Derivation of Stirred Tank Reactor Optimal Control
|
|
|
- Kristina Lee
- 5 years ago
- Views:
Transcription
1 Derivation of Stirred Tank Reactor Optimal Control Lorenz T. Biegler Department of Chemical Engineering Carnegie Mellon University Pittsburgh, PA, 15213, USA Consider the liquid-phase stirred tank reactor shown in Figure 1. We assume Figure 1: Sketch of Hicks Reactor constant liquid volume (V ), flow (F), density (!), heat capacity (C p ), coolant temperature (T c ), coolant flow (F c ), overall heat transfer coefficient (U(F c )), cross sectional area (A c ) and heat of reaction ("H), as well as a first order Arrhenius rate law. Following the notation in the figure, the mass and energy balance for the reactor are given by: V dc!c p V dt = F(c f c(t)) Vk 10 exp( E/RT )c(t), c(0)=c init (1) = F!C p (T f T (t)) + "HVk 10 exp( E/RT )c(t) +U(F c )A c (T c T ), T (0)=T init (2) We define aggregated parameters # = V/F, $u = UA c /(!C p V), y f =!C p T f /"H, n = E!C p /(R"H), y c =!C p T c /"H, and redefine the states: c c/c f, T 1
2 !C p T /"H in order to obtain: dc dt = (1 c(t))/# k 10 exp( n/t )c(t),c(0)=c init (3) = (y f T (t))/# k 10 exp( n/t )c(t)+$u(y c T ),T (0)=T init (4) The parameters are given values in the GAMS file below and the optimal control problem is given by: Min t f 0 $ 1 ( c c(t)) 2 + $ 2 ( T T (t)) 2 + $ 3 (ū u(t)) 2 (5) s.t. (3) (4) (6) where c, T,ū are the desired values of the states and input and $ j are the desired weights. $Title Dynamic Optimization of a Non-Isothermal CSTR $OFFUPPER $OFFSYMXREF OFFSYMLIST option sysout = off; OPTION SOLPRINT = OFF; This file implements the dynamic optimization of non-isothermal CSTR as proposed by Hicks and Ray and later modified to feature multiple steady-state behaviour. Full discretization of the model and input, output variables renders the problem as a NLP. More detail on the model can be found in Flores Tlacuahuac, A., S. Terrazas Moreno, and L. T. Biegler, On Global Optimization of Highly Nonlinear Dynamic Systems, Industrial and Engineering Chemistry Research, 47, 8, pp (2008) Sets i number of finite elements /1 100/ j number of internal collocation points /1 3/; 2
3 Alias (j,k); Scalar cinit initial concentration /0.1367/ tinit initial temperature /0.7293/ uinit initial heat transfer rate /390/ cdes initial concentration /0.0944/ tdes final temperature /0.7766/ udes final heat transfer rate /340/ alpha dimensionless parameter /1.95e-04/ alpha1 dimensionless parameter /1e+06/ alpha2 dimensionless parameter /2e+03/ alpha3 dimensionless parameter /1e-03/ k10 rate constant /300/ n /5/ cf /7.6/ tf /300/ tc /290/ theta /20/ yf /0.3947/ yc /0.3816/ time /10/ point /0/ nfe /100/ ncp /3/ slopec slopet slopeu, ii, jj, point; Table a(j,j) First order derivatives collocation matrix ; Parameter cguess(i,j) tguess(i,j) 3
4 ttguess(i,j) uguess(i,j) h(i) ; Initial guess of the decision variables point = 0; slopec = (cdes-cinit)/(nfencp); slopet = (tdes-tinit)/(nfencp); slopeu = (udes-uinit)/(nfencp); for (ii = 1 to nfe, for (jj = 1 to ncp, point = point+1; cguess(i,j) = slopecpoint+cinit ; tguess(i,j) = slopetpoint+tinit ; ttguess(i,j) = timepoint ; uguess(i,j) = slopeupoint+uinit ; ); ); h(i) = 1/nfe ; Variables c(i,j) concentration t(i,j) temperature tt(i,j) time u(i,j) heat transfer rate cdot(i,j) tdot(i,j) c0(i) t0(i) tt0(i) phi objective function ; Equations fobj criterion definition IT, IC, ITT FECOLc(i,j) FECOLt(i,j) FECOLtt(i,j) CONc(i) CONt(i) 4
