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Proceedings Papers

Publisher: Pipeline Simulation Interest Group

Paper presented at the PSIG Annual Meeting, May 3–7, 2021

Paper Number: PSIG-2101

... parametric study production monitoring upstream oil & gas friction factor model parameter commercial simulator brett christie psig 2101 inlet pressure university critical zone

**reynolds****number**Abstract Crude oil pipelines can occasionally experience flow regimes in the critical section...
Abstract

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.

Proceedings Papers

Publisher: Pipeline Simulation Interest Group

Paper presented at the PSIG Annual Meeting, May 3–7, 2021

Paper Number: PSIG-2113

... model production control upstream oil & gas friction factor production monitoring midstream oil & gas pipeline location detection neuron input data credibility standard deviation equation leakage psig 2113

**reynolds****number**relative error precision PSIG 2113 Verification...
Abstract

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.

Proceedings Papers

Publisher: Pipeline Simulation Interest Group

Paper presented at the PSIG Annual Meeting, May 14–17, 2019

Paper Number: PSIG-1903

... and by whom the paper was presented. Write Librarian, Pipeline Simulation Interest Group, 945 McKinney, Suite #106, Houston, TX 77002, USA info@psig.org. ABSTRACT The Austin-Palfrey equation could be directly applied to a pipeline where both the

**Reynolds****number**and the pipe diameter are not varied...
Abstract

ABSTRACT The Austin-Palfrey equation could be directly applied to a pipeline where both the Reynolds number and the pipe diameter are not varied along the entire length and where there is no initial mixing volume at the start point of the pipeline. If the Reynolds number, or the pipe diameter, or both are varied along a pipeline, the pipeline should be divided into segments based on the point along the pipeline where Reynolds number or the diameter change. The Austin-Palfrey equation should be revised to include effects of the initial mixing volumes in subsequent segments. In this study, the Austin-Palfrey equations were revised by introducing an initial pipe length or an initial length factor to incorporate the initial mixing volumes at the start point of each pipe segment. The revised equations could predict the mixing volume along the entire pipeline length. The initial length factor has an impact on the incremental mixing length in subsequent segments. When the initial length factor is larger than one, the mixing length in subsequent pipe segment tends to decrease. When the initial length factor is less than one, the mixing length in subsequent pipe segment tends to increase.

Proceedings Papers

Publisher: Pipeline Simulation Interest Group

Paper presented at the PSIG Annual Meeting, May 14–17, 2019

Paper Number: PSIG-1926

... 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. INTRODUCTION AND BACKGROUND The absolute roughness of a pipe...
Abstract

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.

Proceedings Papers

Publisher: Pipeline Simulation Interest Group

Paper presented at the PSIG Annual Meeting, May 15–18, 2018

Paper Number: PSIG-1801

... model are widely used for liquid pipelines, one correlates Drag Reduction (DR) as a function of DRA concentration only, and the other correlates DR as a function of DRA concentration and

**Reynolds****number**. Both are pipeline and fluid specific, that is, have limitations to pipelines similar to the tested...
Abstract

ABSTRACT Predicting the efficiency of a DRA is still dependent on the use of models developed through field tests. Two forms of the model are widely used for liquid pipelines, one correlates Drag Reduction (DR) as a function of DRA concentration only, and the other correlates DR as a function of DRA concentration and Reynolds number. Both are pipeline and fluid specific, that is, have limitations to pipelines similar to the tested in pipe size and fluid property, and the former also has limitations in flow rates. This paper presents a comprehensive model in which three more variables are introduced - type of DRA, pipe diameter and fluid viscosity - in addition to DRA concentration and Reynolds number so the model applies to a variety of pipelines and a wider range of fluid properties. Field tests show that DRA degrades, or the effective concentration of a DRA decreases as it flows through pipelines. So, a DRA degradation coefficient was also introduced in the model as a supplement to the variable of DRA concentration. The type of DRA used for crude oils is usually different from that for refined products and, most of all, the difference in fluid viscosity, therefore in Reynolds number, is so great that it is hard to develop a model suitable for both crude oils and refined products, so a separate model is developed for the products. INTRODUCTION AND BACKGROUND Drag reducing agents or DRA have been used in the pipeline industry for decades to improve fluid flow in pipelines. They are any material that reduces frictional pressure loss during fluid flow in a conduit or pipeline. Pressure loss reduction is achieved by reducing the level of turbulent motion in the flow. Using DRA allows increased flow using the same amount of energy or decreased pressure drop for the same flow rate of fluid in pipelines. [1]

Proceedings Papers

#### A Conceptual Framework for Predicting the Effectiveness of a Drag Reducing Agent in Liquid Pipelines

Publisher: Pipeline Simulation Interest Group

Paper presented at the PSIG Annual Meeting, May 6–9, 2014

Paper Number: PSIG-1418

... operating conditions and flow geometry. This work is an attempt to provide a conceptual framework wherein the effects of operating conditions and flow geometry, expressed by

