Purpose
The side valve assembly is required to isolate a lateral from the mainline in situations where a line break may occur or when maintenance of the lateral may be necessary.
TABLE 7-11. Corresponding values of the failure probability Pfand the reliability index
Pf Pf Pf
0.5 0.000 0.04 1.751 104 3.719
0.4 0.253 0.03 1.881 105 4.265
0.3 0.524 0.02 2.054 106 4.753
0.2 0.842 0.01 2.326 107 5.199
0.1 1.282 0.005 2.576 108 5.612
0.05 1.645 0.001 3.090 109 5.998
Equation (7-72) is generalized in the codes to take account of a number of other factors including a safety class factor, so that, for example, in the Canadian Limits States Design approach (CSA Z662-07), one finds:
; R GGþ QQþ EEþ AA
7 73
ð Þ
Where ; = resistance (strength) partial safety factor (0.9) R = characteristic resistance or strength
= safety class factor
G, Q, E, A= load partial safety factors for G, Q, E, and A load effects
G, Q, E, A = permanent, operational, environmental, and accidental load effects respectively.
Figure 7-18 depicts the limit states design methodology used in the Canadian Code (Appendix C of CSA Z662-07). The safety class factor is given in Table 7-8 and the partial load factors in Table 7-9.
Safety class factors are related to the consequence of failure or human exposure to the hazard presented. Their various values are set to ensure that higher consequence failures have a lower probability of occurrence. For this reason the class factors are based upon both the location of the pipeline and its contents. The safety class factor can therefore vary along the length of the pipeline. Zimmerman et al., 1996 in a discussion of CSA Z–662 Appendix C presents in pictorial form (Figure 7-19) a possible relationship between safety class factor, human exposure, and
Figure 7-18. LSD method [Ref CSA Z662, 2007]
target values of annual reliability. Similarly Sotberg et al. (1997) have related acceptable failure probabilities to safety classes and the various generic types of limit states discussed next.
In order to perform a structural reliability analysis, a mathematical model relating the load and resistance needs to be devised. This relationship is expressed in the form of a limit-state function, which can be theoretical, semiempirical, or fully empirical in nature. It does however predict the onset of failure of the pipeline. For pipelines, limit states are defined in accordance with three specific design requirements (Dinovitzer et al. 1999):
The ultimate limit state The serviceability limit state The service limit state
The ultimate limit state (ULS) is the state at which the pipe cannot contain the fluid it is carrying. This limit state clearly has safety and environmental implications.
Examples of this limit state are leaks and ruptures (bursting). The ultimate limit state is generally associated with failure modes involving defects. The serviceability limit state (SLS) is the state at which the pipeline no longer meets the full design requirements but is still able to contain the fluid. In short, it is not fit for purpose, e.g., it cannot pass sufficient fluid/inline maintenance inspection tools. This limit state has no direct safety or environmental implications. Examples of this limit state include permanent deformation due to denting or yielding. The serviceability limit state is generally associated with failure modes of defect free pipe.
The service limit states are those that develop slowly during the operating life of the structure, such as fatigue failure.
Limit states design requires that all potential failure modes be investigated, though in the case of pipeline design it is possible to conceive of some limit states where the state of knowledge is so incomplete (e.g., stress corrosion cracking) that they are currently not suited for inclusion in such a design format. Table 7-10 contains a list of pertinent pipeline design limit states, the first of which, radial yielding, will be used as an example of the LRFD approach.
TABLE 7-8. Safety class factors for ultimate limit states (Ref CSA Z662, 2007) Class
TABLE 7-9. Load and resistance factor values of (Ref CSA Z662, 2007) Appendix C Load Factors
Q
Load Combinations G Pressure Other E A
ULS 1: Max operating 1.25 1.13 1.25 1.07 0
ULS 2: Max environmental 1.05 1.05 1.05 1.35 0
ULS 3: Accidental 1.0 1.0 1.0 0 1.0
ULS 4: Fatigue 1.0 1.0 1.0 1.0 0
SLS 1.0 1.0 1.0 1.0 0
Example:
The limit state function Z for radial yielding can be expressed explicitly in terms of the four basic quantities D, t, P, and Syas:
Z¼ SyPD
2t <0 ð7 74Þ
Figure 7-19. Safety class factor related to target annual reliability [Zimmerman et al., 1996]
TABLE 7-10. Pipeline design limit states
p Strength limit states/ultimate
p Radial pressure-yielding bursting, fracture, fatigue p Axial loading-plastic collapse, fracture, buckling
p Flexural load-yielding, fracture, local buckling, wrinkling p Combination of above with surcharge or thermal effects
Deformation Limit States/Serviceability p Excessive cross-section deformation - ovalization p Excessive beam-column deformation - curvature
p Resonance at the natural frequency with imposed loading
Progressive Degradation Limit States/Service p Fatigue failure due to fluctuating internal loads p Fatigue failure due to external (surcharge) loads p Failure due to corrosion fatigue
p Failure due to crack propagation p Corrosion-induced failure (leakage)
where P is the internal pressure, D the mean pipe diameter, t is the actual wall thickness at any point in the pipe, and Syis the actual value of the yield stress at the same point.
