With the exception of brokaws equation, this group of equations is characterized by relative simplicity of use and limited accuracy. Basic concepts of fluid mechanics astrophysical dynamics, vt 2010 gas dynamics. B if abandonment pressure is 500 psia, calculate the initial gas reserve. Dynamic viscosity of gases is primarily a function of temperature. Throughout this chapter it will be assumed that the continuous phase is an ideal gas. This variation is provided in crane 1988 as a graph for hydrocarbon vapors and natural gases, and as an equation for other common gases.
Kinematic viscosity of propane at varying temperature and 1, 10 and 100 bara 14. Gas dynamics, equations of in the form of conservation laws in an inertial orthonormal coordinate system. The fundamental equations of gas dynamics 1 references for astrophysical gas fluid dynamics 1. To correct the calculation for the consistent temperature, volume, and or virtual leak. Dynamic pressure is the kinetic energy per unit volume of a fluid. Viscosity of interaction this group of equations uses explicit terms for the in. High enthalpy gas dynamics ethirajan rathakrishnan. Compressible flow or gas dynamics is the branch of fluid mechanics that deals with flows having significant changes in fluid density.
Dynamic viscosity the usual symbol for dynamic viscosity used by mechanical and chemical engineers as well as fluid dynamicists is the greek letter mu. The course builds upon foundations laid in an earlier course where the emphasis was on subsonic ideal. Mar 11, 2019 during last decades accurate twophase flow meters are introduced to upstream oil and gas industry. P, v, r, and t, the gas density will be in kgm 3 critical temperature and pressure. Pdf in this chapter, we present two variants of constructing the quasigas dynamic system, which allow us to obtain a concrete form of expressions for. Yo u can add other s as your time and budget allow. These are a set of class notes for a gas dynamicsviscous. Our gas dynamic equations are natural extensions of the navierstokes equations to the near continuum flow regime and can be used for microflow computations. Dynamic pressure is density times the fluid velocity squared times onehalf, assuming no friction and steady fluid flow throughout. His derivation, based on simple meanfreepath argu ments, leads to the expression v qmix i 1 v x. Dynamic viscosity of propane at varying temperature and 1, 10 and 100 bara 14. Dynamic viscosity is the resistance to movement of one layer of a fluid over another and is defined by formula f7. The viscosity on this page is the dynamic absolute viscosity.
Calculation of the viscosity of gas mixtures author. While all flows are compressible, flows are usually treated as being incompressible when the mach number the ratio of the speed of the flow to the speed of sound is less than 0. A gas turbine draws in air from atmosphere at 1 bar and 10oc and compresses it to 5 bar with an isentropic efficiency of 80%. The approximate formula that temperature effect on gas dynamic viscosity is. Computations of the interactions and of the motions of the individual particles are exceedingly difficult, and for this reason a statistical, or continuous, approach is adopted in describing the state of the. The beauty of this correlation is that it does not require the gas composition or the pseudo critical pressure temperature p pc t pc of the natural gas to calculate the viscosity.
These same techniques are later used to deal with two and threedimensional problems. The ranges of variables used in the correlation were 100 psia gas deviation factor at 500 psia 0. For ralph vorse, a new customer with national fuel, the numbers told the story. Dynamic pressure and the bernoulli equation are important in fluid dynamics, which has applications in aeronautical engineering and elsewhere in physics. The air is heated to 1200 k at constant pressure and then expanded through two stages in series back to 1 bar. The following formula given by poiseuille shows the dependence of the viscosity of a liquid on temperature in the case of gases, as mentioned earlier the intermolecular cohesion being negligible the viscosity depends mainly on transfer of molecular momentum in a direction at right angles to the direction of motion. Natural gas conversions natural gas conversions formula. To date dsmc is the basic numerical method in the kinetic theory of gases and rarefied gas dynamics. As noted in the introduction, in order to use the ideal gas law to calculate a gas density, the gas temperature. The aim of this book is to present the concepts, methods and applications of kinetic theory to rarefied gas dynamics.
Force area x time the pascal unit pa is used to describe pressure or stress force per area this unit can be combined with time sec to define dynamic viscosity. Pdf shock waves, vorticity waves, and entropy waves are fundamental discontinuity waves in nature and arise in supersonic or transonic gas flow, or. Fundamental equations 278 2 the equation of continuity 2. Expressed in the specific heat of the respective flue gas component. Dynamic viscosity for liquid fuels is occasionally required for performance calculations in. Natural gas conversions formula national fuel gas distribution corporation, 2016 there is no fuel out there that is beating natural gas. In the continuum flow regime, the new gas dynamic equations au. Theoretical gas dynamics considers the equations of motion applied to a. Below the fundamental aspects of the theory of numerical methods for solving problems in gas dynamics will be considered by writing down the equations of gas dynamics cf. T is gas dynamic viscosity when temperature is, pat s. These values are used to calculate total heat content of flue gases. Calculate available heat for natural gas fuel for industrial. Dynamic viscosity of propane at gas liquid equilibrium pressure.
