A Reliability-P-Median Formulation for Optimization of Gas Detector Layout in Process Facilities

A Reliability-P-Median formulation for optimization of gas detector layout in process facilities

Alberto Benavides-Serrano, Sean Legg, Sam Mannan, Carl Laird

A large number of variables influence the risk associated with gas leaks in process facilities. These variables include leak conditions, fluid properties and dispersion characteristics, process equipment geometry, detection equipment, environmental factors, and safety considerations. Given this large number of variables, the task of gas detector layout in the process industries is challenging. Mixed-integer linear programming (MILP) has been proposed as a quantitative approach for numerical optimization of gas detector layout. Legg et al (2012c) proposed a stochastic programming formulation that seeks a sensor placement that minimizes the expected time to detection across any number of leak scenarios. Extensions to this MILP formulation were proposed to improve the resilience of the solution placement to unforeseen scenarios (Legg et al, 2012a) and the tail-behavior of the distributions of detection times (Legg et al 2012b).

However, this previous work assumed the use of perfect gas sensors; in reality gas sensors are prone to false-positives and false-negatives.  In the process industries, two solutions are usually implemented. First, additional confirmation from other detectors may be required before emergency actions are triggered, and several voting logic schemes are used. Second, the Probability of Failure on Demand (PFD) of the detectors should be considered in the placement strategy. In this work, we present an MILP that performs optimal gas detector placement while considering sensor failure and voting. This problem formulation is closely related to the Reliability-P-Median Problem (RPMP) proposed by Snyder and Daskin (2005) for the facility location problem.

Here, we show the relationship of our stochastic programming formulation to the RPMP formulation. Scenario data for this problem is generated with rigorous CFD simulations of a real process geometry using FLACS with different leak locations and conditions (provided by GexCon). The effectiveness of placement results are analyzed and compared with the previous formulation that ignores sensor reliability and voting.

References

Legg, S., Wang, C., Benavides-Serrano, A.J., Laird, C. (2012a). Optimal Gas Detector Placement Under Uncertainty Considering Conditional-Value-At-Risk. Submitted to the Journal of Loss Prevention in the Process Industries, 2012.

Legg, S., Benavides-Serrano, A.J., Siirola, J., Watson, J.P., Davis, S., Bratteteig, A., Laird, C. (2012b). A Stochastic Programming Approach for Gas Detector Placement Using CFD-Based Dispersion Simulations. Submitted to Computers & Chemical Engineering, 2012.

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

L. Snyder and M. Daskin. Reliability models for facility location: The expected failure cost case. Transportation Science, 39(3):400–416, August, 2005.