For the simulation and optimization of large scale chemical processes, the overall computing time is often dominated by the time needed to solve a large sparse system of linear equations. A parallel frontal solver can be used to significantly reduce the wallclock time required to solve these linear equation systems using parallel/vector supercomputers. This is done by exploiting both multiprocessing and vector processing, using a multifrontal-type approach in which frontal elimination is used for the partial factorization of each front. However, the algorithm is based on a bordered block-diagonal matrix form and thus its performance depends on the extent to which the matrix can be reordered to this form. Various approaches to achieving this ordering are discussed here. The performance of these different matrix reordering strategies for achieving the bordered block-diagonal form is then considered. Results, including a visualization of the different matrix orderings on one problem, are presented for several large scale process engineering problems.