scholarly journals Selected Mathematical Models Describing Flow in Gas Pipelines

Energies ◽  
2022 ◽  
Vol 15 (2) ◽  
pp. 478
Author(s):  
Andrzej J. Osiadacz ◽  
Marta Gburzyńska
Keyword(s):  
Differential Equations ◽  
High Speed ◽  
Gas Flow ◽  
Complex Structure ◽  
Hyperbolic Model ◽  
Gas Flows ◽  
Gas Pipelines ◽  
One Dimensional ◽  
Network Operation ◽  
The Mathematical Model

The main aim of simulation programs is to study the behavior of gas pipe networks in certain conditions. Solving a specified set of differential equations describing transient (unsteady) flow in a gas pipeline for the adopted parameters of load and supply will help us find out the value of pressure or flow rate at selected points or along selected sections of the network. Transient gas flow may be described by a set of simple or partial differential equations classified as hyperbolic or parabolic. Derivation of the mathematical model of transient gas flow involves certain simplifications, of which one-dimensional flow is most important. It is very important to determine the conditions of pipeline/transmission network operation in which the hyperbolic model and the parabolic model, respectively, should be used. Parabolic models can be solved numerically in a much simpler way and can be used to design simulation programs which allow us to calculate the network of any structure and any number of non-pipe elements. In some conditions, however, they describe the changes occurring in the network less accurately than hyperbolic models do. The need for analysis, control, and optimization of gas flows in high-pressure gas pipelines with complex structure increases significantly. Very often, the time allowed for analysis and making operational decisions is limited. Therefore, efficient models of unsteady gas flows and high-speed algorithms are essential.

scholarly journals IMPROVING THE EFFICIENCY OF THE FUNCTIONING OF GAS PIPELINES, TAKING INTO ACCOUNT THE STRUCTURAL FEATURES OF GAS FLOWS

2021 ◽  
Vol 447 (3) ◽  
pp. 34-39
Author(s):  
Elman Kh. Iskandarov
Keyword(s):  
High Speed ◽  
Gas Flow ◽  
Structural Changes ◽  
Oil And Gas ◽  
Structural Features ◽  
Transportation Systems ◽  
Gas Condensate ◽  
Gas Flows ◽  
Gas Pipelines ◽  
Processing Depth

The multi-phase and different composition of gas flows during the development of offshore oil and gas-condensate fields leads to high costs of energy in the system of in-field storage and transportation of well products. The analysis of the existing storage and transportation systems of gas-condensate mixtures shows that the geophysical nature and complexity of the internal structure of the transported fluids must be taken into account when choosing the mode parameters and calculation schemes of the pipelines. High-speed gas lines can be operated in a so-called "dry" mode, in which the liquid is carried along with the gas, the pipeline profile is relatively straight, without ups and downs. In this case, the formation of so-called "stagnant zones" in the pipeline is excluded. However, if the processing depth of the gas does not allow it to be transported in a single-phase state, then the condensing gas factor manifests itself. The hydraulic characteristics of vertical ups and downs on offshore pipelines are complicated, and pipelines are often filled with water and condensate. As a result, the pressure in the pipeline increases and the location of the collection point for condensing gases away from the production site can cause major problems. If we characterize oil and gas-condensate flows as a dynamic system in which alternating structural changes take place, the question of whether these systems are fractal is of great scientific interest. Based on the change in the fractal value, it is possible to diagnose structural changes during the transportation of various systems, including condensing gases in the pipelines. In this article the modes of change of basic parameters of a gas flow (pressure, flow rate and temperature) on various lines of a gas pipeline for the purpose of the producing of diagnostic criterion for revealing of liquid inclusions as a part of transported gas are investigated in this article. It is established, that in the presence of liquid inclusions at movement of gas flows there are the structural changes peculiar to fluid systems, systems which can be identified by variations of fractal dimensions of flowcharacteristics. Studies have shown that the study of the dynamics of structural changes in gas flows can play a role in diagnosing the formation of liquid phase embryos in gas pipelines. For this purpose, diagnostics for the movement of gas streams accompanied by liquid deposits in the pipelines has been proposed.

