a downdraft gasifier, where the object of study was the effect of the biomass moisture content on the final gas composition assuming chemical equilibrium. Lapuerta et al.  predicted the product gas composition as a function of the fuel/ air ratio by means of an equilibrium model. A kinetic model was used to establish the freezing temperature, which is used for equilibrium calculations in combination with the adiabatic flame temperature. The biomass gasification process was modeled by Zainal et al.  based on thermodynamic equilibrium. They analysed the influence of the moisture content and reaction temperature on the product gas composition and its calorific value. Ruggiero and Manfrida  emphasized the potential of the equilibrium model considering the Gibbs free energy. This proceeding can be used under different operating conditions for predicting producer gas composition and the corresponding heating value.
Many studies on the modeling of coal gasifers, in general, and coal gasification in bubbling fluidized beds, in particular, can be found in the literature. Nevertheless, thermodynamic modeling of the biomass gasification in bubbling fluidized beds has not been amply addressed. A few articles on the modeling of biomass bubbling fluidized bed gasifiers (BBFBGs) can be found in the literature. In modeling the biomass gasification (with air) in bubbling fluidized beds (BFBG), Belleville and Capart  developed an empirical model which was successfully applied to the biomass gasifier of Creusot Loire in Clamecy (France). Fan and Walawender  and Van den Aarsen  reported two of the pioneering models, which are well known today; Corella et al.  modeled some non-stationary states of BFBBGs; Bilodeau et al.  considered axial variations of temperature and concentration and applied their results to a 50 kg/h pilot gasifier; Jiang and Morey [12,13] introduced new concepts in this modeling, especially related to the freeboard and the fuel feed rate; Hamel and Krumm  provided interesting axial profiles of temperature, although their work was mainly focused on gasification of coal and did not give many details of their model; Mansaray et al. [15,16] presented two models using the ASPEN PLUS process simulator.
In this work the equilibrium modeling of BFBG has been applied for the biomass waste gasification. The model employs equilibrium constants of all constituent reactions, in addition, the effect of the fuel/air ratio, moisture content of the fuel and gasifying temperature on the mole fraction of product gases of RDF gasification and corresponding higher heating value of it. Moreover, the exergetic efficiency and cold gas efficiency of the BFBG has been evaluated.
2. The model of the BFBG
2.1. Energy analysis
The idealized fluidized bed gasifier model is used with the following assumptions:
(i) The chemical equilibrium between gasifier products is reached, (ii) the ashes are not considered and (iii) heat losses in the gasifier are neglected.
The global gasification reaction can be written as follows:
In which the is the substitution fuel formula which can be calculated by the ultimate analysis of the fuel and the mass fractions of the carbon, hydrogen, oxygen, nitrogen and sulphur. “m” and “w” are the molar quantity of air entering the gasifier and moisture molar fraction in the fuel, respectively. The variable “m” corresponds to the molar quantity of air used during the gasifying process which is entering the BFBG at the temperature of 120º C and the pressure of 45 bar and depends on the gasification relative fuel/air ratio and the stoichiometric fuel/air ratio relating to the biomass waste as a fuel
And w is determined from the moisture content of the fuel
On the right-hand side, ni are the numbers of mole of the species i that are unknown.
In a fluidized bed gasifier, nearly the entire sulfur in the feed is converted to H2S, which must be effectively removed to ensure that the sulfur content of the final gas is within acceptable limits. In the case of fluidized bed gasifiers, limestone can be fed into the gasifier along with coal to capture most of the H2S produced within the bed itself. The limestone (CaCO3) calcines inside the gasifier to produce lime (CaO), which in turn is converted to calcium sulfide (CaS) upon reaction with the H2S inside the gasifier.
The substitution fuel formula can be calculated Starting from the ultimate analysis of the biomass waste and the mass fractions of the carbon, hydrogen, oxygen, nitrogen and sulphur (C, H, O, N, S), assuming a= 1, with the following expressions:
Ultimate analysis of the biomass waste (RDF) used in this model is shown in Table 1.
From the substitution fuel formula, the specific molecular weight of the biomass waste, the molar quantity of water per mole of biomass waste, the stoichiometric fuel/air ratio and the formation enthalpy of the biomass waste can be calculated.
Now for calculating the molar quantity of the product gases 7 equations are needed:
From the molar biomass waste composition and the molar moisture quantity, the atomic balances for C, H, O, N and S are obtained, respectively
There are now only 5 equations to calculate 7variables. To solve the system, two other equations should be added. From the first assumption, two equations in equilibrium can be used. Chemical equilibrium is usually explained either by minimization of Gibbs free energy or by using an equilibrium constant. To minimize the Gibbs free energy, constrained optimization methods are often used which requires a realizing of complex mathematical theories. For that reason, the present thermodynamic model is developed based on the equilibrium constant. Therefore, the remaining two equations were obtained from the equilibrium constant of the reactions occurring in the gasification zone as shown below:
In the reduction zone of the gasifier, hydrogen is reduced to methane by carbon (methanation reaction).
