متدولوژی برای تجزیه و تحلیل حساسیت جهانی از مدل های نتیجه

A methodology is presented for global sensitivity analysis of consequence models used in process safety applications. It involves running a consequence model around a hundred times and using the results to construct a statistical emulator, which is essentially a sophisticated curve fit to the data. The emulator is then used to undertake the sensitivity analysis and identify which input parameters (e.g. operating temperature and pressure, wind speed) have a significant effect on the chosen output (e.g. vapour cloud size). Performing the sensitivity analysis using the emulator rather than the consequence model itself leads to significant savings in computing time. To demonstrate the methodology, a global sensitivity analysis is performed on the Phast consequence model for discharge and dispersion. The scenarios studied consist of above-ground, horizontal, steady-state discharges of dense-phase carbon dioxide (CO2), with orifices ranging in diameter from ½ to 2 inch and the liquid CO2 stagnation conditions maintained at between 100 and 150 bar. These scenarios are relevant in scale to leaks from large diameter above-ground pipes or vessels. Seven model input parameters are varied: the vessel temperature and pressure, orifice size, wind speed, humidity, ground surface roughness and height of the release. The input parameters that have a dominant effect on the dispersion distance of the CO2 cloud are identified, both in terms of their direct effect on the dispersion distance and their indirect effect, through interactions with other varying input parameters. The analysis, including the Phast simulations, runs on a standard office laptop computer in less than 30 min. Tests are performed to confirm that a hundred Phast runs are sufficient to produce an emulator with an acceptable degree of accuracy. Increasing the number of Phast runs is shown to have no effect on the conclusions of the sensitivity analysis. The study demonstrates that Bayesian analysis of model sensitivity can be conducted rapidly and easily on consequence models such as Phast. There is the potential for this to become a routine part of consequence modelling.

