Mathematical Modeling of Isotermal Plug Flow Reactor with Consecutive Reaction Taking into Account the Catalyst Deactivation

Background. Mathematical modeling of continuous chemical-technological processes in non-stationary conditions of their implementation is an urgent problem. Solving specific problem numerically on a computer can only provide a formal adequacy of the model to the original. Consequently, the analytical solutions have undeniable advantages over numerical solutions. In the case of heterogeneous catalysis, deactivation of solid catalyst (Kt) takes place with a reduction of the process selectivity, which leads to economic losses. Therefore, the rational (the maximum-beneficial) catalyst lifetime ]{theta _{max }} > > 1] is the essential part of the problem of industrial Kt selection. Objective. The aim of this study is an analytic solution of the problem of operating mode description of the isothermal system “PFR (τL) (τL) + reaction A1−→−−−−−Kt,kd1k01,n1=1α2A2−→−−−−−Kt,kd2k02,n2=1α3A3 A1→Kt,kd1k01,n1=1α2A2→Kt,kd2k02,n2=1α3A3 + Kt (kd(i)) (kd(i)) ” under influence of destabilizing factor of deactivation Kt and calculation of rational time θmax=τmax/τL θmax=τmax/τL its exploitation. Methods. The modified mathematical model for the calculation of influence deactivation of Kt on the system operation mode is used. Distinctive features of the model are: reactor has a variable length at a constant flow rate and has equal initial and boundary conditions. Results. The relative deviations |εη2|?kd1τ |εη2|?kd1τ of yield of product A2 A2 and εs2?kd1τ εs2?kd1τ of the selectivity for conditions of the deactivation of industrial Kt in the linear approximation analytically are calculated. It was found that the magnitudes of εη2 εη2 and εs2 εs2 are determined by the relation γd/γ0k γd/γ0k of the simplex γd=kd2/kd1 γd=kd2/kd1 of rate constants of Kt deactivation and of the simplex γ0k=k01/k02 γ0k=k01/k02 of stages rate constants. Conclusions. It is proved that with respect to the yield of A2 A2 the self-regulation effect (εη2=0) (εη2=0) of mode takes place. Nomogram for determining of 1