**3.1 Formation of the structure of the combined methods**

The generalized structure of the standard basic and calibration determination of the strength parameters of main oil pipeline systems discussed above (Section 2) reflects the theory and practice of computational and experimental substantiation of strength developed in our country and abroad for six to seven decades. The focus is on the trunk pipelines for the transportation of oil and oil products. The calculation of strength analysis is based on two methods—the method of calculation for permissible stresses (adopted in foreign practice) and the method of calculation for limiting states and limit resistances (adopted in Russian practice).

The most developed and applied is the deterministic strength calculation at the design stage. This solves the direct main problems of determining the wall thickness of the pipeline for given pressures, throughput of pipes and selected pipe steels. The same method is used at the stage of calibration calculations of the strength of the pipelines under construction and the majority of the pipelines being operated.

In those cases when it is necessary to calculate the substantiation of the strength of functioning pipelines with deviations from the design decisions and when defects in pipes occur outside the established norms, it is necessary to carry out calibration calculations using actual statistical information on all the calculated parameters. One of the tasks solved at the same time is the appointment of all the main design parameters according to the obtained statistical information. In these cases the preservation of regulatory reserves is typical.

For the most critical sections of pipelines, statistical strength analysis may be insufficient and unacceptable. Then probabilistic estimates of strength are required using the functions of the distribution of operational loading and the mechanical properties of pipe steels by the parameter of operation time. For these situations, it becomes possible to change the safety margins for the required probabilities of the occurrence of dangerous states.

*Combined Calculated, Experimental and Determinated and Probable Justifications… DOI: http://dx.doi.org/10.5772/intechopen.89036*

#### **Figure 7.**

**3. Implementation of combined methods to substantiate strength**

*Relative decrease in strength margins n with changing probabilistic characteristics of loading and mechanical*

The generalized structure of the standard basic and calibration determination of the strength parameters of main oil pipeline systems discussed above (Section 2) reflects the theory and practice of computational and experimental substantiation of strength developed in our country and abroad for six to seven decades. The focus is on the trunk pipelines for the transportation of oil and oil products. The calculation of strength analysis is based on two methods—the method of calculation for permissible stresses (adopted in foreign practice) and the method of calculation for

The most developed and applied is the deterministic strength calculation at the design stage. This solves the direct main problems of determining the wall thickness of the pipeline for given pressures, throughput of pipes and selected pipe steels.

strength of the pipelines under construction and the majority of the pipelines being

For the most critical sections of pipelines, statistical strength analysis may be insufficient and unacceptable. Then probabilistic estimates of strength are required using the functions of the distribution of operational loading and the mechanical properties of pipe steels by the parameter of operation time. For these situations, it becomes possible to change the safety margins for the required probabilities of the

In those cases when it is necessary to calculate the substantiation of the strength of functioning pipelines with deviations from the design decisions and when defects in pipes occur outside the established norms, it is necessary to carry out calibration calculations using actual statistical information on all the calculated parameters. One of the tasks solved at the same time is the appointment of all the main design parameters according to the obtained statistical information. In these cases the

**3.1 Formation of the structure of the combined methods**

limiting states and limit resistances (adopted in Russian practice).

The same method is used at the stage of calibration calculations of the

preservation of regulatory reserves is typical.

occurrence of dangerous states.

operated.

**156**

**Figure 6.**

*Probability, Combinatorics and Control*

*properties.*

*Block diagram of regulatory foreign and domestic calculations.*

The scientific basis of these calculations is the entire system of calculation expressions (1)–(42) (**Figure 7**).

This system has been and remains basic in all international practice [1–4] to the present time with the development of methods for the design, construction, and operation of trunk pipelines to ensure their strength and deformability expressed in a gradual decrease in margins *n* (1.8 ≥ *nT* ≥ 1.2; 2.5 ≥ *n<sup>в</sup>* ≥ 1.7) и and an increase in the strength characteristics *σ*т, *σ*<sup>в</sup> (200 ≤ *σ<sup>Т</sup>* ≤ 800; 420 ≤ *σ<sup>в</sup>* ≤ 920 MPa).

