Abstract Crude oil pipelines can occasionally experience flow regimes in the critical section where the flow changes from a laminar streamlined flow to a transitional zone with the onset of turbulence where the Reynolds number is located in the range 2100 to 3000. In this range of operation the flow is considered unstable and currently there is no definitive method for evaluating the friction factor with certainty. The result for modeling purposes is that pressure predictions are rendered somewhat less reliable than if the pipe operated in either the laminar or transition zone or fully turbulent zones. In the critical zone, one approach for both providing a reasonable estimate and for maintaining numerical stability is to use a weighted average of the laminar and transitional friction factor equations. This paper intends to quantify the uncertainty in pressure prediction using this approach, by comparing with estimates for the friction factor based on actual instrumented data during both steady state and transient modes of operation in the critical zone. The first step in attempting to achieve this goal reliably would be to provide a verification base state where the uncertainties in all input parameters such as fluid properties, pipe roughness, temperature, elevation profile, pipe internal diameter, and distances have been reduced as feasibly as possible. The approach taken here involves application of the non-linear regression method, Levenberg-Marquardt. Historical data from an actual operating NPS 16 multi-station blended crude pipeline system was available to assist in this parametric study.

Abstract Leaks and ruptures are the most important possible risks for operational oil and gas pipelines. Due to their hazardous effects on the environment, much research has been conducted to prevent and detect possible ruptures on a pipeline to protect people and the environment by enhancing safe operation. Any improvement in leak detection technologies to increase the accuracy and sensitivity while eliminating false leak and rupture alerts will protect the environment and assure hazard-free operation. Data mining algorithms are widely used in many industries, including the energy industry. They have already been implemented as computational leak detection methodologies. To increase confidence and improve accuracy and sensitivity, different algorithms may be introduced to detect ruptures. In our study, a 36" crude oil pipeline with two pump stations was configured in a pipeline simulator. The pipeline parameters of flow, pressure, and temperature were computed for several leak and rupture cases, and data science algorithms such as Logistic Regression, Neural Network, and Multivariate Adaptive Regression Splines were used as classifiers to detect the leaks and ruptures. Multivariate Adaptive Regression Splines (MARS) is an important statistical learning tool for both classification and regression. MARS is nonparametric, adaptive, and effective in high dimensional problems with a proven record for fitting nonlinear multivariate functions. The contribution from the basis functions together with interaction effects between the predictors are used to determine the response variable: MARS produces a resultant model as an explicit formula. MARS proves itself as a comparative classifier to the already known logistic regression and neural network methods as a new leak and rupture detection computation data science technique for pipeline operators.

Abstract Solids transport models are used to predict the fluid velocity required to transport solid particles in hydraulic and pneumatic systems. It is important that the processes in these applications are designed and operated at a sufficient fluid velocity to avoid solid deposition. Mechanistic models are used to provide a reasonable estimate for the minimum fluid velocity needed to transport the particles. However, those models are commonly applicable in their respective ranges of data fitting; and are limited by the applicability of the empirically based closure relations that are a part of such models. Artificial Intelligence (AI) and Machine learning (ML) offer a wealth of techniques to extract information from data that can be translated into knowledge about the underlying fluid mechanics. The purpose of this work is to investigate the use of several ML models to predict the critical velocities of various single-phase carrier fluids in horizontal and inclined flow conditions. A frame of work is developed to predict critical velocities in pipes via machine learning, using accessible parameters as inputs, namely, liquid and particle properties and inclination angles. The ML algorithms are trained on a large dataset (more than 1400 data points) of critical velocities in single-phase carrier fluid that is collected from open source: articles and dissertations. The trained algorithms are Elastic Net, Support Vector Machine, Random Forest, and Extreme Gradient Boosting Decision Trees. Moreover, the influence of key features in critical velocity prediction was identified by the applied algorithms. Finally, the predictive abilities of the models are cross-compared and were further validated by comparing its performance with well-established mechanistic models based on empirical correlations. The ML approach is observed to have superior performance to other models across a wide range of flow conditions and inclination angles.

