Youn-Woo Lee School of Chemical and Biological Engineering Seoul National University , 599 Gwanangro, Gwanak-gu, Seoul, Korea
|
|
- Rosalyn Stanley
- 5 years ago
- Views:
Transcription
1 hemical Reacto esign Y W L Youn-Woo Lee School of hemical and iological Engineeing 55-74, 599 Gwanango, Gwana-gu, Seoul, Koea ywlee@snu.ac.
2 hapte 6 Multiple Reactions hemical Reaction Engineeing
3 Intoduction Seldom is the eaction of inteest the only one that occus in a chemical eacto. Typically, multiple eactions will occu, some desied and some undesied. One of the ey factos in the economic success of a chemical plant is minimization of undesied side eactions that occu along with the desied eaction. In this chapte, we discuss eacto selection and geneal mole balances fo multiple eactions. Fist, we descibe the fou basic types of multiple eactions: seies, paallel, independent, and complex. Next, we define the selectivity paamete and discuss how it can be used to minimize unwanted side eactions by pope choice of opeating conditions and eacto selection.
4 Objectives efine diffeent types of selectivity and yield hoose a eaction system that would maximize the selectivity of the desied poduct given the ate laws fo all the eactions occuing in the system. Size eactos to maximize the selectivity and to detemine the species concentations in a batch eacto, semi-batch eacto, STR, PFR, and PR, systems.
5 6. efinition of Multiple Reaction Paallel xns (competing xns) Seies xns (consecutive xns) omplex xns (Paallel + Seies xns) E Independent xns + E + F
6 Examples of Multiple Reaction Paallel xns (Oxidation of ethylene to ethylene oxide) H =H +O H -H O + H O Seies xns (xn of EO with NH ) O O Monoethanolamine H -H + NH HOH H NH EO EO (HOH H ) NH (HOH H ) N iethanolamine omplex xns (fomation of butadiene fom ethanol) Tiethanolamine H 5 OH H 4 + H O H 5 OH H HO + H H 4 +HHO HO 4 H 6 +HO Independent xns (The cacing of cude oil to fom gasoline) 5 H H 6 + H 6 8 H 8 6 H 4 + H 4
7 esied and ndesied Reaction (esied Poduct) (ndesied Poduct) The economic incentive Maximize the fomation of Minimize the fomation of ompeting o side xn Total cost M sepaation Reaction cost eaction Sepaation cost, Low High Rxn-sepaation system poducing both & Efficiency of a eacto system
8 Instantaneous Selectivity, S (esied Poduct) (ndesied Poduct) The ate laws ae Selectivity tells us how one poduct is favoed ove anothe when we have multiple l eactions. S / Rate of fomation of = Rate of fomation of
9 ~ Oveall Selectivity, S Fo Flow Reacto ~ F Exit mola flow ate of desied poduct S / = = F Exit mola flow ate of undesied poduct Fo atch Reacto ~ S / = N = N No. of moles of desied poduct at the end of xn time No. of moles of undesied poduct at the end of xn time
10 ~ Example 6-: ompaison between S / and S / fo a STR ~ Mission: evelop a elationship between S / and S / in a STR Solution (esied Poduct) S / = ~ F (ndesied Poduct) S / = F Mole balance of and yields F = V and F = V, espectively ~ F = V = = S = / S F / V ~ S / = S /
11 Yields Instantaneous Yield (asis: Reaction Rate) Y = - Oveall Yield (asis: Mole o Mola Flow Rate) N = Fo a batch system: Y = N o -N ~ Mole of desied poduct fomed at the end of eaction Numbe of moles of ey eactant consumed Fo a flow system: ~ F Y = Fo -F
12 Note iffeent e definitions fo selectivity ect ty and yield hec caefully to ascetain the definition intended by the autho Fom an economic standpoint, oveall selectivities and yields ae impotant in detemining pofits The instantaneous selectivities give insights in choosing eactos and eaction schemes that t will help maximize i the pofit
13 6. Paallel Reactions (esied Poduct) (ndesied Poduct) W t t The ate laws ae We want to maximize S /. Rate of fomation of / S = Rate of fomation of Rate of fomation of and ae positive eaction odes
14 6.. Maximizing the esied Poduct fo One Reactant (esied Poduct) (ndesied Poduct) S / ase : >, a = - S / a Maximize S / - eeping the concentation of eactant as high as possible duing the xn -in gas phase xn, we should un it w/o inets and at high pessues to eep high - in liquid phase xn, the use of diluents should be eep to a minimum - use a batch o plug-flow eacto
15 6.. Maximizing the esied Poduct fo One Reactant (esied Poduct) (ndesied Poduct) S ase : >,b= - S / b Maximize S / - eeping the concentation of eactant as low as possible duing the xn - in gas phase xn, we should un it with inets and at low pessues to eep low - in liquid phase xn, the use of diluents should be eep to a maximum - use a STR o ecycle eacto (poduct steam act as a diluent)
16 Maximizing S fo one eactant Whethe the eaction should be un at high o low T? S / ~ e E E RT S ase : E > E - ( ) inceases moe apidly with inceasing temp. than does the. - eeping the tempeatue as high as possible to maximize S. S / E E T ase 4: E > E E E - eeping the tempeatue as low as possible to maximize S S / -not so low that t the desied d xn does not poceed to any significant ifi extent. t T