All uncertainty factors included in the calculations and reflecting the operating conditions, design, and construction technologies were taken into account by the coefficients (*nσ*, *nT*, *nв*) and the standard purpose of guaranteed mechanical properties (*σ*в, *σ*Т).

A generalized analysis of trends and parameters of the development of pipeline transport of oil and oil pipelines and methods for calculating the strength is made in [6, 7].

Expressions (1) and (2) are initial in assessing the strength of pipelines at all the main stages of the life cycle—design, construction, operation, and decommissioning. Currently two tasks are being solved:

• The direct task of a deterministic basic calculation of the wall thickness *δ* of the pipeline at the design stage with a preliminary feasibility study of the diameter *D<sup>в</sup>* and pressure *р* as well as with the selected structural material *σоп*,ð*σв*, *σ<sup>Т</sup>* ) and assigned margin *nσ*,ð Þ *nT*, *n<sup>в</sup>* :

$$\delta \ge \frac{pD\_o}{2[\sigma]} = \frac{pD\_o \cdot n\_\sigma}{2\sigma\_{on}}.\tag{43}$$

Under these conditions, the wall thickness *δ* cannot be less than the value calculated by expression (6) (**Figure 8**).

At the stages of construction, operation, and decommissioning on the basis of (43), deterministic calibration calculations are performed with the following objectives:

• Check of permissible operating pressure [*р*] at specified

$$\mathbb{E}[p] \le 2\frac{\sigma\_{on}}{n\_{\sigma}}.\tag{44}$$

**Figure 8.**

*Regulatory basic and verification calculations for different stages of the pipeline life cycle.*

• Validation of selected and assigned mechanical properties *σоп*,ð Þ *σ<sup>Т</sup>* , *σ<sup>в</sup>* with known *р*, *Dв*, *δ*, *n<sup>σ</sup>*

$$
\sigma\_{on} \ge \frac{pD\_a}{2\delta} \cdot n\_\sigma. \tag{45}
$$

where *n*<sup>п</sup> is the number of measurements of calculated parameters *R*п*i*. According to the obtained statistical information on the parameters *Rпi*, the corresponding histograms are constructed by the intervals of their values. For example, **Figure 9** shows the change in the main design parameters—pressure *р* and

*Combined Calculated, Experimental and Determinated and Probable Justifications…*

Inequality (47) with the parameters included in it, as well as the data from **Figure 9**, are the basis for calculating the determination of *Rp* taking into account the statistical and probabilistic dispersion characteristics. At the same time, the

For the design stage, statistical analysis of the design parameters using expressions (8)–(12) is done using factory test data for sheet blanks for pipes (*δ*), pipes (*δ*, *D*), and laboratory samples for static tension (*σ*Т, *σ*в).The values obtained *δр*, *Dp*, (*σ*Т, *σ*в)*<sup>p</sup>* are entered in the technical conditions or standards. They are the basis of

If these measurements are carried out at the stage of construction or operation, then the data obtained from (49)–(52) are included in deterministic calibration

Technical diagnostics of trunk pipelines (mainly using in-line diagnostics [11]) shows that the most significant from the point of view of strength is the decrease in time *τ* wall thickness parameters *δ* due to such processes as uniform and uneven corrosion, formation and development of cracks of corrosion, and cyclical nature.

The statistical variation of diameters in (11) at the stage of manufacturing, construction, and operation of the linear part of trunk pipelines is small (0.99 ≤ *Dв/ Dm* ≤ 1.01) and can be neglected in deterministic and statistical strength calculations according to (1). However, if during operation there are significant reductions

*P*min ≤*Pm* ≤*Pp* ≤*P*max (49)

*D*min ≤ *Dm* ≤ *Dp* ≤ *D*max (51)

*δ*min ≤*δ<sup>p</sup>* ≤*δ<sup>m</sup>* ≤*δ*max (52)

f g *σT*, *σ<sup>в</sup>* min ≤f g *σT*, *σ<sup>в</sup> <sup>p</sup>* ≤f g *σT*, *σ<sup>в</sup> <sup>m</sup>* ≤f g *σT*, *σ<sup>в</sup>* (50)

assigned parameters *Rр* should correspond to the inequality systems

ultimate strength *σ<sup>в</sup>* [10].

