Introduction |

List of abbreviations |

1 | An approach to numerical simulation of pipeline systems and facilities for their technical inspection |

| 1.1. | Concept of the proposed approach |

| 1.2. | Principles of development or selection of mathematical models |

| 1.3. | Numerical methods used |

| 1.4. | The verification problem |

2 | Numerical simulation of magnetic units operation applied for the technical inspection of pipeline systems |

| 2.1. | Numerical simulation of the MFL pig operation: problem statement |

| 2.2. | The selection of the mathematical model and methods for its numerical analysis |

| 2.3. | Results of the numerical analysis of the MFL pig's operation |

| 2.4. | Numerical simulation of the vibro-velocity sensor operation |

3 | Numerical simulation of gas transmission through pipeline systems |

| 3.1. | General |

| 3.2. | A brief description of the simulated object |

| 3.3. | Problem statement on the development of high-accuracy fluid dynamics simulators for gas transmission enterprises |

| 3.4. | The structure of high-accuracy fluid dynamics simulators for gas transmission enterprises |

| 3.5. | The creation sequence for the high-accuracy fluid dynamics simulators for gas transmission enterprises |

| 3.6. | Numerical analysis of the transmission of gas mixtures through extra-long pipelines |

| | 3.6.1. | Formation of mathematical model |

| | 3.6.2. | Numerical analysis of the mathematical model |

| | 3.6.3. | The construction of higher-order difference schemes |

| | 3.6.4. | Selection of Equations of State |

| | 3.6.5. | Simulation of valve operation |

| | 3.6.6. | Simulation of Gas Pipeline Failures |

| | 3.6.7. | Numerical evaluation of the transmission parameters of associated liquid fractions |

| 3.7. | Numerical simulation of gas transmission through compressor stations |

| | 3.7.1. | Mathematical models for segments of compressor stations |

| | 3.7.2. | Mathematical simulation of the steady-state modes of natural gas transmission through a compressor shop and a gas compressor station |

| | 3.7.3. | Mathematical simulation of transient modes of natural gas transmission through a compressor shop and a gas compressor station |

| | 3.7.3.1. | Consecutive alteration of compressor station steady states |

| | 3.7.3.2. | Analysis of compressor station transient modes |

| | 3.7.4. | On the simulation of complex compressor stations |

| | 3.7.5. | Verification of the methods of numerical simulation of compressor stations |

| 3.8. | Numerical simulation of gas transmission through a gas transmission system |

| | 3.8.1. | The simulation of steady-state modes of natural gas transmission through gas transmission systems |

| | 3.8.2. | The simulation of transient modes of natural gas transmission through gas transmission systems |

| | 3.8.3. | The automatic adjustment of computer-based fluid dynamics simulators for actual parameters of a particular gas transmission enterprise |

4 | Numerical structural analysis of industrial pipeline systems |

| 4.1. | A brief analysis of current methods of strength estimation for pipeline systems |

| 4.2. | Problem statement and mathematical formalization |

| 4.3. | The method for the solution of equilibrium equations for pipeline systems |

| 4.4. | Mathematical models for the analysis of the elastic-plastic behaviour of industrial pipeline systems |

| | 4.4.1. | Elastic-plastic behaviour of pipe steels |

| | 4.4.2. | The simulation of non-linear stress states of soils |

| | 4.4.2.1. | Engineering models of non-linear interactions between buried pipelines and the surrounding soil |

| | 4.4.2.2. | A three-dimensional elastic-plastic soil model |

| 4.5. | Technology for the numerical stress state analysis and strength evaluation of industrial pipeline systems |

| | 4.5.1. | The selection of tools for pipeline stress state simulation |

| | 4.5.2. | Stress state simulation of industrial pipeline system structures |

| | 4.5.2.1. | The beam approximation |

| | 4.5.2.2. | Shell models |

| | 4.5.2.3. | Solid models |

| | 4.5.2.4. | Stress state analysis and the estimate of the strength of industrial pipeline networks |

| | 4.5.3. | The application of numerical simulation to determine parameters of engineering models of pipeline-soil interaction |

| | 4.5.4. | Non-linear structural analysis of cold-formed pipeline bends |

| | 4.5.5. | Strength analysis of excavated pipeline segments |

| | 4.5.6. | Numerical stress state simulation of underwater pipeline crossings |

| | 4.5.6.1. | Specific features of constructions and the operational conditions of underwater pipeline crossings |

| | 4.5.6.2. | Problem statement for the stress state analysis and strength evaluation of underwater pipelines |

| | 4.5.6.3. | Solution methods for the stated problem |

| | 4.5.6.4. | The analysis of underwater pipeline loads from a liquid flow |

| | 4.5.6.5. | Stress state analysis for an underwater pipeline located in a steady liquid flow |

| | 4.5.6.6. | Stress state analysis for an underwater pipeline located in a transient liquid flow |

