ABSTRACT Due to the constant need of improving flow, pressure and pipeline throughput for single phase flow in fluid pipelines and due to extensive injection of DRA into pipeline networks, whether to supply an increased demand of customers or uprate an overall throughput of a pipeline system, a need to find ways to optimize the effect of DRA injection on the flow rate and pressure has become essential in the pipeline industry. This study looked into the effect of drag reducing agents on the flow rate and pressure of single phase flow in fluid pipelines. Reviewing the literature helped a lot in planning a methodology that explains how the investigation is carried. The methodology started with selecting a pipeline network to be case studied and then utilizing an advance tool that can perform hydraulic pipeline calculations to simulate various cases. After that, results are evaluated, analyzed, and discussed to make sure that they match with the obtained current pipeline data. To optimize, a hydraulic simulation tool called SPS is used to simulate cases where effect of DRA on the flow rate and pressure is improved. Having gone through several investigations on how to optimize the effect of DRA on the flow rate and pressure of single phase fluid pipelines, a number of recommendations has been made to modify several factors that eventually lead to optimization of the effect of DRA. Initially, the definition and characteristics of DRAs has been made clear and understood to be able to know more about what is being researched and investigated. Additionally, the mechanics behind drag reduction have been understood and the effect of DRAs on the flow rate and pressure of pipelines once injected has been understood. Factors such as location of DRA injection, DRA type vs. %Dr, and DRA concentration have been proven to be effective in optimizing the effect of DRA based on the results of the simulated cases. Savings reaching up to $4 Million on spending for one type of polymeric DRA injection were the results of only one factor contributing to optimization which was the location of DRA injection.

ABSTRACT One of the most important aspects when transporting multiple different liquid products within the same pipeline, is being able to know where the head and tail of each batch is at any given time based on the current operation to provide an accurate Estimated Time of Arrival (ETA) at upcoming stations. With this information, pipeline operators can be ready to execute valve swings at intermediate delivery and injecting stations helping minimize product contamination. It is relatively simple to track these batches and their interfaces when the pipeline has a uniform and gradual elevation profile. However, when pipelines travel through mountainous regions with high and drastic elevation changes, the ability to track the head and tail of these batches become far more complex due to the presence of slack. When slack is present, the common assumption that the volume of liquid equals the physical volume of the pipe is no longer valid. The fraction of the pipe filled with liquid, called the "liquid holdup", has a large impact on the position of the batch head and tail. As a result, the accuracy of the volume contained within the region and the corresponding Estimated Times of Arrival at upcoming stations are directly affected. An empirical approach using volume accumulation at a pipeline injections and deliveries has been successfully implemented with an end user to account for the liquid volume within a specific region known to have slack during normal operations. However, this approach does not provide an accurate solution for the exact location of where the slack occurs, nor the size of the slack itself, which has a direct effect on the location estimate for when the head or tail is passing through the area. With the current empirical approach, Estimated and Actual Times of Arrival are within a 15-minute time window after a batch has traveled a total distance of 1,200 km (746 mile) with a drastic slack region along the route. This paper provides an analysis on the current empirical approach used in the daily operation by the existing end user, and how the results compared to a full scientific approach running a slack model based on the field instrumentation, and the physical properties of the pipeline.

ABSTRACT It is a challenge to simulate the surge relief valve behavior accurately and handle the "minor frictional losses" from the pipe fittings in the terminal transient analysis. Some hydraulic engineers model the surge relief valve with the assumption that it will perform as ideal default behavior, and proposed relief set points based on the ideal default behavior may not prevent the maximum surge pressures from exceeding 110% maximum operating pressure (MOP) of terminal piping in real-world operations. Furthermore, aggressive relief settings will limit the mainline's capacity. On the other hand, over-conservative relief settings will cause nuisance pipeline start-up failure and relief shutdown events. A terminal hydraulic study was performed, which included both steady-state and transient analyses. Steady-state simulation is applied to determine the terminal system design, while transient simulation is used to assess the surge potential in the piping system to prevent the pressure dynamics from exceeding 110% of the maximum allowable operating pressure. A mainline pump trip scenario in the terminal is usually the most severe surge event; therefore, a surge relief system is typically installed at the pump's suction side (the pressure specification break point) to protect the lower pressure rated terminal piping from an over-pressure condition after the pump station trip. This paper discusses the use of an advanced simulation method to successfully match the real suction surge pressure trends for the worst-case terminal transient scenario: the mainline pump station trip accompanied by a surge relief event. The methodology includes arithmetically coding dynamic relief set points and applications of equivalent length in the terminal transient study.

