BACKGROUND ABSTRACT PSIG 1428

Transcription

1 PSIG 1428 Economic Benefits of Leak Detection Systems: A Quantitative Methodology Trevor Slade, Alyeska Pipeline, Yoshihiro Okamoto, Alyeska Pipeline, Jonathan Talor, Copyright 2014, Pipeline Simulation Interest Group This paper was prepared for presentation at the PSIG Annual Meeting held in Baltimore, Maryland, 6 May 9 May This paper was selected for presentation by the PSIG Board of Directors following review of information contained in an abstract submitted by the author(s). The material, as presented, does not necessarily reflect any position of the Pipeline Simulation Interest Group, its officers, or members. Papers presented at PSIG meetings are subject to publication review by Editorial Committees of the Pipeline Simulation Interest Group. Electronic reproduction, distribution, or storage of any part of this paper for commercial purposes without the written consent of PSIG is prohibited. Permission to reproduce in print is restricted to an abstract of not more than 300 words; illustrations may not be copied. The abstract must contain conspicuous acknowledgment of where and by whom the paper was presented. Write Librarian, Pipeline Simulation Interest Group, P.O. Box 22625, Houston, TX 77227, U.S.A., fax ABSTRACT Effective risk and cost management are paramount concerns for pipeline owners and operators. Leak detection systems (LDS), while having no effect on the probability of a leak occurring, limit the scope of potential damage and reduce risk. The authors propose using a stochastic simulation to quantify the economic effectiveness of these systems in mitigating these low-probability, high impact events for liquid pipelines. When considering any capital investment, it is useful to estimate its expected value; the authors propose using a stochastic simulation to perform an economic analysis on these systems analyzing the ability of these systems to mitigate the impact of oil spills. For this methodology, each leak detection system is measured in terms of the reduction to total oil spill impact. This is accomplished by using leak probabilities to generate theoretical leaks that mimic the expected leak behavior of a pipeline. Next, probability maps are used to generate theoretical onset-to-response times, where the generated times mimic the expected behavior of the LDS. These generated values are used as input to a cost model to estimate the total spill costs for each leak, and repeated application results in an expected value for each subsystem. The costs are converted to a present value using the internal rate of return specified by the operating company. Risk is estimated with and without a proposed change to the current leak detection system; the difference between the two total spill risks is the value or impact of the proposed change. Comparing risk reduction values provides a meaningful way of evaluating LDSs and potential changes to LDSs. Additionally, it can justify the removal of unnecessary LDS components and allow comparison of proposed leak detection projects with other investment options. BACKGROUND A leak detection system and its components operate in tandem with human controllers and process equipment to detect and diagnose pipeline hydraulic anomalies and respond appropriately in the event of a leak. LDSs provide an essential tool for mitigating the risks associated with operating Hazardous Liquid and Gas Pipelines. Adhering to even the best integrity management practices cannot completely eliminate the probability of a leak occurring and the associated hazards of a leak and spill, including loss of life, environmental impact and negative public perception are signif Various factors determine which LDS and subsystems are appropriate for a pipeline: government regulation, pipeline size, location, expected throughput, etc. In order to evaluate what is best for a specific pipeline, the authors propose that the risk reduction through improved response time provided by the LDS be taken into account. LDSs vary in their performance and cost; the correct one should add the most value to the core business. The U.S. Department of Transportation s (USDOT) study on leak detection 1 defined risk in terms of expected cost in dollars/year as: ( ) ( ) LDSs ultimately reduce the economic impact by limiting spill volume and spill area in the event of a leak via two avenues: producing a process response such as a shut down or isolation and speeding up oil spill response activities. Additionally, even the most sensitive system is monitored by human controllers and operators who are ultimately the true detectors of leaks; a system that detects rapidly but is too cumbersome to diagnose efficiently may result in a longer onset-to-response time than a simpler LDS.