5 | Numerical simulation of damage factors caused by gas pipeline ruptures |

| 5.1. | Problem statement |

| 5.2. | Numerical simulation of debris impact at gas pipeline accidents |

| | 5.2.1. | A semi-empirical approach |

| | 5.2.2. | An approach using a numerical simulation for the destruction of the pipeline structure |

| | 5.2.3. | The assessment of possible effects produced by a fragment of debris on industrial personnel and the population |

| | 5.2.4. | Marking debris impact zones on topographic maps |

| 5.3. | Numerical simulation of gas hazards |

| | 5.3.1. | Simulation of plume emission |

| | 5.3.2. | On the application of turbulence models |

| | 5.3.3. | Numerical analysis of the fire hazard at gas pipelines |

| | 5.3.4. | Numerical analysis of the causes and mechanisms of ignition of the formed methane-air mixture |

| | 5.3.5. | Numerical analysis of the combustion of a methane-air mixture on the open country |

| | 5.3.6. | Assessment of thermal impact zones formed during gas pipeline fires |

6 | Cutting costs for the transmission of liquids and gases with high-accuracy computational fluid dynamics simulators |

| 6.1. | The optimization of steady state modes of natural gas transmission through a compressor station |

| 6.2. | The optimization of transient modes of natural gas transmission through a compressor station |

| 6.3. | The optimization of steady state modes of gas transmission through a network of compressor stations |

| 6.4. | The optimization of transient modes of natural gas transmission through a network of compressor stations |

| 6.5. | Particular examples of solving test problems and industrial problems |

| 6.6. | An extension of the suggested approach to gas pipeline network optimization for other industrial energy sector objects |

7 | The concept of making intelligent information-control systems for gas transmission enterprises through applying high-accuracy computational fluid dynamics simulators |

8 | Pipeline defective segment ranking through the application of the PipEst computation technology |

| 8.1. | The structure of the PipEst computation technology and its functional purpose |

| 8.2. | The method of pipeline defective segment ranking |

| 8.3. | Hardware and software systems for the analysis of defective pipeline hazard |

Afterword |

Bibliography |

Appendix 1. The verification of methods and technologies for the numerical simulation of gaseous mixture transmission through long pipelines. *Boychenko A.L., Kiselev V.V., Komissarov A.S., Pryalov S.N., Seleznev V.E.* |

Appendix 2. The construction of a mathematical model for liquid transmission through a system of open channels. *Pryalov S.N., Seleznev V.E., Zelenskaya O.I.* |

Appendix 3. A model of surging effects in the "GCU centrifugal supercharger -- adjacent connecting gas pipelines" system. *Kiselev V.V., Seleznev V.E.* |

Appendix 4. Practical examples of the application of a computational fluid dynamics simulator of a gas transmission enterprise. *Boychenko A.L., Kiselev V.V., Komissarov A.S., Motlokhov V.V., Pryalov S.N., Seleznev V.E.* |

Appendix 5. On the architecture of the computational fluid dynamics simulator of a gas transmission enterprise. *Motlokhov V.V., Seleznev V.E.* |

Appendix 6. A brief analysis of the method implemented in the "RSTRENG" software. *Aleshin V.V.* |

Appendix 7. Variant of the implementation of the finite element method for an analysis of the stress state of industrial pipeline systems. *Aleshin V.V.* |

Appendix 8. On the application of ANSYS and ABAQUS software for the structural analysis of industrial pipelines. *Aleshin V.V., Kobyakov V.V., Seleznev V.E.* |

Appendix 9. Program for automated creation and analysis of pipeline segments in beam approximation. *Aleshin V.V., Kobyakov V.V.* |

