Modelling maintenance decisions of communal gas suppliers

Project Work

Modelling Maintenance Decisions of Communal Gas Suppliers – Conceptual Design and Implementation of Simulation Algorithms using VBA

Authors: Vera B URANOVSKA Matr. Number 2209011 Anton P OPOV Matr. Number 2220161 Levon A LTUNYAN Matr. Number 2217213 Supervisors: Dipl.-Inform. Philipp L IMBOURG ¨ Dr. Dirk K ONIG

University of Duisburg-Essen ¨ fur Fakultat ¨ Ingenieurwissenschaften Abteilung Informatik und Angewandte Kognitionswissenschaft Informationslogistik Prof.Dr.-Ing. H. D. Kochs

Duisburg, September 16, 2007

Abstract The aim of this project is to represent a simulation model used to calculate the number of failures per materials for a natural gas pipeline network system. This is a useful tool for analysing the behaviour of gas pipe systems under different operating conditions. Historical database is used for the careful examination of the gas net and for formulating the simulation model. Gas utilities can utilize the simulation model to create a safe natural gas pipe network system, taking into consideration the material and the year of grounding. Because the natural gas network growth continuously varies with time, a dynamic simulation model is built to display the state variables of the gas pipe system and to provide guidance to a company on how to operate the system properly.

The model can efficiently simulate behaviour of the pipeline system with satisfactory results.

An existing statistical method, such as the Weibull distribution, is used for the precise calculation and simulation. Implemented under Visual Basic for Applications (VBA) code has been utilized to add enhancements to the basic MS Excel package functionality.

1

Contents 1 Introduction 1.1 Historical, Economical and Technical Progress . . . . . . . . .

1.2 Problem Description . . . . . . . . . . . . . . . . . . . . . . .

2 Background 2.1 Engineering Approach to the Problem . . . . .

2.1.1 Materials . . . . . . . . . . . . . . . .

2.1.2 Pipe Maintenance . . . . . . . . . . . .

2.1.3 Possible Pipe Defects . . . . . . . . . .

2.1.4 Accidents . . . . . . . . . . . . . . . .

2.1.5 Failure History and Repair of Damaged 2.2 Statistical Approach to the Problem . . . . . .

2.2.1 Risk Analysis . . . . . . . . . . . . . .

2.2.2 The Weibull Distribution . . . . . . . .

2.2.3 Kaplan-Meier Survival Function . . . .

2.2.4 RIKA Software . . . . . . . . . . . . .

4 4 5

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16 16 17 19 20 28 29

4 Results 4.1 Length . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

4.2 Failure Factor . . . . . . . . . . . . . . . . . . . . . . . . . . .

4.3 Number of Failures . . . . . . . . . . . . . . . . . . . . . . . .

29 29 33 33

3 Methods 3.1 Goals and Purpose 3.2 Research Stage . .

3.3 Simulation Stage .

3.4 Recovery Strategy .

3.5 Pipeline Failures .

3.6 Tests . . . . . . . .

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5 Discussion 35 5.1 Interpretation of the Results . . . . . . . . . . . . . . . . . . . 35 5.2 Summary . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 37 5.3 Outlook . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 38 6 Acknowledgement

39

A Appendix

40

References

42 2

List of Figures 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24

Development of the project . . . . . . . . . . . . . . . . . . . .

Corrosion failures . . . . . . . . . . . . . . . . . . . . . . . . .

Dent, gouge, groove and arc burns defects . . . . . . . . . . .

Pipe body cracking . . . . . . . . . . . . . . . . . . . . . . . .

Effect of the shape parameter Ă&#x; . . . . . . . . . . . . . . . . .

Relation between the simulation and the results used in the RIKA program . . . . . . . . . . . . . . . . . . . . . . . . . .

Context diagram of a gas pipeline network system . . . . . . .

Description of the different stages of the simulation . . . . . .

Input Parameters Table . . . . . . . . . . . . . . . . . . . . .

Input Parameters Table . . . . . . . . . . . . . . . . . . . . .

Code sample including the five procedures . . . . . . . . . . .

Einbaujahr and History columns . . . . . . . . . . . . . . . . .

Total length of the different materials per year . . . . . . . . .

Number of failures for the different materials . . . . . . . . . .

Total length of a pipe network for different materials per years Total length of each material with respect to 2007 . . . . . . .

The opportunity, which the additional button provides . . . .

Real network growth through years . . . . . . . . . . . . . . .

Failure factors for every single material . . . . . . . . . . . . .

Comparison between the real values and the results from the simulation for the number of failures . . . . . . . . . . . . . .

Comparison between the lengths obtained from our simulation and the real values . . . . . . . . . . . . . . . . . . . . . . . .

Percentage of added pipes . . . . . . . . . . . . . . . . . . . .

Percentage of replaced pipes . . . . . . . . . . . . . . . . . . .

Renewal rate of the network down the years . . . . . . . . . .

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5 9 9 10 13 16 18 19 20 23 24 25 26 27 30 31 32 32 33 34 36 40 40 41

1 INTRODUCTION

1 1.1

Introduction Historical, Economical and Technical Progress

During the 19th century, pipe technology developed very fast all over the USA, western Europe and especially in Germany. The main reasons for this growth were the emerging oil industry, the distribution of natural gas and the increasing need for steam and water. Wood was still in use, but towards the end of the 19th century the seamless pipe made its appearance.

Steel-making and pipe manufacturing techniques have reached dramatically improvement in performance and maintenance over time. At the threshold of the 20th century, the piping technology was balanced for unprecedented growth due to improvements in welding, materials and pumping.

After The Second World War German economy was divided mainly into two periods. From 1945 to 1973 the country recovered rapidly from the almost unimaginable devastation caused by the war and then took off, growing faster more than twice as fast as its own historical trends. From 1973 the extensive growth was replaced with intensive one. National engineering societies and industry institutes became an important source of innovation and improvement. For this reason standardisation of materials and design became a financial and safety necessity. Industries came to rely more on codes and standards. European integration was related to the wider process of globalization and was in turn driven by technological advances – development of technology broadly involves the use and application of knowledge, such as scientific, engineering and mathematical, to achieve some practical results. For instance development and increase of iron and steel industries contributed to the rapid rise of pipe production and expansion gas networks as a whole.

The revision of the Old German Energy Law on April 28, 1998, gradually suppressed the protection of supply areas awarded to gas supply companies.

In the future, gas utilities, like electricity utilities, not only face competition from substitutes like light heating oil, but also have to prepare themselves for increasing competition from other gas utilities. This adds to the requirements of the EU Gas Directive, most of which have already been incorporated into German law. [6] In such a competitive situation generated of this new accepted law and liberalisation of the market, gas companies more often use special computer centers for scientific simulations. They help corporations to develop and implement expansion strategies and generate system models. Beside project execution strategies set-up cost controls are developed, major equipment are tendered and facilities are both installed and commissioned. Computer cen4

1.2 Problem Description

1 INTRODUCTION

ters such as Rechenzentrum f¨ ur Versorgungsnetze Wehr GmbH, have a great influence in the area of development of programs for simulations and risk prediction.

