Optimizing Gas Detector Layouts By Considering False Positive and False Negatives Through Unavailability and Voting Considerations

Gas detectors are an important component of an effective safety system in the process industries. The task of optimally placing gas detectors within a facility is especially difficult due to the large number of uncertainties related to gas leaks and quantitative determination of the associated risk. Current industry practice is to place detectors using rules of thumb and/or semi-quantitative approaches that typically do not consider real dispersion behavior and consequences of the gas leaks. Furthermore, when dispersion and consequence modeling simulations are available, they are used only as broad guidelines in order to complement the previously mentioned approaches. Methodologies like these are encouraged in the standards and regulations, however, they do not take advantage of the full extent of the information that consequence modeling can provide. As a result, current gas detector placement schemes can lead to results that are far from the optimum in terms of cost and risk reduction. It is not surprising that the Health and Safety Executive (HSE) reported both in 1997 (HSE, 1997) and 2003 (HSE, 2003) that less than 50% of the known releases in offshore facilities are detected by the facility’s gas detection system. If we also consider the unknown releases, this figure is even lower, making it essential to develop an improved approach for detector placement based on a formal quantitative basis.

Given the improvement of dispersion and consequence modeling tools in the last decade, mathematical programming was assessed as an effective quantitative approach for optimal gas detector placement, providing a formal mechanism to make use of the quantitative information these simulations can provide. Legg et al (2012a-c) proposed the use of a stochastic mixed-integer linear programming (MILP) formulation to approach this problem. This formulation minimizes the expected value of the damage over a large set of gas leak scenarios while assuming perfect detectors.

In reality gas sensors are prone to false positives and false negatives. Two solutions are usually implemented in the process industries. First, additional confirmation from several detectors is required before emergency actions are triggered in order to avoid false positives. This additional confirmation requirement is known as voting. Several voting logic schemes are used to make the system more robust against false alarms. On the other hand, and in order to avoid false negatives, the unavailability of the detectors should be considered in the placement strategy. Unavailability corresponds to the probability that the detector will not be able to perform it’s intended function when required, i.e., the probability of a false negative. Unavailability not only includes situations like random failure, but also considers aspects like the detector being offline due to preventive maintenance and testing, or the absence of the detector due to repairs or replacement.

In this work, we developed two problem formulations to address the issues of false positives and false negatives (Benavides-Serrano et al, 2013): minimization of expected time to detection considering unavailability (SP-R) and minimization of expected time to detection considering unavailability and voting (SP-RV). Both were formulated in Pyomo and the MILP problems were solved using CPLEX 12.2. Detector placement results are presented for a case study based on an actual process geometry while considering uncertainty in the leak locations, process conditions, and weather conditions. The data set, generated by GexCon using FLACS CFD explosion and dispersion modeling software, is composed of 270 release scenarios and 994 potential point detector locations. Simulations were performed on a real, medium-scale (50 m by 70 m in area and 20 m in height), proprietary facility geometry capturing the full process features (e.g., equipment, piping, support structures). Optimal detector placements are compared with those previously obtained when assuming perfect detectors. Consideration of unavailability and voting effects in the formulation alters the final detector placement. Furthermore, our results demonstrate that the quantitative risk can be significantly higher if we neglect these issues when solving for the optimal placement.


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A.J. Benavides-Serrano, S.W. Legg, R. Vázquez-Román, M.S. Mannan, C.D. Laird (2013). A Stochastic Programming Approach for the Optimal Placement of Gas Detectors: Unavailability and Voting Effects, submitted to Industrial & Engineering Chemistry Research.


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