Release:2016, Vol. 2. №2
About the authors:Maxim V. Stolpovskii, Cand. Sci. (Phys-Math.), Senior Lecturer, Department of Physics, Ufa State Petroleum Technological University; firstname.lastname@example.org
Numerical model operation of gas hydrate formation process as a result of cold gas forcing is carried out to the porous medium, which is initially saturated with gas and water. The feature of the mathematical model in this task is not only the accounting of phase changes, but also the accounting of a mass transfer in a porous medium. The necessity to consider flow of gas in a porous medium complicates the task as, though it also comes down to the Stefan’s task, however, the transition temperature in this case depends on pressure. This feature is essential because, as shown in different works, it leads to the emergence of the situation when phase changes are implemented in a stretched area.
To obtain the decisions, which adequately describe the considered process for the subsequent time stages, there is a need for creation of the numerical schemes suitable for layers of terminating extent. Algorithms of the continuous account are especially widely applied to many-dimensional tasks, however, the accuracy of calculating temperature value and the position of the phase boundary strongly depends on the smoothing parameter, to define which is often difficult. In this work to solve the task the method of catching the front in a knot of a space grid is used. At the same time analytical problem solving in a self-similar approximation is used for testing the numerical algorithms based on this method.
It is shown that depending on parameters of the forced gas the hydrate formation can happen both on the frontal surface and in a stretched area. At the same time in the first case the hydrate formation happens without heating the environment, and in the second is followed by its heating, and its size increases with pressure boost of the forced gas. By numerical calculations it is established that the mode with heating of a porous medium is implemented in high-permeability layers, when the size of pressure of the forced gas exceeds the size of the pressure balance corresponding to the initial temperature of layer.