Gaseous emissions from agricultural biomass combustion: a

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Jul 21, 2013 - according to the combustion technology used and the ... satisfy the restrictions of non-negative number of moles and mole balances (Rossi et al., 2011). ... To develop the model, the chemical formula of biomasses is defined either as ..... C is the heat capacity at constant pressure for the standard state (kJ ...
An ASABE Meeting Presentation Paper Number: 131594309

Gaseous emissions from agricultural biomass combustion: a prediction model Sébastien Fournel1,2, Bernard Marcos1, Stéphane Godbout2, Michèle Heitz1 1

Department of Chemical Engineering and Biotechnological Engineering, Faculty of Engineering, Université de Sherbrooke, 2500 boulevard de l’Université, Sherbrooke, QC, Canada. 2 Research and Development Institute for the Agri-Environment (IRDA), 2700 Einstein Street, Quebec City, QC, Canada.

Written for presentation at the 2013 ASABE Annual International Meeting Sponsored by ASABE Kansas City, Missouri July 21 – 24, 2013 Abstract. As the price of the fossil energy resources and the need to reduce the environmental impacts from energy use increase, biomass fuels have regained interest from Quebec’s agricultural sector. Producing and burning energy crops at the farm have become strategies to diversify incomes and decrease dependency to fossil fuels. However, the current absence of emission factors for solid fuel combustion does not allow a sustainable development for energy purposes. Besides, the variety of existing furnaces and biomasses complicates the establishment of such reference values. In order to quantify emissions (CO, CO2, NOx, SO2, CH4, NH3 and HCl) from on-farm combustion of different agricultural biomasses (short-rotation willow, switchgrass, reed canary grass, etc.), a prediction model was established based on the calculation of chemical equilibrium of reactive multicomponent systems. Under constant temperature and pressure, this technique has been judged as relevant for the prediction of product compositions considering inlet conditions in several operations and chemical processes, particularly gasification. The model was first established for wood gasification to be able to compare and validate its results with those of existing models from the literature using the same original data. The model was then adapted to biomass combustion and calibrated with recent results from combustion tests held in the province of Quebec. The preliminary results of the prediction model using data from past combustion experiments with wood, willow and switchgrass revealed good agreement between both measured and predicted values. Other simulation tests are required to increase accuracy of the model. Keywords. Biomass, combustion, gasification, gaseous emissions, prediction model, chemical equilibrium, Gibbs free energy.

Introduction As the price of the fossil energy resources and the need to reduce the environmental impacts from energy use increase (Demirbas, 2009; Kaltschmitt and Weber, 2006), biomass fuels have regained interest, especially from Quebec’s agricultural sector in order to develop production systems with lower energy expenses (Brodeur et al., 2008; Lease and Théberge, 2005). Producing and burning energy crops at the farm have become strategies to diversify incomes and decrease dependency on fossil fuels. However, the current absence of emission factors for solid fuel combustion does not allow a sustainable development for energy purposes (Talluto, 2009). Furthermore, the variety of existing furnaces and biomasses complicates the establishment of such reference values since previous studies (Obernberger et al., 2006; Villeneuve et al., 2012) have revealed that gaseous emissions from biomass combustion differ significantly according to the combustion technology used and the characteristics of the fuel burned (chemical composition, physical properties, etc.). From an experimental point of view, considering all the biomass possibilities would become a laborious and expensive work. To overcome this situation, thermodynamic equilibrium models can become useful engineering tools to assess how fuel characteristics influence the exit gas composition (Baratieri et al., 2008; Kalina, 2011; Melgar et al., 2007). Actually, when the chemical composition of biomass and the equilibrium temperature are specified, thermodynamic models can simply predict the resulting emissions (Ranzi et al, 2011). To achieve this, some of those models are based on minimization of the Gibbs free energy (Jarungthammachote and Dutta, 2008). This technique is mainly used for determining the chemical equilibrium composition of reactive multi-component closed systems under thermodynamic equilibrium (Néron et al., 2012). Therefore, a global minimum of the Gibbs free energy coincides with the stable equilibrium solution under constant temperature and pressure. The equilibrium problem is then solved as an optimization problem of a non-linear constrained system that must satisfy the restrictions of non-negative number of moles and mole balances (Rossi et al., 2011). Lagrange multiplier method is generally used to compute this constrained optimization problem (Baratieri et al., 2008; Jarungthammachote and Dutta, 2008). Even though this theoretical approach has some inherent limitations, it was judged as relevant for the prediction of product compositions in several operations and chemical processes as gasification (Altafini et al., 2003; Baratieri et al., 2008; Gautam, 2010; Jarungthammachote and Dutta, 2007, 2008; Kalina, 2011; Melgar et al., 2007; Néron et al., 2012; Rossi et al., 2009, 2011; Zainal et al., 2011) and combustion (de SouzaSantos, 2010). The model based on chemical equilibrium by minimization of the Gibbs free energy was first established for wood gasification to be able to compare and validate its results with those of existing models from the literature using the same original data. The model was then adapted to biomass combustion and calibrated with recent results from wood and agricultural biomass combustion tests held in the province of Quebec in the past few years.