The Mechanics and Thermodynamics of Steady One-Dimensional Gas Flow

1947 ◽  
Vol 14 (4) ◽  
pp. A317-A336 ◽  
Author(s):  
Ascher H. Shapiro ◽  
W. R. Hawthorne
Keyword(s):  
Heat Transfer ◽  
Dimensional Analysis ◽  
High Speed ◽  
Gas Flow ◽  
Gas Injection ◽  
Wall Friction ◽  
Analytical Treatment ◽  
Area Change ◽  
One Dimensional ◽  
Recent Developments

Abstract Recent developments in the fields of propulsion, flow machinery, and high-speed flight have emphasized the need for an improved understanding of the characteristics of compressible flow. A one-dimensional analysis for flow without shocks is presented which takes into account the simultaneous effects of area change, wall friction, drag of internal bodies, external heat exchange, chemical reaction, change of phase, injection of gases, and changes in molecular weight and specific heat. The method of selecting independent and dependent variables, and the organization of the working equations, leads, it is believed, to a better understanding of the influence of the foregoing effects, and also simplifies greatly the analytical treatment of particular problems. Examples are given first of several simple types of flow, including (a) area change only; (b) heat transfer only; (c) wall friction only; and (d) gas injection only. In addition, examples of flow with combined effects are given, including (a) simultaneous friction and area change; (b) simultaneous friction and heat transfer; and (c) simultaneous liquid injection and evaporation. A one-dimensional analysis for flow through a discontinuity is presented, allowing for energy, shock, drag, and gas-injection effects, and for changes in gas properties. This analysis is applicable to such processes as: (a) the adiabatic normal shock; (b) combustion; (c) moisture condensation shocks; and (d) steady explosion waves.

Mathematical modeling of articulated passenger train spatial vibrations

2021 ◽  
Vol 2021 (2) ◽  
pp. 91-99
Author(s):  
O. Markova ◽  
◽  
H. Kovtun ◽  
V. Maliy ◽  
◽  
...  
Keyword(s):  
Mathematical Model ◽  
Differential Equations ◽  
Dynamic Characteristics ◽  
High Speed ◽  
Ride Quality ◽  
Railway Transport ◽  
Passenger Train ◽  
Wide Range ◽  
Random Track Irregularities ◽  
The Mathematical Model

The problem of high-speed railway transport development is important for Ukraine. In many countries articulated trains are used for this purpose. As the connections between cars in such a train differ from each other, to investigate its dynamic characteristics not a separate car, but a full train vibrations model is necessary. The article is devoted to the development of the mathematical model for articulated passenger train spatial vibrations. The considered train consists of 7 cars: one motor-car, one transitional car, three articulated cars, one more transitional car and again one motor-car. Differential equations of the train motion along the track of arbitrary shape are set in the form of Lagrange’s equations of the second kind. All the necessary design features of the vehicles are taken into account. Articulated cars have common bogies with adjoining cars and a transfer car and the cars are united by the hinge. The operation of the central hinge between two cars is modeled using springs and dampers acting in the horizontal and vertical directions. Four dampers between two adjacent car-bodies act as dampers for pitching and hunting and are represented in the model by viscous damping. The system of 257 differential equations of the second order is set, which describes the articulated train motion along straight, curved, and transitional track segments with taking into account random track irregularities. On the basis of the obtained mathematical model the algorithm and computational software has been developed to simulate a wide range of cases including all possible combinations of parameters for the train elements and track technical state. The study of the train self-exited vibrations has shown the stable motion in all the range of the considered speeds (40 km/h – 180 km/h). The results obtained at the train motion along the track maintained for the speedy motion have shown that all the dynamic characteristics and ride quality index insure train safe motion and comfortable conditions for the travelling passengers.

