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Jerry L. Modisette

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Proceedings Papers

Publisher: Pipeline Simulation Interest Group

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

Paper Number: PSIG-1421

Abstract

ABSTRACT The mechanism of frost heave, also known as frost jacking , is described as it is manifested in warm pipe lines, cold pipelines, and inert objects. It is shown by both descriptions of the physical phenomena and simulations of the seasonal movement of the frost line that the transport of water in unsaturated soil dries the ground around a warm pipe so that frost heave is not expected to affect most buried pipelines. INTRODUCTION Pipeline Simulation in the name of this organization usually refers to simulation of the flow in pipelines. As we developed better flow simulators over the years, we found that accurate flow simulation requires the simulation of many other processes associated with pipelines, such as the heat flow in the ground around the pipe and the expansion of the pipe. Accurate simulators require accurate calculations of fluid properties. Two-phase flow simulators require vapor/liquid equilibrium calculations that may be more complex than the flow calculations. Applications of flow simulators require additional analysis: mass balances for leak detection; wave propagation analysis for leak location, the detailed functioning of pumps, compressors, and valves for surge calculations. Frost heave is another addition to the list of physical processes affected by the flow in pipelines and affecting the pipelines that are important in some applications. Frost heave is known to affect solid objects on or in ground subject to freeze/thaw cycles. When water freezes it expands, by about 12% in volume. If unconstrained this expansion can move the ground and anything in the ground. Repeated cycles of freezing and thawing can significantly displace building foundations and can move rocks up out of the ground.

Proceedings Papers

Publisher: Pipeline Simulation Interest Group

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

Paper Number: PSIG-1002

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-0704

Abstract

ABSTRACT In the United States a small one sentence in a regulation is now causing pipeline companies to spend hundreds of thousands of dollars on "surge studies" covering every mile of mainline transmission liquid line. Every consultant contacted proposes a different surge study. These study differences may include all or some equipment; review the entire pipeline or just parts of the system; and be viable for only the current operations. Will a new surge study be required when operations change, a new piece of equipment is added, or a new product is transported? This paper addresses surges in liquid pipelines; what causes them and the physics associated with the surge. The authors review various surge study techniques and recommend a surge study methodology for general pipeline operations that can help make surge protection proactive instead of reactive for pipeline operators. This paper addresses the DOT requirements for surge analysis on pipelines: the regulatory requirements, the significance of surges in pipelines, the physics of surges, and problems associated with surge simulation. REGULATORY REQUIREMENTS The regulatory requirement is, as Napoleon said constitutions should be, short and vague. In the Code of Federal Regulations, Title 49 Transportation under Part 195 Transportation of Hazardous Liquids by Pipeline § 195.406 Maximum operating pressure (b) No operator may permit the pressure in a pipeline during surges or other variations from normal operations to exceed 110 percent of the operating pressure limit established under paragraph (a) of this section. Each operator must provide adequate controls and protective equipment to control the pressure within this limit. In other words the regulatory authority realizes that there will be instances outside of normal operations where the pipeline will experience surges. This is acceptable as long as the pipeline stays within 110 percent of the operating pressure limit previously established. The operator must have controls and equipment to control the pressure surges within this limit. Lately, the regulators aren't assuming control and equipment on the system is working within these limits and wants proof that the operator is in compliance. The accepted method of proof is to have on file a surge study. So before contracting or performing a surge study perhaps one should review what a surge is. Physics of Surges The physics of a surge is quite simple. In accordance with Newton's second law of motion, stopping the flow in a pipe requires a force. Friction will stop the flow slowly, if the driving pressure is released. To stop the flow quickly by, say, closing a valve, more force is required. This force is provided by a reverse pressure gradient. It's this reverse pressure gradient that is of concern. For fast valve closures, the pressure upstream of the valve can become vary large. There have been cases, notably one in Saudi Arabia in the 1970s, of pipes being ruptured by the pressure increase associated with rapid valve closure.