17 Maximizing S /XY fo the Tambouze Reaction Reactant decomposes by thee simultaneous eactions to fom thee poducts, (desied), X (undesied), and Y (undesied). These liquid phase eactions, along with the appopiate ate laws, ae called the Tambouze eactions. mol dm s X X () (0.005s () ) dm mol s Y Y. () How and unde what conditions (e.g., eacto types, tempeatue, concentations) should the eaction be caied out to maximize the selectivity of? The specific eaction ates ae 00K E =0,000, E =5,000, and E =0,000 cal/mole 0 =0.4M, v 0 =.0 dm /s S/(XY) X Y
18 Maximizing S /XY fo the Tambouze Reaction S /(X+Y) S /(X+Y) S /(XY) X Y S /(X+Y) =(0.005* )/( * ) S 0.84 /(XY) 0 X Y (mol/dm )
19 Maximizing S /XY fo the Tambouze Reaction s we see, the selectivity eaches a maximum at a concentation *. ecause the concentation changes down the length of a PFR, we cannot opeate at this maximum. onsequently, we will use a STR and design it to opeate at this maximum. To find the maximum *, we diffeentiate S /(X+Y) w..t.,setthe deivative to zeo, and solve fo *. That is, deivative to zeo, and solve fo. That is, Y X Y) /(X S * * * Y) /(X - 0 ds * d * s) 0 000(mol/dm * dm 0.8mol/ s) /mol 0.008(dm s) 0.000(mol/dm S * * Y X /XY Y X
20 Maximizing S /XY fo the Tambouze Reaction We now calculate this STR volume and convesion. The net ate of fomation of fom eactions (), (), and () is - X Y STR volume fo this liquid-phase id eaction, 0 V [ ] [ ] * * dm * * [ ] STR volume fo maximum selectivity V 0 * 0 * * 0 * * 78.8s mol/dm s s dm /mol 0 0d.0 dm * 0. /s mol/dm mol/dm s
21 Maximizing S /XY fo the Tambouze Reaction Maximum the selectivity w..t. tempeatue S /XY ase : ase : E E X E E Y E E * * E E E exp RT high tempeatue (w/o side xn) low tempeatue (with insued convesion) E E Fo the activation enegies given above E 5,000 So the selectivity fo this combination of activation enegies is independent of tempeatue!
22 Maximizing S /XY fo the Tambouze Reaction What is the convesion of in the STR? X * 0-0 * If geate than 7% convesion of is equied, then the STR opeated with a eacto concentation of 0. mol/dm should be followed by a PFR because the concentation and selectivity will decease continuously fom * as we move down the PFR to an exit concentation f. Hence the system STR * PFR Would be the highest selectivity while foming moe the desied poduct, beyond what was fomed at * in a STR. How can we incease the convesion and still have a high selectivity S /(X+Y)? f *
23 Maximizing S /XY fo the Tambouze Reaction Optimum STR followed by a PFR. The exit concentation of X, Y, and can be found fom the STR mole balances Species X: Species : Species Y: V V V υ υ 0 X 0 X / X τ 0.000)(78) 0.078mol X υ0 υ υ υ 0 * τ * ( dm ( 0.005)(0.)(78) 0.mol / dm 0 Y 0 Y * / Y τ 0.008)(0.) (78) mol * Y ( dm F X 0 X mol / s, F mol / s, F 0 Y 0 Y mol / s Let s chec to mae sue the sum of all the species in solution equals the initial concentation 0 = X + + Y = =0.4 //// QE
24 Maximizing S /XY fo the Tambouze Reaction The eason we want to use a PFR afte we each the maximum selectivity, S /XY,is that the PFR will continue to gadually educe. Thus, moe will be fomed than if anothe STR wee to follow. If 90% convesion wee equied, then the exit concentation would be f =(-0.9)(0.4 mol/dm )=0.04 mol/dm. The PFR mole balances fo this liquid-phase eaction (v=v 0 )ae d d d X d, X, dv d d d, d Y d 0 Y ombining mole balances with thei espective ate laws yields d d d X d d d d Y d ( at 0, then ( at 0, then ( at 0, then ( at 0, then X Y mol / dm mol / dm mol / dm ) ) mol / dm ) ) =0, 0 the enteing concentations to the PFR ae the exit concentations fom STR.
25 Maximizing S /XY fo the Tambouze Reaction The convesion can be calculated X 0 0 We will use Polymath to plot the exit concentations as a function of and then detemine the volume (V=v 0 ) fo 90% convesion ( =0.04 mol/dm ) and then find X,, and Y at this volume. This volume tuns out to be appoximately 600 dm. ttheexitofthepfr, =0.07, X =0., =0.6, and Y =0.09 all in mol/dm. One now has to mae a decision as to whethe adding the PFR to incease the convesion of fom 0.7 to 0.9 and the mola flow ate of fom 0.6 to 0. mol/s is woth not only the added cost of the PFR, but also the decease in selectivity. This eaction was caied out isothemally; nonisothemal multiple eactions will be discussed in hapte 8.
26 PFR concentation & selectivity pofiles fo the Tambouze Reaction
27 PFR concentation & selectivity pofiles fo the Tambouze Reaction
28 PFR concentation & selectivity pofiles fo the Tambouze Reaction
29 PFR concentation & selectivity pofiles fo the Tambouze Reaction
30 PFR concentation & selectivity pofiles fo the Tambouze Reaction
31 6.. Reacto Selection and Opeating onditions (esied Poduct) Two simultaneous eactions with two eactants + (nwanted Poduct) The ate laws ae S / Rate selectivity paamete Rate selectivity paamete (= Instantaneous selectivity) is to maximized by choosing eacto schemes.
