On the scheduling of leak detection personnel

Abstract

Due to recent environmental regulations concerning the release of volatile organic compounds (VOCs), a virtual army of testing personnel has been assigned the task of detecting and repairing faulty equipment leaks. In this work, we develop a strategy for the cost-effective allocation of these testing personnel. The proposed scheme finds a grounding in the probabilistic theory of reliability analysis and culminates with the formulation of a Mixed Integer Linear Programming (MILP) optimization problem. The goal of this optimization problem is to find a testing schedule that achieves minimum cost while maintaining a bound on the expected number of leaks. The formulation is general enough to capture time-varying failure characteristics (i.e. equipment age), quality/cost variations inherent to different testing methods as well as personnel availability considerations. Finally, the algorithm can be applied in a feedback framework to incorporate recent information (such as test results and maintenance actions) into an updated testing schedule.

Introduction

The US EPA defines fugitive emissions as “those emissions which could not reasonably pass through a stack, chimney, vent, or other functionally-equivalent opening” (NES, 1997). Simply stated, fugitive emissions are releases that occur whenever there are discontinuities in a solid barrier intended to maintain containment.

In a typical refinery, there are thousands of these potential emission sources. Equipment such as valves, flanges, pumps, connectors and compressor seals are the major source locations. Here, we divide fugitive emissions into two classes:

• Nominal emissions, due to imperfect construction

• Leaker emissions, due to failed or faulty equipment

In general, the operator of a processing facility can do very little to reduce the nominal emission rate, other than purchase higher quality parts. As such, we will not consider this class of emissions, but rather focus all of our attention on the second class. The Clean Air Act requires most chemical processing facilities to develop and implement a Leak Detection and Repair (LDAR) program. In general, all process equipment subjected to a LDAR program should be monitored and, if need be, repaired within a predefined time period. The program can be decomposed into the following four tasks (US EPA, 1999):

• Identify equipment to be included in the program;

• Conduct routine monitoring (or testing) to identify leaks;

• Repair leaking equipment within a specified time frame;

• Be prepared to report monitoring results.

In preparation for task 4, the facility must organize a vast amount of information pertaining to the other three tasks. Many agencies suggest the utilization of a Fugitive Emission Management System (FEMS) (Winberry, 2001). These enormous database systems keep records of monitoring and repair activities as well as generate simplified emission and compliance reports. As a convenience to the facility many FEMS include a leak test scheduling algorithm.

Our expectation as to the basis of the scheduling algorithms currently included in various FEMS packages has been derived from the following analysis of EPA regulations. The regulations require all process equipment to be tested at regular intervals. The interval could be anywhere from monthly to annually. Thus, we expect that current scheduling methods simply suggest a test of each piece of equipment during the specified minimum interval. However, the governing agency will typically select the minimum testing interval based on past performance. For example, if the facility achieves a specified performance goal, then the agency will reduce the minimum testing frequency (from something like quarterly testing to annual testing). However, if this performance level can not be maintained, then the minimum interval will revert back. Unfortunately, the large jump to annual testing may be insufficient to maintain the desired performance level. That is, while only annual testing is required by the agency, the actual testing frequency will need to be some level between quarterly and annually. The aim of the current study is to determine a test frequency that will achieve the desired performance but, at a minimum cost.

A number of authors have provided advice concerning the implementation of a LDAR program. Holloway (1999) suggests methods of getting the most out of the dollars spent on a LDAR program while, Siegell (1997) offers recommendations for establishing and improving the performance of a LDAR program. A recent article in Enforcement Alert (US EPA, 1999) suggests that the number of leaking valves and equipment may be up to 10 times greater than expected. The report identifies a number of practices aimed at improving the reliability of a LDAR program. One of these suggestions is to provide more frequent testing than required. Although each of these articles provide invaluable suggestions and guidance to LDAR program managers, none of them focus specifically on the subject of leak test scheduling.

Design questions similar to ours are frequently encountered in the field of process scheduling and planning. A subclass of this field that appears to be very similar to the leak detection problem is that of maintenance scheduling. This is due to the fact that both applications are grounded in the time-dependent theory of reliability analysis contrasted with the economics of limited man-hour and equipment resources. Tan and Kramer (1997) provided a nice overview of the major challenges facing the preventative maintenance scheduling field as well as propose a scheme that combines Monte Carlo simulation with a genetic algorithm. Martorell, Sanchez, and Serradell (1999), considered an equipment age-dependent reliability model for nuclear power plant operation. In particular, they presented the results of a sensitivity study, concluding that maintenance effectiveness had a large impact on the selection of an appropriate maintenance strategy. Usher, Kamal, and Syed (1998) presented a cost optimal maintenance scheduling problem formulation that considers three levels of maintenance actions. They also evaluate three solution procedures, a random search, a genetic algorithm, and a branch-and-bound approach. Others have discussed the scheduling of maintenance through consideration of various parameters such as type of maintenance and availability of maintenance staff (Park, Jung, & Yum, 2000; Vassiliadis & Pistikopoulos, 2001; Vaurio, 1999).

In the following section, a number of concepts from the field of reliability theory are presented and applied to the leak detection problem at hand. In section three, the specific design problem is formulated, while section four contains a discussion of schemes aimed at calculating optimal and sub-optimal testing schedules. In the final section, a couple of examples are presented.