Yaroslav Pyanylo
@iapmm.lviv.ua
Department of Mathematical Modeling of Transfer Processes in Complex Systems
YS Pidstryhach Institute of Applied Problems of Mechanics and Mathematics of the National Academy of Sciences of Ukraine
RESEARCH, TEACHING, or OTHER INTERESTS
Modeling and Simulation, Mathematical Physics
Scopus Publications
Scopus Publications
N. B. Lopuh and Ya.D. Pyanylo
Springer Science and Business Media LLC
Ya. D. Pyanylo
Springer Science and Business Media LLC
Myroslav Prytula, Nazar Prytula, Yaroslav Pyanylo, Zoia Prytula, and Olga Khymko
Private Company Technology Center
The object of this study is underground gas storage facilities (UGSF). The main problem being solved is to ensure effective management of the operation process of underground gas storage facilities (UGSF) at operational and forecast time intervals. One of the main factors that affect the operating modes of UGSF is significantly non-stationary filtration processes that take place in the bottomhole zones of wells. The complexity of assessing the multifactorial impact on depression/repression around the wells affects both the speed and accuracy of calculating the mode parameters of UGSF operation. Analysis of the results of well studies revealed a significant area of uncertainty in the calculation of the filtration resistance coefficients of their bottomhole zones. A satisfactory accuracy of the result in the expected time was achieved by building a model of integrated consideration of the influence of the parameters of all the bottomhole zones of the wells on the mode of UGSF operation. It turned out that the integrated consideration of the impact on the parameters of the bottomhole zones of the wells neutralized the effect of significant changes in the filtration resistance coefficients of the wells and ensured a sufficient speed of calculation of UGSF operation modes. Simultaneous simulation of ten operating UGSFs under the peak mode of withdrawal the entire available volume of active gas takes no more than six minutes. The speed of simulation of filtration processes in the bottomhole zones of wells ensured finding the best of them according to one or another criterion of operation mode quality. As a result of the research, a model was built and implemented by software, which was tested under real operating conditions and provides optimal planning of UGSF operating modes for given time intervals. Its use is an effective tool for the operational calculation of current modes and technical capacity of UGSF for a given pressure distribution in the system of main gas pipelines. The performance of the constructed mathematical methods has been confirmed by the results of numerical experiments
Yaroslav Pyanylo, Sofiya Tvardovska, and Nazariy Lopuh
IEEE
The article studies the vibrations of a porous layer under the influence of an external electric field and in terms of Caputo fractional derivatives are written. The solution of the boundary value problem was obtained by using of the Laplass-Carson integral transform. The time dependences of the movements of the liquid and of the solid-phase framework were obtained, as well as the pressures and stresses that arise were calculated.
Yaroslav Pyanylo, Zoia Prytula, Myroslav Prytula, Olha Hymko, Nazar Prytula, and Halyna Pyanylo
IEEE
Problems of research of underground gas storage (UGS) wells are given. The analysis of the results of well research is carried out and the constant variability of filtration resistance coefficients of bottomhole zones of wells is substantiated. Studies of the influence of bottomhole pressures of wells on the calculated pressure at gas gathering stations (GGS) of underground storage facilities have been carried out. It was found that the calculated filtration resistance coefficients do not allow to calculate the pressures at the gas gathering stations of the underground storage plant with sufficient accuracy. The magnitude of the discrepancy between the measured and calculated pressures on the GGS varies depending on the flow rate and operating time of wells. It is established that the calculation of depression (repression) of pressure in the bottomhole zones of wells in non-stationary conditions of their operation gives underestimated results.
Natalia Iwaszczuk, Myroslav Prytula, Nazar Prytula, Yaroslav Pyanylo, and Aleksander Iwaszczuk
MDPI AG
The object of this study is the underground gas storage facilities of Ukraine, with the aim of developing a systematic mathematical model to describe the flow of gas in complex underground gas storage systems. This model will enable to development of effective methods and algorithms for calculating the modes of operation of such systems. The proposed systematic mathematical model connects the model of the structure of underground gas storage in terms of graph theory with variable topology and various mathematical models of gas flows in facilities with concentrated and distributed parameters. We set the models of gas flows in UGS facilities in the form of analytical relations, differential equations and algorithmically described systems. In order to automate the process of model construction (for given boundary conditions), we developed a system of formation, analysis and synthesis of graphs for underground gas storage facilities, as well as a set of information and mathematical models of facilities.
