Application of mathematical methods for condition monitoring of oil and gas facilities

Abstract

Contaminated areas of anthropogenic origin, particularly surface and underground waters as well as soils, have been
analyzed. The mathematical models of diffusion processes, based on the use of two- and three-dimensional diffusion equations
with a wide range of boundary and initial conditions, have been suggested. It is determined that exact solutions prohibit studying
of the peculiarities of their behavior, depending on the type of boundary conditions; therefore we suggest using numerical
solutions. The difference schemes of the method of variable directions for numerical realization of two-dimensional models in
different frames, accounting for environmental heterogeneity of matter distribution have been presented. The schemes allow to
measure concentration of substances in real objects through building of functions, modeling various boundary conditions. A
software complex for their implementation has been devised and the test findings as well as their analysis have been presented.
To model processes which parameters depend on three spatial coordinates, we have suggested numerical schemes for
implementing three-dimensional models that are absolutely stable and have the second order of accuracy at all spatial
coordinates.