1 DP Flow Introduction TOPIC PAGE 1.1 Introduction... 10 1.2 Objectives... 10 1.3 History of DP Flow... 10 1.4 Pressure... 11 1.5 DP Flow 101... 12 1.6 DP Flow Measurement Applications... 15 1.7 Flowmeter Installations... 15 1.8 Alternate Flow Technologies... 17 1.9 Summary... 17
1.1 INTRODUCTION 1.1.1 Differential Pressure Flow Measurement Differential pressure flow measurement (DP Flow) is one of the most common technologies for measuring flow in a closed pipe. Flow rate of the fluid in the pipe is derived from the pressure differential between the upstream (high) side and downstream (low) side of an engineered restriction in the pipe. There are many reasons for the wide usage of DP Flow technology: Its technology is based on well-known laws of physics, particularly around fluid dynamics and mass transport phenomena Its long history of use has also led to the development of standards for manufacture and use of DP flowmeters Manufacturers offer a large catalog of both general and application-specific instrumentation and installation choices Finally, DP Flow technologies can achieve high accuracy and repeatability 1.2 OBJECTIVES OF THIS BOOK This handbook is intended to help engineers and process technicians bring all the elements of DP Flow together in a comprehensive reference. The book will present enough theory and technical background to provide a solid context for engineering, procurement, and configuration of DP Flow technologies. This includes the following: The necessary equations and calculations commonly needed for developing DP Flow systems A full discussion of components commonly found in DP Flow systems in gas, liquid, and steam applications Discussions of DP Flow instrumentation technologies found in primary elements and transmitters Common uses including the challenges and points to consider with specific applications Installation guidelines Maintenance and calibration procedures This book focuses on practical engineering problems and challenges. That said, the elements of theory found here are crucial to the successful engineering of most DP Flow solutions. 1.3 HISTORY OF DP FLOW Flow measurement in general began thousands of years ago. Ancient Egyptians made approximate predictions of harvests based on the relative level of spring floods of the Nile. Centuries later, as Romans engineered aqueducts to convey water into their cities for sustenance, baths and sanitation, the need to monitor steady flow became important. Operators used flow through an orifice or the welling of water over obstructions to roughly gauge flow rates. Marks on the walls of the flow stream, strength of the stream through the orifice or other methods gave a rough idea of flow rates. Advancements toward measured, repeatable flow metering increased after Newton s discovery of the law of gravitation in 1687. This concept enabled physicists and mathematicians to begin to formulate a broad range of theories and hypotheses around motion and force. These in turn helped develop a range of instruments that quantified flow volumes and rates. 1.3.1 Bernoulli Swiss mathematician Daniel Bernoulli (1700-1782), whose study of hydrodynamics centered on the principle of conservation of energy, provided the first key breakthrough in the development of technologies for flow measurement. Bernoulli strove to discover as much as possible about the flow of fluids and his work led to the development of what is known as Bernoulli s Principle. This states that for a hypothetical fluid with no viscosity, an increase in the speed of the fluid creates a simultaneous decrease in the fluid s potential energy. Conservation of energy is the basis for DP Flow measurements. The Bernoulli principle says that the sum of all energy in the fluid flow remains constant regardless of conditions. When the speed of the fluid increases, its static pressure and potential energy decrease, while its dynamic pressure and kinetic energy increase. 10
Bernoulli s principle dictates that the total pressure within a system is equivalent to the summation of its dynamic and static pressures. Mathematically in the simplest terms, this is expressed in Bernoulli s equation: (1.1) Most famously, he studied the flow of fluids in pipes, and more specifically, the conditions under which the flow transitions from laminar flow to turbulent flow. Out of this was created the dimensionless Reynolds number (Re). The Reynolds number quantifies the relation of inertial forces to viscous forces, thus: Where: q p p 0 = Dynamic pressure = Static pressure = Total pressure Much more detail on Bernoulli s equation can be found in the next chapter. Bernoulli s equation describes the conservation of hydraulic energy across a constriction in a pipe. It states that the sum of the static energy (pressure), kinetic energy (velocity), and potential energy (elevation) upstream and downstream of the constriction are equal. In the years since Bernoulli, many follow-on expressions of Bernoulli-based equations have been developed. These capture the behaviors of a broad range of compressible and incompressible liquids in many types of applications. Much has been developed from Bernoulli s work. For example, flow over an airfoil, the mechanism of lift, harnesses Bernoulli s principle in aircraft. Flow through a restriction, while named for another researcher, Giovanni Battista Venturi (1746-1822), exhibits Bernoulli s principle in carbureted internal combustion engines, where the pressure drop across a venturi sucks gasoline into the air stream entering the engine. 