**Reynolds****number**, and polymer concentration on drag reduction are quantified. The proposed model has been validated over a wide range...
Abstract

ABSTRACT Different types of polymeric Drag-Reducing-Agents (DRA) have been used in liquid pipelines to overcome the capacity limitations and/or reduce the cost of utility by lowering the pressure drop. Optimum usage of DRA depends on how accurately pipeline operators can predict its drag reduction efficiency. The most widely used model in pipeline industry for predicting the drag reduction efficiency correlates drag reduction as a function of DRA concentration alone. However, in reality drag reduction can be significantly different from the predicted one depending on the variations in operating conditions and flow geometry. This work is an attempt to provide a conceptual framework wherein the effects of operating conditions and flow geometry, expressed by Reynolds number, and polymer concentration on drag reduction are quantified. The proposed model has been validated over a wide range of operating conditions, DRA concentrations and pipe diameters for two types of commercially available DRA fluids using field test data. Overall, the proposed model gives an excellent reduction in the variability of drag reduction as a function of respective regressor variables. INTRODUCTION The concept of polymeric drag reducing fluids was introduced in the oil industry as early as 1946; however, its commercial application was not practiced till about 30 years later in the Trans-Alaska pipeline system where the capacity of the pipeline was increased from 1.4 to 2.2 million barrels per day solely by using DRA. Nowadays, different types of drag reducing products are commercially available and pipeline operators benefit from DRA to increase the pipeline capacity and/or reduce the cost of utility by lowering the pressure drop, globally. In some cases the drag reduction is so dramatic, that pipeline operators are able to shutdown selected pump stations without any noticeable drop in the overall throughput.

Proceedings Papers

Publisher: Pipeline Simulation Interest Group

Paper presented at the PSIG Annual Meeting, April 16–19, 2013

Paper Number: PSIG-1305

... commercially available code demonstrated to be able to predict pressure drop and temperature development with high accuracy. Viscosity is considerably less important but starts to influence frictional pressure drop at lower

**Reynolds****number**Correct prediction of viscosity will be more important in...
Abstract

ABSTRACT Gassco has been given the task by the Norwegian Oil Directorate to evaluate and design solutions for subsea pipeline transportation of captured CO 2 from large CO 2 point sources into suitable storage locations on the Norwegian Continental Shelf. As part of the underlying pipeline design work, numerical simulations of the fluid flow have to be undertaken. In this paper the ability of a selection of pipeline flow simulators to calculate fluid temperatures and pressures during steady-state transport of CO 2 has been investigated using different fluid representations. Commercially available pipeline flow simulators were included in the benchmarking study, and two different simulation cases were defined: Planned off-shore pipeline from Kårstø to the Utsira formation, operating in the CO 2 liquid region Existing on-shore US pipeline, operating in the CO 2 super critical region with steady state measurement data. The cases were set up and modeled using the different pipeline simulators. Sensitivities were quantified and analyzed, and the results were ranked according to the ability of treating CO2 as a transport fluid. For case 1, all simulation codes can be used provided an Equation of State (EoS) with appropriate density prediction is chosen. For case 2, only one simulation code could be used reliably, as all the other tools showed to have problems to calculate the flow accurately when the pipeline conditions approached the critical point of CO 2 . This commercially available code demonstrated to be able to predict pressure drop and temperature development with high accuracy. Viscosity is considerably less important but starts to influence frictional pressure drop at lower Reynolds number Correct prediction of viscosity will be more important in transient simulations, with low fluid velocities Further study into the effect of accuracy of heat transfer modeling on pressure drop is recommended.

Proceedings Papers

Publisher: Pipeline Simulation Interest Group

Paper presented at the PSIG Annual Meeting, May 11–14, 2010

Paper Number: PSIG-1002

... Darcy-Weisbach equation with a friction factor which depends on pipe roughness and the

**Reynolds****number**. For laminar flow, the boundary layer essentially fills the pipe. That is, the velocity varies all across the pipe. Steady-state isothermal laminar flow in a pipe, also known as Hagen-Poiseuille flow...
Abstract

