Modeling of Complex Reaction Systems

Abstract

Steam pyrolysis of ethane and naphtha is an important chemical bulk process. It produces ethylene and propylene, which are important base chemicals. In order to be competitive, crackers have to be operated at near optimal conditions. Hence, a simulation program of the process, particularly of the pyrolysis is very helpful. KTI uses and licenses such a program called SPYRO*. Development of this program has started over 20 years ago. Consequently, it uses a closed model. It has been the objective of this study to investigate the feasibility of the development of an open version of SPYRO. Here open means that the equations are written in residual form .This enhances the flexibility of the program very much. For our studies we have used the model of Froment for ethane cracking because the documentation to make an open SPYRO model was insufficient. This Froment model has been modified as to improve the modeling of the bends. It has been checked, whether the solution of this model would pose any problems. It was found that the index might become more than 1 during integration. As yet no sound physical explanation has been found for this phenomena. It also follows from investigation of the index that a start-up problem of the numerical integration exists for the original set of differential equations. We have found a more elegant method to circumvent this problem than Froment. Moreover, we were able to solve the set of equations for bad initial conditions (equal to the boundary conditions). The ordinary differential equations of the model are turned into algebraic equations using orthogonal collocation on finite elements. This allows the model to be solved with an equation solver. The results were compared with various commercial numerical integrators. Excellent agreement was found for limited numbers of sections and collocation points. The speed of solution of the linearized set of modal equations depends on the size, the sparsity and structure of the Jacobian. The latter has an enormous effect on the fill-in of the L and U decomposition matrices. We found a very satisfying structure by modification of the equations and proper arrangement in the Jacobian. On the basis of the above results we may draw the following conclusions regarding the feasibility of the development of an Open SPYRO model. Unfortunately we had to use a simple model of Froment rather than the SPYRO equations themselves. Nevertheless, we have concluded that such a development is feasible. Within a reasonable time an accurate solution will be found even with bad starting values. The computation time can be further reduced with a smart initialization procedure.