1.3.2 Reynolds Osborne Reynolds (1842-1912) is a second key researcher who contributed significantly to the theoretical development of DP Flow technologies. Reynolds was not a physicist but a student of mechanics. His work began with the practical steamfitting of ships, though he progressed to an astonishing array of studies. Among them are the mechanism of the drag of ships in water, condensation of steam, propeller design, turbine propulsion design, and hydraulic brakes. 11 Reynolds number quantifies the relative importance of these two types of flow forces in a given flow condition. Because Reynolds number describes the flow regime of a fluid, under certain conditions it is central to designing and operating DP flowmeters. Specifically, Reynolds number can be applied as a constraint on the range of a flowmeter s applicability. Operating a flowmeter outside of its Reynolds number range constraints can degrade accuracy. 1.4 PRESSURE The most critical background concept in the domain of DP Flow is pressure. Accurate measurement of liquid, gas, and steam pressure is basic to many industrial processes. A typical plant will use more pressure measurement and pressure control devices than all other types of measurement and control instruments combined. 1.4.1 What Is Pressure? Pressure is the amount of force applied over a defined area. The Pressure Equation The relationship between pressure, force, and area is represented in the following formula: Where: P F A = Pressure = Force = Area (1.2) (1.3)
If a force is applied over an area, pressure is being applied. Pressure increases if the force increases, or the size of the area over which the force is being applied decreases. Why Measure Pressure? Four of the most common reasons that process industries measure pressure are: Safety Process efficiency Cost savings Measurement of other process variables Safety: Pressure measurement helps prevent overpressurization of pipes, tanks, valves, flanges, and other equipment; minimizes equipment damage; controls levels and flows; and helps prevent unplanned pressure or process release or personal injury. Process Efficiency: In most cases, process efficiency is highest when pressures (and other process variables) are maintained at specific values or within a narrow range of values. Cost Savings: Pressure or vacuum equipment (e.g., pumps and compressors) uses considerable energy. Pressure optimization can save money by reducing energy costs. Measurement of Other Process Variables: Pressure is used to measure numerous processes. Pressure transmitters are frequently used in a number of applications, including: Flow rates through a pipe Level of fluid in a tank Density of a substance Liquid interface measurement The square root of the differential pressure across a restriction in a pipe is proportional to flow. This is expressed mathematically as: Where: Q ΔP = Flow rate = (signifies proportionality) = Differential pressure (1.4) 1.5 DP FLOW 101 THE ROOTS (SQUARED) 1.5.1 What Is Flow? Flow theory is the study of fluids in motion. A fluid is anysubstance that can flow, and thus the term applies to both liquids and gases. Precise measurement and control of fluid flow through pipes requires in-depth technical understanding, and is extremely important in almost all process industries. 1.5.2 Key Factors of Flow Through Pipes There are 5 factors that are key to flow: 1. Physical piping configuration 2. Fluid velocity 3. Friction of the fluid along the walls of the pipe 4. Fluid density 5. Fluid viscosity 6. Reynolds Number Piping Configuration: The diameter and crosssectional area of the pipe enables both the determination of fluid volume for any given length of pipe and is included in the determination of the Reynolds number for a given application. Velocity: Depends on the pressure or vacuum that forces fluid through the pipe. Friction: Because no pipe is perfectly smooth, fluid in contact with a pipe encounters friction, resulting in a slower flow rate near the walls of the pipe compared to at the center. The larger, smoother, or cleaner a pipe, the less effect on the flow rate. Density: Density affects flow rates because the more dense a fluid, the higher the pressure required to obtain a given flow rate. Because liquids are (for all practical purposes) incompressible and gases are compressible, different methodologies are required to measure their respective flow rates. Viscosity: Defined as the molecular friction of a fluid, viscosity affects flow rates because in general, the higher the viscosity more work is needed to achieve the desired flow rates. Temperature affects viscosity, but not always intuitively. For example, while higher temperatures reduce most fluid viscosities, some fluids actually increase in viscosity above a certain temperature. 12
