Operation Of Gas Pipelines Research Articles

Analysis of the reliability of structures during operation of gas pipelines on piles in areas of heaving soils

The routes of the main, field, and process gas pipelines in the Arctic regions of Siberia run through territories with difficult climatic conditions. Along the route, there are areas with heaving soils, which can be used as natural bases only with the use of special anti-heaving measures, since that they are characterized by high mobility, low bearing capacity, uneven settlement and increased compressibility. This raises concerns about a decrease in the bearing capacity of permafrost soils in the territories of Taimyr, Yamal and other regions. The paper discusses various methods of the above-ground laying of pipelines on heaving soils. A pipeline construction option ensuring safer operation is proposed.

Event classification for natural gas pipeline safety monitoring based on long short-term memory network and Adam algorithm

Hydrate plugging and pipeline leak can impair the normal operation of natural gas pipeline and may lead to serious accidents. Since natural gas pipeline safety monitoring based on active acoustic excitation can detect and locate not only the two abnormal events but also normal components such as valves and pipeline elbows, recognition and classification of these events are of great importance to provide maintenance guidance for the pipeline operators and avoid false alarm. In this article, long short-term memory (LSTM) network is introduced and applied to classify detection signals of hydrate plugging, pipeline leak, and elbow. Adaptive moment estimation (Adam) algorithm is introduced and utilized to accelerate the long short-term memory network convergence in training. Experimental results demonstrate that the network with three layers and 64 units per cell performs the best. The cross-entropy loss in training is 0.0005, and classification accuracies are all 100% in training, validation, and testing which verify the validity of the long short-term memory network. Therefore, the method based on the long short-term memory network and adaptive moment estimation algorithm can work efficiently on pipeline events classification and has great guiding significance for safety assurance of natural gas transmission.

Investigation of the hydraulic efficiency of gathering gas pipelines

The current state of two gathering gas pipelines was analyzed in the article: the first – from the gas gathering station (GGS) of the Narizhnianske oil and gas condensate field (OGCF) to the complex gas treatment unit-2 (CGTU-2) of the Yuliivske OGCF; the second – from the CGTU-1 of the Skvortsivske OGCF to the CGTU-2 of the Yuliivske OGCF. At different times of the year the hydraulic efficiency of gathering gas pipelines was determined, which was in a wide range from 75 % to 98 % on the first, and from 69 % to 96 % on the second gathering gas pipeline respectively. The operating modes of gathering gas pipelines were studied. The volume of contamination in the fields was determined using calculations. The industrial research to measure the volume of contamination, transported together with gas on the CGTU-2 measuring lines, was performed in separators and segregators. It was established that the volume of contamination, determined based on the results of experimental investigations, was higher than the calculated value. The main factors that negatively influence the hydraulic efficiency of gas pipelines were defined. The monitoring of these main factors will prevent the reduction of the hydraulic efficiency coefficient and decrease in the volume of transported gas, it will also help to achieve the planned production figures. The authors determined the main reasons for the reduction in the hydraulic efficiency of gathering gas pipelines resulting from the accumulation of liquid contaminants in the inner cavity and hydrates formation. The proposed solutions to these problems were introduced and are still used in production. In particular, a surfactant solution is fed using a mobile pumping unit, a high-speed gas stream is created to remove the accumulated liquid from the internal cavity of field gas pipelines operating with the CGTU-2 of the Yuliivske OGCF and methanol is supplied using the available pumps from the GGS of the Narizhnianske OGCF and CGTU-1 of the Skvortsivske OGCF. The authors proposed a series of measures to prevent the emergencies and failures and ensure the reliable operation of gathering gas pipelines. The consistency of performed investigations will help to estimate the occurrence probability of complications caused by the accumulation of liquid and hydrates formation.

