Fundamentals of Chemical Reactor Theory
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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. -
Chemical Reactor Engineering*
CHEMICAL REACTOR ENGINEERING* JOHN B. BUTT mental topics, with more specialized applications Northwestern University in later chapters. Descriptive kinetics and data Evanston, IL 60201 interpretation are, logically, accorded first place on each list, followed by introductory material on E. E. PETERSEN reactor design and analysis. The latter is largely University of California limited to ideal reactor models; the effect of tem Berkeley, CA 94720 perature is treated somewhat differently in an organizational manner by the three authors, but HE DEVELOPMENT OF chemical reaction the level and extent of coverage is quite similar. Tengineering as an identifiable area within Concepts of selectivity as well as rate and conver chemical engineering has led to renewed interest sion are presented early in each case and main and emphasis on courses dealing with chemical tained as an important factor in kinetics and re reaction kinetics and chemical reactor design. The actor analysis throughout. Following this intro basic issues concerning instruction in these areas ductory material, each author then turns to prob are probably not much different from those in lems associated with deviations from ideal reactor volved in any other area of chemical engineering performance. Here somewhat more variation is insofar as fundamentals vs. appllcations, extent of apparent in organization and presentation but, coverage, and similar factors. There is, however, again, the net coverage and information is quite a chemical factor involved in this area that may similar. not appear quite so prominently in other endeav The point is that, in terms of information ors, and instruction at the undergraduate level which might form the core content of a typical particularly may be sensitive to the contents of current offerings in chemistry courses. -
CHEMICAL REACTION ENGINEERING* Current Status and Future Directions
[eJij9iviews and opinions CHEMICAL REACTION ENGINEERING* Current Status and Future Directions M. P. DUDUKOVIC and petrochemical industry provided a fertile ground Washington University for further development of reaction engineering con St. Louis, MO 63130 cepts. The final cornerstone of this new discipline was laid in 1957 by the First Symposium on Chemical HEMICAL REACTIONS have been used by man Reaction Engineering [3] which brought together and C kind since time immemorial to produce useful synthesized the European point of view. The Amer products such as wine, metals, etc. Nevertheless, the ican and European schools of thought were not identi unifying principles that today we call chemical reac cal, but in time they converged into the subject matter tion engineering were not developed until relatively a that we know today as chemical reaction engineering, short time ago. During the decade of the 1940's (not or CRE. The above chronology led to the establish even half a century ago!) a transition was made from ment of CRE as an accepted discipline over the span descriptive industrial chemistry to the conceptual un of a decade and a half. This does not imply that all the ification of reaction processes and reactor types. The principles important in CRE were discovered then. pioneering work in this area of industrial practice was The foundation for CRE had already been established done by Denbigh [1] in England. Then in 1947, by the early work of Frank-Kamenteski, Damkohler, Hougen and Watson [2] published the first textbook Zeldovitch, etc., but at that time they represented in the U.S. -
Mixing Time—Experimental Determination and Applications to the Modelling of Crystallisation Phenomena
Preprints (www.preprints.org) | NOT PEER-REVIEWED | Posted: 3 November 2016 doi:10.20944/preprints201611.0022.v1 Article Mixing Time—Experimental Determination and Applications to the Modelling of Crystallisation Phenomena Dragan D. Nikolić *, Giuseppe Cogoni and Patrick J. Frawley Synthesis and Solid State Pharmaceutical Centre, University of Limerick, Limerick, Ireland; [email protected] (G.C.); [email protected] (P.J.F.) * Correspondance: [email protected] Abstract: Performing optimisation and scale-up studies of crystallisation systems requires accurate and computationally efficient mathematical models. The assumption of the ideal mixing conditions in batch reactors typically produce inaccurate results while the computational expense of CFD models is still prohibitively high. Therefore, in this work, a new intermediary approach is proposed that takes into account the non-ideal mixing conditions in the reactor and requires less computational resources than full CFD simulations. Starting with the Danckwerts concept of the intensity of segregation, an analogy between its application to chemical reactions and the kinetics of the crystallisation phenomena (such as nucleation and growth) has been made. As a result, the modified kinetics expressions have been derived which incorporate the effect of non-idealities present in stirred reactors. This way, based on the experimental measurements of the mixing time using the Laser Induced Fluorescence (LIF) technique, computationally more efficient mathematical models can be developed in two ways: (1) the accurate semi-empirical correlations are available for standard mixing configurations with the most often used types of impellers, (2) CFD simulations can be utilised for estimation of the mixing time; in this case it is necessary to simulate only the mixing process. -
