(700b) A Mixed-Integer Programming Framework for Combined Placement of Fire and Gas Detectors in Chemical Processing Facilities

In chemical processing plants, the placement of sensors to alert personnel of hazards is critical for public safety. However, given the large number and variety of chemical and physical sensors necessary to ensure process safety, this optimal placement problem becomes difficult to formulate and solve. A typical petrochemical plant includes many gas (e.g. ultrasonic, catalytic bead) and fire detectors (e.g. point infrared, open path infrared, optical). Gas detectors must be in contact with gas leaks to be effective, while fire detectors require a visual path to the fire, free of obstructions, for successful detection. Thus, it is important that both types of detectors be placed according to their respective characteristics for maximum effectiveness.

The optimal gas detector placement problem was formulated by [1] as a stochastic program based on the p-median facility location problem and relied on scenarios generated from CFD simulations within a petrochemical facility. Their results showed that coupling coverage with expected detection time using a scenario-based method outperformed the existing coverage-only approaches, and has inspired formulations based on Conditional-Value-at-Risk [2], minimization of false positives and false negative alarms with voting schemes [3], maximum risk reduction of scenarios [4], and MINLP approaches for non-uniform failure probabilities [5].

But while gas detectors must be placed in the path of gas leaks for effective detection, fire detectors must be placed within unobstructed visual distance of flames. The optimal placement of visual fire detectors in processing plants can be particularly difficult due to the large number of physical obstructions (e.g. piping, valves, tanks). Most relevantly, [6] has proposed a basic formulation for placing visual fire detectors on the walls of a room with cylindrical objects, weighted by pre-determined hazard levels.

This work focuses on a mixed-integer optimization formulation that integrates placement of both fire (visual) and gas (point) detectors. The scenario-based, p-median approach demonstrated by [1] for gas detectors is combined with a maximum coverage model for fire detectors in a 3D space within a multi-objective framework. We show that this approach allows for the simultaneous placement of both sensor types for a fixed sensor budget while under uncertainty. We demonstrate the effectiveness of this formulation with fire and gas leak simulations from a chemical facility. We further discuss how the framework is readily scalable for larger problem sizes and amenable to various objectives.

References:

[1] Legg, S. W., Benavides-Serrano, A. J., Siirola, J. D., Watson, J. P., Davis, S. G., Bratteteig, A., and Laird, C. D. (2012). A stochastic programming approach for gas detector placement using CFD-based dispersion simulations. Computers and Chemical Engineering, 47:194–201.

[2] Legg, S. W., Wang, C., Benavides-Serrano, A. J., and Laird, C. D. (2013). Optimal gas detector placement under uncertainty considering Conditional-Value-at-Risk. Journal of Loss Prevention in the Process Industries, 26(3):410–417.

[3] Benavides-Serrano, A. J., Legg, S. W., Vázquez-Román, R., Mannan, M. S., Laird, C. D., Vaquez-Roma, R., Mannan, M. S., Laird, C. D., and Kay, M. O. (2014). A stochastic programming approach for the optimal placement of gas detectors: Unavailability and voting strategies. Industrial and Engineering Chemistry Research, 53(13):5355–5365.

[4] Rad, A., Rashtchian, D., and Badri, N. (2017). A risk-based methodology for optimum placement of flammable gas detectors within open process plants. Process Safety and Environmental Protection, 105:175–183.

[5] Liu, J., and Laird, C.D., A Global Stochastic Programming Approach for the Optimal Placement of Gas Detectors with Nonuniform Unavailabilities, to appear in Journal of Loss Prevention in the Process Industries, 2017.

[6] Yang, T. P., Asirvadam, V. S., and Saad, N. B. (2012). Optimal placement of fire detector using dual-view. In 2012 4th International Conference on Intelligent and Advanced Systems (ICIAS2012), pages 599–603. IEEE.