Development and application of new technologies and equipment for in-line pipeline inspection

In-line inspection is one of the most effective technical measures to ensure the safety of oil and gas pipelines. However, the extensive application of oil and gas pipelines of high-carbon steel, large diameter, high pressure and high flow rate in recent years brings about new challenges to in-line inspection. In this paper, we investigated the engineering application of new technologies and equipment, including the in-line inspection technology based on electromagnetic detector array, the extremely low frequency transient weak signal detection technology and new in-line inspection equipment. Then, the new technology and equipment of electromagnetic detector array were developed by applying the active emission and receiving of electromagnetic signal to inspect the metallic defects. Finally, noisy signals were inspected on the basis of Duffing chaotic oscillator, and thus the inspection of extremely low frequency signals in the noise was realized. In addition, the new method and equipment of extremely low frequency transient weak signal detection were developed and verified in actual inspection engineering. And the following research results were obtained. First, the in-line inspection technology based on electromagnetic detector array uses the synergetic effect between DC exciting magnetic field and high-frequency exciting magnetic field, so a perturbation response can be realized even by small signal excitation. Second, with the introduction of a novel compressive sampling of acquisition information composition, the speed bottleneck of in-line detector is broken through, and a new world record of the inspection speed of the electromagnetic detector array is set up, i.e., 8 m/s. Third, under the condition of high-speed movement, the received signals of in-line detector are weak and temporary while tracking and positioning outside the pipeline. And by virtue of the extremely low frequency transient weak signal detection method based on chaos, this technical bottleneck is broken through, and the signal-to-noise ratio (SNR) of transient weak signal in the process of real-time inspection is decreased below −10 dB. In conclusion, the superior performance of these new equipment has already been verified in the inspection engineering of in-service oil and gas pipelines. These research results will provide technical and equipment support for the safe operation of domestic main oil and gas pipelines.

Analysis of Sobolevo — Petropavlovsk-Kamchatsky gas pipeline aboveground crossings operating conditions

The article deals with the operating conditions of Sobolevo — Petropavlovsk-Kamchatsky gas pipeline. Much attention is given to technical assessment of aboveground crossings of this gas pipeline. We report key climatic conditions and other factors affecting gas pipeline operation. Also, we present the results of aboveground crossings partial monitoring and detect the matters of their condition significant degradation.

GENERAL CONCEPT OF CREATING UNIVERSAL DIAGNOSTIC LASER SCANNERS FOR CONSTRUCTION AND OPERATION OF MAIN GAS PIPELINES

Background The article is devoted to common concept development for the creation of diagnostic geodesic laser scanners for the construction and operation of main gas pipelines. Aims and Objectives The aim of work is to develop a general model for diagnosing gas pipelines to detect a gas cloud using a laser scanner and to search for the possibility of determining the optimal modes of such diagnostics. Results In order to be used in the construction and operation of gas pipelines, the general task of creating laser scanners operating in the infrared range was formulated. The optimization of operation mode of the laser scanner for detecting gas leaks in gas pipelines is fulfield. The synthesis of a specialized laser scanner, capable of realizing the geodetic laser scanner functions during gas pipeline construction, as well as diagnosing gas pipeline functions in order to detect gas leaks during its operation, was performed.

THE MATHEMATICAL MODELLING METHODS APPLYING TO ESTIMATE THE PIPELINES TECHNICAL STATE AND ENVIRONMENT SITUATION

In the context of providing trouble-free operation of oil and gas pipelines and preventing possible negative impacts on the environment, the issues of constructing an integrated mathematical model for assessing the technical condition of pipelines and the impact of emergency situations on the state of the environment in the course of hydrocarbon leakage are considered. The model of the evaluation of the stress-strain state of the pipeline according to the data on the displacement of surface points for the above ground and underground sections is given by constructing the law of motion of the site by known displacements of a certain set of surface points using assumptions about the type of deformation of the sections and reproduction of the deformations and stresses tensors components on the basis of different models of deformed solid body.
 The specified model does not require information on the whole complex of forces and loads acting on the investigated object during operation. The flow model has been refined in a pipeline with a violation of its tightness by recording a special type of boundary conditions for a Navier-Stokes equation system in a two-dimensional formulation and developing an original method for its solution on the basis of the finite difference method. In the article the stability conditions of the proposed numerical schemes on basis of the spectral sign of stability are presented. In order to assess possible negative impacts on the environment, a model of propagation of matter at its leakage from the pipeline was developed by solving two-dimensional diffusion equations taking into account the variables and different types of boundary conditions that take into account the number of sources of pollution and their intensity. The results of computations based on computational algorithms implemented by these models and graphic material illustrating these calculations are presented, peculiarities of distribution of harmful substances in the environment near the pipeline are analyzed. Directions of further researches for successful practical realization of the offered models are established.