Methane formation is preferred especially when the gasification products are to be used as a feedstock for other chemical process. It is also preferred in IGCC applications due to methane’s high heating value.
The equilibrium constant relates the partial pressures of the reaction as follows:
Or as a function of the molar composition, assuming the behavior of the product gas to be ideal,
The second reaction, also known as the water gas shift reaction, describes the equilibrium between CO and H2 in the presence of water
The heating value of hydrogen is higher than that of carbon monoxide. Therefore, the reduction of steam by carbon monoxide to produce hydrogen is a highly desirable reaction. The corresponding equilibrium K2 constant is obtained as follows:
Or as a function of the molar composition of the gas
The values of the equilibrium constants K1 and K2 are calculated from the Gibbs free energy
Where is the difference of the Gibbs free energy between the products and the reactants:
Where is the specific heat at constant pressure in (J/mol K) and is a function of temperature. It can be defined by empirical equation below.
In which the coefficients are obtained from the table 2
For calculating K1 and K2, the temperature in the gasification or reduction zone must be known. It should be noted that in bubbling fluidized bed the bed, temperature will be in the range of 900-1200º K by which the equilibrium constants will be calculated.
After defining the corresponding equations, Because of nonlinear nature of some of the equations the Newton-Raphson method has been used to calculate the values n1-n7.
The enthalpy of the product gas is
where xi is mole fraction of species i in the ideal gas mixture and is the enthalpy of formation and represents the enthalpy difference between any given state and at reference state. It can be approximated by
Table 3 shows some the value of for some gas components.
It should be noted that enthalpy of formation for solid fuel can be calculated as:
Where is the enthalpy of formation of the product k under the complete combustion of the solid and is the higher heating value of the solid fuel.
Heat of formation of any biomass waste material can be calculated with good accuracy from the following equation:
Where C, H, O and A are the mass fractions of carbon, hydrogen, oxygen and Ash, respectively in the dry biomass waste.
2.2. Exergy analysis
The entropy of ideal gas is represented by:
Where P is the pressure of the bubbling fluidized bed gasifier, and is entropy at reference state. Table 4 shows some components
The exergy of the product gas is comprised of two components: Exergy chemical exergy and physical exergy.Total exergy of the product gas is given as
The physical exergy is the maximum theoretical work obtainable as the system( here the product gas) passes from its initial state where the temperature is the gasifying temperature and the pressure equals the gasifier pressure to the restricted dead state where the temperature is T0 and the pressure is P0 and is given by the expression
The physical exergy of gas mixture per mole is derived from the conventional linear mixing rule
The chemical exergy is the maximum theoretical useful work obtainable as the system passes from the restricted dead state to the dead state where it is in complete equilibrium with the environment.
And chemical exergy of gas mixture is given by
Where is the standard chemical exergy of a pure chemical compound i which is available in Table 5 for some gas components.
Special considerations apply for the gasifying products when evaluating the chemical and physical exergy. When a product gas mixture is brought to P0, T0, some consideration would occur: At 25º C, 1 atm, the mixture consists of, together with saturated water vapor in equilibrium with saturated liquid. So it would be required to calculate the new composition at the dead state including the saturated liquid. Then the and values required to evaluate the physical exergy and the product gas mole fraction at the dead state essential for evaluating the chemical exergy can be calculated.
The exergy components and the total exergy for the moisture content of the fuel is obtained
For a biomass waste the chemical exergy is obtained as follows
The factor is the ratio of the chemical exergy to the HHV of the organic fraction of biomass waste. This factor is calculated with the following correlation :
Therefore the total exergy of the biomass waste as a fuel can be defined:
2.3. Heating value and efficiencies
2.3.1. Heating value
The heating value of the producer gas can be obtained as the sum of the products of the molar fractions of each of the energetic gases (CO, H2 and CH4) with its corresponding heating value (Table 6).
|LHV (MJ/kg mol)||HHV (MJ/kg mol)||gas|
2.3.1. Evaluation of the efficiency
It is assumed that the fluidized bed gasifier operates as adiabatic and pseudo-homogeneous reactor at atmospheric pressure.
Gasification entails partial oxidation of the feedstock, so chemical energy of biomass waste is converted into chemical and thermal energy of product gas.