Reynolds Number: By factoring in the relationships between the various factors in a given system, Reynolds number can be calculated to describe the type of flow profile. This becomes important when choosing how to measure the flow within the system. There are three different flow profiles that are defined by different Reynolds number regimes. Laminar flow, Reynolds number below 2000, is a smooth flow in which a fluid flows in parallel layers. It is usually characterized with low velocities, very little mixing, and sometimes high fluid viscosity. When a fluid s flow profile has a Reynolds number between 2000 and 4000, it is in a transitional zone. A Reynolds number above 4000 is called turbulent flow. This is characterized by high velocity, low viscosity, and rapid and complete fluid mixing. Best accuracy in DP Flow metering occurs with turbulent flow, where Reynolds number is greater than 4000 (varies primary element to element). This is because in turbulent flow, the point at which the fluid separates from the edge of the flow restriction is more predictable and consistent. This separation of the fluid creates the low pressure zone on the downstream side of the restriction, thus allowing that restriction to function as the primary element of a DP meter. Depending on the type of restriction and design of the flowmeter, the minimum pipe Reynolds number at which a specific meter should be operated can be considerably higher than 4000. 1.5.3 Flow Continuity When liquid flows through a pipe of varying diameter, the same volume flows at all cross sectional slices. This means that the velocity of flow must increase as the diameter decreases and, conversely, velocity decreases when the diameter increases. Volume can be broken down to area multiplied by length: Where: A s = Area = length Flow can thus be expressed as: This can be further simplified, since length divided by time yields velocity: Substituting velocity for s/t: This yields the simplest representation of equation. Hence, (1.6) (1.7) (1.8) (1.9) (1.10) (1.11) (1.12) (1.13) Volumetric flow equates to the volume of fluid divided by time: (1.5) Where: Q V t = Volumetric flow rate = Volume = Time Figure 1.5.3.a - Graphical representation of the simplest representation of the flow law where Q 1 = Q 2. 13
The derivation of flow continuity above describes the basic principle of energy conservation. The Bernoulli equation, which will be covered in more detail in Chapter 3, builds on this principle to define the energy conservation appropriate for flowing fluid. 1.5.4 The DP Flowmeter Differential pressure is the most common flow measurement methodology today. There are three important elements that are combined to create a differential pressure flowmeter. 1.5.5 Primary Element Types There are many kinds of primary elements: Single hole and conditioning orifice plates Single and multiple-port pitot tubes Venturi tubes Flow nozzles Cones Segmental wedges The primary element creates a pressure drop across the flowmeter by introducing a restriction in the pipe. This pressure drop is measured by the secondary element, a differential pressure transmitter. The tertiary element consists of everything else within the system needed to make it work, including impulse piping and connectors that route the upstream and downstream pressures to the transmitter. Flow P High P Low By creating an engineered restriction in a pipe, Bernoulli s equation can be used to calculate flow rate because the square root of the pressure drop across the restriction is proportional to the flow rate. There are some important cautions around DP flow metering, including (1) ensuring that impulse lines do not clog with particles or sludge; (2) orienting impulse lines correctly they have to be sloped to prevent gas accumulation in liquid applications and liquid accumulations in gas applications; and (3) ensuring that periodic calibration does not degrade accuracy avoided by the use of highly accurate calibration equipment. Figure 1.5.5.a - Pressure flow diagram showing how DP Flow works. As fluids pass the restriction from the high side, the restriction induces a pressure drop. Flow is then calculated from the pressure drop (DP) across the restriction. 1.5.6 Transmitter Options There are two main types of pressure transmitters used to calculate flow using differential pressure. The first is the traditional differential pressure type, which only measures differential pressure, with no ancillary functionality. The second is the multivariable transmitter. A multivariable transmitter is a differential pressure transmitter that is capable of measuring a number of independent process variables, including differential pressure, static pressure, and temperature. When used as a mass flow transmitter, these independent values can be used to compensate for changes in density, viscosity, and other flow parameters. Although multivariable transmitters can be more expensive than traditional differential pressure transmitters, they eliminate the need for multiple devices at a single measurement point. This means fewer transmitters, less wiring, fewer process penetrations, and lower overall installed cost. Figure 1.5.4.a - An integrated DP flowmeter. 14