Appendix 10. Program for automated creation of geometrical solid model of the pipeline with surrounding soil. *Aleshin V.V., Dikarev K.I.* |

Appendix 11. Program for automated creation of geometrical solid model of the pipeline segment with corroded defect. *Aleshin V.V., Kobyakov V.V.* |

Appendix 12. Program for automated search for burst pressure for the pipeline segments with outside corroded wall defects. *Aleshin V.V., Kobyakov V.V.* |

Appendix 13. Estimating the effect produced by input data errors on the accuracy of the pipeline structural analysis. *Aleshin V.V., Dikarev K.I., Kobyakov V.V.* |

Appendix 14. Program for automated analysis of stress state of cold bent pipeline segments. *Aleshin V.V., Dikarev K.I., Kobyakov V.V.* |

Appendix 15. Program for automated creation of shell finite-element models of excavated pipeline segments. *Aleshin V.V., Dikarev K.I., Kobyakov V.V.* |

Appendix 16. Program procedures to analyze stress state of underwater pipeline accounting effect of flow surrounding this pipepine. *Aleshin V.V., Dikarev K.I., Seleznev V.E.* |

Appendix 17. An example of computer program in APDL for radiation matrix generation. *Aleshin V.V., Fotin S.V.* |

Appendix 18. An example of computer-aided fire hazard analysis for a gas pipeline segment in the vicinity of a gas regulating station of a power plant. *Aleshin V.V., Fotin S.V.* |

Appendix 19. An example of numerical nonlinear structural analysis for a defective gas pipeline segment under a transient thermal effect of fire. *Aleshin V.V., Fotin S.V.* |

Appendix 20. The application of dynamic programming methods to the optimization of gas transmission modes through a gas pipeline network. *Kiselev V.V., Seleznev V.E.* |

Appendix 21. On estimation of the speed of sound in a real gas. *Pryalov S.N., Seleznev V.E.* |

About the authors |

In recent decades the most critical problems the global community has faced
have been technological disasters and the consequences of a lack of energy
sources. The situation is aggravated by the criminal activities of
international terrorist organizations. These circumstances require an
efficient solution to the problem of improving energy safety in the
industrially developed nations. They require us to reassess the importance
of solving problems related to the increasing of safety levels, and more
efficient, enviromentally-friendly enterprises in the energy sector [1--9].

Among the main components of such enterprises are high pressure gas pipeline
systems. Nowadays the world's pipeline transportation systems and power
plant pipelines are becoming notably less reliable; as a result, the
environment is subject to increasingly harmful impacts. In particular, it
should be noted that industrial objects characterized by technological
(deliberate or accidental) emissions of gas mixtures into the atmosphere are
often located near populated areas, or even within their boundaries
following established town-planning practice. The accident at the
Urengoy--Petrovsk GP of the *Bashtransgaz Ltd.*, which took place on April 9,
2003, and caused the ignition of transported natural gas, can be presented
as a notorious example: three houses burnt down in a neighbouring village as
a result of the accident [282].

Unfortunately, over 550 accidents occurred at transmission pipelines
throughout the world between 1992 and 2001, according to articles
[8, 10--14, 281]. The average annual accident rate is 50--60, and this figure
shows no sign of decreasing. Russia's natural gas transmission pipelines
experienced more than 18 accidents over the period from May 2003 to June
2004, with a methane-air mixture being ignited during 15 of them [282, 289].
Foreign companies operating pipeline systems also suffer from similar
problems. Two major accidents happened in the USA over a short period (from
June 1999 to August 2000): at a gasoline pipeline of *Olympic Pipe Line Co.*,
and at a natural gas pipeline of *El Paso Natural Gas Co* [2]. Those
accidents caused serious public concern about the state of American
pipelines. Both of them were accompanied by heavy fires, in which 14 people
died, let alone huge losses of transported product and the costs of pipeline
restoration.

One of the principal reasons for accidents at industrial pipelines is their
age. The bulk of oil and gas pipelines have been in operation for more than
25 years [6, 7].

Apart from emergency situations, small emissions of harmful gases into the
atmosphere may be produced as a result of planned procedures. In this case
they are made in accordance with gas pipeline regulations. The following are
some examples of these types of emissions: planned, specially organized
emissions of natural gas at gas distributing stations; gaseous emissions
from power plants (steam, carbon dioxide, nitrogen, NO_{x},
SO_{2}+SO_{3}, CO_{x}, СH_{4}, С_{2}H_{4},
С_{20}H_{12} (benzapyrene), V_{2}O_{5}, carbon soot, etc.), etc. [14--17].