2 2 TREVOR SLADE, YOSHIHIRO OKAMOTO, JONATHAN TALOR PSIG 1428 Basics of Leak Alarm Response The process of responding to a leak can be illustrated by splitting it into four phases. The initial phase is the dynamic phase between the moment of pipe integrity failure and the leak rate stabilizing. The second phase is the period where the leak rate has stabilized but the LDS has yet to elicit the appropriate process response. The third phase is the period where the response is taking place, and the fourth and final phase is the time between the completion of the response and the leak stopping. At the onset of a leak, a pipeline integrity failure of some sort creates a path of least resistance through which a portion of the total pipeline flow is diverted. During the initial phase of the leak, the flow through this diversion will typically be larger than the eventual steady state leak rate. This behavior can be estimated using a transient pipeline model, the output of which is an estimate of the total spill size for a given leak rate. After some time, the system reaches a state of stable leak rate. A leak detection system is expected to alarm some time after the onset of the leak. The time required for the system to detect the leak depends on the type of system and its design characteristics. It may not be appropriate to assume that leak alarms will immediately trigger the appropriate process response because it is typical for LDSs to broadcast non-leak (false) alarms. These alarms can affect the time required to elicit a response based on the strategy the pipeline operator uses to handle leak alarms. Some examples of different strategies include: 1. Immediately respond to all leak alarms. 2. Define a maximum alarm analysis time period; the response is initiated if this period expires and if the analyzer s confidence that this is a false alarm has not reached a certain threshold. 3. Respond to the alarm only when the analyzer s confidence that it is a true leak alarm reaches a specified threshold. It is apparent that each strategy has a relative cost: immediately responding to all leak alarms will increase the cost of each false alarm while waiting to analyze the alarms can slow down the response. The choice of alarm management strategy depends on many factors but risk/cost analysis can help balance the need for quick leak response with the objective of maintaining stable operations. When a leak alarm successfully elicits the appropriate process response, the response will consist of manipulating pumps, closing or opening remote valves, etc. It will require time to ramp down the pumps, close remote valves, and whatever other remedial action is required. Rapid shutdown of the system is often limited by the need to prevent pipeline overpressuring via water hammer effects. Other factors that can influence the total leak size are the pipeline s topography and normal operating pressures. Upon completion of the alarm response, which typically ends with complete pipeline isolation, the leak will continue until the static head directly upstream of the leak drops to or below atmospheric pressure. This dynamic depends on remote valve and check valve selection and locations and the elevation of the pipeline. METHODOLOGY Prerequisites In order to evaluate how LDSs can improve leak response, data about their characteristics and behavior must be gathered. rate based LDSs can be vetted by performing commodity withdrawal tests if already in place, and with software based methods, such as those described in PSIG 05A1 2. Using such methods, it is possible to obtain a performance curve for a given LDS and leak rate, where the cumulative probability of detecting a leak is plotted against time after leak onset. A set of these curves over various leak rates can be considered the performance map of that LDS. The performance map used for the sample cases in this paper is shown in Figure 1. For observational LDSs, such as pipeline route inspections or fly-overs, an estimation of the probability of observing a leak is required. Inputs to these methods would be leak size and location, whether it is above or below ground, and the frequency of observation at each location. It could also account for missed observations; due to the highly variable nature of observation based LDSs, we concentrate our analysis in this paper on flow rate based LDSs. To estimate the cost for a given leak, we used the Basic Oil Spill Cost Estimation Model (BOSCEM) published by the Environmental Protection Agency (EPA) 3. This model sums spill response, socio-economic, and environmental costs of a leak and includes influencing factors like oil and terrain type. For even the smallest leaks, there is a substantial base cost, and the increase in cost for increasing leak sizes is less than linear. Additionally, the disparity between high-impact and low-impact areas is significant; a spill in a high-impact environmental area, such as a river used by wildlife or residential land, can cost more than 2.5 times the amount than a spill of the same volume in an industrial area. From BOSCEM, one can construct a cost matrix that contains the estimated cost for a leak of a given volume at any point along the pipeline, Cost(milepost, volume1, volume2, ). Ideally, a full GIS survey would be conducted; in the likely situation that a very detailed survey is available from pipeline route and construction planning. These can be used if no major route changes have occurred. For simplicity, we have assumed fixed coefficients for the entirety of our sample pipeline.