Abstract The paper demonstrates the construction, training, and uncertainty quantification analysis of an artificial neural network model for single phase liquid pipeline leak detection through pressure drop and flow rate monitoring. The demonstrated methods reached acceptable error levels efficiently using theoretical data produced by a theoretical physics model. The results demonstrate that the randomly simulated leakage can be efficiently detected using the trained ANN (Artificial Neural Network) model based on theoretical data derived from physical equations. However, complexity appears when simulated leakage with modeled uncertainty are used in the training of the AI models. The propagation and influence of the uncertainty in the input data on the ANN method are discussed. Randomness following certain probability distributions is introduced into the data to measure the influence on the efficiency and reliability of the training and results of the ANN model. The paper also discusses the influence of the range of input data on the predictability of the ANN model in leak detection. Introduction and Background Data driven Machine Learning technologies such as ANN (Artificial Neural Networks) provide great innovation opportunities towards the design and operation of oil and gas pipeline systems. ANN based models have proved to be efficient in predicting the pressure drop within a pipeline (Brkic, D., and Cojbasic, Z., 2016; Shayya, W.H., and Sablani, S.S, 1998; Salmasi, F., etc. 2012; Fadare, D.A., and Ofidhe, U.I., 2009) as well as solving the inverse problems such as detecting pipeline roughness progression, inner diameter change, and leakage (Cheng, D., Zeosky, D., 2019). The increasing interest towards machine learning models causes the need to highlight the concerns of uncertainty propagation into the engineering applications of the methods. Machine learning models are developed through analysis of data derived either from physics models or measurements.

Abstract Software for the simulation of the transient behavior of natural gas pipelines commercially available, however, due to their high computational demands, they do not allow real time simulations. Further, they are difficult to set up if the goal is to match measurement data from SCADA systems or compressor stations for existing pipelines. To overcome this difficulty, a state space approach is used to capture the transient behavior of the pipeline. The general approach takes a published method from the literature that derives transfer functions and state space equations from one-dimensional Navier-Stokes and extends the method to reduce uncertainty in modeling parameters. The present method is validated against results in the literature. Then, a pipeline is modeled with commercially available, well established software, and the transient behavior is simulated and the results are compared with the present method. The main contribution of the paper is the extension of the stat-space formulation to remove uncertainty in pipe-roughness assumptions through systematic estimation of friction factors. Introduction Natural Gas Pipelines are an efficient method to transport energy over large distances. The transportation of natural gas and/or blends of natural gas and hydrogen over large geographic areas requires efficient operation of compressors and other related facilities. The scheduling of flows throughout a piping network is a great challenge to control theory. Many gas pipelines are operated under unsteady operating conditions, which in turn causes significant fluctuations in the operating conditions for the compressor stations in these pipelines. These fluctuations are the result of varying demand, as well as varying gas supply. For a given pipeline segment, the gas supply pressure and flow into the pipe are subject to change as are the pressure and flow demand on the delivery side of the pipe. These conditions, as well as their timing are only predictable to a degree.

Abstract There are occasions when one might want to use results from one simulator as input to another simulator, for example, when preparing data for a leak sensitivity study where data from an offline simulator is used to synthesize measurement data for a real time model. Alternatively, one might want to compare results between different simulators, as with the PSIG test cases. Clearly, ensuring the pipeline parameters and fluid parameters are the same in both simulators is an essential step in this process. However, nuances and differences in modelling philosophies can lead to differences in the results that can be difficult to explain. In this paper we present an incremental approach to ensuring that results between simulators match to within desired tolerances and, where they do not match, provide insight to where the source of the differences lie. The key parameters used to measure the agreement, or otherwise, between the simulators are explained and the effect of the different modeling parameters investigated. To demonstrate, the approach is applied to an offline single-phase simulator, an offline multiphase simulator, a spreadsheet model and a Real Time Transient Model. In the example presented the various steps in the process are described and differences in modelling approaches are highlighted. Finally, we demonstrate that, for the example used, excellent agreement between the different simulators can be achieved. Motivation and Overview The reasons for wanting to ensure that different simulators agree are many and varied. For example, we might want to generate data using one simulator for consumption by another simulator, such as when undertaking a leak sensitivity study. Another example would be independent verification of a flow assurance study.

