**5. Method for determining the allowable sizes of pipe defects by risk criteria**

In this section the probabilistic methodology is use for develop a semiprobabilistic method for assessing the admissible sizes of defects in subsea

#### *Defects Assessment in Subsea Pipelines by Risk Criteria DOI: http://dx.doi.org/10.5772/intechopen.94851*

*P li* >*l* ð Þ¼ *<sup>r</sup>*

*Issues on Risk Analysis for Critical Infrastructure Protection*

bility of defects is represented in the form:

where [*R*] is the acceptable risk.

following condition for the admissibility of a defect:

where *l*[*R*] is the size defect at which the risk *R* is acceptable.

*P li* >*l* ð Þ¼ *<sup>r</sup>*

ð *li*

*f l*ð Þ*<sup>r</sup> dlr* ≤ *Rf*

0

*li* ≤ *l*

**5. Method for determining the allowable sizes of pipe defects by risk**

In this section the probabilistic methodology is use for develop a semiprobabilistic method for assessing the admissible sizes of defects in subsea

On this basis, similarly to (5), the following condition for the admissibility of

where *l*[*Rf*] is the size of the defect at which the probability of losses belongs to a

Expressions (4) and (6), in fact, are a semi-probabilistic solution to problems (3) and (5), since they relate fixed random variables, one of which has a given proba-

factors.

namely:

defects can be written:

given class.

bilistic support.

**criteria**

**154**

ð ∞ ∞ð

*f l*ð Þ*<sup>i</sup> f l*ð Þ*<sup>r</sup> dlrdli* (2)

*P li* > *l* ð Þ� *<sup>r</sup> C l*ð Þ ≤½ � *R* , (3)

*li* ≤*l*½ � *<sup>R</sup>* (4)

� � (5)

½ � *<sup>R</sup> <sup>f</sup>* (6)

*lr*

Exceeding the sizes *lr* leads to some losses *C* = *F*(*l*) due to the need to carry out repair operations or leakage and structural failure. Moreover, the larger the defect, the more significant losses can be. It should be emphasized that the losses are also random in magnitude, since it depends on the many technical and socio-economic

Joint analysis of the probabilistic nature of defects, their hazard and possible losses leads to the concept of the admissibility of defects according to risk criteria [11, 18]. The essence of this concept is that the criterion condition for the admissi-

Assuming the defect size *li* as a fixed random variable from (3) we can obtain the

Due to the unresolved problem of assessment and statistical analysis of losses, currently, sufficiently substantiated proposals for determining the allowable risk have not been developed. As a rule, losses are categorized into some qualitative classes: negligible, acceptable, unacceptable, etc. [19, 20]. Each class of losses is associated with a certain acceptable level of its probabilities [*Rf*]. Taking this into account, instead of (3), one can go to a simpler form of assessing the admissibility of defects by risk criteria, which does not require a direct assessment of damages,

0

inter-field pipelines based on risk criteria. The basis of this method are requirements of standards [7, 9]. The risk is defined as the probability *Rf* negative consequences of pipeline accident, the scale of which is determined by the hazard class. The proposed hazard classes (risk matrix) for inter-field subsea pipelines are presented in **Table 1**. Quantitative economic and environmental damage assessments are not considered here.

The suitability of the pipeline for operation is determined by three-level assessment of the allowable size of defects by risk criteria (**Figure 2**). The first, basic level, determines the allowable defect sizes by the strength characteristics of metal for pipelines exposed to the main loads - internal overpressure and hydrostatic external pressure. The second, extended level, determines the allowable defect sizes by the strength characteristics for metal, taking into account the effect on pipelines of additional longitudinal and bending loads. The third, special level, determines the allowable sizes of cracks, crack-like defects and delamination by the characteristics of crack resistance of the metal.

The calculations use information about: pipe sizes, location of the pipeline on the seabed, loads and impacts; the size, location and types of defects; mechanical properties, industry standard requirements, and pipe specifications.