ABSTRACT While single-phase pipe flow is almost always assumed to be one-dimensional, that is, homogeneous across the pipe's diameter, there can potentially be two-dimensional thermal effects in the laminar flow of high-viscosity oil. The heat that's initially imparted to the oil by heaters or by the pumping inefficiencies must conduct through the outer part of the oil before it can leave the pipe. If the oil has a strongly temperature-dependent viscosity, this can lead to significant viscosity variations across the pipe, and in turn to a flow regime that differs significantly from the usual Hagen-Poiseuille solution for laminar pipe flow. This article investigates the conditions necessary for the one-dimensional approximation to introduce significant errors in the frictional pressure gradient. INTRODUCTION Flow in pipelines is generally assumed to be one-dimensional. That is, the pressure, temperature, and velocity are assumed to be uniform across the pipe. The one-dimensional approximation for the pressure is quite accurate under nearly all conditions, since any pressure gradient across the pipe will cause the fluid to move so as to balance the pressure. There is a small increase in pressure from the top of the pipe to the bottom to balance the gravitational head, and from the inside to the outside of a bend to balance the centrifugal force of the flow turning around the bend. For pipe lines these variations are small fractions of the pressure in the pipe. Actually, it is the head that is constant across the pipe. There are variations in the velocity and the temperature near the pipe wall, because the temperature of the environment is generally different from that of the fluid and the velocity of the wall is, of course, zero. For turbulent flow the eddy conductivity is so high that the constant temperature approximation is still valid, although not perfectly accurate. Heat transfer to the pipe wall can be calculated by a heat transfer coefficient or, usually, by calculating the conduction in the pipe wall and the surrounding environment. There is always a boundary layer near the pipe wall in which the velocity varies from the bulk fluid velocity to zero at the wall. For turbulent flow this boundary layer is very small compared to the pipe radius. The momentum transfer, which we usually refer to as the frictional resistance to the flow, can be calculated from the Darcy-Weisbach equation with a friction factor which depends on pipe roughness and the Reynolds number. For laminar flow, the boundary layer essentially fills the pipe. That is, the velocity varies all across the pipe. Steady-state isothermal laminar flow in a pipe, also known as Hagen-Poiseuille flow is one of the few fluid flow problems for which an exact solution can be found1. The velocity profile across the pipe is a parabola, with zero velocity at the wall and a centerline velocity equal to twice the

Proceedings Papers

Publisher: Pipeline Simulation Interest Group

Paper presented at the PSIG Annual Meeting, October 23–26, 2007

Paper Number: PSIG-0702

... (lb/f3) CP = heat capacity, Btu/lb oF P = thermal expansion factor, oF-1 Substituting (21) into (20) for subcritical phase, ( ) ( ) 2 12 2 1 V D Lfyyg C TT p P (23) For laminar flow, the friction factor will be a function of only the

**Reynolds****number**. For more turbulent zones of flow, the...
Abstract

ABSTRACT Changes in pipeline fluid temperature can be attributed to many effects, including heating due to operating pump units or compressors, or cooling when the pressure drops below the dew point in a gas pipeline. The typically dominant effect for temperature change along the pipeline length is due to the transfer of heat to or from the surrounding ground cover. There are instances where viscous effects are significant, giving rise to a "frictional heating" effect. This paper intends to analyze the frictional heating effect for pumped fluids in the liquid, supercritical and superheated phases. The approach is to assume an adiabatic pipeline and to consider the Joule Thomson effect in detail. The focus is on hydrocarbons in liquid phase, although some interesting gas phase examples are presented. The destruction of mechanical energy into internal energy is typically implicit in the complete solution of the conservation equations. The aim here is to assist with quantification of the particular effect to confirm whether it remains significant enough to warrant careful consideration, or to dismiss it as negligible. Example real pipeline data is presented in the interest of comparing with the predictions. Derivations are provided using the first law along with available empirical data. INTRODUCTION The simulation of pressure in a pipeline is highly dependent on the density of the transported fluid. Density is highly temperature dependent; hence it is important to have a realistic and accurate temperature profile. Numerous physical effects cause temperature to vary along a flowing pipeline and the dominant effect for temperature change along the pipeline length is generally due to the transfer of heat to or from the surrounding ground cover. This paper considers the contribution to the temperature variation along the pipelines due to the turbulent viscous frictional heating effect. The frictional heating effect is discussed for pumped fluids that exist in the liquid, supercritical and superheated phases. The intention is to determine the direction and amount that temperature changes as pressure changes. Also explored are the frictional effects that cause the pressure to drop. For example, how does the velocity influence the pressure drop and hence the temperature? The background behind the theoretical basis is described followed by an introduction to the Joule Thomson coefficient and Inversion curves. A subcritical (liquid phase) fluid is described along with an example taken from practice. The supercritical and superheated regimes are also described followed by a comparison with a real-world example. BACKGROUND The total energy of a flowing compressible pipeline system consists of four parts: internal, kinetic, potential and flow energies. The combination of internal energy and flow work is termed "enthalpy". The changes in kinetic and potential energy are considered negligible in this analysis. From the first law of thermodynamics an energy balance between the inlet and outlet of the pipeline is performed. Since the purpose is to study the frictional effect at steady state conditions, the heat transfer and external work interactions are considered to be zero.