*Histograms of pressures and strengths.*

*DOI: http://dx.doi.org/10.5772/intechopen.89036*

**Figure 9.**

deterministic calculations.

**159**

calculations and expressions (44)–(47) (**Figure 10**).

These processes, as a rule, increase the variation of values *δ* in (52).

• Check by (6) the permissible wall thickness ½ � *δ* at

$$\left[\delta\right] \geq \frac{pD\_o n\_\sigma}{2\sigma\_{on}}.\tag{46}$$

• Checking the allowable strength margin[*nσ*]with known

$$m\_{\sigma} \geq \frac{\sigma\_{\text{on}} \cdot 2\delta}{pD\_{\sigma}}.\tag{47}$$

In deterministic calculations according to (1) and (2), a systematic analysis of uncertainty factors affecting the quantities *nσ*, *n*, *m*, *KI*, and *K<sup>н</sup>* is carried out. These factors [6–10] included such factors as:


#### **3.2 Databases for calculations**

On the basis of statistical measurements and estimates of all specified design parameters (pressures *р*, mechanical properties *σ<sup>Т</sup>* , *σв*, geometrical dimensions *δ* and *Dв* with variations within {min, max}), first of all, the determination of their average (median) values becomes important

$$R\_{\rm int} = \frac{1}{n\_{\rm in}} \sum R\_{\rm ni},\tag{48}$$

*Combined Calculated, Experimental and Determinated and Probable Justifications… DOI: http://dx.doi.org/10.5772/intechopen.89036*

#### **Figure 9.**

• Validation of selected and assigned mechanical properties *σоп*,ð Þ *σ<sup>Т</sup>* , *σ<sup>в</sup>* with

½ � *<sup>δ</sup>* <sup>≥</sup> *<sup>р</sup>Dвn<sup>σ</sup>* 2*σоп*

*<sup>n</sup><sup>σ</sup>* <sup>≥</sup> *<sup>σ</sup>оп* � <sup>2</sup>*<sup>δ</sup> рD<sup>в</sup>*

In deterministic calculations according to (1) and (2), a systematic analysis of uncertainty factors affecting the quantities *nσ*, *n*, *m*, *KI*, and *K<sup>н</sup>* is carried out. These

• Temperature–time change in mechanical properties *σ<sup>Т</sup>* , *σв*, which determines

On the basis of statistical measurements and estimates of all specified design parameters (pressures *р*, mechanical properties *σ<sup>Т</sup>* , *σв*, geometrical dimensions *δ* and *Dв* with variations within {min, max}), first of all, the determination of their

> *<sup>R</sup>*<sup>п</sup>*<sup>m</sup>* <sup>¼</sup> <sup>1</sup> *n*п

<sup>2</sup>*<sup>δ</sup>* � *<sup>n</sup>σ:* (45)

*:* (46)

*:* (47)

<sup>X</sup>*R*<sup>п</sup>*i*, (48)

*<sup>σ</sup>оп* <sup>≥</sup> *pD<sup>в</sup>*

*Regulatory basic and verification calculations for different stages of the pipeline life cycle.*

• Check by (6) the permissible wall thickness ½ � *δ* at

factors [6–10] included such factors as:

**3.2 Databases for calculations**

**158**

the processes of aging and degradation

average (median) values becomes important

• Availability of welded joints with altered properties

• Checking the allowable strength margin[*nσ*]with known

• The effect of the absolute dimensions of the sections ð Þ *Dв*, *δ*

• Type of stress–strain state (components of the main stress *σ*1, *σ*2, *σ*3)

known *р*, *Dв*, *δ*, *n<sup>σ</sup>*

*Probability, Combinatorics and Control*

**Figure 8.**

*Histograms of pressures and strengths.*

where *n*<sup>п</sup> is the number of measurements of calculated parameters *R*п*i*.