5 CONtt(i) ODEc(i,j) ODEt(i,j); fobj.. phi =e= sum((i,j), h(i)a(j, 3 )(alpha1(sqr(cdes-c(i,j)))+alpha2 sqr(tdes-t(i,j))+alpha3sqr(udes-u(i,j)))); FECOLc(i,j)$(ord(i) le nfe).. c(i,j)=e=c0(i) +timeh(i)sum(k,a(k,j)cdot(i,k)) ; FECOLt(i,j)$(ord(i) le nfe).. t(i,j) =e= t0(i) +timeh(i)sum(k,a(k,j)tdot(i,k)) ; FECOLtt(i,j)$(ord(i) le nfe).. tt(i,j) =e= tt0(i) +timeh(i)sum(k,a(k,j)) ; CONc(i)$(ord(i) gt 1 and ord(i) le nfe).. c0(i) =e= c0(i-1) + timeh(i-1)sum(j, cdot(i-1,j)a(j, 3 )); CONt(i)$(ord(i) gt 1 and ord(i) le nfe).. t0(i) =e= t0(i-1) + timeh(i-1)sum(j, tdot(i-1,j)a(j, 3 )); CONtt(i)$(ord(i) gt 1 and ord(i) le nfe).. tt0(i) =e= tt0(i-1) + timeh(i-1)sum(j, a(j, 3 )); ODEc(i,j)$(ord(i) le nfe).. cdot(i,j) =e= (1-c(i,j))/theta -k10exp(-n/t(i,j))c(i,j) ; ODEt(i,j)$(ord(i) le nfe).. tdot(i,j) =e= (yf-t(i,j))/theta +k10exp(-n/t(i,j))c(i,j)-alphau(i,j)(t(i,j)-yc) ; IC.. c0( 1 ) =e= cinit; IT.. t0( 1 ) =e= tinit; ITT.. tt0( 1 ) =e= 0; TTT.. time =e= transtime ; Model hicks /all/; c.lo(i,j) = 0; c.up(i,j) = 1; 5
6 t.lo(i,j) = 0.1; t.up(i,j) = 1; u.lo(i,j) = 0; u.up(i,j) = 500; c0.lo(i) = 0; c0.up(i) = cinit ; t0.lo(i) = 0.1; t0.up(i)= 1; c.l(i,j) = cguess(i,j); t.l(i,j) = tguess(i,j); tt.l(i,j) = ttguess(i,j); u.l(i,j) = uguess(i,j); c0.l(i) = cinit ; t0.l(i) = tinit ; cdot.l(i,j) = 1 ; tdot.l(i,j) = 1 ; option nlp = coinipopt; option nlp = baron; option nlp = conopt; option nlp = minos; hicks.optfile = 1; Solve hicks minimizing phi using nlp; display tt0.l, c0.l, t0.l; option nlp = conopt; Solve hicks minimizing phi using nlp; 6
Simultaneous Scheduling and Control of Multi-Grade Polymerization Reactors
Simultaneous Scheduling and Control of Multi-Grade Polymerization Reactors Antonio Flores-Tlacuahuac Department of Chemical Engineering Universidad Iberoamericana México, DF mailto:antonio.flores@uia.mx
A Brief GAMS Tutorial
A Brief GAMS Ttoria L. T. Bieger Chemica Engineering Department University Pittsbrgh, PA To access GAMS The compters in the onge have a been provisioned with GAMS 22.7. GAMS is accessibe from the command
Integration of Scheduling and Control Operations
Integration of Scheduling and Control Operations Antonio Flores T. with colaborations from: Sebastian Terrazas-Moreno, Miguel Angel Gutierrez-Limon, Ignacio E. Grossmann Universidad Iberoamericana, México
Simultaneous Cyclic Scheduling and Control of a Multiproduct CSTR Reactor
Simultaneous Cyclic Scheduling and Control of a Multiproduct CSTR Reactor Antonio Flores-Tlacuahuac Departamento de Ingeniería y Ciencias Químicas, Universidad Iberoamericana Prolongación Paseo de la Reforma
CHAPTER 2 CONTINUOUS STIRRED TANK REACTOR PROCESS DESCRIPTION
11 CHAPTER 2 CONTINUOUS STIRRED TANK REACTOR PROCESS DESCRIPTION 2.1 INTRODUCTION This chapter deals with the process description and analysis of CSTR. The process inputs, states and outputs are identified
Simultaneous Cyclic Scheduling and Control of Tubular Reactors: Parallel Production Lines
Simultaneous Cyclic Scheduling and Control of Tubular Reactors: Parallel Production Lines Antonio Flores-Tlacuahuac Departamento de Ingeniería y Ciencias Químicas, Universidad Iberoamericana Prolongación
Development of Dynamic Models. Chapter 2. Illustrative Example: A Blending Process
Development of Dynamic Models Illustrative Example: A Blending Process An unsteady-state mass balance for the blending system: rate of accumulation rate of rate of = of mass in the tank mass in mass out
Simultaneous Scheduling and Control of Multiproduct Continuous Parallel Lines
Simultaneous Scheduling and Control of Multiproduct Continuous Parallel Lines Antonio Flores-Tlacuahuac Departamento de Ingeniería y Ciencias Químicas, Universidad Iberoamericana Prolongación Paseo de
A First Course on Kinetics and Reaction Engineering. Class 20 on Unit 19