THE PREDICTION OF STATIONARY MODES OF OPERATION OF GAS SUPPLY SYSTEMS BY THE METHOD OF INTEGRAL COEFFICIENTS

The authors present the methods of generating the system of the integral coefficients of influence for gas transmission systems aiming at the estimation of the parameters of its work on stationary operating modes. Each change of the technological parameters of the operation mode at the input of the gas transmission system will necessarily cause the reaction of the system which will manifest itself in changing the corresponding parameters at its output. Obviously, the parameters of the input and output of the system are interconnected by a complex system of equations, the implementation of which requires certain time costs and gathering additional information about the technical and hydrogasdynamic states of the system at each moment. Under the conditions of incomplete loading of the gas transmission system, which involves frequent changes in its operation modes, the accomplishment of the task is not always possible. It is suggested to create a system of integral coefficients of influence which characterize the ratio of input and output information in different stationary modes, and formally submit it in a matrix form. The processes characterized by integral coefficients of influence implicitly contain the technological parameters of the gas pipeline (length, diameter, hydraulic resistance coefficient, heat transfer to the environment, etc.) which can not always be determined with sufficient accuracy by the deterministic methods. The suggested methodology involves the creation of simple and effective methods of predicting which allow estimating the state of the gas pipeline by the costs and pressures at the inputs and outputs of the system, that is, by the operational data that are being monitored. On the basis of the proposed methodology, it is suggested to create an operational system that will allow managing the modes of operation of the main gas pipeline in cases of frequent changes in pumping volumes. When changing the technological scheme of the gas transmission system, there is a need to adapt the integral coefficients of influence. The application of the proposed methods is illustrated by the example of the main gas pipeline Soyuz.

Materials and Technologies Ensuring Environmental Safety of Reconstruction and Overhaul of Trunk Pipelines

The paper presents an overview of the studies of Russian and foreign scientists exploring the issues of reliable operation of trunk pipelines transporting oil and gas. It is found that subsea pipeline networks pose a greater danger in terms of their functional failures and environmental effects and appear more prone to stress corrosion cracking. Certain materials and technologies are brought into focus to demonstrate that their use allows curbing the environmental expansion or ensures the reliable operation of oil and gas pipelines. It is noted that one of the most promising methods for reconstruction and overhaul of trunk pipelines provide for the application of composite materials to the internal surface of a damaged pipes. The appropriate formulation of composite materials depends on the condition of the internal pipeline cavity. Also, there are scientific breakthroughs which may serve to reduce corrosion activity of clayey soils. Stress is laid on the importance of innovations in the development of technologies and materials ensuring the maintenance of ecological balance in the areas where oil and gas transmission networks operate.

Shale gas transmission and housing prices

In this study, we exploit residential property sales data in New York to value the external environmental costs of the proposed Constitution Pipeline, a high-capacity transmission pipeline designed to transport hydraulically-fractured natural gas in Pennsylvania to large northeastern markets. Results from difference-in-differences models suggest post-announcement price declines of 9% (∼$12,000) for those properties located within three kilometers of the pipeline. These results are strongly robust to different specifications and subsets of the data, as well as falsification testing. Additionally, we find some evidence of attenuation in our treatment effect over time, which is indicative of either declining salience or expectations of the pipeline over time. Our results suggest that homebuyer expectations of the environmental externalities of natural gas pipeline construction and operations are large and negative.

Device and Methods for Measuring of Acoustic Anisotropy and the Residual Stress in the Main Gas Pipelines’ Metal

