Simulation of chemical reactors using the least-squares spectral element method

In this work, we address the issue of solving detailed mathematical models of chemical reactors by using a method based on the least-squares formulation. The article presents the resolution of an axial dispersion model, and makes an analysis of relevant issues that are involved when solving this type of models using the least-squares spectral element method. A central issue is that C1 elements are required if no additional variables are to be defined. We analyze two different alternatives for achieving global first-order differentiability without increasing the number of variables: using C1 Hermite elements and imposing the constraint weakly using C0 elements.We include numerical examples for the case of the transformation of natural gas into synthesis gas. The least-squares spectral element method showed no major difficulties in solving the model equations of the model, in spite of the steep variations obtained. We conclude that the optimal choice for achieving global first-order differentiability depends on the problem and the objectives of the calculation. For the model presented here, the Hermite approach gave the fastest results, although it required a high condition number of the problem matrix.