The hazard of pipe defects depends on their shape and size. The sizes of defects are determined by their spatial coordinates *l* = {*lx*, *ly*, *lz*} (**Figure 3**). By shape the defects can be classified into volumetric and flat. For the volumetric defects the size *lx* ≥ *ly* ≥ *lz*, for the flat defects the size *lx* ≥ *ly*> > *lz*. The defect hazard calculations usually use relative defect sizes <sup>~</sup>*lx* <sup>¼</sup> *lx*ffiffiffiffi *Dt* <sup>p</sup> , <sup>~</sup>*lz* <sup>¼</sup> *lz <sup>t</sup>* . These relative dimensions are used in this technique taking into account the classification of defects shape.

The limit state function L for pipe volumetric defects may be write as: for hoop stress

$$\mathcal{L}\left(P, D, t, \sigma\_f, \tilde{l}\_\mathbf{x}, \tilde{l}\_\mathbf{x}\right) = \sigma\_f \frac{2t}{D} RF\left(\tilde{l}\_\mathbf{x}, \tilde{l}\_\mathbf{x}\right) - P = \mathbf{0} \tag{7}$$

for equivalent stress

$$\mathcal{L}\left(P, D, t, \sigma\_f, \tilde{l}\_\mathbf{x}, \tilde{l}\_\mathbf{x}\right) = \sigma\_f - \sigma\_\epsilon RF\left(\tilde{l}\_\mathbf{x}, \tilde{l}\_\mathbf{x}\right) = \mathbf{0} \tag{8}$$


#### **Table 1.**

*Hazard classes of fracture for subsea inter-field pipeline.*

*Issues on Risk Analysis for Critical Infrastructure Protection*

where *<sup>σ</sup> <sup>f</sup>* <sup>¼</sup> min *Re*

� � <sup>¼</sup> <sup>1</sup>�~*lz*

stress; *RF* ~*lz*,~*lx*

partial safety factor.

for hoop stress

for equivalent stress

fracture probability [*Rf*]:

according to **Table 2**.

thickness *t* of pipes.

fracture [*Rf*].

pressure.

**Table 2.**

**157**

*Values of quantiles up.*

*γe* ; *Rm γm*

*Defects Assessment in Subsea Pipelines by Risk Criteria DOI: http://dx.doi.org/10.5772/intechopen.94851*

<sup>1</sup>�~*lz=<sup>M</sup>* <sup>~</sup>ð Þ*lx*

sizes ~*lz* for given sizes ~*lx* with use partial safety factors:

~*lz* ≤ 1 *γd*

~*lz* ≤ 1 *γd*

*<sup>γ</sup><sup>R</sup>* <sup>¼</sup> <sup>1</sup> � *up*

n o is fracture stress; *<sup>σ</sup><sup>e</sup>* <sup>¼</sup>

equivalent stress; *σ<sup>h</sup>* is hoop stress; *σ<sup>l</sup>* is longitudinal stress; *τhl* is tangential shear

is risk-factor of defect; *M* ~*lx*

If the components of limit state functions have a Gaussian distribution, then from the solutions of Eqs. (7) and (8) it is possible to determine the allowable

*<sup>σ</sup> <sup>f</sup>* � <sup>0</sup>*:*<sup>75</sup> *<sup>γ</sup>RPD*

*σ <sup>f</sup> γ<sup>S</sup>* � *σeγσ* <sup>1</sup>*:*1*<sup>σ</sup> <sup>f</sup> <sup>γ</sup><sup>S</sup>* � *<sup>σ</sup>eγσ*

where *γd*, *γR*, *γs*, *γσ* are safety factors determined by the admissible of risk

*V*2 *<sup>f</sup>* <sup>þ</sup> *<sup>V</sup>*<sup>2</sup>

The safety factor *γ<sup>R</sup>* is determined taking into account the admissible level of

1 � *upv <sup>f</sup>*

where *up* is the quantile corresponding to the probability [*Rf*]; *Vf* is the coefficient of variation of the fracture pressure; *Vp* is coefficient of variation of operation

The *up* quantile is set taking into account the accepted safety class of the pipeline

The coefficients of variation of fracture pressure and operation pressures *Vf* and *Vp* are determined by statistical methods based on data for statistical scattering of the operation pressure, pipe metal mechanical characteristics, diameter *D* and wall

The partial safety factor for the defect size *γ<sup>d</sup>* is determined taking into account

**Hazard classes Probability of fracture** *up* I - Low ≤ 10�<sup>2</sup> 2.33 II - Meddle ≤ 10�<sup>3</sup> 3.1 III - High ≤ 10�<sup>4</sup> 3.72 IV – Very high ≤ 10�<sup>5</sup> 4.27

requirements [7] base on the value standard deviations S*h/t* of the defect size (**Table 3**). The partial safety factors *γ<sup>s</sup>* and *γσ* are set according to **Tables 4** and **5**. The hazard of defect is determined by the design point position, given by the

actual coordinates ~*lz* and ~*lx*on the design diagram (**Figure 4**).

