7. Statistical characteristics and probabilistic modeling of pipeline systems

Multiparameter pipelines with a wide range of service lives are functioning nowadays in Russia and in various countries across the world, according to parts 1 and 2 (Figure 7).

In further analysis of their initial and residual strength, durability, and crack resistance, both statistical data on service life τ and statistical data on changes in the mechanical properties of tubular steels σy, σи, KIc, as well as on developing defects ℓ, should be taken into account. This consideration can be performed on the basis of Eqs. (1)–(15) in both deterministic and statistical forms.

According to statistical data [20] on oil pipelines of Russia with a total length of more than 70,000 km (see Table 1), about 70% of them have a service life of more than 30 years. Their age structure is shown in Figure 7.

Statistical studies of mechanical properties (tensile strength σи) of 29 tube steels were carried out in 217 pipe sections manufactured at 14 plants. Upward bias from data on technical conditions was revealed in 8.9% cases and downward bias 2.6%.

Primary and repeated in-tube condition diagnostics on the length of more than 80,000 km of oil and gas pipelines revealed the presence of unacceptable corrosion and mechanical and erosive damage in 0.2–0.3% of pipes. This required repair and restoration works, as well as replacement of pipes or its sections. These works over the past 20 years have made it possible to reduce the frequency of accidents on pipelines from 0.14–0.16 to 0.09–0.10 per 1000 km per year.

The generally recognized statistical characteristic of the technical condition and safety of pipelines with due regard of their period of operation is [1, 3–7, 17–20] the number of system failures (failures N<sup>o</sup> ð Þτ ) generated per time unit. The failure of a specific section of the pipeline is a very

Figure 7. Statistics on the service life of pipelines.

• ℓ<sup>к</sup> – The critical size (depth) of the defect at which the margin of safety ny (or nи) in Eq. (10)

The calculations <sup>ℓ</sup><sup>к</sup> take an elliptical (ℓ=<sup>а</sup> <sup>≈</sup> <sup>1</sup>=3<sup>Þ</sup> or extended ð Þ <sup>ℓ</sup>=<sup>а</sup> ! <sup>∞</sup> fracture shape. Typically, the most dangerous ones are surface cracks, taking into account more intensive accumu-

The second and most common way of assessing the strength of pipelines is to estimate

fracture mechanics [3, 7, 10, 16]. In this approach, the stress intensity factors are determined

ffiffiffiffiffiffi

When a sample or a pipe with a crack breaks up, a critical value of the stress intensity factor is reached at the crack tip in accordance with the linear fracture mechanics. Then, in calculating the crack, resistance (survivability) of pipes with cracks by analogy with Eq. (2) introduced a

> nk <sup>¼</sup> KIc Ks I

¼ ny; n<sup>и</sup>

In the event of plastic deformations, instead of the stress intensity factors KI and KIc, the strain

The difference in margins according to Eqs. (11) and (14) should not be significant.

<sup>I</sup> and KI<sup>с</sup> and Eqs. (9) and (13), the equation below can be obtained:

� � � KIc σy; σ<sup>и</sup> � � ffiffiffiffiffiffi

<sup>е</sup> and ð Þ n<sup>и</sup> <sup>е</sup> according to the equations and criteria of linear and nonlinear

<sup>n</sup>max in Eq. (1) and Fkf g <sup>D</sup>; <sup>δ</sup>; <sup>ℓ</sup>; <sup>a</sup> in Eq. (9):

<sup>π</sup><sup>ℓ</sup> <sup>p</sup> � Fkf g <sup>D</sup>; <sup>δ</sup>; <sup>ℓ</sup>; <sup>a</sup> (12)

: (13)

: (14)

<sup>π</sup><sup>ℓ</sup> <sup>p</sup> � Fk

lation of corrosion, erosion, and mechanical damage in the surface layers.