32 Reacto Selection iteia Selectivity Yield Tempeatue contol Safety ost
33 Figue 6- iffeent eactos and schemes fo maximizing the desied poduct (a) STR (b) tubula eacto (c ) batch (d) semi-batch (e) semi-batch (f) Tubula eacto with side steams (g) Tubula eacto with side steams (h) Seies of small STRs
34 Figue 6- iffeent eactos and schemes fo maximizing the desied poduct The two eactos with ecycle shown in (i) and (j) can be used fo highly exothemic eactions. Hee ecycle steam is cooled and etuned to the eacto to dilute and cool the inlet steam theeby avoiding hot spots and un-away eactions. The PFR with ecycle is used fo gas-phase eactions, and the STR is used fo liquid-phase eactions. (i) Tubula eacto with ecycle (j) STR with ecycle
35 Figue 6- iffeent eactos and schemes fo maximizing the desied poduct The last two eactos, () and (l), ae used fo themodynamically limited eactions whee the equilibium lies fa to the left (eactant side) + + nd one of the poducts must be emoved (e,g., ) fo the eaction to continue to completion. The membane eacto () is used fo themodynamically limited gas-phase eactions, while eactive distillation (l) is used fo liquid-phase eaction when one of the poducts has a high volatility (e.g., ) than the othe species in the eacto. + () Membane eacto (l) Reactive distillation
36 Example 6-: Minimizing unwanted poducts fo two eactants Fo the paallel eactions, conside all possible combinations of eaction odes and select the eaction scheme that will maximize S /. + (esied Poduct) (ndesied Poduct) ase I : >, >, a = - > 0, b = - > 0 the ate selectivity paamete S a b To maximize the S, maintain the concentation of both and as high as possible a tubula eacto (Figue 6. (b)) a batch eacto (Figue 6. (c)) high pessues (if gas phase), and educe inets
37 Example 6-: Minimizing unwanted poducts fo two eactants fo the paallel eactions + (esied Poduct) ) (ndesied Poduct) ase II : >, <, a = - > 0, b = - > 0 the ate selectivity it paamete a S b To maximize the S, maintain high and low. a semibatch eacto in which is fed slowly into. (Figue 6.(d)) a tubula eacto with side steam of continually (Figue 6.(f)) a seies of small STRs with fed only to the fist eacto and small fed to each eacto. (Figue 6.(h))
38 Example 6-: Minimizing unwanted poducts fo two eactants fo the paallel eaction + (esied Poduct) (ndesied Poduct) ase III : <, <, a = - > 0, b = - > 0 the ate selectivity paamete S a b To maximize the S, maintain the concentation of both and as low as possible astr(figue6(a)) 6.(a)) a tubula eacto in which thee is a lage ecycle atio (Figue 6.(i)) a feed diluted with inet mateial low pessues (if gas phase)
39 Example 6-: Minimizing unwanted poducts fo two eactants fo the paallel eaction + (esied Poduct) ) (ndesied Poduct) ase IV : <, >, a = - > 0, b = - > 0 the ate selectivity it paamete b S a To maximize the S, maintain the concentation of both and as high as possible a semibatch eacto in which is slowly fed to a lage amount of (Figue 6.(e)) a membane eacto o tubula eacto with side steam of (Figue 6.(g)) a seies of small STRs with fesh fed to each eacto (Figue 6.(h))
40 6. Maximizing the desied poduct in seies eaction In paallel xns, maximize the desied poduct by adjusting the eaction conditions (e.g., ) by choosing the pope eacto In seies xns, maximize the desied poduct by adjusting the space-time fo a flow eacto by choosing eal-time fo a batch eacto
41 Maximizing the desied poduct in seies eaction esied Poduct If the fist eaction is slow and second eaction is fast, it will be extemely difficult to poduce species. If the fist eaction (fomation of ) is fast and the eaction to fom is slow, a lage yield of can be achieved. Howeve, if the eaction is allowed to poceed fo a long time in a batch eacto o if the tubula flow eacto is too long, the desied poduct will be conveted to. In no othe type eaction is exactness in the calculation of the time needed to cay out the eaction moe impotant than in seies eactions.
42 Example 6-4: Maximizing the yield of the intemediate poduct The oxidation of ethanol to fom acetaldehyde is caied out on a catalyst of 4 wt% u-wt% on l O. nfotunately, acetaldehyde is also oxidized on this catalyst to fom cabon dioxide. The eaction is caied out in a dilute concentations (ca. 0.% ethanol, % O, and 98.9% N ). onsequently, the volume change with the eaction can be neglected. etemine the concentation of acetaldehyde as a function of space time. H H OH(g) H HO O ethanol O H O acetaldehyde 5 O H O The xns ae ievesible and fist-ode in ethanol and acetaldehyde, espectively.
43 Solution
44 0 e τ
45 e τ e 0 τ
46
47
48 Reaction paths fo diffeent s in seies eaction Fo / >, a Lage quantity of an be obtained Fo / <, a Little quantity of an be obtained ' ' ' ~ st xn is slow nd xn is fast Long xn time in batch o long tubula eacto will be conveted to
If there are multiple rxns, use concentrations not conversions. These might occur in combination or by themselves.