<sup>1</sup>*:*1*<sup>σ</sup> <sup>f</sup>* � *<sup>γ</sup>RPD* 2*t* 1 *M*

*t*

*M*

ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi

*<sup>p</sup>* � *upV fVp* � �<sup>2</sup> q

� �<sup>2</sup> (11)

ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi

*<sup>l</sup>* � *<sup>σ</sup>hσ<sup>l</sup>* <sup>þ</sup> <sup>3</sup>*τ*<sup>2</sup> *hl* <sup>q</sup>

� � is Folies factor; *<sup>γ</sup>e*, *<sup>γ</sup><sup>m</sup>* are

is

(9)

(10)

*σ*2 *<sup>h</sup>* <sup>þ</sup> *<sup>σ</sup>*<sup>2</sup>

**Figure 2.** *Scheme for calculating the allowable size of defects.*

**Figure 3.** *Idealization of volumetric (a) and flat (b) defects shape.*

*Defects Assessment in Subsea Pipelines by Risk Criteria DOI: http://dx.doi.org/10.5772/intechopen.94851*

where *<sup>σ</sup> <sup>f</sup>* <sup>¼</sup> min *Re γe* ; *Rm γm* n o is fracture stress; *<sup>σ</sup><sup>e</sup>* <sup>¼</sup> ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi *σ*2 *<sup>h</sup>* <sup>þ</sup> *<sup>σ</sup>*<sup>2</sup> *<sup>l</sup>* � *<sup>σ</sup>hσ<sup>l</sup>* <sup>þ</sup> <sup>3</sup>*τ*<sup>2</sup> *hl* <sup>q</sup> is equivalent stress; *σ<sup>h</sup>* is hoop stress; *σ<sup>l</sup>* is longitudinal stress; *τhl* is tangential shear stress; *RF* ~*lz*,~*lx* � � <sup>¼</sup> <sup>1</sup>�~*lz* <sup>1</sup>�~*lz=<sup>M</sup>* <sup>~</sup>ð Þ*lx* is risk-factor of defect; *M* ~*lx* � � is Folies factor; *<sup>γ</sup>e*, *<sup>γ</sup><sup>m</sup>* are partial safety factor.

If the components of limit state functions have a Gaussian distribution, then from the solutions of Eqs. (7) and (8) it is possible to determine the allowable sizes ~*lz* for given sizes ~*lx* with use partial safety factors:

for hoop stress

$$\tilde{l}\_x \le \frac{1}{\chi\_d} \frac{\sigma\_f - 0.75 \frac{\chi\_p PD}{t}}{1.1 \sigma\_f - \frac{\chi\_p PD}{2t} \frac{1}{M}} \tag{9}$$

for equivalent stress

$$\tilde{l}\_x \le \frac{1}{\gamma\_d} \frac{\sigma\_f \chi\_S - \sigma\_\epsilon \chi\_\sigma}{1.1 \sigma\_f \chi\_S - \frac{\sigma\_\epsilon \chi\_\sigma}{M}} \tag{10}$$

where *γd*, *γR*, *γs*, *γσ* are safety factors determined by the admissible of risk fracture [*Rf*].

The safety factor *γ<sup>R</sup>* is determined taking into account the admissible level of fracture probability [*Rf*]:

$$\gamma\_R = \frac{\mathbf{1} - \boldsymbol{u}\_p \sqrt{\boldsymbol{V}\_f^2 + \boldsymbol{V}\_p^2 - \left(\boldsymbol{u}\_p \boldsymbol{V}\_f \boldsymbol{V}\_p\right)^2}}{\mathbf{1} - \left(\boldsymbol{u}\_p \boldsymbol{v}\_f\right)^2} \tag{11}$$

where *up* is the quantile corresponding to the probability [*Rf*]; *Vf* is the coefficient of variation of the fracture pressure; *Vp* is coefficient of variation of operation pressure.

