1) This document discusses fluid flow in pipelines and the mechanical energy balance equation. It provides differential and integral forms of the equation accounting for changes in potential energy, kinetic energy, and friction losses.
2) It also discusses the Darcy-Weisbach equation for calculating friction losses and how to determine the friction factor from the Moody diagram.
3) Methods are presented for calculating pressure drops in compressible and incompressible flow, including the use of the Bernoulli equation and equations of state to relate pressure, temperature, and density for gases.
The document discusses fluid flow in pipes and provides examples of applying key principles like continuity, Bernoulli's equation, and Torricelli's theorem. It summarizes the Trans-Alaskan pipeline that transports oil over 800 miles through a single 48-inch diameter pipe. Key equations are defined for volume, weight, and mass flow rates. Bernoulli's equation relates pressure, elevation, and velocity changes between two points. Examples show applying continuity to find velocity and Bernoulli's equation to find pressure. Torricelli's theorem governs velocity from an orifice based on fluid height.
This document contains solutions to 6 fluid mechanics problems involving concepts like Bernoulli's equation, dynamic pressure, and flow rate calculations. Problem 6.70 asks the reader to express the mass flow rate through a nozzle in terms of the pressure difference ∆p between the inlet and exit, the inlet temperature T1, and the diameters D1 and D2 of the inlet and exit. The solution uses Bernoulli's equation between the inlet and exit, along with the relationship between flow velocity and pipe diameter, to derive an expression for the exit velocity V2 in terms of these parameters.
The document describes four thermodynamic cycles: Otto, Diesel, Dual, and air-standard cycles. It provides equations for calculating work, heat transfer, and efficiency for each cycle. It explains that the Dual cycle generalizes the Otto and Diesel cycles by allowing both constant volume and constant pressure heat addition. It also notes that the Diesel cycle has lower efficiency than the Otto cycle at the same compression ratio but is used in combustion engines because it requires higher compression to ignite fuel.
This document discusses the application of first order differential equations in mechanical engineering analysis. It begins with an overview of first order differential equations and solution methods. It then discusses specific applications in fluid dynamics, including the design of containers and funnels using equations for fluid flow and Bernoulli's equation. The document provides examples of using first order differential equations to model and solve problems related to draining water tanks and tapered funnels.
EES Functions and Procedures for Forced convection heat transfertmuliya
This file contains notes on Engineering Equation Solver (EES) Functions and Procedures for Forced convection heat transfer calculations. Some problems are also included.
These notes were prepared while teaching Heat Transfer course to the M.Tech. students in Mechanical Engineering Dept. of St. Joseph Engineering College, Vamanjoor, Mangalore, India.
It is hoped that these notes will be useful to teachers, students, researchers and professionals working in this field.
Contents:
• Forced convection – Tables of formulas
• Boundary layer, flow over flat plates, across cylinders, spheres and tube banks –
• Flow inside tubes and ducts
185817220 7e chapter5sm-final-newfrank-white-fluid-mechanics-7th-ed-ch-5-solu...Abrar Hussain
This document summarizes the solutions to several problems involving dimensional analysis. Some key points:
- Problem 5.1 calculates the volume flow rate needed for transition to turbulence in a pipe based on given parameters.
- Problem 5.2 uses dimensional analysis to determine the prototype velocity matched by a scale model wind tunnel test.
- Problem 5.6 calculates the expected drag force on a scale model parachute based on full-scale test data, showing the forces are exactly the same due to dynamic similarity.
EES Functions and Procedures for Natural convection heat transfertmuliya
This file contains notes on Engineering Equation Solver (EES) Functions and Procedures for Natural (or, free) convection heat transfer calculations. Some problems are also included.
These notes were prepared while teaching Heat Transfer course to the M.Tech. students in Mechanical Engineering Dept. of St. Joseph Engineering College, Vamanjoor, Mangalore, India.
It is hoped that these notes will be useful to teachers, students, researchers and professionals working in this field.
Contents:
• Natural convection formulas - Tables
• Natural convection from Vertical plates & cylinders, horizontal plates, cylinders and spheres, from enclosed spaces, rotating disks and spheres, and from finned surfaces
• Combined Natural and forced convection
- Francis turbines are radial flow turbines used in hydroelectric power generation. They have adjustable guide vanes and runners that control water flow.
- Key dimensions include the diameters and widths at the inlet and outlet, as well as the rotational speed. These dimensions are calculated based on design criteria like flow rate, head, and hydraulic efficiency.
- Dimensions are chosen to satisfy requirements for net positive suction head (NPSH) and minimize hydraulic losses while maintaining high hydraulic efficiency.
The document discusses fluid flow in pipes and provides examples of applying key principles like continuity, Bernoulli's equation, and Torricelli's theorem. It summarizes the Trans-Alaskan pipeline that transports oil over 800 miles through a single 48-inch diameter pipe. Key equations are defined for volume, weight, and mass flow rates. Bernoulli's equation relates pressure, elevation, and velocity changes between two points. Examples show applying continuity to find velocity and Bernoulli's equation to find pressure. Torricelli's theorem governs velocity from an orifice based on fluid height.
This document contains solutions to 6 fluid mechanics problems involving concepts like Bernoulli's equation, dynamic pressure, and flow rate calculations. Problem 6.70 asks the reader to express the mass flow rate through a nozzle in terms of the pressure difference ∆p between the inlet and exit, the inlet temperature T1, and the diameters D1 and D2 of the inlet and exit. The solution uses Bernoulli's equation between the inlet and exit, along with the relationship between flow velocity and pipe diameter, to derive an expression for the exit velocity V2 in terms of these parameters.
The document describes four thermodynamic cycles: Otto, Diesel, Dual, and air-standard cycles. It provides equations for calculating work, heat transfer, and efficiency for each cycle. It explains that the Dual cycle generalizes the Otto and Diesel cycles by allowing both constant volume and constant pressure heat addition. It also notes that the Diesel cycle has lower efficiency than the Otto cycle at the same compression ratio but is used in combustion engines because it requires higher compression to ignite fuel.
This document discusses the application of first order differential equations in mechanical engineering analysis. It begins with an overview of first order differential equations and solution methods. It then discusses specific applications in fluid dynamics, including the design of containers and funnels using equations for fluid flow and Bernoulli's equation. The document provides examples of using first order differential equations to model and solve problems related to draining water tanks and tapered funnels.
EES Functions and Procedures for Forced convection heat transfertmuliya
This file contains notes on Engineering Equation Solver (EES) Functions and Procedures for Forced convection heat transfer calculations. Some problems are also included.
These notes were prepared while teaching Heat Transfer course to the M.Tech. students in Mechanical Engineering Dept. of St. Joseph Engineering College, Vamanjoor, Mangalore, India.
It is hoped that these notes will be useful to teachers, students, researchers and professionals working in this field.
Contents:
• Forced convection – Tables of formulas
• Boundary layer, flow over flat plates, across cylinders, spheres and tube banks –
• Flow inside tubes and ducts
185817220 7e chapter5sm-final-newfrank-white-fluid-mechanics-7th-ed-ch-5-solu...Abrar Hussain
This document summarizes the solutions to several problems involving dimensional analysis. Some key points:
- Problem 5.1 calculates the volume flow rate needed for transition to turbulence in a pipe based on given parameters.
- Problem 5.2 uses dimensional analysis to determine the prototype velocity matched by a scale model wind tunnel test.
- Problem 5.6 calculates the expected drag force on a scale model parachute based on full-scale test data, showing the forces are exactly the same due to dynamic similarity.
EES Functions and Procedures for Natural convection heat transfertmuliya
This file contains notes on Engineering Equation Solver (EES) Functions and Procedures for Natural (or, free) convection heat transfer calculations. Some problems are also included.
These notes were prepared while teaching Heat Transfer course to the M.Tech. students in Mechanical Engineering Dept. of St. Joseph Engineering College, Vamanjoor, Mangalore, India.
It is hoped that these notes will be useful to teachers, students, researchers and professionals working in this field.
Contents:
• Natural convection formulas - Tables
• Natural convection from Vertical plates & cylinders, horizontal plates, cylinders and spheres, from enclosed spaces, rotating disks and spheres, and from finned surfaces
• Combined Natural and forced convection
- Francis turbines are radial flow turbines used in hydroelectric power generation. They have adjustable guide vanes and runners that control water flow.
- Key dimensions include the diameters and widths at the inlet and outlet, as well as the rotational speed. These dimensions are calculated based on design criteria like flow rate, head, and hydraulic efficiency.
- Dimensions are chosen to satisfy requirements for net positive suction head (NPSH) and minimize hydraulic losses while maintaining high hydraulic efficiency.
The document summarizes key concepts in fluid mechanics including:
1) Types of fluid flow such as steady, unsteady, uniform, and non-uniform flow. It also discusses the continuity, Bernoulli, and momentum equations used to solve fluid problems.
2) Applications of Bernoulli's equation such as flow over weirs, through orifices and pipes, and venturi meters. It also discusses concepts like total energy, hydraulic grade line, and more.
3) Examples are provided calculating velocity, pressure, flow rates, and more at different points in pipe systems using the governing equations.
Applied thermodynamics by mc conkey (ed 5, ch-12)anasimdad007
A reciprocating compressor takes in a gas and delivers it at a higher pressure through the cyclic action of pistons in cylinders. There are two main types - single-acting and double-acting. The compression process can follow different thermodynamic paths like isothermal, polytropic, or isentropic on a pressure-volume or temperature-entropy diagram. Isothermal compression provides the minimum work and highest efficiency. The indicated power and efficiency of a reciprocating compressor depends on parameters like mass flow rate, inlet and outlet pressures and temperatures, and the compression process path.