Ks <sup>I</sup> <sup>¼</sup> <sup>σ</sup><sup>s</sup> nmax

ny � � ℓ ;ð Þ n<sup>и</sup> <sup>ℓ</sup> n o

becomes less than 1

94 Probabilistic Modeling in System Engineering

Figure 6. Influence of defects (such as cracks) on safety margins.

margins ny

� �

By the values of K<sup>s</sup>

by the calculation for the given σ<sup>s</sup>

margin by the stress intensity factor:

intensity factors should be used [4, 6, 8].

Figure 8. Age structure of long-term running main pipelines of large diameter.

rare event, even for a fairly long period of time τ. But taking into account the considerable length of the whole system (more than 70,000 km), the reduced frequency or failure flow Po ð Þτ at the length L (L = 1000 km) will have a finite value depending on the time of operation τ<sup>s</sup> :

$$P^o(\tau) = \frac{dN^o(\tau)/d\tau^s}{L}.\tag{15}$$

ð18Þ

97

), associated with unacceptable

http://dx.doi.org/10.5772/intechopen.75078

τ<sup>I</sup> << τII < τIII: (19)

Probabilistic Analysis of Transportation Systems for Oil and Natural Gas

According to operational statistical data on failures N<sup>о</sup> and failure flows dN� / d , the standard (permissible) operating time [ ] can be established—a resource of reliable operation excluding

Operational experience shows that the service life of the pipeline, as well as of other complex

• Stabilization period (τII), when the number of failures is minimal and their increase is

• Wear period (τIII), associated with a steady increase in the number of failures and a decrease in throughput due to the occurrence of damage accumulation processes and the formation and development up to critical dimensions (K) of the initial and operational

For mastered deterministic technologies of designing and manufacturing, the following corre-

τ<sup>k</sup> ¼ τ<sup>I</sup> þ τII þ τIII:

The allowed period [ ] of reliable operation of pipelines based on the allowed failure flow may

technical systems, can be conveniently divided into three main periods (Figure 9):

defects in construction and installation works and factory defects in pipes

the transition of the MPS to the critical (ultimate) state.

include periods τ<sup>I</sup> and τII and part of the period:

insignificant

lations are fulfilled:

• Run-in period (τI), when there is a high failure rate (N<sup>о</sup>

defects of metal pipes, welded joints, protective coatings, etc.

Figure 9. The failure of technical systems in dependence from the period of operation.

The failure flow Po ð Þτ , in our country and abroad, of oil and gas pipelines decreases over time —from 0.3 to 0.4 in the 1960s and 1970s to 0.012–0.015 at the present.

According to Eq. (15), the reliability Ро(τ) of section L at a given time τ can be estimated [1, 4, 6, 7, 18] by the failure flow P<sup>o</sup> ð Þτ :

$$P\_o(\tau) = 1 - P^\circ(\tau). \tag{16}$$

In this case, the value of Ро(τ) can be considered as a statistical and probabilistic indicator of the technical risk Ro(τ) of the failure:

$$R\_o(\tau) \,=\, 1 - P^o(\tau) \tag{17}$$

On the basis of (16) and (17), the safety S<sup>о</sup> (τ) of the MPS functioning at can be considered as.

$$\mathbf{S}^o(\tau \ ) = \mathbf{I} \cdot \ R\_o(\tau \ ) = P\_o(\tau \ ) \tag{18}$$

According to operational statistical data on failures N<sup>о</sup> and failure flows dN� / d , the standard (permissible) operating time [ ] can be established—a resource of reliable operation excluding the transition of the MPS to the critical (ultimate) state.

Operational experience shows that the service life of the pipeline, as well as of other complex technical systems, can be conveniently divided into three main periods (Figure 9):


For mastered deterministic technologies of designing and manufacturing, the following correlations are fulfilled:

$$
\pi\_k = \pi\_I + \pi\_{II} + \pi\_{III}.
$$

$$
\pi\_I << \pi\_{II} < \pi\_{III}.\tag{19}
$$

The allowed period [ ] of reliable operation of pipelines based on the allowed failure flow may include periods τ<sup>I</sup> and τII and part of the period:

Figure 9. The failure of technical systems in dependence from the period of operation.