Emissions of the so-called greenhouse gases into the atmosphere, and their
generation during the violent fires, are dangerous contributions to global
climate change. In the light of the latest international treaties on global
climate change, the problem of cutting emissions of carbon dioxide and
methane in the energy sector is of particular importance [3--5]. Natural gas
accounts for more than 60% of global emissions of harmful gases into the
atmosphere.

In addition to consequences for the environment, accidents in pipeline
networks of energy sector enterprises cause notable economic damage [18, 19].
Thus, according to the data presented by the *Associated Limited company*
(Canada), material damage caused by a small plume emission of natural gas
into the atmosphere can be up to 175000 US dollars, while emission on
a larger scale can cost as much as 50 million dollars [13].

All of the above facts demonstrate that the problem of increasing fire and
environmental safety of pipeline networks of energy systems is urgent
indeed.

Solving the problem of safety improvement should go hand in hand with
solving the problem of cutting the costs of product transportation by
pipelines. The importance of such a solution may be illustrated by the
following example: Even at the stage of delivering natural gas from the
field to the consumer, more than twenty percent of the gas being transported
may be burnt at gas-turbine units of compressor stations [20--22]. Therefore,
large amounts of natural gas become internal costs to the relevant
gas-transport company and do not reach the market.

In view of the modern level of industrial development, solving the problems
of increasing safety and efficiency of pipeline transport requires the
application of numerical simulation methods. These methods allow a detailed
integrated analysis of complicated technological systems to be made with
a high level of reliability and accuracy.

The application of simplified methods of pipeline structural analysis, as
ways of determining possibly damaged zones during accidents at pipeline
transportation facilities, or using simplified computational simulators of
pipeline networks for their operational optimization give rough estimates of
actual parameters of physical processes. These estimates do not meet the
requirements of pipeline system design and operation or lead to inaccurate
results. This can be illustrated with several practical examples.

In-line magnetic flux leakage (MFL) pigs are used for the technical
inspection of transmission pipelines. Calculated estimates of magnetic field
parameters, as well as values for the forces that act on the pig structure
and are caused by these fields, are required for a scientifically based
development and advancement of the means and techniques of in-line technical
inspection. Up until the mid-1990-s such estimates were generally made by
means of analytical and semi-empirical dependencies [23].

The application of analytical and semi-empirical dependencies, for the
analysis of changes in electromagnetic field parameters and values of
forces, is only acceptable for defects of the simplest shapes (in terms of
strict geometrical classification) and significantly simplified analytical
models of pig structures. With actual defects and forces in place, the
difference between analytical models and results of on-site measurements can
reach tens to hundreds of per cent [24, 25].

Similar observations can be applied to traditional techniques of analytical
models for the stress state analysis of pipeline structures, those tecniques
being based on methods of the strength of materials and structural mechanics
(e.g. see [26--29]). They do not allow for adequate structural analysis of
complex pipelines to be made with the required accuracy, and in some cases
may give a wrong assesment of the structure's
stress state [30--33].

One of the most common accidents at gas pipelines is their rupture. Some
researchers suggest applying isothermic models of gas flow through pipeline
systems (or their modifications) in order to promptly locate the accident
and take measures to contain it [34--36]. These models, having been applied to
real accidents in Russia and West European countries, turned out to be
inconsistent, as the calculated values of gas flow through damaged systems
were inaccurate [37, 38].

OND-86 and OND-90 techniques are used for evaluation of concentrations of
harmful chemical species in gaseous emissions produced by factories
[39, 165, 166. These techniques are based on semi-empirical dependencies and
impose a number of important limitations on the elevation of the
contamination source, and the wind speed, taking into account the local
relief, buildings and other structures. They make it possible to calculate
the distribution of contaminant concentrations in the surface air, i.e. at
the altitude of 2.0 meters above the ground. As a rule, the proponents of
such methods proceed from experimentally observable laws of concentration
distribution over long periods of time, and set the parameters such that
experimentally observable concentration values should not exceed the
calculated values under any climatic conditions with 90% probability,
which means that the method cannot be used for the calculation of the
current state of concentration field.

