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Ideal-Gas Mixtures and Real-Gas Mixtures
Thermodynamics: An Engineering Approach, 6th Edition Yunus A. Cengel, Michael A. Boles McGraw-Hill, 2008 Chapter 13 GAS MIXTURES Copyright © The McGraw-Hill Companies, Inc. Permission required for reproduction or display. Objectives • Develop rules for determining nonreacting gas mixture properties from knowledge of mixture composition and the properties of the individual components. • Define the quantities used to describe the composition of a mixture, such as mass fraction, mole fraction, and volume fraction. • Apply the rules for determining mixture properties to ideal-gas mixtures and real-gas mixtures. • Predict the P-v-T behavior of gas mixtures based on Dalton’s law of additive pressures and Amagat’s law of additive volumes. • Perform energy and exergy analysis of mixing processes. 2 COMPOSITION OF A GAS MIXTURE: MASS AND MOLE FRACTIONS To determine the properties of a mixture, we need to know the composition of the mixture as well as the properties of the individual components. There are two ways to describe the composition of a mixture: Molar analysis: specifying the number of moles of each component Gravimetric analysis: specifying the mass of each component The mass of a mixture is equal to the sum of the masses of its components. Mass fraction Mole The number of moles of a nonreacting mixture fraction is equal to the sum of the number of moles of its components. 3 Apparent (or average) molar mass The sum of the mass and mole fractions of a mixture is equal to 1. Gas constant The molar mass of a mixture Mass and mole fractions of a mixture are related by The sum of the mole fractions of a mixture is equal to 1. -
An Empirical Model Predicting the Viscosity of Highly Concentrated
Rheol Acta &2001) 40: 434±440 Ó Springer-Verlag 2001 ORIGINAL CONTRIBUTION Burkhardt Dames An empirical model predicting the viscosity Bradley Ron Morrison Norbert Willenbacher of highly concentrated, bimodal dispersions with colloidal interactions Abstract The relationship between the particles. Starting from a limiting Received: 7 June 2000 Accepted: 12 February 2001 particle size distribution and viscos- value of 2 for non-interacting either ity of concentrated dispersions is of colloidal or non-colloidal particles, great industrial importance, since it e generally increases strongly with is the key to get high solids disper- decreasing particle size. For a given sions or suspensions. The problem is particle system it then can be treated here experimentally as well expressed as a function of the num- as theoretically for the special case ber average particle diameter. As a of strongly interacting colloidal consequence, the viscosity of bimo- particles. An empirical model based dal dispersions varies not only with on a generalized Quemada equation the size ratio of large to small ~ / Àe g g 1 À / is used to describe particles, but also depends on the g as a functionmax of volume fraction absolute particle size going through for mono- as well as multimodal a minimum as the size ratio increas- dispersions. The pre-factor g~ ac- es. Furthermore, the well-known counts for the shear rate dependence viscosity minimum for bimodal dis- of g and does not aect the shape of persions with volumetric mixing the g vs / curves. It is shown here ratios of around 30/70 of small to for the ®rst time that colloidal large particles is shown to vanish if interactions do not show up in the colloidal interactions contribute maximum packing parameter and signi®cantly. -
Colloidal Suspensions
Chapter 9 Colloidal suspensions 9.1 Introduction So far we have discussed the motion of one single Brownian particle in a surrounding fluid and eventually in an extaernal potential. There are many practical applications of colloidal suspensions where several interacting Brownian particles are dissolved in a fluid. Colloid science has a long history startying with the observations by Robert Brown in 1828. The colloidal state was identified by Thomas Graham in 1861. In the first decade of last century studies of colloids played a central role in the development of statistical physics. The experiments of Perrin 1910, combined with Einstein's theory of Brownian motion from 1905, not only provided a determination of Avogadro's number