Chapter 9
Dynamic Consequence Analysis through Computational Fluid Dynamics Modeling
G. Landucci1, M. Pontiggia2, N. Paltrinieri3,4, and V. Cozzani5 1University of Pisa, Pisa, Italy 2D'Appolonia S.p.A., San Donato Milanese (MI), Italy 3Norwegian University of Science and Technology (NTNU), Trondheim, Norway 4SINTEF Technology and Society, Trondheim, Norway 5University of Bologna, Bologna, Italy
Abstract
Consequence assessment in conventional quantitative risk assessment studies is carried out with simplified tools and conservative assumptions, leading to static worst-case representation of the magnitude associated with accidents. Computational fluid dynamic (CFD) models may constitute an advanced tool to analyze dynamic scenarios. CFD models may capture the interaction among the released hazardous substances and the geometry of the surrounding environment, thus allowing for detailed three-dimensional analysis in the presence of obstacles, bunds, and congested industrial layouts. In this chapter, relevant CFD consequence assessment studies are collected and discussed, highlighting the key features and advantages with respect to conventional model application. At the same time, possible limitations of CFD models are addressed, providing information for selection between integral models and CFD.
Keywords
Computational fluid dynamics; Consequence assessment; Dispersion; Explosion; Fire; Source terms models
1. Introduction
Risk analysis involves the estimation of accident consequences using engineering and mathematical techniques [1]. Consequences are aimed at determining the contribution of magnitude to the risk, representing the impact of the expected accidents. Magnitude is related to both vulnerability of territory and severity of scenarios; hence it is often considered a static term associated with the potential hazard in conventional quantitative risk assessment (QRA) frameworks.
Moreover, in dynamic risk assessment (DRA), the magnitude of accidents is not usually involved in the update process, because DRA studies are meant to reassess risk in terms of updating initial failure probabilities of events (causes) and safety barriers as new information is made available during a specific operation [2]. Bayesian [3] and non-Bayesian approaches [4] are thus focused on the dynamic improvement in likelihood of accidents (ie, frequency) rather than focusing on the dynamic variation in accident effects, also accounting for possible mitigation action of safety barriers.
The transient evolution of an accident plays an important role in the estimation of the magnitude, because obstacles, change in meteorological conditions, and site-specific factors connected to the layout of equipment may alter the nature of the impact associated with an accident. Moreover, the intervention of multiple safety layers or barriers may reduce the physical effects associated with accident scenarios.
Computational fluid dynamics (CFD) modeling is a consolidated tool to support industrial project development and was recently adopted in the framework of consequence assessment and safety studies [5]. The advanced features of CFD models, such as handling complex three-dimensional geometries and environments and analyzing reactive or nonreactive flow of compressible or noncompressible fluids, make them a promising tool to support dynamic consequence assessment in the perspective of implementation in DRA studies.
2. Implementation of Computational Fluid Dynamics Modeling into Dynamic Risk Assessment
CFD models solve Navier–Stokes equations of fluid flow (conservation of mass, momentum, and scalar quantities) in a three-dimensional space [6]. The problem is reduced to the solution of a system of partial-differential (or integral-differential) equations that need to specify appropriate boundary conditions and discretization methods for their numerical solution. Boundary conditions allow determination of the possible energy and/or mass inlet/outlet and relevant features of the system under analysis (ie, obstacles or other walls that alter the nature of the flow). The discretization method approximates the differential equations in a system of algebraic equations, which can be solved on high-performance computers. In typical commercial codes, the finite volumes approach is adopted. In this approach, the geometrical domain under analysis is first subdivided into a computational grid (ie, the mesh), which allows determining control volumes when the governing equations (ie, conservation of mass, energy, and momentum and the radiative heat transfer equation) are solved.
Therefore, CFD models may capture the interaction among the released hazardous substances and the geometry of the equipment, pipes, and structures, as well as topography and vegetation surrounding an industrial site where risk assessment is carried out. The advantage of CFD is also related to the dynamic nature of the results, which can be used to trace the transient evolution of the physical effects associated with the accident scenario.