Multivariable transmitters, unlike traditional differential pressure transmitters, are capable of calculating mass flow, energy flow, volumetric flow, and totalized flow. 1.6 DP FLOW MEASUREMENT APPLICATIONS DP Flow measurement allows the optimization of many different aspects of a process including the following: Product consistency Production efficiency Process variable control Safety Internal billing/allocation Custody transfer Product Consistency: Batch-based products depend on accurate proportions of ingredients DP Flow helps ensure the accurate of delivery of liquids and gases. Production Efficiency: Metering and measurement of flow are part of a broad range of process control variables related to efficiency, from batch control, to by-product scavenging, to emissions monitoring. Internal Billing & Resource Allocation: Tighter control over inventories and process rates contributes directly to profitability. For many sophisticated producers, internal billing around process costs directly impacts the bottom line. Custody Transfer: Flow metering is the cash register for products sold by volume or weight. An accurate measurement on the dispensing side accounts for every drop and on the receiving side minimizes overcharging. 1.7 FLOWMETER INSTALLATIONS: TRADITIONAL VERSUS INTEGRATED Sensor and process instrumentation in general has seen a great deal of integration of both form and function over the last two decades with DP Flow being no exception. At this point in time, there are two broad types of DP flowmeters installations: traditional and integrated. 1.7.1 Traditional The Traditional Installation Method calls for three separate component categories. 1. Primary element (differential pressure producer) 2. Secondary element (transmitter) 3. Tertiary elements (impulse lines, connecting hardware, tubing, fittings, valves, etc.) 1 Figure 1.6.a - Utility monitoring is a major component of production efficiency. 3 2 Process Variable Control: Processes often include multiple variable inputs. Control over these variables, including flow rates, is key to quality production. Safety: DP Flow helps prevent a broad range of threats to safety including overfilling, reactor control, and others. 15 Figure 1.7.1.a - The traditional DP Flow installation has separate primary element, top left, tertiary elements (impulse lines, valves, connectors, and manifold), and secondary element, the transmitter, center right).
The traditional form enables component-bycomponent engineering to meet a wide variety of applications and can be engineered to meet custody transfer standards. Owing to its long history, many traditions around DP-based flow measurement have emerged. Some of these traditions, however, have led to inherent limitations or problems. These include multiple potential leak points at connectors, separate/incorrect piping and manifolding; accuracy problems traceable to long impulse lines. In addition, installation is complex, requiring long straight runs (dependent on the primary element used) and careful configuration of components. Much work has been done over the years to correct for some of these issues, and thus extend the usefulness and value of DP Flow installations. 1.7.2 Integrated The integrated flowmeter integrates the primary element and the transmitter into a single flowmeter assembly. It was in large part developed to minimize the issues around installations of the older-style traditional flowmeter. As a result, its installation calls for components and less labor than traditional flowmeters installations. The integrated flowmeter works much the same way as that of the traditional flowmeter. It uses the same equations, works largely with the same primary elements, and is available with the same transmitters (both differential pressure and multivariable). 1.7.3 Benefits of the Integrated Flowmeter An integrated flowmeter design eliminates the need for fittings, tubing, valves, adapters, manifolds, and mounting brackets. Compared to traditional installation, the benefits of integrated flowmeters include: Fewer potential leak points (factory leakchecked) Fewer flow measurement error sources Simplified ordering and installation Decreased susceptibility to freezing and plugging More compact footprint Rosemount integrated flowmeters combine industry leading transmitters with innovative primary element technologies and connection systems. There are in effect 10 devices in one flowmeter, simplifying engineering, procurement, and installation. 2 3 4 5 6 1 10 7 8 9 Figure 1.7.2.a - This integrated DP flowmeter combines both the primary element and the transmitter into a single flowmeter assembly, reducing potential leak points during installation and use.. Figure 1.7.3.a - Traditional DP Flow structure. See page 17 for callouts. 16