The document provides information on the dimensions and performance of Kaplan turbines, including diagrams showing dimensions such as diameter, blade height and spacing for turbines in Nigeria and Chile. It also contains graphs depicting hydraulic efficiency and cavitation effects in relation to parameters like speed and blade angle. The example calculation at the end demonstrates how to determine the diameter, blade height and number of vanes given design criteria like power output, head and flow rate.
This document provides information about various air standard cycles used in internal combustion engines, including the Otto, Diesel, and Dual cycles. It defines the key processes and equations for each cycle. The Otto cycle involves four processes: isentropic compression, constant volume heat addition, isentropic expansion, and constant volume heat rejection. The Diesel cycle involves: isentropic compression, constant pressure heat addition, isentropic expansion, and constant volume heat rejection. The Dual cycle combines aspects of the Otto and Diesel cycles, involving five processes. Thermodynamic relationships between pressure, volume, temperature and other variables are defined through equations for each cycle.
This document describes the design process for a Pelton turbine. It begins with the key dimensions and equations for Pelton turbines. It then provides an example of dimensioning a Pelton turbine with the given parameters of flow rate, head, and power output. The process involves choosing values for variables like number of nozzles and buckets, then calculating dimensions like jet diameter, runner diameter, and speed based on the design equations.
Heat and Mass Transfer: Free Convection : Formulas and solved examples... Use of Heat and Mass transfer data book is necessary in order to obtain certain values.
An isobaric process is a constant pressure process where pressure (P) remains constant. Work (W) done is equal to pressure (P) times the change in volume (ΔV). For an ideal gas, the change in internal energy (ΔU) is equal to heat (Q) added.
An isometric process is a constant volume process where volume (V) remains constant. Work (W) done is zero since there is no change in volume. For any substance, the change in internal energy (ΔU) is equal to the heat (Q) added.
An isothermal process is a constant temperature process where temperature (T) remains constant. For an ideal gas, the ratio
thermodynamic and heat transfer examplesfahrenheit
This document outlines homework problems for a thermodynamics course. It includes 4 multi-part problems involving analyzing Otto, gas turbine, internal combustion, and Diesel cycles. The problems require calculating temperatures, pressures, work, efficiency, and other variables at each step in the thermodynamic cycles. Tables of constants are provided and equations shown. Drawings of P-V diagrams are requested to be labeled with the relevant values.
The document describes three common internal combustion engine cycles: the Otto, Diesel, and Dual cycles. It provides diagrams and equations to illustrate the thermodynamic processes involved in each cycle, including compression, combustion, and expansion processes. Key parameters like compression ratio, cut-off ratio, pressure ratio, and thermal efficiency are defined. The cycles are compared in terms of their heat addition processes, net work output, and thermal efficiency calculations.
Air enters a combustion chamber with a mach number of 0.15. Sufficient heat is added to raise the stagnation temperature ratio to 3 and the final mach number is 0.8. To determine:
1) The entry mach number is 0.15
2) Due to heating, the static pressure decreases along the flow. The percentage loss in static pressure needs to be determined.
3) The properties of air (γ, Cp) are given to solve the problem.
This document discusses the assumptions and equations used in air-standard cycle analysis of internal combustion engines. It covers:
- The assumptions of the ideal air-standard cycle, including constant specific heats, reversible processes, and no combustion.
- The relevant thermodynamic equations for analyzing the Otto cycle of intake, compression, combustion, expansion, exhaust.
- How real engine cycles differ from the ideal cycle assumptions due to varying composition and properties during combustion, finite combustion duration, valve overlap effects.
- How to account for pump work from intake/exhaust pressures and residual exhaust gases in the clearance volume.
The document provides solutions to several exercises related to slurry transport. For Exercise 4.1, the solution analyzes shear stress and shear rate data for a phosphate slurry and determines it follows a power-law relationship with a flow index of 0.15 and consistency index of 23.4 Ns0.15/m2. Exercise 4.2 verifies an equation for pressure drop in pipe flow of a power-law fluid. Exercise 4.3 similarly verifies an equation incorporating a yield stress. Subsequent exercises provide solutions for pressure drop, slurry concentration, and rheological properties calculations using data given.
This document contains solved problems from chapter 12 on positive displacement machines. Problem 12.1 calculates the indicated power and delivery temperature for air compression in a single-stage reciprocating compressor under isentropic, isothermal and polytropic processes. Problem 12.2 calculates the bore size required for the compressor running at 1000 rpm with a stroke to bore ratio of 1.2:1. Problem 12.3 calculates various parameters like bore, stroke, volumetric efficiency and indicated power for a single-stage single-acting air compressor running at 1000 rpm.
This document describes a conjugate heat transfer analysis of an electronics cooling system using OpenFOAM. It outlines the objectives to develop a CFD model for CHT analysis and validate it with experiments. The methodology section describes the governing equations solved for fluid and solid regions as well as the interface coupling. A simple circuit board cooling case is modeled and tested. Additionally, a server cooling case is proposed with details on geometry, meshing, boundary conditions and results showing temperature distributions.
This document provides information about the Otto cycle, which is the ideal thermodynamic cycle that models the processes in a spark-ignition internal combustion engine.
It includes:
- A flow diagram and PV diagram of the Otto cycle processes
- Equations for calculating temperature, pressure, heat transfer, work, efficiency, and mean effective pressure at each state point
- Two example problems applying the Otto cycle equations
- Key parameters like compression ratio, heat added, expansion ratio, and state variables
The goal is to analyze the thermodynamics of the ideal Otto cycle as a basis for comparing spark-ignition engines. Sample calculations are provided to illustrate applying the cycle equations.
Introduction to chemical engineering thermodynamics, 6th ed [solution]Pankaj Nishant
This document contains solutions to math problems involving concepts of thermodynamics, including calculations of work, heat, internal energy, enthalpy, and phase changes. Problem 1 calculates the work done in lifting a mass and the resulting internal energy change. Problem 2 determines the heat transferred and final temperature when water gains a small amount of heat. Problem 3 is a series of thermodynamic steps where the initial and final internal energies must sum to zero.
This document contains comments on the textbook "Thermodynamics: An Engineering Approach, 7th ed. (SI Units)" by Yunus Cengel and Michael Boles. It notes several errors, inconsistencies, and places where clarification or improved explanation would enhance understanding. Over 100 specific comments are provided regarding figures, examples, problems, equations, explanations, and notations throughout the textbook. The goal is to improve the accuracy and pedagogical effectiveness of the textbook.
Fox and McDonalds Introduction to Fluid Mechanics 9th Edition Pritchard Solut...KirkMcdowells
Full download : https://alibabadownload.com/product/fox-and-mcdonalds-introduction-to-fluid-mechanics-9th-edition-pritchard-solutions-manual/ Fox and McDonalds Introduction to Fluid Mechanics 9th Edition Pritchard Solutions Manual
The document summarizes key concepts in fluid mechanics including:
1) Types of fluid flow such as steady, unsteady, uniform, and non-uniform flow. It also discusses the continuity, Bernoulli, and momentum equations used to solve fluid problems.
2) Applications of Bernoulli's equation such as flow over weirs, through orifices and pipes, and venturi meters. It also discusses concepts like total energy, hydraulic grade line, and more.
3) Examples are provided calculating velocity, pressure, flow rates, and more at different points in pipe systems using the governing equations.
Applied thermodynamics by mc conkey (ed 5, ch-12)anasimdad007
A reciprocating compressor takes in a gas and delivers it at a higher pressure through the cyclic action of pistons in cylinders. There are two main types - single-acting and double-acting. The compression process can follow different thermodynamic paths like isothermal, polytropic, or isentropic on a pressure-volume or temperature-entropy diagram. Isothermal compression provides the minimum work and highest efficiency. The indicated power and efficiency of a reciprocating compressor depends on parameters like mass flow rate, inlet and outlet pressures and temperatures, and the compression process path.
The document provides information on the dimensions and performance of Kaplan turbines, including diagrams showing dimensions such as diameter, blade height and spacing for turbines in Nigeria and Chile. It also contains graphs depicting hydraulic efficiency and cavitation effects in relation to parameters like speed and blade angle. The example calculation at the end demonstrates how to determine the diameter, blade height and number of vanes given design criteria like power output, head and flow rate.
This document provides information about various air standard cycles used in internal combustion engines, including the Otto, Diesel, and Dual cycles. It defines the key processes and equations for each cycle. The Otto cycle involves four processes: isentropic compression, constant volume heat addition, isentropic expansion, and constant volume heat rejection. The Diesel cycle involves: isentropic compression, constant pressure heat addition, isentropic expansion, and constant volume heat rejection. The Dual cycle combines aspects of the Otto and Diesel cycles, involving five processes. Thermodynamic relationships between pressure, volume, temperature and other variables are defined through equations for each cycle.
This document describes the design process for a Pelton turbine. It begins with the key dimensions and equations for Pelton turbines. It then provides an example of dimensioning a Pelton turbine with the given parameters of flow rate, head, and power output. The process involves choosing values for variables like number of nozzles and buckets, then calculating dimensions like jet diameter, runner diameter, and speed based on the design equations.
Heat and Mass Transfer: Free Convection : Formulas and solved examples... Use of Heat and Mass transfer data book is necessary in order to obtain certain values.
An isobaric process is a constant pressure process where pressure (P) remains constant. Work (W) done is equal to pressure (P) times the change in volume (ΔV). For an ideal gas, the change in internal energy (ΔU) is equal to heat (Q) added.
An isometric process is a constant volume process where volume (V) remains constant. Work (W) done is zero since there is no change in volume. For any substance, the change in internal energy (ΔU) is equal to the heat (Q) added.