Proceedings Papers

Publisher: Pipeline Simulation Interest Group

Paper presented at the PSIG Annual Meeting, October 23–26, 2007

Paper Number: PSIG-07B3

... wave attenuation amplitude measurement and control equation midstream oil & gas disturbance piping design detector

**reynolds****number**measuring point diameter pipeline leak detection barabanov formula piping simulation Copyright 2003, Pipeline Simulation Interest Group This paper was...
Abstract

ABSTRACT In this article we present experimental results of measurements of the wave attenuation coefficient in trunk pipelines, analyzing and comparing theory with experiment. We propose an approximation for the attenuation coefficient as a function of nondimensional parameters. We also identify criteria that allow optimizing the number of pressure detectors for a pipeline based on a cost-to-effectiveness ratio of leak detection, and determine the maximum permissible distance between pressure detectors registering pressure waves. INTRODUCTION In view of the increasingly greater focus on sensitivity and other parameters of Leak Detection Systems (LDS), requirements for measuring equipment are becoming especially high. This in turn raises the cost of its delivery and installation. The cost of measuring equipment itself is only a part of the problem, as installation of a pressure detector requires installing additional telemetry systems in what is a very labor-intensive and costly process. This raises a pivotal issue as to where and how to install pressure detectors. The key to this problem lies in methods and algorithms used to detect a leak and its location. The pressure surge method is one of the most common methods of leak detection. It is founded on the use of pressure detectors (PD) that detect a negative-pressure wave (downsurge) caused by the pipeline leak. However, the wave amplitude diminishes the farther it moves from the leak point in a process known as wave attenuation, which means that if pressure detectors are installed too far apart, the leak of a certain quantity will not be detected. The problem of wave attenuation and the spacing of pressure detectors along the pipeline are the focus of research in this article. EXPERIMENT While it is possible to imagine the operation of a pipeline in a laminar flow mode, in practice this can happen only in exceptional cases. For instance, when the pipeline's operation is suspended, at one point the flow velocity will become so slow as to cause a laminar flow that will exist until the flow stops entirely. In pipelines we most often deal with a turbulent flow. When analyzing the propagation of waves in a turbulent flow, we faced the difficulty of isolating the signal of a disturbance wave against the background of constant hydrodynamic noise. For this reason, when processing experiment results we selected only those processes of disturbance propagation that had a strongly pronounced steep wave front and large amplitude. Such processes in the pipeline happed for reasons of: real leaks, closing of line valves, shutting down and starting of pumping units. Experiments were conducted only on straight-line pipeline sections without loops or with closed loops. The objects of our research were three pipeline sections. Table 1 shows physical properties of pumped fluid and flow parameters for each pipeline section.

Proceedings Papers

Publisher: Pipeline Simulation Interest Group

Paper presented at the PSIG Annual Meeting, November 7–9, 2005

Paper Number: PSIG-0505

... incompressible flow, only), and the flow furthermore is considered isothermal, the remaining part of Equation 5 can be integrated into m u / x & ( ) L D f pp TRz M m g 122 2 1__ = Equation 7 where the friction factor f(Re) has been kept constant, in view of the fact that the

**Reynolds****number**PSIG 0505 An...
Abstract

ABSTRACT An accurate calculation of a pipeline's hydraulic capacity is crucial for an optimal utilization of the gas transport network. The calculated capacity is the capacity that is made available for sale to the owners and shippers of the gas. This capacity is found by means of a capacity test, where the wall roughness is used to tune the model to match the flow conditions from the steady state test period. Based on this roughness the friction factor is extrapolated along the appropriate Colebrook-White friction factor curve to find the hydraulic capacity. This method is based on the assumption that the Colebrook-White curves are the best tool for capacity estimation available. The Colebrook-White formula is a combination of the law of the smooth and the rough turbulent flow found by Nikuradse. These two formulas have been widely employed for almost one century. However, the transition region where the roughness elements start to protrude significantly into the viscous sublayer bears significant uncertainty. Most of the pipelines operated by Gassco are in the early phase of this transition. Research conducted by many parties suggests different descriptions of the fluid behaviour and hence the friction factor in this region, which subsequently leads to different capacity calculations. A more accurate description of the pressure loss would enable Gassco, and other pipeline operators, to perform more accurate calculations of the pipeline capacity, and hence in most cases increase the transport capacity. Furthermore, the online models will be more accurate, allowing an improved capacity exploitation. This was the reason for starting the work that will be presented here. This paper documents research indicating that the use of the Colebrook-White friction factor correlation in commercially available pipeline simulation tools may be improved. A database of historical steady state operational data from real pipelines have been collected and analyzed. The friction factor is used to tune the pipeline model to match the measured pressure drop and flow rates for a range of operational conditions. It has been found that the friction factor, when applied to the simulation models, decreases faster than predicted by the Colebrook-White correlation. Reynolds numbers in the range has have been investigated. Transition from smooth to rough turbulent flow is expected for such operating conditions in systems having the pipeline feautures treated in this paper. 6104010⋅− It is shown how these results influence the capacity calculations. A low flow rate in the capacity test will lead to a conservative calculation of the capacity as the friction factor decreases faster than predicted by Colebrook-White. The potential for increased calculated capacity is shown to be in the range 0.5-2.0 %. This amounts to a potential annual increase in the gas export from the Norwegian Continental Shelf by 100-400 million $.