The *up* quantile is set taking into account the accepted safety class of the pipeline according to **Table 2**.

The coefficients of variation of fracture pressure and operation pressures *Vf* and *Vp* are determined by statistical methods based on data for statistical scattering of the operation pressure, pipe metal mechanical characteristics, diameter *D* and wall thickness *t* of pipes.

The partial safety factor for the defect size *γ<sup>d</sup>* is determined taking into account requirements [7] base on the value standard deviations S*h/t* of the defect size

(**Table 3**). The partial safety factors *γ<sup>s</sup>* and *γσ* are set according to **Tables 4** and **5**. The hazard of defect is determined by the design point position, given by the

actual coordinates ~*lz* and ~*lx*on the design diagram (**Figure 4**).


**Table 2.** *Values of quantiles up.*

**Figure 2.**

**Figure 3.**

**156**

*Scheme for calculating the allowable size of defects.*

*Issues on Risk Analysis for Critical Infrastructure Protection*

*Idealization of volumetric (a) and flat (b) defects shape.*


determines the conditions of ductile fracture of structural elements with crack-like

� <sup>0</sup>*:*<sup>3</sup> <sup>þ</sup> <sup>0</sup>*:*7 exp f�*μL*<sup>6</sup>

*f L*ð Þ *<sup>r</sup>* <sup>¼</sup> <sup>1</sup> *<sup>L</sup>*ð Þ *<sup>n</sup>*�<sup>1</sup> *<sup>=</sup><sup>n</sup> <sup>r</sup>* <sup>1</sup>≤*Lr* <sup>≤</sup> *Lmax*

*<sup>r</sup>* ¼ 0*:*5 1 þ

*<sup>μ</sup>* <sup>¼</sup> *min* <sup>0</sup>*:*001*<sup>E</sup>*

*<sup>n</sup>* <sup>¼</sup> <sup>0</sup>*:*3 1 � *Rm*

*Kr* <sup>¼</sup> *f L*ð Þ*<sup>r</sup> γK*

The risk of fracture is taken into account by introducing safety factors for crack

The values of safety factors *γ<sup>K</sup>* and *γ<sup>L</sup>* are taken according to **Tables 6** and 7. The load parameter *Lr* is defined as the ratio of the working pressure *P* to the plastic flow pressure *Py* of the section of a pipe with a crack, *Lr* = *P*/*Py*. The plastic flow pressure *Py* is determined taking into account the geometry and orientation of the crack in the pipe. The fracture toughness parameter *Kr* or *Jr* is defined as the ratio of the effective stress intensity factor *Keff* or *J*-integral *JI* to the fracture

The effective stress intensity factor *Keff* is determined taking into account the geometry and orientation of the crack in the pipe using fracture mechanics methods

**Hazard classes Low Middle High Very high** γ*<sup>K</sup>* 1.41 1.73 2.23 3.16

**Hazard classes Low Middle High Very high** γ*<sup>L</sup>* 1.5 1.8 2.25 3.0

*Re*

*r*

*r*

� � (13)

� � (14)

� � (15)

(12)

(16)

� �, *Lr* < 1

*Ry Rm*

; 0*:*6

*Ry*

, *Lr* <sup>¼</sup> *Lmax r γL*

*Kr* ¼ *Keff =Kmat*, *Jr* ¼ *J*I*=Jmat* (17)

defects. The fracture diagram is given by the following Equations [9, 10]:

*<sup>r</sup>* is calculated by the formula:

*Lmax*

*f L*ð Þ¼ *<sup>r</sup>*

Parameter *Lmax*

resistance and load:

or by finite element method.

**Table 6.**

**Table 7.**

**159**

*Values of safety factor*γ K.

*Values of safety factor γ*L.

