Glossary of Glacier Mass Balance and Related Terms
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On the Multi-Physics of Mass-Transfer Across Fluid Interfaces
On the multi-physics of mass-transfer across fluid interfaces Dieter Bothe Center of Smart Interfaces TU Darmstadt [email protected] Abstract Mass transfer of gaseous components from rising bubbles to the ambient liquid can be described based on continuum mechanical sharp-interface balances of mass, momentum and species mass. In this context, the stan- dard model consists of the two-phase Navier-Stokes equations for incom- pressible fluids with constant surface tension, complemented by reaction- advection-diffusion equations for all constituents, employing Fick’s law. This standard model is inconsistent with the continuity equation, the mo- mentum balance and the second law of thermodynamics. The present paper reports on the details of these severe shortcomings and provides thermodynamically consistent model extensions which are required to cap- ture various phenomena which occur due to the multi-physics of interfacial mass transfer. In particular, we provide a simple derivation of the interface Maxwell-Stefan equations which does not require a time scale separation, while the main contribution is to show how interface concentrations and interface chemical potentials mediate the influence on mass transfer of a transfer component exerted by the change in interface energy due to an adsorbing surfactant. Keywords: Soluble surfactant, interface chemical potentials, interfacial en- tropy production, interface Maxwell-Stefan equations, jump conditions, surface tension effects, high Schmidt number problem, artificial boundary conditions. Introduction The standard model for the continuum mechanical description of mass transfer across fluid interfaces is based on the incompressible two-phase Navier-Stokes equations for fluid systems without phase change. To be more precise, inside the fluid phases the governing equations are arXiv:1501.05610v1 [physics.flu-dyn] 22 Jan 2015 ∇ · v =0, (1) visc ∂t(ρv)+ ∇ · (ρv ⊗ v)+ ∇p = ∇ · S + ρg (2) with the viscous stress tensor T Svisc = η(∇v + ∇v ), (3) 1 where the material parameters depend on the respective phase. -
MATERIAL BALANCE NOTES Revision 3 Irven Rinard Department
MATERIAL BALANCE NOTES Revision 3 Irven Rinard Department of Chemical Engineering City College of CUNY and Project ECSEL October 1999 © 1999 Irven Rinard CONTENTS INTRODUCTION 1 A. Types of Material Balance Problems B. Historical Perspective I. CONSERVATION OF MASS 5 A. Control Volumes B. Holdup or Inventory C. Material Balance Basis D. Material Balances II. PROCESSES 13 A. The Concept of a Process B. Basic Processing Functions C. Unit Operations D. Modes of Process Operations III. PROCESS MATERIAL BALANCES 21 A. The Stream Summary B. Equipment Characterization IV. STEADY-STATE PROCESS MODELING 29 A. Linear Input-Output Models B. Rigorous Models V. STEADY-STATE MATERIAL BALANCE CALCULATIONS 33 A. Sequential Modular B. Simultaneous C. Design Specifications D. Optimization E. Ad Hoc Methods VI. RECYCLE STREAMS AND TEAR SETS 37 A. The Node Incidence Matrix B. Enumeration of Tear Sets VII. SOLUTION OF LINEAR MATERIAL BALANCE MODELS 45 A. Use of Linear Equation Solvers B. Reduction to the Tear Set Variables C. Design Specifications i VIII. SEQUENTIAL MODULAR SOLUTION OF NONLINEAR 53 MATERIAL BALANCE MODELS A. Convergence by Direct Iteration B. Convergence Acceleration C. The Method of Wegstein IX. MIXING AND BLENDING PROBLEMS 61 A. Mixing B. Blending X. PLANT DATA ANALYSIS AND RECONCILIATION 67 A. Plant Data B. Data Reconciliation XI. THE ELEMENTS OF DYNAMIC PROCESS MODELING 75 A. Conservation of Mass for Dynamic Systems B. Surge and Mixing Tanks C. Gas Holders XII. PROCESS SIMULATORS 87 A. Steady State B. Dynamic BILIOGRAPHY 89 APPENDICES A. Reaction Stoichiometry 91 B. Evaluation of Equipment Model Parameters 93 C. Complex Equipment Models 96 D. -
Introduction to Oxidation and Mass & Energy Balances
