Keyword: «computational experiment»

The improvement of the computer modeling teaching technique assumes the development of physical sys-tems simple computer models. In this article the author suggests the Visual Basic Application macroses which allow to study by method of computer modeling: 1) forced swings of a spring pendulum; 2) chaotic swings of Duffing’s pendulum; 3) Van-der-Pole’s auto oscillations; 4) Lorenz’s attractor; 5) electrical oscilla-tions in oscillatory circuit. The developed programs provide series of the computational experiments realiza-tion with various researched system parameters, initial conditions and external influences.

The work is devoted to a mathematical modeling of the decomposition of natural gas hydrate in compacted sand samples under decompression. The 1D mathematical model of the process includes equations of mass and heat balance, equation of gas state, equation of gas flow and empirical dependencies related to the kinetics of hydrate dissociation in a porous medium. An empirical dependence of the equilibrium pressure of natural gas hydrate on temperature in a porous medium is used. As a result of the simulation, the distributions of the main physical parameters in the sample and their evolution over time were obtained.

In a computational experiment, the analysis of the influence of taking into account the dependence of the equilibrium conditions of hydrate formation on the reservoir waters mineralization type on the formation of hydrates in wells during natural gas production was carried out. The study was carried out within the framework of the model of joint operation of the system "reservoir – well" during its thermal interaction with surrounding rocks. The dynamics of changes in temperature, pressure, moisture content of gas and flow section in wells are predicted. It was found that when taking into account the mineralization of reservoir waters, the time interval from the moment of starting wells to the their complete blockage with hydrates increases.

An algorithm is proposed for determining the dynamics of changes in the mass flow rate of natural gas in a well by measuring the pressure at the wellhead, based on the method of half division (bisection, dichotomy), which has unconditional convergence. In the course of solving the problem during the gas hydrates formation and deposition, the dynamics of changes in gas pressure and temperature, as well as the flow section along the length of the well, are also calculated. Comparison of the calculation results showed that at a constant bottom-hole pressure, the implementation of this algorithm, in contrast to the previously proposed algorithm for the inverse problem, leads to an increase in the duration of the process of complete blockage of the well with hydrates and, accordingly, to an increase of the produced gas total amount.

Mathematical modeling methods assess the possibility of natural gas storage by converting them to a hydrate state when gas is injected into permafrost aquifers. The model of multiphase nonisothermal filtration takes into account the main physical features of this process, including gas compressibility, the Joule-Thomson effect, adiabatic expansion, joint movement of water and gas, mass transfer between gas, water and a hydrate. To conduct computational experiments, the results of laboratory experiments of the equilibrium conditions of the natural gas hydrates formation in a free volume and in a porous medium saturated with water and aqueous solutions of sodium bicarbonate were used. The influence of phase equilibrium conditions on the main indicator of the process efficiency – the hydrate saturation of the created storage is studied.