Proceedings Papers

Publisher: Pipeline Simulation Interest Group

Paper presented at the PSIG Annual Meeting, October 15–17, 2003

Paper Number: PSIG-0302

...). This average )(xv is the same as the one-dimensional )(xv defined earlier, so this foray into multiple dimensions can now be terminated. The laminar friction factor (also obtained from the exact solution) is: )Re(64)( xxf = where Re is the

**Reynolds****number**for the flow, )( Re( x xDxvxx µ = For...
Abstract

ABSTRACT This paper discusses the current understanding of aspects of the physics of fluid flow in pipelines relevant to pipeline flow simulations. Topics include fluid properties, the laminar/turbulent transition, friction (including methods of drag reduction), energy flow and dissipation, and the effect of more than one phase in the pipeline. Practical issues are described in terms of fundamental physics, as contrasted with an empirical approach. INTRODUCTION Flow through tubes was the subject of some of the earliest attempts to understand the physics of fluid flow. Reynolds' original experiments on turbulence were done with ink streams in water flowing in tubes. Steady-state axial laminar flow in a cylinder is one of the few fluid flow problems for which an exact solution of the fundamental flow equations can be found. Flow in pipelines is usually analyzed by numerical simulations based on a special case of the Navier-Stokes equations for fluid flow, in which the viscous stresses are consolidated into a friction force term based partly on physics and partly on empirical results. The Navier-Stokes equations are essentially expressions of the conservation of mass and momentum. Only in recent years has the flow and dissipation of energy been added to such simulations. There remain substantial shortcomings in the understanding of the laminar-turbulent transition and in the definition and effect of varying fluid properties. The understanding of pipeline hydraulic operations involves forces, motion, and energy transformations, which are the elements of what we call the physics of pipeline flow. Our objective in this paper is to present a review of the current state of this understanding, including some of its history, and calling attention to notable deficiencies. Who cares about the Physics? It is possible to design, build, and operate a pipeline using rules of thumb and practical experience, with no reference to the underlying fundamentals. We believe this approach is fraught with hazard, because pipelines and their modes of operation vary a great deal. The physics does not vary, although there are some things not well understood. Knowing what isn't understood is also useful. So, pipeliners should care about the physics. Fluid Properties - Liquids vs. Gases An unfortunate, in our opinion, development in the practice of pipeline simulation has been a tendency to treat gas and liquid pipelines separately, even though the flow equations and the numerical methods are the same. With an appropriate equation of state and minor adjustments in time and distance steps, a good simulator can be used for either gases or liquids. Devices, on the other hand, especially pumps, compressors, and throttling valves, behave differently for liquids and gases. Liquids and gases have different macroscopic properties arising from the fundamental differences in the two types of fluid. It is a strength of the pipe flow equations, which are essentially expressions of the conservation of the fundamental quantities, mass, momentum, and energy, that the same equations and methods work for both.

Proceedings Papers

Publisher: Pipeline Simulation Interest Group

Paper presented at the PSIG Annual Meeting, October 23–25, 2002

Paper Number: PSIG-0202

... evaluate transmission factors in its network planning and design work, in fact in any gas pipeline simulation work. Some other equations have also been used, but by and large Colebrook-White and its approximations have been the most popular. Due to the high

**Reynolds**-**Number**the flow type in gas pipelines is...
Abstract

ABSTRACT New pipeline materials, increasing pressures in pipelines, increasing flows in existing pipelines and proposed international interconnections have raised issues in the accuracy and applicability of existing transmission factor formulae for natural gas. The results of flow tests have sometimes appeared to be contradictory and difficult to explain. The paper will describe the development of a very general formula that can be used as an alternative to the well-known Colebrook-White formula and the reasons for this alternative approach. A small amount of liquid in a pipeline can have a dramatic effect on the flow characteristics and this is explored with results from limited flow tests. Finally the paper will indicate those areas where further flow tests are required to improve our knowledge and help tune the parameters of the new formula. The work was supported by GERG Research Project 1.19. GERG (Groupe Europeen de Recherches Gazieres), founded in 1961, consists of members from eight European countries. INTRODUCTION "Taking the Rough with the Smooth" gives a good hint at what this paper is all about. For many years the gas industry has relied on the Colebrook-White equation to evaluate transmission factors in its network planning and design work, in fact in any gas pipeline simulation work. Some other equations have also been used, but by and large Colebrook-White and its approximations have been the most popular. Due to the high Reynolds-Number the flow type in gas pipelines is always turbulent. There are two main types of turbulent flow behaviour in gas pipelines that have to be modelled: smooth pipe flow and rough pipe flow The Colebrook-White equation attempts to model both of these kinds of flow by having a gentle transition from one flow regime to the other: it takes the rough with the smooth. Flow test results sometimes indicate that this transition between smooth to rough pipe behaviour is not as gentle as Colebrook-White would lead us to believe. As we shall see, with current knowledge, there are a number of reasons why the Colebrook-White equation is flawed and can be improved upon. Much of this paper is based on research carried out as part of GERG Research Project 1.19. during 1995 to 1999. An article describing some of the findings was published in 2000 [1]. GERG (Groupe Europeen de Recherches Gazieres), founded in 1961, consists of members from eight European countries. This paper gives a background to pipe flow equations and transmission factor formulae. It then presents a new suggested formula and how it incorporates the most up to date knowledge. Finally it presents some flow test results Background on pipe flow equations So what is a transmission factor and what does it tell us about the flow of gas in a pipeline? A good survey of the subject is the paper presented at the 2001 PSIG meeting by Don Schroeder [2], but here is a brief survey of some basics to set the scene.

