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GCPS 2013 __________________________________________________________________________ Using Explicit Finite Element Analysis to Simulate the Effects of External Chemical Explosions on Single and Double-Walled Storage Tanks Phillip E. Prueter The Equity Engineering Group Inc., Shaker Heights, Ohio peprueter@equityeng.com David J. Dewees, P.E. The Equity Engineering Group Inc., Shaker Heights, Ohio djdewees@equityeng.com Prepared for Presentation at American In
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  GCPS 2013 __________________________________________________________________________    Using Explicit Finite Element Analysis to Simulate the Effects of External Chemical Explosions on Single and Double-Walled Storage Tanks Phillip E. Prueter The Equity Engineering Group Inc., Shaker Heights, Ohio peprueter@equityeng.com David J. Dewees, P.E. The Equity Engineering Group Inc., Shaker Heights, Ohio djdewees@equityeng.com  Prepared for Presentation at American Institute of Chemical Engineers 2013 Spring Meeting 9th Global Congress on Process Safety San Antonio, Texas April 28 – May 1, 2013 UNPUBLISHED AIChE shall not be responsible for statements or opinions contained in papers or printed in its publications  GCPS 2013 __________________________________________________________________________    Using Explicit Finite Element Analysis to Simulate the Effects of External Chemical Explosions on Single and Double-Walled Storage Tanks Phillip E. Prueter David J. Dewees, P.E. The Equity Engineering Group Inc., Shaker Heights, Ohio peprueter@equityeng.com Keywords: Explicit Finite Element Analysis, Blast Loading, CONWEP, Accidental Explosions, Storage Tanks Abstract Accurately simulating the overpressure or shock wave associated with a given far-field chemical explosion is extremely valuable in assessing the structural response and possible failure modes of critical process equipment such as storage tanks, piping, or pressure vessels. Furthermore, assessing the potential damage from an overpressure wave can provide valuable information about protecting structures from external explosions and improving designs that advocate blast damage mitigation. Such analyses become all the more important should the contents of the tank or vessel exposed to such a potentially catastrophic event pose a risk to humans or the surrounding environment. This paper discusses the underlying theory and examines the practical application of multiple finite element based explicit computational techniques for simulating the load acting on a structure due to an external blast. Explicit three-dimensional blast analysis of single and double-walled storage tanks that carry an extremely high consequence of failure is  performed. The structural response of the tanks due to postulated accidental explosions is investigated and likely failure modes are discussed. The two explicit computational blast loading methods discussed in this paper are the incident wave loading model and the Conventional Weapons Effects Blast Loading Model or CONWEP. The CONWEP model is appropriate for detonations of conventional explosions, and in this case automates many crucial features of analysis, such as developing the overpressure time history (positive and negative phases), defining overpressure spatial decay, and accounting for spatially varying reflection effects. Large vapor cloud explosions are known to behave very differently from conventional explosives, and for these cases, the more manual, but also general, incident wave loading approach permits the user to define their own time-varying overpressure amplitude. Additionally, this method also allows for coupled structural-acoustic analysis (should reflection effects need to be considered in detail). While it is not necessary to model the fluid medium using acoustic elements when using the incident wave loading model, it does become essential if reflection effects dominate the response of the given problem. If the fluid medium is modeled (air in this case), the acoustic elements can be coupled to the structural elements and the loading surface becomes the boundary of the acoustic mesh closest to the blast source. While  GCPS 2013 __________________________________________________________________________ this approach can be accomplished, it is extremely resource and time intensive, and is generally not necessary (which will be discussed later in this paper). Three-dimensional examples of the above blast loading approaches are presented in this paper; incident wave, and CONWEP. Comparisons are made between these methods and the corresponding computational results. Furthermore, commentary on the structural response and likely failure modes of the storage tanks is provided and a discussion regarding design features that supplement blast damage mitigation and process safety is rendered. The advanced computational methods discussed herein permit realistic evaluation of complex, three-dimensional process equipment subjected to accidental explosions. Simulating and understanding the possible failure modes due to blast loading of critical process equipment in the petrochemical and related industries is very beneficial in not only improving process safety, but also providing plant operators and safety personnel with crucial information regarding the possibility of equipment failure should a catastrophic explosion occur. 