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 Heavy oil accounts for more than half the word's total oil reserves. However, heavy oil as extracted from the reservoir has an extremely high viscosity and the transportation of these fluids in a pipeline requires the use of technologies to lower the viscosities of this oil. Among these technologies are heating or dilution of the heavy oil and sometimes a mixture of both of these methods. The majority of oil storage terminals contain pipes that are installed above ground and in northern countries are prone to experiencing cold temperatures during winter months. In part of the terminal where the fluid stays stagnant in the pipes (such as relief piping and manifold pipes) the cold weather can impact the viscosity of the fluid, even after it has been diluted. When the pumping system has to move fluid that has been stagnant in the pipe and has become colder, the pressure required to achieve this is very high. The transient surge pressures created in these cases can become extreme to the point of exceeding the maximum operating pressures of the pipe. When performing transient simulations, it is important to consider the fluid with higher viscosities that have been kept in the pipes and that will require higher pressures to pump them down the line, so that pressure surges can be more accurately calculated and mitigated. This paper will present comparisons of how the transient pressures change between cases of heavy oils at different temperatures and viscosities. It will show that if heavy oil is kept stagnant in a pipe that is subject to cold temperatures, the pressures required to push this fluid down the pipe increases as the viscosity becomes higher. IN particular, it will present the case where the relief piping has been installed above ground and when the fluid needs to be displaced, the surge pressures can become significantly higher than expected.

ABSTRACT LNG Terminals represent key infrastructure for gas markets in many regions. With markets shifting to a more global approach, what happens when your operational cases evolve, and the original design specifications are challenged? Or worse an operational event exposes weakness in the design? The priorities on any site continue to be around safe, profitable operation and maximising capacity/uptime. Under normal operation piping systems can withstand the resulting stresses. Events such as rapid PERC (powered emergency release coupling) closures, Emergency Shut Downs (ESDs), valve operations, and pump trips can all create transient effects. Consequences can include excessive surge pressures which in turn lead to increased pipe stresses and structural loads. An ongoing relationship with a large LNG terminal operator has driven studies into hydraulic surge in pipelines following Emergency Shut Down (ESD) events and developed this hydraulic understanding to include bend forces and resolved pipe forces which could be passed into targeted structural analysis. Over time, scenarios have become more complex including for example an increasing need to be able to re-load ships from a site originally designed as an import terminal. Alongside the technical challenge of these studies; a key factor was generating justifiable rationalisation of all permutations of operating scenarios into a manageable quantity of worst-case simulations for a multi-tank and multi-jetty site. Combined with the increasing complexity of cases we were required to develop methods to run simultaneous simulations and manage the model files and outputs in a reliable fashion. More recent work has led to feeding the force outputs into static and dynamic load analysis to understand the force and harmonic interactions with the physical structures on the site. Pressure and force results were extracted for each scenario using a high-fidelity hydraulic model and then utilized in structural analysis tools for further analysis. This paper outlines the evolution of a complex modelling problem, and the effects of working on an inherited model from a 3rd party and architecture built on scripting tools to solve problems now integrated into our modelling solution. With the concept of simultaneous modelling runs and parametric studies commonplace in today's environments, we consider the progression of this approach to meet future requirements.

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 Many gas compressor stations use multiple gas turbine driven centrifugal compressors. In many instances, the units are not identical. The challenge is to control the units such, that certain operational parameters, for example fuel consumption, pipeline capacity or maintenance requirements, are optimized. The discussion includes the use and sizing of multiple units, the arrangement of units, the arrangement as push or pull compression, as well as examples of optimization strategies at various levels of sophistication, up to and including the integration of hydraulic and turbomachinery optimization. The benefits of methods that control compressors for the same turndown, or to control all gas turbines for the same load. This methodology can be derived and discussed for the case of identical machines, and will be expanded for the case where the compressors and their drivers are not identical. The control system has to rely on measurable parameters, but the system has to be reliable even if parameters that are not directly measured change during operation. The paper describes a variety of optimization methods, starting with a simple algorithm, then comparing equalization methods, and finally illustrating the capability of methods that combine turbomachinery optimization and the optimization of pipeline hydraulics. An example demonstrating the potential fuel savings of such an optimization is given.