A First Course on Kinetics and Reaction Engineering Class 20 on Unit 19 Part I - Chemical Reactions Part II - Chemical Reaction Kinetics Where We re Going Part III - Chemical Reaction Engineering A. Ideal
CHAPTER 3 : MATHEMATICAL MODELLING PRINCIPLES
CHAPTER 3 : MATHEMATICAL MODELLING PRINCIPLES When I complete this chapter, I want to be able to do the following. Formulate dynamic models based on fundamental balances Solve simple first-order linear
Simultaneous Cyclic Scheduling and Optimal Control of Multi-Grade Polymerization Reactors
Simultaneous Cyclic Scheduling and Optimal Control of Multi-Grade Polymerization Reactors Sebastian Terrazas-Moreno, Antonio Flores-Tlacuahuac Departamento de Ingeniería y Ciencias Químicas, Universidad
Use of Differential Equations In Modeling and Simulation of CSTR
Use of Differential Equations In Modeling and Simulation of CSTR JIRI VOJTESEK, PETR DOSTAL Department of Process Control, Faculty of Applied Informatics Tomas Bata University in Zlin nám. T. G. Masaryka
A Lagrangean Heuristic Approach for the Simultaneous Cyclic Scheduling and Optimal Control of Multi-Grade Polymerization Reactors.
A Lagrangean Heuristic Approach for the Simultaneous Cyclic Scheduling and Optimal Control of Multi-Grade Polymerization Reactors. Sebastian Terrazas-Moreno, Antonio Flores-Tlacuahuac Departamento de Ingeniería
PROPORTIONAL-Integral-Derivative (PID) controllers
Multiple Model and Neural based Adaptive Multi-loop PID Controller for a CSTR Process R.Vinodha S. Abraham Lincoln and J. Prakash Abstract Multi-loop (De-centralized) Proportional-Integral- Derivative
Module 6 : Solving Ordinary Differential Equations - Initial Value Problems (ODE-IVPs) Section 3 : Analytical Solutions of Linear ODE-IVPs
Module 6 : Solving Ordinary Differential Equations - Initial Value Problems (ODE-IVPs) Section 3 : Analytical Solutions of Linear ODE-IVPs 3 Analytical Solutions of Linear ODE-IVPs Before developing numerical
Model-based On-Line Optimization Framework for Semi-batch Polymerization Reactors
Preprints of the 9th International Symposium on Advanced Control of Chemical Processes The International Federation of Automatic Control MoA1.1 Model-based On-Line Optimization Framework for Semi-batch
Solutions for Tutorial 3 Modelling of Dynamic Systems
Solutions for Tutorial 3 Modelling of Dynamic Systems 3.1 Mixer: Dynamic model of a CSTR is derived in textbook Example 3.1. From the model, we know that the outlet concentration of, C, can be affected
Optimization Algorithms for Integration of Design, Control, and Scheduling for Chemical Processes Subject to Disturbances and Uncertainty
Optimization Algorithms for Integration of Design, Control, and Scheduling for Chemical Processes Subject to Disturbances and Uncertainty by Robert Koller A thesis presented to the University of Waterloo
Chemical reactors. H has thermal contribution, pressure contribution (often negligible) and reaction contribution ( source - like)
Chemical reactors - chemical transformation of reactants into products Classification: a) according to the type of equipment o batch stirred tanks small-scale production, mostly liquids o continuous stirred
Kinetic Model Parameter Estimation for Product Stability: Non-uniform Finite Elements and Convexity Analysis
Kinetic Model Parameter Estimation for Product Stability: Non-uniform Finite Elements and Convexity Analysis Mark Daichendt, Lorenz Biegler Carnegie Mellon University Pittsburgh, PA 15217 Ben Weinstein,
13 th Aug Chemical Reaction Engineering CH3010. Home work problems
13 th ug 18. Chemical Reaction Engineering CH31. Home work problems 1. Batch reactor, variable volume. Consider a gas phase reaction B, conducted isothermally and at constant pressure in a batch reactor.
