Stress analysis of lines connected to API tanks is very critical. I am sure most of you have done stress analysis of lines connected to equipment nozzles. However when it comes to tank nozzle, there are some differences, due to which the approach followed for equipment nozzle cannot be followed.
In the Stress analysis of lines connected to normal Equipment nozzle (Vessel, Column, Heat Exchanger etc.), generally there are only 2 things which we have to account during Caesar modelling.
- Nozzle’s thermal movements, and
- Nozzle flexibility
But in additional to those two things, there are two additional points which we have to account in the Caesar modelling during analysis of tank connected piping system. These are,
- Nozzle rotations due to tank bulging, and
- Tank settlement
About the first two, i.e. Nozzle’s thermal movements and Nozzle flexibility, we all are well aware, and therefore I will not be covering these in this article.
We will see other two effects, about which we may not be aware, or if aware, not very clear how to model these in Caesar and take care of these along with Nozzle’s thermal movements, and Nozzle flexibility.
So first in the current article we will see Nozzle Rotation due to tank bulging.
What is this Tank Bulging?
In case of tank, tank is filled with liquid.
This liquid has varying height.
Due to this, there is varying liquid pressure on tank wall.
It has more pressure at bottom.
Due to this, tank wall try to expand more at bottom (as seen in Fig. 1).
But the bottom plate prevents this expansion and holds the bottom end of shell in position.
Due to this, actual shape of tank is formed similar to as shown in Fig. 1.
This is called bulging of tank shell.
Due to tank shell bulging, the nozzle on the shell moves radially outward, and rotates in vertical plane, depending upon their position.
The nozzle on lower portion of the tank rotates downwards whereas nozzle on upper portion rotates upwards.
This effect is not seen in other equipments, mainly because
- Equipment diameter is relatively much small (up to 3 m). Therefore the amount of radial growth is much less. Whereas tank diameters are generally large, of the order of 10 m to 60 m. Due to this the amount of radial growth is significant.
- Also, equipment has internal pressure, not only pressure due to fluid weight. Thus pressure variation from top to bottom is not so much where as in tank, pressure on top is zero.
- At the same time, the bottom of equipment is not flat like tank, which does not deflect but acts like stiffener, to holds the shell ends.
However the main difference is due to tank diameter only.
How Tank Bulging is calculated?
In the design code API 650, which governs the design of tank, this bulging effects is covered in Appendix – P.
This Appendix – P is mandatory for tanks greater than 36 m diameter and for tank with diameter 36 m & below, it is optional or mandatory only if specified by purchaser.
The intent of 36 m diameter condition is to inform the user that the bulging effect is significant in large diameter tanks, which code has considered as above 36 m diameter, hence put as mandatory.
For smaller diameter it is considered as insignificant, hence kept as non-mandatory.
The formulas for calculation of Radial movement and rotation due to tank bulging is provided in API 650 and produced in Fig 2 and Fig 3 for your reference.
If you calculate the outward radial movement and rotation using the above formulas it can be found that the effect of tank bulging on nozzle at higher elevation is insignificant.
Pipe routing guidelines to minimize effect of tank bulging:
Due to bulging, nozzle at lower levels rotates downward. This causes pipe to move vertically downwards. To minimize the amount of this movement:
- Piping shall be rotated through 90° as close to the tank wall as practical. 2D (D=outer diameter of pipe) spool may be provided to avoid elbow stiffening due to flanged elbow. This is shown in Fig. 4