but also laid to rest remaining doubts about the molecular composition of matter. An important event in the development of a quantitative description of colloidal systems was the derivation of effective pair potentials of charged colloidal particles. Much subsequent work, largely in the domain of chemistry, dealt with the stability of charged colloids and their aggregation under the influence of van der Waals attractions when the Coulombic repulsion is screened strongly by the addition of electrolyte. Synthetic colloidal spheres were first made in the 1940's. In the last twenty years the availability of several such reasonably well characterised "model" colloidal systems has attracted physicists to the field once more. The study, both theoretical and experimental, of the structure and dynamics of colloidal suspensions is now a vigorous and growing subject which spans chemistry, chemical engineering and physics. A colloidal dispersion is a heterogeneous system in which particles of solid or droplets of liquid are dispersed in a liquid medium. -
Liquid-Liquid Extraction
OCTOBER 2020 www.processingmagazine.com A BASIC PRIMER ON LIQUID-LIQUID EXTRACTION IMPROVING RELIABILITY IN CHEMICAL PROCESSING WITH PREVENTIVE MAINTENANCE DRIVING PACKAGING SUSTAINABILITY IN THE TIME OF COVID-19 Detecting & Preventing Pressure Gauge AUTOMATIC RECIRCULATION VALVES Failures Schroedahl www.circor.com/schroedahl page 48 LOW-PROFILE, HIGH-CAPACITY SCREENER Kason Corporation www.kason.com page 16 chemical processing A basic primer on liquid-liquid extraction An introduction to LLE and agitated LLE columns | By Don Glatz and Brendan Cross, Koch Modular hemical engineers are often faced with The basics of liquid-liquid extraction the task to design challenging separation While distillation drives the separation of chemicals C processes for product recovery or puri- based upon dif erences in relative volatility, LLE is a fication. This article looks at the basics separation technology that exploits the dif erences in of one powerful and yet overlooked separation tech- the relative solubilities of compounds in two immis- nique: liquid-liquid extraction. h ere are other unit cible liquids. Typically, one liquid is aqueous, and the operations used to separate compounds, such as other liquid is an organic compound. distillation, which is taught extensively in chemical Used in multiple industries including chemical, engineering curriculums. If a separation is feasible by pharmaceutical, petrochemical, biobased chemicals distillation and is economical, there is no reason to and l avor and fragrances, this approach takes careful consider liquid-liquid extraction (LLE). However, dis- process design by experienced chemical engineers and tillation may not be a feasible solution for a number scientists. In many cases, LLE is the best choice as a of reasons, such as: separation technology and well worth searching for a • If it requires a complex process sequence (several quali ed team to assist in its development and design. -
How Compressible Are Innovation Processes?
1 How Compressible are Innovation Processes? Hamid Ghourchian, Arash Amini, Senior Member, IEEE, and Amin Gohari, Senior Member, IEEE Abstract The sparsity and compressibility of finite-dimensional signals are of great interest in fields such as compressed sensing. The notion of compressibility is also extended to infinite sequences of i.i.d. or ergodic random variables based on the observed error in their nonlinear k-term approximation. In this work, we use the entropy measure to study the compressibility of continuous-domain innovation processes (alternatively known as white noise). Specifically, we define such a measure as the entropy limit of the doubly quantized (time and amplitude) process. This provides a tool to compare the compressibility of various innovation processes. It also allows us to identify an analogue of the concept of “entropy dimension” which was originally defined by R´enyi for random variables. Particular attention is given to stable and impulsive Poisson innovation processes. Here, our results recognize Poisson innovations as the more compressible ones with an entropy measure far below that of stable innovations. While this result departs from the previous knowledge regarding the compressibility of fat-tailed distributions, our entropy measure ranks stable innovations according to their tail decay. Index Terms Compressibility, entropy, impulsive Poisson process, stable innovation, white L´evy noise. I. INTRODUCTION The compressible signal models have been extensively used to represent or approximate various types of data such as audio, image and video signals. The concept of compressibility has been separately studied in information theory and signal processing societies. In information theory, this concept is usually studied via the well-known entropy measure and its variants. -