The simplified model now consists only of Eq. 5. Degrees of freedom for the simplified model: 2-1
. a) Overall mass balance: d( ρv ) Energy balance: = w + w w () d V T Tref C = wc ( T Tref ) + wc( T Tref ) w C T Because ρ = constant and ( Tref ) V = V = constant, Eq. becomes: () w = + () w w b) From
9. The Monopsonist. π = c x [g s + s Gs] (9.1) subject to. Ax s (9.2) x 0, s 0. The economic interpretation of this model proceeds as in previous
![9. The Monopsonist. π = c x [g s + s Gs] (9.1) subject to. Ax s (9.2) x 0, s 0. The economic interpretation of this model proceeds as in previous](/thumbs/83/87996701.jpg "9. The Monopsonist. π = c x [g s + s Gs] (9.1) subject to. Ax s (9.2) x 0, s 0. The economic interpretation of this model proceeds as in previous")
9. The Monopsonist An economic agent who is the sole buer of all the available suppl of an input is called a monopsonist. We will discusss two categories of monopsonists: the pure monopsonist and the perfectl
Linear Parameter Varying and Time-Varying Model Predictive Control
Linear Parameter Varying and Time-Varying Model Predictive Control Alberto Bemporad - Model Predictive Control course - Academic year 016/17 0-1 Linear Parameter-Varying (LPV) MPC LTI prediction model
Model Predictive Control
Model Predictive Control Linear time-varying and nonlinear MPC Alberto Bemporad http://cse.lab.imtlucca.it/~bemporad 2018 A. Bemporad - "Model Predictive Control" 1/30 Course structure Linear model predictive
BITS-Pilani Dubai, International Academic City, Dubai Second Semester. Academic Year
BITS-Pilani Dubai, International Academic City, Dubai Second Semester. Academic Year 2007-2008 Evaluation Com anent: Com rehensive Examination Closed Book CHE UC441/11NSTR UC 45'1 PROCESS CONTROL Date:
Simultaneous mixed-integer dynamic optimization for integrated design and control
Computers and Chemical Engineering 31 (2007) 588 600 Simultaneous mixed-integer dynamic optimization for integrated design and control Antonio Flores-Tlacuahuac, Lorenz T. Biegler Department of Chemical
Name. Honor Code: I have neither given nor received unauthorized aid on this examination, nor have I concealed any violations of the Honor Code.
ChE 344 Fall 014 Mid Term Exam II Wednesday, November 19, 014 Open Book Closed Notes (but one 3x5 note card), Closed Computer, Web, Home Problems and In-class Problems Name Honor Code: I have neither given
CHEMICAL ENGINEERING KINETICS/REACTOR DESIGN. Tony Feric, Kathir Nalluswami, Manesha Ramanathan, Sejal Vispute, Varun Wadhwa
CHEMICAL ENGINEERING KINETICS/REACTOR DESIGN Tony Feric, Kathir Nalluswami, Manesha Ramanathan, Sejal Vispute, Varun Wadhwa Presentation Overview Kinetics Reactor Design Non- Isothermal Design BASICS OF
CONTROL OF MULTIVARIABLE PROCESSES
Process plants ( or complex experiments) have many variables that must be controlled. The engineer must. Provide the needed sensors 2. Provide adequate manipulated variables 3. Decide how the CVs and MVs
Strong formulation for fixed charge network flow problem
Strong formulation for fixed charge network flow problem Consider the network topology given by the graph G = (V, E) in the figure, where V = {a, b, c, d}. Each node represents a router of the network,
H-Infinity Controller Design for a Continuous Stirred Tank Reactor
International Journal of Electronic and Electrical Engineering. ISSN 974-2174 Volume 7, Number 8 (214), pp. 767-772 International Research Publication House http://www.irphouse.com H-Infinity Controller
Lecture 4: Numerical solution of ordinary differential equations
Lecture 4: Numerical solution of ordinary differential equations Department of Mathematics, ETH Zürich General explicit one-step method: Consistency; Stability; Convergence. High-order methods: Taylor
Performance improvement and dynamical behaviour analysis of a cascade of two CSTRs
University of Wollongong Research Online Faculty of Informatics - Papers (Archive) Faculty of Engineering and Information Sciences 2007 Performance improvement and dynamical behaviour analysis of a cascade
Introduction to the Thermodynamics of Materials
Solutions Manual to accompany Introduction to the hermodynamics of Materials Sixth Edition David R. Gaskell School of Materials Engineering Purdue University West Lafayette, IN David E. Laughlin ALCOA
Optimization of Batch Processes
Integrated Scheduling and Dynamic Optimization of Batch Processes Yisu Nie and Lorenz T. Biegler Center for Advanced Process Decision-making Department of Chemical Engineering Carnegie Mellon University
Scheduling of oil-refinery operations
Felipe Díaz-Alvarado 2, Francisco Trespalacios 1, Ignacio Grossmann 1 1 Center for Advanced Process Decision-making. Carnegie Mellon University 2 Department of Chemical and Biotechnological Engineering.