hapte 6 MLTIPLE RETIONS If thee ae multiple xns, use concentations not convesions. intemediate. Seies Reactions onsecutive xns. Paallel Reactions. omplex Reactions: Seies and Paallel 4. Independent None
More informationCSTR - PFR - PBR
1. Mole Balances o The Rate of Reaction, - o The Geneal Mole Balance Equation o Continuous low Reactos - CSTR (Continuous-Stied Tank Reacto) - PR (Tubula Reacto) - PBR (Packed-Bed Reacto) o Industial Reactos
More informationChapter 2: Conversion and Reactor Sizing
CHEMICL RECTIO EGIEERIG (SK3223) Chapte 2: Convesion and Reacto Sizing W ORHRYTI W SLLEH hayati@petoleum.utm.my RIZI MD. KSMI afiziana@petoleum.utm.my Convesion, To quantify how fa a eaction has pogessed
More informationChapter 1: Mole Balances
CHEMICL RECTION ENGINEERING (SK3223) Chapte : Mole Balances WN NORHRYTI WN SLLEH hayati@petoleum.utm.my RIZIN MD. KSMNI afiziana@petoleum.utm.my Rate of Reaction The eaction ate is the ate at which a species
More informationEntropy and Free Energy: Predicting the direction of spontaneous change The approach to Chemical equilibrium
Lectue 8-9 Entopy and Fee Enegy: Pedicting the diection of spontaneous change The appoach to Chemical equilibium Absolute entopy and the thid law of themodynamics To define the entopy of a compound in
More informationChemical Reaction Engineering
Lectue 3 hemical Reaction Engineeing (RE) is the field that studies the ates and mechanisms of chemical eactions and the design of the eactos in which they take place. Web Lectue 3 lass Lectue 9-Thusday
More informationChemical Reaction Engineering
Lectue hemical Reaction Engineeing (RE) is the field that studies the ates and mechanisms of chemical eactions and the design of the eactos in which they take place. Web Lectue lass Lectue 8-husday Multiple
More informationSynthesis of Epichlorohydrin from Glycerol. Hydrochlorination of Glycerol
Synthesis of Epichloohydin fom yceol. Hydochloination of yceol Geogy Dmitiev S.*, Leonid Zanaveskin N. Fedeation State Unitay Oganization "Kapov Institute of Physical hemisty" Russia, Moscow, Minusinskaya
More informationLecture 2 - Thermodynamics Overview
2.625 - Electochemical Systems Fall 2013 Lectue 2 - Themodynamics Oveview D.Yang Shao-Hon Reading: Chapte 1 & 2 of Newman, Chapte 1 & 2 of Bad & Faulkne, Chaptes 9 & 10 of Physical Chemisty I. Lectue Topics:
More informationDownloaded from
Chapte Notes Subject: Chemisty Class: XI Chapte: Themodynamics Top concepts 1. The banch of science which deals with study of diffeent foms of enegy and thei inteconvesion is called themodynamics. 2. A
More informationSupporting information
Electonic Supplementay Mateial (ESI) fo Physical Chemisty Chemical Physics. This jounal is the Owne Societies 18 Suppoting infomation Nonstoichiometic oxides as a continuous homologous seies: linea fee-enegy
More informationStudy of C5/C6 isomerization on Pt/H-zeolite catalyst in industrial conditions
Ovidius Univesity Annals of Chemisty Volume, Numbe, pp. -6, Study of / isomeization on Pt/H-zeolite catalyst in industial conditions Claudia Iina KONCSAG*, Ioan Alexandu TUTUN and Cistian SAFTA Ovidius
More informationVisit us on the Web : Copyright 2011 Pearson Education,Inc.
The authos and the publishe have taken cae in the pepaation of this book but make no expessed o implied waanty of any kind and assume no esponsibility fo eos o omissions. No liability is assumed fo the
More informationNumerical solution of diffusion mass transfer model in adsorption systems. Prof. Nina Paula Gonçalves Salau, D.Sc.
Numeical solution of diffusion mass tansfe model in adsoption systems Pof., D.Sc. Agenda Mass Tansfe Mechanisms Diffusion Mass Tansfe Models Solving Diffusion Mass Tansfe Models Paamete Estimation 2 Mass
More informationChem 453/544 Fall /08/03. Exam #1 Solutions
Chem 453/544 Fall 3 /8/3 Exam # Solutions. ( points) Use the genealized compessibility diagam povided on the last page to estimate ove what ange of pessues A at oom tempeatue confoms to the ideal gas law
More informationPulse Neutron Neutron (PNN) tool logging for porosity Some theoretical aspects
Pulse Neuton Neuton (PNN) tool logging fo poosity Some theoetical aspects Intoduction Pehaps the most citicism of Pulse Neuton Neuon (PNN) logging methods has been chage that PNN is to sensitive to the
More information9.2 Reaction rate and rate equation
9.2.1 Expession of eaction ate The ate () of a chemical eaction is defined as the concentation change of a eactant o a poduct pe unit time. mean ate [A] c c = t t t 2 1 2 1 c c 1 instantaneous ate: Physical
More informationChemical Reaction Engineering. Multiple Reactions. Dr.-Eng. Zayed Al-Hamamre
Chemical Reaction Engineering Multiple Reactions Dr.-Eng. Zayed Al-Hamamre 1 Content Types of Reactions Selectivity Reaction Yield Parallel Reactions Series Reactions Net Rates of Reaction Complex Reactions
More informationac p Answers to questions for The New Introduction to Geographical Economics, 2 nd edition Chapter 3 The core model of geographical economics
Answes to questions fo The New ntoduction to Geogaphical Economics, nd edition Chapte 3 The coe model of geogaphical economics Question 3. Fom intoductoy mico-economics we know that the condition fo pofit
More informationSingle Particle State AB AB
LECTURE 3 Maxwell Boltzmann, Femi, and Bose Statistics Suppose we have a gas of N identical point paticles in a box of volume V. When we say gas, we mean that the paticles ae not inteacting with one anothe.