Although consequence assessment may provide detailed and dynamic results through CFD, the evaluation of accident scenarios in typical QRA is based on conservative simplifications and a rather static approach [7]. This is due to the large number of scenarios considered. Disregarding the dynamic nature of the accidental release may potentially lead to overestimation of the release severity. Fig. 9.1 illustrates a scheme in which the application of CFD models is associated with each relevant scenario, also highlighting the limitations of conventional static approaches.
Finally, it is worth noting the possible limitations of CFD codes. Models need to be specifically tuned for the case under analysis, and the related calculations may need high-computational resources. Specific validation against experimental data should be carried out for reliability and accuracy. However, experimental studies are few and require relevant economic resources. The general application process is time consuming and requires skilled users. Owing to these limitations, CFD application in conventional QRA studies is not yet consolidated [8], but the advanced features of the results make CFD an attractive tool for supporting DRA studies.
3. Computational Fluid Dynamic Models for Specific Accidental Scenarios
3.1. Advanced Source Terms and Outflow Models
Release source terms are used to quantify the flow rate at which accidental releases of dangerous substances may occur and/or to estimate release quantity and duration. In typical QRA studies, source terms and outflow models are simplified expressions, often providing rough and static worst-case estimations. Advanced CFD tools may predict the dynamic development of the release and complicating phenomena resulting from obstacles or change in wind conditions, thus supporting dynamic consequence assessment.
3.1.1. Computational Fluid Dynamic Modeling of Jet Releases
The assessment of jet releases is a challenging task because of the likelihood of high turbulence and complex premixing phenomena. Moreover, jet releases contacting the ground and obstacles may be altered in structure and effects. CFD studies may achieve detailed prediction of jet structure in terms of pressure, temperature, and composition profiles able to support advanced dispersion studies in the presence of obstacles or wall barriers. In the past decade, safety studies in the literature have focused on high-momentum jet releases of mainly methane and hydrogen [9]. More recently, in the perspective of the development of carbon capture and sequestration technologies, CFD models were adopted to predict the complex phenomena associated with accidental carbon dioxide release from pipelines or transport tankers. Gant et al. [10] investigated the formation of a carbon dioxide jet from a pressurized vessel, accounting for the formation of sublimating particles as well as for the contribution of moisture in the entrainment of water droplets in the jet. The sound modeling of carbon dioxide jet behavior is crucial for supporting (1) the tracing of the three-phase flow and (2) the following toxic dispersion studies (such as the ones discussed in Section 3.2).
3.1.2. Computational Fluid Dynamic Modeling of Pool Spreading and Evaporation
Liquid spillage due to failure of equipment and pipelines may lead to the spreading of a pool and its vaporization. This stage of an accident scenario provides important information for the subsequent analysis of atmospheric dispersion. Additional criticality is associated with pool spreading, especially for cryogenic liquids. In fact, the effects of terrain, release characteristics, and obstacles are critical in the modification of heat and material balance.
Relevant studies concerning the application of CFD models to cryogenic pool spreading and evaporation were concentrated on liquefied natural gas (LNG) and liquefied hydrogen (LH2). Gavelli et al. [11] addressed the prediction of LNG behavior in an impoundment through CFD modeling implemented on ANSYS Fluent software. A critical issue in the modeling was the characterization of the LNG spill, because the evaluation of spill velocity is crucial for the determination of turbulent kinetic energy associated with the pool spread and its propensity to entrain air. GexCon As (Bergen, Norway) showed the capabilities of the flame acceleration simulator CFD code in predicting LH2 release evolution to support dispersion and explosion studies through the introduction of dedicated submodels for determining thermal and kinematic equilibrium among liquid and vapor phases [12].
3.2. Dispersion Studies
Risk assessment of accidental releases of hazardous gases, both flammable and toxic, is largely performed using integral dispersion models, the most widely used being DEGADIS, SLAB, ALOHA, and Unified Dispersion Model (UDM) [8]. Integral models are lumped-parameter models that provide reliable results only in open field conditions, that is, when almost no obstacles are present in the cloud region. Moreover, the source term providing the dispersed flow rate is usually assumed to be constant [1,7]. When complex situations are analyzed, the adoption of CFD is needed to perform a dynamic three-dimensional simulation of the involved geometry. Typical examples are the analysis of congested industrial layouts with neighboring equipment, pipes, or obstacles [13–15] or an urban environment (buildings and street canyons) [16–19]. The following sections address representative studies of complex environment CFD dispersion, considering both flammable and toxic gases. Moreover, an approach for the selection of suitable modeling strategies is discussed.