Solutions for Tutorial 4 Modelling of Non-Linear Systems
Solutions for Tutorial 4 Modelling of Non-Linear Systems 4.1 Isothermal CSTR: The chemical reactor shown in textbook igure 3.1 and repeated in the following is considered in this question. The reaction
Chemical Reactions and Chemical Reactors
Chemical Reactions and Chemical Reactors George W. Roberts North Carolina State University Department of Chemical and Biomolecular Engineering WILEY John Wiley & Sons, Inc. x Contents 1. Reactions and
Lecture 4. Mole balance: calculation of membrane reactors and unsteady state in tank reactors. Analysis of rate data
Lecture 4 Mole balance: calculation of membrane reactors and unsteady state in tank reactors. nalysis of rate data Mole alance in terms of Concentration and Molar Flow Rates Working in terms of number
MATLAB Ordinary Differential Equation (ODE) solver for a simple example 1. Introduction
MATLAB Ordinary Differential Equation (ODE) solver for a simple example 1. Introduction Differential equations are a convenient way to express mathematically a change of a dependent variable (e.g. concentration
5. Collection and Analysis of. Rate Data
5. Collection and nalysis of o Objectives Rate Data - Determine the reaction order and specific reaction rate from experimental data obtained from either batch or flow reactors - Describe how to analyze
Theoretical Models of Chemical Processes
Theoretical Models of Chemical Processes Dr. M. A. A. Shoukat Choudhury 1 Rationale for Dynamic Models 1. Improve understanding of the process 2. Train Plant operating personnel 3. Develop control strategy
CHEE 222: PROCESS DYNAMICS AND NUMERICAL METHODS
CHEE 222: PROCESS DYNAMICS AND NUMERICAL METHODS Winter 2017 Module 1: Introduction to Process Modeling Dr. Xiang Li 1 Module 1 Outline 1. Process and Model - Concepts of process and model - Classification
MATHCAD SOLUTIONS TO THE CHEMICAL ENGINEERING PROBLEM SET
MATHCA SOLUTIONS TO THE CHEMICAL ENGINEERING PROBLEM SET Mathematical Software Session John J. Hwalek, epartment of Chemical Engineering University of Maine, Orono, Me 4469-5737 (hwalek@maine.maine.edu)
CBE 142: Chemical Kinetics & Reaction Engineering
CBE 142: Chemical Kinetics & Reaction Engineering Midterm #2 November 6 th 2014 This exam is worth 100 points and 20% of your course grade. Please read through the questions carefully before giving your
Kinetic Modeling for a Semi-Interpenetrating Polymer Network (SIPN) Process
Kinetic Modeling for a Semi-Interpenetrating Polymer Network (SIPN) Process Weijie Lin Advisor: Lorenz T. Biegler, Annette Jacobson Chemical Engineering Department Carnegie Mellon University, Pittsburgh,
10.34 Numerical Methods Applied to Chemical Engineering. Quiz 2
10.34 Numerical Methods Applied to Chemical Engineering Quiz 2 This quiz consists of three problems worth 35, 35, and 30 points respectively. There are 4 pages in this quiz (including this cover page).
Chemical Process Operating Region
Inherently Safer Design Oriented Segregation of Chemical Process Operating Region Wang Hangzhou, Yuan Zhihong, Chen Bingzhen * Zhao Jinsong, Qiu Tong, He Xiaorong, Institute of Process System Engineering,
On Practical Applications of Active Disturbance Rejection Control
2010 Chinese Control Conference On Practical Applications of Active Disturbance Rejection Control Qing Zheng Gannon University Zhiqiang Gao Cleveland State University Outline Ø Introduction Ø Active Disturbance
ChE 344 Winter 2011 Final Exam + Solution. Open Book, Notes, and Web
ChE 344 Winter 011 Final Exam + Solution Monday, April 5, 011 Open Book, Notes, and Web Name Honor Code (Please sign in the space provided below) I have neither given nor received unauthorized aid on this
ξ Da nc n = c Pe ξ = c o ( θ ) (95) c ξ = 0 (96) θ = 0 ; c= c i ξ ( ) (97) (98) Pe z = u L E z
5. THE AXIAL DISPERSION MODEL The axial dispersion model can readily be extended to apply to turbulent flow conditions. Under such conditions the velocity profile is almost flat and averaging with respect
Midterm II. ChE 142 April 11, (Closed Book and notes, two 8.5 x11 sheet of notes is allowed) Printed Name
ChE 142 pril 11, 25 Midterm II (Closed Book and notes, two 8.5 x11 sheet of notes is allowed) Printed Name KEY By signing this sheet, you agree to adhere to the U.C. Berkeley Honor Code Signed Name_ KEY
i;\-'i frz q > R>? >tr E*+ [S I z> N g> F 'x sa :r> >,9 T F >= = = I Y E H H>tr iir- g-i I * s I!,i --' - = a trx - H tnz rqx o >.F g< s Ire tr () -s
5 C /? >9 T > ; '. ; J ' ' J. \ ;\' \.> ). L; c\ u ( (J ) \ 1 ) : C ) (... >\ > 9 e!) T C). '1!\ /_ \ '\ ' > 9 C > 9.' \( T Z > 9 > 5 P + 9 9 ) :> : + (. \ z : ) z cf C : u 9 ( :!z! Z c (! $ f 1 :.1 f.
