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Chöông 2 Xöû lyù döõ kieän ñoäng hoïc Chapter 2 Interpretation of Batch Reactor Data A rate equation characterizes the rate of reaction Its form may either be suggested by theoretical considerations o[.]
CHAPTER INTERPRETATION OF BATCH REACTOR DATA REACTION RATE EQUATION A rate equation characterizes the rate of reaction Its form may either be suggested by theoretical considerations or simply be the result of an empirical curve-fitting procedure The value of the constants of the equation can only be found by experiment; predictive methods are inadequate at present The determination of the rate equation is usually a two-step procedure: the concentration dependency is found at fixed temperature the temperature dependence of the rate constants is found, yielding the complete rate equation MONITORING THE BATCH REACTOR By following the concentration of a given component By following the change in some physical property of the fluid, such as the electrical conductivity or refractive index By following the change in total pressure of a constant-volume system By following the change in volume of a constant-pressure system ANALYZING KINETIC DATA Integral methods The integral method is easy to use and is recommended when testing specific mechanisms, or relatively simple rate expressions, or when the data are so scattered that we cannot reliably find the derivatives needed in the differential method The integral method can only test this or that particular mechanism or rate form Differential methods : More complicated situations but requires more accurate or larger amounts of data.; the differential method can be used to develop or build up a rate equation to fit the data 2.1 CONSTANT-VOLUME BATCH REACTOR constant-density reaction system V = const dN i d(C i V ) C i dV V dC i dC i ri V dt V dt V dt dt dpi ri RT dt (2.1) (2.2) ANALYSIS OF TOTAL PRESSURE DATA OBTAINED IN A CONSTANT-VOLUME SYSTEM p A N A N A0 a x N A0 a N N0 CA RT V V V n V Or a p A C A RT p A0 (P P0 ) n For R p R C R RT p R0 r (P P0 ) n (2.3) (2.4) 2.1.1 INTEGRAL METHOD OF ANALYSIS OF DATA General Procedure 1) Assume the rate equation dC A rA kf(C) dt dC A kdt f(C A ) CA t dC A F (C A ) k dt kt 2) Intergrate f(C A ) C A0 3) Calculate F(CA) by experimental data 4) Plot F(CA) vs t 5) If the fit is unsatisfactory, another rate HOW FIT OR SATISFY (1) IRREVERSIBLE UNIMOLECULAR-TYPE FIRST-ORDER REACTIONS A products dC A k CA dt CA t dC A k dt CA C A0 CA ln kt C A0 CONVERSION, XA N A N A0 (1 X A ) N A N A0 (1 X A ) CA C A0 (1 X A ) V V dC A C A0 dX A XA t dX A k(1 X A ) dt dX A k dt ln (1 X A ) kt 1 XA 0