OCR Text |
Show 5. fraction of burners out of service, degree of air staging; weight-fraction of nitrogen bound in the fuel, and 6. degree of ammonia injection (or other amoniacal reagent) for the case of selective catalytic reduction (SCR) or selective non-catalytic reduction (SNCR). Previous work1 gives the theoretical explicit function of NOx in response to the above variables. The relation is c x H^OJ = c0+^ + c2y + c3\n{jJ + ^,-r + llcjxjy + llcicxic 0) A | A j k where the brackets [ ] denote volume concentration of the enclosed species; x is a dummy variable for any menu item in lines 4, 5, and 6; and /, j, and k are indices for the dummy variables. From this general equation, one may formulate the N O x relation for a particular system of interest. For example, suppose a system uses • flue-gas recirculation (line 3), • some fraction of landfill gas in a landfill gas/natural gas fuel blend, x42 (line 4, item 2), • some mass flow of injected water, x43 (line 4, item 3), and • some fraction of burners out of service, x5\ (line 5, item 1). Then from Equation (1), the specific NOx relation is ln[NOJ = c0+^ + c2^+c3ln(yw) + c42^- + c43^ + c51Jc51i)/ (2) where c0 through c5i are the respective constants. The equation is linear in the parameters c0, ch etc. Therefore, linear regression unambiguously determines its coefficients. This makes the models amenable to use with statistically designed experiments, particularly response surface methods2 (RSM). In fact, with the appropriate variable transformations (e.g., ln[NOx], \n(yw), 1/A, ...) factorial experimental designs4'5'7 regress the coefficients directly. This report refers to this semi-empirical approach as the modified response surface method ( M R S M ) . That is, M R S M comprises a theoretically derived equation form in conjunction with empirically determined coefficients. Equation (2) differs from the general response surface method (RSM). RSM would comprise all possible variables, binary interactions, and pure quadratic terms. The M R S M case, Equation (2), comprises six variables ( A , y, yw, JC42, x43, x5i) and seven terms (c0, ch C2, Ci, c42, c43, c5i). R S M would require 28 terms (c0 + 6 variable terms + 15 variable interaction terms + 6 quadratic terms). Derivation Comments In general, those factors that directly affect temperature interact with 1/A; factors that affect oxygen concentration interact with y, and w^-order unimolecular kinetics are directly proportional to ln[NOx]. Reference 1 provides more extensive derivation details. But briefly, the model terms arise from kinetic relations of the form 2 |