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Show d (NO) k,(O)(N2 + k2(N)(02) dt (4) d (N) k,(O)(N2) dt (5) dd(Nt ) ° (N) k,(O)(N2) k2(02) (6) d(NO) dt 2k, (Keqo(02» '/2(N2) (7) dxno 2 k,Kpo dt AT p1/2 (X02) 112 (XN2) (8) In equation (8), R = 32.054 at~cm3/grmole ok and T is expressed in ok. >Y.tarteney expressed k, as 7E + 13 exp(-38000!T). 16he value of Kp can be obtained from the JANAF tables and no~e that K po K ~ eqo (RT)~ Values of X02 and XN2 can be obtained from graphics similar to figure 10. In this figure equilibrium concentrations of NO,N2, 02 and H20 are presented for different temperatures using natural gas and regular air with 0% excess air. These values were calculated using the chemical equilibrium computer program. Many authors have added to the original reactions of the Zeldovich mechanism, one being [N] + [OH] NO + [H[ (R4) k-4 The contribution of this reaction must be small because the reaetmg species are both radicals which are present in very small quantities. The set of reactions R1, R2 and R4 is known as the extended Zeldovich mechanism. Figure 11 presents values of the rate of NO calculated with equation (8) for different flame temperatures. Note that this is plotted on loglog scale. Using equation(8) for a given set of conditions and knowing the equilibrium concentration of NO in mole fraction at those conditions, the time it will take for NO to reach equilibrium can be calculated using: XNO teq ( d~o) dt Figure 9 gives results of these values for different flame temperatures using regular air and 193 0- Q) !!!.. Q) E i= E :I 4 g 3 '3 CT 2 w 1 '0 OJ 0 0 -l -1 -2 -3 -4 1.5 2.5 Birmingham Natural Gas 0% Excess Air 21 % Oxygen in Air Temperature (F) (thousands) 3.5 4.5 FIGURE 9. TIME FOR NO TO REACH EQUILIBRIUM VS TEMPERATURE c: .2 t> as It Q) (5 ~ '0 OJ S -1 -2 -3 -4 -5 Birmingham Natural Gas 0% Excess Air 21 % Oxygen in Air -7~ ____ ~ ____ ~ ______ ~ ____ ~ ____ -L ____ ~ ____ --l 1.5 2.5 3.5 Flame Temperature (F) (thousands) 4.5 FIGURE 10. EQUILIBRIUM COMPOSITION OF PRODUCTS OF COMBUSTION natural gas with 0% excess air. Values of ~O are taken from figure 10 and values of the rate of NO formation from figure 11. The actual residence time represents the time that the combustion gases spend in the furnace. The time calculated using equation 9, the equilibrium time, is usually higher than the actual residence time. Thus, the actual NO concentration is normally smaller than the one predicted by equilibrium calculations. In estimating the actual residence time the combustion gases spend in a specific furnace, one would need to know the variation of temperature in the furnace with time and in space. One does know that the temperature of the gases varies from a high, which is the peak temperature, to a low, which is the temperature at which the flue gases leave the furnace. In order to accurately |