1.2

Problem Description

The main purpose of this work is a simulation based on a historical database using MS Excel and Visual Basic for Applications (VBA). An important part is the usage of statistical tools for analysis and calculations of the recovering strategy of a gas pipe network, including steps as removing pipes, changing old with new ones and increasing their overall length. Past maintenance decisions are taken into consideration for the precise prediction of the damage rates. That is why in our case the information for every changed pipe segment, in particular the year of repair and the material, is saved. Finally, the probability of faults is computed with help of the Weibull distribution.

1) Analysing 1) Analysing the task spesification

2.2) Modeling of the algorithms the algorithms and their implementa‐ tion in VBA

2 1) 2.1) Research stage → Chapter 3.1

3) Simulation → Chapters 3.2 3.4 3.2‐3.4

4) Validation of the results → results → Chapter 4

Figure 1: Development of the project

5

2 BACKGROUND

2

Background

This chapter includes two main sections which describe the statistical and engineering approach to the problem as well as the main idea of this project.

Based on our knowledge and the information introduced in the following paragraphs the goal of our work, a computer based simulation, is achieved.

A computer simulation is a computer program that attempts to simulate an abstract model of a particular system. Computer simulations have become a useful part of mathematical modelling in the process of modern engineering technology, to gain insight into the operation of those systems.

After estimation and validation of a model, a simulation of the output can be done. Therefore, results can be used in predicting future situations. The use of MS Excel and the built in VBA language improves and automates such simulations, which are in help for risk analysis and prediction.

2.1

Engineering Approach to the Problem

The following chapter deals with information related to engineering problems, that have occurred through out our work. It deals as well as with pipe materials, maintenance, possible failures and their repair.

2.1.1

Materials

This section describes the materials needed for pipe production, their properties and usage.

In order to select the most suitable material for a pipe system some important factors need to be considered. The pipes must be capable of: • transferring the required flow • withstanding internal pressure created by pumping without bursting • if laid under roads, withstand crushing loads caused by vehicle traffic • withstanding accidental damage caused by mechanical and manual digging, which is a common problem in urban areas Metal pipes must be protected against corrosive action by groundwater and soils.

These factors are internally linked and only when all have been satisfied the correct type of pipe system can be selected.

There are different criteria for choosing and using a certain type of a pipeline - the material itself and the advantages and disadvantages that it 6

2.1 Engineering Approach to the Problem

2 BACKGROUND

offers. The most commonly used pipes however remain the steel ones. ”Steel pipes and fittings are alloys of iron (Fe) and carbon, containing less than 1.7% carbon. They can be classified in three groups: carbon steels, low alloy steels and high alloy steels.” [1] Nevertheless only carbon steel pipes are used in gas pipe network systems. ”Starting in the early 1960’s metal gas pipes have been made out of ductile cast iron (GGG) which is a type of iron invented in 1942 by Keith Millis.

While most varieties of cast iron are brittle, ductile iron is much more ductile.

Ductile iron pipe is stronger, easier to tap, requires less support and provides greater flow area compared to pipe made from other materials. In difficult terrain it can be a better choice than a PVC, a concrete, a polyethylene or a steel pipe.”[1] In the early 1970’s preferred for usage became gray cast irons (GG)material with other elements added to it to improve its properties. Particular attention has been paid to GG pipes, since they are usually the oldest pipes in a given gas system and almost always have the highest rate of failure. ”However, there have been a number of gaps in the existing knowledge on the causes of failures, their identification, prevention and repair.” [1] PVC pipes made their appearance for the first time in 1930’s. In the beginning of 1980’s they became more popular, reliable and preferred for usage. This kind of material has excellent chemical resistance. ”Due to its long-term strength characteristics, high stiffness and cost effectiveness, PVC systems are suitable for a wide diversity of plastic piping installations. PVC is resistant to many acids, bases, salts, halogens and alcohols. It is not resistant to solvents, aromatics and some chlorinated hydrocarbons.” [1] Polyethylene (PE) pipes were introduced to the gas industry in the late 1960’s, offering corrosion resistance, easier installation and cost-effectiveness.

As a result, PE pipes almost totally replaced metallic pipe materials because of better material’s size and pressure range.

Since 1945 fibre cement pipes, known as Faserzement/Asbestzement (AZ) in Germany, have been used extensively in the pipe production. Fibre cement pipes have proved over the years their suitability and economic competitivity for diverse applications such as gas and water supply throughout the region.

7

2.1 Engineering Approach to the Problem

2.1.2

2 BACKGROUND

Pipe Maintenance

Risk strategies taken into consideration require different maintenance strategy of gas pipes. The main purpose of such a management is to create effective recovery programs, to increase the general public’s ability to respond constructively during and after an accident and also to minimise losses of life and property damage due to a failure. Equally important is the limitation or reducing danger to the public health, environmental damage, and economic impact from risky materials incidents. ”Reliability of supply and low operating cost are the main targets of pipeline operators. Preventive maintenance forms the substantial part of all cost components. Inspection and leakage check for a gas network is done on a regular, scheduled basis by the responsible sides of the utility company.

Based on these information, a maintenance plan is made on a monthly or quarterly basis.” [3] Renewal parameters are important part of the pipe maintenance. The variable terms taken into account, in particular the replacement material percentage and the network grow, should be chosen in a manner that assures a better sharing of the budget, thus leading to a more accurate simulation and effective recovery strategy. ”Only about 1/8 of the total repair cost is on account of material and on immediate labor for pipeline replacement. Another quarter is spent for earthworks and the half of the cost goes to reconstruction of road surface. Pooling of activities in close local proximity thus holds large savings potential, cause a least part of side setup cost can be saved. Considering the list of preventive maintenance measures this calls for a computerised spatial decision support system.” [3] 2.1.3

Possible Pipe Defects

Usually, piping failures are caused by a corrosion problem. Sometimes, however, they are due to engineering design - such as the use of thin wall pipe, cut grooved piping, or due to faulty construction methods. Gas pipelines carry millions of cubic meters of gas and risky fluids across hundreds of kilometers across Germany. Leaks, resulting from severe weather, improper installation or maintenance occur frequently. Precautions are available and must be undertaken to minimise these failures and their effects.

Therefore computer simulations are made. One of the important elements taken into consideration is risk characterisation, which reviews all of the previous items and makes calculations based on data, with all the assumptions clearly stated. Often the conclusion is that more data and/or improvement

8

2.1 Engineering Approach to the Problem

2 BACKGROUND

in methodology is needed and that no numerical risk number can be derived to express accurately the magnitude of risk.

In the following paragraph pipe failures that can occur are described in more details and their possible repair is discussed.