ABSTRACT Upstream gas supply planning and allocation contains 3 cycles namely long term (20 years - end of life of a field) mid-term (up to 1 year) and short term (72 hours). Since the upstream assets are owned/operated by different companies under various production sharing contracts, each of the operating companies prefer to maximize their production and recover the investment costs at the earliest. A regulator acts as a custodian to ensure that all stakeholder's entitlements are protected. The custodian relies on economic and hydraulic modelling to analyse the production plateau's shared by various operating companies together with the demand profiles for viability. The commercial planning team of the custodian works closely with flow assurance engineers before confirming the production numbers as the planners are unaware of any capacity constraints in the physical network for flow. In the short term, an integrated network operator breaks the long term demand numbers and controls the network for seamless delivery of gas from upstream to LNG plants (mostly). The purpose of the paper is to highlight the challenges faced by planners and engineers during the planning cycles and to make appropriate recommendations.

ABSTRACT In the design and operation stages of multiphase pipelines, prediction of flow temperatures and pressure variations is important. Dynamic evaluation of process changes in real-time and calculation of thermodynamic properties of multi-component mixtures is challenging. In this paper a mechanism to counter phase change losses due incorporating real-time dynamics is presented. A case-study for a major oil and gas distribution company with real-world deployment and observation has been included. The model provides notification of changes and displays a PT-phase diagram using different gas compositions and oil assay data to compare the phase changes in model and commercial pipelines in real-time. With density and viscosity considerations in the approach, gas condensation alarms are raised dynamically depending on the total vapor fraction in the mixture.

ABSTRACT This paper defines and studies a simple, efficient method for discretizing pipeline equations in time. In many ways the solutions of pipe flow equations look like the solutions of nonlinear diffusion equations, so it is natural that schemes that work well for diffusion problems might have analogs for pipe flow problems. The method presented here is based on backward Euler (BE). To advance the solution from time t to time t+dt it uses a single step of BE with step size dt and two steps of BE with step size ????/2. The results are then combined to give a second-order correct scheme. This process is called step doubling with local extrapolation (SDoLE) and has been rigorously analyzed for nonlinear diffusion problems in the context of Galerkin spatial discretizations. [1] Here a collocation scheme is the underlying discretization in space and time. The backward Euler that forms the basis of this method is done using a linearization technique instead of solving a nonlinear system. This is extended to minimize the computational costs associated with evaluation of the nonlinearities in the equations. The resulting discretization technique is called affine step doubling with local extrapolation (ASDoLE). The properties of the method are explained by looking first at a scalar ODE and then by presenting examples based on pipeline operation. A single pipe case is given followed by a simple gun barrel example.

ABSTRACT An important variable considered in the sizing and design of pipelines is the absolute roughness of the pipe, which is used to calculate the pressure loss during fluid flow through the pipeline. The default value for absolute roughness of commercial steel pipe, as generally used in the industry, is 1800 micro-inch (or 46 micro-metre). This value appears to have originated from studies carried out by scientists such as Pigott, Colebrook, Moody and Nikuradse, among others, more than half a century ago. However, pipe manufacturing and treatment methods have become more advanced since these studies were performed. Indeed, recent studies have suggested overestimation of the pressure drop across a pipeline during design resulting in less accurate cost estimates for pipeline projects. In this study, the absolute roughness of various pipeline samples was measured using a Mitutoyo SJ-201 surface roughness gauge. The samples were obtained from commercial steel pipes of different diameters that had been manufactured with various methods including: seamless hot-rolling, cold-drawing, cold pilgering, hot expanding, and welded HFIW and DSAW processes. Absolute roughness values were also obtained for pipes treated differently by: simulated post-weld heat treatments, sandblasting, and ultrasonic cleaning. Recorded average pipe roughness values ranged from 57 micro-inch for stainless steel pipe to 1034 micro-inch for heat treated carbon steel pipe. All measured values were less than the generally used 1800 micro-inch (or 46 micro-metre) value. There did not appear to be any correlation between the diameter of the pipe sample and the absolute roughness observed. The pipes that were manufactured using the hot-rolled method typically showed higher absolute roughness values. Furthermore, simulated post-weld heat treatments at higher temperatures correlated with higher absolute roughness values for heat treated pipe. This paper also examined the impact of applying a range of measured absolute roughness values during the design of liquid and gas pipelines. The pipeline pressure loss was calculated using different roughness values for case studies involving multiple crude oil pipelines and a natural gas pipeline. The results indicated that gas pipelines are more sensitive to the absolute roughness value. Furthermore, liquid pipelines with relatively high Reynolds number are more likely to undergo noticeable capacity loss because of absolute roughness increases due to pipe degradation.