An Entropy-Stable Hybrid Scheme for Simulations of Transcritical Real-Fluid
Journal of Computational Physics 340 (2017) 330–357 Contents lists available at ScienceDirect Journal of Computational Physics www.elsevier.com/locate/jcp An entropy-stable hybrid scheme for simulations of transcritical real-fluid flows Peter C. Ma, Yu Lv ∗, Matthias Ihme Department of Mechanical Engineering, Stanford University, Stanford, CA 94305, USA a r t i c l e i n f o a b s t r a c t Article history: A finite-volume method is developed for simulating the mixing of turbulent flows at Received 30 August 2016 transcritical conditions. Spurious pressure oscillations associated with fully conservative Received in revised form 9 March 2017 formulations are addressed by extending a double-flux model to real-fluid equations of Accepted 12 March 2017 state. An entropy-stable formulation that combines high-order non-dissipative and low- Available online 22 March 2017 order dissipative finite-volume schemes is proposed to preserve the physical realizability Keywords: of numerical solutions across large density gradients. Convexity conditions and constraints Real fluid on the application of the cubic state equation to transcritical flows are investigated, and Spurious pressure oscillations conservation properties relevant to the double-flux model are examined. The resulting Double-flux model method is applied to a series of test cases to demonstrate the capability in simulations Entropy stable of problems that are relevant for multi-species transcritical real-fluid flows. Hybrid scheme © 2017 Elsevier Inc. All rights reserved. 1. Introduction The accurate and robust simulation of transcritical real-fluid effects is crucial for many engineering applications, such as fuel injection in internal-combustion engines, rocket motors and gas turbines. -
Selection of Thermodynamic Methods
P & I Design Ltd Process Instrumentation Consultancy & Design 2 Reed Street, Gladstone Industrial Estate, Thornaby, TS17 7AF, United Kingdom. Tel. +44 (0) 1642 617444 Fax. +44 (0) 1642 616447 Web Site: www.pidesign.co.uk PROCESS MODELLING SELECTION OF THERMODYNAMIC METHODS by John E. Edwards [email protected] MNL031B 10/08 PAGE 1 OF 38 Process Modelling Selection of Thermodynamic Methods Contents 1.0 Introduction 2.0 Thermodynamic Fundamentals 2.1 Thermodynamic Energies 2.2 Gibbs Phase Rule 2.3 Enthalpy 2.4 Thermodynamics of Real Processes 3.0 System Phases 3.1 Single Phase Gas 3.2 Liquid Phase 3.3 Vapour liquid equilibrium 4.0 Chemical Reactions 4.1 Reaction Chemistry 4.2 Reaction Chemistry Applied 5.0 Summary Appendices I Enthalpy Calculations in CHEMCAD II Thermodynamic Model Synopsis – Vapor Liquid Equilibrium III Thermodynamic Model Selection – Application Tables IV K Model – Henry’s Law Review V Inert Gases and Infinitely Dilute Solutions VI Post Combustion Carbon Capture Thermodynamics VII Thermodynamic Guidance Note VIII Prediction of Physical Properties Figures 1 Ideal Solution Txy Diagram 2 Enthalpy Isobar 3 Thermodynamic Phases 4 van der Waals Equation of State 5 Relative Volatility in VLE Diagram 6 Azeotrope γ Value in VLE Diagram 7 VLE Diagram and Convergence Effects 8 CHEMCAD K and H Values Wizard 9 Thermodynamic Model Decision Tree 10 K Value and Enthalpy Models Selection Basis PAGE 2 OF 38 MNL 031B Issued November 2008, Prepared by J.E.Edwards of P & I Design Ltd, Teesside, UK www.pidesign.co.uk Process Modelling Selection of Thermodynamic Methods References 1. -
Distillation Theory
