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 specified conversionξ or iso-conversion curves. Since, for any moment in time and any species, it holds that: nj =nj,0 +νjξnk,0 according to the full selectivity assumption, meaning only the specified re- action will happen with no side reactions. 1.1 Activities Evaluation The main advantage is that now, the partial pressures are: pj =yjP = nj∑ lnl P = nj,0 +νjξnk,0 n0 +δξn k,0 P = yj,0 +νjξyk,0 1 +δξy k,0 P with δ = ∑ lνl. The activities follow, for the gas phase: aj = ˆfj(T,P, y) f r j = ˆφj(T,P, y)yjP Pr = ˆφj(T,P, y)P Pr yj,0 +νjξyk,0 1 +δξy k,0 with ˆfj(T,P, y) being the fugacity in the real mixture, and the respective fugacity coefficient ˆφj(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(ξ))→R(T,P,ξ ) with such function usually depicted with the pressure as a value parameter, or R(T,ξ ;P ) in the rate-temperature plot. Moreover, this function is equal to zero at the equilibrium conversionξeq and is maximum at a specific value(T ∗,ξ ∗). This is because, atξ = 0 only the direct reaction occurs, thus leading a monotone increasing function of temperature. Ifξ >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 specific 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…