Optimal Placement of Gas Detectors in Process Facilities Using Conditional-Value-At-Risk

Optimal Placement of Gas Detectors in Process Facilities Using Conditional-Value-at-Risk

Sean Legg, Alberto Benavides, Sam Mannan, Carl Laird

Gas detection systems are an integral part of modern process safety systems. These systems are reliant upon intelligent placement of the gas detectors to provide effective and timely response. A multi-scenario, mixed-integer programming (MILP) formulation for the optimal placement of gas detectors in petrochemical facilities is presented here. Early development of a basic MILP formulation for gas detector placement was presented by Legg et. al. (2012). The formulation was designed to minimize the expected detection time across the full set of scenarios. Additional constraints were added to enforce a minimum coverage area between sensors to improve solution resiliency in the face of unanticipated scenarios. In this work, we also discuss a modified formulation to improve tail-behavior in the distribution of detection times for the scenarios by considering Conditional-Value-at-Risk (CVaR). All data used in the problem scenarios were generated using the computational fluid dynamics software FLACS (GexCon 2011).

Here, three MILP formulations are presented: minimization of the expected detection time (SP), minimization of the expected detection time considering coverage (SPC), and minimization of the expected detection time considering CVaR (SP-CVaR). Results for each of these formulations are compared to a placement based solely on coverage (C). We include a comparison of all formulations on the entire scenario set and the results based on sampled subsets of the full scenario set. For the entire set, we show that each of the mixed-integer formulations greatly outperform the placement based solely on coverage. Additionally, results comparing the distribution of detection times from (SP-CVaR) and (SP) shows that the addition of a constraint on CVaR greatly improves the tail-behavior of the detection time distribution. By determining a placement with a subsample from the full scenario set, we can use the remaining scenarios to evaluate the resiliency of this solution to unanticipated scenarios. (SPC) shows significantly more resiliency to unknown scenarios than either (SP) or (C). Each of the results presented show that an optimization based approach to the placement of gas detectors shows significant promise in improving modern safety systems.

References:

GexCon. (2011). FLACS CFD Disperson Modeling and Explosion Software. http://gexcon.com/FLACSoverview.

Legg, S., Siirola, J., Watson, J.P., Davis, S., Bratteteig, A., Laird, C. (2012). A Stochastic Programming Approach for Gas Detector Placement in Process Facilities. Proceedings of the 2012 FOCAPO Conference, Savannah, January, 2012.