(

Parameter *μ* is calculated as:

Parameter *n* is calculated by the formula:

toughness characteristic of the material *Kmat* or *Jmat*:

<sup>1</sup> <sup>þ</sup> <sup>0</sup>*:*5*L*<sup>2</sup> *r* � ��1*=*<sup>2</sup>

*Defects Assessment in Subsea Pipelines by Risk Criteria DOI: http://dx.doi.org/10.5772/intechopen.94851*

#### **Table 3.**

*Values of safety factor γd.*


#### **Table 4.**

*Values of safety factor γS.*


#### **Table 5.**

*Values of safety factor γσ.*

**Figure 4.** *Diagram for determining the allowable size of defects.*

The assessment of the allowable sizes of flat defects (cracks and crack-like defects, delamination) in pipes is based on a Failure Assessment Diagram (FAD). The FAD concept combines the approaches of fracture mechanics to the analysis of brittle and quasi-brittle fractures, with the approaches of limiting analysis, which

determines the conditions of ductile fracture of structural elements with crack-like defects. The fracture diagram is given by the following Equations [9, 10]:

$$f(L\_r) = \begin{cases} \left(\mathbf{1} + \mathbf{0.5L\_r^2}\right)^{-1/2} \times \left[\mathbf{0.3} + \mathbf{0.7}\exp\left\{-\mu L\_r^6\right\}, \quad L\_r < \mathbf{1}\right] \\ f(L\_r = \mathbf{1})L\_r^{(n-1)/n} & \mathbf{1} \le L\_r \le L\_r^{\max} \end{cases} \tag{12}$$

Parameter *Lmax <sup>r</sup>* is calculated by the formula:

$$L\_r^{\text{max}} = \mathbf{0.5} \left( \mathbf{1} + \frac{R\_\mathbf{y}}{R\_m} \right) \tag{13}$$

Parameter *μ* is calculated as:

$$\mu = \min\left\{\frac{0.001E}{R\_{\varepsilon}}; 0.6\right\} \tag{14}$$

Parameter *n* is calculated by the formula:

$$m = 0.3 \left( 1 - \frac{R\_m}{R\_\circ} \right) \tag{15}$$

The risk of fracture is taken into account by introducing safety factors for crack resistance and load:

$$K\_r = \frac{f(L\_r)}{\chi\_K}, L\_r = \frac{L\_r^{\max}}{\chi\_L} \tag{16}$$

The values of safety factors *γ<sup>K</sup>* and *γ<sup>L</sup>* are taken according to **Tables 6** and 7.

The load parameter *Lr* is defined as the ratio of the working pressure *P* to the plastic flow pressure *Py* of the section of a pipe with a crack, *Lr* = *P*/*Py*. The plastic flow pressure *Py* is determined taking into account the geometry and orientation of the crack in the pipe. The fracture toughness parameter *Kr* or *Jr* is defined as the ratio of the effective stress intensity factor *Keff* or *J*-integral *JI* to the fracture toughness characteristic of the material *Kmat* or *Jmat*:

$$K\_r = K\_{\rm eff} / K\_{\rm mat}, \\ J\_r = J\_1 / J\_{\rm mat} \tag{17}$$

The effective stress intensity factor *Keff* is determined taking into account the geometry and orientation of the crack in the pipe using fracture mechanics methods or by finite element method.


#### **Table 6.**

*Values of safety factor*γ K.


**Table 7.** *Values of safety factor γ*L.

The assessment of the allowable sizes of flat defects (cracks and crack-like defects, delamination) in pipes is based on a Failure Assessment Diagram (FAD). The FAD concept combines the approaches of fracture mechanics to the analysis of brittle and quasi-brittle fractures, with the approaches of limiting analysis, which

**Hazard classes Partial safety factor***γ <sup>d</sup>*

II - Meddle *γ<sup>d</sup>* ¼ 1*:*0 þ 4*:*0*Sh=<sup>t</sup> Sh=<sup>t</sup>* <0*:*04

**Hazard classes Low Middle High Very high** *γ<sup>S</sup>* 0.76 0.72 0.63 0.6

**Hazard classes Low Middle High Very high** *γσ* 1.12 1.4 1.5 1.6

*<sup>γ</sup><sup>d</sup>* <sup>¼</sup> <sup>1</sup>*:*<sup>0</sup> <sup>þ</sup> <sup>5</sup>*:*5*Sh=<sup>t</sup>* � <sup>37</sup>*:*5*S*<sup>2</sup>