More informationMacromolecular Chemistry
Macomolecula Chemisty R R O H 2 C CH + CO CH 2 CH C Lectue 13 Fee Radical Co-polymeization Fee Radical Copolymeization ~ ~ ~ ~ ~ ~ ~ ~ Assume chain end concentations ae constant at steady state If If 1
More informationMECHANICAL PULPING REFINER MECHANICAL PULPS
MECHANICAL PULPING REFINER MECHANICAL PULPS Histoy of efine mechanical pulping Fo many yeas all mechanical pulp was made fom stone goundwood (SGW). This equied whole logs. Stating in the 950s, but eally
More informationDesign of a Fuel Processor System for
ChE class and home poblems The object of this column is to enhance ou eades collections of stimulating poblems in chemical engineeing education. Ideal poblems, which may be open-ended, ae those that motivate
More informationx 1 b 1 Consider the midpoint x 0 = 1 2
1 chapte 2 : oot-finding def : Given a function f(), a oot is a numbe satisfying f() = 0. e : f() = 2 3 = ± 3 question : How can we find the oots of a geneal function f()? 2.1 bisection method idea : Find
More informationChemical Reaction Engineering
Lectue 25 hemical Reaction Enineein (RE) is the field that studies the ates and mechanisms of chemical eactions and the desin of the eactos in which they take place. Web Lectue 25 lass Lectue 21 4/2/2013
More information4. Some Applications of first order linear differential
August 30, 2011 4-1 4. Some Applications of fist ode linea diffeential Equations The modeling poblem Thee ae seveal steps equied fo modeling scientific phenomena 1. Data collection (expeimentation) Given
More informationChapter 2: Basic Physics and Math Supplements
Chapte 2: Basic Physics and Math Supplements Decembe 1, 215 1 Supplement 2.1: Centipetal Acceleation This supplement expands on a topic addessed on page 19 of the textbook. Ou task hee is to calculate
More informationBifurcation Analysis for the Delay Logistic Equation with Two Delays
IOSR Jounal of Mathematics (IOSR-JM) e-issn: 78-578, p-issn: 39-765X. Volume, Issue 5 Ve. IV (Sep. - Oct. 05), PP 53-58 www.iosjounals.og Bifucation Analysis fo the Delay Logistic Equation with Two Delays
More informationExample
Chapte.4 iffusion with Chemical eaction Example.4- ------------------------------------------------------------------------------ fluiize coal eacto opeates at 45 K an atm. The pocess will be limite by
More information2.25 Advanced Fluid Mechanics
MIT Depatment of Mechanical Engineeing 2.25 Advanced Fluid Mechanics Poblem 4.27 This poblem is fom Advanced Fluid Mechanics Poblems by A.H. Shapio and A.A. Sonin u(,t) pg Gas Liquid, density Conside a
More informationA Comment on Increasing Returns and Spatial. Unemployment Disparities
The Society fo conomic Studies The nivesity of Kitakyushu Woking Pape Seies No.06-5 (accepted in Mach, 07) A Comment on Inceasing Retuns and Spatial nemployment Dispaities Jumpei Tanaka ** The nivesity
More informationC/CS/Phys C191 Shor s order (period) finding algorithm and factoring 11/12/14 Fall 2014 Lecture 22
C/CS/Phys C9 Sho s ode (peiod) finding algoithm and factoing /2/4 Fall 204 Lectue 22 With a fast algoithm fo the uantum Fouie Tansfom in hand, it is clea that many useful applications should be possible.
More informationABSTRACT SIMULATION OF DYNAMIC PRESSURE- Professor Timothy A. Barbari Department of Chemical Engineering
ABSTRACT Title: SIMULATION OF DYNAMIC PRESSURE- SWING GAS SORPTION IN POLYMERS Heathe Jane St. Piee, Maste of Science, 2005 Diected By: Pofesso Timothy A. Babai Depatment of Chemical Engineeing A tanspot
More informationCASCADE OPTIMIZATION AND CONTROL OF BATCH REACTORS
CASCADE OPIMIZAION AND CONROL OF BACH REACORS Xiangming Hua, Sohab Rohani and Athu Jutan* Depatment of Chemical and Biochemical Engineeing Univesity of Westen Ontaio, London, Canada N6A B9 * ajutan@uwo.ca
More information763620SS STATISTICAL PHYSICS Solutions 2 Autumn 2012
763620SS STATISTICAL PHYSICS Solutions 2 Autumn 2012 1. Continuous Random Walk Conside a continuous one-dimensional andom walk. Let w(s i ds i be the pobability that the length of the i th displacement
More informationThe Millikan Experiment: Determining the Elementary Charge
LAB EXERCISE 7.5.1 7.5 The Elementay Chage (p. 374) Can you think of a method that could be used to suggest that an elementay chage exists? Figue 1 Robet Millikan (1868 1953) m + q V b The Millikan Expeiment:
More informationSubstances that are liquids or solids under ordinary conditions may also exist as gases. These are often referred to as vapors.