Simulation of HDS Tests in Trickle-Bed Reactor
Simulation of HDS Tests in Trickle-Bed Reactor V. Tukač1, A. Prokešová1, J. Hanika1, M. Zbuzek2 and R. Černý2 1Institute of Chemical Technology, Prague, Technická 5, CZ-16628 Prague, Czech Rebublic 2Research and education centre UniCRE Litvínov, CZ-43670 Litvínov, Czech Rebublic Keywords: Hydrodesulfurization Simulation, Catalyst Tests, Trickle-Bed Reactor. Abstract: The paper deals with methodology of simulation study devoted to evaluation of reliability of HDS catalyst testing procedure in pilot three phase fixed bed reactor. Hydrodynamic behaviour of test reactor was determined by residence time distribution method. Residence time and Peclet number of axial dispersion of liquid phase were obtained by nonlinear regression of experimental data. Hydrodesulfurization reaction kinetics was evaluated by analysis of concentration data measured in high pressure trickle-bed reactor and autoclave. Simulation of reaction courses were carried out both by pseudohomogeneous model of ODE in Matlab and heterogeneous reactor model of PDE solved by COMSOL Multiphysics. Final results confirm presumption of eliminating influence of hydrodynamics on reaction kinetic results by dilution of catalyst bed by inert fine particles. 1 INTRODUCTION were supplemented by kinetic measurement of reaction rate constants and activation energies of Sustainable development demands ultra-low selected sulfuric compounds. Parallel to HDS concentrations of sulfur and nitrogen compounds in reaction also hydrodenitrogenation (HDN) takes produced engine fuels – gasoline and diesel. Present place in the catalytic reactor. Hydrodynamic data sulfur content valid in EU 10 ppm represents less were evaluated by residence time distribution (RTD) than one thousands of sulfur content of original method in laboratory glass model of pilot reactor. crude oil. Deep hydrodesulfurization (HDS) of Mathematical models of the process (Ancheyta, engine fuels is dominantly carried out in catalytic 2011) were formulated both like 1D trickle-bed reactors. -
Steady State Simulation of Continuous Stirred Tank Reactor (CSTR) System Using Aspen Plus
View metadata, citation and similar papers at core.ac.uk brought to you by CORE provided by ethesis@nitr A Project Report On Steady state simulation of continuous stirred tank reactor (CSTR) system using Aspen Plus Submitted by Telagam Setty Maayedukondalu (Roll No: 111CH0504) In partial fulfillment of the requirements for the degree in Bachelor of Technology in Chemical Engineering Under the guidance of Dr. Pradip Chowdhury Department of Chemical Engineering National Institute of Technology Rourkela May 2015 CERTIFICATE This is certified that the work contained in the thesis entitled “Steady state simulation of continuous stirred tank reactor (CSTR) system using Aspen Plus” submitted by Telagam Setty Maayedukondalu(111CH0504), has been carried out under my supervision and this work has not been submitted elsewhere for a degree. __________________ Date: Place: (Thesis Supervisor) Dr. Pradip Chowdhury Assistant Professor, Department of Chemical Engineering NIT Rourkela 769008 Acknowledgements First and the foremost, I would like to offer my sincere gratitude to my thesis supervisor, Dr. Pradip Chowdhury for his immense interest and enthusiasm on the project. His technical prowess and vast knowledge on diverse fields left quite an impression on me. He was always accessible and worked for hours with me. Although the journey was beset with complexities but I always found his helping hand. He has been a constant source of inspiration for me. I am also thankful to all faculties and support staff of Department of Chemical Engineering, National Institute of Technology Rourkela, for their constant help and extending the departmental facilities for carrying out my project work. I would like to extend my sincere thanks to my friends and colleagues. -
Temperature Simulation and Heat Exchange in a Batch Reactor Using Ansys Fluent