3.2.1. Computational Fluid Dynamic Modeling of Flammable Gas Dispersion
The aim of dispersion studies of flammable materials is the evaluation of the potential flammable cloud extension and features, that is, the zone in which the concentration of the released gas is within the flammable limits [7]. As mentioned in Section 2, this is crucial for the assessment of flash fire and vapor cloud explosion scenarios.
Several examples are available in the literature, mainly focusing on natural gas dispersion following accidental LNG spills [14,15]. This is a complex phenomenon requiring a dedicated preliminary assessment because it involves the formation of a liquid pool that spreads and evaporates. The natural gas evaporated from the pool is at extremely low temperatures (about 112–115 K), implying a density higher than the air density (heavy gas dispersion). The gas is stratified on the ground and influenced by obstacles close to the release point.
The presence of obstacles may lead to scenario mitigation because of the turbulence increment in the gas cloud, which increases its dilution with air, and the warming due to the heat exchange with the atmosphere. This is considered a key strategy for reducing the hazards associated with heavy gas dispersion, as pointed out by Busini and Rota [20]. Relevant CFD studies of heavy gas dispersion were also undertaken for the consequence assessment of the LPG flash fire that occurred in Viareggio, Italy, in 2009 [18,19]. More details on this issue are extensively covered in Chapter 10.
The release of light buoyant gas in the presence of high-momentum jet releases was undertaken in similar studies carried out by Wilkening and Baraldi [9], which simulated the dispersion of gaseous H2 and CH4 from the pipe rupture in a refueling station located in a residential area.
3.2.2. Computational Fluid Dynamic Modeling of Toxic Gas Dispersion
Several CFD dispersion studies were carried out to capture the effect of toxic substances dispersed over congested and complex areas, especially in the framework of transportation risk assessment studies. In this case, toxic concentrations such as emergency response planning guidelines, immediately dangerous to life and health concentration, and lethal concentration, 50% (see Ref. [7] for more details) and/or toxic doses are traced to assess the potential damages associated to toxic cloud dispersions. Table 9.1 summarizes relevant examples carried out with different substances and in different types of zones (ie, industrial and urban).
Table 9.1
Summary of Relevant Computational Fluid Dynamics Dispersion Studies Carried Out for the Assessment of Toxic Effects
| ID | References | Substance | Release Source | Type of Environment |
| A | [13] | Hydrogen chloride | Accidental leak from process pipe | Industrial area (chemical plant close to a nuclear plant) |
| B | [16] | Ammonia-water solution (10%, w/w) | Catastrophic rupture of road tanker | Urban area (Lecco, Italy) |
| C | [17] | Chlorine | Punctured railroad car | Industrial park (Festus, US); urban area (Chicago, US) |
Figure 9.2 Methodology for the selection of the more effective modeling strategy for dispersion studies in the presence of obstacles. Adapted from Derudi M, Bovolenta D, Busini V, Rota R. Heavy gas dispersion in presence of large obstacles: selection of modeling tools. Industrial & Engineering Chemistry Research 2014;53:9303–10.
3.2.3. Guidelines for the Selection of the Most Suitable Modeling Strategy
The collected CFD studies are relevant examples demonstrating the potential of CFD models in assessing complex dispersion scenarios. Nevertheless, the usage of a CFD tool must be restricted to cases significantly influenced by geometry, because it could lead to a waste of computational resources in the case of relatively simple geometries. For this reason, a methodology based on the comparison among CFD and integral model simulations was established to drive the selection of the proper modeling strategy. More details are reported by Derudi et al. [21]. The methodology, which is based on the preliminary simulation though integral models and on the characterization of defects in the area of interest, is summarized in Fig. 9.2.
3.3. Fire Studies
Fire dynamic simulation is of utmost importance for assessing the severity of fire events following the accidental ignition of flammable substances. CFD models may significantly contribute to the assessment of heat radiation effects as well as to the analysis of fire-driven fluid flow. Moreover, convective effects associated with direct flame engulfment and development of smoke and toxic gases may be traced.