Chapte 0. Gases Chaacteistics of Gases All substances have thee phases: solid, liquid, and gas. Substances that ae liquids o solids unde odinay conditions may also exist as gases. These ae often efeed
More informationChemical Reaction Engineering
Lectue 5 hemical Reaction ngineeing (R) is the field that studies the ates and mechanisms of chemical eactions and the design of the eactos in which they tae place. Lectue 5 Tuesday //0 nzymatic Reactions
More informationThe condition for maximum intensity by the transmitted light in a plane parallel air film is. For an air film, μ = 1. (2-1)
hapte Two Faby--Peot ntefeomete A Faby-Peot intefeomete consists of two plane paallel glass plates A and B, sepaated by a distance d. The inne sufaces of these plates ae optically plane and thinly silveed
More informationCBE Transport Phenomena I Final Exam. December 19, 2013
CBE 30355 Tanspot Phenomena I Final Exam Decembe 9, 203 Closed Books and Notes Poblem. (20 points) Scaling analysis of bounday laye flows. A popula method fo measuing instantaneous wall shea stesses in
More informationChemical Engineering 412
Chemical Engineeing 41 Intoductoy Nuclea Engineeing Lectue 16 Nuclea eacto Theoy III Neuton Tanspot 1 One-goup eacto Equation Mono-enegetic neutons (Neuton Balance) DD φφ aa φφ + ss 1 vv vv is neuton speed
More informationPartition Functions. Chris Clark July 18, 2006
Patition Functions Chis Clak July 18, 2006 1 Intoduction Patition functions ae useful because it is easy to deive expectation values of paametes of the system fom them. Below is a list of the mao examples.
More informationRelated Rates - the Basics
Related Rates - the Basics In this section we exploe the way we can use deivatives to find the velocity at which things ae changing ove time. Up to now we have been finding the deivative to compae the
More informationTHERMODYNAMICS OF SURFACES AND INTERFACES
THERMODYNAMIC OF URFACE AND INTERFACE 1. Intoduction Eveything has to end somewhee. Fo solids, o liquids that "somewhee" is a suface, o an inteface between phases. Fo liquids, the inteface is between the
More informationModeling of the fermentation in an internal loop airlift reactor
17 th Euopean Symposium on Compute Aided Pocess Engineeing ESCAPE17 V. Plesu and P.S. Agachi (Editos) 7 Elsevie B.V. All ights eseved. 1 Modeling of the fementation in an intenal loop ailift eacto Ivan
More informationThe Catalytic Hydrogenation of Aromatic Nitro Ketone in a Microreactor: Reactor Performance and Kinetic Studies
TERATOAL JOURAL OF EMAL REATOR EGEERG Volume 6 008 Aticle A The atalytic ydogenation of Aomatic ito etone in a Micoeacto: Reacto Pefomance and inetic Studies Sunitha Tadepalli Adeniyi Lawal Stevens nstitute
More information. Using our polar coordinate conversions, we could write a
504 Chapte 8 Section 8.4.5 Dot Poduct Now that we can add, sutact, and scale vectos, you might e wondeing whethe we can multiply vectos. It tuns out thee ae two diffeent ways to multiply vectos, one which
More informationSolution to Problem First, the firm minimizes the cost of the inputs: min wl + rk + sf
Econ 0A Poblem Set 4 Solutions ue in class on Tu 4 Novembe. No late Poblem Sets accepted, so! This Poblem set tests the knoledge that ou accumulated mainl in lectues 5 to 9. Some of the mateial ill onl
More informationyou of a spring. The potential energy for a spring is given by the parabola U( x)
Small oscillations The theoy of small oscillations is an extemely impotant topic in mechanics. Conside a system that has a potential enegy diagam as below: U B C A x Thee ae thee points of stable equilibium,
More informationRevision of Lecture Eight
Revision of Lectue Eight Baseband equivalent system and equiements of optimal tansmit and eceive filteing: (1) achieve zeo ISI, and () maximise the eceive SNR Thee detection schemes: Theshold detection
More informationDetermining solar characteristics using planetary data
Detemining sola chaacteistics using planetay data Intoduction The Sun is a G-type main sequence sta at the cente of the Sola System aound which the planets, including ou Eath, obit. In this investigation
More information6. Multiple Reactions
6. Multiple Reactions o Selectivity and Yield o Reactions in Series - To give maximum selectivity o Algorithm for Multiple Reactions o Applications of Algorithm o Multiple Reactions-Gas Phase 0. Types
More informationOne-Dimensional, Steady-State. State Conduction with Thermal Energy Generation
One-Dimensional, Steady-State State Conduction with Themal Enegy Geneation Implications of Enegy Geneation Involves a local (volumetic) souce of themal enegy due to convesion fom anothe fom of enegy in
More informationAnalysis of high speed machining center spindle dynamic unit structure performance Yuan guowei
Intenational Confeence on Intelligent Systems Reseach and Mechatonics Engineeing (ISRME 0) Analysis of high speed machining cente spindle dynamic unit stuctue pefomance Yuan guowei Liaoning jidian polytechnic,dan
More informationChemistry Exam I 28 February 2018
Chemisty - Exam I 8 Feuay 018 Name Show all wok o cedit. State any assumptions made to solve a polem. State all answes with the coect nume o signiicant igues. All answes in scientiic notation must e in
More informationEM Boundary Value Problems
EM Bounday Value Poblems 10/ 9 11/ By Ilekta chistidi & Lee, Seung-Hyun A. Geneal Desciption : Maxwell Equations & Loentz Foce We want to find the equations of motion of chaged paticles. The way to do
More informationChapter 2 ONE DIMENSIONAL STEADY STATE CONDUCTION. Chapter 2 Chee 318 1
hapte ONE DIMENSIONAL SEADY SAE ONDUION hapte hee 38 HEA ONDUION HOUGH OMPOSIE EANGULA WALLS empeatue pofile A B X X 3 X 3 4 X 4 Χ A Χ B Χ hapte hee 38 hemal conductivity Fouie s law ( is constant) A A
More informationASTR415: Problem Set #6
ASTR45: Poblem Set #6 Cuan D. Muhlbege Univesity of Mayland (Dated: May 7, 27) Using existing implementations of the leapfog and Runge-Kutta methods fo solving coupled odinay diffeential equations, seveal
More informationLiquid gas interface under hydrostatic pressure
Advances in Fluid Mechanics IX 5 Liquid gas inteface unde hydostatic pessue A. Gajewski Bialystok Univesity of Technology, Faculty of Civil Engineeing and Envionmental Engineeing, Depatment of Heat Engineeing,
More informationMEASURING CHINESE RISK AVERSION
MEASURING CHINESE RISK AVERSION --Based on Insuance Data Li Diao (Cental Univesity of Finance and Economics) Hua Chen (Cental Univesity of Finance and Economics) Jingzhen Liu (Cental Univesity of Finance
More information6 PROBABILITY GENERATING FUNCTIONS
6 PROBABILITY GENERATING FUNCTIONS Cetain deivations pesented in this couse have been somewhat heavy on algeba. Fo example, detemining the expectation of the Binomial distibution (page 5.1 tuned out to
More informationDo not turn over until you are told to do so by the Invigilator.
