Sloshing

SLOSHING EFFECTS IN SPHERICAL VESSELS
AND THEIR SUPPORTS

# A CASE STUDY OF A SYSTEM OF INSULATION SISMIC FOR LIQUEFIED GAS STORAGE TANK

# Search for TECNI SYSTEME INSTITUTE

The progam will research the applicability of innovative anti-seismic techniques,such as seismic isolation,components of industrial plants to high risk.

The purpose of this research is to demonstrate the viability of seismic techniques are being developed in Italy and abroad and their usefulness for industrial plants.

The research developed by choosing a real component of a chemical plant and comparing the risk in the condition improved by the conventional seismic techniques.

**The study was conducted jointly by ANPA;ENEA and the University of Rome La Sapienza and is divided into six business lines summarized below:**

**1**.Identification of a typical component of a chemical plant.

**2**.Definition of the vibratory motion design appropiate to the site wehre the plant is located.

**3**.Analysis oft he component selected with regard to boht mechanical and structural engineering aspects in the current situation without insulation.

**4**.Choosing the most suitable isolation system fort he component under consideration and ist detailed design.

**5**.Analysis oft he isolated component, with evaluation oft he effects of isolation on resistance, functionality, layout and costs.

**6**.Collection of evidence fort he generalization of results to other components.

The first phase has led to a tank for liquified gas,butane, Enichem Priolo.Si plant site is a steel tank spherical with a diameter of about 21 m. It is based on eleven high cylindrical columns about 12,5 m. The total weight in the case of the empty vessel is 315 tons,while in the case of tank full ( 80% )is about 3315 tons,while the full (100 %) hast he total weight of 4143 tons.

- Diameter of the tank D= 21,165 m.

- Diameter of the circle containing the column center Dg=20,512m.

- Sheet thichness of the shell Ss= 0.022 m.

- Distance from the center of ball from the ground H= 12.870m.

- Diameter oft he columns d= 1.0660m.

- Sheet thickness oft he columns Sc= 0.0095m.

- Height of columns L = 12,500m.

- Quote of the diagonals h = 6810m.

- Area of diagonal Ad= 9.62E-4m2

**DEFINITION OF SHARE**

It is assumed that the structure in questioni s subject to vertical load due to weight and Liquid contained in it, and the action of vertical sisma.Per with actions,we consider three different loading conditions,relating to cases of empty vessel,filled to 40% and full al’ 80% .

Assuming that the gas content liquefied butane gas in the tnk is characterized by a density of 6 KN / m3,at the three loading conditions has the following weight values:

--Tank full to 80% ( condition 1 ): P = 26520 KN

--Tank full to 40% ( condition 2 ): P = 14810 KN

--Empty tank ( condition 3 ): P = 3100 KN

The third phase consisted in the analysis of the shell of the operating conditions and accidental including action seismic activity.This has required ist modeling using a finite element numerical code.

The analysis aims to determine both the dynamic characteristics,ie natural frequencies and modes of vibrate serving for subsequent determinations of the best solution for seismic isolation,both the state of membering that serves as a stress in comparison with that oft he solution chosen .

**The results analysis is:**

--The first natural frequency is low ,approximately equal to 1 HZ,,corrisponding to a mode of vibration characterized by an almost rigid movement and deformation of the sphere centered on the columns carriers.They are in fact very flexible.

--The calculation was made in the condition of tank full,which corresponds to the case of filling up to 80% of butane gas.In this first survey been taken into account, an approximate the motion of splashing (sloshing )oft he liquid.

--If the tank is empty the first natural frequency is around 2.8 HZ.The maximum stress at the base of the columns is very high,higher than the yeld under the action of weight and seismic load, envisaged in the ANPA and AENEA multiplied by the importance factor of 1.4.

PROBLEM SLOHING

Is created inside a spherical Tank with support columns and raised on the ground,through an abrupt shift of the oscillating liquid gas that is inside the sphere,creating a strong mechanical force that is transmitted to the pillars, creating the risk of any rutture and the collapse of them, and as a result of a catastrophic accident that can be transmitted to the entire area.