3.3.1. Computations Fluid Dynamic Modeling of Dynamic Fire Scenarios
Conventional QRA studies are carried out assuming a static geometry of the flame and, consequently, steady state effects. In fact, pool fires and jet fires are simulated without accounting for complicating phenomena, which may alter the shape of the flame and the heat radiation effects on potential targets.
Pool fire modeling through CFD has been extensively carried out since the 1990s, determining the potentialities of distributed parameter codes in capturing the effects of bunds, wind profiles, and confinement in the determination of flame structure and associated effects [22]. More recently, Sun and Guo [23] provided a dynamic LNG pool fire simulation comparing the effect with and without mitigation through high-expansion foam at different burning times. CFD studies were adopted to predict the effectiveness of the foam and to provide indication of optimal foam-delivering conditions.
As a result of higher turbulence, jet fire modeling is a more crucial task and was improved in recent years. Wang et al. [24] adopted FireFOAM to study the radiation characteristics of hydrogen and hydrogen/methane jet fires, capturing the fluctuations in flame length and radiant fraction.
Jang et al. [25] simulated a hydrogen jet fire from an accidental leak, determining the dynamic evolution of the flame temperature and shape into a complex three-dimensional layout. A real-scale pipe rack was reproduced, determining the flame impact zone as well as the heat radiation profiles.
3.3.2. Assessment of Domino Effect Triggered by Fire
Fires may affect process and storage equipment, causing severe damage and potential accident escalation owing to the domino effect [26].
CFD models may be set up to simulate pressurized vessels exposed to accidental fires, determining the transient behavior of the stored fluid during heat-up. CFD allows for the prediction of velocity and temperature profiles, obtaining the pressurization rate in the vessel and providing key indications for the evaluation of the vessel resistance as well as for the design of heat-resistant coating for fireproofing. The results can then be implemented in finite elements modeling for the assessment of the mechanical response of the structure/equipment affected by the fire, thus determining the time to failure (TTF). TTF is a crucial element for the analysis of domino effect scenarios and for emergency management. Fig. 9.3 summarizes the modeling strategy adopted by Landucci et al. for the integrated assessment of the thermal [27] and mechanical [28] response of pressurized vessels exposed to fires to estimate TTF and to support the advanced assessment of the domino effect triggered by fires.
3.4. Explosion Studies
In recent years, CFD codes became a routine tool for the simulation of the consequences of vapor cloud explosions or partially confined explosions, as in the case of vented equipment or offshore rigs, characterized by a high level of confinement and congestion [29]. Several engineering analyses of large-scale industrial explosions were carried out through the Reynolds-averaged Navier–Stokes (RANS) approach. However, the RANS for the reproduction of large-scale, compressible, reactive systems is questionable, and very large uncertainties are intrinsically produced as the result of several conservative assumptions about the complex combustion phenomena involved in explosions. Recently, the use of large eddy simulation has been proposed. This technique is still under development and is limited by the available computational power [30].
With respect to conventional lumped parameter models adopted for the analysis of explosions, CFD may provide the dynamic development of the pressure wave and of the flame zone, capturing complex phenomena such as the deflagration to detonation transition, which is critical in extremely congested environments [31].
The same type of approach shown in Section 3.3.2 for the domino effect triggered by fires may be extended to the analysis of equipment and pipes affected by a shock wave. In this case, CFD simulation is preliminarily carried out for the assessment of the blast load on the equipment or asset under analysis. More details on the combined CFD–finite element method analysis of explosion effects are reported elsewhere [32].
4. Conclusions
This chapter presented the application of CFD models for the evaluation of the impact of transient accidental scenarios, in particular considering dispersion, fires, and explosions. Relevant studies and examples highlighted the potentialities in the implementation of DRA studies, because CFD models can capture the presence of obstacles and barriers and reduce the impact of accidents, as well as considering the modification in weather conditions (ie, wind speed and direction, humidity, etc.).
Nevertheless, the complexity of input information and data together with computer time and man-hours required to build the numerical domain pose important limitations for extensive CFD application, which should be limited to more critical cases. Hence, examples driving the choice between lumped models and advanced CFD simulations were provided.
To provide more details on the implementation of CFD models in a dynamic consequence assessment framework, Chapter 10 outlines a tutorial in which a dynamic dispersion study is carried out through the use of a CFD model.
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