The four-dimensional basic quantity ‘‘space’’ is split into two regions by the equation Z = 0. That part where Z < 0 is called the ‘‘failure region,’’ while the portion defined by Z > 0 is denoted the safe region. The surface defined by Z = 0 is referred to as the failure surface or failure boundary. Introducing the quantity SH= PD/2t, that is the applied hoop stress, the failure function can be rewritten as:
Z Sð y; SHÞ ¼ SH Sy ð7 75Þ
The problem is now reduced to two quantities, one describing the load (SH) and the other representing the pipe strength or resistance (Sy). A pictorial representation of the concept of the failure region, failure surface, and safe region is given in Figure 7-20.
Both the stress caused by the applied load SH and the pipe strength Sy in Equation (7-75) are represented by statistical distributions. The probability density function (PDF) for the yield strength is found by a statistical analysis of measured test values from pipe mill certification records. Similarly, the mean value and variability of the wall thickness and diameter are found from pipe delivery records. Since the pipe is
Figure 7-20. Pictorial definition of limit sate concept
made to a specification this limits the amount of variability present in the delivered pipe. In Level 1, load resistance factored design terms, the limit state described in Equation (7-74) can be written as
QSH ySy ð7 76Þ
The interplay between the load [the left-hand side of Equation (7-76)] and resistance is shown in Figure 7-21. By altering the values of /, the amount of overlap of the tails of the two distributions can be altered. As will be described later in the description of the level 2 methods of analysis, the convolution integral of the joint probability density functions in these overlapping tails is directly related to the probability of failure.
The choice of partial load factors in the LRFD approach should be such as to be in accord with previous engineering experience. In the case of radial yielding, we know from a deterministic analysis (working stress design) that:
PD
2t 0:8 Sy
while from Equation (7-76) the LRFD format is Q PD
2t Sy ð7 77Þ
Figures 7-21. Partial factors in LSD
Since the partial safety factor in the Canadian Code is 0.9 and for nonsour gas in a class location 1 the safety class factor is 1.0 (from Table 7-8), it follows that:
Q ¼ 0:8 or
Q ¼
0:8 ¼ 0:9
0:8 1¼ 1:13
which is the partial load factor found in Table 7-9. for the ultimate limit state due to pressure.
Calibrating LRFD Partial Load Factors
The use of the LRFD approach to pipeline design enables the designer to include probabilistic information without having to be deeply versed in probability theory. To do so with confidence though means that the various partial safety factors contained in Tables 7-8 and Table 7-9 have to be determined such that their use does not lead to designs that are drastically different from existing general practice. The calibration of the partial factors to ensure predetermined probabilities of failure is performed using Level 2/Level 3 methods and follows the steps outlined in Figure 7-22. It will be sufficient here to limit the argument
Figure 7-22. Flowchart for selection of partial safety factors of a probability-based design code
to the Level 2 approach, though the interested reader is referred to Thoft-Christensen and Baker (1982), Chen and Nessim (1994), and Ellinas et al. (1986) for a description of the Level 3 approach.
Level 2 Method
The previous example on radial yielding can be written in more general terms as follows.
Suppose that the random loading in the pipe is denoted by L and its resistance or capacity is denoted by R, then the safety margin Z of the pipe is defined as:
Z¼ R L ð7 78Þ
Since R and L are random variables, Z must also be a random variable with a corresponding probability density function fZ(z).
In this case, and as shown in Figure 7-20, failure is clearly the event (Z0), so the probability of failure is:
Pf ¼ Z0
1
fzð Þdz z ¼ Fz 0ð Þ ð7 79Þ
Graphically, this is represented by the area under fZ(z) to the left of 0, as shown in Figure 7-23.