According to one study [40], comparison of SO_{2} concentrations obtained
experimentally from a chimney of the *Karabashmed* company to those calculated
with the OND-86 method showed a divergence of results of 40 div 80 times.
A similar comparison of experimentally obtained and calculated values of
SO_{2} concentrations emitted from chimneys of power plant N21,
belonging to the *Mosenergo* company, gave a divergence of results of 1.2 div 2.4 times [17].

These examples confirm that transition from simplified analytical methods to
high-accuracy mathematical modelling based on numerical methods of continuum
mechanics, mathematical optimization and a broad application of modern
computer technology is necessary [41]. Input data for this modelling may
come in the automated mode from up-to-date diagnostic equipment, automated
information-control systems, geographical information systems,
meteorological services, etc.

The present publication presents a generalized and comprehensive study of the
theoretical basis, algorithms, computer-based implementation and industrial
application of technologies aimed at improving safety and operational
efficiency of industrial pipeline systems. The technologies in question have
been developed and improved by scientists and specialists of the *Computational Mechanics Technology Center of SPE VNIIEF-VOLGOGAZ Ltd.* (Russia)
since the early 1990s [21, 42--46, 167]. Ever
since the launch of these developments, their scientific consultation has been
provided by Dr.Sc. R.I.Il'kaev, Academician of the Russian Academy of
Sciences.

These developments are based on a mathematical approach to the numerical
simulation of complicated pipeline systems using well-known basic models of
continuum mechanics, numerical methods of mechanics and hybrid methods of
mathematical optimization proposed in previous studies [42, 47, 58, 63]. These
techniques are currently being successfully applied to numerous industrial
problems related to making industrial pipeline transportation networks in
gas, oil, chemical and energy industries more efficient, safe and
environment-friendly (e.g. see [32, 33, 38, 48, 167, 168]). They are also used
for the development and efficiency analysis of anti-terrorist measures,
creating software and hardware complexes for the early detection of
dangerous deviations of transportation parameters during the operation of
pipeline systems (e.g. see [44--46, 49--53] and details of the International
Science and Technology Center Projects: N1482, N1806 and N2409 [54]).

**Chapter 1** of the monograph deals with the description of the
numerical simulation of pipeline systems for improving their safety and
efficiency. The chapter presents the principles of construction or selection
of the corresponding mathematical models and methods of their numerical
analysis, and gives an example of validation techniques being developed
(during on-site trials).

**Chapter 2** considers the technology of numerical simulation of
the operation of magnetic instruments for technical inspection of pipeline
networks.

**Chapter 3** presents methods and technologies for the development
and application of high-accuracy computational fluid dynamics simulators for
numerical analysis of gas transportation modes through long branched
pipeline systems during their normal operation and in emergency situations.

**Chapter 4** is concerned with methods and technology for numerical
structural analysis of industrial pipeline systems.

**Chapter 5** describes the technology of numerical simulation of
damage factors acting during the failure of high pressure pipelines.

**Chapter 6** considers the theoretical footing and background of the
industrial application of high-accuracy computational fluid dynamics simulators
for cutting costs associated with the transportation of gases and fluids
through extensive pipeline networks.

**Chapter 7** presents the conception of intelligent
information-control systems for gas transmission enterprises using
high-accuracy fluid dynamics simulators.

**Chapter 8** describes approaches to pipeline defective segment
ranking using the PipEst computation technology.

Chapters 1, 2, 7 and 8 are written by R.I.Il'kaev, V.E.Seleznev, V.V.Aleshin, and G.S.Klishin. Chapters 3, 5 and 6 are written by V.E.Seleznev,
Chapter 4 by V.V.Aleshin.