Generalized gas dynamic equations semantic scholar. For the data from which the correlation was developed, the standard deviation in the calculated gas viscosity was 2. Expressed in mass of the respective flue gas component. C based on a 500 psia abandonment pressure, calculate the remaining gas. Ralph calculated his payback to be approximately three years when he converted his stove, furnace and water heater from propane to natural gas. Be able to calculate the viscosity of a gas at a specified temperature if the sutherland constant for the gas is known and the viscosity of the gas at a suitable reference temperature is known. The new solver is based on the implementation of regularized, or quasigas dynamic qgd equations. A former propane user, ralph knew he wanted to convert to clean, comfortable, efficient natural gas after he did. Transport properties of the dense gas and liquid 18 4. Natural gas transmission pipeline temperature drop calculation. Kinetic theory of gases is a part of statistical physics where the flow.
Newtons law of viscosity, pressure and temperature. Calculation of gas density and viscosity ced engineering. Compressible flow or gas dynamics is the branch of fluid mechanics that deals with flows. Derivation of approximate mixture viscosity formula an approximate formula for the viscosity of gas mixtures was derived by sutherland ref. Viscosity of gases the viscosity of a gas can be thought of as a measure of its resistance to flow and is measured in the cgs unit poise dyne seccm 2. Where total heat content of the respective flue gas component. Kinematic viscosity of propane at gas liquid equilibrium pressure. Shock tube calculator enter values and press the calculate button state 1 is driven, 2 is shocked and 5 is reflected. Th e international gas trade is dominated by a reference pricing mechanismoil indexationthat originated in europe in the 1960s but is under growing pressure there, bringing into question how natural gas may be priced in the future, not only in europe, but in asia and beyond. A simple and accurate method for calculating viscosity of. After its first introduction by gilbert flowing and gaslift well performance.
Natural gas pricing and its future carnegie endowment for. Calculate available heat for natural gas fuel 4 such as n 2, co 2, h 2 o, etc. Pdf in this chapter, we present two variants of constructing the quasigasdynamic system, which allow us to obtain a concrete form of expressions for. Dynamic measurement can be described as that measurement of a natural gas liquid while the liquid is flowing in a pipe. May 20, 2012 a read is counted each time someone views a publication summary such as the title, abstract, and list of authors, clicks on a figure, or views or downloads the fulltext. The first basic law of gas dynamics to be considered is the equation of continuity, which describes the conservation of mass in a noninteracting flow of velocity v. Dynamic viscosity an overview sciencedirect topics. Derivation of pressure loss to leak rate formula from the. Mathematical expressions of the fundamental laws of conservation of the mass, the momentum and the energy of a gas, which describe the state of the gas. The mixed finitevolume and finitedifference approximation is constructed on unstructured space.
Nitrogen is also one of common inject gases in gas injection projects, thus an accurate estimation of its viscosity is vital to analyze reservoir performance. Dynamic pressure is in fact one of the terms of bernoullis equation, which can be derived from the conservation of energy for a fluid in motion. Static measurements can be performed on either a direct or inferred mass basis. After introducing the basic tools, problems in plane geometry are treated using approximation techniques perturbation and numerical methods. A read is counted each time someone views a publication summary such as the title, abstract, and list of authors, clicks on a figure, or views or downloads the fulltext. Kinematic viscosity is dynamic viscosity divided by density formula f7. Many practical flow problems are essentially cases of isentropic flow. To these equations of motion, we must add equations of state for both phases. In simplified cases, the dynamic pressure is equal to the difference between the stagnation pressure and the static pressure.
A year later he decided to convert his wood burning fireplace as well. Gasdynamic analogy in the theory of stratified liquid flows with a. A presentation of two semiempirical general equations for the viscosity of a mixture of n gaseous components. C is dimensionless number associated with the kind of gas. This equation has the same mathematical form as inviscid equations of gas dynamics which give rise to discontinuous shock waves. The viscosity of gases near room temperature are in the centipoise range, so that is a commonly used unit. A gas is a population of a large number of particles molecules, atoms, ions in continuous chaotic motion. Shu the physics of astrophysics volume ii gas dynamics 3. High concentration nitrogen in natural gas affects not only the heat value of natural gas, but also gas viscosity which is critical to petroleum engineering.