One of the main conditions of safe operation of gas pipelines is the use of non-destructive diagnostic methods. Particularly important problem is the earlier operational diagnosis of pipes’ material of main gas pipelines based on the evaluation of the stress-strain state, elastic moduli and properties anisotropy by acoustic methods. The aim of the work is to develop methods for acoustic assessment of the stress-strain state, the elastic moduli and the properties anisotropy of pipeline material and to study these characteristics in different sections of main pipelines using a device based on contactlessEMAtransducers.Methods are implemented using specialized equipment (the structurescopeSEMA) and non-contact electromagnetic acoustic transducers. As an object of research, we used fragments – the cuttings of gas pipelines with circumferential welds both after fabrication and removed from service with stress corrosion cracking, including ones with corrosion damage and without visible damage.The method of determining the plane stress-strain state of pipeline elements is based on the phenomenon of acoustoelasticity – the dependence of the propagation velocity of ultrasonic waves on mechanical stresses. The method for determining the elastic characteristics of materials and the anisotropy of their properties is based on the relationship between the velocities of ultrasonic waves and the elastic properties of the medium. Both techniques are implemented by sounding the sample in one section using a longitudinal wave and two shear waves with mutually perpendicular polarization planes coinciding with the main stresses, and measuring their propagation times.It is shown that the stress state distribution both in the circumferential direction and along the generatrix is uneven which is caused by the peculiarities of samples (presence of a welded joint, stress corrosion cracking, long-term operation). The smallest acoustic anisotropy is observed for the Young's modulus. The anisotropy of the properties of most samples is in the range of 12–14 % for shear modulus, 9–10 % for Young’s modulus, 13–15 % for Poisson’s ratio. For samples with stress corrosion cracking a sharp decrease in the anisotropy coefficient is observed which makes it possible to use the indicated characteristics as informative parameters in detecting stress corrosion cracking.A feature of the proposed methods is high accuracy, due to the absence of necessity to determine the material density and precision measurement of its thickness, the measurement error of which is significant by known methods.Keywords:main gas pipeline, elastic moduli, acoustic anisotropy of properties, the biaxial stress-strain state, longitudinal and transversal waves.

GUARANTEED STRENGTH OF PIPES WITH TRANSVERSE CRACKS UNDER STRESS

Background One of the priority tasks to ensure reliable operation of main gas pipelines is to identify defects in pipe walls. Modern intratubal flaw detectors provide reliable finding of defects such as «transverse cracks» and «transverse cracks zone» at a level of at least 20 % of the pipe wall thickness. This circumstance implies that pipes with these defects types (with a depth of less than 20 %) remain in operation, but they can lead to accidental failures of gas pipelines. In this regard, there is a need to assess the cracks risk in terms of brittle fracture, as the most unpredictable and rapid process. Aims and Objectives Based on the numerical calculation of the stress intensity factor, to determine the level of longitudinal stresses, which guarantees the strength of the pipeline section with transverse cracks under stress. Methods A stretchable strip of infinite length with a transverse crack is taken as the computational model. To account for the viscous component in the fracture of the pipe wall, the problem was considered in the elastoplastic formulation, with the calculation of the Cherepanov-Rice integral. Results In the absence of data, the following values are used to estimate the growth rate of developing defects: the growth rate of the stress-corrosion defect: 1.0 mm / year in depth, 4.0 mm / year in length and width. A theoretically undetected crack 3.14 mm deep over 2 years of operation (the frequency of in-line inspection in areas with identified stress-corrosion cracking defects) may increase to a depth of 5.14 mm and actually lead to destruction over a given period of time. The presented calculation results show the need to determine the pipe steel ductility characteristics: fracture toughness, elastoplastic fracture toughness, and also allow to determine the longitudinal stresses level for guaranteed strength of a section of the main gas pipeline.

DEVELOPMENT OF THE COMPLEX SYSTEM OF LINEAR PART OF THE OPERATED MAIN GAS PIPELINES STEP-UP UPGRADE WHEN USING THEIR TECHNICAL CONDITION

Background The main task of the gas transmission system of PJSC Gazprom is the long-term, reliable and safe operation of main gas pipelines in order to ensure timely delivery of gas to consumers in the required volumes. In terms of reliable and safe operation, the industry fulfilled all the requirements for the main gas pipelines in a timely and efficient manner by maintaining and extending their service life, as well as all arrangements for the maintenance of the system as a whole. However, at present, most of the gas pipelines have been in operation for more than 50 years, and they require special treatment to their further reliable and safe operation. Aims and Objectives Prove the need to develop a system «Update». Results The necessity of developing a complex system of linear part of the operated main gas pipelines step-up upgrade when using their technical condition has been established. It was noted that the industry has scientific and practical prerequisites for the implementation of this task, in addition, the gas transmission system in multi-thread design with technological crosspieces between the pipes will make it possible to carry out all the planned renovation work. The solution of this task will allow to increase the efficiency, durability, reliability and safety of the gas supply transmission system to consumers.