**TECNI SYSTEME INSTITUTE**.

**SLOSHING EFFECTS IN SPHERICAL VESSELS AND THEIR SUPPORTS**

The present work investigates the response of a half-full spherical pressure (vessel tank)
under earthquake excitation.
The fluid motion due to the free surface usually referred to as "sloshing" is examined in
detail with respect to its influence on the response of the tank/support system, in terms of
the base shear force and overturning moment.

The present study adopts a semi-analytical solution of sloshing in spherical vessels, and
proposes a simplified mechanical model to desribe the vessel behavior, including the
flexibility of its supports.

Two case studies from actual industrial applications are considered.

ln those vessels, the importance of including sloshing effects is examined. Furthermore, the
maxirnum base shear and overturning moment obtained through the direct analysis of a real
seismic event are compared with the corresponding values from aspectralanalysis
procedure.

Table 1: The frequencies of the sloshing in the spherical container {R = 1}.

It is very important to note that the eigenvalues depend on the truncation of equation and
this is because the functions used in an equatlon are not mutually orthogonal.

ln Figure 3 the variation of the first {fundamental} of its frequency is shown in terms of
the truncation terms of size N {n_N}. Note that three terms {n = 3} are necessary so that a
very good accuracy is achieved.

The totalforce FT applied to the liquid to the tank is obtained by the integration of
pressure on the vessel wall in the direction sf excitation {say x direction}.
This force has two components, an impulsive Fw and a sloshing Fs:
where Kb isthestiffness of theleg/supportsystem toning,and X-XG is the relative
displacement of the spherical tank relative to the ground.

Where Ms is half the liquid mass and it is referred to as sloshing mass.
It can be shown that the total force based on one sloshing mode is a good approximation of the
corresponding force assuming the complete solution.

The equilibrium of the forces implied by equation needsalso be considered.

ln this equation, the total horizontal force is to be equilibrated by the elastic forces of the supports
and, therefore, the impulsive force should include the mass of the steel tank. Conducting the

appropriate integration for the sloshing part as indicated by equations, the total force is readily
obtained.
The response of elevated spherical tanks under seismic loading is of panicular importance,
because of practical applications in the petrochemical industry.
Herein, two case studies are examined; a LNG terminal and a propylene terminal, both located in
Greece.

The stress resultants (. base shear and overturning moment) on the foundation are computed
using the simplified 2DOF model formulation and the ground motion record from a recent Greek
earthquake, the 1995 Kozani earthquake.

The base resultants are compared with the coresponding values when liquid sloshing is not
considered.

In addition, a spectral analysis is performed according to the general provisions of the Greek
Seismic Code [21], using the eigenfrequencies obtained in the course of the present work, and the
corresponding stress resultants are also obtained.

where Mw is the total liquid mass {323wMR), which was actually expected, because in the impulsive
motion every liquid particle follows the motion of the tank.

Another important issue is the location of the above forces.

Since the pressure is always normal to the tank wall, those forces are applied on the center of the
tank.

This observation is applicable to spherical tanks filled up to an arbitrary depth (not only half-full) and
it is important in order to obtain the corresponding overturning moment the above formulation and
solution assumes that the motion of the tank X(t) is known.

ln the case of a spherical tank supported by a system of legs and X-braces, only the ground motion
Xg(t) is known, whereas X(t) is unknown and should be calculated.

The additional equation required to determine X(t) is the equilibrium of forces at the base: the total
horizontal inertia force FT is equilibrated by the support force Fb (Figure 4).
This means that where K B is the stiffness of the leg/bracing support system, and X-X G is the
rela- tive displacement of the tank with respect to the ground.

Based on an analytical series solution of sloshing in half-full spherical tanks, it is possible to develop a
simplified model for the analysis of such tanks under earthquake excitation-

Using this simple formulation, the seismic analysis of two typical vessels is conducted.

The results show that sloshing has a considerable effect on the overall response, especially on the
values of base shear and overturning moment.

Furthermore, the results from a spectral analysis are compared with the results of the present
analysis.
The present study is of particular interest to the petrochemical industry, and provides a simple and
effective tool for analyzing sloshing effects in half-full spherical liquid-storage vessels.
The results are expected to contribute towards better understanding of the sloshing phenomenon
and towards safer terminal design.