The goal of this paper is to use geometrical theory of nonlinear partial differential equations and singularities theory to obtain the general scheme for constructing an optimal control for fronts of petroleum displacement by active reagent. We illustrate our geometric approach to evolutionary models of petroleum deposits. Original simulation methods for the frontal displacement of oil by water and solutions of active reagents in porous medium of oilfield reservoirs with and without capillary forces has been developed. For simplicity and clarity of presentation the only one-dimensional models of fluid filtration between parallel batteries of production and injection wells (Buckley-Leverett and Rapoport-Liss models) has been considered. The model for oil displacement by solutions of active reagents in hot water has been also analyzed. The proposed results are generalized for two- and three-dimensional filtration models in reservoir engineering using vertical and horizontal wells, which greatly facilitates the statement and development of simulation and optimal control methods for reservoir engineering in general.