3 PSIG 1428 ECONOMIC BENEFITS OF LEAK DETECTION SYSTEMS: A QUANTITATIVE METHODOLGY 3 Secondly, a leak probability matrix must be created, P_Leak(milepost, rate1, rate2, ). This information can be obtained via risk analysis studies of the pipeline and deductions from operating data. Though these probabilities will differ along the length of the pipeline for example, leaks often tend to occur closer to pump stations or at the bottom of downhill segments we have assumed that every location and leak rate has equal probability. Another consideration is the operator response time after a leak alarm has been issued. This can vary by milepost, as instrumentation may be of better quality in different parts of the pipeline. Custody transfer meters at the supply and delivery points usually have a higher degree of accuracy, but in-line flow meters may be less accurate. Furthermore, smaller leak rates may take longer to interpret, as they cause less disturbance in the normal operating data displayed to the controller/operator. Procedure The probabilistic nature of leak detection encouraged the authors to use a stochastic simulation to estimate the value of leak detection systems. In these simulations, each variable is represented by a probability distribution. The simulation steps forward in time and at each time step generates random numbers for each variable and compares them to the probability distribution to determine the outcome. A large number of trials are important in order for the random distribution to accurately reflect the determined performance of the LDS. After a leak occurs, the total volume of the leak can be estimated by finding the length of time between the onset of the leak and the time at which operational response takes effect. If a leak detection system successfully detects the leak, the series of events is illustrated in Figure 2. After the leak starts, the leak detection system will require a length of time for detection, which can be estimated using a random number and the leak detection system s performance map. After an alarm is successfully broadcast, the alarm needs to elicit an appropriate response. For most pipelines, a field response requires time to take effect; this amount of time is the final component of determining the total response time. The series of events in Figure 2 shows a completely successful response to a leak. It is important to recognize the possibility of failure at each step. A leak simulation starts by stepping forward in time by a designated time step. At each time step, a random number is generated and if the random number is less than the probability of a leak occurring, a leak is simulated. Otherwise, no leak occurs and the leak simulation moves on to the next time step. When triggered, the leak simulation determines the location and size of the leak using a cumulative probability function of these variables and a random number for each. For our sample cases, each location and leak rate has an equal probability of occurring, but an analysis of pipeline-specific factors could improve the accuracy by generating a more realistic distribution of leaks along the profile of the pipeline. Possible contributions to an increased leak probability at a specific point include vulnerability to over pressurizing or an area where water could collect and cause corrosion. When a leak occurs as defined by the simulations, the leak simulation pauses and a leak detection simulation begins. The leak detection simulation first computes the cumulative probability of detecting a leak for the given location and leak rate from the LDS performance map. If multiple leak detection systems exist, the joint probability of the group of systems detecting a leak should be estimated. A random number from 0 to 1 is generated and compared to the cumulative probability of a leak having been detected at the current time. If that number is less than the detection probability, the leak is considered detected. Otherwise, the leak simulation continues onto the next time step and repeats until the leak is determined to be caught or the maximum time for detection elapses. Detecting a leak with the leak detection systems will trigger the response simulation. Once the response threshold is achieved, the time required for the response to take effect is added to the time required to elicit a response and the time required for the leak detection systems to alarm in order to estimate the time to response. The total required time is used to calculate the total leak volume, which is input into a cost estimation model. These steps will be repeated thousands of times. The average present value of the leak costs is then computed as the current risk associated with an oil spill. An overview of this methodology is given in Figure 3. It is unfortunately common for an LDS to broadcast non-leak alarms. These alarms are caused by pipeline transients and/or instrumentation uncertainties that create data inputs that can be confused for a leak. Tuning a LDS often requires a tradeoff between increasing sensitivity and increasing the number of non-leak alarms. The costs associated with false alarms can be estimated by measuring the total number of non-leak (false) alarms that occur in a given time period. The cost of the non-leak alarms depends on the strategy used to handle leak alarms. The common strategy in which all leak alarms are immediately responded to means that 100% of alarms will trigger the appropriate response. It also means that 100% of false alarms will shut the pipeline down for a specified period of time. The cost of false alarms for this type of management can be estimated by considering the cost of shutting the pipeline down for each false alarm. If a period is specified, such that within this time it must be