An isothermal process is a constant temperature process where temperature (T) remains constant. For an ideal gas, the ratio
thermodynamic and heat transfer examplesfahrenheit
This document outlines homework problems for a thermodynamics course. It includes 4 multi-part problems involving analyzing Otto, gas turbine, internal combustion, and Diesel cycles. The problems require calculating temperatures, pressures, work, efficiency, and other variables at each step in the thermodynamic cycles. Tables of constants are provided and equations shown. Drawings of P-V diagrams are requested to be labeled with the relevant values.
The document describes three common internal combustion engine cycles: the Otto, Diesel, and Dual cycles. It provides diagrams and equations to illustrate the thermodynamic processes involved in each cycle, including compression, combustion, and expansion processes. Key parameters like compression ratio, cut-off ratio, pressure ratio, and thermal efficiency are defined. The cycles are compared in terms of their heat addition processes, net work output, and thermal efficiency calculations.
Air enters a combustion chamber with a mach number of 0.15. Sufficient heat is added to raise the stagnation temperature ratio to 3 and the final mach number is 0.8. To determine:
1) The entry mach number is 0.15
2) Due to heating, the static pressure decreases along the flow. The percentage loss in static pressure needs to be determined.
3) The properties of air (γ, Cp) are given to solve the problem.
This document discusses the assumptions and equations used in air-standard cycle analysis of internal combustion engines. It covers:
- The assumptions of the ideal air-standard cycle, including constant specific heats, reversible processes, and no combustion.
- The relevant thermodynamic equations for analyzing the Otto cycle of intake, compression, combustion, expansion, exhaust.
- How real engine cycles differ from the ideal cycle assumptions due to varying composition and properties during combustion, finite combustion duration, valve overlap effects.
- How to account for pump work from intake/exhaust pressures and residual exhaust gases in the clearance volume.
The document provides solutions to several exercises related to slurry transport. For Exercise 4.1, the solution analyzes shear stress and shear rate data for a phosphate slurry and determines it follows a power-law relationship with a flow index of 0.15 and consistency index of 23.4 Ns0.15/m2. Exercise 4.2 verifies an equation for pressure drop in pipe flow of a power-law fluid. Exercise 4.3 similarly verifies an equation incorporating a yield stress. Subsequent exercises provide solutions for pressure drop, slurry concentration, and rheological properties calculations using data given.
This document contains solved problems from chapter 12 on positive displacement machines. Problem 12.1 calculates the indicated power and delivery temperature for air compression in a single-stage reciprocating compressor under isentropic, isothermal and polytropic processes. Problem 12.2 calculates the bore size required for the compressor running at 1000 rpm with a stroke to bore ratio of 1.2:1. Problem 12.3 calculates various parameters like bore, stroke, volumetric efficiency and indicated power for a single-stage single-acting air compressor running at 1000 rpm.
This document describes a conjugate heat transfer analysis of an electronics cooling system using OpenFOAM. It outlines the objectives to develop a CFD model for CHT analysis and validate it with experiments. The methodology section describes the governing equations solved for fluid and solid regions as well as the interface coupling. A simple circuit board cooling case is modeled and tested. Additionally, a server cooling case is proposed with details on geometry, meshing, boundary conditions and results showing temperature distributions.
This document provides information about the Otto cycle, which is the ideal thermodynamic cycle that models the processes in a spark-ignition internal combustion engine.
It includes:
- A flow diagram and PV diagram of the Otto cycle processes
- Equations for calculating temperature, pressure, heat transfer, work, efficiency, and mean effective pressure at each state point
- Two example problems applying the Otto cycle equations
- Key parameters like compression ratio, heat added, expansion ratio, and state variables
The goal is to analyze the thermodynamics of the ideal Otto cycle as a basis for comparing spark-ignition engines. Sample calculations are provided to illustrate applying the cycle equations.
Introduction to chemical engineering thermodynamics, 6th ed [solution]Pankaj Nishant
This document contains solutions to math problems involving concepts of thermodynamics, including calculations of work, heat, internal energy, enthalpy, and phase changes. Problem 1 calculates the work done in lifting a mass and the resulting internal energy change. Problem 2 determines the heat transferred and final temperature when water gains a small amount of heat. Problem 3 is a series of thermodynamic steps where the initial and final internal energies must sum to zero.
This document contains comments on the textbook "Thermodynamics: An Engineering Approach, 7th ed. (SI Units)" by Yunus Cengel and Michael Boles. It notes several errors, inconsistencies, and places where clarification or improved explanation would enhance understanding. Over 100 specific comments are provided regarding figures, examples, problems, equations, explanations, and notations throughout the textbook. The goal is to improve the accuracy and pedagogical effectiveness of the textbook.
Fox and McDonalds Introduction to Fluid Mechanics 9th Edition Pritchard Solut...KirkMcdowells
Full download : https://alibabadownload.com/product/fox-and-mcdonalds-introduction-to-fluid-mechanics-9th-edition-pritchard-solutions-manual/ Fox and McDonalds Introduction to Fluid Mechanics 9th Edition Pritchard Solutions Manual
The document discusses using ethnographic research methods like observation and interviews to understand a dance group called TrancenDANCE better. Observations revealed challenges like teachers forgetting choreography and students needing a larger practice space. Interviews found that students enjoy the group but the fees are a financial burden. Desk research showed college costs stress students financially. A proposal for a shared space and fundraising help from celebrities aims to address the group's needs.
BẠN MUỐN PHÁT TRIỂN THƯƠNG HIỆU MÀ KHÔNG CẦN PHẢI SUY NGHĨ Mỹ Hoàng
Cty Cổ Phần Dream Paradise Media chúng tôi mang đến cho quý khách những dịch vụ tốt nhất cho tất cả thương hiệu, xây dựng chiến lược nếu bạn chưa biết sẽ phát triển thương hiệu của mình ra sao, cung cấp lượng khách hàng tiềm năng cho Sales BĐS và hỗ trợ các nhãn hàng mỹ phẩm tìm kiếm đại lý phân phối. Chúng tôi cam kết sẽ mang đến cho quý khách một dịch vụ hàng đầu tốt nhất.
From selecting, managing and evaluating outside counsel to building stronger client relationships, and delivering cost predictability and forecasting, metrics can add up to valuable insight and positive change for both corporations and firms.
Brand management with respective of CaburyPrateek Pawar
All of us are consumers. We consume things of daily use; we also consume and buy the products according to our needs, preferences and buying power. These can be consumable goods, durable goods, specialty goods or, industrial goods.
This document summarizes a paper analyzing Turkey's response to the Syrian refugee crisis. It begins with an introduction to the crisis and conceptualizes refugee protection as a public good subject to collective action problems. It then discusses three ways to address these problems: international institutions, policy harmonization, and specialization. The document argues specialization is most promising as it allows countries to contribute in ways aligning with their comparative advantages. It introduces role theory as a framework for understanding how countries' refugee policies relate to their domestic, regional, international, and ideological roles and goals. The remainder will use Turkey as a case study to evaluate how well its response achieves these various roles.
El documento presenta los cruceros de lujo de Silversea para 2013, que ofrecerán más destinos, lujo y valor. Sus barcos acogedores de tamaño medio ofrecerán un servicio todo incluido de gran calidad, con suites espaciosas y un servicio personalizado de mayordomo. Los pasajeros podrán disfrutar de comidas de alta cocina, bebidas ilimitadas, propinas incluidas y traslados a los puertos.
Eurostat a publié le 13 décembre 2016 un communiqué de presse sur la consommation par habitant en standards de pouvoir d'achats en 2015.
Selon Eurostat, la consommation par habitant a varié entre 53% en Bulgarie et 137% au Luxembourg de la moyenne de l'UE.
Outre le Luxembourg qui avec 37% au dessus de la moyenne de l'UE est le pays qui affiche le niveau le plus élevé; la France également se situe au dessus de la moyenne de l'UE avec 112%.
Wilhelmina Models is one of the most prominent talent management agencies in the world, founded in 1967 in the Netherlands. Wilhelmina Dubai was established in 2012 in the United Arab Emirates by Al Tamimi Investments to be the first international model agency in the Middle East. Wilhelmina Dubai works closely with Wilhelmina International to provide high caliber professional models and industry experts to the UAE and region. The agency has three divisions: Models, Hostess, and Creative.
Este documento presenta un estudio de riesgo sísmico realizado para el proyecto Caserones ubicado en la III Región de Chile. Describe el ambiente sismotectónico de la zona, caracterizado por la subducción de la placa de Nazca, y analiza la sismicidad histórica. Lleva a cabo una evaluación probabilística y determinística de la amenaza sísmica considerando múltiples fuentes sísmicas, y determina espectros de respuesta elástica para el diseño sísmico del proyecto.
Este documento presenta los productos tecnológicos de Positivo BGH BUSINESS, incluyendo notebooks, all-in-one y tablets. Ofrece soluciones flexibles para empresas con respaldo posventa. Sus líneas de producto son notebooks FYS2, FX1000 y ONE 2302 PRO; y tablets Y1000 y Y420, que ofrecen rendimiento, portabilidad, conectividad, seguridad y diseño.
El documento proporciona información sobre la marca StarClass de cruceros de lujo. StarClass ofrece cruceros en barcos más pequeños con menos pasajeros y una mayor proporción de espacio por pasajero, lo que permite un servicio más exclusivo y personalizado. Los cruceros StarClass ofrecen una amplia gama de comodidades y lujos, como camarotes más amplios y suites con terraza privada.
This document summarizes key concepts in advanced thermodynamics including:
- Pressure-temperature and pressure-volume diagrams for pure fluids and the phase change curves and points they depict.
- Equations of state relating pressure, volume, and temperature for homogeneous fluids in equilibrium.