rare event, even for a fairly long period of time τ. But taking into account the considerable length

dN<sup>o</sup>

According to Eq. (15), the reliability Ро(τ) of section L at a given time τ can be estimated [1, 4, 6,

In this case, the value of Ро(τ) can be considered as a statistical and probabilistic indicator of

RoðτÞ ¼ <sup>1</sup> � <sup>P</sup><sup>o</sup>

<sup>P</sup>оð Þ¼ <sup>τ</sup> <sup>1</sup> � <sup>P</sup><sup>o</sup>

ð Þ<sup>τ</sup> <sup>=</sup>dτ<sup>s</sup>

ð Þτ , in our country and abroad, of oil and gas pipelines decreases over time

ð Þτ at the

:

<sup>L</sup> : (15)

ð Þτ : (16)

ð Þτ (17)

(τ) of the MPS functioning at can be consid-

of the whole system (more than 70,000 km), the reduced frequency or failure flow Po

length L (L = 1000 km) will have a finite value depending on the time of operation τ<sup>s</sup>

Po ð Þ¼ τ

—from 0.3 to 0.4 in the 1960s and 1970s to 0.012–0.015 at the present.

ð Þτ :

Figure 8. Age structure of long-term running main pipelines of large diameter.

The failure flow Po

ered as.

7, 18] by the failure flow P<sup>o</sup>

96 Probabilistic Modeling in System Engineering

the technical risk Ro(τ) of the failure:

On the basis of (16) and (17), the safety S<sup>о</sup>

$$
\tau^s \le \tau\_I + \tau\_{II} + k\tau\_{III} < \tau\_{k\prime}\left[\tau\right] = \frac{\tau\_k}{n\_\tau} \tag{20}
$$

where k—coefficient of using the pipeline with damages (k < 1); and nτ—service life margin.

Equations (15) and (16) are valid both for MPS and for their individual elements when failures are associated with the development in the length of time of operational defects. At the same time, for the main pipeline transport, the period of operation and margins n<sup>τ</sup> with deterministic, statistical, and probabilistic approaches should be taken into account under Eqs. (15)–(20).

The period of stable operation of the pipeline according to Eq. (20) can be increased by carrying out special organizational and technical measures, including the implementation of local or major repairs, diagnostic surveys, efficiency improvement of the corrosion protection system, etc. The most important aim of these measures is the extension of the safe operation period for the entire system (MPS) as well as for individual sections and pipes (the transition from curve 1 to curve 2 in accordance with Figure 9), subject to specified safety and reliability parameters.

Considering economic consequences Voð Þ<sup>τ</sup> , failures <sup>N</sup><sup>o</sup> ð Þ<sup>τ</sup> , risks <sup>R</sup><sup>o</sup> ð Þτ , and costs for improving reliability and safety Zð Þτ allows us to evaluate the economic effectiveness of integrated measures to improve the working capacity of MPS:

$$V\_o(\tau) = V^o(\tau) \left[ 1 - k\_p P^o(\tau) \right] = V^o(\tau) P^o(\tau),\tag{21}$$

n ¼ n ko ð Þ ; kп, m (23)

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99

ko ¼ 1 � zpvи, y; k<sup>п</sup> ¼ 1 þ zpvs, (25)

<sup>р</sup> are calculated by multiplying their

ð Þτ , and effi-

<sup>р</sup> <sup>¼</sup> <sup>k</sup><sup>п</sup> <sup>σ</sup><sup>s</sup> ð Þm: (24)

As a result, the calculated strength (σ<sup>р</sup>

mathematical expectation by the corresponding factors:

distribution curves, and the strength in Figure 9:

the normal distribution law.

σр

of the material; and vs—variation factor of the operational load.

life of the functioning facilities and while designing new MPS:

<sup>и</sup>, σ<sup>р</sup>

Figure 10. The scheme for determining the probability of fracture Рр by parameters of reliability and durability.