Proceedings Papers

Publisher: Pipeline Simulation Interest Group

Paper presented at the PSIG Annual Meeting, October 23–25, 2002

Paper Number: PSIG-02W3

... reservoir surveillance friction factor correlation production logging low load production control

**reynolds****number**TWO PHASE FLOW : ACCOUNTING FOR THE PRESENCE OF LIQUIDS IN GAS PIPELINE SIMULATION by Ben Asante Enron Transportation Services Houston, Texas, USA ABSTRACT Multiphase flow of gas and low...
Abstract

ABSTRACT Multiphase flow of gas and low loads of liquids occurs frequently in natural gas gathering and transmission pipelines for both onshore and offshore operations. Literature and experimental investigations indicate that dispersed droplet and stratified flow patterns are obtained when gas and small quantities of liquids flow concurrently in a pipe. Very few correlations exist for the prediction of holdup and pressure drop for these systems and fewer still give satisfactory results. Experimental studies for air-oil and air-water systems flowing through small diameter plastic and steel horizontal pipes ranging in size from 1-inch to 3-inches were performed. The experiments were carried out at the multiphase flow laboratories of Imperial College in London and the University of Calgary in Canada. Data from actual operating gas pipeline systems transporting small amounts of hydrocarbon liquids were also evaluated. Based on the experimental results and the operating data, two approaches for modeling these systems are proposed: A homogeneous approach for very low liquid loads (holdups up to 0.005), typical in gas transmission systems. A friction factor correlation based on the holdup has been developed for this flow regime. A mechanistic stratified two-phase approach for higher liquid loads (holdups greater than 0.005) usually found in gas gathering systems with consideration given to: The reduction in the available flow area and extent of wetting of the pipe perimeter by the liquid film. The gas/liquid interface was observed to be either flat or curved. The interfacial friction factor between the liquid film and the gas. A new correlation based on the liquid and gas Reynolds numbers as well as the film thickness and hold up has been developed. This correlation has been successfully tested against both experimental and actual pipeline operating data. 1.0 INTRODUCTION The joint flow of gas and liquids in pipes is common in the chemical process industry, particularly for oil and gas pipeline flow. Numerous theories and correlations have been proposed in the last 50 years for the prediction of pressure drop and liquid holdup in pipelines. None of them, however, gives consistently reliable results for all the identified flow patterns in multiphase gas-liquid flow. Systems transporting gas and low loads of liquids are perhaps some of the least studied in multiphase history and consequently literature and data for these systems are limited. In the petroleum industry this phenomenon occurs frequently in natural gas gathering and transmission pipelines for both onshore and offshore operations. The accompanying liquids are usually heavy hydrocarbon fractions and water and may be introduced from several sources. Liquids from compression facilities (e.g. lube oil) and treatment plants (e.g. glycol) as well as products from retrograde condensation may accompany the gas during transportation. Some water from the reservoir formation may also contribute to the liquid load. The accompanying liquids affect the transportation efficiency of the system. Most gathering pipelines (which typically have liquid loads up to 100 barrels per million cubic feet of gas (bbls/MMSCF)) transport fluids as multiphase components.

Proceedings Papers

Publisher: Pipeline Simulation Interest Group

Paper presented at the PSIG Annual Meeting, October 17–19, 2001

Paper Number: PSIG-0111

... laminar until the fluid comes to rest. correlation freita rachid shutdown batch transfer wasan pipeline equation krantz upstream oil & gas assumption concentration

**reynolds****number**procedure concentration distribution evaluation velocity profile time instant dispersion...
Abstract