• ”Corrosion defects are caused by a chemical reduction action on the surface of the pipe material, resulting in localised thinning of the pipe wall. Failure occurs first by yielding at the corrosion site, followed by rupture of the steel membrane.” [8]

Figure 2: Corrosion failures [8] Unfortunately, the corrosion is a continuous and unstoppable process.

The end product is simply the result of an electrochemical reaction through which the higher energy processed metal is slowly reverted back to its naturally occurring form.

Figure 3: Dent, gouge, groove and arc burns defects [8] • The main reason for gouge, groove or arc burns and dent failures (fig.3) are either third-party damage or non-acceptable maintenance, and may include stress concentrators such as cracking. Defects occur by the pipe material containing the failure flexing because of internal pressure

9

2.1 Engineering Approach to the Problem

2 BACKGROUND

differences, which in turn causes cracking. When the crack extensions become critical, rupture occurs.

The repair of such failures is possible through eliminating flexing in the pipe material, eliminating fatigue, crack extension, and rupture.

• Chemical action (Stress Corrosion Cracking) is the reason for Pipe Body Cracking . Failure occurs when crack becomes unstable (fig.4).

Permanently reducing the stress state in the material surrounding the possibility of crack failure extension is limited.

Figure 4: Pipe body cracking [8] • Weld defects are caused by poor maintenance. Failure occurs when the strength of the weld is insufficient to neutralise the applied forces.

Permanent mechanical support to the weld area is needed to reduce the strain by the external forces.

• Grind defect are the result of a mechanically removing metal from the surface of the pipe material. ”Failure occurs first by bulging (yielding) at the grinding area, followed by rupture of the steel membrane. Additionally, the presence of stress concentrators could act as initiation points for rupture at lower strain levels.” [8] Decreasing of such failures is possible by preventing bulging by permanently providing mechanical support to the localised thinned section.

Using sleeve in this cases also eliminates metal movement and reduces the strain induced in the material by the external forces.

• ”A leak occurs when a hole in the pipe wall allows the gas to escape, while the pipe wall continues to contain the internal pressure preventing a rupture from occurring. It is possible both leaking defects and active internal corrosion to proceed through the wall of the pipe if left unrepaired.

At present, development is underway to research and test a unique technique to repair both leaking defects and active internal corrosion.”

[8] 10

2.1 Engineering Approach to the Problem

2.1.4

2 BACKGROUND

Accidents

In 1998 the Energy-related Severe Accident Database (ENSAD) was established. Assessment of severe accident risks was primarily based on this Probabilistic Safety Assessment’s (PSI) database. Its main purpose is to continuously maintain and update the data using a variety of information sources, that eliminate some forces which are encountered in many other accident databases driven by the local availability of information. The rights of the cases allow to perform analysis of accident risks, including processing, storage, transports and waste management.

The definition of a ”severe accident” is connected to the minimum damage level for each type of consequence (injured persons, evacuees, or economic losses). ”The PSI database ENSAD uses seven criteria to define a severe accident: • at least five deaths • at least ten injured • at least 200 evacuees • extensive ban on consumption of food • releases of hydrocarbons exceeding 10 000 t • enforced clean-up of land and water over an area of at least 25 km2 • economic losses of at least five million Euro (2000) ” [2] The accident is considered to be severe, if any one of the above criteria is satisfied. However, distinct types of consequences are covered to various extents because of differences in availability and quality of information.

ENSAD database also includes information for smaller accidents. Nevertheless their level of completeness is much lower than it is the case for the severe accidents. Therefore, smaller accidents were only taken into account in the context of specific evaluations, for which a sufficient statistical basis is provided. ”Although, severe natural gas accidents in Germany attract a great deal of public and media attention, they are rather rare events (around 1% of all accidents) when compared to smaller accidents that constitute the large majority. Regarding death cases and injured people, severe accidents in gas distribution account only for about 10 to 20% of the respective totals, indicating that smaller accidents are again the dominant contributor.

11

2.1 Engineering Approach to the Problem

2 BACKGROUND

Normalized accident rates decreased over the period 1981-2002. This was evident for fatalities and even more pronounced for injured, and is thus likely to indicate a process of continuous improvement of safety in the gas industry.” [2] 2.1.5

Failure History and Repair of Damaged Pipes

One aspect of the gas pipes concerns the usage of history data of faults and failures during the years, collected from operational use, to improve reliability of gas system. Information contained in these databases describes the nature of defects for a specific pipe segment/material type. The objectives are to use the history to determine how to prevent and remove faults. Finally, the histories may present problems indicating the need for better methods to prevent or detect failures, enabling in this way justifiable research ideas.

The repair cost of damaged pipelines depends on the available money and should be achieved with the means of a reasonable budget. The decision, what exactly ”reasonable” means, should be decided from the particular gas supply company.

If the gas pipes are in a dangerous condition, they must be repaired before gas can be leaked out. Pipes located in distance of one meter from house side are responsibility of the house owner. The others are responsibility of gas suppliers. In order to minimise the sum of investments and operating costs, determination of optimal diameter for each pipe is made. The company must decide about investments in the network taking into account the future operating and investment costs.

Before any decision for renewal is taken, all other possibilities should be explored, for example the use of engineering calculations to allow acceptance of the failure. Before the renewing is attempted on a pipeline, a number of details should be obtained. These include pipe details, pipeline operating conditions, pipeline product specification, pipe burial and current conditions and details of damage.

Depending on the nature and extend of the damage, and whether the pipeline is leaking or not, the repair operation may need to be carried out: • without interrupting the flow, perhaps using a temporary leak clamp in the first instance • by replacing the pipe section after stopping the flow

12

2.2 Statistical Approach to the Problem

2.2

2 BACKGROUND

Statistical Approach to the Problem

In the following paragraphs more details concerning mathematical and statistical methods are represented. Also definitions related to our work and the importance of the simulation results are described.

2.2.1

Risk Analysis

”The main purpose of risk analysis is to evaluate the probability of occurrence of a certain event using analytical or statistical methods. These calculations involve system quantitative reliability and maintainability information, such as failure rate, or repair rate”. [7] A prediction is a statement or claim that a particular event will occur in the future. Methods such as probability are used in prediction in science.

Governments typically apply probability methods in environmental regulation where it is called ”pathway analysis”. Here probability theory has been used as a tool for gas risk prediction.

Such techniques have been under development and have seen increasing application to engineering problems for the last 50 years.

2.2.2

The Weibull Distribution

The Weibull distribution is most commonly used in life data analysis, though it has other applications as well. Weibull distributions may also be used to represent manufacturing and delivery times in industrial engineering problems. It is a very popular statistical model in reliability engineering and failure analysis. Due to its flexibility it can relate to the behaviour of other statistical distributions such as the normal and the exponential. An understanding of the failure rate provides insight to what is causing the faults (fig.5):

Figure 5: Effect of the shape parameter ß 13

2.2 Statistical Approach to the Problem

2 BACKGROUND

1. A decreasing failure rate leads to the conclusion that the defective items fail early and one would note the presence of the decreasing of the failure rate over time (β < 1).