scholarly journals Quotients of Euler Equations on Space Curves

Symmetry ◽  
2021 ◽  
Vol 13 (2) ◽  
pp. 186
Author(s):  
Anna Duyunova ◽  
Valentin Lychagin ◽  
Sergey Tychkov
Keyword(s):  
Partial Differential Equations ◽  
Differential Equations ◽  
Ordinary Differential Equations ◽  
Euler Equations ◽  
Gas Flow ◽  
Euler System ◽  
Partial Differential ◽  
One Dimensional ◽  
Space Curves ◽  
Ode System

Quotients of partial differential equations are discussed. The quotient equation for the Euler system describing a one-dimensional gas flow on a space curve is found. An example of using the quotient to solve the Euler system is given. Using virial expansion of the Planck potential, we reduce the quotient equation to a series of systems of ordinary differential equations (ODEs). Possible solutions of the ODE system are discussed.

Investigation of gas gathering pipelines operation efficiency and selection of improvement methods

2021 ◽  
Vol 2 (107) ◽  
pp. 75-86
Author(s):  
V.B. Volovetskyi ◽  
Ya. Doroshenko ◽  
G. Kogut ◽  
A.P. Dzhus ◽  
I.V. Rybitskyi ◽  
...  
Keyword(s):  
Pressure Loss ◽  
High Speed ◽  
Gas Flow ◽  
Cfd Simulation ◽  
Experimental Studies ◽  
Dynamic Processes ◽  
Hydraulic Efficiency ◽  
Gas Pipelines ◽  
Pressure Losses ◽  
Gas Dynamic

Purpose: The article implies theoretical and experimental studies of the liquid pollution accumulations impact on the efficiency of gathering gas pipelines operation at the Yuliivskyi oil and gas condensate production facility (OGCPF). Research of efficiency of gas pipelines cleaning by various methods. Design/methodology/approach: The research methodology consists of determining the hydraulic efficiency of gathering gas pipelines before and after cleaning of their internal cavity by different methods and comparing the obtained results, which allows to objectively evaluate the efficiency of any cleaning method. CFD simulation of gas-dynamic processes in low sections of gas pipelines with liquid contaminants. Findings: Experimental studies of cleaning efficiency in the inner cavity of the gas gathering pipelines of the Yuliivskyi OGCPF by various methods, including: supply of surfactant solution, creating a high-speed gas flow, use of foam pistons were performed. It was established that cleaning the inner cavity of gas gathering pipelines by supplying a surfactant solution leads to an increase in the coefficient of hydraulic efficiency by 2%-4.5%, creating a high-speed gas flow by 4%-7%, and under certain conditions by 8%-10 % and more. However, for two gas pipelines the use of foam pistons allowed to increase the coefficient of hydraulic efficiency from 5.7 % to 10.5 % with a multiplicity of foam from 50 to 90. be recommended for other deposits.The results of CFD simulation showed that the accumulation of liquid contaminants in the lowered sections of gas pipelines affects gas-dynamic processes and leads to pressure losses above the values provided by the technological regime. With the increase in liquid contaminants volume the pressure losses occur. Moreover, with a small amount of contamination (up to 0.006 m3), liquid contaminants do not have a significant effect on pressure loss. If the contaminants volume in the lowered section of the pipeline is greater than the specified value, the pressure loss increases by parabolic dependence. The increase in mass flow leads to an increase in the value of pressure loss at the site of liquid contamination. Moreover, the greater the mass flow, the greater the impact of its changes on the pressure loss. The CFD simulation performed made it possible not only to determine the patterns of pressure loss in places of liquid contaminants accumulation in the inner cavity of gas pipelines, but also to understand the gas-dynamic processes in such places, which is an unconditional advantage of this method over experimental. Research limitations/implications: The obtained simulation results showed that the increase in the volume of liquid contaminants in the inner cavity of gas gathering pipelines leads to an increase in pressure losses above the value provided by the technological regime. To achieve maximum cleaning of gas gathering pipelines, it is necessary to develop a new method that will combine the considered. Practical implications: The performed experimental results make it possible to take a more thorough approach to cleaning the inner cavity of gas gathering pipelines and to forecast in advance to what extent the hydraulic efficiency of gas gathering pipelines can be increased. Originality/value: The obtained results of CFD simulation of gas-dynamic processes in lowered sections of gas pipelines with liquid contaminants, experimental studies of the effectiveness of various methods of cleaning the inner cavity of gas gathering pipelines has original value.