- Properties and examples of ideal gas behavior and the virial equation of state for real gases.
- Calculation of work, heat, internal energy, and enthalpy changes for various thermodynamic processes involving ideal gases including isothermal, adiabatic, constant pressure, and throttling processes.
This document summarizes key concepts in thermodynamics including:
- Pressure-temperature and pressure-volume diagrams and important points like the triple point and critical point.
- Equations of state relating pressure, volume, and temperature for pure fluids.
- Ideal gas behavior and equations like the ideal gas law.
- Thermodynamic processes like isothermal, adiabatic, and their calculations.
- Use of concepts and equations to calculate work, heat, internal energy and enthalpy change for processes involving ideal gases.
The drift flux model is applicable to two-phase flows like gas-liquid flows and fluidized beds. It accounts for the relative velocity between phases using the concept of drift flux. The model equations can be solved graphically or numerically to obtain void fraction and drift velocity for different flow regimes like cocurrent, countercurrent flows. Correlations are provided to estimate drift velocity and void profile parameter based on flow conditions.
This document discusses the volumetric properties of pure fluids. It covers pressure-temperature diagrams and pressure-volume diagrams, including phase change curves, triple points, and critical points. Equations of state are presented that relate pressure, volume, and temperature for fluids in equilibrium. The ideal gas law and virial equations of state are also discussed. Specific heat capacities, isothermal compressibility, and volume expansivity are defined. Several examples problems calculate work, heat, internal energy and enthalpy changes for ideal gas processes including compression, expansion, heating and cooling.
1. The document discusses the concepts of Euler's equation, Bernoulli's equation, and their applications in fluid dynamics problems involving one-dimensional steady flow.
2. Bernoulli's equation relates the total pressure, velocity, and elevation along a streamline. It is used to analyze flow through orifices, venturi meters, and orifice meters.
3. Measurement techniques like the pitot-static tube and manometers are used to experimentally determine velocities and pressure losses based on the equations.
This document discusses convective heat and mass transfer in confined flows, such as flow through a tube or hollow fiber. It provides the dimensional and non-dimensional forms of the governing equations, including the transport equation, continuity equation, and momentum equation. It also defines important non-dimensional numbers like the Peclet number, Reynolds number, Nusselt number, and Sherwood number. An example problem examines heat transfer on a flat plate and temperature distribution in a tube with specified wall temperatures.
This chemistry problem set covers topics in thermodynamics including:
1) Calculating the isothermal compressibility of ideal gases and van der Waals gases.
2) Finding work, heat, internal energy and enthalpy change for ideal gas processes including isothermal compression/expansion and cooling.
3) Deriving an expression for work during isothermal reversible expansion of a van der Waals gas.
4) Calculating enthalpy changes for hydrogenation reactions of unsaturated hydrocarbons.
5) Deriving a relationship between initial and final temperatures for adiabatic ideal gas processes.
The document discusses the derivation of entropy from the second law of thermodynamics. It defines entropy as a quantitative measure of microscopic disorder for a system. Entropy is derived by applying the first law of thermodynamics to a heat engine and system undergoing a cyclic process. This leads to the Clausius inequality and the definition of entropy change between two states. Entropy change has contributions from both heat transfer and irreversible processes (entropy generation). Expressions for entropy change are derived for incompressible substances, ideal gases, and gases with variable specific heats.
1) The second law of thermodynamics leads to the definition of entropy, which is a measure of microscopic disorder and energy unavailable for useful work.
2) The Clausius inequality derives the working definition of entropy and mathematically expresses the second law. It states that the net work done by a heat engine in a cycle must be less than or equal to zero.
3) Entropy changes can be calculated using the Tds equation, where the integral of dQ/T over a reversible process between two states equals the change in entropy between those states. This allows entropy to be analyzed on temperature-entropy diagrams.
The first law of thermodynamics states that the change in internal energy of a system is equal to the heat supplied to the system minus the work done by the system. For a closed system undergoing a process, this can be expressed as ΔU=Q-W. The first law applies to both closed systems undergoing non-flow processes as well as open systems undergoing steady flow processes. For non-flow processes such as constant volume, constant pressure, isothermal, and adiabatic processes, the first law allows determining the relationships between heat, work and changes in internal energy or enthalpy. For steady flow processes, the general energy equation accounts for changes in kinetic and potential energy of the fluid in addition to heat
This document provides an overview of basic hydraulic concepts and one-dimensional design techniques for centrifugal pumps. It defines key terms like specific speed, Euler equations, velocity triangles, and slip. It also provides equations and charts for calculating design parameters like impeller diameter, discharge width, meridional velocities, and head. The design process involves calculating specific speed, selecting the number of vanes, solving for impeller diameter, and using constants to determine other geometry and flow properties.
The document discusses flow properties in open channels including:
- The Reynolds number and Froude number, which characterize flow regimes as turbulent or laminar and subcritical/supercritical.
- Hydraulic properties such as depth, area, wetted perimeter, hydraulic radius, and section factor which describe channel geometry.
- Critical flow occurs when the Froude number equals 1. Subcritical flow has a Froude number less than 1 while supercritical flow has a Froude number greater than 1.
- Examples are provided to demonstrate calculating hydraulic properties for given channel cross sections.
This document discusses thermodynamic properties and calculations. It defines thermodynamic properties as quantities that characterize a system's overall state, like temperature, pressure, and volume. It also outlines the first and second laws of thermodynamics. The first law states that energy is conserved, while the second law concerns the direction of spontaneous processes and limits energy conversions. Examples are provided to demonstrate calculating work, heat, internal energy, and enthalpy changes for ideal gases undergoing various thermodynamic processes.
1. The chapter discusses momentum and forces in fluid flow, including the development of the momentum principle using Newton's second law and the impulse-momentum principle.
2. The momentum equation is developed for two-dimensional and three-dimensional flow through a control volume, accounting for forces, velocities, flow rates, and momentum correction factors.
3. Examples of applying the momentum equation are presented, including forces on bends, nozzles, jets, and vanes.
The document summarizes key concepts from the first and second laws of thermodynamics:
1) The first law of thermodynamics states that energy is conserved in thermodynamic processes. It describes energy balance for open and closed systems undergoing various processes like mixing, heating, work etc.
2) The second law states that entropy always increases in spontaneous processes. It introduces the concept of entropy and explains why heat flows spontaneously from hot to cold bodies.
3) Applications of the first and second laws include heat engines, refrigerators, heat pumps and their analysis in terms of thermal efficiency. The Carnot cycle establishes the maximum possible efficiency for heat engines and refrigerators.
The document summarizes key aspects of pressure derivatives in well testing:
1) The pressure derivative has important diagnostic properties and allows matching field curves to type curves to better analyze flow regimes like radial flow.
2) During radial flow, the logarithmic pressure derivative will be constant, appearing as a horizontal line on a diagnostic plot. During wellbore storage, it will be a straight line with a slope of one.
3) For buildup testing, the pressure derivative can also identify flow regimes like afterflow or radial flow, appearing as different characteristic lines on a diagnostic plot.
4) Derivatives are approximated numerically, requiring filtering of noise, with algorithms using weighted averages of nearby points to smooth
The document provides information about air standard cycles. It discusses the Otto cycle and Diesel cycle, which are the ideal cycles for spark-ignition and compression-ignition engines respectively. The Otto cycle consists of isentropic compression, constant volume heat addition, isentropic expansion, and constant volume heat rejection. The thermal efficiency of the Otto cycle is calculated using the temperature ratios. The Diesel cycle consists of isentropic compression until the cut-off ratio, constant pressure heat addition, isentropic expansion, and isentropic compression. An example calculation is provided to illustrate determining various parameters of the Otto cycle.
Drilling Hydraulic of Compressible and In-compressible Drilling FluidAmir Rafati
Incompressible Fluids
1. static Well Conditions
• Hydrostatic Pressure in Liquid Columns
• Hydrostatic Pressure in Mixed Columns
• Kick Identification
• Buoyancy and Effect of Buoyancy on Buckling
2. Non-static Well Conditions
• Flow Through Jet Bits
• Shear Stress V.S. Shear Rate (Laminar)
3. Rheological Models
• Newtonian
• Non-Newtonian
• Rotational Viscometer
• Initial Circulating of Well
4. Laminar Flow In Pipes & annulus
• Newtonian Flow In Pipes & annulus
• Newtonian Flow In Pipes & annulus (As a Slot)
5. Turbulent Flow In Pipes & annulus
• Moody Diagram
• Critical Velocity
• Hanks Turbulence Criterion
6. Extension Equations For Flow
• Hydraulic Radius
• Apparent Viscosity
7. Jet Nozzle Size Selection
• Pressure loss Simplification
• Maximum Nozzle Velocity
• Maximum Bit Hydraulic Horsepower
• Maximum Jet Impact Force
• Minimum needed annular Velocity
8. Surge and swab pressure of Vertical Pipe Move
9. Particle Slip Velocity
10. Known Cleaning Needs
Compressible Fluids
11. Basic Technology
• Introduction
• Surface Equipment
• Down hole Equipment
• Compressors
• Shallow Well Drilling Applications
12. Circulation Systems
• Reverse Circulation
• Direct Circulation
13. Comparison of Mud and Air Drilling
• Pressure profile
• Heat capacity
• Density profile
• Kinetic energy profile
14. Surface Equipment Summery
• Drilling Location
• Flow Line to the Rig
• Wellhead Equipment
• Flow Line from Rig
15. Downhole Equipment Summery
• Rotary Drill String
• Drill Bits
• Bottom hole Assembly
• Drill Pipe
• Safety Equipment
• Drill String Design
16. Compressors type Nominations
• Continuous Flow
• Intermittent Flow
17. Power Requirements
• Single Stage Shaft
• Multistage Shaft
• Prime Mover Input
18. Reciprocating Compressor Unit
19. Shallow Well Drilling Applications
• Shallow Well Drilling Planning
• Direct Circulation
• Reverse Circulation
• Direct Circulation Based on Weight Rate of Flow
• General Derivation
• Wet and Dry Air and Gas Drilling Model
• Unstable and Stable Foam Drilling
• Aerated Fluid Drilling Model
20. Direct Circulation Hydraulic Sections
• the injection pressure into the top of the drill string
• pressure at bottom of drill pipe inside the drill string
• pressure at bottom of drill collars inside the drill string
• pressure above drill bit inside the drill string
• pressure at bottom of drill collars in the annulus
• pressure at bottom of drill pipe in the annulus
• pressure at the bottom of casing in the annulus
• pressure at the top of the annulus
21. Air and Gas Drilling Models
• Deep Well Drilling Planning
• Minimum Volumetric Flow Rate
• Terminal Velocities
• Injection Pressure and Selection of Compressor Equipment
• Prime Mover Fuel Consumption
• Water Injection
• Drilling and Completion Problems
22. Major & Minor Loss & Injection Pressure
• Non-Frictional Approximation
• Frictional Approximation
Trilinear embedding for divergence-form operatorsVjekoslavKovac1
The document discusses a trilinear embedding theorem for divergence-form operators with complex coefficients. It proves that if matrices A, B, C are appropriately p,q,r-elliptic, then there is a bound on the integral of the product of the gradients of the semigroups associated with the operators. The proof uses a Bellman function technique and shows the relationship to the concept of p-ellipticity. It generalizes previous work on bilinear embeddings to the trilinear case.
