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This paper deals with a phenomenological model for methanol conversion to olefins. A system of linear independent reactions is built from the global reaction of methanol transformation. The mechanism of reaction, a development based on carbenoid intermediates of the above set of chemical reactions, has 27 reactions and 18 molecular species. The kinetic parameters identified using nonlinear optimization techniques, and the model predictions, agree satisfactorily with experimental data and data available in the literature.

A nested non-linear multigrid algorithm is developed to solve the Navier-Stokes equations which describe the steady incompressible flow past a sphere. The vorticity-streamfunction formulation of the Navier-Stokes equations is chosen. The continuous operators are discretized by an upwind finite difference scheme. Several algorithms are tested as smoothing steps. The multigrid method itself provides only a first-order-accurate solution. To obtain at least second-order accuracy, a defect correction iteration is used as outer iteration. Results are reported for Re=50, 100, 400 and 1OOO.

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