ANFIS Gain Scheduled Johnson s Algorithm based State Feedback Control of CSTR
International Journal of Computer Applications (975 8887) ANFIS Gain Scheduled Johnsons Algorithm based State Feedback Control of CSTR U. Sabura Banu Professor, EIE Department BS Abdur Rahman University,
Dr. Trent L. Silbaugh, Instructor Chemical Reaction Engineering Final Exam Study Guide
Chapter 1 Mole balances: Know the definitions of the rate of reaction, rate of disappearance and rate of appearance Know what a rate law is Be able to write a general mole balance and know what each term
Effect of Random Noise, Quasi Random Noise and Systematic Random Noise on Unknown Continuous Stirred Tank Reactor (CSTR)
Applied Mathematical Sciences, Vol., 7, no. 6, 35-37 HIKARI Ltd, www.m-hikari.com https://doi.org/.988/ams.7.7983 Effect of Random Noise, Quasi Random Noise and Systematic Random Noise on Unknown Continuous
Physical Chemistry I CHEM 4641 Final Exam 13 questions, 30 points
Physical Chemistry I CHEM 4641 Final Exam 13 questions, 30 points Name: KEY Gas constant: R = 8.314 J mol -1 K -1 = 0.008314 kj mol -1 K -1. Boltzmann constant k = 1.381 10-23 J/K = 0.6950 cm -1 /K h =
A First Course on Kinetics and Reaction Engineering Example 30.1
Example 30.1 Problem Purpose This problem will help you determine whether you have mastered the learning objectives for this unit. It illustrates the general approach to solving the design equations for
Lecture 8. Mole balance: calculations of microreactors, membrane reactors and unsteady state in tank reactors
Lecture 8 Mole balance: calculations of microreactors, membrane reactors and unsteady state in tank reactors Mole alance in terms of Concentration and Molar Flow Rates Working in terms of number of moles
Trade Patterns, Production networks, and Trade and employment in the Asia-US region
Trade Patterns, Production networks, and Trade and employment in the Asia-U region atoshi Inomata Institute of Developing Economies ETRO Development of cross-national production linkages, 1985-2005 1985
Dynamic Real-Time Optimization: Linking Off-line Planning with On-line Optimization
Dynamic Real-Time Optimization: Linking Off-line Planning with On-line Optimization L. T. Biegler and V. Zavala Chemical Engineering Department Carnegie Mellon University Pittsburgh, PA 15213 April 12,
Optimization of an Ammonia Synthesis Reactor using Simultaneous Approach
197 A publication of CHEMICAL ENGINEERING TRANSACTIONS VOL. 43, 015 Chief Editors: Sauro Pierucci, Jiří J. Klemeš Copyright 015, AIDIC Servizi S.r.l., ISBN 978-88-95608-34-1; ISSN 83-916 The Italian Association
Modeling and Optimization of Semi- Interpenetrating Polymer Network (SIPN) Particle Process
Modeling and Optimization of Semi- Interpenetrating Polymer Network (SIPN) Particle Process Weijie Lin, Lorenz T. Biegler, Annette Jacobson Chemical Engineering Department Carnegie Mellon University, Pittsburgh,
10.34 Numerical Methods Applied to Chemical Engineering
10.34 Numerical Methods Applied to Chemical Engineering Quiz 1 This quiz consists of three problems worth 0, 40 and 40 points respectively. The problem statements are found on pages, 3 and 5 in this exam
GAMS assignment for Nonlinear Optimization (WI3 031)
GAMS assignment for Nonlinear Optimization (WI3 031) January 13, 2003 1 This assignment In the past we have found that 20 hours is enough to complete the assignment. In order to do the assignment you will
ChE 344 Winter 2011 Final Exam. Open Book, Notes, and Web
ChE 344 Winter 2011 Final Exam Monday, April 25, 2011 Open Book, Notes, and Web Name Honor Code (Please sign in the space provided below) I have neither given nor received unauthorized aid on this examination,
INTRODUCTION TO CHEMICAL PROCESS SIMULATORS
INTRODUCTION TO CHEMICAL PROCESS SIMULATORS DWSIM Chemical Process Simulator A. Carrero, N. Quirante, J. Javaloyes October 2016 Introduction to Chemical Process Simulators Contents Monday, October 3 rd
Chemical Reaction Engineering
Lecture 2 Chemical Reaction Engineering (CRE) is the field that studies the rates and mechanisms of chemical reactions and the design of the reactors in which they take place. 1 Lecture 2 Review of Lecture
Power Systems Control Prof. Wonhee Kim. Modeling in the Frequency and Time Domains
Power Systems Control Prof. Wonhee Kim Modeling in the Frequency and Time Domains Laplace Transform Review - Laplace transform - Inverse Laplace transform 2 Laplace Transform Review 3 Laplace Transform
CHEMICAL REACTORS - PROBLEMS OF REACTOR ASSOCIATION 47-60
2011-2012 Course CHEMICL RECTORS - PROBLEMS OF RECTOR SSOCITION 47-60 47.- (exam jan 09) The elementary chemical reaction in liquid phase + B C is carried out in two equal sized CSTR connected in series.