<sup>и</sup>,y ¼ ko σи,<sup>y</sup> 

<sup>y</sup>) and load σ<sup>s</sup>

<sup>m</sup>; <sup>σ</sup><sup>s</sup>

The values of the factors in Eqs. (23) and (24) will depend on the assumed probability of fracture Рр, which is determined by the safety characteristic Soð Þτ , the shape of the load

where vи, y, zp—factors of variability and quantiles of distribution of the strength characteristics

Statistical analysis [5, 7] of the distribution functions of the mechanical properties of low-alloy steels (type 15ХСНD-С 0.12–0.18, Ci 0.4–0.7, Mn 0.4–0.7, Ni 0.3–0 (6%)) on a large number of n = 2500 laboratory samples from a 15-mm-thick sheet showed the acceptability of the use of

The generalization (Figure 11) of the test results of this steel at n = 22.000 samples with thickness of 5 to 24 mm revealed while increasing thickness δ, decrease of the yield strength

In the generally accepted normative calculations for the strength of the MPS, the time parameters τ are not explicitly introduced in Eqs. (1) and (2). They become necessary in the future

ciency Voð Þτ under Eqs. (15)–(25) in case of assessing the technical condition and extending the

for the probabilities P = (1%, 50%, 99%), as well as the variation coefficients v.

specified calculations of the strength <sup>σ</sup>иð Þ<sup>τ</sup> and <sup>σ</sup>yð Þ<sup>τ</sup> , reliability Poð Þ<sup>τ</sup> , safety So

where <sup>V</sup>оð Þ<sup>τ</sup> and <sup>V</sup><sup>o</sup> ð Þτ —designed throughput of the system with and without consideration for reliability; and kp—coefficient of influence of failures on the throughput.

Therefore, in accordance with Eqs. (1)–(4), the requirements for MPS operation efficiency are inextricably linked to the high requirements for ensuring reliability Poð Þτ , safety Soð Þτ , and risk management Roð Þ<sup>τ</sup> in the process of its operation <sup>τ</sup> <sup>¼</sup> <sup>τ</sup><sup>s</sup> , which determines the priority importance of economic, environmental, and industrial safety of transportation of oil, oil products, and gas. These issues are assigned to the scope of strategic planning at the federal, regional, and sectoral levels.

Statistical information on the quantities σ<sup>s</sup> and σи, σ<sup>y</sup> makes it possible to construct the probability density functions <sup>f</sup> <sup>σ</sup><sup>s</sup> ð Þ and <sup>f</sup> <sup>σ</sup>и; <sup>σ</sup><sup>y</sup> (Figure 10) describing the operational loads (nominal σ<sup>s</sup> and strength characteristics) from Eq. (21).

The probability of fracture Рр as an extremely dangerous (critical) failure, accident, and catastrophe will be determined by the overlapping of the distribution density functions <sup>f</sup> <sup>σ</sup><sup>s</sup> ð Þ and f σи; σ<sup>y</sup> . In general, all the parameters of Eq. (21) are time-dependent <sup>τ</sup> <sup>¼</sup> <sup>τ</sup><sup>s</sup> .

Parameter Ррð Þτ is taken into account when assigning the safety margins {nи, ny}, and Eq. (2) makes it possible to estimate the strength properties in accordance with the following equation:

$$P\_{p^{\sigma}}(\tau) = 1 - P\_p(\tau). \tag{22}$$

In the calculations for the permissible stress under codes and rules for building [16], this approach is reflected in the separation from the total factor of margin n factors of homogeneity ko, overload kп, and operating conditions m:

<sup>τ</sup><sup>s</sup> <sup>≤</sup> <sup>τ</sup><sup>I</sup> <sup>þ</sup> <sup>τ</sup>II <sup>þ</sup> <sup>k</sup>τIII <sup>&</sup>lt; <sup>τ</sup>k, ½ �¼ <sup>τ</sup>

where k—coefficient of using the pipeline with damages (k < 1); and nτ—service life margin. Equations (15) and (16) are valid both for MPS and for their individual elements when failures are associated with the development in the length of time of operational defects. At the same time, for the main pipeline transport, the period of operation and margins n<sup>τ</sup> with deterministic, statistical, and probabilistic approaches should be taken into account under Eqs. (15)–(20). The period of stable operation of the pipeline according to Eq. (20) can be increased by carrying out special organizational and technical measures, including the implementation of local or major repairs, diagnostic surveys, efficiency improvement of the corrosion protection system, etc. The most important aim of these measures is the extension of the safe operation period for the entire system (MPS) as well as for individual sections and pipes (the transition from curve 1 to curve 2 in accordance with Figure 9), subject to specified safety and reliability parameters.