2. A constant failure rate suggests that items are failing from random events (β = 1).

3. An increasing failure rate suggests wear out - parts are more likely to fail with aging (β > 1).

Failure factors are determined with the help of the Weibull function. The following formula is utilized: b · (tb−1 ) ab where a, b = damage parameters for different groups of pipe materials λ=

2.2.3

(1)

Kaplan-Meier Survival Function

As a result of the failure rate determination, calculation and simulation of the probability of the failures for the different groups of pipes along with the failure documentation can be also done by the use of the Kaplan-Meier function.

The survival function, also known as a reliability function, is a property of any random variable that maps a set of events, usually associated with failure of some system, into time. It captures the probability that the system will survive beyond a specified time. The term reliability function is common in engineering while the term survival function is used in a broader range of applications such as medicine.

The Kaplan-Meier survival function is a simple way of computing the survival curve. In engineering field this method is used to measure the time until failure of machine parts, in our case for calculating the failure of pipe segments which will occur.

The Kaplan-Meier function, also known as the product limit estimator, can be used to calculate values for nonparametric reliability for data sets with multiple failures and suspensions. The equation of the estimator is given by: ˆ i) = R(t

i Y n j − rj j−1

nj

where 14

, i = 1, ..., m

(2)

2.2 Statistical Approach to the Problem

2 BACKGROUND

m = the total number of data points, n = the total number of units The Kaplan-Meier survival curve is often illustrated graphically. It looks like a poorly designed staircase, with vertical steps downward at the time a failure occurred.

2.2.4

RIKA Software

An important statistical method used for risk analysis in a gas network is the software packet RIKA, created by the Information Logistics Department at the University of Duisburg-Essen in cooperation with the Rechenzentrum f¨ ur Versorgungsnetze Wehr GmbH and four communal power supply companies. The program can be used to effectively plan the replacement strategies of gas pipe networks. The goal of the risk-oriented maintenance is to keep the number of failures as well as the risk constant or to lower them. Such behavior can be simulated with the help of RIKA. By simulating the net aging and the renewal rate, the program can estimate the development of damage rates and risk during longer periods of time. The accurate modelling results in a renewal plan for each year, which consists of the pipe segments which can be changed. This can be used as the basis for planing the actual maintenance strategy. The plans can be used in shorter periods of time and should not be used as a replacement of the decisions which the engineers in charge of the maintenance of the gas network should take. Furthermore, the program cannot foresee all factors which influence the network from outside.

[4] A renewal plan requires that: • unnecessary investments should be avoided • essential investments should be established • a full advantage should be taken from a limited year budget • if the budget is insufficient, this should not be a reason for decreasing the quality and increasing of the risk in the network [9] By means of the program RIKA the risk, computed for each pipe segment of the gas network, is defined as follows: R(t) = λ(t) · L · q · S · (1a/finspection ) where 15

(3)

3 METHODS

λ(t) = material dependent failure factor, L = length of the pipe segment, q = gas exit rate(pressure dependent), finspection = frequency inspection per a, s = sensibility factor of the buildings, which are affected by the damages caused by a pipe segments [5] It can be shown that a reduction in the budget will increase the number of failures and the risk in the gas network. With the help of RIKA, the communal gas suppliers can take a full advantage of their knowledge and existing data basis for taken in the past strategy decisions, in a way that future ones can be developed and improved. In this manner a damageoriented can be changed with a risk-oriented maintenance policy. [4]

calculates l l t

Simulation

Results

is used for comparison

are part of

RIKA software

Figure 6: Relation between the simulation and the results used in the RIKA program

3

Methods

This chapter deals with the purpose of the project, as well as with the different stages of its development. The used methods and tools are described in more details.

3.1

Goals and Purpose

Our work is a part of a bigger project, which aims to predict and validate damage rates. Therefore, the goal of our project is the development and implementation of a program which simulates the historical behaviour and 16

3.2 Research Stage

3 METHODS

network structure of a communal gas system. In other words by calculation of the number of failures, a situation which resembles the real one should be achieved. Taking into consideration aging of the network and the renewal rates, the development of the damage rates during long periods of time should be obtained. It is necessary to develop a suitable procedural and flexible model for the computing of the failure rates behaviour in the time period 1960-2007. In addition the accurate modelling should permit the plans for renewal to be determined. On the other hand the real failures in the period 1988-2006 are provided. The second objective is to compare them with the failure rates which were obtained from our simulation.

The actual situation was analysed. The MS Excel environment enhanced with the built-in programming language Visual Basic for Applications and the used methods were the ones most suitable for the concrete problem.

A rough estimation of the expected damage probabilities can be obtained from a historical development of the network. That is why for a more precise simulation new entries till the present year should be added to the given damage database. In this way a situation close to the real state can be achieved. The two tasks were developed in several phases.

The first step of the first task is simulation of the recovery strategy of a gas pipe network. This includes removing pipes, changing old with new ones and increasing the length of the whole net. The length of the pipe segments per material is calculated. Furthermore, the failure factors are computed according to the information for the pipe lengths at disposal. In addition, the number of failures have to be predicted. They depend on the damage parameters ”a” and ”b” (fig.9) and in the same time on the total length per year.

The second task consists of comparison of the real values and the results obtained from our simulation. This part is also subdivided in two assignments. First, the differences and similarities between the provided damage rates and our results should be described. The reason for the inaccuracy of the resolve are discussed in Discussion chapter (Section 5). Second, a comparison between the material distributions in reality and the values from the simulation for the year 2007 should be made. Moreover, discussion about its influence over the number of failures should be interpreted.

3.2

Research Stage

Before proceeding to the simulation itself, we have made a preliminary thorough research work. In this way after analysing the task description, we were prepared for solving the problem – working out our ideas and developing the task.

17

3.2 Research Stage

3 METHODS

For our research we have iterated cycles of analysis, simulation and experimentation to reach an effective solution of the problems, which have occurred. The first phase of the work was to understand correctly the problem and model it (fig.7). The next one was the implementation in VBA source code.

The following context diagram helped us to develop our ideas, realise enhancement algorithms, implement them in VBA, analyse the data and finally to carry out the simulation.

The context diagram explains clearly our notions for the algorithms and their implementation. The network depends on the following components: pipe segments, material, length, year and failures.

Total network length increasing

Pipe Segments

Renewal strategy

mai Pipe nten anc e

Material

Network

Failures occured

Increasing length

Failures Year grou of nding

of Year out g diggin

Repair failures

Material replacement

Length

Year

Figure 7: Context diagram of a gas pipeline network system The most essential link is the connection Network–Pipe segments. The main reason for an active system is the ”renewal strategy” relation, including pipe maintenance, network grow of the whole network for every single year and pipe exchange depending on the determined percentage. Relations such as Material–Network and Length–Network depend on the permitted budget of the gas supply company. The connection Year–Network is substantial because important information such as year of grounding and year of digging out is saved during the simulation. It is used for creating the failure history.

The last relation is Failures–Network. All failures that have occurred in time and their repair are included here.

