One-dimensional models of frontal displacement of petroleum by active reagents are considered. These models are described by nonlinear systems of two first order partial differential equations — so called Jacobi systems (see Lychagin (1992); Kushner, Lychagin, Rubtsov (2007)). This article can be considered as a continuation of our work on the application of differential geometric methods in control theory the development of oil fields (see Akhmetzianov, Kushner, Lychagin (2013,-) and Kushner, Lychagin, Rubtsov (2007); Lychagin (1992, 1993)).