A Stochastic Programming Approach for the Optimal Placement of Gas Detectors: Unavailability and Voting Strategies

The task of detector placement is especially difficult due to the large number of variables that influence the risk associated with gas leaks; these include leak conditions, fluid properties, dispersion characteristics, process equipment geometry, and detection equipment. Existing work on optimal gas detector placement does not take into account two key considerations associated with gas detector equipment and policies: the possibility that the detector is not able to perform its intended function and the requirement for a voting logic. Two stochastic Mixed-Integer Linear Programming (MILP) formulations, SP-U and SP-UV, are proposed to address this issue. Formulation results are presented and compared with optimal placement results from a formulation that ignores these two considerations. Unavailability and voting logic considerations result in changes to the optimal detector placement, and significant improvements in the expected time to detection when false positives and false negative alarms are acknowledged.