Once we had a good idea of what the research challenges are, the next step involved evaluation of the potential solutions and set to the simulation.

Our implementation and simulation results led to further analysis, validation and improvement of the solutions. Some of the major results are 18

3.3 Simulation Stage

3 METHODS

described in the Results chapter (Section 4).

3.3

Simulation Stage

The simulation is a useful tool for risk predictions which visualise various network properties such as expected damage rates. The algorithms, representing the simulation, are based on conceptual design and methodological work. An inexact estimation of damage probabilities is obtained from the historical damage database. Basis of the implementation in VBA is past maintenance behaviour of the network system. Thus, failure rates are validated. From this results it will be possible a more accurate determination of damage rates of the gas pipe network system.

The sequence of the simulation steps is described with the help of the following activity diagram (fig.8):

Input data parameters Executon of the program through the “Simulate“ button Copy table “Leitungen“ in sorted form Sorting Save Information for year of replacement in “History“ column Network Growth taken into consideration Replacement Material taken into consideration Sum of the length of every material for the current year Calculation of λ using the computed length Calculation of number of failures using computed λ Graphical representation of the results

Figure 8: Description of the different stages of the simulation 19

3.4 Recovery Strategy

3 METHODS

On an Intel Celeron M 370 (1.50GHz/1MB/400FSB) computer the simulation takes less than a minute.

Although we defer some details of our simulation extensions to later chapters, two main stages are briefly described here: 1. Recovering strategy 2. Number of failures per pipeline depending on material types

3.4

Recovery Strategy

For a more precise simulation new entries until the current 2007 are added to the initially given database. In this way the obtained results will be closer to the real situation.

The input tables shown in fig.9 and fig.10 consist of several criteria taken into consideration during the execution of the program. First, the table has ”year to stop simulation”. In our case this is the year of 2007. Additionally the aging of gas pipes is taken into account. Here, the criterion for replacement is set to 40 years.

Second, the damage rate parameters for every material are included. The values for ”a” and ”b” assist in the calculation of the failure factors of the gas pipes with help of the Weibull function.

Figure 9: Input Parameters Table 20

3.4 Recovery Strategy

3 METHODS

Third, the network grow percentage for every single year from 1960 till the current 2007 for the different materials is presented. The simulation supports, as an additional option, the calculation for several more possible materials, for which additional columns are present.

Finally, the replacement materials are represented for every single year.

Here, additional materials can be added as well. The database is filled in based on the tendencies in past time periods. This information is used both for the network grow and the replacement. The input data table also represents the recovering rate per year. It depends on the historical and economical maintenance of the network system down the years.

The input parameters provide the opportunity for manual changes in the criteria. A ”Simulate” button is created to ensure an user friendly interface.

After pressing it the whole simulation is executed. The sequence, in which this is done, is as follows: 1. Order the given data and make a copy of it to prevent data loss 2. Calculation of the length of the pipes separately for different materials 3. Simulation of the network grow and the renewal strategy for the current year 4. Calculation of the number of failures and putting them into failure table 5. Changing of the simulation year 6. Repetition of points from 2 till 5 until the simulation year became the last year 7. Graphical representation of the results for the lengths and failures behaviour This succession includes the enumerated list of methods: • main() – executes the following five described procedures • Calc Length – calculate the length of all pipes which are of the same material • Exchange Pipes – take into consideration the pipes which should be exchanged • Net Grow – take into account the pipes which should be added to the network 21

3.4 Recovery Strategy

3 METHODS

• failure factors – compute the failure factor λ • NF – calculates the number of failures with the help of failure factors function and the calculated length The following set of some of the used and important arrays helped in the description of the stated procedures: • Percent(100) – store the percentage values of the renewal rate • Net Gr(100) – store the percentage values of the network grow • Kmat(10) – save the corresponding string values for the ten materials used in the network growth • Pmat(10) – save the corresponding string values for the ten materials used for the replacement • ex array(10) – store the kinds of the materials which have to be exchanged • ng array(10) – save the lengths of the pipes, which have to be added The program itself is executed as one module that consists out of 8 subroutines. By clicking the ”Simulate” button on the ”Parameters” worksheet the ”main” module is called - the module, that performs the sequence of actions in the order, that they have to be executed. In the program several standard data types for the employed variables (integer, floating point, string) are used. They are utilized to make the functionality proper and optimised. The meaning of all variables will be explained according to their chronological order of usage.

As stated previously, the program takes a table with the state of a gas pipe system in 1960 and performs simulation till a manually input end year.

The condition for termination can be manually adjusted in the ”Parameters” table. This starting simulation year is stored in variable Cur Year, which is always increased by one in the main loop. Main loop breaks when this variable becomes equal to end year of simulation, which is stored in variable Max Year. If the starting year of simulation is not suitable, it can be also varied, but it should be taken into consideration that the ”Parameters2” table (fig.10) must be filled in an appropriate manner- the starting year of the simulation is set as first entry. In addition the input table is filled in based on the comparison with the real situation and analysed material distribution. Therefore, our assumptions reached so close values with the 22

3.4 Recovery Strategy

3 METHODS

real results. Starting state table ”Leitungen” must be also of the state of the starting year.

The execution starts with the copy of the initial table to a new additional worksheet (”Copy Leitungen”), which ensures that the given database information remains unaffected from the subsequently carried out procedure steps. From this point on all operations are made with the copied data.

First, the data is stored according to the year of grounding (”Einbaujahr”).

Thus, we facilitate our further data manipulations.

Figure 10: Input Parameters Table

Next, the ”Parameters2” table (fig.10) is selected. Here, several arrays are used – Percent(100), Net Gr(100), Kmat(10) and Pmat(10). The first two, serve as storage for the percentage values of the renewal rate and network growth per year. In Kmat(10) and Pmat(10), based on the present material types (in this particular case 10), corresponding enumeration is carried out.

The percentage values, according to the input table at disposal, are stored in Kmat(10) array for more optimised work with the data. This values are then placed into ”Copy Leitungen” table as headers of the columns in which the subsequent lengths calculations will be saved. The variables Min Year, 23

3.4 Recovery Strategy

3 METHODS

Cur Year and Criteria obtain their values from the ”Parameters” table (fig.9) (taken from the year of simulation and the renewal criteria input cells respectively). The Min Year is the year of the beginning of the simulation. It is put in the first position. When the last year is known, the material distribution, the renewal rate and the network growth are known as well.

New entries in ”Copy Leitungen” are added. When the Cur Year minus Min Year is greater than zero, the given information is taken, new pipes toward the network growth percentage are added and the pipes according to the renewal rate are replaced. When values for the permitted network grow and renewal rate are reached, the rehabilitation for this year is stopped and changed with the next one. If the Cur Year is greater than the Max Year the simulation should stop.

