Pyanylo Ya.D. Analytical-numerical modeling of mass transfer in gas pipelines and natural porous media. – Manuscript.
Thesis for competition of scientific degree of doctor of engineering by specialty 01.05.02 “mathematical modeling and numerical methods.” – National University ”Lviv Politekhnika”, Lviv, 2007.
The work deals with investigation of processes of propagation of gas in pipelines. Gas filtration in porous media (underground gas holders) and propagation of admixtures substances in near to the surface ground layers. The corresponding mathematical methods and analytical-numerical methods for solving the stated problems were constructed.
Influence of hydrodynamic characteristics of gas and geometrical parameters of pipelines on the process of its motion was studied. We suggested technique for determination of operating conditions in gas-transport networks and considered problems of optimization of flow distribution by different criteria (minimum of fuel gas on compressor stations, minimization of transient times, etc.).
We construct and investigate mathematical model of distribution of gas pressure in porous media of complex structure (underground gas holders) under the presence of lumped sources and investigated influence of gas hydrodynamic characteristics and geometrical parameters of medium on the function of pressure distribution.
The process of hetero-diffusion propagation of admixtures in near to the surface ground layers was investigated in two ways, i.e., with taking into account convective transport on one of it. On the basis of the stated problem of mathematical physics we conducted comparative analysis of main methods for its solving.
At the same time we obtained a number of results of mathematical character (approximation of functions by orthogonal series, inversion for the Laplace integral, solving differential and integral equations of convolution type by spectral methods), which have independent significance and can be applied on investigation of physical processes described by nonlinear differential equations.
Keywords: mathematical model, non-stationary process, spectral method, error of calculations, numerical information processing, diffusion, adaptive method.