Chapter 2 Distillation Theory by Ivar J. Halvorsen and Sigurd Skogestad Norwegian University of Science and Technology Department of Chemical Engineering 7491 Trondheim, Norway This is a revised version of an article published in the Encyclopedia of Separation Science by Aca- demic Press Ltd. (2000). The article gives some of the basics of distillation theory and its purpose is to provide basic understanding and some tools for simple hand calculations of distillation col- umns. The methods presented here can be used to obtain simple estimates and to check more rigorous computations. NTNU Dr. ing. Thesis 2001:43 Ivar J. Halvorsen 28 2.1 Introduction Distillation is a very old separation technology for separating liquid mixtures that can be traced back to the chemists in Alexandria in the first century A.D. Today distillation is the most important industrial separation technology. It is particu- larly well suited for high purity separations since any degree of separation can be obtained with a fixed energy consumption by increasing the number of equilib- rium stages. To describe the degree of separation between two components in a column or in a column section, we introduce the separation factor: ()⁄ xL xH S = ------------------------T (2.1) ()x ⁄ x L H B where x denotes mole fraction of a component, subscript L denotes light compo- nent, H heavy component, T denotes the top of the section, and B the bottom. It is relatively straightforward to derive models of distillation columns based on almost any degree of detail, and also to use such models to simulate the behaviour on a computer. -
Lecture 3. the Basic Properties of the Natural Atmosphere 1. Composition
Lecture 3. The basic properties of the natural atmosphere Objectives: 1. Composition of air. 2. Pressure. 3. Temperature. 4. Density. 5. Concentration. Mole. Mixing ratio. 6. Gas laws. 7. Dry air and moist air. Readings: Turco: p.11-27, 38-43, 366-367, 490-492; Brimblecombe: p. 1-5 1. Composition of air. The word atmosphere derives from the Greek atmo (vapor) and spherios (sphere). The Earth’s atmosphere is a mixture of gases that we call air. Air usually contains a number of small particles (atmospheric aerosols), clouds of condensed water, and ice cloud. NOTE : The atmosphere is a thin veil of gases; if our planet were the size of an apple, its atmosphere would be thick as the apple peel. Some 80% of the mass of the atmosphere is within 10 km of the surface of the Earth, which has a diameter of about 12,742 km. The Earth’s atmosphere as a mixture of gases is characterized by pressure, temperature, and density which vary with altitude (will be discussed in Lecture 4). The atmosphere below about 100 km is called Homosphere. This part of the atmosphere consists of uniform mixtures of gases as illustrated in Table 3.1. 1 Table 3.1. The composition of air. Gases Fraction of air Constant gases Nitrogen, N2 78.08% Oxygen, O2 20.95% Argon, Ar 0.93% Neon, Ne 0.0018% Helium, He 0.0005% Krypton, Kr 0.00011% Xenon, Xe 0.000009% Variable gases Water vapor, H2O 4.0% (maximum, in the tropics) 0.00001% (minimum, at the South Pole) Carbon dioxide, CO2 0.0365% (increasing ~0.4% per year) Methane, CH4 ~0.00018% (increases due to agriculture) Hydrogen, H2 ~0.00006% Nitrous oxide, N2O ~0.00003% Carbon monoxide, CO ~0.000009% Ozone, O3 ~0.000001% - 0.0004% Fluorocarbon 12, CF2Cl2 ~0.00000005% Other gases 1% Oxygen 21% Nitrogen 78% 2 • Some gases in Table 3.1 are called constant gases because the ratio of the number of molecules for each gas and the total number of molecules of air do not change substantially from time to time or place to place. -
Distillation Accessscience from McgrawHill Education
6/19/2017 Distillation AccessScience from McGrawHill Education (http://www.accessscience.com/) Distillation Article by: King, C. Judson University of California, Berkeley, California. Last updated: 2014 DOI: https://doi.org/10.1036/10978542.201100 (https://doi.org/10.1036/10978542.201100) Content Hide Simple distillations Fractional distillation Vaporliquid equilibria Distillation pressure Molecular distillation Extractive and azeotropic distillation Enhancing energy efficiency Computational methods Stage efficiency Links to Primary Literature Additional Readings A method for separating homogeneous mixtures based upon equilibration of liquid and vapor phases. Substances that differ in volatility appear in different proportions in vapor and liquid phases at equilibrium with one another. Thus, vaporizing part of a volatile liquid produces vapor and liquid products that differ in composition. This outcome constitutes a