Chemical Engineering - Industrial Organic Chemistry

Rate temperature plot

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1 Rate-Temperature plot for single reaction We have the plot of the intrinsic reaction rate as a function of temperature, with specied conversionor iso-conversion curves. Since, for any moment in time and any species, it holds that: nj= n j;0+  jn k;0 according to the full selectivity assumption, meaning only the specied re- action will happen with no side reactions. 1.1 Activities Evaluation The main advantage is that now, the partial pressures are: pj= y jP =n jP ln lP =n j;0+  jn k;0n 0+ n k;0P =y j;0+  jy k;01 + y k;0P with=P l l. The activities follow, for the gas phase: aj=^ fj( T ; P;y)f r j= ^ j( T ; P;y)y jPP r= ^ j( T ; P;y)PP ry j;0+  jy k;01 + y k;0 with^ fj( T ; P;y)being the fugacity in the real mixture, and the respective fugacity coecient^ j( T ; P;y)is evaluated by well known expressions1 de- pending on the given equation of state. 1.2 Rate-Temperature Function Inserting the partial pressures or activities within a rate expression, it is possible to parametrize it as a function of the conversion, since: R(T ; P;a(T ; P;y))!R(T ; P;y())!R(T ; P; ) with such function usually depicted with the pressure as a value parameter, orR(T ; ;P)in the rate-temperature plot. Moreover, this function is equal to zero at the equilibrium conversion eq and is maximum at a specic value(T ;  ). This is because, at= 0only the direct reaction occurs, thus leading a monotone increasing function of temperature. If >0, then the inverse reaction, as a decreasing function of the temperature, is summed to the direct reaction contribution.This sum leads a convex function with a specic set of temperature- conversion maximal points, or path, which is the optimal path to be followed by the reactor. However, it is almost always not possible to follow such path due to design constraints. One example is heat production and removal, for which the temperature is increased or decreased by the reaction enthalpy.1 Hu, J.et al.(2008). Some useful expressions for deriving component fugacity coe- cients from mixture fugacity coecient. Fluid Phase Equilibria, 268(1-2), 713 1 1.3 The Deacon Reaction We have an example of the Deacon reaction2 : 4 HCl + O2! 2 Cl 2+ 2 H 2O The rate expressionR(T ; P;y())is taken from existing literature3 , as- suming Langmuir-Hinshelwood type mechanism of surface reaction with Per- fect Gas equation of state, which reads: R(T ; P;y()) =k 1 +K 1p HCl+ K 2p1 =2 O2+ K 3p Cl2 3 p2 HClp1 =2 O2p Cl2p H2OK eq( T)! with the partial pressures evaluated as in the previous section. All the kinetic and equilibrium constants are reported in the reference of footnote 3.Once the molar fractions are expressed within the conversion, the rate- temperature plot is drawn:Figure 1: Rate-Temperature plot of the Deacon reaction, showing the pre- dicted behavior of convexity at xed conversion values.2 López, N., Gómez-Segura, J., Marín, R. P., & Pérez-Ramírez, J. (2008). Mechanism of HCl oxidation (Deacon process) over RuO2. Journal of Catalysis, 255(1), 29-39.3Till, Z., Varga, T., Réti, J., & Chovàn, T. (2017). Optimization Strategies in a Fixed- Bed Reactor for HCl Oxidation. Industrial & Engineering Chemistry Research, 56(18), 5352-5359. 2 Knowing the location of the maxima at each conversion, it is possible to evaluate the optimal value(T ;  ), as well as the equilibrium conversion for eacht temperature:Figure 2: Conversion-Temperature plot of the Deacon reaction, showing the optimal behavior of a reactor operating close ot maximum rate. However, reactor congurations bound by design constraints only approach, not lying on, the maximum rate path. 3