According to the obtained statistical information on the parameters *Rпi*, the corresponding histograms are constructed by the intervals of their values. For example, **Figure 9** shows the change in the main design parameters—pressure *р* and ultimate strength *σ<sup>в</sup>* [10].

Inequality (47) with the parameters included in it, as well as the data from **Figure 9**, are the basis for calculating the determination of *Rp* taking into account the statistical and probabilistic dispersion characteristics. At the same time, the assigned parameters *Rр* should correspond to the inequality systems

$$P\_{\min} \le P\_m \le P\_p \le P\_{\max} \tag{49}$$

$$\{\sigma\tau,\sigma\_{\theta}\}\_{\min} \leq \{\sigma\tau,\sigma\_{\theta}\}\_{p} \leq \{\sigma\tau,\sigma\_{\theta}\}\_{m} \leq \{\sigma\tau,\sigma\_{\theta}\} \tag{50}$$

$$D\_{\min} \le D\_m \le D\_p \le D\_{\max} \tag{51}$$

$$
\delta\_{\min} \le \delta\_p \le \delta\_m \le \delta\_{\max} \tag{52}
$$

For the design stage, statistical analysis of the design parameters using expressions (8)–(12) is done using factory test data for sheet blanks for pipes (*δ*), pipes (*δ*, *D*), and laboratory samples for static tension (*σ*Т, *σ*в).The values obtained *δр*, *Dp*, (*σ*Т, *σ*в)*<sup>p</sup>* are entered in the technical conditions or standards. They are the basis of deterministic calculations.

If these measurements are carried out at the stage of construction or operation, then the data obtained from (49)–(52) are included in deterministic calibration calculations and expressions (44)–(47) (**Figure 10**).

Technical diagnostics of trunk pipelines (mainly using in-line diagnostics [11]) shows that the most significant from the point of view of strength is the decrease in time *τ* wall thickness parameters *δ* due to such processes as uniform and uneven corrosion, formation and development of cracks of corrosion, and cyclical nature. These processes, as a rule, increase the variation of values *δ* in (52).

The statistical variation of diameters in (11) at the stage of manufacturing, construction, and operation of the linear part of trunk pipelines is small (0.99 ≤ *Dв/ Dm* ≤ 1.01) and can be neglected in deterministic and statistical strength calculations according to (1). However, if during operation there are significant reductions in wall thickness *δ*, then a significant local increase in diameter *D<sup>в</sup>* (by 5–10 due to plastic deformations with the formation of shape defects) is possible. Similar processes of loss of shape and increase in *Dв* are possible with nonstandard bending of pipelines with loss of stability and formation of corrugations.

In the process of development (in time ) of pipeline transportation of hydrocarbons in Russia and abroad, three trends remain dominant using deterministic (D), statistical (C), and probabilistic (P) methods (**Table 1** and **Figure 13**).

*Combined Calculated, Experimental and Determinated and Probable Justifications…*

*DOI: http://dx.doi.org/10.5772/intechopen.89036*

**No. Description Symbols Value** 1. Coefficient of working conditions *m* 0.6–0,9 2. Load reliability factor *K*<sup>1</sup> 1.1–1,5 3. Material reliability factor *K*<sup>2</sup> 1.34–1,55 4. Reliability factor to destination *K*<sup>н</sup> 1.0–1,05

**Figure 12.**

**Table 1.**

**Figure 13.**

**161**

*Calculated standard values of coefficients.*

*Distribution function of the ultimate strength of pipe steels 17G1S.*

*The main regularities of changes in the estimated parameters of pipelines.*

The change in the average values and variation of the design characteristics of strength ð*σ*в, *σ*Т) according to (50) is associated with the instability of technological processes for the production of pipe steels, rolling and heat treatment of sheets, pipe manufacturing, construction of pipeline systems, as well as temporary processes of aging and degradation.