Abstract Liquid Pipeline scheduling varies from being simple to very complex as the size of the network grows and a point will be reached where an initially deployed legacy or home-made solution may no longer support the current requirements. This problem is further exacerbated by an ageing work force and lack of knowledge transfer from one generation of schedulers to the next. It is often the case that when pipelines were constructed initially, the process and systems were lacking in complexity and functionality leaving most matters being dealt with by using standard rule of thumb or set practices. But with increasingly complex network growth, numbers of products being transported, stringent interface management and increased focus on optimization, the legacy systems and spreadsheets may no longer support the increasing demands. Migrating from a legacy application to a standard industry bench-marked solution helps the pipeline company to reduce dependency on individuals and makes scheduling a more process driven approach, enabling greater control over the scheduling process. A modern product-based solution also helps in identifying beneficial practices that were previously unapproachable such as optimization of the costs incurred while running combinations of pumps, or optimized usage of drag reduction agents, or a combination of both. Besides offering greater visibility of the schedule for a pre-defined period across various hierarchical levels, a modern scheduling tool will also have interfaces to enterprise applications such as SAP and SCADA thereby facilitating the improvement in the fidelity of the scheduling by utilizing the most recent data for e.g., tank levels or line fill data. This paper pulls together experiences of implementations of scheduling solutions and their varying level of user acceptance. The paper highlights common reasons that hinder a scheduler from fully utilizing an available system. The paper identifies the most common amongst these (like non-availability of external interfaces that leads to a lot of data entry) which when provided may enable a higher user level acceptance of an implementation. The paper also tries to define the optimal time when a pipeline company with a medium to complex pipeline network should consider migrating from a legacy application to a standard, or a tailor made, solution by considering the level of maturity of systems and the processes that exist at various levels within the organization. Recognizing that the pipeline system will continue to evolve indicates that the tolls supporting the pipeline will also continue to evolve and therefore the paper considers what steps should be in place for scaling up the solution from time to time. Finally, the paper discusses what is required to achieve the all-important user buy-in and acceptance of the system.

Abstract Leaks may occur at any time and location in a liquid transmission pipeline. One of the significant complexities in the leak detection process arises when the leak happens in a pipeline in the presence of phase change. A set of experiments are conducted on a 374-meter (1227-ft) pipe to examine the performance of CPM-based Leak-Detection algorithms. Different intensities of slack from the bubbly flow to the complete cavitating zone are managed to be present before performing various leak tests in terms of size and location. Flow and pressure values are measured at different locations along the length of the pipeline and used as the initial and boundary conditions or constraint points and fed to the algorithms. Two CPM-based leak detection algorithms are considered. The first algorithm performs the leak detection based on a CPM model, which does not model the hydraulics involving phase change. The second algorithm takes advantage of a CPM solver with a precise model to take phase change (cavitation) and the presence of vaporous phase (slack) into account. The ability and quality of these leak detection algorithms are examined against the experiments. The results show the importance of the phase change modelling ability of the CPM to avoid false positives and detect the leaks of different types, which would have otherwise been masked under operating conditions that involve phase change.

Abstract This paper presents a new methodology for addressing onshore oil & gas production and the constraints inherent in these networks. By translating production network models into objective functions, optimization routines can run directly on the model optimizing the entire network. Just as important, the results keep the network within operating boundaries. To scale the solution for large networks, interpolation and machine learning algorithms are employed to keep the problem from exponentially increasing in computation time. Introduction and Background Onshore oil and gas production typically involves dozens of wells operated by different companies. Production from these wells are transferred to midstream companies at Lease Automatic Custody Transfer (LACT) units [1]. From the LACT units, the oil and gas are transported to processing facilities. Since multiphase flow presents a number of fluid transport issues, it is preferable or usually required that the liquid and gas be separated before being exported. Therefore, large holding tanks are a common sight on wellpads. These tanks hold the liquid until it can be carried out by tankers or pumped to an export line. If many well pads pump liquid from their holding tanks at the same time, this can cause a large pressure drop in the export line, and if the pressure exceeds the Maximum Allowable Operating Pressure (MAOP), a shutdown is triggered and regulatory action is required [2], which ultimately lowers the daily production from the field. When export lines are designed, engineers typically look at average production profiles. However, when liquids are cached and then exported at once, this exceeds the operating parameters of the pipeline. Given a steady supply of oil, the designed capacity is likely far greater than the capacity in practice. That’s because of the discrete nature of the pumps filling and draining without any coordination across fields. Expansion of onshore networks also pose a threat to pipeline capacity limits [3]. Coupled with the inherently transient operations, midstream pipelines can become unreliable. The approach below outlines a method of improving up-time.