The main body of the monograph is supplemented and illustrated with
materials presented in twenty-one appendices. Materials presented in
Appendices 1 and 4 are prepared by V.E.Seleznev jointly with S.N.Pryalov,
A.L.Boychenko, A.S.Komissarov and V.V.Kiselev. Appendix 2 is written by
V.E.Seleznev, S.N.Pryalov and O.I.Zelenskaya, Appendices 3 and 20 by V.E.Seleznev and V.V.Kiselev, Appendix 5 by V.E.Seleznev and V.V.Motlokhov,
Appendices 6 and 7 by V.V.Aleshin, Appendix 8 by V.V.Aleshin, V.V.Kobyakov and V.E.Seleznev, Appendices 9, 11 and 12 by V.V.Aleshin and V.V.Kobyakov, Appendix 10 by V.V.Aleshin and K.I.Dikarev, Appendices 13, 14
and 15 by V.V.Aleshin, V.V.Kobyakov and K.I.Dikarev, Appendix 16 by V.V.Aleshin, K.I.Dikarev and V.E.Seleznev, Appendices 17, 18 and 19 by V.V.Aleshin and S.V.Fotin, Appendix 21 is prepared by S.N.Pryalov.

The authors wish to express their gratitude and appreciation to the staff of
the *Computation Mechanics Technology Center of SPE VNIIEF-VOLGOGAZ Ltd.*
Irina Skiteva, Olesya Korshunova and Oksana Ustyushina for their work on the
translation of the manuscript into english and their assistance in preparing
the manuscript for publication.

The authors are sincerely thankful to the collective of the *URSS
Publishers* for their considerate and friendly attitude towards them and for
the high quality editing of the translation, professional preparation and
printing of the monograph.

Preparation of the monograph's manuscript was financially supported by the
*International Science and Technology Center* within the framework of the ISTC
Project N2759 and in collaboration with *Los Alamos National Laboratory*
(USA). Some of the developments described in the monograph were carried out
with financial support of the *International Science and Technology Center*
within the framework of the ISTC Projects N1452, 1806 and 2409, and in
collaboration with the *Fraunhoffer Institute for Non-Destructive Testing*
(Germany), *Sandia National Laboratories* (USA) and the *Environmental
Protection Agency* (USA). The computational equipment used at the stage of
writing the manuscript was offered to the authors within the framework of
the Russian-American Intergovernmental Agreement of September 22, 1998 under
the Nuclear Cities Initiative Program (NCI Project N04446000-99-35). The
costs related to the publication of the monograph were paid by the
*Computation Mechanics Technology Center of SPE VNIIEF-VOLGOGAZ Ltd*.

**Il'kaev Radii Ivanovich**

Director of the Russian Federal Nuclear
Centre--All-Russian Scientific Research Institute of Experimental Physics
(RFNC--VNIIEF). Doctor of Science, Academician of the Russian Academy of
Sciences, Academician of the Russian Academy of Rocket and Artillery
Sciences, Laureate of three State Prizes. Honoured worker of science.
Awarded with the Order of Merit for Fatherland of the third degree.
Principal field of specialization: high energy density physics. Professional
interests: physical science and technology of dual application. Author and
co-author of more than 350 scientific works.

**Seleznev Vadim Evgenevich**

Deputy Chief Designer of the RFNC--VNIIEF, Head of the Computation
mechanics technology centre of SPE VNIIEF-VOLGOGAZ Ltd. (CMTC). Doctor of
Science. Principal field of specialization: mathematical simulation of
industrial facilities of energy systems and complexes. Professional
interests: computation mechanics, mathematical optimization, conversion of
defense science and technology. Author and co-author of more than 170
scientific works dedicated to improving safety, efficiency and the
environmental friendliness of complex technological systems by means of
computation mechanics and mathematical optimization.

**Aleshin Vladimir Vasilevich**

Deputy Chief of department of the RFNC--VNIIEF, Deputy Head of the CMTC.
Doctor of Science. Principal field of specialization: mathematical
simulation of industrial facilities of energy systems and complexes.
Professional interests: computation mechanics, conversion of defense science
and technology. Author and co-author of more than 120 scientific works
dedicated to improving industrial and fire safety of complex technological
systems by means of computational mechanics.

**Klishin Gennady Semenovich** (1944--2004)

Chief Designer of the RFNC--VNIIEF, Director of SPE VNIIEF-VOLGOGAZ
Ltd. Principal field of specialization: instrumentation and automation of
industrial facilities of energy systems and complexes. Professional
interests: theory of creation and operation of intelligent
information-control hardware and software systems, conversion of defense
science and technology. Author and co-author of more than 120 scientific
works dedicated to creation and practical application of intelligent
information-control hardware and software systems and computation
technologies for integrated assessment of state of the fuel and energy
complex industrial facilities.