Proceedings Papers

Publisher: Pipeline Simulation Interest Group

Paper presented at the PSIG Annual Meeting, October 11–13, 2006

Paper Number: PSIG-0606

Abstract

ABSTRACT This paper was prepared in response to a request by a respondent to the attendee questionnaire at the PSIG 2005 Annual Meeting in San Antonio, Texas. The request correctly implied that authors always talk about the great things provided by pipeline simulation, but never discuss the problems. The author has been involved with many pipeline simulation projects over 30 years, and has had many things go wrong in the course of developing, using, or implementing pipeline simulators. This paper discusses many of the problems encountered by the author, following the format: Problem - Definition of the problem Cause - The reason for the problem Solution - What was done to solve the problem Notes - Rather subjective comments by the author with in the hope of aiding a general understanding of what is involved in successful pipeline simulation projects. TYPES OF PROBLEMS Ultimately, all problems are managementproblems! However, the following factors areoften not dealt with by management in time toprevent problems with the simulators: Model Deficiencies - Model deficiencies are less common than they were a few years ago. There are many simulators available now that are essentially complete and correct. Problems still arise in setting proper time and distant steps, and in setting correct operating parameters. There are also still a few things about pipelines, such as the transition between laminar and turbulent flow, which are not completely understood. Bad Data - There will always be bad data, in the sense of instrumental or encoding errors. The issue is one of finding and correcting the errors, and designing the simulator so that it does not become hopelessly disabled in the meanwhile. There is also inaccurate information or assumptions about such things as ground thermal properties or pipeline roughness. The best real-time simulators can determine better values of these quantities by automatic tuning. Configuration Errors - There will also always be configuration errors. Finding and correcting such errors is a major part of any simulator implementation. It is essential that the user be able to readily create and change configurations. Unrealistic (Impossible?) Expectations - Both users and vendors are responsible for understanding and making clear the true capabilities of a simulator and applications based on it. Overselling will only work if there are customers wanting more than they can understand or are willing to pay for. Computer Problems - Computers are amazingly reliable. Most computer problems are caused by conflicting uses. Inadequate Instrumentation - This type of problem applies primarily to real-time simulations. If there are not enough measurements to provide boundary conditions, no unique solution can be found. If measurements are spaced too far apart, accuracy and response time will suffer. Generally, real-time models need additional measurements for tuning of unknown parameters, such as ground thermal properties. There are special situations, e.g. If the temperature of the fluid reaches equilibrium before the fluid reaches the end of the pipe, intermediate temperature measurements are needed.

Proceedings Papers

Publisher: Pipeline Simulation Interest Group

Paper presented at the PSIG Annual Meeting, October 20–22, 2004

Paper Number: PSIG-0409

Abstract

ABSTRACT Flow simulations are usually made in Eulerian coordinates, which are fixed with the observer. In the case of a pipeline simulation, the coordinate system is fixed in the pipeline. This seems reasonable, since measurements are made in the pipeline's coordinate system and, ultimately, results are wanted in that system. However, the laws of motion were originally formulated for the motion of fixed masses. The mass in a volume element fixed in pipeline space is continually changing, both in identity and amount, as mass flows in and out. Not only does the mass change, but other properties change due to the difference in velocity, temperature, and composition of the flows in and out. These changes in pressure, temperature, density, velocity, and composition, due to convection , are in addition to the changes due to forces acting on the fluid in the volume element (pressure gradient, friction, gravity), and to conduction and diffusion. The equations of motion, usually formulated as conservation laws, have additional terms, with ensuing additional complexity, to take this convection of mass, momentum, energy, and composition into account. In a coordinate system moving with the fluid, there is no convection in or out of the moving fluid elements, and the equations of motion are substantially simpler. For example, the mass and composition of the moving fluid element do not change at all, except slightly by diffusion in special situations. The density is determined by the expansion or compression of the fluid volume element. Simpler equations of motion are simpler to solve numerically. Countering the simpler equations, there are the additional housekeeping tasks of accounting for the moving fluid elements, and of mapping the solution results back into the fixed system for output. Moving element simulators are used in aerodynamics, primarily for the increased accuracy given by higher point densities in the compressed air around flying objects. In a pipeline the major advantage, other than simpler flow equations, is that all tracking (batches, composition, thermal fronts, additives, heating value, point of origin…) is done automatically. This paper describes a numerical fluid flow simulator for pipelines based on a Lagrangian coordinate system, in which the model points or fluid elements move with the fluid. It discusses the practical advantages and disadvantages, and compares results with conventional fixed coordinate system simulators. Solution Procedures Equations (1a) , (2a) , and (3a) together with an equation of state can be solved for the four dynamic variables (density, velocity, temperature, and pressure) by numerical methods. In addition, the positions of the fluid elements must be calculated at each time step. Although implicit1 methods may provide better accuracy and stability, in order to make the procedures and interactions more transparent, an explicit numerical 1 Explicit numerical methods calculate changes from values of the dynamic variables at the beginning of the time step.