UNIVERSITY OF EAST ANGLIA School of Mathematics Main Seies UG Examination 2015 16 FLUID DYNAMICS WITH ADVANCED TOPICS MTH-MD59 Time allowed: 3 Hous Attempt QUESTIONS 1 and 2, and THREE othe questions.
More informationChapter 13 Gravitation
Chapte 13 Gavitation In this chapte we will exploe the following topics: -Newton s law of gavitation, which descibes the attactive foce between two point masses and its application to extended objects
More informationLECTURER: PM DR MAZLAN ABDUL WAHID PM Dr Mazlan Abdul Wahid
M 445 LU: M D MZL BDUL WID http://www.fkm.utm.my/~mazlan hapte teady-tate tate One Dimensional eat onduction M bdul Wahid UM aculty of Mechanical ngineeing Univesiti eknologi Malaysia www.fkm.utm.my/~mazlan
More informationPHYSICS 151 Notes for Online Lecture #20
PHYSICS 151 Notes fo Online Lectue #20 Toque: The whole eason that we want to woy about centes of mass is that we ae limited to looking at point masses unless we know how to deal with otations. Let s evisit
More informationA scaling-up methodology for co-rotating twin-screw extruders
A scaling-up methodology fo co-otating twin-scew extudes A. Gaspa-Cunha, J. A. Covas Institute fo Polymes and Composites/I3N, Univesity of Minho, Guimaães 4800-058, Potugal Abstact. Scaling-up of co-otating
More informationVoltage ( = Electric Potential )
V-1 of 10 Voltage ( = lectic Potential ) An electic chage altes the space aound it. Thoughout the space aound evey chage is a vecto thing called the electic field. Also filling the space aound evey chage
More informationThe Combined Effect of Chemical reaction, Radiation, MHD on Mixed Convection Heat and Mass Transfer Along a Vertical Moving Surface
Available at http://pvamu.edu/aam Appl. Appl. Math. ISSN: 93-966 Vol. 5, Issue (Decembe ), pp. 53 53 (Peviously, Vol. 5, Issue, pp. 63 6) Applications and Applied Mathematics: An Intenational Jounal (AAM)
More informationThe Substring Search Problem
The Substing Seach Poblem One algoithm which is used in a vaiety of applications is the family of substing seach algoithms. These algoithms allow a use to detemine if, given two chaacte stings, one is
More informationElectromagnetism Physics 15b
lectomagnetism Physics 15b Lectue #20 Dielectics lectic Dipoles Pucell 10.1 10.6 What We Did Last Time Plane wave solutions of Maxwell s equations = 0 sin(k ωt) B = B 0 sin(k ωt) ω = kc, 0 = B, 0 ˆk =
More informationThe geometric construction of Ewald sphere and Bragg condition:
The geometic constuction of Ewald sphee and Bagg condition: The constuction of Ewald sphee must be done such that the Bagg condition is satisfied. This can be done as follows: i) Daw a wave vecto k in
More informationComputational Methods of Solid Mechanics. Project report
Computational Methods of Solid Mechanics Poject epot Due on Dec. 6, 25 Pof. Allan F. Bowe Weilin Deng Simulation of adhesive contact with molecula potential Poject desciption In the poject, we will investigate
More informationWhat molecular weight polymer is necessary to provide steric stabilization? = [1]
1/7 What molecula weight polyme is necessay to povide steic stabilization? The fist step is to estimate the thickness of adsobed polyme laye necessay fo steic stabilization. An appoximation is: 1 t A d
More information5.4 Second Law of Thermodynamics Irreversible Flow 5
5.4 Second Law of hemodynamics Ievesile Flow 5 5.4 Second Law of hemodynamics Ievesile Flow he second law of themodynamics fomalizes the notion of loss. he second law of themodynamics affods us with a
More informationSTUDY ON 2-D SHOCK WAVE PRESSURE MODEL IN MICRO SCALE LASER SHOCK PEENING
Study Rev. Adv. on -D Mate. shock Sci. wave 33 (13) pessue 111-118 model in mico scale lase shock peening 111 STUDY ON -D SHOCK WAVE PRESSURE MODEL IN MICRO SCALE LASER SHOCK PEENING Y.J. Fan 1, J.Z. Zhou,
More informationRight-handed screw dislocation in an isotropic solid
Dislocation Mechanics Elastic Popeties of Isolated Dislocations Ou study of dislocations to this point has focused on thei geomety and thei ole in accommodating plastic defomation though thei motion. We
More informationCOLD STRANGLING HOLLOW PARTS FORCES CALCULATION OF CONICAL AND CONICAL WITH CYLINDRICAL COLLAR
COLD STANGLING HOLLOW PATS OCES CALCULATION O CONICAL AND CONICAL WITH CYLINDICAL COLLA Lucian V. Sevein, Taian Lucian Sevein,, Stefan cel Mae Univesity of Suceava, aculty of Mechanical Engineeing, Mechatonics
More informationNumerical Integration
MCEN 473/573 Chapte 0 Numeical Integation Fall, 2006 Textbook, 0.4 and 0.5 Isopaametic Fomula Numeical Integation [] e [ ] T k = h B [ D][ B] e B Jdsdt In pactice, the element stiffness is calculated numeically.