1.   Introduction   An explosion in air creates a blast wave as a result of the atmosphere surrounding the explosion  being pushed back. In general, the pressure of the compressed air at the blast wavefront decays as it moves away from the blast source. As discussed in references [1-6], a typical blast wave, as observed at a location removed from the center of a chemical explosion, reaches a peak value of overpressure and begins to decay exponentially (as shown in Figure 1), eventually decreasing  below atmospheric pressure. This peak overpressure decreases as the distance from the explosion source increases. The amount of time it takes the wavefront to reach a given point is known as the arrival time. The overpressure profile can be divided into the positive pressure  portion (positive phase) and negative pressure portion (negative phase). Furthermore, the amount of time it takes the peak overpressure to decay below atmospheric pressure is known as the positive phase duration and is closely related to the damage capabilities of a given blast wave. Similarly, the amount of time it takes for the negative pressure to return to atmospheric  pressure is the negative phase duration [1]. The area under the curve during the positive phase duration is the positive blast wave impulse. Figure 1: Typical pressure-time amplitude for a chemical explosion [7].  GCPS 2013 __________________________________________________________________________ In some cases, the positive phase impulse is calculated and an equivalent triangular impulse with the same peak overpressure is used to approximate the realistic overpressure amplitude shown in Figure 1. In many cases, this approximation is appropriate because the positive phase portion of the incident pressure wave is typically the most damaging. Generally, structural response is more sensitive to capturing the correct incident wave reflection. Accurately simulating a realistic  blast wavefront on a structure for a given explosive scenario is challenging because the peak overpressure, positive phase duration, amount of explosives, and distance from the explosion source all affect the overpressure amplitude. Furthermore, accounting for reflection effects on a loading surface adds further complication to the blast loading model. Two different explicit finite element techniques used to simulate blast loading due to external chemical explosions in air will be discussed herein; incident wave loading and the Conventional Weapons loading model (CONWEP) [8]. CONWEP is well suited for simulating the overpressure wave associated with the detonation of conventional explosives while incident wave loading permits reasonable analysis of vapor cloud explosions. The underlying methodology of each approach will be discussed as well as the advantages and applications of each. Furthermore, both computational methods will be compared for the explicit dynamic simulations of realistic explosive overpressure waves (from a postulated concentrated explosion source and a vapor cloud) impacting single and double-walled storage tanks that carry an extremely high consequence of failure. 2.   Blast Curve Generation In order to develop the blast parameters required to generate realistic overpressure curves for conventional explosives, the equivalent TNT method is most commonly used. TNT equivalency of an explosive is simply the ratio of the mass of TNT to the mass of explosive such that both yield equal pressure and impulse [9]. In order to compare shock wave parameters to available  published data, a scaled distance from an explosion source to the loaded structure may be used. As discussed in [10], the most common form of blast scaling is the Hopkinson-Cranz or cube-root scaling method following where  Z   is the scaled distance,  R  is distance from the explosion source to the loading point, and W   is the weight of TNT. This formulation implies that self-similar blast waves are produced at identical scaled distances when two different sized explosive charges (of similar geometry and chemical composition) are detonated in the same atmosphere. Using published empirical data, this scaled distance from the explosion source to a loading surface can be used to determine specific blast parameters. The CONWEP blast loading model discussed herein is based on a TNT explosion (assumed surface blast). Thus, when using CONWEP, it is necessary to convert the mass of explosives in question to an equivalent amount of TNT. As outlined in [11], a major limitation associated with the equivalent TNT method is that the  blast yield is a function of the amount of explosives and not the combustion mode; making this method not preferred when analyzing vapor cloud explosions. As discussed in References [12-
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