Yaroslav Pyanylo
IEEE
The influence of the order of the fractional derivatives on the process of gas filtration in complex porous media has been investigated in the presented paper. A model of gas filtration based on the capillary approach is proposed. The last one allows studying the effect of capillary topology on the pressure distribution in porous media layers. The obtained theoretical results were approbated in the course of numerical experiments.
Yaroslav Pyanylo and Sofiya Tvardovska
IEEE
The paper considers the propagation of mechanoelectromagnetic waves in porous medium saturated by an electrolyte solution under the action of an external electric field, using fractional time derivatives. The equations of electromagnetic mechanics are written, and also partial cases of construction of system of equations for finding wave numbers of plane mekchanoelectromagnetic waves are considered. The analysis of the solution is carried out with the use of fractional time derivatives.
Nazariy Lopuh and Yaroslav Pyanylo
IEEE
A new numerical model of gas filtration in a porous medium is proposed and investigated. Gas filtration is modeled with a nonlinear differential equation in partial derivatives. Methods of solving of the equation are discussed. Computer experiment basing on real-experiment-extracted input physical and geometrical parameters is performed and its results are analyzed. The received results agree well with the corresponding experimental data.
Myroslav Prytula, Nazar Prytula, Yaroslav Pyanylo, Zoia Prytula, and Olga Khymko
Private Company Technology Center
The object of this study is underground gas storage facilities (UGSF) as part of the gas transmission system (GTS), in the process of joint operation of which a significant synergistic effect is achieved. The problem under consideration is to ensure the joint effective operation of the integrated UGSF and GTS complex as a single thermal-hydraulic one. A method of daily calculation of the maximum productivity of underground gas storage facilities has been devised. The optimization potential of UGSF operating modes has been studied. It is shown to range within 11‒20 %. The problems of planning the operation of UGSF have been stated and solved both under gas pumping modes and gas withdrawal modes. An algorithm for planning gas withdrawal modes at intervals of peak-free UGSF operation been developed. The achieved computational complexity of problem-solving algorithms is in the range of 2‒10 seconds. The problem of combining simultaneous operation of UGSF under an optimal mode for fuel gas and ensuring the necessary peak operation of UGSF at projected time intervals has also been considered. The joint UGSF performance was calculated at the projected time intervals according to the established criteria. At the same time, thermal-hydraulic coordination of UGSF operating modes with the operation of the GTS main gas pipeline system with which they are integrated was ensured. The problem was solved as a result of the implementation of a universal approach to the construction of functional models of complex systems – a single information support, the representation of the structure of the system in terms of graphs, the statement of proper mathematical problems, the development of methods for guaranteed convergence of systems with different mathematical representations of equations, the development of computational algorithms for combinatorial optimization of minimum complexity processes with discrete and irregular influences on their behavior
Yaroslav Pyanylo, Anatoliy Lopatiev, Andriy Vlasov, Mykhailo Petrus, Andriy Demichkovskyi, and Nazar Shtangret
IEEE
The paper reviews main methods of numeric series analysis. Major characteristics of probabilistic processing of digital information are presented. As medical and biological processes are very often periodic in nature, the paper presents main methods of determination of parameters of hidden periodicities. In order to validate the need for such research, an actual heart rate spectrum is presented.
Yaroslav Pyanylo, Valentyna Sobko, Halyna Pyanylo, Mykhailo Petrus, and Andriy Demichkovsky
IEEE
In the work on the basis of classical orthogonal polynomials orthogonal systems of functions are constructed, their properties are investigated and the computational experiment on model problems is carried out, the influence of various errors on approximation is investigated. The method of application of the theory of spectral schedules, the theory of moments and statistical-probabilistic methods of processing of the digital information received at preparation of sportsmen for competitive activity, in particular at data processing of heart rate (HR) is offered. The paper shows the relationship of the moments of the distribution function with the generalized spectra of orthogonal decompositions, the question of determining the sample size to obtain research results.