A SYSTEMATIC RISK ASSESSMENT APPROACH FOR SECURING THE SMART IRRIGATION SYSTEMSIJNSA Journal
The smart irrigation system represents an innovative approach to optimize water usage in agricultural and landscaping practices. The integration of cutting-edge technologies, including sensors, actuators, and data analysis, empowers this system to provide accurate monitoring and control of irrigation processes by leveraging real-time environmental conditions. The main objective of a smart irrigation system is to optimize water efficiency, minimize expenses, and foster the adoption of sustainable water management methods. This paper conducts a systematic risk assessment by exploring the key components/assets and their functionalities in the smart irrigation system. The crucial role of sensors in gathering data on soil moisture, weather patterns, and plant well-being is emphasized in this system. These sensors enable intelligent decision-making in irrigation scheduling and water distribution, leading to enhanced water efficiency and sustainable water management practices. Actuators enable automated control of irrigation devices, ensuring precise and targeted water delivery to plants. Additionally, the paper addresses the potential threat and vulnerabilities associated with smart irrigation systems. It discusses limitations of the system, such as power constraints and computational capabilities, and calculates the potential security risks. The paper suggests possible risk treatment methods for effective secure system operation. In conclusion, the paper emphasizes the significant benefits of implementing smart irrigation systems, including improved water conservation, increased crop yield, and reduced environmental impact. Additionally, based on the security analysis conducted, the paper recommends the implementation of countermeasures and security approaches to address vulnerabilities and ensure the integrity and reliability of the system. By incorporating these measures, smart irrigation technology can revolutionize water management practices in agriculture, promoting sustainability, resource efficiency, and safeguarding against potential security threats.
Advanced control scheme of doubly fed induction generator for wind turbine us...IJECEIAES
This paper describes a speed control device for generating electrical energy on an electricity network based on the doubly fed induction generator (DFIG) used for wind power conversion systems. At first, a double-fed induction generator model was constructed. A control law is formulated to govern the flow of energy between the stator of a DFIG and the energy network using three types of controllers: proportional integral (PI), sliding mode controller (SMC) and second order sliding mode controller (SOSMC). Their different results in terms of power reference tracking, reaction to unexpected speed fluctuations, sensitivity to perturbations, and resilience against machine parameter alterations are compared. MATLAB/Simulink was used to conduct the simulations for the preceding study. Multiple simulations have shown very satisfying results, and the investigations demonstrate the efficacy and power-enhancing capabilities of the suggested control system.
Electric vehicle and photovoltaic advanced roles in enhancing the financial p...IJECEIAES
Climate change's impact on the planet forced the United Nations and governments to promote green energies and electric transportation. The deployments of photovoltaic (PV) and electric vehicle (EV) systems gained stronger momentum due to their numerous advantages over fossil fuel types. The advantages go beyond sustainability to reach financial support and stability. The work in this paper introduces the hybrid system between PV and EV to support industrial and commercial plants. This paper covers the theoretical framework of the proposed hybrid system including the required equation to complete the cost analysis when PV and EV are present. In addition, the proposed design diagram which sets the priorities and requirements of the system is presented. The proposed approach allows setup to advance their power stability, especially during power outages. The presented information supports researchers and plant owners to complete the necessary analysis while promoting the deployment of clean energy. The result of a case study that represents a dairy milk farmer supports the theoretical works and highlights its advanced benefits to existing plants. The short return on investment of the proposed approach supports the paper's novelty approach for the sustainable electrical system. In addition, the proposed system allows for an isolated power setup without the need for a transmission line which enhances the safety of the electrical network
Using recycled concrete aggregates (RCA) for pavements is crucial to achieving sustainability. Implementing RCA for new pavement can minimize carbon footprint, conserve natural resources, reduce harmful emissions, and lower life cycle costs. Compared to natural aggregate (NA), RCA pavement has fewer comprehensive studies and sustainability assessments.
A review on techniques and modelling methodologies used for checking electrom...nooriasukmaningtyas
The proper function of the integrated circuit (IC) in an inhibiting electromagnetic environment has always been a serious concern throughout the decades of revolution in the world of electronics, from disjunct devices to today’s integrated circuit technology, where billions of transistors are combined on a single chip. The automotive industry and smart vehicles in particular, are confronting design issues such as being prone to electromagnetic interference (EMI). Electronic control devices calculate incorrect outputs because of EMI and sensors give misleading values which can prove fatal in case of automotives. In this paper, the authors have non exhaustively tried to review research work concerned with the investigation of EMI in ICs and prediction of this EMI using various modelling methodologies and measurement setups.
Introduction- e - waste – definition - sources of e-waste– hazardous substances in e-waste - effects of e-waste on environment and human health- need for e-waste management– e-waste handling rules - waste minimization techniques for managing e-waste – recycling of e-waste - disposal treatment methods of e- waste – mechanism of extraction of precious metal from leaching solution-global Scenario of E-waste – E-waste in India- case studies.
1. PIPELINE ENGINEERING
FLUID FLOW
Mechanical Energy Balance
g z vdp
V
W Fo∆ ∆+ +
⎛
⎝
⎜
⎜
⎞
⎠
⎟
⎟ = −∫ ∑
2
2
(1-1)
potential energy expansion work Kinetic energy Work added/ Sum of friction
change change subtracted by losses
compressors
or pumps/expanders
Note that the balance is per unit mass. In differential form
FWVdVvdpgdz o δδ −=++ (1-2)
Rewrite as follows
( )dp g dz V dV F Wo= − ⋅ − ⋅ − +ρ δ δ (1-3)
Divide by dL (L is the length of pipe)
dp
dL
g
dz
dL
V
dV
dL
F
L
W
LTot
o= − ⋅ + ⋅ + −ρ ρ ρ
δ
δ
ρ
δ
δ
(1-4)
or:
dp
dL
dp
dL
dp
dL
dp
dLTot elev accel frict
⎞
⎠
⎟ =
⎞
⎠
⎟ +
⎞
⎠
⎟ +
⎞
⎠
⎟ (1-5)
(
δ
δ
W
L
o
is usually ignored, as the equation applies to a section of pipe)
The above equation is an alternative way of writing the mechanical energy balance. It is not a
different equation.
The differential form of the potential energy change is
2. Natural Gas Basic Engineering Copyright: Miguel Bagajewicz.
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2
dZ
φ
dL
g
dZ
dL
g= sin φ (1-6)
Friction losses: We use the Fanning or Darcy-Weisbach equation (Often called Darcy equation)
δF
V f
D
dL=
2 2
(1-7)
an equation that applies for single phase fluids, only (two phase fluids are treated separately).
The friction factor, in turn, is obtained from the Moody Diagram below.
Figure 1-1: Moody Diagram
Friction factor equations. (Much needed in the era of computers and excel)
Laminar Flow f =
16
Re
(1-8)
3. Natural Gas Basic Engineering Copyright: Miguel Bagajewicz.
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3
Turbulent Flow f a
=
0 046.
Re
(1-9)
smooth pipes: a=0.
Iron or steel pipes a=0.16
Turbulent Flow
1
2
37
2 51
10
f D f
= − +
⎛
⎝
⎜
⎞
⎠
⎟log
.
.
Re
ε
(Colebrook eqn) (1-10)
Equivalent length of valves and fittings: Pressure drop for valves and fittings is accounted for
as equivalent length of pipe. Typical values can be obtained from the following Table.
Table 1-1: Equivalent lengths for various fittings.
Fitting eL
D
45O
elbows 15
90O
elbows, std radius 32
90O
elbows, medium radius 26
90O
elbows, long sweep 20
90O
square elbows 60
180O
close return bends 75
180O
medium radius return bends 50
Tee (used as elbow, entering run) 60
Tee (used as elbow, entering branch) 90
Gate Valve (open ) 7
Globe Valve (open ) 300
Angle Valve (open) 170
Pressure Drop Calculations
Piping is known. Need pressure drop. (Pump or compressor is not present.)
