Combustion time, defined as “total time for burnout of the particle” (Tillman, 1991) can be calculated with the following formula:

(5.19)

where:

tbo — total burnout of the particle td — time for heating and drying tp — time for solid particle pyrolysis and tco — time for char oxidation.

Table 5.5. Some relevant gas-phase homogenous reactions (Haseli et al., 2011).

cH5o X exP 10-45 [s-1]

K = 2.78 x 103exp(-1510/Tg) [kmol-1 m3 s-1] K* = 0.0265exp(3968/Tg) [-]

Source Reaction rate expression Kinetic parameters

Table 5.6. Thermochemical data for cellulose combustion (Di Blasi, 1993; Antal and Varhegyi, 1995; Branca and Di Blasi, 2004; Parker and LeVan, 1989). Activation Frequency Reaction Reaction energy [kJ/mol] factor [s-1 ] enthalpy [kJ/g] Product Reference Charring 110 6.7 x < 105 -1.0 Char formed Di Blasi (1993) Volatilization 198 3.2 > <1014 0.3 Volatiles Antal and formed Varhegyi (1995) Char oxidation 183 1.4 x < 1011 -33 Char Branca and Di oxidized Blasi (2004) Volatile oxidation 188 2.6 x <1013 -14 Volatiles Parker and oxidized LeVan (1989)

The evaluation of combustion times can be done also with single particle combustion models. Besides important effort in the research of modeling of single particle combustion has been done (Yang et al., 2008) and some models evaluate also particle burnout (Saastamoinen et al.,

2010) . The combustion rate or burning rate can be considered as the mass of fuel consumed per unit of time. This influences heat release and so this parameter is important for the design of the combustion system. Typical design heat release rates, expressed per unit grate area, are 2-4MWt/m2 (Brown, 2011), even though some fluidized beds can reach 10MWt/m2 (Jenkins, 1998). Combustion rates can be calculated starting from some thermochemical data, such as those shown for cellulose in Table 5.6 (Sullivan and Ball, 2012).

The reaction of charring starts with hydrolysis of cellulose and then continues with dehy­dration, decarbonylation, decarboxylation cross-linking and aromatization reactions to produce primary char.

The volatilization reactions of cellulose can be thought as the formation of levoglucosan, while char oxidation and volatile oxidation complete the combustion process. As has been previously discussed the more important reaction from the point of view of combustion velocity control is char oxidation influenced by oxygen penetration inside the particle. This is why for practical and engineering purposes the most adequate formula to express the burning rate is that proposed by Kuo (1998). Kuo’s method is based on the assumption that solid fuel bed-burning rate is proportional to the oxygen consumption rate as air flows through the fuel bed.

(5.23)

where:

mbio = biomass mass flow [kg/h]

qLHV = lower heating value of biomass [kJ/kg]

mfuel = auxiliary fuel mass flow [kg/h]

qfuel = heating value of auxiliary fuel [kJ/kg]

mpa = primary air mass flow [kg/h]

hpa = specific enthalpy of primary air [kJ/kg]

msa = secondary air mass flow [kJ/h]

hsa = specific enthalpy of secondary air [kJ/kg]

tnfwat = boiler feed water mass flow [kg/h]

hfwat = specific enthalpy of boiler feed water [kJ/kg]

mst = steam mass flow [kg/h]

hst = specific enthalpy of steam [kJ/kg]

tnfgas = exhaust gas mass flow [kg/h]

hfgas = specific enthalpy of exhaust gas [kJ/kg]

niash = ashes mass flow [kg/h]

hash = specific enthalpy of ashes [kJ/kg]

m curb, ioSS = unbumed carbon mass flow [kg/h] qcorb = heating value of unburned carbon [kJ/kg]

Qloss = heat loss outwards from the furnace/boiler system [kJ/h].

mbio = (pairMB/Mair) (Fpa + Fsa)/(4-76 (1. + є) rof)

where:

Fpa = primary air flow rate [Nm3/h]

Fsa = secondary air flow rate [Nm3/h] pair = air density [kg/m3]

MB = molecular weight of biomass [-]

Mair = molecular weight of air [-] є = excess air ratio [-]

rf = stoichiometric oxygen-to-fuel mole ratio [-].

5.2 COMBUSTORS