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“…In this section, we argue that the description of the processes of transport from the inner to the outer phase, reaction in the outer phase and transport back to the inner phase, together, takes equations identical with those for a (possibly different) set of first-order reactions solely among inner-phase species and independent of additional details of the mixing. This result is similar in spirit to Wei's (1962) extension of the Thiele-Zeldovitch problem. He shows that diffusion into a catalyst followed by a set of true isothermal first-order reactions and diffusive exit from the catalyst has a reduced description as an apparent set of first-order reactions.…”

confidence: 80%

“…(2a) becomes immediate ifr only depends on C. This assumption is due to the fact that an expression for the rate of a catalytic reaction can be given as a function of the sole mobile fluid phase concentration (Wei, 1962;Shinnar and Rumschitzki, 1989). Then, Eq.…”

confidence: 97%

“…The penultimate integral in Equation (10) integrates a linear transformation (which, at steady state, is a rate constant matrix) acting on the inner phase concentration vector (actually, cf., Appendix B, only on its components that correspond to transferring species). It will turn out that at steady state (where the initial conditions no longer appear and where s = 0), this term will represent the outer phase reactions in the final equations; (in the spirit of Wei, 1962) it will look as if a set of first order reactions comprised of true inner phase reactions ( B ) and truly-outer-phase-but-apparentlyinner-phase reactions (whose rate constant matrix is given by R(s = 0)) is taking place, at least in this integral sense for all 7. Moreover, for a given chemistry, this R ( s ) is the same for all reactors in the class outlined under Assumptions; this will lead to a scaling procedure for the Laplace transformed dynamics amongst reactors in that class.…”

confidence: 99%