4 4 TREVOR SLADE, YOSHIHIRO OKAMOTO, JONATHAN TALOR PSIG 1428 determined whether to respond or not, it is assumed whoever is analyzing the alarm must prove that the alarm is not indicative of a leak. During this analysis, if a confidence level is specified, the performance maps that show the confidence level as a function of leak size and time after leak onset can be used in conjunction with a stochastic simulation to determine whether each false alarm was attributed in time. For the case which requires the analyzer to reach a specified confidence level prior to initiating a response, the performance maps can be used in conjunction with a stochastic simulation to determine the average number of cases where the analyzer mistakenly reaches the specified confidence level when given a false alarm. SAMPLE CASES A simplified example pipeline was created to illustrate the different types of results that can be obtained by this type of economic analysis. There are three different cases of the same pipeline, where the area classification can change based on milepost. The first case is a pipeline whose entire route spans a low consequence area, the second has interspersed high consequence areas that account for 20% of the total pipeline length, and the third is a pipeline that goes entirely through high consequence areas. For the mixed case, the high impact areas are evenly distributed in three sections at the beginning, middle, and end of the pipeline. These high-impact sections can be placed to cover any 20% of the pipeline because we have assumed that the probability of a leak in any location is uniform across the entire pipeline. In a real pipeline, this would not be the case because the pipeline route is fixed and has non-uniform probabilities for leak occurrence. Additionally, it is possible to create any number of sections with different impacts along the pipeline; the sample cases are simple, but real pipelines can and do cross multiple environmentally or economically important areas. We created representative, but realistic, detection probabilities corresponding to different leak rates:,,,, and of flow (Figure 1). All had 100% detection at 24 hours after leak onset. The maximum leak time is also 24 hours. The leak volume over 24 hours was used to calculate the risk with no LDS. For each case, we separated out each leak rate and investigated the total volume reduction provided by the LDS. We also looked at the effect of pipeline integrity (designated by the number of leaks a pipeline can expect to have in one year) on the risk reduction gained by LDS implementation. The results of these sample cases are detailed in Tables 1-9 and Figures 4-6. For each case, we ran 100,000 trials and varied the pipeline integrity with 0.1, 0.2 and 1 leak per year. The tables show the estimated risk with and without the LDS, as well as the risk reduction for a single integrity value across the different leak rates. The figures compare the effect of pipeline integrity on risk reduction for each leak rate. Case 1 Low Consequence The percentage risk reduction ranges from 46-6 for a pipeline experiencing 1 leak per year for 10 years, increasing to 79-86% for a pipeline with 1 leak per 10 years. The highest reduction for each integrity value is experienced at the low and high ends of the leak rates. Case 2 Mixed Low/High Consequence The percentage risk reduction ranges from 42-60% for a low integrity pipeline, increasing to 78-86% for a high integrity pipeline. Again, the highest reduction for each integrity value is experienced at the low and high ends of the leak rates. Case 3 High Consequence Similar to the previous two cases, though with greatly increased actual cost, the risk reduction ranges from 49-65% in the low integrity scenario to 80-86% in the high integrity one; again showing the largest reduction at for the largest and smallest leak rates. DISCUSSION Overall, the risk reduction is very similar in these cases, with a slight trend towards better reduction in higher impact areas. However, pipelines constructed in high consequence areas (wildlife reservations, near water resources, etc.) often have additional technical challenges that can reduce the performance of LDSs. These can include altered pipeline construction, e.g. alternating above- and below-ground sections designed not to disturb wildlife migration routes, or having to rapidly cool the oil from a supply station in order for the heat not to damage a delicate tundra environment. While, in our examples, we assumed that the LDS performed equally well on the high consequence pipeline as the low consequence one, this is not necessarily the case in real operations. It is important that the risk reduction provided by LDSs be influenced by the number of leaks that occur over the operating lifespan of the pipeline. This implies a cooperative effect between good pipeline maintenance and the effectiveness of leak detection. This effect is reflected in the coefficients in the BOSCEM model, which scale at a less than linear rate (i.e. it costs less per barrel spilt for a 100,000 BBL spill than a 10,000 BBL spill). Given equivalent total spill volumes, a single large leak will most likely be less costly than the sum of multiple smaller leaks. Therefore, reducing the probability of leaks occurring through good pipeline integrity maintenance bolsters the effectiveness of LDSs. The extra risk reduction gained by leak detection can be viewed as enhancing the benefits of maintenance and infrastructure, which is another aspect that should be taken into account when choosing a LDS. When combined, it is possible that a high performing, albeit expensive LDS could prove cheaper than a