OPTIMIZATION OF GAS PIPELINE BALLASTING COST WORKS

Background The wide distribution of various cryogenic geological processes in the Far North complicates the operating conditions of the gas pipeline. The task of ensuring a high level of reliability and efficiency of main gas pipelines operation is a complex problem. The movement of a gas pipeline from a set position as a result of landscape and soil features is one of the reasons for its capacity. Therefore, it is extremely important to consider the technology of work using ballasting to ensure the safe functioning of gas pipelines. Various designs and methods for ballasting and fixing gas pipelines are widespread in the practice of linear construction. Aims and Objectives To substantiate the relevance of using linear programming to solve problems in order to optimize costs in the conditions of limited resources. Methods Linear programming methods, potential method. Results A method is proposed for optimizing the cost of a gas pipeline ballasting project in the conditions of the marshland of the Far North on the example of the project «Construction the Gas Pipeline - 6.659 km Section of Achimov Deposit» by GazEnergoStroy LLC. The scope of work provided by the project includes the installation of a gas pipeline, methanol pipeline; equipping a crane unit; installation work of the purification device starting unit; installation work of the purification device receiving unit. The raw material base and the cost of materials are studied depending on the location of the facilities under the project. Using linear programming methods, cost and constraint matrices are compiled. The analysis of the system limitations, depending on the capabilities of the supplier has been fulfilled. Using the potential method, an optimal procurement plan has been obtained. This decision will reduce the cost of this work by 22.28 %, and also all project on the whole.

Effect of strain rate and sulfate reducing bacteria on stress corrosion cracking behaviour of X70 pipeline steel in simulated sea mud solution

In order to reduce the damage to the operation of oil and gas pipelines，the stress corrosion cracking (SCC) behavior of X70 pipeline steel in the South China Sea mud simulation solution under different strain rates and diverse growth days of sulfate-reducing bacteria (SRB) was investigated through slow strain rate test, scanning electron microscopy, and energy-dispersive spectroscopy. Results showed that the sensitivity of SCC initially increased and then decreased with the increase of strain rate when the number of SRB growth days was fixed. When the strain rates were 1 × 10−6 s−1 and 4 × 10−6 s−1, greater SRB growth days indicate more sensitivity of the SCC. When the strain rate increased to 7.5 × 10−6 s−1, the degree of the SCC in metals under the aseptic solution was small, and serious SCC would occur when SRB existed in the environment. The SCC sensitivity was maximum under the synergistic effect of strain rate of 4 × 10−6 s−1 and SRB number of 5.7 × 106 cells/ml.

ANALYSIS OF STATISTICS OF ACCIDENTS AND FAILURES OF THE MASTAKH - BERGE - YAKUTSK MAIN GAS PIPELINE

The problem of analyzing the causes of accidents and failure occurrences, risk assessment and prediction of critical changes of the complex technical systems state is among the most relevant areas of fundamental and applied research, serious attention is paid to this problem. Operation of oil and gas pipelines laid in the cryolithozone conditions is carried out in extremely contrasting conditions and natural environments with the active occurrence of complex climatic and geological processes interacting with the pipeline. A number of works are devoted to data analysis and classification of the causes of accidents and failure occurrences during operation of the gas pipeline «Srednevilyuyskoye Gas Condensate Field (SVGKM) - Mastakh - Berge - Yakutsk». The paper provides a statistical analysis of the causes leading to accidents and failures on the linear part of the main gas pipeline. Data on accidents and failure occurrences of the Mastakh - Berge - Yakutsk gas pipeline are collected, analyzed and entered into the geographic information database. This paper presents a statistical analysis of the causes of accidents and failure occurrences on the linear part of the main gas pipeline. The results of studies of emergency situations show that the combined effect of several factors leads to the destruction of the pipe. For each group of causes, the contribution to the total number of accidents (share of all cases), the distribution of damage for each emergency from this group of causes was calculated. Using the Pareto diagram, a set of reasons that lead to the greatest losses of gas is determined. The dependence of the accident rate on the development of hazardous geological processes in the area and the service life of gas pipelines was considered. The study of statistical data in this work allowed to outline the contribution of various factors to the accident rate of pipelines. Emergency situations caused by the loss of stability in geocryological changes of soils constitute a sufficient percentage of the total number of accidents, which leads to the feasibility of the organization of geotechnical monitoring of the natural and technical system, which allows to detect the initial stages of activation of dangerous geological processes and predict the occurrence of accidents. To solve the problems of monitoring and ensuring the safe operation of main gas pipeline, it is necessary to create a geoinformation database of the distribution of natural and man-made sources of danger. As the initial information for the formation of the database, the materials of remote sensing of the earth, data of ground survey and special works, statistical and natural resource information are used. This kind of data is necessary when ranking sections of the main gas pipeline according to the degree of danger and carrying out preventive measures, such as drainage, installation of thermal stabilizers and other protection measures.