Modeling Piston-Ring Dynamics, Blowby, and Ring-Twist Effects

1998 ◽  
Vol 120 (4) ◽  
pp. 843-854 ◽  
Author(s):  
T. Tian ◽  
L. B. Noordzij ◽  
V. W. Wong ◽  
J. B. Heywood
Keyword(s):  
High Speed ◽  
Gas Flow ◽  
Great Influence ◽  
Operating Conditions ◽  
Spark Ignition Engine ◽  
Gas Flows ◽  
Ring Groove ◽  
Ring Dynamics ◽  
Low Load ◽  
Groove Configurations

A ring-dynamics and gas-flow model has been developed to study ring/groove contact, blowby, and the influence of ring static twist, keystone ring/groove configurations, and other piston and ring parameters. The model is developed for a ring pack with three rings. The dynamics of the top two rings and the gas pressures in the regions above the oil control ring are simulated. Distributions of oil film thickness and surface roughness on the groove and ring surfaces are assumed in the model to calculate the forces generated by the ring/groove contact. Ring static and dynamic twists are considered, as well as different keystone ring/groove configurations. Ring dynamics and gas flows are coupled in the formulation and an implicit scheme is implemented, enabling the model to resolve detailed events such as ring flutter. Studies on a spark ignition engine found that static twist or, more generally speaking, the relative angle between rings and their grooves, has great influence on ring/groove contact characteristics, ring stability, and blowby. Ring flutter is found to occur for the second ring with a negative static twist under normal operating conditions and for the top ring with a negative static twist under high-speed/low-load operating conditions. Studies on a diesel engine show that different keystone ring/groove configurations result in different twist behaviors of the ring that may affect the wear pattern of the keystone ring running surfaces.

An Analysis of the Motion of Pigs Through Gas Pipelines

1984 ◽  
Vol 106 (4) ◽  
pp. 374-379 ◽  
Author(s):  
J. S. Weingarten ◽  
A. J. Chapman ◽  
W. F. Walker
Keyword(s):  
Differential Equations ◽  
Computer Program ◽  
Numerical Solution ◽  
Cross Section ◽  
Nonlinear Differential Equations ◽  
Gas Pipeline ◽  
Gas Pipelines ◽  
Governing Equations ◽  
One Dimensional ◽  
Solution Scheme

A one-dimensional, quasi-steady, model describing the motion of a pig moving in a gas pipeline is developed for the cases of a solid pig, which obstructs the cross section of the pipe, and one with a concentric hole through it. The resultant governing equations constitute a set of seven nonlinear differential equations. A numerical solution scheme, implemented by a computer program, is described. Results and discussion are presented for a set of typical cases.

Computerized Analysis of Dynamic Pressure Exchanger Scavenge Processes

1975 ◽  
Vol 189 (1) ◽  
pp. 149-158 ◽  
Author(s):  
P. H. Azoury ◽  
S. M. Hai
Keyword(s):  
Differential Equations ◽  
Specific Heat ◽  
High Performance ◽  
Gas Flow ◽  
Previous Analysis ◽  
Dynamic Pressure ◽  
Ideal Gas ◽  
Wave Processes ◽  
One Dimensional ◽  
Good Agreement

The present work supplements a previous analysis by Azoury of the basic wave processes in a d.p.e. (dynamic pressure exchanger) cell. A hybrid computerized method of integrating the differential equations of unsteady one-dimensional ideal gas flow is used to analyse the component scavenge processes of the d.p.e. in a looped arrangement. These processes are employed to investigate the effect of the relative nature of the interacting gases on d.p.e. performance. A criterion of high performance is proposed in terms of the overall strength of the interface between the gases and their relative specific heat ratios. The criterion gives good agreement with theory when tested with experimental results obtained on two d.p.e. test units.