As a next step, the ”Lambda calculation” procedure is called. It creates a new table in which the failure factors (λ) of the gas network are stored (”Lambda” worksheet). These values are used as the basis of the failure rates calculations. For this reason all the data from this table is stored in a matrix, named lam array(200, 10). This matrix saves up to 10 materials for the maximum number of 200 years. Now all preliminaries are fulfilled and our main loops is ready for execution. It consists out of five different subroutine calls (fig.11).

Figure 11: Code sample including the five procedures The first procedure is the ”Calc length”. It sums up the length of all pipes which are of the same material type and saves it under the corresponding column. The ex length and inc length variables, which stand for the exact length of pipes that has to be renewed and for the newly placed ones, obtain the totalled values. All these actions are done inside the loop. In this way for every simulation year a new row in the lengths table is added.

24

3.4 Recovery Strategy

3 METHODS

The second procedure in the main loops is ”Exchange Pipes”. It contains the array of lengths ex array(10). Here the kinds of materials which have to be exchanged is saved. This procedure has also two more additional Boolean variables, which are used to check if there are still pipes that are older than a given criteria and if there is still at least one material, for which an additional pipe can be exchanged. First step in this part is sorting out of the given data according to the year of grounding (”Einbaujahr”). Thus, it is ensured that the oldest pipes are placed at the top of the table. Therefore, the loop starts from the very beginning of the copied table. Going through it, the algorithm checks what are the allowed kinds of materials for the current piece of pipe.

If there is a matching one, the value of ”Einbaujahr” of the current pipe is saved under the respective cell in the ”History” column (fig.12). After this the value of the Cur Year of simulation replaces the year of grounding for the exchanged pipe entry. The material type property is exchanged with the appropriate one. Thus, we should decrease the corresponding values for the index of the ex array(i) and of the ex length with respect to the currently substituted length. At this point the index counter is increased and the simulation proceeds with the next row – a new pipe entry. The loop is being executed until we will have value less or equal to zero for ex length or there will be no pipes older then the given criteria.

Figure 12: Einbaujahr and History columns

25

3.4 Recovery Strategy

3 METHODS

The third procedure is called ”Net Grow”. It makes use of an array ng array(10), that has the same purpose as ex array(10) in the previous procedure, namely to store the lengths of the pipes, depending on their material type. As ”Net Grow” and ”Exchange Pipes” are pretty similar, here we also find one Boolean variable, which checks if further actions concerning the pipes are necessary. The procedure, first fills in the array ng array(10) with the corresponding values, that are directly dependent on the percentage values in the ”Parameters2” worksheet. The data container is created in accordance to the current year of simulation. The value for it is stored in a global variable with name Bcount. When the end of the database table is found, the counter is set to this particular position and from this position on the simulation starts to automatically generate additional new pipe entries. For the implementation of this idea random values from each column to the last row of the data base for the current simulation year are taken. Then, they are copied, and for this particularly newly added entry rows, their column properties ”Einbaujahr” and ”Material” are exchanged with the value of the Cur Year variable and the next found material type, which corresponds to a ng array(i) value more than zero. After this the counters are increased, so the procedure continues with the next row. Here the lengths variables are decreased as well. The loop inside this procedure is executed, until there is no length greater then zero in ng arraya(10), or at the point when the lengths of pipes, that has to be put, will become less than zero. This check is made by comparing the value of the inc length variable.

After the execution of the first, the second and the third procedures (”Calc length”, ”Exchange Pipes” and ”Net Grow”), the corresponding values of the cells are calculated and output (fig.13).

Figure 13: Total length of the different materials per year 26

3.4 Recovery Strategy

3 METHODS

The fourth procedure in the main loop is the ”failure factors”. It has one variable, namely tcount, which is used to go through the data table and to assure that for every single pipe segment its age as well as the corresponding failure factor (λ) value taken from lam array (200, 10), that was previously filled in, is taken. These failure factor values are multiplied with the pipe segment lengths, therefore the obtained failures for every data entry is directly obtained. The last step consists of storing this values. For this purpose a global array consisting of floating point numbers with identifier f array(80000) is defined. This array is big enough to store failure values for data tables with up to 80 000 data entries. The calculation ends when tcount reaches the last entry in the data table.

Last function in the main loop is ”NF”. The name is taken from the task description, this procedure takes the ”fresh” calculated f array(80000) and puts its values into a ”FailureRates” worksheet (fig.14) taking into account the corresponding columns with material types. As the indexes in the f array(i) correspond to the row ones in the data table, it is easy to check each time which material type is at the current row position and to put its value to the respective column in the ”FailureRates” table.

Figure 14: Number of failures for the different materials The main loop executes each time all of the above described five procedures in the same sequence. The Cur Year value is changed to the next one as well as the Bcount value to get access to the next row in the tables that are created by this simulation.

27

3.5 Pipeline Failures

3.5

3 METHODS

Pipeline Failures

Our prediction method is based on a statistical model which is developed from the historical database. The model describes the failure rate of pipes as a function of their age, length and material. It ranks pipes according to their condition (defined as the estimated failure rate per kilometer for the next year). Using this, gas utilities can decide to replace the most critical ones.

The models can be validated by comparing the actual performance with that predicted one.

Utility companies have an interest in repair and replace assets in a way which minimises long-term costs. This requires not only a knowledge of the costs of repair and replacement, but also a way of predicting the expected number of failures for each pipe in the network.

The failure factors (λ) are computed using the Weibull function. The simulation represent their calculation for the given damage parameters (a and b) of the initially provided materials in the historical database. Furthermore, the algorithm works for additional materials as well. Thus the constants for newly introduced types of pipes can be input and the respective values for (λ) will be obtained.

Calculations are carried out till the age of the oldest pipe in network is reached. In the Results chapter (Section 4) a graph representing the failure factors (λ) for every single material (GG, GGG, St, PVC, Pe, AZ) is shown (fig.19).

The number of faults for every removed pipe is saved in a failure history.

Equally important is that the pipes under service within the gas network in the current year also have to be taken into consideration and included in the failure history. To compute the failure rate the following formula is utilized: fi (t) = λi .li

(4)

where λi = failure factor for a certain material, li = length of every pipe from the database, from a certain material till current year of simulation Computation of the number of failures is made by summing the failure rates per material for a year. The following formula is used: NF =

X

fi (t)

(5)

where NF = number of failures for the current year of the running simulation

28

3.6 Tests

3.6

4 RESULTS

Tests

The following test were made to prevent bugs in the program.

• Test 1 → Network growth and renewal rate are both set to 0%. The awaited constant values for the length of the two initially provided materials came up to our expectations.

• Test 2 → Network growth is set to 10%, renewal rate is also 10%. All materials have values of 0%. The network length grows sharply, due to high percentage of network growth, consisting of only two materials GG and St (all other materials are not used in this scenario).

• Test 3 → Network growth is set to 2%, renewal rate to 0%. The GGG material value equals 100%, all other material-0%. Constant values for GG and St are observed, as well as dramatically climb of GGG, owing to higher percentage of use of this material.