1. INTRODUCTION The transport of different petroleum products or different grades of a same product through a single pipeline is known as batch transfer and is a very common practice in the pipeline industry. Unless mechanical separators are used such as scrapers, there will be a certain amount of mixing between the products' interface which is called mixing volume. To ensure the quality of the products being transported, the mixing volume should be accurately predicted and/or continuously monitored so that the contaminant can be isolated without harming the products' specifications. The mixing zone which develops at 1 the batches' boundary increases in extension as the batches travels along the pipe. Such a phenomenon is driven by dispersion of matter and is currently evaluated by a number of classical models (Aunicky, 1970; Austin and Palfrey, 1964; Levenspiel, 1958; Ovffadi and Torok, 1977; Sjenitzer, 1958; Smith and Schulze, 1948a; Netchval et al., 1972) which assume, as a basic hypothesis, continuous pumping during the transfer. However, in many practical situations, the pumping must be interrupted either by voluntary or unintentional operational events. In such cases pipeline flow rate experiences significant variations and so does the dispersion coefficient. So, a question arises as to the suitability of the classical models in predicting mixing volumes under these conditions. On the other hand, it has been pointed out by some specialists that the act of stopping the line during a batch transfer could be one of the factors responsible for the increase in the mixing volume. Since the occurrence of mixing zones implies in additional costs associated to shipping the mixture back to refinery for later reprocessing, it becomes evident the reason for investigating the influence of pumping shut-down on the mixing volume. A new model capable to evaluate mixing volumes under pump shut-down and start-up events is presented in this paper. The model is formed by a set of differential equations that describes the momentum conservation and concentration distribution for the fluids, which are considered as incompressible. By assuming that the concentration distribution does not affect substantially the momentum variation, the time-dependent flow rate in the line is firstly computed by solving the momentum equation and then used as an input in the solution of the dispersion equation. Numerical simulations carried out for a specific batch have shown that if the pumping shut-down operation is repeated several times during the transfer it may induce a significant growth in mixing volume. 2. THEORETICAL DEVELOPMENT To manage different products in the line, product pipelines conveying batches are commonly susceptible to pump-shut down operational conditions. In such a event, the hydraulic gradient line is severely reduced causing the fluids to de accelerate and even to stop in the entire pipeline extension. The flow, which is in general highly turbulent in batch transfers, becomes laminar until the fluid comes to rest.

Proceedings Papers

Publisher: Pipeline Simulation Interest Group

Paper presented at the PSIG Annual Meeting, October 28–30, 1998

Paper Number: PSIG-9808

... study of pressure drop in pipes at high

**Reynolds****numbers**has been carried out to determine the effect of roughness on the transport capacity of natural gas pipelines. In a high pressure flow loop the pressure drop was measured in 19.7 ft (6 m) long test pipes with 5.9 in (150 mm) inner diameter. The...
Abstract

ABSTRACT An experimental study of pressure drop in pipes at high Reynolds numbers has been carried out to determine the effect of roughness on the transport capacity of natural gas pipelines. In a high pressure flow loop the pressure drop was measured in 19.7 ft (6 m) long test pipes with 5.9 in (150 mm) inner diameter. The measurement of pressure drop of a coated pipe and a bare steel pipe showed the drag reducing effect of pipeline coating. The measurements were performed at Reynolds numbers which are typical for subsea pipelines in the North Sea (Re - 107). At a Reynolds number of 1 x 107 the friction factor for the coated pipe was 31 % lower than for the steel pipe, which corresponded to an increase in the transport capacity of 21 %. Roughness values obtained by direct measurements on the pipe wall were compared to the roughness values obtained from flow tests (equivalent sand-grain roughness &). For the steel pipe the measured roughness parameter R, (mean peak to valley height) corresponded well with,&. In the coated pipe the k, was not easily defined because the flow never reached fully rough flow conditions at the maximum Reynolds number. Introduction Internal coatings have been used with success in gas pipelines since the 1950's [l]. Economic studies [2] show that the typical pay-back time for the investment in internal coating is 3 - 5 years due to improvements in pipeline hydraulics. It is well known that internal coatings reduce the friction in the pipeline and therefor reduce the operating cost of compressors. In Norway 35 % of offshore generated power [3] is used for gas export compressors. The use of coatings to reduce the operating cost of compressors is therefor important. In addition the coatings protect the pipe wall against corrosion and reduce the need for maintenance of the pipeline [l]. Also, pigging operations are improved. The aim of this study was to study the friction factor of coated pipes. In Norway internal coatings are used in the export pipelines which transport gas from the Norwegian shelf to continental Europe. The object has been to establish more accurate friction factor correlations for coated gas pipelines and thus being able to predict the capacity of large diameter trunk lines accurately. The flow in offshore gas pipelines is characterized by large Reynolds numbers (Re - 107) due to the low viscosity and the relative high density at typical operating pressures 1450 - 2610 psi (100 - 180 bar). From the classical Colebrook-White friction factor correlation [4] it is seen that even very minute irregularities on the pipe wall will have a significant effect on the friction in the pipeline at high Reynolds numbers. However the measurements from which the Colebrook-White correlation was developed reached a Reynolds number of 1 x 106 as maximum, one decade lower than what is typically encountered in offshore gas pipelines.