Complex Protection of Pipelines Using Silicate Materials Based on Local Raw Materials of the Far East

Modern trends in the development of the oil and gas infrastructure of the Russian Far East are considered. The main threats in the operation of oil and gas pipelines are described. The technology of complex protection of pipeline surfaces is proposed. Protection of the inner surface is achieved through the use of silicate enamel coatings, protection of the external surface – through the use of foam glass. On the basis of local silicate raw materials the technology of the described materials is developed, and their main properties are determined. Recommendations on the application of the developed technology for the protection of pipelines are given.

The corrosion damage mechanisms of the gas pipelines in the Republic of Sakha (Yakutia)

The article provides examples and analysis of critical damage to a long-term gas pipeline in the Republic of Sakha (Yakutia) resulting from the development of corrosion processes. This is the accident in August 2006 at the gas pipeline branch to the city of Pokrovsk and the accident in December 2018 at the «Taas-Tumus-Yakutsk» gas pipeline. The mechanisms and scenarios of the development of corrosion damage in the permafrost zone are discussed. The studied gas pipeline was put into operation in 1967 and is still in operation. The construction and operation of the gas pipeline in the permafrost zone was of both industrial and experimental nature. Wherein, over 50 years of operation, damage and accidents caused by corrosion processes have occurred extremely rarely. But, taking into account the duration of the development of corrosion processes in the permafrost zone, an increase in the number of damages to the long-running main gas pipeline due to corrosion wear is expected in the near future. The stage of diffuse damage during long-term operation is confirmed by an increase in loss of efficiency due to corrosion damage over the last 25 years of operation of the main gas pipeline.

Reliability of linear main gas pipelines after longer operation in cryolithozone conditions

Ensuring the reliability of gas main pipelines, after long-term operation in a cryolithozone, is a very urgent task. Due to changes in the mechanical properties of metal pipes after their long-term operation, changes in spatial positions relative to design positions in permafrost, accidents and incidents have become more frequent. At the same time, the nature of damage to pipelines of gas pipelines in different regions of Russia is different. In the regions of Russia with high air humidity and soils that freeze to a shallow depth in winter, the onset of defect formation is on the surface of pipes, mainly in the form of corrosion, whereas, in areas where cryolithozone propagates, the onset of formation of defects is in the “body” of the pipe wall and an increase in these defects leads to more disastrous consequences. Also, in areas of distribution of cryolithozone, corrosion damage is rarely observed. The article deals with one of the sections of the linear trunk gas pipeline where the incident occurred in the form of pipeline discharge. The main cause of the release is considered to be the constantly changing topography of this area as a result of periodic thawing of permafrost. The existing regulatory documents on the construction of gas pipelines contain calculations, often referring to the general rules of building mechanics. Thus, the design organization may not sufficiently take into account modern developments in scientific research in the field of cold resistance and operation of gas pipelines in the areas of cryolithozone distribution under conditions of extremely low temperatures.

On the Turnpike Phenomenon for Optimal Boundary Control Problems with Hyperbolic Systems

We study problems of optimal boundary control with systems governed by linear hyperbolic partial differential equations. The objective function is quadratic and given by an integral over the finite time interval $(0,\, T)$ that depends on the boundary traces of the solution. If the time horizon $T$ is sufficiently large, the solution of the dynamic optimal boundary control problem can be approximated by the solution of a steady state optimization problem. We show that for $T\rightarrow\infty$ the approximation error converges to zero in the sense of the norm in $L^2(0,\,1)$ with the rate $1/T$, if the time interval $(0,\, T)$ is transformed to the fixed interval $(0,\, 1)$. Moreover, we show that also for optimal boundary control problems with integer constraints for the controls the turnpike phenomenon occurs. In this case the steady state optimization problem also has the integer constraints. If $T$ is sufficiently large, the integer part of each solution of the dynamic optimal boundary control problem with integer constraints is equal to the integer part of a solution of the static problem. A numerical verification is given for a control problem in gas pipeline operations.