Numerical Solution of the Direct Problem in Chemical Kinetics

Numerical Solution of the Direct Problem in Chemical Kinetics 

As an example, let s calculate a kinetic curve for an intermediate in a consecutive reaction where the second step is of the second order  

Analytical solution of this problem was discussed in the Sect. 1.3.2, so we can compare numerically- and analytically-obtained results. 

The way of using Given/Odesolve solver and the results of its work are shown in Fig. 3.1. The following values were used initial concentration A = 0.5 M, 

Korobov and V.F. Ochkov, Chemical Kinetics with Mathcad and Maple, DOI 10.1007/978-3-7091-0531-3 3, Springer-VerlagAVien 2011 

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Numerical Solution of the Direct Problem in Chemical Kinetics Table 3.1 Numerical methods for solving ordinary differential equations in Maple suite ... 

The command dsolve of the Maple system was previously discussed as a method of analytical solution of the direct problem in chemical kinetics. This command also can be used for a numerical solving of ODEs or their sets. In this case one should use the following syntax ... 

Takeuchi et al. 7 reported a membrane reactor as a reaction system that provides higher productivity and lower separation cost in chemical reaction processes. In this paper, packed bed catalytic membrane reactor with palladium membrane for SMR reaction has been discussed. The numerical model consists of a full set of partial differential equations derived from conservation of mass, momentum, heat, and chemical species, respectively, with chemical kinetics and appropriate boundary conditions for the problem. The solution of this system was obtained by computational fluid dynamics (CFD). To perform CFD calculations, a commercial solver FLUENT has been used, and the selective permeation through the membrane has been modeled by user-defined functions. The CFD simulation results exhibited the flow distribution in the reactor by inserting a membrane protection tube, in addition to the temperature and concentration distribution in the axial and radial directions in the reactor, as reported in the membrane reactor numerical simulation. On the basis of the simulation results, effects of the flow distribution, concentration polarization, and mass transfer in the packed bed have been evaluated to design a membrane reactor system. 

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