reliability and safety Zð Þτ allows us to evaluate the economic effectiveness of integrated

Therefore, in accordance with Eqs. (1)–(4), the requirements for MPS operation efficiency are inextricably linked to the high requirements for ensuring reliability Poð Þτ , safety Soð Þτ , and risk

tance of economic, environmental, and industrial safety of transportation of oil, oil products, and gas. These issues are assigned to the scope of strategic planning at the federal, regional,

Statistical information on the quantities σ<sup>s</sup> and σи, σ<sup>y</sup> makes it possible to construct the proba-

The probability of fracture Рр as an extremely dangerous (critical) failure, accident, and catastrophe will be determined by the overlapping of the distribution density functions <sup>f</sup> <sup>σ</sup><sup>s</sup> ð Þ and

Parameter Ррð Þτ is taken into account when assigning the safety margins {nи, ny}, and Eq. (2) makes it possible to estimate the strength properties in accordance with the following equation:

In the calculations for the permissible stress under codes and rules for building [16], this approach is reflected in the separation from the total factor of margin n factors of homogeneity

ð Þ<sup>τ</sup> <sup>¼</sup> <sup>V</sup><sup>o</sup>

ð Þ<sup>τ</sup> <sup>1</sup> � kpP<sup>o</sup>

for reliability; and kp—coefficient of influence of failures on the throughput.

. In general, all the parameters of Eq. (21) are time-dependent <sup>τ</sup> <sup>¼</sup> <sup>τ</sup><sup>s</sup>

Considering economic consequences Voð Þ<sup>τ</sup> , failures <sup>N</sup><sup>o</sup>

management Roð Þ<sup>τ</sup> in the process of its operation <sup>τ</sup> <sup>¼</sup> <sup>τ</sup><sup>s</sup>

bility density functions <sup>f</sup> <sup>σ</sup><sup>s</sup> ð Þ and <sup>f</sup> <sup>σ</sup>и; <sup>σ</sup><sup>y</sup>

ko, overload kп, and operating conditions m:

inal σ<sup>s</sup> and strength characteristics) from Eq. (21).

<sup>V</sup>оð Þ¼ <sup>τ</sup> <sup>V</sup><sup>o</sup>

measures to improve the working capacity of MPS:

where <sup>V</sup>оð Þ<sup>τ</sup> and <sup>V</sup><sup>o</sup>

98 Probabilistic Modeling in System Engineering

and sectoral levels.

f σи; σ<sup>y</sup>

τk nτ

ð Þ<sup>τ</sup> , risks <sup>R</sup><sup>o</sup>

ð Þ<sup>τ</sup> Po

(Figure 10) describing the operational loads (nom-

Рро ð Þ¼ τ 1 � Ррð Þτ : (22)

ð Þτ —designed throughput of the system with and without consideration

ð Þτ , and costs for improving

ð Þτ , (21)

, which determines the priority impor-

.

(20)

Figure 10. The scheme for determining the probability of fracture Рр by parameters of reliability and durability.

$$m = n(k\_o, k\_{n\_r} m) \tag{23}$$

As a result, the calculated strength (σ<sup>р</sup> <sup>и</sup>, σ<sup>р</sup> <sup>y</sup>) and load σ<sup>s</sup> <sup>р</sup> are calculated by multiplying their mathematical expectation by the corresponding factors:

$$
\sigma\_{\mathfrak{u},\mathfrak{y}}^{\mathbb{P}} = k\_o (\sigma\_{\mathfrak{u},\mathfrak{y}})\_{\mathfrak{m}'} \circ\_{\mathbb{P}}^{\mathbb{s}} = k\_{\mathfrak{n}} (\sigma^{\mathfrak{s}})\_{\mathfrak{m}}.\tag{24}
$$