separation among the components in the original liquid. Through appropriate configurations of repeated vaporliquid contactings, the degree of separation among components differing in volatility can be increased manyfold. See also: Phase equilibrium (/content/phaseequilibrium/505500) Distillation is by far the most common method of separation in the petroleum, natural gas, and petrochemical industries. Its many applications in other industries include air fractionation, solvent recovery and recycling, separation of light isotopes such as hydrogen and deuterium, and production of alcoholic beverages, flavors, fatty acids, and food oils. Simple distillations The two most elementary forms of distillation are a continuous equilibrium distillation and a simple batch distillation (Fig. 1). http://www.accessscience.com/content/distillation/201100 1/10 6/19/2017 Distillation AccessScience from McGrawHill Education Fig. 1 Simple distillations. (a) Continuous equilibrium distillation. -
Distillation Design the Mccabe-Thiele Method Distiller Diagam Introduction
Distillation Design The McCabe-Thiele Method Distiller diagam Introduction • UiUsing r igorous tray-bby-tray callilculations is time consuming, and is often unnecessary. • OikhdfiifbOne quick method of estimation for number of plates and feed stage can be obtained from the graphical McCabe-Thiele Method. • This eliminates the need for tedious calculations, and is also the first step to understanding the Fenske-Underwood- Gilliland method for multi-component distillation • Typi ica lly, the in le t flow to the dis tilla tion co lumn is known, as well as mole percentages to feed plate, because these would be specified by plant conditions. • The desired composition of the bottoms and distillate prodillbifiddhiilldducts will be specified, and the engineer will need to design a distillation column to produce these results. • With the McCabe-Thiele Method, the total number of necessary plates, as well as the feed plate location can biddbe estimated, and some ifiinformation can a lblso be determined about the enthalpic condition of the feed and reflux ratio. • This method assumes that the column is operated under constant pressure, and the constant molal overflow assumption is necessary, which states that the flow rates of liquid and vapor do not change throughout the column. • To understand this method, it is necessary to first elaborate on the subjects of the x-y diagram, and the operating lines used to create the McCabe-Thiele diagram. The x-y diagram • The x-y diagram depi icts vapor-liliqu id equilibrium data, where any point on the curve shows the variations of the amount of liquid that is in equilibrium with vapor at different temperatures. -
Chapter 3 3.4-2 the Compressibility Factor Equation of State
Chapter 3 3.4-2 The Compressibility Factor Equation of State The dimensionless compressibility factor, Z, for a gaseous species is defined as the ratio pv Z = (3.4-1) RT If the gas behaves ideally Z = 1. The extent to which Z differs from 1 is a measure of the extent to which the gas is behaving nonideally. The compressibility can be determined from experimental data where Z is plotted versus a dimensionless reduced pressure pR and reduced temperature TR, defined as pR = p/pc and TR = T/Tc In these expressions, pc and Tc denote the critical pressure and temperature, respectively. A generalized compressibility chart of the form Z = f(pR, TR) is shown in Figure 3.4-1 for 10 different gases. The solid lines represent the best curves fitted to the data. Figure 3.4-1 Generalized compressibility chart for various gases10. It can be seen from Figure 3.4-1 that the value of Z tends to unity for all temperatures as pressure approach zero and Z also approaches unity for all pressure at very high temperature. If the p, v, and T data are available in table format or computer software then you should not use the generalized compressibility chart to evaluate p, v, and T since using Z is just another approximation to the real data. 10 Moran, M. J. and Shapiro H. N., Fundamentals of Engineering Thermodynamics, Wiley, 2008, pg. 112 3-19 Example 3.4-2 ---------------------------------------------------------------------------------- A closed, rigid tank filled with water vapor, initially at 20 MPa, 520oC, is cooled until its temperature reaches 400oC.