Aerodynamic Focusing of Microparticles in Gas Flows With Shock Waves

2013 ◽  
Author(s):  
Alexander Osiptsov ◽  
Irina Golubkina ◽  
Oyuna Rybdylova
Keyword(s):  
Shock Waves ◽  
High Speed ◽  
Gas Flow ◽  
Particle Beam ◽  
Gas Flows ◽  
High Concentration ◽  
Interaction Point ◽  
Processing Technologies ◽  
Focusing Effect ◽  
Aerodynamic Focusing

The effect of aerodynamic focusing of microparticles in gas-particle flows is employed mainly for creating collimated particle beams. These beams are used in various technical applications, such as coating, “direct-write”, surface processing technologies, needle-free injections, etc. In this study, we propose and investigate two new flow schemes in which the effect of aerodynamic focusing of small low-inertia particles may be realized in high-speed gas flows with shock waves. The first one is a steady-state dusty-gas flow behind the point of interaction of two crossing shock waves. The convergence of the carrier-phase streamlines and the presence of particle inertia result in the formation of a high-concentration particle beam behind the shock interaction point. In the second flow scheme considered, the particle focusing effect is attributable to the action of the Saffman lateral force, exerting on the particles in boundary layers behind a shock wave travelling in a narrow channel with a constant cross-section. In both cases, the ranges of governing parameters are found for which the focusing is “optimal”, i.e. a very thin collimated beam of microparticles is formed.

A Steady State, Adiabatic Compression and One-Dimensional Generalized Flow Analysis of a Natural Gas Pipeline Using Soave-Redlich-Kwong Equation of State

2013 ◽  
Author(s):  
Hicham T. Oumechouk ◽  
Mohand A. Ait-Ali
Keyword(s):  
Steady State ◽  
Equation Of State ◽  
Natural Gas ◽  
Differential Equations ◽  
Specific Volume ◽  
Gas Flow ◽  
Adiabatic Compression ◽  
Gas Pipeline ◽  
One Dimensional ◽  
Gas Properties

Steady state adiabatic compression and one-dimensional generalized gas flow is analyzed using governing conservation laws and Redlich-Kwong-Soave (R-K-S) equation of state applied to a representative mixture of natural gas. The objective of this work is to obtain the state properties of the natural gas considered as an open thermodynamic system at compressor and gas pipeline exits, then the compressor power and energy auto-consumptions for a few diameters and pipe line lengths configurations. The adiabatic, irreversible compression process is analyzed with formal state property definitions where departures from ideal gas properties are obtained using R-K-S equation of state. The one-dimensional generalized gas flow problem is analyzed with continuity, momentum and energy equations, combined with the equation of state; Reynolds analogy between heat transfer and flow friction is adopted. This problem is thus defined with four non linear coupled differential equations; the variables to be determined are pressure, temperature, specific volume and velocity at the gas pipeline exit. The adopted calculation procedure to obtain the gas properties is iterative. It assumes pressure and temperature initial values, solves the equation of state for the specific volume and the continuity equation for the velocity, then corrects for pressure and temperature with integrated values to be used with the next iteration from a solution of the differential equations of motion and energy. This procedure is applied to a few gas pipeline configurations of pipe diameters sections and number of boosting compressor stations for a gas pipeline capacity of 13.5 billions standard cubic meters per year to be delivered to a natural gas liquefaction plant located at a sea port at a distance of some 350 miles.

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