• Test 4 → Network growth is 0%, the value for renewal rate - 1%. The pipes are exchanged only with one material-GGG (100%). All other material are 0%. The awaited situation is observed - GG and St have a considerable decline, while GGG increases sharply, due to the only one used material.

• Test 5 → Failure factors(λ) are set to 0. Renewal rate has value of 0%.

As expected, the values for GG and St are constant.

All discussed simulations stood the tests.

4

Results

In the following chapter the results based on the used algorithms and their implementation in VBA are represented. In addition the obtained graphs are discussed.

The graphs are obtained on the basis of the input tables, shown on fig.9 and fig.10.

4.1

Length

Fig.15 gives us a comparison of the total length of the pipe network during the years. The years are indicated on the x-axis whereas the y-axis stands for the length of the network (in km). The area type graph shows the results 29

4.1 Length

4 RESULTS

400000

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Figure 15: Total length of a pipe network for different materials per years obtained from our simulation. The bar chart represents the real values of the network length for the year 2006. Thus, the changes in the total length of the different materials in the gas pipe net over time are observed and the state for 2006 can be easily compared with our results.

The GG length slightly decreases in the period 1960-1977. Then insignificant falls and rises are observed until 1996. As pointed in chapter Materials (Section 2.1.1), due to the replacement with other materials and the limited use the length of GG drops considerably till 2007.

With its appearance in the beginning of 1960â&#x20AC;&#x2122;s, the GGG became the most preferred material during this time. This is the reason for the substantial rise until 1974. In the period 1975-1979 the graph slightly increases. During 1980-2007 the values are almost constant.

The length of St pipes is nearly constant till 1977. Then slight rises and drops in the period 1978-2007 are observed.

Due to the better properties of the PVC material the graph is with slight slope till 1965. Owing to preferred usage during 1980-1990, in the period 1966-1990 the PVC length increases significantly. After 1991 the values are again with slight climb.

The length of the Pe increases considerably from 1969 till 1975 because 30

4.1 Length

4 RESULTS

of the best properties of the material in comparison with the other five described. A slight rise in the period 1976-1997 is observed. After this period till the 2007 the graph is with substantial climb.

The length of AZ is constant until 1994. After this period the graph is with slight decline.

Situation in 2007 140000

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Figure 16: Total length of each material with respect to 2007 Fig.16 shows the best approximation of the actual situation that we have achieved. Adjusting the input data in ”Parameters2” worksheet (fig.10) is based on our assumptions. They are led by observation of the real state and the historical usage of the materials. Identical lengths for the year 2007, in reality and compared to this from our simulation, can be observed.

Our program also provides an opportunity the real values in the period 1948-2006 to be input. By default the table consists of zero values for all years except the year 2006. By pressing the ”calculate lengths using all states” button, the values are filled in (fig.17) and the graph in fig.21 can be observed. In this way the true situation of the pipe lengths can be compared with the results from our simulation.

The real network growth percentages shown in fig.18 reflects in more accurate way the real situation in our simulation.

31

4.1 Length

4 RESULTS

Figure 17: The opportunity, which the additional button provides

Network Growth 6,000%

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1,000%

Figure 18: Real network growth through years

32

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4.2 Failure Factor

4.2

4 RESULTS

Failure Factor

In fig.19 the failure factors are described. The x-axis shows the difference between the current and the year of grounding in ascending order while the y-axis expresses the failure factors (λ).

0,00025

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Difference between the current year and year of grounding

Figure 19: Failure factors for every single material The steel and AZ failure factors are represented as exponential functions with significant slope. The difference is that for steel better properties are observed. Therefore, it has lower values of λ. The GG graph is also exponential with slight rise during the whole period. The GGG failure factors are represented with the principle square root function which slightly increases until 2007. The PVC line is represented as a linear function slope. The Pe values are nearly constant and their limit goes to zero.

4.3

Number of Failures

On fig.20 the number of failures for different materials per year are shown.

The time variable, represented in units of years, is indicated on the x-axis whereas the y-axis shows the number of failures per material. The area type graph represent the results calculated by the simulation, while the bar chart shows the real number of failures in the period 1988-2006.

33

4.3 Number of Failures

4 RESULTS

18 16 14

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Figure 20: Comparison between the real values of the number of failures and the results obtained from the simulation for each material within a year The observation with respect to time shows that Pe has low number of failures compared with the other materials. The graph has slight climb till 2007. The maximum number of failures down the years is 0.054. On the other hand the real situation for the number of failures in the period 19882006, for which we have information, is different. Until 1990 the number of failures is zero, due to the shorter period of use of this material. After this period substantial rises and fall till 2006, when it reaches a value of 0, are observed. A peak value of 3 is reached in 1993 and 1998.

The St graph slightly increases until 1994, then a considerable fall till 1997 is observed followed by a considerable rise till the year of termination of the simulation. In 2007 it reaches a peak value of 0.71 number of failures.

Database information for St number of failures in the period 1988-2006 is missing. Therefore, the comparison is not possible.

The GG line is with insignificant climbs and drops till 1996 when it reaches a peak value of 2.11 number of failures. Then a substantial decline till 2007 is observed. In reality the GG state is more dynamic. The graph increases till 1992. Then a considerable fall till 1994 is observed. After this period the graph has slight rises and falls till 2003, when it reaches its peak value of 5 number of failures. Then again a significant drop is observed until 2005, when 34

5 DISCUSSION

the lowest value is reached – one. From 2006 the graph slightly increases.

The GGG number of failures has slight climb all over the period. In a similar manner the real values are low. The graph has insignificant rises and falls in the period 1988-2006. The values vary between zero and one number of failures per year.

The PVC graph is exponentially increasing, reaching its peak value of 0.0536 number of failures in 2007. On the contrary the real situation is more active. Dramatically climbs and declines during the whole period are observed. A peak value of 8 is reaches in 1995, the lowest value of zero-in 2000.

The AZ line is with exponential rise till 1994. Then a slight drop and again climb till 2007 is observed. It reaches its peak value of 1.635 number of failures in 2007. Conversely, actual graph has significant rises and falls during the whole period. A peak value of 4 is reached in 1994 and 2005.

5 5.1

Discussion Interpretation of the Results

In our opinion the simulation results are discrepant to some extend with the actual state. The differences and similarities between the simulation and the real situation are described in the following paragraphs.

After adjusting the input data in the ”Parameters2” worksheet (fig.10) we have succeeded to approximate the same materials length distributions as the values which describe the real situation of the gas network in 2007.

In fig.16 is shown the best approximation, based on our assumptions for the possible values, which can be regarded as sensible percentage allocations, that we have achieved. As it can be seen the lengths are almost identical to those for the real situation. However, if we compare now the values for the real failure rates and those, which were calculated by our program, it can be easily seen that there is a huge difference between them (fig.20).