Abstract This paper investigates the technology and business benefits of a web-based model scheduling application, which integrates a transient model to other business applications that provide injection and demand schedules. The application provides a simple method to input complex scenarios, including compressor, regulator, and routing operations. The paper shows how the system allows non-modellers to use a complex transient model, reducing non-optimal operational decisions which could impact the wholesale natural gas price or supply to end user customers such as households or businesses. Other operational metrics are discussed. Introduction and Background Independent System Operators’ (ISOs) and Transmission System Operators’ (TSOs) use of transient pipeline models to manage nominations and allocations is seemingly an easy operational premise. The Australian Energy Market Operator (AEMO) operates the gas Declared Transmission System (DTS) which serves Victoria, a state in Australia. The DTS network consists of approximately 2,200 km of transmission pipelines with various lengths and diameters, and transports gas to a network from up to 10 different suppliers. The high pressure meshed transmission network supplies gas to 148 custody transfer points which spans the geographical extremities of the state. The DTS is becoming increasingly more complex, with changes to flow paths and dynamic demand regimes. AEMO, like other TSOs and ISOs, is utilising transient pipeline models to inform operational strategies. This paper explores the challenges facing ISOs and TSOs in the United Kingdom, The United States, and Victoria Australia. Specific reference is made to AEMO’s gas transmission network. The issues explored cover a range of subjects including financial and macro policy but all lead to the impact on a transmission network. The paper does not attempt to solve each transmission operator’s challenges in detail. However, within the context of AEMO’s operations, it attempts to identify the similarities with other TSOs and highlight how AEMO’s transient hydraulic model helps it deal with its challenges.

Abstract We propose a modeling framework and computational method to examine the impacts of operational contingencies on a pipeline system’s capacity to transport natural gas, and study the resulting effect on the reliability of an electric power transmission system that relies on that pipeline for generation fuel. A stochastic model is used to simulate the prevalence of unplanned events that lead to outages that decrease transport capacity, and that may cause curtailments to gas-fired generators that do not hold firm pipeline transportation contracts. We use a transient optimal gas flow as an integrated model that serves as a proxy for pipeline financial and physical operations that involve human-in-loop decisions including compressor setpoint changes. The resulting effects on energy delivery by both the electric power and natural gas sectors is evaluated using transient pipeline simulation and power flow analysis. We consider contingencies occurring during normal operations and collect statistics related to pipeline performance. The proposed approach can be used to discover system vulnerabilities and could ultimately guide development of reliability standards. Introduction Many electric power systems throughout the world now heavily rely on natural gas pipeline networks to supply fuel for gas-fired generation [1]. This has led to growing demand for natural gas transportation in large-scale pipelines, but also increased variability and intermittence in high volume gas flows to dispatched gas-fired generators, which result from operational decision making for the power grid. Although the wholesale power and gas delivery sectors have taken actions to improve market efficiency and implement formal coordination mechanisms [2], [3], it is becoming increasingly problematic for power generation asset managers to procure natural gas during periods of pipeline congestion for both base load and ancillary services [4], which may lead to load curtailments [5] such as during the recent cold weather event in Texas.

Abstract Air-water two-phase flow in circular pipes has been studied by many investigators. Because of the important effect of flow patterns on the flow and heat transfer, investigations on flow patterns are still very active. On the other hand, investigations of flow patterns in noncircular pipes are still very rare. Triangular tubes have found a great deal of applications in many fields of industry, especially in heat transfer equipment, such as compact heat exchanges, solar heat collectors, miniature heat pipes, nuclear reactor cores and electronic cooling systems. While a large number of studies have been made of turbulent single-phase flow in triangular geometries, very little has been done with two-phase flow. The present investigation was to study the effects of triangular pipe geometry and orientation on flow patterns, slug frequency, and liquid film dryout in gas-liquid flows. Experimental investigations on the flow patterns of air-water two-phase flow in horizontal circular and triangular pipes were carried out. The circular test section consists of a 2-inch (50.8 mm) ID, 28 ft (8.53 m) long clear PVC pipe followed by an equilateral triangular pipe 20 ft (6.1 m) in length having a side length of 2.7-inch (68.6 mm), corresponding to hydraulic diameter of 1.56-inch (39.6 mm). In addition, the effect of corners on the liquid distribution was investigated using two different orientations of triangular channel (apex upward and downward) with comparison to round tubes. Video cameras were positioned 60 and 120 diameters from the inlet of each test section to investigate the flow development. Superficial liquid and gas velocities that ranged from 0.3 to 6.6 ft/s and from 3.1 to 65.6 ft/s, respectively. Different understandings of two-phase flow regimes affected by the shapes of the cross-sections of the channels were obtained by flow visualization. The following flow patterns at different air and water superficial velocities were recognized for both pipe geometries: slug flow, pseudo-slug flow, stratified-wavy flow, and annular flow. Visual observations revealed that the slug frequency in the triangular channel is lower than the frequency obtained in the circular pipe.