The values of the factors in Eqs. (23) and (24) will depend on the assumed probability of fracture Рр, which is determined by the safety characteristic Soð Þτ , the shape of the load distribution curves, and the strength in Figure 9:

$$k\_o = 1 - z\_p v\_{u,y}; k\_n = 1 + z\_p v\_{s\prime} \tag{25}$$

where vи, y, zp—factors of variability and quantiles of distribution of the strength characteristics of the material; and vs—variation factor of the operational load.

Statistical analysis [5, 7] of the distribution functions of the mechanical properties of low-alloy steels (type 15ХСНD-С 0.12–0.18, Ci 0.4–0.7, Mn 0.4–0.7, Ni 0.3–0 (6%)) on a large number of n = 2500 laboratory samples from a 15-mm-thick sheet showed the acceptability of the use of the normal distribution law.

The generalization (Figure 11) of the test results of this steel at n = 22.000 samples with thickness of 5 to 24 mm revealed while increasing thickness δ, decrease of the yield strength for the probabilities P = (1%, 50%, 99%), as well as the variation coefficients v.

In the generally accepted normative calculations for the strength of the MPS, the time parameters τ are not explicitly introduced in Eqs. (1) and (2). They become necessary in the future specified calculations of the strength <sup>σ</sup>иð Þ<sup>τ</sup> and <sup>σ</sup>yð Þ<sup>τ</sup> , reliability Poð Þ<sup>τ</sup> , safety So ð Þτ , and efficiency Voð Þτ under Eqs. (15)–(25) in case of assessing the technical condition and extending the life of the functioning facilities and while designing new MPS:

assignment with the introduction of basic requirements and criteria for strength, resource, and safety in accordance with applicable standards and development of physical and mathematical models for regular, damaged, and emergency situations. When designing facilities of new generations, strength analysis should be carried out in accordance to the basic standard and additional verification calculations, based on known internal and external influences and object characteristics, parameters of stress-strain state, and damaging factors with justification

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101

In the subsequent stages of design and manufacturing, reliability problems will be addressed, including selection, justification, and development of materials technology and control in accordance with existing norms and rules. Generally, for the manufactured elements of MPS, the actual mechanical properties and their deviations from the technical requirements, the level of real defectiveness, the geometry parameters, and their deviations should be established. On their grounds, the basic design parameters of strength and resource will be refined. At this stage, the issues of stability and safety of the elements require an analysis of possible failures for reasons of technological heredity. At the operational stage, the system of routine diagnostics of the main characteristics of the MPS facility and the external environment that determine reliability will be specified, and information will be collected on confirming or adjusting design decisions on strength and resource. As the finalized design resource is exhausted, an evaluation of the residual life of safe operation should be carried out. To harmonize all deterministic, statistical, and probabilistic information for all stages of the life cycle of an object, it is necessary to use unified mathematical and physical

In the future, considering formation of a new legal and regulatory framework, in which the

of decisive importance, reverse solutions will be decided. At the same time, all the scientific and methodological potential accumulated in previous years will be fully utilized in selecting models,

Voð Þτ in engineering design and technological and operational solutions for pipeline systems for oil

This work was financially supported by the Russian Science Foundation (grant #14 19 00776-P).

, Vladimir A. Nadein<sup>2</sup>

ð Þτ , as well as economic efficiency Voð Þτ will be

\* and Dmitriy A. Neganov<sup>1</sup>

ð Þ<sup>τ</sup> , Ro

ð Þτ , and

ð Þ<sup>τ</sup> , risks Ro

methods, design equations, and design parameters to achieve the required values S<sup>o</sup>

models, calculation equations, criteria, and computer programs for MPS.

of initial resources for reliable and safe operation.

standardized requirements for safety So

, Nikolay A. Makhutov<sup>1</sup>

\*Address all correspondence to: vladimir\_nadein@ogsed.ru

1 The Pipeline Transport Institute (PTI, LLC), Moscow, Russia

2 LLC "Oil and Gas Safety – Energodiagnostika", Moscow, Russia

and gas transportation.