Model development Gasification and combustion reactions To develop the model, the chemical formula of biomasses is defined either as CHyOzNa or CHyOzNaSbClc. The former corresponds to a woody biomass with negligible sulfur and chlorine contents and is implied in the global gasification reaction for simulation comparison with other gasification models as described later. The latter term characterizes a general biomass containing carbon, hydrogen, oxygen, nitrogen, sulfur and chlorine. It is utilized in the combustion reaction. Both gasification and combustion reactions (eqs. 1 and 2, respectively) can then be expressed as CHyOzNa + wH2O+ e(O2 + 3.76N2) = n1H2+ n2CH4 + n3CO + n4CO2 + n5H2O + n6N2

(1)

and

The authors are solely responsible for the content of this meeting presentation. The presentation does not necessarily reflect the official position of the American Society of Agricultural and Biological Engineers (ASABE), and its printing and distribution does not constitute an endorsement of views which may be expressed. Meeting presentations are not subject to the formal peer review process by ASABE editorial committees; therefore, they are not to be presented as refereed publications. Citation of this work should state that it is from an ASABE meeting paper. EXAMPLE: Author’s Last Name, Initials. 2013. Title of Presentation. ASABE Paper No. ---. St. Joseph, Mich.: ASABE. For information about securing permission to reprint or reproduce a meeting presentation, please contact ASABE at [email protected] or 269-932-7004 (2950 Niles Road, St. Joseph, MI 49085-9659 USA). 2013 ASABE Annual International Meeting Paper

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CHyOzNaSbClc + wH2O + e(O2 + 3.76N2) = n2CH4 + n3CO + n4CO2 + n5H2O + n6N2 + n7O2 + n8NO + n9NO2 + n10N2O + n11NH3 + n12SO2 + n13HCl,

(2)

where y, z, a, b and c are respectively the numbers of atoms of hydrogen (H), oxygen (O), nitrogen (N), sulfur (S) and chlorine (Cl) per atom of carbon (C) in the solid fuel, w and e are respectively the amount of moisture and dioxygen in air per kmol of feedstock and ni are the numbers of mole of the species i. Those species correspond to: 1. Dihydrogen (H2); 2. Methane (CH4); 3. Carbon monoxide (CO); 4. Carbon dioxide (CO2); 5. Water vapor (H2O); 6. Dinitrogen (N2); 7. Dioxygen (O2); 8. Nitrogen monoxide (NO); 9. Nitrogen dioxide (NO2), 10. Nitrous oxide (N2O); 11. Ammonia (NH3); 12. Sulfur dioxide (SO2); 13. Hydrogen chloride (HCl). They were identified as the main products from either solid fuel gasification or combustion. All inputs on the left-hand side of equations 1 and 2 are supposed entering the combustion system at 25°C. On the right-hand side, the stoichiometric coefficients ni are unknown and the model consists in evaluating the concentrations of the species to calculate them. Assumptions The resolution of the stoichiometric coefficients ni using a thermodynamic model was based on the following assumptions: 

The residence time is long enough to achieve thermodynamic equilibrium. This might not be true, yet the degree of error introduced by this assumption is acceptable and the applicability of this assumption is confirmed in literature (de Souza-Santos, 2010; Jenkins et al., 2011; Ragland and Bryden, 2011). The reaction system is then considered working at steady-state conditions with mass flows and average properties of each input and output stream remaining constant.



All carbon, nitrogen, sulphur and chlorine contents in biomass are converted into gaseous form. Mass balances on carbon and nitrogen revealed good agreement with this statement since less than 2.5wt% of both elements are found in ash (Godbout et al., 2012). Sulfur and chlorine are mainly present in ash (Obernberger et al., 2006); however their low content in biomass compared to other elements involves only a small error. An empirical factor to be included in the model could fix the problem.