The first law thermodynamic or cold gas efficiency can be defined as the relation between the energy leaving the gasifier i.e. the energy content of the producer gas, and the energy entering the gasifier, i.e. the biomass waste and moisture. We assume the gas leaves the process at the reference temperature (25º C), loosing the energy corresponding to its sensible enthalpy, and define the cold gas efficiency as
Where HHVgas and HHVbiomass are the net heats of combustion (lower heating values) of gas and biomass waste, respectively.
The exergetic efficiency may be defined as the ratio between chemical exergy as well as physical exergy of product gas and the total exergy of the entering streams i.e. the biomass waste and the moisture and fluidizing air.
In this work variations of the exergy efficiency, cold gas efficiency and product gas concentration will be investigated as a function of temperature, gasifying fuel/air ratio (Frg), and moisture content of the fuel (φ).
3. Results and discussion
3.1. Validation of the model
The model presented in this article has been compared to the experimental work for the wood particles presented by Narvaez et al. . By way of illustration the predicted HHV producer gas by the model and the results from the experiments are presented in Figure 1.
3.2. Sensitivity analyses
The effect of Frg on product gas composition and higher heating value for RDF gasification is presented in Figure 2. An increase in Frg brings about an increase in the concentration of H2 and CO and a substantial decrease in CO2 concentration in dry gas product. This is because of the decreasing role of the char combustion in the bed compared to its gasification reaction, which results in higher concentration of combustible gases and lower CO2.
The effect of moisture content of the fuel on product gas composition and higher heating value for RDF gasification is presented in Figure 3. As shown in the figure, an increase in moisture content brings about an increase in the concentration of H2 and CH4 and decrease in the concentration of CO. This is because of the increasing role of the moisture content of the fuel and effect of the methanation reaction (equation8) and the water-gas shift reaction (equation11) in which the molar concentration of the CO decreases because of the reaction with H2O and production of H2, ‘ and resulting an increase in the molar quantity of CH4. Therefore the higher heating value will decrease as the moisture content increases.
The effect of gasifying temperature on product gas composition is shown in Figure 4. The figure shows that an increase in temperature brings about an increase in the concentration of H2 and CO of RDF. This is because of the increasing role of the temperature in the equilibrium constants (16), (17) in which the equilibrium constant is dependent on the BFBG temperature, so an increase in temperature causes more production of combustible gases. The higher heating value in this temperature range at the constant Frg is to some extent constant that is valid according to experimental works .
The effect of Frg with moisture content of the fuel on exergetic efficiency and cold gas efficiency for RDF gasification are presented (by line & flood contour type) in Figures 5, 6. It is shown that the exergetic efficiency of BFBG increases with rising fuel/air ratio because when less air is admitted to the process, the variations in mole fractions of product gases will influence the exergy of the product in comparison to exergy of the fuel. Higher moisture content will increase the exergetic efficiency because of its considerable effect on enthalpy of the product gases (figure5). An increase in Frg, as discussed before, brings about an increase in the concentration of combustible gases and higher heating value which yields an increase in cold gas efficiency and an increase in moisture content of the fuel, as discussed before, causes decrease in the concentration of combustible gases and higher heating value which yields a decrease in the cold gas efficiency (figure6).
The effect of Frg and the bed temperature on exergetic efficiency and cold gas efficiency for RDF gasification are presented (by line & flood contour type) in Figures 7, 8. It is shown that the exergetic efficiency of BFG increases with rising fuel/air ratio as discussed for figures 5 and 6. Higher temperature will increase the exergetic efficiency because of its considerable effect on enthalpy of the product gases (figure7). An increase in bed temperature, as discussed for figure 4, brings about an increase in the concentration of combustible gases and higher heating value which yields an increase in cold gas efficiency (figure8)
An equilibrium model was developed for the biomass waste gasification in the bubbling fluidized bed waste gasification. It was shown that higher moisture would decrease the product gas higher heating value as well as cold gas efficiency while increase the exergetic efficiency. Moreover, It was concluded that higher temperature and higher Frg would increase both the product gas higher heating value, cold gas efficiency and the exergetic efficiency.
|C||mass fraction of carbon|
|H||mass fraction of hydrogen|
|gasification relative fuel/air ratio|
|stoichiometric biomass waste/air ratio|
|M||molecular weight (kg/mol)|
|biomass waste molecular weight (kg/mol)|
|N||mass fraction of nitrojen|
|molar quantity of air|
|molar quantity of biomass waste moisture content|
|Product gas total Exergy|
|gibbs free Energy((kJ/mol)|
|O||mass fraction of oxygen|
|HHVdb||higher heating value in dry base|
|S0||standard Entropy(KJ/mol K)|
|S||mass fraction of sulphur|