Introduction to Oxidation and Mass & Energy Balances Michael Mannuzza IT3/HWC OBG BaltimoreBaton Rouge,2014 LA 2016 Combustion • Combustion is an oxidation reaction: Fuel + O2 ---> Products of Combustion + Heat Energy • In addition to traditional burner fuels, incinerator fuel can include solid, gaseous and liquid waste. IT3/HWC • The Products of Combustion (POC) are the BaltimoreBaton primary concern from an Air Pollution Control Rouge,2014 LA 2016 (APC) perspective. Air Pollutants and Regulatory Drivers • The type of APC system required for an incinerator will be decided based on the system’s POCs and the regulatory limits mandated for specific pollutants. • Emissions of the following pollutants are typically regulated for most incinerator applications: • IT3/HWC • Dioxin/Furans NOx • Particulate Matter BaltimoreBaton • Mercury (Hg) Rouge,2014 LA • VOCs & Total Hydrocarbons 2016 • Semi-Volatile Metals (Cd, Pb) • Carbon Monoxide • Low-Volatility Metals (As, Be, Cr) • HCl & Cl2 • SOx • Others Identifying APC Requirements Three Steps: 1. Quantify anticipated POCs 2. Identify Regulatory Emission Constraints (establish abatement requirements) IT3/HWC 3. Quantify the discharge flow rate of the system. BaltimoreBaton Rouge,2014 LA 2016 Waste Feed Properties I. Begin by identifying the properties of the waste feed and quantifying the constituency of the waste: 1. Material Take-Offs 2. Proximate, Ultimate, and Ash Analysis 3. Sample & Analyze for Specific Compounds 4. Employ Other Empirical Methods PROXIMATE ANALYSIS ULTIMATE ANALYSIS ASH ANALYSIS -
1Eng -Design Basics, Mass Balance, Kinetics.Pdf
Applied chemical process Basic terms, mass balance Engineering thinking description of the industrial apparatus + description of the chemical and physical operation in the process precise formulation of the problem + design the right solution Process technology development design finish design development end of end construction of KH delivery KH Intensity Intensity year 1 Operations • Chemical processes - reactors • Mechanical processes - transport, mixing, filtration, grinding, sedimentation… • Diffusion processes - extraction, distillation, crystallization, drying • Thermal processes – coolig, warming-up, condensation, evaporation Description of the technology Maximal yield x minimum cost • Amount and composition of the products – reactants, products, waste (material balance) • Energy consumption – stream, cooling water, electrical energy, cooling air (enthalpy balance) • Industrial devices – wattage, type, dimension, output (design and check calculation) • Costs – raw materials, energy, investments, payroll (economic balance) Economic efficiency of the process • Costing and price of the product • Energy costs • Depreciation and maintenance • Cost of human work = Production costs + Corporate overhead = Complete costs + Profit = Total Price 2 Cost versus production - development of a new product 1) Old process production fall off Not simultaneously 2) Application of the modern technology Influence of capacity to the relative cost raw materials cost relative invest cost energy capacity (t/year) Type of the system – based on the exchange -
On the Modeling and Design of Zero-Net Mass Flux Actuators
ON THE MODELING AND DESIGN OF ZERO-NET MASS FLUX ACTUATORS By QUENTIN GALLAS A DISSERTATION PRESENTED TO THE GRADUATE SCHOOL OF THE UNIVERSITY OF FLORIDA IN PARTIAL FULFILLMENT OF THE REQUIREMENTS FOR THE DEGREE OF DOCTOR OF PHILOSOPHY UNIVERSITY OF FLORIDA 2005 Copyright 2005 by Quentin Gallas Pour ma famille et mes amis, d’ici et de là-bas… (To my family and friends, from here and over there…) ACKNOWLEDGMENTS Financial support for the research project was provided by a NASA-Langley Research Center Grant and an AFOSR grant. First, I would like to thank my advisor, Dr. Louis N. Cattafesta. His continual guidance and support gave me the motivation and encouragement that made this work possible. I would also like to express my gratitude especially to Dr. Mark Sheplak, and to the other members of my committee (Dr. Bruce Carroll, Dr. Bhavani Sankar, and Dr. Toshikazu Nishida) for advising and guiding me with various aspects of this project. I thank the members of the Interdisciplinary Microsystems group and of the Mechanical and Aerospace Engineering department (particularly fellow student Ryan Holman) for their help with my research and their friendship. I thank everyone who contributed in a small but significant way to this work. I also thank Dr. Rajat Mittal (George Washington University) and his student Reni Raju, who greatly helped me with the computational part of this work. Finally, special thanks go to my family and friends, from the States and from France, for always encouraging me to pursue my interests and for making that pursuit possible. iv TABLE OF CONTENTS page ACKNOWLEDGMENTS ................................................................................................ -