ABSTRACT A risk assessment for a new pipeline system is an authority requirement. The risk assessment for a new pipeline system is based on several assumptions and parameters for planned design and operation and is in most cases conservative due to uncertainty in actual conditions. During the lifetime of a pipeline systems these parameters are likely to change, and consequently the risk assessment is no longer representative for the actual operational risk level. Authority requirements also states that a new risk assessment shall be performed when significant assumptions change. In-depth knowledge of risk calculations, pipeline simulations and assumptions are a prerequisite to be able to evaluate whether a change is significant with regards to risk level. The pipeline risk assessment must be well known by the operator to ensure solid risk management for a pipeline in operation. This implies knowledge of uncertainty in assumptions, condition of integrity, operational parameters, environmental data and how these parameters will affect the risk level in certain areas. This paper will discuss the uncertainty of different assumptions and parameters and how they affect the operational risk level for oil/condensate pipeline systems. The focus in this work has been to create a standardized cross-discipline work process to increase operational knowledge of risk factors and decrease the level of uncertainty in assumptions and input data. A combination of data sources and simulation tool are used to calculate a representative pipeline risk level, which will give the operator a solid basis for continuous risk management, decision support and emergency preparedness planning.

ABSTRACT Refining NZ is New Zealand's only oil refinery and the leading supplier of refined petroleum products to the New Zealand market, including gasoline, diesel, jet fuel and other products. It supplies most of the fuel needs for Auckland through a 169 kilometre (105 mile) long, 273 millimetre (10.75 inch) diameter pipeline terminating at the Wiri Terminal in South Auckland. To meet the growing demand for jet fuel, Refining NZ started a pipeline capacity increase project in 2017. The first 2 of 3 phases of this project have been completed with the 3rd phase due to kick-off in 2019. Refining NZ rely on an Online Real-Time Transient Modelling (RTTM) system to provide decision support applications for the pipeline controllers such as batch tracking, scraper tracking and leak detection. The RTTM was updated in 2017 to include the changes made in the pipeline operation. On September 14th, 2017, Refining NZ experienced a significant incident on the pipeline which threatened their business. This paper details how Refining NZ use their RTTM as a decision support tool, some key learnings from the incident, including analysis of the incident using the RTTM, and what Refining NZ has done to improve its operations as a result of the incident and the subsequent analysis.

ABSTRACT Pipeline data analysis utilizing machine learning method is present in this paper. Three machine learning models using Artificial Neuro Network methods are constructed to use nominal flow rate and head loss as input and pipeline roughness change, internal diameter change, a potential leak (location and leakage rate) as output. Half of the data created from the hydraulics model were used to train the Neuro Network. The rest of the data were used to validate the results of the network. The Neuro Network model was trained with the assistance of hydraulics equations. The advantage of the new method is that it provides an artificial intelligence to reveal the flow condition such as the ID, roughness, and leakage directly from the pressure and flow rate measurement data through machine learning without the necessity to compare with hydraulics model. The study presented in the paper try to demonstrate the potential way of using machine learning and artificial intelligence in pipeline data analysis and operation analysis.

ABSTRACT Ultrasonic flow meters, in addition to calculating flow rate, measure the speed of sound in the fluid at the local fluid pressure and temperature. It is desirable to be able to compute the crude oil specific gravity at base (i.e. standard temperature and pressure) conditions from this measurement. However, there is no straightforward way to do this, in large part because there is no accepted standard for computing crude oil sonic velocity as a function of pressure, temperature, and base density. The authors develop an approach for computing sonic velocity for crude oil. Using this as a foundation, they propose a calculation approach to compute crude oil specific gravity as a function of observed speed of sound, pressure, and temperature. OVERVIEW The motivation for this work was to be able to compute crude oil density from sonic velocity, pressure, and temperature. Pipeline companies often have ultrasonic flow meters at pump stations that, as part of measuring flow, compute sonic velocity. Because of cost, densitometers are usually much more sparsely spaced. Since elevation head depends directly on density, a measurement of fluid density can improve hydraulic modeling calculations.