9 10 2 3 1 5 Figure 1.7.3.b - Integrated multivariable instrumentation. In Figures 1.7.3.a and 1.7.3.b: 1. Flow Computer 2. Primary Element 3. Thermowell 4. Temperature Sensor 5. Temperature Transmitter 6. Sensor Wiring 7. Pressure Transmitter 8. DP Transmitter 9. Manifold 10. Connection Hardware 1.8 ALTERNATE FLOW TECHNOLOGIES Flow measurement can be performed with a broad range of technologies other than pressure-based. These include open channel, mechanical, ultrasonic, electromagnetic, Coriolis, optical, thermal mass, and vortex types. Electromagnetic flowmeters, which require an electrically-conductive fluid and a means for inducing magnetic energy to the flow, use electrodes to sense current induction from the magnetic flux. 7 4 8 6 Optical flow meters use photodetectors to gauge the movement of particles in an illuminated fluid stream. Vortex flow meters use electrical pulse generators commonly a piezoelectric crystal to measure flow disturbances (vortices) around a calibrated obstruction. Each of the various flow measurement technologies in existence today has its ideal range of applications. However, thanks to its long history, its ease of use, and its immense range of applicability, DP Flow remains the most commonly used form of flow measurement in industry. 1.9 SUMMARY Differential pressure flow metering is the most common technology for measuring flow in a closed pipe. The technology is based on well-known laws of physics, fluid dynamics and mass transport Its long history of use has led to the creation of basic and practical engineering solutions for a broad range of applications Manufacturers offer a large catalog of general and application-specific DP Flow instrumentation 1.9.1 History Over the past centuries great strides have been made in the advancement of flow measurement. Two major of the major players in these advancements were Daniel Bernoulli and Osborne Reynolds. Decreased susceptibility to freezing and plugging More compact footprint Rosemount integrated flowmeters combine industry leading transmitters with innovative primary element technologies and connection systems. There are in effect 10 devices in one flowmeter, simplifying engineering, procurement, and installation. Coriolis flow meters, as the name implies, use the Coriolis effect, which induces distortion in a vibrating tube. 17
1.9.2 The Phenomenon of Pressure The most crucial background concept in the domain of DP flow is pressure, the physical phenomenon that is harnessed to derive measurements. Accurate measurement of liquid, gas, and steam pressure is basic to many industrial processes and, of course, specific to DP flow measurement. 1.9.3 DP Flow 101 The Basics A DP flowmeter consists of two major elements, a primary element, a restrictor in a pipe; and a secondary element, the differential pressure transmitter. There are many kinds of primary elements: Orifice plates Venturi tubes Elbows Flow nozzles Single - and multiple-port pitot tubes Cones Segmental wedges 1.9.4 Applications of DP Flow Measurement Process engineering and cost engineering are the two primary disciplines that exploit DP flow. The primary objectives include engineering for: Product consistency Production efficiency Process variable control Safety Internal billing/allocation Custody transfer 1.9.5 Instrument Form Factors: Traditional Versus Integrated There are two broad types of DP flow meters available, traditional and integrated. The traditional form consists of three component categories. 1. Primary element (Differential pressure producer) 2. Secondary element (transmitter) 3. Tertiary elements (impulse lines, connecting hardware, tubing, fittings, valves, etc.) The integrated form integrates the primary element and the transmitter into a single entity. See figure 1.9.3.a. 1.9.6 Alternate Flow Technologies Figure 1.9.3.a - The modern DP flowmeter which integrates the primary and secondary elements. Flow measurement can be performed with a broad range of technologies other than pressure-based. These include: Open channel Mechanical Ultrasonic Electromagnetic Coriolis Optical Thermal mass Vortex Thanks to its range of usability and its critical mass of knowledge, DP flow remains the most-used form of flow measurement in industry. 18
Standard Terms and Conditions of Sale can be found at: www.rosemount.com/terms_of_sale. The Emerson logo is a trademark and service mark of Emerson Electric Co. Rosemount and Rosemount logotype are registered trademarks of Rosemount Inc. All other marks are the property of their respective owners. 2015 Rosemount Inc. All rights reserved. www.rosemount.com Literature reference number: 00805-0100-1041 Rev AA March 2015