Efficiency Evaluation Of Implementation Of Optimization Methods Of Operation Modes Of The "Plast - Gas Pipeline" System By The Methods Of Mathematical Modeling

To date, Ukraine's mature gas fields, which are being developed in the gas regime, are at the final stage of development, which is characterized by a significant depletion of reservoir energy. The final stage of development requires solving complex problems related to watering wells, destruction of the reservoir, removal of formation water and mechanical impurities, increasing back pressure in the system, as well as the moral and physical wear and tear of industrial equipment. In the conditions of falling gas production, a significant part of the operating well stock is unstable, in the mode of unauthorized stops due to the accumulation of liquid at the bottom and insufficient gas velocities for removal to the surface, and also the accumulation of the liquid phase in the lowered places of the gas gathering system.Within the framework of the conducted studies, the gas dynamic models of the operation of the gas collection system of 3 oil/gas-condensate fields (OGCF) are created. A single model of the gas production system "reservoir - well - gas gathering system - inter-field gas pipeline - main facilities" is built. The current efficiency of the gas production, collection and transportation system is assessed. On the basis of model calculations, the current production capabilities of the wells are defined, as well as the "narrow" places of the system.It is established that the introduction of modern technologies for the operation of watered wells without optimizing the operation of the entire gas production system is irrational, since the liquid that is carried out from the wellbore will accumulate in the plumes and increase the back pressure level in the ground part. In conditions of increasing gas sampling, liquid flowlines can be taken out of the loops and deactivated the separation equipment.The feasibility of introducing methods for optimizing the operation modes of the gas production - gathering and transportation system is estimated, which allows choosing the optimal method for increasing the efficiency and reliability of its operation.For the first time in the Ukrainian gas industry, an integrated model of the field is created as a single chain of extraction, collection, preparation and transportation of natural gas, which can be adapted for the development and arrangement of both new and mature deposits.The main advantage of the application for the hydrocarbon production sector is the simulation of the processes, which makes it possible to evaluate the operating mode of the well in the safe zone while reducing the working pressure and introducing various intensification methods, and also to estimate the increase in hydrocarbon production. For the equipment of the ground infrastructure – "midstream" – the main advantage is a reduction in the time required to perform design calculations for gas pipelines, trains and pipelines for transporting multiphase media using public models.The creation and use of integrated models of gas fields gives an understanding of the integral picture of available resources and ensures an increase in the efficiency of field development management.The results of the calculation are clearly correlated with the actual data, which makes it possible to use the models constructed to obtain numerical results

Inverse spectral problems for energy-dependent Sturm-Liouville equations

We study the inverse spectral problem of reconstructing energy-dependent Sturm-Liouville equations from their Dirichlet spectra and sequences of the norming constants. For the class of problems under consideration, we give a complete description of the corresponding spectral data, suggest a reconstruction algorithm, and establish uniqueness of reconstruction. The approach is based on connection between spectral problems for energy-dependent Sturm-Liouville equations and for Dirac operators of special form.Comment: AMS-LaTeX, 28 page

Asymptotic, Algorithmic and Geometric Aspects of Groups Generated by Automata

This dissertation is devoted to various aspects of groups generated by automata. We study particular classes and examples of such groups from different points of view. It consists of four main parts. In the first part we study Sushchansky p-groups introduced in 1979 by Sushchansky in "Periodic permutation p-groups and the unrestricted Burnside problem". These groups represent one of the earliest examples of Burnside groups and, at the same time, show the potential of the class of groups generated by automata to contain groups with extraordinary properties. The original definition is translated into the language of automata. The original actions of Sushchansky groups on p- ary tree are not level-transitive and we describe their orbit trees. This allows us to simplify the definition and prove that these groups admit faithful level-transitive actions on the same tree. Certain branch structures in their self-similar closures are established. We provide the connection with so-called G groups introduced by Bartholdi, Grigorchuk and Suninc in "Branch groups" that shows that all Sushchansky groups have intermediate growth and allows us to obtain an upper bound on their period growth functions. The second part is devoted to the opposite question of realization of known groups as groups generated by automata. We construct a family of automata with n states, n greater than or equal to 4, acting on a rooted binary tree and generating the free products of cyclic groups of order 2. The iterated monodromy group IMG(z2+i) of the self-map of the complex plain z -> z2 + i is the central object of the third part of dissertation. This group acts faithfully on the binary rooted tree and is generated by 4-state automaton. We provide a self-similar measure for this group giving alternative proof of its amenability. We also compute an L-presentation for IMG(z2+i) and provide calculations related to the spectrum of the Markov operator on the Schreier graph of the action of IMG(z2 + i) on the orbit of a point on the boundary of the binary rooted tree. Finally, the last part is discussing the package AutomGrp for GAP system developed jointly by the author and Yevgen Muntyan. This is a very useful tool for studying the groups generated by automata from the computational point of view. Main functionality and applications are provided

Resolvent convergence of Sturm-Liouville operators with singular potentials

In this paper we consider the Sturm-Liuoville operator in the Hilbert space $L_2$ with the singular complex potential of $W^{-1}_2$ and two-point boundary conditions. For this operator we give sufficient conditions for norm resolvent approximation by the operators of the same class.Comment: 6 pages, to appear in Math. Note