If R and L are assumed to be normally distributed with mean values R and L, respectively, and variances Z2
and R2, then the function Z = RL is also normal, based on
Figure 7-23. Distribution of safety margin
the assumption of independence. Fz(0)is the value of the cumulative density function (cdf ) corresponding to Z = 0. Thus for normal distributions one can write:
Z ¼ R L and 2Z ¼ 2R þ 2L
Furthermore, the standardized safety margin (Z - z)/Zis normally distributed with a zero mean and a standard deviation equal to one. The probability of failure is computed as follows:
Pf ¼ FZð Þ ¼ 0 ð z=ZÞ
where is the standard normal CDF. It can be seen that the probability of failure is a function of the ratio: = Z/Z, which is usually called the Cornell safety index. Thus
¼ R L
ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi
2
Rþ 2L q
Hence if one knows these quantities for the load and resistance distributions, then the safety index is readily found.
For lognormal quantities (which often are used to describe the variables that make up L and R), it is easier to consider
Z¼ R=L ð7 80Þ
Let the means and coefficients of variation be denoted R, L and R, L, respectively, where R = R/L, that is the ratio of the mean value and the standard deviation of the distribution. Then the logarithm of Z is normally distributed with a mean and variance equal to
Consequently, the probability of failure is equal to
Pf ¼ Prob. R=L < 1ð Þ ¼ Prob. ‘nZ < 0ð Þ ð7 83Þ
which is the value of the normal cumulative frequency distribution at ‘nZ=0. The normal and log normal distributions adequately describe the variability in the parameters of interest in pipeline design so that Equations (7-78) and (7-83) are most often used to determine the probability that a limit state has been violated, i.e., the probability of failure. The safety or reliability index and the probability of failure are uniquely related and since is a quantity defining the safety of the pipeline structure, it is often used as the target measure of structural performance. Table 7-11 provides some corresponding values of Pf and , other values may be found from the standard table for the cumulative normal distribution.
Having determined a target reliability index say = 3.719 with a corresponding probability of failure of 104, the necessary values of the particular factors are found by the trial-and-error-loop depicted in Figure 7-22.
VALVE ASSEMBLIES
Block Valves
Purpose
Block valve assemblies are used to isolate sections of mainline or long laterals when isolation is required in the event of a line break or if maintenance in a section of the line is necessary. Since their fuction is to provide a leak tight seal, it is important that they do not experience undue deflection. For this reason, they are substantially stiffer than the adjacent pipe and their stress levels are about half of the pipe.
Required Components
The following are the main components required for a block valve assembly:
p A gate or ball valve the size of the mainline to allow passage of pigs.
p Two blowdowns (gas only), either remote from or directly connected to the mainline, interconnected for equalizing the pressure on both sides of the block valve.
p A riser on each side of the block valve to provide a power supply for a hydraulic/
pneumatic operator, or for taking fluid samples, connecting pressure gauges or performing flow tests.
Location
Code requirements for maximum block valve spacing vary with class location as shown in Table 7-12:
Ease of access and site conditions should always be evaluated when selecting a location for a valve assembly.
A detailed review of valve location requirements and need for valve automation to reduce oil spill in the event of a rupture in liquid lines is given by Mohitpour et al. (2003).
Side Valves
Purpose
The side valve assembly is required to isolate a lateral from the mainline in situations where a line break may occur or when maintenance of the lateral may be necessary.
TABLE 7-11. Corresponding values of the failure probability Pfand the reliability index
Pf Pf Pf
0.5 0.000 0.04 1.751 104 3.719
0.4 0.253 0.03 1.881 105 4.265
0.3 0.524 0.02 2.054 106 4.753
0.2 0.842 0.01 2.326 107 5.199
0.1 1.282 0.005 2.576 108 5.612
0.05 1.645 0.001 3.090 109 5.998
Required Components
A side valve assembly consists of the following components:
p A gate or ball valve the size of the lateral
p A check valve and bypass line (for receipt laterals) p A blowdown with appropriate valving (gas only)
p A flange and insulation set to separate the lateral electrically from the mainline p Test leads from the mainline and the lateral
Note that the purpose of a check valve in the assembly is to prevent reverse flow. It will also prevent flow from the mainline into the inflowing lateral when the pressure in the lateral is less than that in the mainline. Check valves are not required on sales (offtake) laterals.
Location
These assemblies are located on the lateral immediately adjacent to the mainline.