Incompressible Flow
a) Isothermal (ρ is constant)
Tot
dp dZ dV dF
= - g +V +
dL dL dL dL
ρ
⎛ ⎞
⎜ ⎟
⎝ ⎠
(1-11)
for a fixed φ ⇒ V constant ⇒ dV = 0
4. Natural Gas Basic Engineering Copyright: Miguel Bagajewicz.
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4
2
2
L
F V f
D
δ
δ
⎛ ⎞
= ⋅ ⋅⎜ ⎟
⎝ ⎠
(1-12)
∆ ∆p g Z V f
L
D
F= − ⋅ + ⋅ ⋅ +
⎡
⎣
⎢
⎤
⎦
⎥∑ρ 2 2
(1-13)
b) Nonisothermal
It will not have a big error if you use ρ(Taverage), v(Taverage)
Exercise 1-1:
Consider the flow of liquid water (@ 20o
C) through a 200 m, 3” pipe, with an elevation change
of 5 m. What is the pressure drop?
Can the Bernoulli equation assuming incompressible flow be used for gases? The next figure
illustrates it.
5. Natural Gas Basic Engineering Copyright: Miguel Bagajewicz.
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5
Figure 1-2: Error in Bernoulli equation
In conclusion, if
p p
p
out in
in
−
≤ −0 2 0 3. . using the assumption of incompressibility is OK.
Compressible Flow (Gases)
a) Relatively small change in T (known)
6. Natural Gas Basic Engineering Copyright: Miguel Bagajewicz.
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6
For small pressure drop (something you can check after you are done) can use Bernoulli and
fanning equation as flows
2
V
gdz+vdp+d = -dF
2
⎛ ⎞
⎜ ⎟
⎝ ⎠
(1-14)
Then
2 2 2
g 1 V dF
dz+ dp+ dV = -
v v v v
(1-15)
but
G
V = v
A
, where
V = Velocity (m/sec)
v = Specific volume (m3
/Kg)
G = Mass flow (Kg/sec)
A = Cross sectional area (m2
)
Then,
2
2 2
g 1 G dV dF G dL
dz+ dp+ = - = -2f
v v A v v A D
⎛ ⎞ ⎛ ⎞
⎜ ⎟ ⎜ ⎟
⎝ ⎠ ⎝ ⎠
(1-16)
Now put in integral form
g
dz
v
dp
v
G
A
dV
V
G
A D
f dL2
2 2
2
1
∫ ∫ ∫ ∫+ +
⎛
⎝
⎜
⎞
⎠
⎟ = − ⋅
⎛
⎝
⎜
⎞
⎠
⎟ ⋅ ⋅ (1-17)
Assume
in out
av
T +T
T =
2
(1-18)
2
3
in out
av in out
in out
p p
p p p
p p
⎡ ⎤
= + −⎢ ⎥
+⎣ ⎦
which comes from
out
in
av out
in
p p dp
p
p dp
=
∫
∫
(1-19)
in in out out
av
f(T ,P )+ f(T ,P )
f =
2
(1-20)
The integral form will now be
7. Natural Gas Basic Engineering Copyright: Miguel Bagajewicz.
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7
ρav
in
out
out
in
avg z
dp
v
G
A
V
V
G
A
f
L
D
2
2 2
2⋅ ⋅ + +
⎛
⎝
⎜
⎞
⎠
⎟
⎛
⎝
⎜
⎞
⎠
⎟ = − ⋅
⎛
⎝
⎜
⎞
⎠
⎟ ⋅ ⋅∫∆ ln (1-21)
Now use p v
Z R T
M
⋅ =
⋅ ⋅
, where M: Molecular weight. Then av
av
av av
p M
Z R T
ρ = , which leads to:
( ) ( )2 2 2 2
2 2
av
out in out in
av av av av av
dp M M
p dp p p p p
v Z RT Z RT p
ρ
= ⋅ = − = −
⋅∫ ∫ (1-22)
Therefore;
( )
2 2
2 2 2
ln 2
2
av out
av out in av
av in
VG G L
g z p p f
p A V A D
ρ
ρ
⎛ ⎞⎛ ⎞ ⎛ ⎞
⋅∆ + − + = −⎜ ⎟⎜ ⎟ ⎜ ⎟
⎝ ⎠ ⎝ ⎠⎝ ⎠
(1-23)
but,
V
V
Z T
Z T
p
p
out
in
out out
in in
in
out
=
⋅
⋅
⎛
⎝
⎜
⎞
⎠
⎟ ⋅ (1-24)
Then
( )
2 2
2 2 2
ln 2
2
av out out in
av out in av
av in in out
Z T pG G L
g z p p f
p A Z T p A D
ρ
ρ
⎛ ⎞⋅⎛ ⎞ ⎛ ⎞
⋅∆ + − + ⋅ = −⎜ ⎟⎜ ⎟ ⎜ ⎟
⋅⎝ ⎠ ⎝ ⎠⎝ ⎠
(1-25)
To calculate Zav Kay’s rule is used. This rule states that the reduced pressure and temperature
of the gas is obtained using the average pressure and temperature (as above calculated) and a
pseudo critical pressure and temperature.
,
av
r
C
p
p
p
= (1-26)
,
av
r
C
T
T
T
= (1-27)
In turn the critical pressure and temperatures are obtained as molar averages of the respective
components critical values.
,
,C i C i
i
p y p= ∑ (1-28)
,
,C i C i
i
T y T= ∑ (1-29)
With these values the Z factor comes from the following chart:
8. Natural Gas Basic Engineering Copyright: Miguel Bagajewicz.
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8
Figure 1-3: Natural Gas Compressibility Chart
Equation (1-25) can be further simplified. First neglect the acceleration term because it is
usually small compared to the others, to obtain:
9. Natural Gas Basic Engineering Copyright: Miguel Bagajewicz.
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9
( )
2
2 2 2
2 0
2
av
av out in av
av
G L
g z p p f
p A D
ρ
ρ
⎛ ⎞
⋅∆ + − + =⎜ ⎟
⎝ ⎠
(1-30)
Form this equation we can get G, as follows:
( )
2 2
2 22 5
2
32 2
av
in out av av
av av av av av
M p
g z
M p p Z RTD
G
f L Z RT Z RT
π
⎡ ⎤
⋅∆⎢ ⎥−
⎢ ⎥= −
⎢ ⎥
⎢ ⎥
⎣ ⎦
(1-31)
But the volumetric flow at standard conditions is given by s s s
G
p Q Z RT
M
= where the
subscript s stands for standard conditions. Therefore:
( )
2
2 2
2 22 5
2
2
2
32 2
av
in out
s s av av
s av av av
M p
p p g z
Z T Z RTR D
Q
Mp Z T L f
π
⎡ ⎤
− − ⋅∆⎢ ⎥
⎢ ⎥=
⎢ ⎥
⎢ ⎥
⎣ ⎦
(1-32)
Now, if z∆ =0, we get
( )2 22 22 5
2
2
32 2
in outs s
s av av av
p pZ TR D
Q
Mp Z T L f
π ⎡ ⎤−
⎢ ⎥=
⎢ ⎥⎣ ⎦
(1-33)
which can be rearranged as follows:
2 2 2
in outp p K Q− = (1-34)
where
2
2 2 2 5
64 s av av av
s s
Mp Z T f
K L
R Z T Dπ
= and is known to be W×L, a product of a resistant factor W
times the length L. With this, we have
2
2 2 2 5
64 s av av av
s s
Mp Z T f
W
R Z T Dπ
= .
To calculate pressure drop we recognize that average pressures are a function of outp , which is
unknown. Then we propose the following algorithm:
a) Assume (1)
outp and calculate (1)
avp
b) Calculate
2 ( ) ( ) ( )
( )
2 2 2 5
64 i i i
i s av av av
s s
Mp Z T f
K
R Z T Dπ
=
b) Use formula to get a new value 1 2 ( ) 2(i ) i
out inp = p K Q+
−
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d) Continue until
(i+1) (i)
out out
(i)
out
p - p
p
ε≤
Depending on the choice of friction term expression, several formulas have been reported for
equation (1-34). They are summarized in the following table.
Table 1-2: Different forms of compressible flow equations
11. Natural Gas Basic Engineering Copyright: Miguel Bagajewicz.
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11
Table 1-2 (continued): Different forms of compressible flow equations
Exercise 1-2:
Natural gas (84,000 std m3
/hr at 49 atm and 38o
C) is sent from a gas refinery to a city, through
a 16” pipeline. The distance is 170 Km. The gas reaches the other end at ground temperature,
(5 o
C). The gas to have the following molar fractions: Methane: 98%, ethane: 1.2%, propane:
0.75%, and water: 0.05%. We also assume Re~5 106
and ε/D =0.01.
As a first approximation, we recommend using the Panhandle A equation: 2 2 1.855
in outp p K Q− =
W= 2.552 × 10-4
Tin×s0.855
/D4.586
(Wilson G.G., R. T. Ellington and J. Farwalther, 1991, Institute
of Gas Technology Education Program, Gas distribution Home Study Course) , where s is the
gas gravity (=Mgas/Mair)=0.65 for natural gas), Tin is in o
R and D in inches)
What is the pressure drop?
12. Natural Gas Basic Engineering Copyright: Miguel Bagajewicz.
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12
Heat Transfer Effects
To account for temperature changes due to heat transfer, we use total energy balance
( ) ogdz+d vp +VdV du = q wδ δ+ + (1-35)
where the following is identified:
- Potential energy change: g dz
- Rate of work done on the fluid element by pressure forces: d(vp)
- Kinetic energy change: VdV
- Internal energy changes: du
- Heat transfer: qδ . This is given per unit mass flowing (Kcal/h)/(m3
/h)
- Work added: owδ . This term is due to pumps and compressors. Since we will treat
these separately, this term is usually set to zero for pipes.
