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Show COMBUSTION MEASUREMENTS IN AN INDUSTRIAL GAS FIRED ALUMINUM RECYCLING FURNACE 8 I^L=(- 1 4.76a-1 (3) Assuming an error in the measurements of a and b, given by ea and eb, the expression for the total error in the concentration of oxygen or carbon dioxide, e„ is given by < • & " (4) where F is the functional dependence of both concentrations on a and b as given by Eqs. (2) and (3). Evaluating the partial derivatives of Eqs. (2) and (3) to be used in Eq. (4) one obtains d[02\dry _ 8.52-3.761? da (b +4.16a-\)2 %C°iL'd ry -_ 4.16 da (b + 4.16a -1)' and and d[o2] dry _ 3.16a + 1 db (b + 4.16a-\f jg^L _ -i db (b + 4.16a-\y (5) (6) The fractional errors, e, given by evaluating Eq. (4) using Eqs. (5) and (6) and the concentrations of oxygen and carbon dioxide [Eqs. (2) and (3)] are then en = [o.l dry 1 6 +4.76a-1 8.52-3.760 a + b-2 el + 3.16a + 1 a + b-2 -\Vi (7) -co, 1 'CO, [co2] dry b + 4.16a-\ -\{-4.16?e] + (-l)2^ (8) Variations in the concentrations of oxygen and carbon dioxide in the products of combustion [Eqs. (2) and (3)] and the accompanying relative error in each measurement [given by Eqs. (7) and (8), respectively] assuming a 5 % error in air and oxygen flow rates (ea and eb = 0.05) are shown in Figs. 4 and 5, respectively, for oxygen-enriched combustion (50% O2/50% air). The analysis reveals that an error of 5% in both air and oxygen flow rates can lead to errors in 0 2 concentration (dry) of up to 200%, depending on stoichiometry. Moreover, the 0 2 and C O z concentrations measured are consistent with respect to each other, given the possibility of an experimental error in measuring the supply flow rates of oxygen and air. For the case of the air/fuel firing, assuming that the methane and oxygen flow rates were correct, the measured 0 2 concentration of 2.2 vol% would correspond to an air flow of 157,000 SCFH (an error of less than 1 0 % in the reported operating setting of 174,000 SCFH), which would make the overall stoichiometry 2.21 with a corresponding C O , concentration of 10.5 vol% (11 vol% was the measured value). |