Yaroslav Pyanylo
IEEE
The paper analyzes the mathematical models of filtration of substances in complex porous media. The mathematical model of the filtration process by the capillary system is proposed.
Ya. D. Pyanylo, , O. B. Bratash, and
Lviv Polytechnic National University
Yaroslav Pyanylo
IEEE
In the paper, the method of linearization of nonlinear systems of differential equations is proposed, describing the processes of gas hydrodynamics. The basis of the found solution of the nonlinear boundary value problem is the question of adaptation of the mathematical model to the real physical process.
Ya. Pyanylo, , O. Bratash, G. Pyanylo, , and
Lviv Polytechnic National University
Побудовано математичну модель руху газу в трубопроводах для випадку, коли не-
усталений процес описано похiдною дробового порядку за часовою змiнною. Сфор-
мульовано крайову задачу. Рiшення задачi знаходять спектральним методом в бази-
сах многочленiв Чебишева–Лагерра за часовою змiнною та многочленiв Лежандра за
координатою. Знаходження рiшення в результатi зведено до системи алгебраїчних
рiвнянь. Проведено числовий експеримент.
Ya. Pyanylo, , V. Sobko, O. Bratash, , and
Lviv Polytechnic National University
The method of solving problems of mathematical physics, in particular for pressure distribution finding in the water in the underground gas storage layers on the basis of the biorthogonal polynomials constructed by the authors is proposed in the paper. The way of the problem solving by the method of separation of variables on the basis of the biorthogonal polynomials is studied. The solution of the problem is found in the form of the series sum of the biorthogonal and quasi-spectral polynomials. The comparative analysis for the different values of parameters is performed. The impact of the methods parameters, in particular the partial sum order, the bit grid and the calculation error on the accuracy of the solution obtained is studied. The calculation results are presented in the form of the tables. The algorithm of the process of the gas motion in the pipelines using fractional derivatives is constructed.
Ya. Pyanylo, , P. Vavrychuk, and
Lviv Polytechnic National University
N. Prytula, , Ya. Pyanylo, M. Prytula, , and
Lviv Polytechnic National University
We consider the problem of operating mode control of compressor stations to ensure optimal operating mode of the main gas in a wide range of gas transmission volumes for the different options of initial and boundary conditions. We propose an adaptive algorithm of designing control actions, which ensures optimality criterion and does not violate existing technological limitations. Розглянуто задачу керування режимами роботи компресорних станцiй для забезпечення оптимального режиму роботи магiстрального газопроводу в широких дiапазонах змiни об’ємiв транспортування газу за рiзних можливих варiантiв початкових та крайових умов. Запропоновано адаптивний алгоритм формування керуючих дiй, який забезпечує критерiй оптимальностi i водночас не порушуються наявнi технологiчнi обмеження.
Ya. Pyanylo, , V. Sobko, and
Lviv Polytechnic National University
Ya. P'yanylo, , H. P'yanylo, M. Vasiunyk, , and
Lviv Polytechnic National University
The investigations of the spectral methods are represented for solving applied tasks, in particular, the processing of digital information (problem of approximation, compression of information, filtration of signals, determination of nature of physical process which is modeled), also imposition of boundary conditions for the formulated problems of mathematical physics, etc. The essence of these methods consists in representation of known and required functions by orthogonal series in the chosen bases and construction of the algorithms for calculation of coefficients of these series (the generalized spectra). The methods of these calculation depend on the type of input information (analytic or discrete types). Approximation method for functions of two variables in domains of noncanonical form is suggested. Дослiджено спектральнi методи розв’язування прикладних задач, зокрема обробка цифрової iнформацiї (задачi апроксимацiї, стиску iнформацiї, фiльтрацiї сигналiв), визначення характеру фiзичного процесу, який моделюється, та побудови крайових умов пiд час формулювання задач математичної фiзики тощо. Суть цих методiв полягає в поданнi вiдомих i шуканих функцiй ортогональними рядами у вибраних
базисах i побудовi алгоритмiв для обчислення коефiцiєнтiв цих рядiв (узагальнених спектрiв). Методи їх обчислення залежать вiд способу задання вхiдної iнформацiї (в дискретному або аналiтичному видах). Запропоновано спосiб апроксимацiї функцiй двох змiнних в областях неканонiчної форми.