All the gaseous products are assumed to behave as ideal gases. This leads to insignificant errors because gasification and combustion reactions are conducted at high temperature (> 700°C) and low pressure (1 atm) (Gautam, 2010).



The products taken into account in equations 1 and 2 are the main products formed during those processes (Jarungthammachote and Dutta, 2008; van Loo and Koppejan, 2008). Other gases such as hydrocarbons (CxHy), other than CH4, are assumed negligible.



Ash in biomass is assumed inert although it holds typically only for reactions less than 700°C. Agricultural biomasses contain silicon (Si) and potassium (K) as the major mineral content which lowers ash fusion temperature below 700°C whereas gasification and combustion processes occurs at temperatures higher than 700°C. Therefore, the relations derived in this study cannot be used

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effectively for biomass with high mineral content (Gautam, 2010). Minimization of Gibbs free energy The composition of the gas produced at thermodynamic equilibrium can be estimated using different approaches: kinetic or dynamic models (Gøbel et al., 2007; Ranzi et al, 2011), equilibrium constants (Gautam, 2010; Jarungthammachote and Dutta, 2007; Melgar et al., 2007; Zainal et al., 2001) or Gibbs energy minimization (Altafini et al., 2003; Baratieri et al., 2008; Jarungthammachote and Dutta, 2008; Kalina, 2011; Néron et al., 2012; Rossi et al., 2009, 2011). The key advantage of the latter is that it has a more general application with predictive capability and does not require the selection of appropriate chemical reactions or an extended set of data to train the model (Baratieri et al., 2008; Néron et al., 2012). The Gibbs energy minimization method is based on the assumption that the Gibbs energy (G) reaches a minimum value at thermodynamic equilibrium (Jarungthammachote and Dutta, 2008; Néron et al., 2012). Considering a closed chemical system with an arbitrary number of species present in one or several phases at uniform temperature (T) and pressure (P) (not necessarily constant) evolving from a non-equilibrium initial state to a closer-to-equilibrium final state and restricting the process to constant T and P, all irreversible process (occurring at constant T and P) evolve in the direction that causes a decrease of G. The equilibrium state of a closed system is the one for which G reaches a minimum with respect to all possible changes at the given T and P. The Gibbs energy minimization method, then, consists in writing an expression for G as a function of the number of moles of the species present and then finding the set of values for the mole number that minimizes this function, subject to the constraints of mass conservation and stoichiometry. Moreover, the expression for G can be extended for open systems, in which the number of moles of the species (ni) can vary because of mass exchange with the surroundings. In this case, it is necessary to introduce a chemical potential (i) that is a function of the ni moles of the different compounds (Baratieri et al., 2008): N

G   ni i .

(3)

i

If all gases are assumed as ideal gases at one atmosphere, i can be written as

i  G f○,i  RT ln yi  ,

(4)

where G f ,i is the standard Gibbs free energy of formation of species i (kJ kmol-1), R is the universal gas ○

constant (8.314 kJ kmol-1 K-1), T is the equilibrium temperature (K) and yi is the mole fraction of gas species i and the ratio of ni and the total number of moles of the reaction mixture (ntot). Substituting equation 4 into equation 3, G (kJ) becomes N N  n G   ni G f○,i   ni RT ln i i i  ntot

  . 

(5)

The next step is to find the values of ni which minimizes the objective function G subject to constraints on the allowable ni. The problem is then solved as an optimization problem of a non-linear constrained system that must satisfy the restrictions of mole balances and non-negative number of moles corresponding to the KarushKuhn-Tucker (KKT) conditions (Néron et al., 2012). Based on this principle, the Gibbs free energy minimization is generally solved by the Lagrange multiplier method (Koukkari and Pajarre, 2006). The first constraint of this problem is the elements conservation as follows: N

a n ij

i

 Aj

j = 1, 2, 3,…, k,

(6)

i

where aij is the number of atoms of the jth element in a mole of the ith species and Aj is defined as the total number of atoms of the jth element in the reaction mixture. The product of the Lagrange multipliers (j) by the elemental balance constraints is subtracted from G in the Lagrangian function (L), defined as k  N  L  G    j   aij ni  A j  , j  i 

(7)

and the partial derivatives are set equal to zero in order to find the minimum point: 2013 ASABE Annual International Meeting Paper

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 L     0 .  n  i

(8)

Equation 8 produced a matrix that has i rows, which are solved simultaneously with the constraints defined in equation 6. The second constraint enlightens that the solutions ni have to be real and positive numbers so that 0 ≤ ni ≤ ntot.