For example the occurrence of failures for PVC10 is sometimes 3 times bigger than the predicted ones. The same situation can be observed for all other material types. Although the number of failures depend on the total length, they are also strongly related to the aging of the pipes. This is the reason why the same length does not guarantee similar values for the past years as well as similar number of failures. Nevertheless, we consider that the results from our simulation are reasonable, according to the provided damage parameters (”a” and ”b”) and database filled in with certain amount of pipe entries.

35

5.1 Interpretation of the Results

5 DISCUSSION

The calculated λ parameters are strongly dependent on the provided ”a” and ”b” damage material specific constants, which are input in the ”Parameters” worksheet (fig.9). Thus, they are correct with respect to them. A possible error deviation from the real situation in them leads to miscalculations in λ.

The calculation algorithms were accordingly tested with the help of appropriate value scenarios, and in all of them we did not encounter any problems.

Thus, we consider that there are no extreme mistakes (bugs) in the computation of the number of failures, and in the other results, which leads us to the conclusion that the simulation program works in an appropriate manner.

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Figure 21: Comparison between the lengths obtained from our simulation and the real values Furthermore, we would like to direct the readers attention to the development of the network growth through the years. What can be seen from the first sight is that only by reaching the very last year of simulation, the network has the same values as those for the real situation. For all previous year periods before 2005-2007, the simulated length is bigger than it was expected. The state of 2006 was analysed and the pipes there were sorted according to the year of installation. As is can be seen in fig.21, the state of 1960 is five times bigger than the calculated one. Within further simulation years this difference becomes smaller, because newer pipes are put. This be36

5.2 Summary

5 DISCUSSION

haviour is observed due to the fact that the provided data was not that full.

Having only the states of the system for only the beginning and the end of the simulation period, namely in 1960 and in 2006 is the main reason for this phenomena. For all other years in between the values are taken from the data entry for the last (2006) year, which of course does not contain all pipes. At this point, some of the pipes were already exchanged, so they are not present anymore in the net, due to this deviations from the real situations occur.

That is why we consider, that our simulated lengths must be proportionally higher, depending on the current stage of the simulation. This correction coefficient factor should be conformable to the difference between the real and simulated results, and must be higher for 1965 than for 1990 for example.

The reason for this is that the pipes which are older, for example such from 1965, are more likely to be replaced than those from 1990. Furthermore, the input table with preferred replacement materials (fig.10) is based on our assumptions, influenced by the past maintenance decisions and information only for the pipes which are still in the ground. The renewal rate of the gas pipe network system depends exclusively on the gas company’s policy.

5.2

Summary

In summary we would like to point out, that some factors were not taken into consideration in the simulation. For example, the human factor, was not fully taken into account. Considering, that a typical gas network consists out of approximately 350 000 kilometers of pipes, it follows that also the number of people which are residing through out such a vast area should be considered. Moreover, such a communal network is not only consisting out of a gas system, but also it contains other infrastructures such as water and communication ones. There is a high probability that some of them can influence directly the gas net in an unpredictable manner. Undoubtedly, there is a certain percentage of failures connected with wrong installation of pipe segments, damages produced by road repairs or water supply system problems, pipes located in mining regions. Different damage models, divided in subgroups according to the reason of failures, exist. However, the more models are available, the more information about them and the faults is needed. Unfortunately we do not have such a data at dispose. Due to the lack of information a concrete examples can not be provided.

As a result the consideration of only specific material damage constants (”a” and ”b”) gives us only one part of the overall behaviour of the number of failures. One possible solution, would be, by simple adjusting them in a manner we get possible approximately the same situation not only for lengths but also for the values of the failure distribution. On the other hand, if we 37

5.3 Outlook

5 DISCUSSION

assume that there are no human factor influences which have taken place, then it is possible that the failure constants ”a” and ”b” from ”Parameters” worksheet(fig.9) to be unreasonable.

5.3

Outlook

The simulation described in this project has shown to be valuable tool for calculation of the number of failures and prediction of possible future defects on the pipe segments all over the network.

Our developed algorithms can be combined with statistical methods or programs used for special calculations such as RIKA. This will lead to a more precise risk prediction and in the same time a more accurate prognosis of the future situation.

38

6 ACKNOWLEDGEMENT

6

Acknowledgement

We would like to take the opportunity to say THANK YOU to our supervisors for their time, support and guidance during the development of this project. Without them this work would not have been possible.

Vera窶的 would like to thank my family for their undivided love and support. Special thanks to a very important person for me, whom I own everything I achieved in my life. Last but not least thanks to Levon and Anton for their patience and understanding.

Anton窶的 would like to thank Levon and Vera for taking their responsibilities seriously and for showing nice team-work, also my friends and everybody, who knew that I窶冦 writing a project and was not taking my valuable time for other things!

Levon窶的 would like to thank my good friends and colleges - Vera Buranovska and Anton Popov - without who, this project work would not be so pleasant and fruitful experience. Furthermore, I would like to thank my parents, which have provided me with the opportunity to learn and face so many things. Last but not least, I would like to thank one special member of my family, namely my dog - Archi, for the inspiration he has been giving me, during the times of hopeless laziness, independently from the distance which is dividing us.

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A APPENDIX

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Figure 22: Percentage of added pipes for every different material down the years 100%

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Figure 23: Percentage of replaced pipes for every different material down the years

41 2006 6

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1998 8

1996 6

1994 4

1992 2

1990 0

1988 8

1986 6

1984 4

1982 2

1980 0

1978 8

1976 6

1974 4

1972 2

1970 0

1968 8

1966 6

1964 4

1962 2

1960 0

A APPENDIX

2,50%

Renewal Rate

2,00%

1,50%

1,00% Renewal rate

0,50%

0,00%

Figure 24: Renewal rate of the network down the years

REFERENCES

REFERENCES

References [1] George Antaki. Piping and Pipeline Engineering. Marcel Dekker. Inc, New York, USA, 2003.

[2] Peter Burgherr and Stefan Hirschberg. Comparative assessment of natural gas accident risks. PSI Report, January 2005.

[3] The Geospatual Resource Portal http://www.gisdevelopment.net, 2007.

(GIS

Development).

[4] Hans-Dieter Kochs, Philipp Limbourg, and J¨org Petersen. Explosiver Wettbewerb - Risikoorientierte Planung erh¨alt das Sicherheitsniveau und senkt Wartungskosten f¨ ur Gasnetze. FORUM Forschung - Universit¨ at Duisburg Essen, 2005/2006.

[5] Dirk K¨onig. Gasnetzmanagement - Risikoanalyse und Unterhaltsstrategie. GWA, October 2006.

[6] German Energy Law. http://www.energylaw.de, 2007.

[7] Vlasta Molak. Fundamentals of Risk Analysis and Risk Management.

Lewis Publishers, Boca Raton, Florida, USA, 1997.

[8] Petrosleeve Home Page. http://www.petrosleeve.com, 2007.

[9] Rudi Wehr and Dirk K¨onig. Die Instandhaltung von Versorgungsnetzen mit risiko- und kostenorientierter Ersatzerneuerung. GWF Waser Abwasser, (13):42–49, 2007.

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