Proceedings Papers

Publisher: Pipeline Simulation Interest Group

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

Paper Number: PSIG-0302

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 17–19, 2001

Paper Number: PSIG-0108

Abstract

INTRODUCTION Pipelines operations are inherently transient processes. Inlet and outlet flows change, pumps and compressors start and stop, control setpoints change, different products and compositions move down the line, and temperatures change with changing ambient conditions. These facts would seem to indicate that a useful pipeline flow model should be a transient model, that is, it should solve the time-dependent flow equations. However, steady-state models are widely used to design pipelines, and to estimate the flow and line pack. Succession-of-steady-states (SSS) solutions corresponding to sequences of boundary conditions, control setpoints, equipment statuses, and interface positions are used for tracking or estimating the movement of products through pipelines. This paper addresses the two types of models and their suitability for various purposes. Purposes of Pipeline Flow Models The appropriateness of a particular type of flow model depends on the use to be made of the model results. Pipeline flow models are used for the following purposes: Product Tracking - Batches of different products, composition, quality, cost, origin, and ownership can be tracked through a pipeline. The objective for offline product tracking models is usually to estimate schedules. For real-time models the objective is usually to estimate interface arrival times. Product tracking may also be used to estimate allocations of ownership and specific (as opposed to average) transmission costs. For both real-time and offline models knowledge of interface locations is necessary for accurate hydraulic calculations. Line Balance - The net flow in and out of the pipeline, by batch or over time intervals, is a check on the integrity of the pipeline and/or the metering process. A flow model permits the calculation of more accurate line balances by estimating the change in line pack. Line Pack Distribution - Flow models are used to estimate the distribution of product in the pipeline as an aid to managing the product inventory temporarily stored in the pipeline. Pressure Monitoring - Flow models provide estimates of the maximum/minimum pressures at points between pressure sensors. Deliverability - The maximum achievable delivery flow rates at specified points can be estimated with flow models. Pump/Compressor Performance Monitoring - By comparing model estimates of current performance with manufacturer's specifications, changes in the performance of pump or compressor stations and individual units can be detected. Fundamental Differences Between Transient and SSS Models The underlying difference between transient and steady state models lies in the equations of motion. The transient equations contain terms for the rates of change with time of the dynamic variables: pressure, temperature, density, and velocity. By setting these rates of change equal to zero, which is the mathematical expression of the steadystate condition, the steady-state equations of motion are obtained. However, in considering the suitability of transient vs. SSS for various purposes, differences in the results are of more interest than differences in the equations. The results of the two approaches have in common the production of spatial arrays of the dynamic variables at successive points in time.

Proceedings Papers

Publisher: Pipeline Simulation Interest Group

Paper presented at the PSIG Annual Meeting, October 28–30, 2000

Paper Number: PSIG-0008

Abstract

Introduction As the art of pipeline flow simulation has advanced, the rigor and, we trust, the accuracy of the many elements making up a flow model have increased. Steady-state models have given way to transient solutions, fluid properties are calculated and tracked along the pipeline, and configurations are represented in more detail. Isothermal models have been replaced with solutions of the energy flow equation supported by real-fluid thermodynamics and ground heat flow models. Accurate fluid properties and thermodynamics require accurate equations of state. There are many more equations of state than could be reasonably discussed in a single paper. This tutorial reviews current practice using equations of state in the simulation of fluid flow in pipelines, starting with fundamental considerations, following with a discussion of several ancient & modern equations of state, and concluding by discussing what's reasonable to use. Reasonable is a subjective word, and the decisions as to which equations to consider and which to use for what are based on the author's experience in simulating the flow of gases, liquids, supercritical fluids, two-phase systems, on preferences arising from that experience, and on externally imposed requirements. What's an Equation of State? An equation of state is a relationship between state variables, such that specification of two state variables permits the calculation of the other state variables. There are many state variables; usually in fluid dynamics we talk about pressure, temperature, and density because these variables appear in the equations of motion. What Do We Want from an Equation of State? In pipeline flow simulations we use equations of state for the following: Determine the density from the temperature & pressure for: Linepack calculations Flowmeter calibration Pressure drop calculations Determine thermodynamic variables for; Thermal modeling Compressor calculations Vapor-liquid equilibrium These uses imply certain characteristics of an effective equation of state: Accuracy (<0.1% for custody transfer flow meters) Applicable over wide temperature and pressure ranges Applicable over wide range of compositions Rigorous (for thermodynamics; Not quite the same thing as accuracy) Works for liquids too Easy to use !!! There is usually a contradiction between the last characteristic and the others. How does the Ideal Gas Law Stack Up? The ideal gas law was originally developed in the form of equation (6), rather than equation (1) because it is easier to measure gas volumes than gas densities, and because chemists tend to think in terms of moles rather than masses. Although the ideal gas law was originally derived from Boyle's law and Charles' law, it can also be obtained from the kinetic theory of gases. Getting the ideal gas law from the kinetic theory of gases requires a couple of assumptions which give us some insight into the physics: The gas molecules occupy no volume, which was already implied by Boyle's law. There are no forces between the molecules except at the instant of collision. For a gas at atmospheric (standard) conditions, these two assumptions are nearly satisfied.