ABSTRACT One of the urgent and time-consuming problems in the area of oil and oil products transportation is the problem of oil cargo flows scheduling in trunk pipeline systems. The problem is complicated by the necessity to take into account both the characteristics of the oil pipelines themselves, the properties of oil and capacity of tank terminals. The relevance of this topic is due to the deterioration in the composition and properties of incoming oil to the pipeline systems from suppliers, the increase in the share of high-sulfur oils and the need to supply low-sulfur oil to consumers. The article considers a new approach to oil transportation scheduling in branched oil pipeline systems. A new approach based on mathematical model that solves the optimization transport problem. The transport problem is formalized as a system of objective function and constraints then this system is solved using linear and sequential quadratic programming methods. The system can be varied depending on the needs of a given pipeline system. The approach allows to compute oil flow distribution during the certain time period (day, week, month, etc.) with given time sampling (hour, day, week, etc.) considering pipeline characteristics (flow capacity, technological regimes, etc.), oil properties (mass sulfur fraction, density, etc.) and capacity of tank terminals. Also, the approach allows to optimize oil transportation by energy consumption. The possibilities of the proposed approach are shown using a system of 10 oil pipelines, 4 transitional tank terminals, 3 oil suppliers and 6 oil consumers. The result of flow distribution calculation in a branched system is the schedule of cargo flows for each pipeline in a whole pipeline system with all constraints satisfied and optimized objective function.

ABSTRACT Presently one of the methods of increasing pipeline capacity is using the drag reducing agents (DRA). DRA are typically high molecular mass polymers that are added at very low concentrations to reduce the pressure drop necessary to generate a given flow rate in a turbulent flow. They can be used in case if building of extra loops or pumping stations is impossible or the need to increase pipeline capacity is seasonal. Scheduling pumping regimes and calculating the amount of drag reducing additive necessary to achieve the specified pumping parameters, requires a mathematical model. This paper proposes a method that allows to integrate DRA into a mathematical model of viscous fluid motion in a pipeline. The model takes into account the degradation of DRA as the agents travel forward the pipeline. This article focuses on the question of theoretical model adjustment to the characteristics of a certain pipeline. Using the nominal information about DRA (provided by manufacturers) generally leads to a strong error and some information needed for the modeling might not be provided at all. Thus, the model needs to be tuned to the real DRA characteristics and the main source of data are real measurements of flow parameters (pressures, flow rates, etc.). Methods of using operational pipeline data for identifying DRA characteristics are considered. The issues of data collection and further data processing are discussed. The results of comparing modeling computations with real data from operating pipelines are presented. The characteristics of these pipelines are very diverse: internal diameters vary from 0.4 m to 1 m, different DRAs are used, and different types of liquid (oils, oil products and gas-condensates) are pumped.

ABSTRACT Economically optimizing DRA within a crude pipeline is simple when using an optimization program, however it is challenging and important to understand how the optimization works. This paper will address a methodology of how DRA and power are optimized to minimize economic costs. Then an analysis will look into how velocity, fluid viscosity, DRA performance, pump spacing, pipe size, cost of electricity, and cost of DRA affect economic optimization results. Finally, this paper discusses several key factors that affect decisions such as building new stations or laying new pipelines versus increasing DRA injection rates into existing assets. APPROACH Energy is consumed in order to move a barrel of oil. DRA decreases the amount of energy that is required to move that barrel of oil. A price associated with both energy consumption to transport a barrel of oil and DRA utilized to reduce the energy consumption. The goal of optimizing DRA usage is to minimize the total cost to move each barrel of oil from origination to destination.