Graduate Theses, Dissertations, and Problem Reports 2018 Temperature Simulation and Heat Exchange in a Batch Reactor Using Ansys Fluent Rahul Kooragayala Follow this and additional works at: https://researchrepository.wvu.edu/etd Recommended Citation Kooragayala, Rahul, "Temperature Simulation and Heat Exchange in a Batch Reactor Using Ansys Fluent" (2018). Graduate Theses, Dissertations, and Problem Reports. 6006. https://researchrepository.wvu.edu/etd/6006 This Thesis is protected by copyright and/or related rights. It has been brought to you by the The Research Repository @ WVU with permission from the rights-holder(s). You are free to use this Thesis in any way that is permitted by the copyright and related rights legislation that applies to your use. For other uses you must obtain permission from the rights-holder(s) directly, unless additional rights are indicated by a Creative Commons license in the record and/ or on the work itself. This Thesis has been accepted for inclusion in WVU Graduate Theses, Dissertations, and Problem Reports collection by an authorized administrator of The Research Repository @ WVU. For more information, please contact [email protected]. Temperature simulation and heat exchange in a batch reactor using Ansys Fluent Rahul Kooragayala Thesis submitted to the Benjamin M. Statler College of Engineering and Mineral Resources at West Virginia University in partial fulfillment of the requirements for the degree of Master of Science in Mechanical Engineering Cosmin Dumitrescu, Ph.D., Chair Hailin Li, Ph.D. Vyacheslav Akkerman, Ph.D. Department of Mechanical and Aerospace Engineering Morgantown, West Virginia 2018 Keywords: Ansys Fluent, batch reactor, heat transfer, simulation, water vaporization Copyright 2018 Rahul Kooragayala Abstract Temperature simulation and heat exchange in a batch reactor using Ansys Fluent Rahul Kooragayala Internal combustion (IC) engines are the main power source for on-road and off-road vehicles. -
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 -
Ideal Models of Reactors - A
CHEMICAL ENGINEEERING AND CHEMICAL PROCESS TECHNOLOGY – Vol. III - Ideal Models Of Reactors - A. Burghardt IDEAL MODELS OF REACTORS A. Burghardt Institute of Chemical Engineering, Polish Academy of Sciences, Poland Keywords: Thermodynamic state, conversion degree, extent of reaction, classification of chemical reactors, mass balance, energy balance, reactor models, reactor design. Contents 1. Introduction 2. Thermodynamic State of a System 3. The Plug Flow Reactor 4. The Perfectly Mixed Tank Reactor 5. The Batch Reactor 6. The Cascade of Tank Reactors 7. Comparison of Different Types of Reactors 7.1. Size Comparison of Single Reactors 7.2. The Cascade of Tank Reactors 7.3. Multireaction systems Bibliography Biographical Sketch Summary The range of application of chemical reactors is extremely broad not only in the chemical industry but also in the petrochemical industry and in refineries. Recently these apparatuses have also been more often used in the dynamically developing field of biotechnology as well as in the processes connected with environmental protection. The main goal of the discipline named chemical reaction engineering is to elaborate quantitative fundamentals for reactor design and for a proper operation of these apparatuses in real industrial conditions. The tool applied in these investigations is modeling, whose task is to establish relationships which could quantitatively describe the course ofUNESCO the process in reactors of various – EOLSStypes and scales. These relationships constitute the mathematical model. The mathematical model is usually much simpler than the real physical object but should comprise all these features and parameters whose influence on the process is crucial. SAMPLE CHAPTERS The rational basis for developing these models is provided by the principles of conservation of mass, momentum and energy. -
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 -
CHAPTER 9 Nonisotbermal Reactors 287
________---""C"'--H APT E RL-- 9""'---- Nonisothermal Reactors 9.1 I The Nature of the Problem In Chapter 3, the isothennal material balances for various ideal reactors were derived (see Table 3.5.1 for a summary). Although isothermal conditions are most useful for the measurement of kinetic data, real reactor operation is nonnally nonisothennal. Within the limits of heat exchange, the reactor can operate isothennally (maximum heat exchange) or adiabatically (no heat exchange); recall the limits of reactor be havior given in Table 3.1.1. Between these bounds of heat transfer lies the most com mon fonn of reactor operation-the nonisothermal regime (some extent of heat ex change). The three types of reactor operations yield different temperature profiles within the reactor and are illustrated in Figure 9.1.1 for an exothennic reaction. If a reactor is operated at nonisothennal or adiabatic conditions then the ma terial balance equation must be written with the temperature, T, as a variable. For example with the PFR, the material balance becomes: vir(Fi,T) (9.1.1) Since the reaction rate expression now contains the independent variable T, the material balance cannot be solved alone. The solution of the material balance equation is only possible by the simult<meous solution of the energy balance. Thus, for nonisothennal re~ actor descriptions, an energy balance must accompany the material balance. 9.2 I Energy Balances Consider a generalized tlow reactor as illustrated in Figure 9.2.1. Applying the first law of thennodynamics to the reactor shown in Figure 9.2.1, the following is obtained: (9.2.1) CHAPTER 9 Nonisotbermal Reactors 287 ~ ---·I PF_R ..