(599at) 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.