*γ<sup>d</sup>* ¼ 1*:*2 0*:*08≤*Sh=<sup>t</sup>* ≤0*:*16

*h=t*

*h=t*

*<sup>h</sup>=<sup>t</sup>* 0*:*04≤*Sh=<sup>t</sup>* ≤0*:*08

I - Low *γ<sup>d</sup>* ¼ 1*:*0 þ 3*:*0*Sh=<sup>t</sup>*

*Issues on Risk Analysis for Critical Infrastructure Protection*

III - High *<sup>γ</sup><sup>d</sup>* <sup>¼</sup> <sup>1</sup>*:*<sup>0</sup> <sup>þ</sup> <sup>4</sup>*:*6*Sh=<sup>t</sup>* � <sup>13</sup>*:*9*S*<sup>2</sup>

IV – Very high *<sup>γ</sup><sup>d</sup>* <sup>¼</sup> <sup>1</sup>*:*<sup>0</sup> <sup>þ</sup> <sup>4</sup>*:*3*Sh=<sup>t</sup>* � <sup>4</sup>*:*1*S*<sup>2</sup>

**Table 3.**

**Table 4.**

**Table 5.**

**Figure 4.**

**158**

*Diagram for determining the allowable size of defects.*

*Values of safety factor γd.*

*Values of safety factor γS.*

*Values of safety factor γσ.*

Based on results of the calculations a fracture diagram is constructed (**Figure 5**). The danger of defect is determined by the position of the design point, given by the coordinates (*Kr*, *Lr*) on the diagram. If the calculated point is inside the diagram, then the considered defect is admissible, with a given level of risk fracture.

~*lz* ≤ *θ*

1 *β* � �, *Sl* <sup>¼</sup> *<sup>θ</sup>*

*μ<sup>l</sup>* ¼ *θ*Γ 1 þ

*Defects Assessment in Subsea Pipelines by Risk Criteria DOI: http://dx.doi.org/10.5772/intechopen.94851*

**6. Estimation of allowable defect sizes**

*The defects hazard diagram (with indicate defect numbers).*

where Γ(*x*) is Gamma function.

to the subject pipeline.

the specified probability.

<sup>10</sup><sup>5</sup> MPa, *<sup>α</sup><sup>t</sup>* = 1.1 � <sup>10</sup>�<sup>5</sup>

**Figure 6.**

**161**

q

ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi � ln 1 � *P <sup>f</sup>* � � *<sup>β</sup>*

Γ 1 þ

The mean value *μl*, standard deviation *Sl*, coefficient of variation *Vl* of the defect sizes can be determine based on experimental, calculated or literature data related

The risk diagram can be constructed based on calculations for different probabilities *Pf* similar as shown above. The permissible defect sizes must be below

The presented probabilistic fracture model can be used to assess the risk of accidents based on the methodology of Probabilistic Risk Analysis (PRA). Features of solving this problem for subsea pipelines can be found in the works [21, 22].

As an example, **Figure 6** shows the results of a calculated assessment of the risk of metal loss defects in an inter-field subsea gas pipeline∅ 406.4 � 17.5 mm by risk criteria. The pipe material is steel X60 (*Ry* � 415 MPa, *Rm* � 520 MPa, *E* = 2.06 �

difference is ΔT = 50°C. The total number of detected defects is 916 pcs: *h*/*t* = from 20 to 39%, � 5 defects, *h*/*t* = from 10 to 19% � 82 defects, *h*/*t* < 9% � 829 defects.

The presented results show, that three defects are located in a hazard area with a

Of these, 16 defects are unacceptable according to the standard [2].

risk level higher than 10�<sup>3</sup> and require immediate elimination. Two defects correspond to a risk level above 10�<sup>4</sup> and can be corrected in a planned manner.

). The operation pressure is 16 MPa. Temperature operation

ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi

� <sup>Γ</sup><sup>2</sup> <sup>1</sup> <sup>þ</sup>

1 *β* <sup>s</sup> � � (20)

2 *β* � �

where *Pf* is the fracture probability corresponding to the given fracture risk *Rf*. The parameters *β* and *θ* are related to the mean value *μ<sup>l</sup>* and standard deviation *Sl*:

(19)