**Figures 11** and **12** show histograms and distribution functions of the mechanical properties of a long-term (up to 50 years) operated 17G1S tubular steel. This information is used in the implementation of calculations for paragraphs 2.1–2.3.

**Figure 10.**

*Statistics on the relative decrease or increase in operating time.*

**Figure 11.** *Strength tensile histograms (total number of tests n = 160).*

*Combined Calculated, Experimental and Determinated and Probable Justifications… DOI: http://dx.doi.org/10.5772/intechopen.89036*

In the process of development (in time ) of pipeline transportation of hydrocarbons in Russia and abroad, three trends remain dominant using deterministic (D), statistical (C), and probabilistic (P) methods (**Table 1** and **Figure 13**).

**Figure 12.** *Distribution function of the ultimate strength of pipe steels 17G1S.*


#### **Table 1.**

in wall thickness *δ*, then a significant local increase in diameter *D<sup>в</sup>* (by 5–10 due to plastic deformations with the formation of shape defects) is possible. Similar processes of loss of shape and increase in *Dв* are possible with nonstandard bending of

The change in the average values and variation of the design characteristics of strength ð*σ*в, *σ*Т) according to (50) is associated with the instability of technological processes for the production of pipe steels, rolling and heat treatment of sheets, pipe manufacturing, construction of pipeline systems, as well as temporary processes of

**Figures 11** and **12** show histograms and distribution functions of the mechanical properties of a long-term (up to 50 years) operated 17G1S tubular steel. This information is used in the implementation of calculations for paragraphs 2.1–2.3.

pipelines with loss of stability and formation of corrugations.

aging and degradation.

*Probability, Combinatorics and Control*

**Figure 10.**

**Figure 11.**

**160**

*Statistics on the relative decrease or increase in operating time.*

*Strength tensile histograms (total number of tests n = 160).*

*Calculated standard values of coefficients.*

**Figure 13.** *The main regularities of changes in the estimated parameters of pipelines.*


**References**

USSR; 1986

2004. 1104p

47-59

**163**

Service. USA; 2007

17457. Germany; 1985

[1] SNIP 2.05.06-85. Trunk Pipelines.

*DOI: http://dx.doi.org/10.5772/intechopen.89036*

*Combined Calculated, Experimental and Determinated and Probable Justifications…*

[2] API 579/ASMEFFS-1 Fitness for

[3] DIN. Stainless Welded Pipe DIN

[4] Mazur II, Ivantsov OM. Safety of Pipeline Systems. Moscow: ITS-ELIMA;

Маkhutov NА, Gadenin ММ, Lisin YV, Neganov DА, et al. Prospects for research in the field of risk analysis to improve government regulation and improve the safety of petrochemical complex. Safety in Industry. 2017;**9**:5-13

[6] Маkhutov NА. Strength and Safety:

[7] Lisin YV, Makhutov NA, Nadein VA, Neganov DA. In: Kostogryzov A, editor. Probabilistic Modeling in System Engineering. Рrobabilistic Analysis of Transportation Systems for Oil and Natural Gas. Rijeka, Croatia: InTechOpen; 2018. pp. 81-103

[8] Lisin YV, Маkhutov NА, Neganov DА, Skorodumov SV, Studenov ЕP. Comprehensive mechanical tests to calculate the strength of the main pipeline transport and petroleum products. Factory Laboratory. Diagnostics of Materials. 2018;**84**(4):

[9] Security of Russia. Security of Energy Storage and Transportation Facilities.

[10] Маkhutov NА, Permyakov VV. Resource Safe Operation of Pipelines. Novosibirsk: Nauka; 2005. 516p

МGОF/Znanie; 2019. 928p

Basic and Applied Research. Novosibirsk: Nauka; 2008. 528p

[5] Radionova SG, Zhulina SА,

• Reduction of strength margins *n<sup>Т</sup>* (от 1.8–3,2 до 1.2–1,5) and (от 2.4–3,5 до 1.6–1,8) in expression (3) and the estimated coefficients in expression (5)
