Calculation of vessels

Haga, G.P. (1971) Calculation of vessels of super-high pressure, (Preprint), Institute for physics of metals of NACU, 81 p. (mss)... 

The calculation was carried out using the ANSYS F.E.M. code. The pressure vessel was meshed with a 4 nodes shell element. Fig. 18 shows a view of the results of calculation of the sum of principal stresses on the vessel surface represented on the undeformed shape. For the calculation it was assumed an internal pressure equal to 5 bar and the same mechanical characteristics for the test material. 

Blast Characteristics Accurate calculation of the magnitude of the blast wave from an exploding pressure vessel is not possible, but it may be estimated from several approximate methods that are available. 

Note that the wetted surface A used to calculate heat absoiption for a practical fire situation is normally taken to be the total wetted surface within 7.5 m of grade. "Grade" usually refers to ground level, but any other level at which a major fire could be sustained, such as a platform, should also be considered. In the case of vessels containing a variable level of liquid, the average level is considered. Specific inteipretations of A to be used for various vessels are as... 

In the present context, the term BLEVE is used for any sudden loss of containment of a liquid above its normal boiling point at the moment of its failure. It can be accompanied by vessel fragmentation and, if a flammable liquid is involved, fireball, flash fire, or vapor cloud explosion. The vapor cloud explosion and flash fire may arise if container failure is not due to fire impingement. The calculation of effects from these kinds of vapor cloud explosions is treated in Sections 4.3.3 and 5.2. 

Vessel Rupture. The energy needed to rupture a vessel is very low, and can be neglected in calculation of explosion energy. For a typical steel vessel, rupture energy is on the order of 1 to 10 kJ, that is, less than 1% of the energy of a small explosion. 

The general procedure of the basic method is shown in Figure 6.20. This method is suitable for calculations of bursts of spherical and cylindrical pressure vessels which are filled with an ideal gas, placed on a flat surface, and distant from other obstacles which might interfere with the blast wave. 

Equation (6.3.15) is not accurate for the calculation of explosion energy of vessels filled with real gases or superheated liquids. A better measure in these cases is the work that can be performed on surrounding air by the expanding fluid, as calculated from thermodynamic data for the fluid. In this section, a method will be described for calculating this energy, which can then be applied to the basic method in order to determine the blast parameters. 

Rgure 6.29. Calculation of energy of flashing liquids and pressure vessel bursts filled with vapor or nonideal gas. 

In accidental releases, pressure within a vessel at time of failure is not always known. However, depending on the cause of vessel failure, an estimate of its pressure can be made. If failure is initiated by a rise in initial pressure in combination with a malfunctioning or inadequately designed pressure-relief device, the pressure at rupture will equal the vessel s failure pressure, which is usually the maximum allowable working pressure times a safety factor. For initial calculations, a usual safety factor of four can be applied for vessels made of carbon steel, although higher values are possible. (The higher the failure pressure, the more severe the effects.)... 

In this chapter, applications of the calculation methods used to predict the hazards of BLEVEs, as described in Chapter 6, are demonstrated in the solution of sample problems. Fire-induced BLEVEs are often accompanied by fireballs hence, problems include calculation of radiation effects. A BLEVE may also produce blast waves and propel vessel fragments for long distances. The problems include calculations for estimating these effects as well. Calculation methods for addressing each of these hazards will be demonstrated separately in the following order radiation, blast effects, and fragmentation effects. 

In this section, three examples of blast calculations of BLEVEs and pressure vessel bursts will be given. The first example is designed to illustrate the use of all three methods described in Section 6.3.2. The second is a continuation of sample problem 9.1.5, the BLEVE of a tank truck. A variation in the calculation method is presented instead of determination of the blast parameters at a given distance from the explosion, the distance is calculated at which a given overpressure is reached. The third example is a case study of a BLEVE in San Juan Ixhuatepec (Mexico City). 

This calculation takes into account only the blast from the expansion of vessel contents. In fact, this blast may be followed by one from a vapor cloud explosion. This possibility must be considered separately with the methods presented in earlier chapters. 

It is wortli noting tluit design calculations for tlie sizing of relief systems (relief valves, headers, scmbbers and knock-out drums, etc.) are conservative in order to protect tlie integrity of vessels and relief systems. Tlie calculations used for risk assessments are tliose which most accurately describe the discliarge rate from tlie luizardous incident being modeled. 

Calculate the pump dowTitime for a system of vessels and piping with a volume of 500 liters. The final pressure is to be 0.01 torr, starting at atmospheric. From the speed-pressure curve of a manufacturer s pump at 0.01 torr, speed is 2.0 liters/sec. At atmospheric pressure, = 2.V5 liters/sec with P"q = 760 torr. From the manufacturer s data, Rps = 15 and = 0.5 liters. 

Due to gas expansion from external fire, the API code [10] provides for calculation of the pressure relief valve orifice area for a gas containing vessel exposed to external fire on die unwetted surface ... 

An interesting application of electrode potentials is to the calculation of the e.m.f. of a voltaic cell. One of the simplest of galvanic cells is the Daniell cell. It consists of a rod of zinc dipping into zinc sulphate solution and a strip of copper in copper sulphate solution the two solutions are generally separated by placing one inside a porous pot and the other in the surrounding vessel. The cell may be represented as ... 

Despite the advantages of continuous cultures, the technique has found little application in the fermentation industry. A multi-stage system is the most common continuous fermentation and has been used in the fermentation of glutamic add. The start-up of a multi-stage continuous system proceeds as follows. Initially, batch fermentation is commenced in each vessel. Fresh medium is introduced in the first vessel, and the outflow from this proceeds into the next vessel. The overall flow rate is then adjusted so that the substrate is completely consumed in the last vessel, and the intended product accumulated. The concentration of cells, products and substrate will then reach a steady state. The optimum number of vessels and rate of medium input can be calculated from simple batch experiments. 

The calculation of heat transfer film coefficients in an air-lift bioreactor is more complex, as small reactors may operate under laminar flow conditions whereas large-scale vessels operate under turbulent flow conditions. It has been found that under laminar flow conditions, the fermentation broths show non-Newtonian behaviour, so the heat transfer coefficient can be evaluated with a modified form of the equation known as the Graetz-Leveque equation 9... 

Although the absorption of a gas in a gas-liquid disperser is governed by basic mass-transfer phenomena, our knowledge of bubble dynamics and of the fluid dynamic conditions in the vessel are insufficient to permit the calculation of mass-transfer rates from first principles. One approach that is sometimes fruitful under conditions where our knowledge is insufficient to completely define the system is that of dimensional analysis. 

The model in its present form cannot be used for the design of gas-liquid contacting systems, for several reasons. The model requires a knowledge of the average bubble velocity relative to the fluid, U, a variable that is not available in most cases. This model only permits the calculation of the average rate per unit of area, and unless data are available from other sources on the total surface area available in the vessel, the model by itself does not permit the calculation of the overall absorption rate. 

Design of vessel and vent line pipe supports is very important because very large forces can be encountered as soon as venting begins. Figure 4 shows the equations and nomenclature to calculate forces on pipe bends. The authors have heard of situations where vent line bends have been straightened, lines broken off, or vent catch tanks knocked off their foundations by excessive forces. For bends, the transient effects of the initial shock wave, the transition from vapor flow to two-phase flow, and steady state conditions should be considered. Transient conditions, however, are likely to be so rapid as to not have enough dura-... 

---