5 PSIG 1428 ECONOMIC BENEFITS OF LEAK DETECTION SYSTEMS: A QUANTITATIVE METHODOLGY 5 moderately performing, but inexpensive to install LDS. It may be noted there was a small, but consistent, drop in risk reduction in the mid-range leak sizes (1- flow). This can be explained in two ways: for very small leaks (< flow), any level of detection represents a significant reduction versus over letting the leak persist. For large leaks (> flow), the rapidity of detection ensures that the large final cost of a continued leak never reaches that potential. Though we have given equal weight to leak sizes, most leaks that occur in real pipelines are smaller in size, which would increase the overall LDS risk reduction slightly. It is important to note that high sensitivity at low leak sizes, P(Alarm Leak), is often correlated with higher false alarms, P(Alarm No Leak) and smaller leak sizes will take longer to diagnose. Additionally, it is possible for LDSs to have different types of alarms, each requiring separate investigation. The controller s time to response was set at a static number in our model. An analysis of false alarms and their effects on response time would improve its accuracy. Though our simplified pipeline did not have additional instrumentation or other equipment, real pipelines often have isolation valving that should be taken into account. During the progression of a leak, without check valves and remotely operated valves, a pipeline would drain until the leak could be stopped. Even if the pipeline were shut down, differences in pressure based on topography would cause additional spillage until equalized. The strategic placement of valving is, therefore, an important consideration in pipeline construction. When choosing a LDS, there can be a tradeoff between the effectiveness of that system and the configuration of the valving along the pipeline. rate-based LDSs require that the instrumentation used to provide them with data have access to the pipeline hydraulic measurements; they cannot function in sections of the pipeline where they cannot see. One possible further analysis would be to look at how often a pipeline shuts down (for example for maintenance purposes) and look at what visibility the LDS has into the pipeline under these operating conditions. This could be used to further refine the cost model by including the probability that the pipeline is shut down when a leak occurs and reverting to a detection probability for those trials. It is not uncommon for pipeline operators to employ multiple LDSs, each with different inputs, such that at least one can be used in the event that input data becomes unavailable for one or more of them. Having these backup leak detection systems is important, and can justify keeping lower performing systems or subsystems in operation. CONCLUSIONS Although the cases considered in this paper were very simple compared to real world leak detection management problems, they illustrate that the risk reduction of a leak detection system can be estimated. This type of analysis can be used to assist pipeline operators to make informed management decisions concerning leak detection systems including selection of new systems, tuning of existing systems and prioritizing system maintenance. REFERENCES 1. United States Department of Transportation. Leak Detection Study DTPH56-11-D Carpenter P, Nicholas E, Henrie M. Accurately Representing Leak Detection Capability and Determining Risk. Pipeline Simulation Interest Group, October Etkin D. Modeling Oil Spill Response and Damage Costs. FSS, April Kristiansen M. Leak Detection Metrics: What Should I Focus on? Pipeline Simulation Interest Group, May ACKNOWLEDGEMENTS The authors would like to acknowledge Hugh Robinson and Jon Barley for their efforts in helping review this paper. We also acknowledge Phil Carpenter, Ed Nicholas, and Morgan Henrie, for their extensive experience and investigation into determining the performance of rate based leak detection systems. Finally, we acknowledge Morten Kristiansen for his PSIG paper on choosing leak detection systems, which influenced the direction of ours. ABOUT THE AUTHORS Trevor Slade is a Process Controls Engineer at Alyeska Pipeline Services Company in Anchorage, Alaska. He has experience with pipeline leak detection, process safety management, and DCS systems. Trevor has a Bachelor s of Science in Chemical Engineering from Brigham Young University in Provo, Utah. Yoshihiro Okamoto is an Automation Engineer at Alyeska Pipeline Services Company in Anchorage, Alaska. He is a recent graduate and is currently working on SCADA systems. Yoshihiro has a Bachelor s of Science in Electrical Engineering from the University of Alaska, Anchorage. Jonathan Talor is a Project Engineer at Energy Solutions International in Houston, Texas. He has experience with pipeline leak detection and simulation. Jonathan has a Bachelor s of Science in Chemical and Biomolecular Engineering from the University of Pennsylvania in Philadelphia, PA.

6 6 TREVOR SLADE, YOSHIHIRO OKAMOTO, JONATHAN TALOR PSIG 1428 TABLES Case 1 No. of Trials: , Leaks/Year: 1, Max Leak Time: 1 Day, Operation: 10 Risk, No LDS ($MM) , Risk, LDS ($MM) Risk Reduction (%) 56.06% % 52.89% 62.35% Table 1 Risk Reduction, Case 1; Trials per, 1 Leak per Year, Max Leak Time = 1 Day, Operation = 10 Case 1 No. of Trials: , Leaks/Year: 0.2, Max Leak Time: 1 Day, Operation: 10 Risk, No LDS ($MM) Risk, LDS ($MM) Risk Reduction 71.88% 66.18% 65.24% 69.37% 75.70% Table 2 Risk Reduction, Case 1; Trials per, 1 Leak per 5, Max Leak Time = 1 Day, Operation = 10 Case 1 No. of Trials: , Leaks/Year: 0.1, Max Leak Time: 1 Day, Operation: 10 Risk, No LDS ($MM) Risk, LDS ($MM) Risk Reduction 83.18% 79.90% % Table 3 Risk Reduction, Case 1; Trials per, 1 Leak per 10, Max Leak Time = 1 Day, Operation = 10 Case 2 No. of Trials: , Leaks/Year: 1, Max Leak Time: 1 Day, Operation: 10 Risk, No LDS ($MM) , Risk, LDS ($MM) Risk Reduction (%) 55.55% % 50.04% 60.16% Table 4 Risk Reduction, Case 2; Trials per, 1 Leak per Year, Max Leak Time = 1 Day, Operation = 10