ABSTRACT Sand management technology has become more prevalent in the petroleum industry to increase well production. Sand may deposit on pipeline walls, causing problems such as pipe blockage, reduced flow area, structural pipe issues, abrasion, corrosion, and low production in wells. This paper explores the multiphase model and computation algorithms used to simulate multiphase flow with sand particles through a subsea pipeline to predict the pressure gradient, transport velocity, and sand deposition. Being able to predict sand accumulation and understanding real-time sand velocity in a pipeline can help define design criteria for subsea pipelines and help pipeline operators maximize production while minimizing well and pipeline downtime. INTRODUCTION Sandstone reservoirs are the source for most of the world's hydrocarbons; however, sand is a common by-product of oil and gas production, especially when producing from reservoirs with low formation strength. When rock around the well perforations is weak, the reservoir fluids can push sand or solid material into the wellbore. Sand in the produced oil and gas enters the pipeline network, which can increase frictional pressure loss, pipeline damage due to erosion, potential equipment failure, and sand deposition (causing flow assurance problems and pressure changes). The traditional sand management method involves preliminary sand extraction from the produced fluid before it is released into the main pipeline. Unfortunately, this method is expensive and not applicable in all cases, such as deep, subsea pipelines. As a result, newer sand management methods focus on tracking the amount of sand in the pipeline and operating the pipeline at conditions that minimize the risks. With these new sand management methods, pipeline simulations become an even more powerful tool for pipeline operators to identify the influence sand has on pressure and temperature changes in the pipeline, detecting erosion and sand deposition, and understanding the impact different operating conditions have on the pipeline performance and safety. This paper discusses a set of sand management modeling and simulation algorithms and approach to detect sand deposition and erosional velocity. The approach was applied to a cluster of offshore platforms and wells connected by a subsea pipeline; in the case described, these simulated sand deposition and erosional velocity events were compared to real-time pipeline data—including theoretical and actual pipeline pressure loss—and verified, allowing the pipeline operator to take appropriate mitigation actions and reduce lost production opportunity.

ABSTRACT This paper presents specialized simulation techniques addressing some of the unique challenges related to modeling of heavy crude (dilbit) pipeline systems. These techniques were developed to improve the accuracy and effectiveness of modeling efforts associated with simulation of seasonal operation and product blending, and include methods to modify fluid properties and other characteristics with simulation coding. INTRODUCTION AND BACKGROUND Heavy crude generally refers to oil of density higher than 900 kg/m 3 . Pipelines shipping products from oil sands production sites typically transport fluids heavier than those servicing conventional oil fields. The bitumen produced either by open mining or SAGD method is often mixed with light condensate ("diluent") to meet pipeline specifications. The mixture of bitumen and diluent is called "dilbit". The dilbit system discussed in this paper can be viewed in Figure 1 . This system originates at the SAGD facilities in northern Alberta and terminates in Edmonton. It includes: LACT (Lease-Automatic Custody Transfer) facilities at each of the SAGD sites. 300 km (186 mile) of NPS42 pipeline ("Upstream Pipeline") 50 km (31 mile) of NPS30 pipeline ("Delivery Pipeline") Trim blending (diluent injection) and product quality monitoring facilities located between the Upstream Pipeline and the Delivery Pipeline. Mainline block valve stations Pig launchers and receivers for each pipeline This paper will discuss the major considerations and simulation techniques in connection with the unique challenges associated with modelling dilbit systems.

ABSTRACT Liquid pipelines through mountainous terrain often experience slack flow: the pressure at the high point drops to the fluid's vapor pressure and a bubble of vapor separates out of the liquid. The bubble grows and shrinks as conditions in the line change and as hydraulic transients move through. Accurately simulating this situation is necessary for leak detection or any other transient model application on such a system. Physically, the start of the vapor bubble is usually "pinned" to the top of a hill with the bubble extending downhill and downstream. As hydraulic transients move through, the bubble grows longer and shorter at the downstream end. The movement of the bubble end over a model time step is typically much smaller than a model's distance step, so it is a challenge to model it accurately. Traditionally, slack models have approximated the movement of the bubble end by fudging the amount of liquid in the mesh intervals around the end so that mass was conserved. This work describes a new model that ties a moving mesh point to the downstream end of the vapor bubble, so as to exactly capture the transient variations of bubble size. The paper will discuss the challenges in simulating this moving knot in a semi-explicit model; extension of this model to the complete draining and filling of a pipe; dealing with bad or limited knowledge of the pipe elevation profile, which is critical to the behavior of the two-phase region; and will also show comparisons between this simulation and slack-region draining and filling on a real pipeline. INTRODUCTION AND BACKGROUND Many liquid pipelines experience slack. Slack is combined vapor and liquid flow that occurs when the pressure in the pipeline drops to the vapor pressure of the liquid. It is also commonly called "slack-line flow", "column separation", and "vapor pockets". Slack can be caused in several ways. It can happen in a flowing pipeline, even in steady conditions, when the pipe goes over a large mountain; it can happen in a shut-in pipeline as it cools (even in the absence of any large elevation changes); and it can happen downstream of a valve that is suddenly closed, due to pressure drop from the surge. All of these types of slack will be discussed in detail below.