Proceedings Papers

Publisher: Pipeline Simulation Interest Group

Paper presented at the PSIG Annual Meeting, October 18–19, 1984

Paper Number: PSIG-8401

Abstract

1.0 Introduction Dynamic models for the flow in pipelines have reached a degree of maturity, indicated by the commercial availability of a variety of off-line and real-time software products from several vendors. The models in current use are based on three different numerical techniques and a number of physical approximations. Our purpose in this paper is to discuss these different approaches, and to present results for simulations of a simple transient scenario, showing how the different numerical approaches compare for a fixed set of physical assumptions, and also showing the effects of various physical approximations with a fixed numerical scheme. 2.0 Equation of Motion The equations of motion presented below are the generally accepted one-dimensional equations for pipe flow. The momentum and mass equations derive from the Navier-Stokes equations for fluid flow, with the viscous stress terms replaced by the Fanning/Darcy/Weisbach friction force term. 2.3 Energy (Temperature) Equation The energy equation takes into account the balance between work on the fluid by pressure, friction, and gravitational forces and the changes in the internal energy, kinetic energy of bulk motion, and gravitional potential energy of the fluid. Many formulations of the energy equation are available, differing primarily in the choice of thermodynamic functions used to express the internal energy and its conversion to and from mechanical work. The particular form presented here was developed by Dr. Glenn Bernard. 2.4 Equation of State The equation of state provides a relation between the pressure, density, and temperature of the fluid. 3.0 Numerical Methods Differential equations describing real systems, as opposed to ideal systems usually dealt with in mathematics courses, are usually not solvable by analytic methods. The difficulty lies both in the form of the fundamental equations and in the dependance of various properties on the physical variables. Numerical methods are based on approximating the derivatives appearing in the differential equations by averages calculated over some interval in space or time. In some formulations, it is also necessary to assume that certain quantities appearing in the equations do not change over the intervals. The numerical techniques commonly used for pipeline flow simulations may be divided into explicit methods, implicit methods, and the method of characteristics. Typical numerical procedures include the following sequence: Initial profiles are established with a steady-state solution Changes in the dependent variables are calculated for a time interval by numerical approximations to the equations of motion The changes are added to the previous vs1ues to establish the new profile at the end of the time interval 3.1 Explicit Integration In explicit methods, the numerical approximation of the equations of motion are expressed in terms of the values at the beginning of the time interval, as indicated in Figure 1a. These values are known from the previous time step or the initial profiles, so the calculation of the changes in the flow variables is explicit. Our explicit method uses the equations of motion in terms of the physical variables velocity, density, pressure, and temperature.

Proceedings Papers

Publisher: Pipeline Simulation Interest Group

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

Paper Number: PSIG-8302

Abstract

INTRODUCTION Two-phase flow is the simultaneous flow of liquid and gas in the same pipe, duct, or channel. This paper is concerned with transient two-phase flow in pipes, as occurs in gathering, transmission, or distribution systems or in steam pipes. Two-phase flow has generally been of more concern to nuclear or chemical engineers than pipeline engineers, because pipeline practice is to separate the phases where possible, while the presence of two phases may be essential to chemical processes. In analysing nuclear problems, one is commonly faced with forcing emergency cooling water down the same duct from which steam is escaping. However, some pipeline situations necessarily involve two phase flow, namely, sour gas systems, off-shore gathering systems, and distribution systems for evaporated LPG. Sour gas systems commonly use injected oil as a corrosion preventive; for off-shore gathering systems two-phase flow may be an alternative to barge collection or laying a second pipe; and cold weather condensation may be unavoidable for residential LPG distribution systems. It is known that the presence of a liquid phase in a gas pipeline usually increases the resistance to the flow out of proportion to the volume of the pipe filled with liquid. This is basically because of efficient momentum transfer at the gas/liquid interface, which may be enhanced by surface waves and entrainment. Since the liquid generally has a higher viscosity, so that it has more friction with the wall, the net effect is more resistance to the gas. Much of the problem in understanding two-phase flow in detail reduces to that of understanding the interface: its configuration and the momentum transfer. Much of the work done on two-phase flow by various investigators has been directed towards defining the conditions under which various types of interfaces, commonly referred to as "flow regimes", occur. Although there are some differences in nomenclature among the various investigators, it has been established that two-phase flow in pipes can occur as stratified, annular, slug, bubble, and mist. In a previous paper (Modisette. 1983), we have proposed an adaptation of the flow regime concept for modeling steady-state flow in pipelines. Stratified and annular flow are treated in a single model by assuming a transition from stratified to annular flow by a mechanism which consists of the liquid climbing the wall. The transition is smooth, and is driven in the model by the changing value of the Taitel-Dukler (1976) transition parameter which they use to define the boundary between the two regimes. Figure 2 illustrates the geometry of the transition. The transition to slug flow is modeled by increasing the momentum transfer between the liquid and the gas. In the steady-state paper, the model results were compared with the data of Beggs (1972) for air and water in small pipes at low pressure. The results of the steady-state model compared with the Fayed and Otten measurements are shown in figure 3. THE TRANSIENT MODEL The transient model solves the coupled equations of motion for the liquid and gas separately.