(46c) Path-Sampling and Dynamic Risk Assessment for Rare Abnormal Events – Part II – Alarm Rationalization Strategies

Chemical manufacturing processes can pose serious hazards. Thus, safety considerations play an important role in their design. Indeed, to minimize the risk of catastrophic accidents, which can result in loss of human life or major environmental impacts, extensive instrumentation such as control systems, alarms, and automated Safety Instrumented Systems (SIS), are routinely employed in chemical processes. While such efforts are successful in mitigating the most likely postulated abnormal events, it is challenging to anticipate and mitigate the effects of infrequent, un-postulated, abnormal events in real-time. Importantly, such rare safety events, which have not been considered in plant design, can lead to the most severe consequences.

In this research, novel, multivariable alarms and safety systems are introduced using process modelling and path-sampling for un-postulated abnormal events resulting from perturbations in one or more process variables. Forward-flux sampling (FFS), developed to discover rare molecular dynamics pathways, is applied (Allen et al., 2009). For a proportional-only controlled exothermic CSTR approximate process model with perturbed feed concentration, the FFS algorithm is applied to identify rare trajectories between high- and low-conversion steady states, with key process variables saved at various ‘crossing points’ (Sudarshan et al., 2021). Then, committor probabilities, p_B, are computed at each crossing point (Borrero and Escobedo, 2007), yielding a mathematical model that expresses p_B as a function of the key process variables; i.e., the reactor temperature, cooling-water flow-rate, and cooling-water temperature (Sudarshan et al., 2022). Alarm thresholds, i.e., L-low, LL-low-low and ESD (emergency shutdown), and their corresponding safety actions, are suggested by computing the critical ranges of the process variables, given the p_B ranges for every alarm threshold.

Next, as described herein, using alarm rationalization strategies, the acceptability of every alarm threshold is evaluated, with the alarm thresholds and/or safety actions modified accordingly, based on key statistical metrics — this ensures that every alarm is a quality alarm, and its safety action is justified appropriately. Lastly, their real-time performance is evaluated using dynamic risk assessment, in which, the risk associated with the alarms and safety systems is analyzed by estimating the failure probabilities of the safety systems. These failure probabilities are estimated based on multiple dynamic simulations for the process, inclusive of control, alarms and safety systems, and the low-variance probability distribution constructed using these estimated failure probabilities is referred to as the informed prior distribution. Given the unavailability of safety system failure data, the likelihood distribution is constructed using assumed data, following which, the posterior distribution is constructed using Bayes’ Rule. Expectedly, the posterior distribution constructed using the informed prior has a much lower variance compared to one constructed using a flat prior — the latter depends entirely on the likelihood distribution having a larger variance, and hence, is unreliable.

Keywords: Un-postulated Abnormal Events, Forward-flux Sampling, Committor Probabilities, Alarm Rationalization, Dynamic Risk Assessment

References:

Allen, R.J., Valeriani, C., Rein Ten Wolde, P., 2009. Forward flux sampling for rare event simulations. Journal of Physics Condensed Matter 21.

Borrero, E.E., Escobedo, F.A., 2007. Reaction coordinates and transition pathways of rare events via forward flux sampling. Journal of Chemical Physics 127.

Sudarshan, V., Seider, W.D., Patel, A.J., Arbogast, J.E., 2021. Understanding rare safety and reliability events using forward-flux sampling. Computers and Chemical Engineering 153.

Sudarshan, V., Seider, W.D., Patel, A.J., Oktem, U.G., Arbogast, J.E., 2022. Path Sampling and Dynamic Risk Analysis for Rare Abnormal Events – Part I – Design of Multivariable Alarms and Safety Systems for an Exothermic CSTR – in preparation.