Acknowledgements

Author details

Yuriy V. Lisin<sup>1</sup>

Figure 11. Dependence of yield strength σy, factors of variation v of yield strength σy, strength δи, and elongation δ<sup>k</sup> from the rolled thickness δ.

The currently developed combined probability statistical method [4] makes it possible to assess the reliability Poð Þ<sup>τ</sup> as a function of time <sup>τ</sup><sup>s</sup> on the basis of analysis of the initial deterministic, statistical, and probabilistic information about the design Кð Þτ and technological Тð Þτ features of MPS objects, the operating loads Qð Þτ and environmental impacts Фð Þτ , stressstrain states in the coordinates σ τð Þ� еð Þτ and probable mechanisms of accumulation of damage dð Þτ , and nucleation and development of defects lð Þτ .

The main design parameters will be determined under:

$$\left\{\sigma\_{u}(\tau),\sigma\_{y}(\tau),S^{\diamond}(\tau),P\_{o}(\tau)\right\} = \begin{cases} F\_{u}\{K(\tau),T(\tau),Q(\tau),\Phi(\tau)\}; \\ F\_{p}\{\sigma(\tau),e(\tau)\}; \\ F\_{n}\{d(\tau),l(\tau)\}, \end{cases} \tag{26}$$

The abovementioned basic calculated dependencies in equations (1)–(26) allow [1, 3–7, 18–20] to make the transition from traditional deterministic engineering calculations of strength with the standard characteristics of mechanical properties σy, σ<sup>и</sup> to calculations of strength, durability, crack resistance, reliability, and safety using new developing statistical and probabilistic methods of mathematical and physical modeling and refined calculations.

#### 8. Conclusion

Ultimately, the problems of functional and strength reliability, resource, and safety of pipeline systems should cover all stages of the life cycle of facilities, representing three interrelated and interdependent processes: design, construction, and operation.

Designing while taking into account the prospects of statistical and probabilistic modeling of reliability and safety criteria should include the development and coordination of the technical assignment with the introduction of basic requirements and criteria for strength, resource, and safety in accordance with applicable standards and development of physical and mathematical models for regular, damaged, and emergency situations. When designing facilities of new generations, strength analysis should be carried out in accordance to the basic standard and additional verification calculations, based on known internal and external influences and object characteristics, parameters of stress-strain state, and damaging factors with justification of initial resources for reliable and safe operation.

In the subsequent stages of design and manufacturing, reliability problems will be addressed, including selection, justification, and development of materials technology and control in accordance with existing norms and rules. Generally, for the manufactured elements of MPS, the actual mechanical properties and their deviations from the technical requirements, the level of real defectiveness, the geometry parameters, and their deviations should be established. On their grounds, the basic design parameters of strength and resource will be refined. At this stage, the issues of stability and safety of the elements require an analysis of possible failures for reasons of technological heredity.

At the operational stage, the system of routine diagnostics of the main characteristics of the MPS facility and the external environment that determine reliability will be specified, and information will be collected on confirming or adjusting design decisions on strength and resource. As the finalized design resource is exhausted, an evaluation of the residual life of safe operation should be carried out. To harmonize all deterministic, statistical, and probabilistic information for all stages of the life cycle of an object, it is necessary to use unified mathematical and physical models, calculation equations, criteria, and computer programs for MPS.

In the future, considering formation of a new legal and regulatory framework, in which the standardized requirements for safety So ð Þ<sup>τ</sup> , risks Ro ð Þτ , as well as economic efficiency Voð Þτ will be of decisive importance, reverse solutions will be decided. At the same time, all the scientific and methodological potential accumulated in previous years will be fully utilized in selecting models, methods, design equations, and design parameters to achieve the required values S<sup>o</sup> ð Þ<sup>τ</sup> , Ro ð Þτ , and Voð Þτ in engineering design and technological and operational solutions for pipeline systems for oil and gas transportation.