Consequence modelling is used in the process industries for many purposes, from plant design to risk assessment and incident investigation. In many applications, the inputs to the consequence model (e.g. operating temperature and pressure, wind speed) are either poorly defined or they feature a large degree of variability. It is important in these cases to know the effect of the range in input conditions on the model predictions. The results may be quite insensitive to certain inputs, but for some inputs a small difference may produce a critical change in the study outcome. With experience, modellers can often develop an understanding of the important factors in a given situation, but in complex multi-phase reacting flows this may be challenging, and model behaviour can sometimes be counter-intuitive. The purpose of a sensitivity analysis is primarily to determine which input parameters have a significant effect on the model outputs. Knowing which factors are important can be useful in driving model refinement and in producing more reliable predictions. For example, in the analysis of dense gas dispersion in the Buncefield Incident, Gant and Atkinson (2011) initially found that the model predictions were sensitive to the slope of the ground and the presence of obstacles. As a consequence, to refine their model they used detailed topographical data from a site survey to construct the final Computational Fluid Dynamics (CFD) geometry. This type of uncertainty that can be reduced through improved knowledge of the system is known as epistemic uncertainty. Another type of uncertainty that cannot be reduced in this way, known as aleatoric uncertainty, arises from the inherent variability in the physical system or environment that is being modelled. For instance, in modelling atmospheric dispersion there is a natural uncertainty in the wind speed due to the random nature of atmospheric turbulence. To account for this, the wind speed may be expressed in terms of a probability distribution that represents the likelihood of the wind speed taking a particular value over time. In a risk assessment, where the objective is to determine the cumulative risk over a year, the results from multiple simulations for a range of wind speeds may be combined and weighted using this distribution to account for the range in likely values. In a sensitivity analysis, it is also beneficial to identify the inputs that have a negligible effect on the model output. This information can be used to limit the number of simulations required in a given study. For example, in a risk assessment involving a jet fire, if the ambient wind is demonstrated to have practically no effect on the thermal dose predictions, the risk assessment may not need to consider running multiple jet fire simulations for a range of different wind speeds, which may considerably reduce the total computing effort required. The issue of sensitivity and uncertainty in consequence modelling has long been appreciated, and a number of examples can be found in the literature (Carpentieri, Salizzoni, Robins, & Soulhac, 2012; Jahn, Rein, & Torero, 2008; Khoudja, 1988; Witlox, Stene, Harper, & Nilsen, 2011). Often the approach used in these studies to examine model sensitivity has consisted of selecting a baseline case and then varying one input parameter at a time, i.e. local sensitivity analysis. This choice has often been taken due to the limitations of computing time and the ease of interpreting the results. In recent years, a more rigorous approach to model sensitivity analysis has started to be applied to process safety applications, e.g. Brohus, Nielsen, Petersen, and Sommerlund-Larsen (2007) and Pandya, Gabas, and Marsden (2012). In the latter study, a global sensitivity analysis was performed on the consequence model Phast (DNV, 2012), where multiple input parameters were varied at the same time in order to understand the interactions between the different inputs. The calculations involved running Monte-Carlo experiments on Phast directly, with sample sizes of 20,000 simulations and computing times of around 24 h, using several computers in parallel. Despite these examples of global sensitivity analysis being applied to consequence models, such analyses have yet to become widely used by engineers in the chemical process safety industry. This has perhaps been due to the perception that such exercises are time-consuming and costly, and the fact that much of the literature describing sensitivity analysis is aimed at mathematicians rather than practising engineers. The aim of the present work is to demonstrate an approach to global sensitivity analysis that is easy to use and can be applied routinely to consequence modelling for process safety applications. The approach involves running a consequence model around a hundred times and then using the results to construct a statistical model (essentially a curve fit, or response surface). This statistical model is then used to undertake the sensitivity analysis and identify important input parameters. The statistical analysis is undertaken here using the Gaussian Emulation Machine (GEM) software produced by Marc Kennedy and colleagues at Sheffield University (Kennedy, 2005). This software is freely-available for non-commercial use, and features an easy-to-use Graphical User Interface (GUI) and good documentation. The process safety scenarios examined consist of horizontal, above-ground, steady-state discharges of high-pressure carbon dioxide (CO2). Consequence model predictions have been obtained using the discharge and dispersion models contained in the hazard assessment software package Phast (DNV, 2012). Seven key Phast model input parameters have been varied and the results analysed for main effects and interactions.

A global sensitivity analysis has been performed on Phast using an emulator to identify the important factors affecting the dispersion distance in steady-state horizontal releases of CO2 over flat terrain. The parameters varied include the CO2 vessel temperature and pressure, orifice size, wind speed, humidity, surface roughness and height of the release. The output parameter of interest has initially been taken as the distance from the release point to a CO2 concentration of 6.9% v/v. The results have shown that for the range of conditions tested, the orifice diameter has a far greater impact than any of the other parameters varied. The second-largest effect was from the release height, with a lower release height producing a plume that extends further, due to the reduction in air entrainment. When the dispersion distance output was defined differently, using a lower limiting value of the CO2 concentration, the results showed that the dominant input parameters change and the effect of the ambient wind speed becomes more important. Tests on the sample size used to construct the emulator indicated that a hundred Phast runs were sufficient to provide an acceptable degree of accuracy. The global sensitivity analysis of Phast typically required less than 30 min of computing time on a standard office laptop computer. This includes the time necessary for the hundred Phast runs and the statistical analysis. Due to the speed and ease of implementation, similar analyses could readily be incorporated into industrial design studies, risk assessments and incident investigations at little extra cost. There are significant benefits to be gained from such analyses in terms of identifying the important physical processes in complex flows, and in narrowing the scope of further simulations or experimental measurements. These methods are therefore likely to become widely used in the process industry in the coming years. In the present work, uniform probability distributions were applied for each of the input variables. For example, any wind speed was considered equally likely, within the range of conditions modelled. In future work, techniques for uncertainty analysis will be tested which apply realistic probabilities for wind speed, atmospheric stability etc. based on meteorological data. Further extensions to this work may also consider model calibration, using experimental datasets.