Optimal Scenario Based Gas Detector Placement in Process Facilities

摘要

Gas detection, specifically the detection of combustible and toxic gas release events, is a key component of modern process safety. This work addresses this need by developing a multi- scenario, mixed-integer linear programming (MILP) formulation [Berry 2005] for optimally placing gas detectors in petrochemical facilities. Given a large number of potential gas detector locations and a rigorous dispersion model with actual geometry from the process facility, hundreds of different scenarios are simulated using FLACS [GexCon 2011] with different leak locations, process conditions, and weather properties. This provides the necessary data for the MILP formulation. Pyomo [Coopr 2009], a python-based optimization package, is used to formulate the multi-scenario, mixed-integer programming problem. Using CPLEX to solve the formulations, different objective functions are explored. Optimal results are presented for the minimum number of sensors required to detect all scenarios, the minimum expected time to detect events using a fixed number of sensors, and a robust formulation that minimizes the maximum time to detection across all scenarios. In all of these examples, the formulation can be solved efficiently for real, large-scale problems. The first formulation developed is for determining the minimum number of sensors needing to be placed to detect all of the potential release scenarios in the data set. Solving this problem using CPLEX required only a few seconds of computing time and revealed that 43 sensors were necessary to detect all 270 of the potential release events in the available data set. Additionally, a formulation was developed to minimize the expected time to detection, assuming a given number of sensors. As expected, increasing the number of gas detectors produces a decrease in the expected time to detection. However, this study shows that using more than 71 detectors provides no additional decrease in the expected time to detection. This result is, of course, a function of the number of leak scenarios considered. Finally, a formulation was produced to minimize the maximum time to detection across all scenarios. There is a clear decrease in the maximum time to detection from 43 to 61 sensors, after which no perceivable decrease in the maximum time to detection exists. All of these formulations were solved efficiently on a multi-core computer using Pyomo for the formulation and CPLEX as the solver. Three different formulations were shown for optimally placing gas detection sensors in a petrochemical facility. These formulations were tested and results were provided. In the future, it would be beneficial to adapt these formulations to include confidence intervals for the objective function to ensure than an adequate number of scenarios have been included in the data set. Additionally, it would be desirable to develop a two-stage problem to mitigate potential sensor failures [Berry 2009], as well as a formulation that minimizes nuisance trips by requiring multiple sensors to detect before an event is confirmed. This work is currently submitted as [Legg, et al 2011].