ABSTRACT A novel model is used to predict the inception moment and location of a phenomenon known as the column separation or slack line. The existing models for prediction of the cavitation phenomenon in internal flow systems in general are primarily formulated for the capture of the inception moment and initial location of the event only. Hence questions such as where the incepted cavities and bubbles tend to go, or the detailed state of a slack line in time should be addressed using a different approach. The model presented in this paper is validated and verified against experimental data available in the literature before being applied to a 53 Km (33 miles) industrial pipeline. Imposing conditions at the injection and delivery ends of the line tests various scenarios causing column separation. Hydraulic parameters such as pressure head and flowrate as well as interfacial mass transfer rate of the incepting and collapsing bubbles and cavity zones are predicted in real time over the entire domain of space and time. The results predicted the fate of the separated column of the fluid, whether they rejoin or continue to change the size with different rates or even if they become stabilized stationary cavity pockets after passage of minutes or hours. Results are also compared based on the initial cause of the column separation such as huge transients. Also, accurate prediction of the whole column separation event, distinguishes it from other events, which would commonly mimic or mask the column separation by exhibiting identical hydraulic footprints.

ABSTRACT The purpose of the paper is to demonstrate the experience with distributed computing systems using evolutionary strategies for optimization problems in the gas industry. Two different approaches of distributed computing (cooperating agents and Client-Server) are presented. INTRODUCTION Transient optimization of a gas transport is a long-term challenge [2], [5]. Various optimization procedures have been proposed in the past, which excessively simplified the transport system: e.g., eliminated technological constraints on compressors and pipelines. In addition, a network without controllers or check valves is often assumed. However, these simplifications can lead to inapplicable solutions. The aim of this article is to optimize the transition between two steady states using a sufficiently realistic simulation, with a complete optimization lasting no more than 30 min. It means to get sufficiently accurate results in a time sufficiently short for practice. Our design is based on an already developed gas transport simulator (for 1 CPU) that takes into account a large number of real technological and contract constraints [8], [9]. The optimization solution based on existing simulator opens a possibility of using other simulators in a similar way.

ABSTRACT Transient optimization of gas pipelines has experienced a resurgence of interest inspired by the need to coordinate intraday operations of wholesale electricity and natural gas transmission networks. Comprehensive modeling of pipeline components and network topologies; scalability, speed, and accuracy of computations; and data assimilation of state estimates and forecasts in industrial systems continue to present challenges. Yet, a mechanism for organized exchange of information between optimization-based auction markets for scheduling energy production and delivery over electricity and gas networks is increasingly critical. Implementing an economically and operationally efficient intra-day coordination mechanism for these systems will require advances in how pipeline optimization uses real-time data streams to produce real-time control solutions. In this paper, we review recent progress to test possible gas-electricity system coordination mechanisms, and highlight research and development needs required to field a future transient optimization-based decision support system for midstream gas transportation.

ABSTRACT We present an algorithm that dynamically reorders the evaluations in a parametric study to find the "interesting" areas sooner rather than later. In some circumstances it can be much faster than traditional studies. Reduced time means faster turnaround for studies, shorter decision cycles, and allows a higher number of dimensions than would normally be considered. We give a simple explanation of the method and present some specific use cases on existing pipelines. We believe this algorithm will be useful for broad categories of problems in pipeline (and other) industries.

ABSTRACT Analysis of the operating risk due to hazardous liquid pipeline spills is a challenging task. One reason for this is the fact that the spill probability and the magnitude of the release are both difficult to quantify for any particular pipeline. One source of comprehensive information regarding spills in the United States is the Department of Transportation (DOT) Pipeline and Hazardous Materials Safety Administration (PHMSA) hazardous incident database. This database is a mandatory compendium of spill incidents dating from 1968, and relies on self-reporting on the part of pipeline operators. We use this database to calculate historical average spill incident rates for various designated spill causes, and demonstrate a methodology using a tail risk analysis of the limited release orifice information supplied by the database to calculate a more complete aperture probability distribution for those causes. The incident rates developed by this analysis are then adapted to obtain more reliable incident rates for a particular pipeline by using the PHMSA results as a prior estimate and implementing a Bayesian posterior update based on historical sparse spill information for that system. We conclude by showing how the information obtained can be used in conjunction with pipeline hydraulic, leak detection performance, logistic response, and other models to perform a probabilistic cost-based risk analysis for the pipeline system.