Applicability of Simple Mass and Energy Balances in Food Drum Drying
J. Basic. Appl. Sci. Res., 4(1)128-133, 2014 ISSN 2090-4304 © 2014, TextRoad Publication Journal of Basic and Applied Scientific Research www.textroad.com Applicability of Simple Mass and Energy Balances in Food Drum Drying Tomislav Jurendić Bioquanta Ltd, Dravska 17, 48000 Koprivnica, Croatia Received: November 16 2013 Accepted: December 10 2013 ABSTRACT Drum drying is one of the most important drying methods in the production of dried food. Drum dryers are robust in construction and consume huge quantity of energy. Holding the drying process under control can be of high importance for both saving the energy and reducing the costs. Mass and energy balances represent a very good basis towards efficient process control and quick estimation of the process state, as well as are unavoidable step in the design of food processes, respectively. In this work the using of simple mass and energy balances in practical industrial applications is demonstrated. KEY WORDS: baby food, drum drying, energy balance, mass balance, process calculations 1. INTRODUCTION Drum drying (Figure 1) has been widely used in food industry for drying of various liquid, semiliquid and paste-like food materials. That way, many dried food products such as milk powder, baby foods, starch, fruit and vegetables pulps, honey, malto-dextrins, yeast creams and many other food and non-food products can be produced [1-6]. The obtained dried product is porous and easy to rehydrate, ready to use [6]. As well, the manufactured dried products can be employed as semi-finished products in milk, drinking, confectionary and other industries [4]. However, the purpose of food drying is to extend shelf life of products with minimum packaging requirements and reduced shipping weights [4]. -
Lecture 3 Fluid Dynamics and Balance Equations for Reacting Flows
Lecture 3 Fluid Dynamics and Balance Equations for Reacting Flows 3.-1 Basics: equations of continuum mechanics - balance equations for mass and momentum - balance equations for the energy and the chemical species Associated with the release of thermal energy and the increase in temperature is a local decrease in density which in turn affects the momentum balance. Therefore, all these equations are closely coupled to each other. Nevertheless, in deriving these equations we will try to point out how they can be simplified and partially uncoupled under certain assumptions. 3.-2 Balance Equations A time-independent control volume V for a balance quality F(t) The scalar product between the surface flux φf and the normal vector n determines the outflow through the surface A, a source sf the rate of production of F(t) Let us consider a general quality per unit volume f(x, t). Its integral over the finite volume V, with the time-independent boundary A is given by 3.-3 The temporal change of F is then due to the following three effects: 1. by the flux φf across the boundary A. This flux may be due to convection or molecular transport. By integration over the boundary A we obtain the net contribution which is negative, if the normal vector is assumed to direct outwards. 3.-4 2. by a local source σf within the volume. This is an essential production of partial mass by chemical reactions. Integrating the source term over the volume leads to 3. by an external induced source s. Examples are the gravitational force or thermal radiation. -
Chapter 4 Continuity, Energy, and Momentum Equations