(9)

Thermodynamic properties In order to determine G f ,i , the values of the standard enthalpy of formation (  H ○

o f ,i

, kJ kmol-1) and standard

o

entropy of formation (  S f , i , kJ kmol-1 K-1) at the equilibrium temperature are needed because ○ G f○,i  H ○ f ,i  TS f ,i .

(10)

Both H f ,i and S f ,i can be computed by the following definitions of enthalpy and entropy changes occurring ○



when a compound is formed stoichiometrically from its stable elements at T:

 H

○ H ○ f (T )  H comp (T ) 

l elem

○ l

(T )

(11)

(T ) ,

(12)

l

and

 S

○ S ○ f (T )  S comp (T ) 

l elem

l

○ l





where l is the stoichiometric coefficient for element l. Enthalpy ( H , kJ kmol-1) and entropy ( S , kJ kmol-1 K1

) in equations 11 and 12 as much for the compound as for its elements are defined by T



H ○(T )  H ○ f (T0 )  C p T

(13)

T0

and T

S ○(T )  S ○ f (T0 ) 

Cp

T

T ,

(14)

T0

where C p is the heat capacity at constant pressure for the standard state (kJ kmol-1 K-1) and T0 is the inlet temperature of reactants (K). Besides, it is important to note that the arbitrary base selected for calculating the enthalpy value is zero at 25°C in the case of reference elements and thus H ○ f (298.15) equals zero for all reference elements. Since heat capacity, enthalpy and entropy are functions of temperature, it would be easier for the model computation that those properties are described in terms of polynomial equations as follows:

Cp R

H ○ f (T0 ) RT0

 a1  a2T  a3T 2  a4T 3  a5T 4 , 2

3

(15) 4

aT aT aT aT b  a1  2 0  3 0  4 0  5 0  1 2 3 4 5 T0

(16)

and

S ○ f (T0 ) R

2

 a1 ln(T )  a2T0 

2013 ASABE Annual International Meeting Paper

3

4

a3T0 aT aT  4 0  5 0  b2 . 2 3 4

(17)

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These equations were established by the NASA technical memorandum 4513 (McBride et al., 1993). All coefficients for equations 15 to 17 can also be found in this report. Energy balance The energy balance is introduced as an energy constraint when the studied system can exchange heat with the environment. In this case, the equilibrium temperature differs from the initial temperature (Néron et al., 2012). If the heat duty is known, the equilibrium temperature can be obtained from the first law of thermodynamics for the combustion process:

Qloss 

n H

r  react

r

r

(T0 ) 

n

p  prod

p

H p (T )  H ,

(18)

where Qloss is the heat loss from the combustion process (kJ) and H r and H p are respectively the enthalpies of each reactant and each product at the specified temperatures (kJ kmol-1) . Both enthalpies can be calculated by equation 13. The enthalpy of formation of a solid fuel can be calculated by the equation developed by de Souza-Santos (2010) as follows

H ○ f , fuel  LHV 

n

p  prod

p

H○ f ,p ,

(19)



where H f , p is the enthalpy of formation of product p under complete combustion of the solid fuel (kJ kmol-1) and LHV is the lower heating value of the biomass (kJ kmol-1) . Solver The thermodynamic equilibrium model using Gibbs free energy minimization approach as described before has been developed in Matlab environment. The code first requires entering the necessary input values such as the characterization of biomass and the initial temperature. The nonlinear programming model, comprising the objective function to be minimized (eq. 5) and the constraints (eq. 6), is solved by using the fmincon function contained in Matlab. The fmincon function applies the interior-point algorithm to solve nonlinear programming problems. In different steps, the algorithm obtains Lagrange multipliers by approximately solving the KKT conditions. A detailed description of the use of the fmincon function in Matlab can be found elsewhere (MathWorks, 2013). For calculating the equilibrium temperature, the initial temperature is assumed and used to perform the minimization of Gibbs free energy. Knowing the predicted gas composition, the energy balance is calculated. Depending on the sign of H in equation 18, the reaction temperature is adjusted. The minimization is hence solved iteratively until H becomes zero. The complete calculation procedure is illustrated in figure 1.

START

INPUT: Biomass, CHyOzNbScCld Moisture content, MC Air/biomass ratio and flows Initial temperature, T0 Initial estimate of ni, n0

MODEL CALCULATION: ,

,

,

,

ni by Gibbs free energy minimization Constraints satisfied? H by energy balance Adjusted T

NO

END

YES

abs(H)