SOLUTIONS TO EXERCISES FOR. MATHEMATICS 133 Part 2. I. Topics from linear algebra
SOLUTIONS TO EXERCISES FOR MATHEMATICS 133 Part Fall 013 NOTE ON ILLUSTRATIONS. Drawings for several of the solutions in this file are available in the following document: http://math.ucr.edu/ res/math133/math133solutionsa.figures.f13.pdf
A COMSOL Multiphysics -based Model for Simulation of Methane-Hydrate Dissociation by Injection of Superheated CO 2. CH 4 -CO 2 -hydrate conversion
A COMSOL Multiphysics -based Model for Simulation of Methane-Hydrate Dissociation by Injection of Superheated CO 2 CH 4 -CO 2 -hydrate conversion Experimental setup CTD PTS Raman IR CO 2 CH 4 CO 2 CH 4
Chemical Kinetics and Reaction Engineering
Chemical Kinetics and Reaction Engineering MIDTERM EXAMINATION II Friday, April 9, 2010 The exam is 100 points total and 20% of the course grade. Please read through the questions carefully before giving
Modeling and Parameter Estimation of Interpenetrating
Modeling and Parameter Estimation of Interpenetrating Polymer Network Process EWO Spring Meeting March, 2009 Weijie Lin Advisors: Lorenz T. Biegler, Annette Jacobson Department of Chemical Engineering,
6XSSO\ VLGH FRQVWUDLQWV DQG ERWWOHQHFNV
ABCE study design F - 1 2 - - - - - - - - - - - - - - - - - - - - - - - - 19 ABCE IN KENYA 1 M 1 F M 2 F M L M M ART M G M F ical c a l a ip t aacy- a ical c a l a ip t aacy- a c a l a ip t ical c a l
Simultaneous Cyclic Scheduling and Control of Tubular Reactors: Single Production Lines
Simultaneous Cyclic Scheduling and Control of Tubular Reactors: Single Production Lines Antonio Flores-Tlacuahuac Departamento de Ingeniería y Ciencias Químicas, Universidad Iberoamericana Prolongación
Theory and Applications of Constrained Optimal Control Proble
Theory and Applications of Constrained Optimal Control Problems with Delays PART 1 : Mixed Control State Constraints Helmut Maurer 1, Laurenz Göllmann 2 1 Institut für Numerische und Angewandte Mathematik,
MATH107 Vectors and Matrices
School of Mathematics, KSU 20/11/16 Vector valued functions Let D be a set of real numbers D R. A vector-valued functions r with domain D is a correspondence that assigns to each number t in D exactly
A First Course on Kinetics and Reaction Engineering Unit 30.Thermal Back-Mixing in a PFR
Unit 30.Thermal Back-Mixing in a PFR Overview One advantage offered by a CSTR when running an exothermic reaction is that the cool feed gets heated by mixing with the contents of the reactor. As a consequence
ECE Introduction to Artificial Neural Network and Fuzzy Systems
ECE 39 - Introduction to Artificial Neural Network and Fuzzy Systems Wavelet Neural Network control of two Continuous Stirred Tank Reactors in Series using MATLAB Tariq Ahamed Abstract. With the rapid
6. Well-Stirred Reactors III
6. Well-Stirred Reactors III Reactors reaction rate or reaction velocity defined for a closed system of uniform pressure, temperature, and composition situation in a real reactor is usually quite different
FAULT-TOLERANT CONTROL OF CHEMICAL PROCESS SYSTEMS USING COMMUNICATION NETWORKS. Nael H. El-Farra, Adiwinata Gani & Panagiotis D.
FAULT-TOLERANT CONTROL OF CHEMICAL PROCESS SYSTEMS USING COMMUNICATION NETWORKS Nael H. El-Farra, Adiwinata Gani & Panagiotis D. Christofides Department of Chemical Engineering University of California,
~i~, ~';J M.1 "A.X;t7~~
Ci1 ;w -,IL I MX-- AA.R- v-r ';t ""lz"""" f 7ll\1. 13/cd Vt.dJt-l (l{ t f1.)-: ) -;::- r,.o.