Ch 4. Continuity, Energy, and Momentum Equation Chapter 4 Continuity, Energy, and Momentum Equations 4.1 Conservation of Matter in Homogeneous Fluids • Conservation of matter in homogeneous (single species) fluid → continuity equation positive dA1 - perpendicular to the control surface negative 4.1.1 Finite control volume method-arbitrary control volume - Although control volume remains fixed, mass of fluid originally enclosed (regions A+B) occupies the volume within the dashed line (regions B+C). Since mass m is conserved: mmm m (4.1) ABBtttdt Ctdt m m mmBBtdt t A t C tdt (4.2) dt dt •LHS of Eq. (4.2) = time rate of change of mass in the original control volume in the limit mmBB m tdt t B dV (4.3) dt t t CV 4−1 Ch 4. Continuity, Energy, and Momentum Equation where dV = volume element •RHS of Eq. (4.2) = net flux of matter through the control surface = flux in – flux out = qdA qdA nn12 where q = component of velocity vector normal to the surface of CV q cos n dV qdAnn12 qdA (4.4) CV CS CS t ※ Flux (= mass/time) is due to velocity of the flow. • Vector form dV qdA (4.5) t CV CS where dA = vector differential area pointing in the outward direction over an enclosed control surface qdAq dA cos positive for an outflow from cv, 90 negative for inflow into cv, 90 180 If fluid continues to occupy the entire control volume at subsequent times → time independent 4−2 Ch 4. Continuity, Energy, and Momentum Equation LHS: dV dV (4.5a) ttCV CV Eq. -
Entropy Production As a Measure for Resource Use
Entropy production as a measure for resource use Method development and application to metallurgical processes D I S S E R T A T I O N zur Erlangung des Doktorgrades des Fachbereichs Physik der Universit¨at Hamburg vorgelegt von Stefan G¨oßling aus Herford Hamburg 2001 Gutachter der Dissertation: Prof. Dr. H. Spitzer Prof. Dr. G. Mack Gutachter der Disputation: Prof. Dr. H. Spitzer Prof. Dr. G. Zimmerer Datum der Disputation: 23. 10. 2001 Sprecher des Fachbereichs Physik und Vorsitzender des Promotionsausschusses Prof. Dr. F.{W. Bußer¨ There are only two things in the world that grow when you give them away: Love and Entropy (Anonymous) Abstract In this thesis, entropy production is introduced as a measure for resource use based on the laws of thermodynamics. The main motivation for the development of this measure is given by two facts: resource use is an important parameter in the ecological assessment of human activity and there exists as yet no satisfactory measure for the resource use of industrial processes. Also, linking ecological and economical aspects of industrial processes, entropy production and entropy export play an important role for the development of living structures. On the grounds of the laws of thermodynamics, the mathematical framework for analysing the entropy production of arbitrary processes is developed, including a method to compensate for incomplete data. Several basic applications of the concept of entropy analysis are given, which verify the proposition that entropy production and resource use are equivalent. In order to prove the method's practicability, an industrial-scale case-study is performed on the production of copper from ore concentrates and secondary (recycled) material. -
Introduction to Combustion Analysis
College of Engineering and Computer Science Mechanical Engineering Department Mechanical Engineering 483 Alternative Energy Engineering II Spring 2010 Number: 17724 Instructor: Larry Caretto Introduction to Combustion Analysis INTRODUCTION These notes introduce simple combustion models. Such models can be used to analyze many industrial combustion processes and determine such factors as energy release and combustion efficiency. They can also be used to relate measured pollutant concentrations to other measures of emissions such as mole fractions, mass fractions, mass of pollutant per unit mass of fuel, mass of pollutant per unit fuel heat input, etc. These notes provide the derivation of all the equations that are used for these relations. BASIS OF THE ANALYSIS The simple combustion model assumes complete combustion in which all fuel carbon forms CO2, all fuel hydrogen forms H2O, all fuel sulfur forms SO2, and all fuel nitrogen forms N2. This provides results