The presented approach is applied in practice, taking into account the following provisions. The decision on the identified defects is made on the basis of all available information about their type, size and location, as well as the stability of the working loads and the operating conditions of the pipeline. Defects corresponding to the level of fracture probabilities *Rf* less than 10�<sup>5</sup> according to the defect hazard diagrams are considered as allowable under the given operating conditions. Defects located in the zone of probability of destruction 10�<sup>5</sup> < *Rf* ≤ 10�<sup>4</sup> are considered as potentially dangerous and are allowed for operation provided that there is a monitoring system and automatic limitation of internal pressure in the pipeline, and periodic non-destructive testing. Defects located in the zone of destruction probability 10�<sup>4</sup> < *Rf* ≤ 10�<sup>3</sup> are considered dangerous and must be repaired in a planned manner. Defects located in the destruction probability zone *Rf* > 10�<sup>3</sup> according to the defect hazard diagrams are considered unacceptable and must be repaired immediately.

More promising is the transition from the described approach to probabilistic approach for determining allowable sizes of defects. Such approach is developed on the basis of taking into account probability density functions of distributions defects sizes *f*(*l*). This approach assumes that the probability density *f*(*l*) is a mixture of distributions of random variables included in the limiting state equation, and is approximated by the Weibull distribution [11]:

$$f(l) = \frac{\beta}{\theta} \left(\frac{l}{\theta}\right)^{\beta - 1} \exp\left\{-\left(\frac{l}{\theta}\right)^{\beta}\right\} \tag{18}$$

Substitution of expression (18) into (5) gives the following expression for the admissible size of the defect ~*lz*:

**Figure 5.** *Failure assessment diagram with risk level.*

*Defects Assessment in Subsea Pipelines by Risk Criteria DOI: http://dx.doi.org/10.5772/intechopen.94851*

$$\tilde{I}\_x \le \theta \sqrt[\ell]{-\ln\left(\mathbf{1} - P\_f\right)}\tag{19}$$

where *Pf* is the fracture probability corresponding to the given fracture risk *Rf*. The parameters *β* and *θ* are related to the mean value *μ<sup>l</sup>* and standard deviation *Sl*:

$$\mu\_l = \theta \Gamma \left( \mathbf{1} + \frac{\mathbf{1}}{\beta} \right), \mathbf{S}\_l = \theta \sqrt{\Gamma \left( \mathbf{1} + \frac{2}{\beta} \right) - \Gamma^2 \left( \mathbf{1} + \frac{\mathbf{1}}{\beta} \right)}\tag{20}$$

where Γ(*x*) is Gamma function.

Based on results of the calculations a fracture diagram is constructed (**Figure 5**). The danger of defect is determined by the position of the design point, given by the coordinates (*Kr*, *Lr*) on the diagram. If the calculated point is inside the diagram, then the considered defect is admissible, with a given level of risk fracture.

The presented approach is applied in practice, taking into account the following provisions. The decision on the identified defects is made on the basis of all available information about their type, size and location, as well as the stability of the working loads and the operating conditions of the pipeline. Defects corresponding to the level of fracture probabilities *Rf* less than 10�<sup>5</sup> according to the defect hazard diagrams are considered as allowable under the given operating conditions. Defects located in the zone of probability of destruction 10�<sup>5</sup> < *Rf* ≤ 10�<sup>4</sup> are considered as potentially dangerous and are allowed for operation provided that there is a monitoring system and automatic limitation of internal pressure in the pipeline, and periodic non-destructive testing. Defects located in the zone of destruction probability 10�<sup>4</sup> < *Rf* ≤ 10�<sup>3</sup> are considered dangerous and must be repaired in a planned manner. Defects located in the destruction probability zone *Rf* > 10�<sup>3</sup> according to the defect hazard diagrams are considered unacceptable and must be repaired

More promising is the transition from the described approach to probabilistic approach for determining allowable sizes of defects. Such approach is developed on the basis of taking into account probability density functions of distributions defects sizes *f*(*l*). This approach assumes that the probability density *f*(*l*) is a mixture of distributions of random variables included in the limiting state equation, and

Substitution of expression (18) into (5) gives the following expression for the

*exp* � *<sup>l</sup>*

*θ* � �*<sup>β</sup>* ( )

(18)

is approximated by the Weibull distribution [11]:

*Issues on Risk Analysis for Critical Infrastructure Protection*

admissible size of the defect ~*lz*:

*f l*ðÞ¼ *<sup>β</sup> θ l θ* � �*<sup>β</sup>*�<sup>1</sup>

immediately.