But the heat qδ is given by interactions with the ambient surroundings:
( )o
D
q U T T dL
G
π
δ = − (1-36)
where U is the heat transfer coefficient, To is the outside pipe temperature, DdL dAπ = (see
next figure) and G is the flowrate.
Figure 1-4: Area element
Then, (ignoring δwo because there are no pumps) to get:
( )2
oU T -T DdLV
gdz+dh+d =
2 G
⎛ ⎞
⎜ ⎟
⎝ ⎠
(1-37)
Integrate and solve for hout (use Tav in the heat transfer equation)
( )
( )
2 2
2 1
2
o av out in
out in
U T T DL V V
h h g z z
G
π− ⎡ ⎤−
= + − − −⎢ ⎥
⎣ ⎦
(1-38)
But
V v
G
A
Z
RT
p M
G
A
out out av
av
out
= ⋅ = ⋅ (1-39)
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Finally, to obtain the outlet temperature, one would need to obtain it form the enthalpy and
pressure in the outlet
( )out out out outT = T p ,h (1-40)
The procedure suggested is then:
a) Assume Tout, pout
b) Use mechanical energy balance to obtain (1)
outp
c) Use total energy balance to obtain (1)
outh
d) get temperature (1)
outT
e) Go to b) and continue until convergence
SCENARIO II
One has a turbine or Compressor/pump and needs Wo. We use total energy with δq = 0 and
dz =0
2
o
dV
dh= w -
2
δ (1-41)
Integrating, one obtains:
2
o
W V
w h
G 2
⎛ ⎞
= = ∆ + ∆⎜ ⎟
⎝ ⎠
(1-42)
In this expression, we have wo given in Joules/Kg, W in Joules/sec and h in Joules/Kg. Thus,
the work of the compressor/pump is given by:
2
V
W G h
2
⎡ ⎤⎛ ⎞
= ∆ + ∆⎢ ⎥⎜ ⎟
⎝ ⎠⎣ ⎦
(1-43)
For compressors, W is positive, while for turbines, it is negative. However, ∆h is known for
liquids because enthalpy does not vary much with pressure. In addition, there isn’t much
temperature change in pumps). However, for gases, ∆h is much harder to obtain. Therefore we
go back to the Mechanical Energy equation for pumps/compressors. Indeed, the Bernoulli
equation gives
2
V
W G vdp G vdp
2
⎡ ⎤⎛ ⎞
= + ∆ ≈⎢ ⎥⎜ ⎟
⎝ ⎠⎣ ⎦
∫ ∫ (1-44)
where the acceleration term has been neglected. For pumps, the density is constant, so one
obtains:
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W
G
p=
ρ
∆ (1-45)
For compressors, one needs to obtain an expression of volume knowing that the evolution is
isentropic (or nearly isentropic). Thus, pvn
= constant (n=Cp/Cv for ideal gases n>Cp/Cv for
real gases). Substituting v p vs
n
s
n
= ⋅ ⋅
⎛
⎝
⎜
⎞
⎠
⎟
1
1
1
ρ
integrate to get
1
1
1
n
n
out
in in
in
pn
W G p v
n p
−
⎡ ⎤
⎛ ⎞⎡ ⎤ ⎢ ⎥= −⎜ ⎟⎢ ⎥ ⎢ ⎥+⎣ ⎦ ⎝ ⎠⎢ ⎥⎣ ⎦
(1-46)
The above expression does not include the compressibility factor. A better expression, which
includes the efficiency, is
1
1
1
1 2
n
n
in out out
in
a in
Z Z pn
W G RT
n pη
−
⎡ ⎤
⎛ ⎞+⎡ ⎤ ⎢ ⎥= −⎜ ⎟⎢ ⎥ ⎢ ⎥+⎣ ⎦ ⎝ ⎠⎢ ⎥⎣ ⎦
(1-47)
The efficiency factor is usually between 60 to 80% and normally given by the manufacturer.
One expression for such factor is:
1
1
n
n
out
in
in
a
out in
p
T
p
T T
η
−
⎡ ⎤
⎛ ⎞⎢ ⎥−⎜ ⎟⎢ ⎥⎝ ⎠⎢ ⎥⎣ ⎦=
−
(1-48)
Finally, the outlet temperature is obtained from
n n
in in out outp v p v= (1-49)
Using the gas law to obtain /in outv v in terms of temperatures and pressures, substituting and
rearranging, on e obtains:
[ ]
1
1
n
nn
out out n
in in
T p
CR
T p
−
−⎡ ⎤
= =⎢ ⎥
⎣ ⎦
(1-50)
where CR is the compression ratio. Normally, manufacturers recommend not exceeding 300 o
F
at the outlet.
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15
Exercise 1-3:
The natural gas of exercise 1-2, is available originally at 2 atm. Calculate the compression
work needed to reach delivery pressure (49 atm) using one compressor. Calculate the outlet
temperature and determine the duty needed to cool the gas down to the corresponding inlet
conditions. Is it acceptable to use one compressor?
We now discuss the compression ratio. This is limited in compressors to the range 1.2 to 6.
Extra compressors should be added if the CR >6, and after-coolers need to be added to control
the temperature. If more than one compressor is to be used, the practice is to use the same CR
for all.
Exercise 1-4:
Consider two compressors.
- Write the power expression for each one assuming the gas is cooled down to its inlet
temperature after compression.
- Add both expressions to obtain the total work as a function of the intermediate
pressure (the rest should not be a variable)
- Take first derivative and obtain the desired result that CR1=CR2
Exercise 1-5:
Obtain the set of compressors needed to compress the gas of exercise 1-2 properly, that is,
limiting the temperature and using the right CR.
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Two Phase Flow
Two phase flow has several regimes, which are depicted in the next figure:
Figure 1-5: Two phase flow regimes
The two extreme cases are:
- Bubble: Vapor and Liquid in Equilibrium (Benzene 40%, Toluene 60%)
- Dispersed: Liquid and gas (air and benzene).
The latter is common in gas pipelines; the former is common in crude pipelines, especially light
crudes.
Dispersed
Annular
Stratified
Froth
Wavy
Slug
Plug
Bubble
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One important thing to recognize is that except for the extreme cases, the phases travel at
different velocities. Typical velocities are shown in the next table:
Table 1-3: Typical velocities of two phase flows
REGIME LIQUID VEL(ft/sec) VAPOR VEL.(ft/sec)
Dispersed Close to vapor > 200
Annular <0.5 > 20
Stratified <0.5 0.5-10
Slug 15 (But less than vapor vel.) 3-50
Plug 2 < 4
Bubble 5-15 0.5-2
To predict the flow patterns, one needs to use the Baker Plot (next Figure) for horizontal pipes
(there is a similar one for vertical pipes).
Figure 1-6: Two phase flow regimes transitions
In this diagram, we have g
g
W
G
A
⎛ ⎞
= ⎜ ⎟
⎝ ⎠
, L
l
g
W
G
W
λ
⎛ ⎞
= ⎜ ⎟⎜ ⎟
⎝ ⎠
, (W in lb/h, A in in2
) which are the
superficial velocity of the vapor and the liquid, respectively. In turn, the parameters are given
by 0.463 L gλ ρ ρ= (with densities given in lb/ft3
)
1/3
2/3
1147 L
L
µ
ψ
σ ρ
= (with the surface tension
given in dyn/cm and the viscosity in cp)
We note that:
1) λ and ψ depend on the fluid property only
2) Gl depends on the ratio of flows (Known beforehand. Not a design parameter)
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3) Gg depends on the vapor/gas superficial velocity. It can be modified changing the
diameter
4) Transition boundaries are not at all that sharp.
From this diagram, we notice that following change of regimes in a pipe. As the pressure drop
is large, then the density of the vapor is lower.
1) gλψ ρ ⇒ l gG λψ ρ ⇒ Abscissa decreases
2)
1 1
g
λ ρ
⇒ 1g
g
G
λ ρ
⇒ Ordinate increases
Thus trajectories are always "up" and "to the left". Thus a bubbly flow may become, plug, slug
or annular, an annular may become wavy or dispersed, depending on the starting position in the
plot, and so on.
PRESSURE DROP
Lockart and Martinelli (1949) developed one of the first correlations. It is based on multiplying
the pressure drop obtained by considering the vapor phase occupying the whole pipe, by a
factor
2
TwoPhase VaporPhasep pφ∆ = ∆ (1-51)
In turn, the correction factor is given by b
aXφ = , where LiquidPhase
VaporPhase
p
X
p
∆
=
∆
. The following table
gives some typical values of the corresponding constants:
Table 1-4: Constants for Lockart and Martinelli’s correlation
a b
Bubble 14.2 0.75
Slug 1190 0.82
Stratified 15400 1
(horizontal)
Plug 27.3 0.86
Annular 4.8 -0.3125 D(in) 0.343-0.021 D(in)
We notice that there are several more modern correlations, which will be explored later. In
turn, the pressure drop due to gravity, is given by
(1 ) sing g g l
gravity
dp
g
dL
ε ρ ε ρ θ
⎞
⎡ ⎤= + −⎟ ⎣ ⎦
⎠
(1-52)
where gε is the (void) fraction of gas. We omit the pressure drop due to acceleration.
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Hydrate Formation
Hydrates are crystalline structures between water and hydrocarbons. One typical example is
given in the figure below:
Figure 1-7: Methane Hydrate
The next figure shows the Pressure-Temperature diagram of water-hydrocarbon systems. Curve
1-1 represents the curve for vapor pressure of the hydrocarbon.