that are accurate to about 0.1% to 0.2% for well operating combustion processes in stationary combustion devices. It is not valid when the combustion process is fuel rich. Complete combustion of model fuel formula with oxygen – The typical fuel can be represented by the fuel formula CxHySzOwNv. With this fuel formula we can analyze a variety of fuels including pure chemical compounds, mixtures of compounds, and complex fuels such as petroleum and coals where the elemental composition of the fuel is measured. This type of measurement is said to provide an ultimate analysis. Regardless of the source of data for x, y, z, w and v, the mass of fuel represented by this formula1 can be found from the atomic weights of the various elements: M fuel = x M C + y M H + z M S + w M O + v M N [1] The oxygen required for an assumed complete combustion of this fuel formula can is determined from the oxygen requirements for complete combustion of the individual elements. -
Chemical Engineering Kinetics
CHEMICAL ENGINEERING KINETICS Based on CHEM_ENG 408 at Northwestern University BRIEF REVIEW OF REACTOR ARCHETYPES | 1 TABLE OF CONTENTS 1 Brief Review of Reactor Archetypes .................................................................................... 3 1.1 The Mass Balance ......................................................................................................................... 3 1.2 Batch Reactor ................................................................................................................................ 3 1.3 Continuous-Stirred Tank Reactor ................................................................................................. 4 1.4 Plug-Flow Reactor ........................................................................................................................ 4 2 Power Law Basics .................................................................................................................. 6 2.1 Arrhenius Equation ....................................................................................................................... 6 2.2 Mass-Action Kinetics .................................................................................................................... 7 2.2.1 Overview ................................................................................................................................................. 7 2.2.2 First Order Kinetics ................................................................................................................................ -
2. Fluid-Flow Equations Governing Equations
2. Fluid-Flow Equations Governing Equations • Conservation equations for: ‒ mass ‒ momentum ‒ energy ‒ (other constituents) • Alternative forms: ‒ integral (control-volume) equations ‒ differential equations Integral (Control-Volume) Approach Consider the budget of any physical quantity in any control volume V V TIME DERIVATIVE ADVECTIVE + DIFFUSIVE FLUX SOURCE + = of amount in 푉 through boundary of 푉 in 푉 → Finite-volume method for CFD Mass Conservation (Continuity) Mass conservation: mass is neither created nor destroyed d u (mass) = net inward mass flux d푡 V un A d (mass) + net outward mass flux = 0 d푡 d mass + mass flux = 0 d푡 faces Mass in a cell: ρ푉 Mass flux through a face: 퐶 = ρu • A Mass Conservation - Differential Equation t Conservation statement: d z mass + net outward mass flux = 0 w n d푡 y b e d s ρ푉 + (ρ푢퐴) − (ρ푢퐴) + (ρ푣퐴) − (ρ푣퐴) + (ρ푤퐴) − (ρ푤퐴) = 0 x d푡 푒 푤 푛 푠 푡 푏 d ρΔ푥Δ푦Δ푧 + [(ρ푢) − ρ푢) Δ푦Δ푧 + [(ρ푣) − ρ푣) Δ푧Δ푥 + [(ρ푤) − ρ푤) Δ푥Δ푦 = 0 d푡 푒 푤 푛 푠 푡 푏 Divide by volume: dρ (ρ푢) − (ρ푢) (ρ푣) − (ρ푣) (ρ푤) − (ρ푤) + 푒 푤 + 푛 푠 + 푡 푏 = 0 d푡 Δ푥 Δ푦 Δ푧 dρ Δ(ρ푢) Δ(ρ푣) Δ(ρ푤) + + + = 0 d푡 Δ푥 Δ푦 Δ푧 Shrink to a point: 휕ρ 휕(ρ푢) 휕(ρ푣) 휕(ρ푤) 휕ρ + + + = 0 + ∇ • (ρu) = 0 휕푡 휕푥 휕푦 휕푧 휕푡 Continuity in Incompressible Flow t z w n b y s e d x (volume) + net outward volume flux = 0 d푡 휕푢 휕푣 휕푤 + + = 0 ∇ • u = 0 휕푥 휕푦 휕푧 Momentum Equation Momentum Principle: force = rate of change of momentum F If steady: force = (momentum flux)out – (momentum flux)in If unsteady: force = d/d푡(momentum inside control volume) + (momentum flux)out – (momentum flux)in