**Figure 5.**

**160**

*Failure assessment diagram with risk level.*

The mean value *μl*, standard deviation *Sl*, coefficient of variation *Vl* of the defect sizes can be determine based on experimental, calculated or literature data related to the subject pipeline.

The risk diagram can be constructed based on calculations for different probabilities *Pf* similar as shown above. The permissible defect sizes must be below the specified probability.

The presented probabilistic fracture model can be used to assess the risk of accidents based on the methodology of Probabilistic Risk Analysis (PRA). Features of solving this problem for subsea pipelines can be found in the works [21, 22].

#### **6. Estimation of allowable defect sizes**

As an example, **Figure 6** shows the results of a calculated assessment of the risk of metal loss defects in an inter-field subsea gas pipeline∅ 406.4 � 17.5 mm by risk criteria. The pipe material is steel X60 (*Ry* � 415 MPa, *Rm* � 520 MPa, *E* = 2.06 � <sup>10</sup><sup>5</sup> MPa, *<sup>α</sup><sup>t</sup>* = 1.1 � <sup>10</sup>�<sup>5</sup> ). The operation pressure is 16 MPa. Temperature operation difference is ΔT = 50°C. The total number of detected defects is 916 pcs: *h*/*t* = from 20 to 39%, � 5 defects, *h*/*t* = from 10 to 19% � 82 defects, *h*/*t* < 9% � 829 defects. Of these, 16 defects are unacceptable according to the standard [2].

The presented results show, that three defects are located in a hazard area with a risk level higher than 10�<sup>3</sup> and require immediate elimination. Two defects correspond to a risk level above 10�<sup>4</sup> and can be corrected in a planned manner.

**Figure 6.** *The defects hazard diagram (with indicate defect numbers).*

Five defects are in the risk zone 10<sup>5</sup> –10<sup>4</sup> and can be repaired as planned at a later date. Defects below the level 10<sup>5</sup> can be allowed for operation, provided that periodic non-destructive testing is carried out.

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*Defects Assessment in Subsea Pipelines by Risk Criteria DOI: http://dx.doi.org/10.5772/intechopen.94851*

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Thus, the proposed method provides a more flexible and more substantiated scheme for assessing the hazard of defects. On the one hand, this assessment takes into account the risk of accidents, thereby ensuring the required level of safety. On the other hand, it allows a more rational use of financial and material resources allocated for diagnostics and repair of subsea pipelines.

### **7. Conclusion**

The paper discusses the possibilities of implementing the risk-based control method for inter-field subsea pipelines. The results obtained allow us to draw the following conclusions. Currently, there are a number of methods for assessing the hazard of pipeline defects based on deterministic approaches. Risk-based inspection provides greater opportunities for prioritizing, planning, justifying and evaluating the results of non-destructive testing. For the practical implementation of the riskbased control method, it is necessary to develop special probabilistic and semiprobabilistic calculation methods for assessing the hazard of pipeline defects taking into account random factors.

The proposed semi-probabilistic methodology is a development of the provisions of the DNVGL-ST-F101, SINTAP and DNV-RP-F116 standards. The novelty of the methodology lies in the justification of the safety factors through the level of failure probabilities corresponding to a given class of damage and loss. This opens up new possibilities for solving the problem of admissibility of defects in inter-field subsea pipelines from the standpoint of the concept of serviceability according to risk criteria.

#### **Author details**

Anatoly Lepikhin<sup>1</sup> \*, Victor Leschenko<sup>2</sup> and Nikolay Makhutov<sup>3</sup>

1 Federal Research Center for Information and Computational Technologies, STC "Neftegazdiagnostika", Moscow, Russia

2 STC "Neftegazdiagnostika", Moscow, Russia

3 Mechanical Engineering Research Institute of the Russian Academy of Sciences, Moscow, Russia

\*Address all correspondence to: aml@ict.nsc.ru

© 2020 The Author(s). Licensee IntechOpen. This chapter is distributed under the terms of the Creative Commons Attribution License (http://creativecommons.org/licenses/ by/3.0), which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

*Defects Assessment in Subsea Pipelines by Risk Criteria DOI: http://dx.doi.org/10.5772/intechopen.94851*