Example 8: CSTR with Multiple Solutions
Example 8: CSTR with Multiple Solutions This model studies the multiple steady-states of exothermic reactions. The example is from Parulekar (27) which in turn was modified from one by Fogler (1999). The
Direct Methods. Moritz Diehl. Optimization in Engineering Center (OPTEC) and Electrical Engineering Department (ESAT) K.U.
Direct Methods Moritz Diehl Optimization in Engineering Center (OPTEC) and Electrical Engineering Department (ESAT) K.U. Leuven Belgium Overview Direct Single Shooting Direct Collocation Direct Multiple
Introduction to Biomathematics. Problem sheet
Introction to Biomathematics Problem sheet 1. A model for population growth is given in non-dimensional units in the form = u1 u ) u0) > 0. a) Sketch the graph of the function fu) = u1 u ) against u for
Chemical Engineering Applications in Scilab
Chemical Engineering Applications in Scilab Prashant Dave Indian Institute of Technology Bombay (IIT Bombay) Introduction In Chemical Engineering the type of problems that occur are Modeling and Simulation
Chemical Reaction Engineering. Dr. Yahia Alhamed
Chemical Reaction Engineering Dr. Yahia Alhamed 1 Kinetics and Reaction Rate What is reaction rate? It is the rate at which a species looses its chemical identity per unit volume. The rate of a reaction
Dynamic Behavior. Chapter 5
1 Dynamic Behavior In analyzing process dynamic and process control systems, it is important to know how the process responds to changes in the process inputs. A number of standard types of input changes
MASSACHUSETTS Election Statistics
. MASSACHUSETTS Eletin Statistis 1984 In ardane with the prvisins f the Massahusetts General Laws, Chapter 54, Setin 133 ffie f the Massahusetts Seretary f State Mihael Jseph Cnnlly, Seretary Publiatins
Model identification
SE5 Prof. Davide Manca Politecnico di Milano Dynamics and Control of Chemical Processes Solution to Lab #5 Model identification Davide Manca Dynamics and Control of Chemical Processes Master Degree in
T( C) k 1/T lnk 172,2 0, , , ,7 0, , , ,6 0, , , ,1 0, , ,19481
Exemplo 1: T( C) k 1/T lnk 172,2 0,0000997 0,002246-9,21334 187,7 0,000301 0,002171-8,1084 202,6 0,00078 0,002103-7,15622 218,1 0,00204 0,002036-6,19481 -6,0-6,5 Equation y = a + b*x Adj. R-Square 0,9999
INTEGRATED CIRCUITS. For a complete data sheet, please also download:
INTEGRATED CIRCUITS DATA SEET For a complete data sheet, please also download: The IC0 74C/CT/CU/CMOS Logic Family Specifications The IC0 74C/CT/CU/CMOS Logic Package Information The IC0 74C/CT/CU/CMOS
SOLUTION SET. Chapter 9 REQUIREMENTS FOR OBTAINING POPULATION INVERSIONS "LASER FUNDAMENTALS" Second Edition. By William T.
SOLUTION SET Chapter 9 REQUIREMENTS FOR OBTAINING POPULATION INVERSIONS "LASER FUNDAMENTALS" Second Edition By William T. Silfvast C.11 q 1. Using the equations (9.8), (9.9), and (9.10) that were developed
CHAPTER THERMODYNAMICS
54 CHAPTER THERMODYNAMICS 1. If ΔH is the change in enthalpy and ΔE the change in internal energy accompanying a gaseous reaction, then ΔHis always greater than ΔE ΔH< ΔE only if the number of moles of
P a g e 5 1 of R e p o r t P B 4 / 0 9
P a g e 5 1 of R e p o r t P B 4 / 0 9 J A R T a l s o c o n c l u d e d t h a t a l t h o u g h t h e i n t e n t o f N e l s o n s r e h a b i l i t a t i o n p l a n i s t o e n h a n c e c o n n e
ChE 344 Winter 2013 Mid Term Exam II Tuesday, April 9, 2013
ChE 344 Winter 2013 Mid Term Exam II Tuesday, April 9, 2013 Open Course Textbook Only Closed everything else (i.e., Notes, In-Class Problems and Home Problems Name Honor Code (Please sign in the space
PHEN 612 SPRING 2008 WEEK 1 LAURENT SIMON
PHEN 612 SPRING 2008 WEEK 1 LAURENT SIMON Chapter 1 * 1.1 Rate of reactions r A A+B->C Species A, B, and C We are interested in the rate of disappearance of A The rate of reaction, ra, is the number of
BAE 820 Physical Principles of Environmental Systems
BAE 820 Physical Principles of Environmental Systems Type of reactors Dr. Zifei Liu Ideal reactors A reactor is an apparatus in which chemical, biological, and physical processes (reactions) proceed intentionally,