7 PSIG 1428 ECONOMIC BENEFITS OF LEAK DETECTION SYSTEMS: A QUANTITATIVE METHODOLGY 7 Case 2 No. of Trials: , Leaks/Year: 0.2, Max Leak Time: 1 Day, Operation: 10 Risk, No LDS ($MM) Risk, LDS ($MM) Risk Reduction % 63.40% Table 5 Risk Reduction, Case 2; Trials per, 1 Leak per 5, Max Leak Time = 1 Day, Operation = 10 Case 2 No. of Trials: , Leaks/Year: 0.1, Max Leak Time: 1 Day, Operation: 10 Risk, No LDS ($MM) Risk, LDS ($MM) Risk Reduction 80.96% % 85.55% Table 6 Risk Reduction, Case 2; Trials per, 1 Leak per 10, Max Leak Time = 1 Day, Operation = 10 Case 3 No. of Trials: , Leaks/Year: 1, Max Leak Time: 1 Day, Operation: 10 Risk, No LDS ($MM) , , , Risk, LDS ($MM) Risk Reduction (%) % 49.40% 56.38% 65.6 Table 7 Risk Reduction, Case 3; Trials per, 1 Leak per Year, Max Leak Time = 1 Day, Operation = 10 Case 3 No. of Trials: , Leaks/Year: 0.2, Max Leak Time: 1 Day, Operation: 10 Risk, No LDS ($MM) Risk, LDS ($MM) Risk Reduction % 67.09% 71.54% 77.68% Table 8 Risk Reduction, Case 3; Trials per, 1 Leak per 5, Max Leak Time = 1 Day, Operation = 10

8 8 TREVOR SLADE, YOSHIHIRO OKAMOTO, JONATHAN TALOR PSIG 1428 Case 3 No. of Trials: , Leaks/Year: 0.1, Max Leak Time: 1 Day, Operation: 10 Risk, No LDS ($MM) Risk, LDS ($MM) Risk Reduction 82.50% 80.36% % 86.46% Table 9 Risk Reduction, Case 3; Trials per, 1 Leak per 10, Max Leak Time = 1 Day, Operation = 10

9 PSIG 1428 ECONOMIC BENEFITS OF LEAK DETECTION SYSTEMS: A QUANTITATIVE METHODOLGY 9 FIGURES 100% Leak Detection Probability for Various s Leak Detection Probability (%) 90% 80% 70% 60% 50% 40% 30% 20% 10% 0% Hours Figure 1 Leak Detection Probability for Various s LEAK! Time required for Leak Detection System to Alarm LEAK ALARM Time required for Leak Alarm to Elicit the Appropriate Response RESPONSE Time required for Response to Take Effect END TOTAL LEAK VOLUME Figure 2 - Diagram of the series of events initiated by a leak START, CURRENT TIME LEAK SIMULATON, Time, Location Leak Simulation Time of Alarm Response Simulation Time Response Takes Effect COST MODEL END, PRESENT VALUE OF LEAK COST Next Time Step Next Time Step Next Time Step Figure 3 Overview of Stochastic Simulation

10 10 TREVOR SLADE, YOSHIHIRO OKAMOTO, JONATHAN TALOR PSIG 1428 Risk Reduction 100% 90% 80% 70% 60% 50% 40% 30% 20% 10% 0% Case 1 - Risk Reduction Figure 4 Case 1: Risk Reduction for Each and Interval 1 Leak/Year 0.2 Leaks/Year 0.1 Leaks/Year Risk Reduction 100% 90% 80% 70% 60% 50% 40% 30% 20% 10% 0% Case 2 - Risk Reduction Figure 5 Case 2: Risk Reduction for Each and Interval 1 Leak/Year 0.2 Leaks/Year 0.1 Leaks/Year

11 PSIG 1428 ECONOMIC BENEFITS OF LEAK DETECTION SYSTEMS: A QUANTITATIVE METHODOLGY 11 Risk Reduction 100% 90% 80% 70% 60% 50% 40% 30% 20% 10% 0% Case 3 - Risk Reduction Figure 6 Case 3: Risk Reduction for Each and Interval 1 Leak/Year 0.2 Leaks/Year 0.1 Leaks/Year