Proceedings Papers

Publisher: Pipeline Simulation Interest Group

Paper presented at the PSIG Annual Meeting, October 20–21, 1988

Paper Number: PSIG-880

... f.low equation usage. flow equation i s included. factor equations and t h e i r re la t i on t o the Moody Diagram. This includes the diameter dependent,

**Reynold's****Number**dependent and the recently developed e x p l i c i t f r i c t i o n factor equations. considerations o f using the Fundamental Flow...
Abstract

ABSTRACT This paper provides detailed information in three different areas of flow equation usage. First, a step by step development of the fundamental flow equation is included. factor equations and their relation to the Moody Diagram. This includes the diameter dependent, Reynold's Number dependent and the recently developed explicit friction factor equations. considerations of using the Fundamental Flowequation. ranges, sensitivity, and efficiency factor usage are included. I. Introduction As Computers became more prevalent in the workplace, many of us lost touch with the origins of various formulas or software packages. Because of the flow equation's implicit nature, variations were developed. flow situations, and were incorporated into the computer world. Too often, a program is used without knowing which flow formula variation is inccrporated into the program, or what assumptions are contained within a particular formula. For this reason, a review of the General Flow equation is considered desirable. These variations were used as approximations for differing The myriad of flow formulas are all related to the General Flow equation. technology. For example, as higher yield strength pipe was manufactured, system operated at higher pressures and flows. This changed the commonly used friction factor relationships, thereby requiring a new adaptation of the General Flow equation. A number of the equations were developed when computers were not available, these equations were great time savers because a slide rule could be used, rather than using tables. The original assumptions and subtleties of these early variations are not commonly known among those of the computer age. Most were developed to fit the existing pipe or computational The Moody diagram, as derived by using Colebi~ok's implicit friction factor equation, is considered the industry standard for determining friction factors. Today's desktop computers have the capability of handling the iterative solutions required by Colebrook's equation. Therefore, pipe system models should use the General Flow equation with a Colebrook Friction factor. To reduce computing time or cost, some explicit approximations of the Colebrook equation provide a good correlation over the entire range of the Moody diagram. These equations include Chen's, Shacham's and others docmented later easier.

Proceedings Papers

Publisher: Pipeline Simulation Interest Group

Paper presented at the PSIG Annual Meeting, October 27–28, 1983

Paper Number: PSIG-8303

... flow equation midstream oil & gas panhandle pipeline efficiency turbulent flow pipeline simulation interest group downstream pressure piping simulation pipeline leak detection upstream pressure general flow equation measurement and control

**reynolds****number**production monitoring...
Abstract

PURPOSE OF TALK The purpose of this talk is to discuss a few flow equations and hopefully to discover which flow equation is best, or if it makes any difference. We may also discover that one equation is good for a certain flow condition but not good for other flow conditions. Hopefully we can also discover when to use a certain flow equation. All of the equations I am going to discuss are based on the General Flow Equation. The difference is in the definition of the transmission factor. While most of the papers presented are the results of work done by the authors; this paper is more a discussion of work done by others and the flow equations which resulted from their work. In particular I want to give credit to: The American Gas Association, Inc.; The N.B.-13 Committee, Sponsored by the Pipeline Research Committee; The Institute of Gas Technology "Technical Report No. 10", and their publication, " Steady Flow In Gas Pipelines". SOME EXPERIENCES OF FLORIDA GAS TRANSMISSION COMPANY During the early 1960's Florida Gas Transmission Company noticed that certain segments of its system had excessive pressure loss and efficiency tests were run to determine the pipeline efficiency. We were using the panhandle "A" equation for all flow calculations during this period. Certain valve segments had efficiency in the 70% range while other segments had efficiencies in the 90% range. Above ground plug valves were installed throughout this segment of our mainline and therefore a sandblasting program was established to improve pipeline efficiency. This program was effective and system throughput was increased slightly. In 1964 we started installing 30" loop lines to increase our system capacity. After reading the AGA Report, "Steady Flow in Gas Pipelines", I used the same efficiency test data and solved for the effective roughness ke. I was surprised to find that although the efficiency factor had decreased significantly the effective roughness (ke) was essentially constant. In some cases slightly higher in other cases slightly lower, which I attribute to the accuracy of the test data. Based on the AGA report and on the results of these tests, I believe the General Flow Equation using the rough pipe law of Nikuradse for the friction term and including a term for compressibility will give accurate results, when the effective roughness is known. Tests along our system have indicated that a mean, or average, value for ke is 1.000 micro inches. Some new pipe has a ke value of 400 micro inches or less. Test data for segments of pipeline which have been stored for long periods of time and/or have been coated with distallate or compressor oils have an effective roughness of several thousand micro inches. Now we will compare the various ways that the transmission factor (l/f)·5 is defined. WEYMOUTH As mentioned, these are all based on the General Flow Equation with the only difference being the way in which the transmission factor (l/f),5 is defined.