Figure 1-8: Generic Hydrate P-T diagram
Cage of water molecules
CH4 molecule in the center
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The next figure shows some specific cases of hydrocarbons:
Figure 1-9: Hydrate P-T diagram for various hydrocarbons
Clearly, in high pressure pipelines, favorable thermodynamic conditions for hydrate formation
can be encountered. It is therefore important to keep in mind that these conditions need to be
avoided. These hydrates can be prevented from forming through heating, pressure change (not
a choice in pipelines) and the introduction of inhibitors. These inhibitors are salts, alcohols,
glycols, ammonia and MEA. The most widely used is methanol. The next figure shows the
depression of hydrate formation temperature observed for various hydrates.
Figure 1-10: Hydrate temperature formation depression
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Pipeline Costs
Historical pipeline and compressors installed cost data were obtained from the Oil & Gas
Journal special report on Pipeline Economics, September 3, 2001.
Pipeline per mile cost
distribution for different pipe diameters and compressor installed cost for different horsepower
requirement are plotted in the following figure. All cost figures are updated to 2005 dollars
using Marshal & Swift cost indexes.
y = 43.2x + 100
0
500
1000
1500
2000
2500
3000
0 10 20 30 40 50
Figure 1-11: Pipe average cost (k$/mile) vs. ID
y = 1.65x
0
20000
40000
60000
80000
100000
0 10000 20000 30000 40000
Figure 1-12: Compressor cost (k$) vs. horsepower
Fixed Capital Investment were calculated by adding the installed cost of a pipe length (assumed
5000 miles) and the cost of all required recompression stations. The Fixed Capital Investments
obtained are then divided by the pipe length to obtain a per mile cost profile for different flow
rates. The curve in the next figure shows that this cost profile takes a logarithmic shape.
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22
y = 0.001659x + 0.001108
B$ 0.000
B$ 0.001
B$ 0.001
B$ 0.002
B$ 0.002
B$ 0.003
B$ 0.003
B$ 0.004
B$ 0.004
B$ 0.005
B$ 0.005
0 0.2 0.4 0.6 0.8 1 1.2 1.4 1.6
BSCFD
Figure 1-13: Pipeline fixed cost (b$/mile) vs. capacity (BSCFD)
A linear correlation gives the following form:
001108.0)(*001659.0)/$( += BSCFDCapacitymileBFCI
Operating costs for pipelines were estimated as follows; an average of 5 operators is assumed
to be the requirement for each compression station, with an hourly wage of $21. Direct
supervisory and clerical labor is assumed to be 20% of operating labor. Compressor fuel
requirement is estimated at 8,000 Btu / BHP-HR, and fuel cost at $2.5 per million Btu.
Maintenance cost is assumed to be 7% of the FCI for compressors and 3% for pipes while
insurance is 1% for compressors and 0.4% for pipes. Operating cost per pipeline mile versus
capacity is plotted in the next figure:
y = 7E-05x + 4E-05
B$0.000000
B$0.000050
B$0.000100
B$0.000150
B$0.000200
B$0.000250
0 0.5 1 1.5
Figure 1-14: Pipeline per mile annual operating cost vs. capacity
This estimate should be reasonable with about 40% accuracy. Similar linear approximation to
that of the FCI is assumed. Linear regression was used to estimate the operating cost
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dependence of the capacity, ignoring capacities less than 100 MMSCFD. This gave a general
correlation of the following form:
00004.0)(*00007.0)//$(. += BSCFDCapacityyearmileBCostOper
Exercise 1-9:
Consider the pipeline of Exercise 1-8:
- Vary the pipeline maximum pressure (1200 psia) to some lower and higher value.
Adjust the diameter accordingly and calculate the number of recompression
stations.
- Calculate the cost. Can you say that 1200 psia is the right pressure?
Pipeline Looping
Pipeline looping is the practice of designing pipelines with segments run in parallel. This
practice increases the pipeline flow capacity without altering the final pressure. If temperature
is close to ambient temperature, the location of a loop does not change the final delivery
pressure. However, when temperature changes substantially, then the location of a loop has an
influence. Thus, in these cases, for example, it is recommended to loop in the upstream region,
where the gas is hotter. This allows the gas to cool down faster and therefore increase the
delivery pressure.
Consider the following example: A 100 Km length (20” OD) pipeline is used to send 289
MMSFD at an inlet pressure of 1,200 psia and a temperature of 45 o
C. The pipe roughness is
750 µ inches, and a soil temperature of 10 o
C.
Three alternatives were studied for this pipeline. a) No looping, b) Looping the first 25 Km,
and c) Looping the last 25 Km. The results of a simulation are shown in the next figure:
Figure 1-15: Results from Looping
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Exercise 1-10:
Verify the results of figure 1-15 using the simulator.
Retrograde condensation
One very common phenomenon in pipelines is retrograde condensation. Consider the P-T plot
of the next figure. It corresponds to a gas with the following composition: Methane: 93.47 %,
Ethane: 3.52%, Propane: 0.585%, n-butane: 0.16%, i-butane: 0.11%, pentane: 0.055%, i-
pentane 0.05%, hexane: 0.09%, heptane: 0.04%, octane: 0.03%, nonane: 0.01%, CO2: 0.0545,
N2: 1.34%. Assume a 15”, 200 Km pipeline starts at 60 atm and 15 o
C. If the external
temperature is 5 o
C (U=1 BTU/hr-ft2o
F), then it is clear that there will be liquid formation in
this pipeline, even if the operation is isothermal.
Figure 1-16: P-T diagram of example gas and retrograde condensation
Interestingly, if the pressure at the other end is low enough, then the liquid might vaporize
again. This means that the pressure drop regime inside the pipe might change and one has to be
careful in performing the simulations.
Exercise 1-11:
Generate the answers for the above example using the simulator. Change the pipe diameter and
the length to verify the statements.
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Pipeline Optimization Process
J-Curve Analysis
Conventional Pipeline design methods, which rely mostly on hand calculations or at best on
simple spreadsheet suggest that the compressor size and the pipe diameter be varied and the
cost of service ($/(m3
*Km) for the first year be plotted as a function of flowrate. Typical
assumptions are that there is no volume buildup in the pipe, the time value of money is
neglected and that the facilities are designed to sustain the flows.
For example, Figure 1-17 shows one such exercise performed for three different diameters and
parametric at different maximum operating pressures (MOP) and compression ratios.
Efficient operating ranges that are flat are preferred
Figure 1-17: J-Curves for various diameters
Exercise 1-12:
Explain why J-curves go through a minimum.
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Optimization Parameters
J-Curves are a simplistic first approach but one that can provide a first approximation to the
right diameter and compressors. Thus one needs to establish
- Route: In most cases this is defined by a variety of other factors and given to the
designer.
- Pipeline Initial Capacity: Most pipelines are constructed taking into account the
fact that demand at the receiving end(s) will increase through time. Thus, one is
faced with the decision of designing for future capacity and underutilize the pipeline
for some time or design for current or more short term capacity and use loops to
expand later.
- Expansions: If capacity expansions are considered, then they need to take place
through looping. Not only the new loop has to be designed, but its timing and
capacity be selected.
- Maximum operating pressure: This choice has already been considered in
constructing the J-Curves. However, in more complex situations, one is faced with
multiple delivery points with different delivery pressures, etc.
- Pipe Size: This choice has already been considered in the J-Curve selection but
needs to be revisited anyway in view of the influence of the other factors.
- Load Factor: This factor is the ratio between the average daily volume delivered
divided by the peak volume. If this ratio is too small, then storage facilities for
inventory holding (salt caverns, underground caverns, abandoned reservoirs, etc if
available, or large LNG or high pressure, CNG, storage tanks) are more convenient
than more powerful compressors and larger diameters. The issue to resolve is when
these are substituted by inventory holding sites. In addition, the question remains
where these holding sites should be located.
- Compressor Station Spacing: While an earlier exercise suggests that when
multiple compressors are used it is best to keep the compression ratio equal, this
hypothesis needs verification. Reciprocating compressors are chosen when the
power requirement is smaller than 5,500 Kw. Compression ratios recommended for
centrifugal compressors are generally in the range of 1.25 to 1.35 and smaller than
1.5 for reciprocating compressors.
Exercise 1-13:
Consider the pipeline of Exercise 1-8:
- Assume two compression stations will be used.
- Determine (by inspection and using a simulator what is the best compression ratio
for each compressor. Aim at minimizing total work only.
- Heating and Cooling: Clearly, cooling leads to significant savings because
pressure drop is reduced. However, money needs to be spent to install and run the
coolers. Thus the trade-off needs to be resolved.
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Exercise 1-14:
Consider the shown in the following figure
- The piping is in the ground and is not insulated. Assume a ground temperature of
25o
C and a ground conductivity of 0.7 W/(m o
C). The gas elevation profiles are
provided in the following table:
Km Elevation (m)
0 42
115 7
143 14.93
323 60
550 10
609 120
613 122
630 235
638 470
650 890
- The gas ((1.9% methane, 5% Ethane, 2% propane, 1% n-butane and 0.1% n-
pentane) is supplied at the two points indicated in the diagram at 1,367 kPa and
35o
C in the first station (Km 0), and 1520 kPa and 30o
C in the second (Km 143).
- Determine using simulations a) Piping diameter, b) Compressors at the supply
station, c) cooling required. Do not use a pressure above 5,600 Kpa. Use cost data
provided above.
- Will new compressors be needed/beneficial?
Supply: 10,407,840 m3/d
2,148,200 m3/d
Supply: 5,722,000 m3/d
18,240 m3/d
6,595,200
m3/d
134,400
m3/d
64,600 m3/d
Km 0 115 143 323 550 609 630 Km 650
2,832,000 m3/d
613
638
3,617,400 m3/d
384,000 m3/d
336,,000
m3/d
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OPTIMAL DESIGN
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