More information4/18/2005. Statistical Learning Theory
Statistical Leaning Theoy Statistical Leaning Theoy A model of supevised leaning consists of: a Envionment - Supplying a vecto x with a fixed but unknown pdf F x (x b Teache. It povides a desied esponse
More informationQUALITATIVE AND QUANTITATIVE ANALYSIS OF MUSCLE POWER
QUALITATIVE AND QUANTITATIVE ANALYSIS OF MUSCLE POWER Jey N. Baham Anand B. Shetty Mechanical Kinesiology Laboatoy Depatment of Kinesiology Univesity of Nothen Coloado Geeley, Coloado Muscle powe is one
More informationPulse Neutron Neutron (PNN) tool logging for porosity
Pulse Neuton Neuton (PNN) tool logging fo poosity Some theoetical aspects Hotwell Handelsges.m.b.H Oedenbuge Stasse 6 7013 Klingenbach, AUSTRIA Tel.: +43 (0) 687-48058 Fax: +43 (0) 687 48059 office@hotwell.at
More informationEXAM NMR (8N090) November , am
EXA NR (8N9) Novembe 5 9, 9. 1. am Remaks: 1. The exam consists of 8 questions, each with 3 pats.. Each question yields the same amount of points. 3. You ae allowed to use the fomula sheet which has been
More informationLight Time Delay and Apparent Position
Light Time Delay and ppaent Position nalytical Gaphics, Inc. www.agi.com info@agi.com 610.981.8000 800.220.4785 Contents Intoduction... 3 Computing Light Time Delay... 3 Tansmission fom to... 4 Reception
More informationGauss Law. Physics 231 Lecture 2-1
Gauss Law Physics 31 Lectue -1 lectic Field Lines The numbe of field lines, also known as lines of foce, ae elated to stength of the electic field Moe appopiately it is the numbe of field lines cossing
More informationPROBLEM SET #1 SOLUTIONS by Robert A. DiStasio Jr.
POBLM S # SOLUIONS by obet A. DiStasio J. Q. he Bon-Oppenheime appoximation is the standad way of appoximating the gound state of a molecula system. Wite down the conditions that detemine the tonic and
More informationBlack Body Radiation and Radiometric Parameters:
Black Body Radiation and Radiometic Paametes: All mateials absob and emit adiation to some extent. A blackbody is an idealization of how mateials emit and absob adiation. It can be used as a efeence fo
More informationCurrent, Resistance and
Cuent, Resistance and Electomotive Foce Chapte 25 Octobe 2, 2012 Octobe 2, 2012 Physics 208 1 Leaning Goals The meaning of electic cuent, and how chages move in a conducto. What is meant by esistivity
More information, the tangent line is an approximation of the curve (and easier to deal with than the curve).
114 Tangent Planes and Linea Appoimations Back in-dimensions, what was the equation of the tangent line of f ( ) at point (, ) f ( )? (, ) ( )( ) = f Linea Appoimation (Tangent Line Appoimation) of f at
More informationAn Application of Fuzzy Linear System of Equations in Economic Sciences
Austalian Jounal of Basic and Applied Sciences, 5(7): 7-14, 2011 ISSN 1991-8178 An Application of Fuzzy Linea System of Equations in Economic Sciences 1 S.H. Nassei, 2 M. Abdi and 3 B. Khabii 1 Depatment
More informationChapter 5 Linear Equations: Basic Theory and Practice
Chapte 5 inea Equations: Basic Theoy and actice In this chapte and the next, we ae inteested in the linea algebaic equation AX = b, (5-1) whee A is an m n matix, X is an n 1 vecto to be solved fo, and
More informationF-IF Logistic Growth Model, Abstract Version
F-IF Logistic Gowth Model, Abstact Vesion Alignments to Content Standads: F-IFB4 Task An impotant example of a model often used in biology o ecology to model population gowth is called the logistic gowth
More informationTo Feel a Force Chapter 7 Static equilibrium - torque and friction
To eel a oce Chapte 7 Chapte 7: Static fiction, toque and static equilibium A. Review of foce vectos Between the eath and a small mass, gavitational foces of equal magnitude and opposite diection act on
More informationEffect of no-flow boundaries on interference testing. in fractured reservoirs
Effect of no-flo boundaies on intefeence testing in factued esevois T.Aa. Jelmet 1 1 epatement of petoleum engineeing and applied geophysics,, Noegian Univesity of Science and Tecnology, NTNU. Tondheim,
More informationCHAPTER 3. Section 1. Modeling Population Growth
CHAPTER 3 Section 1. Modeling Population Gowth 1.1. The equation of the Malthusian model is Pt) = Ce t. Apply the initial condition P) = 1. Then 1 = Ce,oC = 1. Next apply the condition P1) = 3. Then 3
More informationTest 2, ECON , Summer 2013
Test, ECON 6090-9, Summe 0 Instuctions: Answe all questions as completely as possible. If you cannot solve the poblem, explaining how you would solve the poblem may ean you some points. Point totals ae
More informationDo Managers Do Good With Other People s Money? Online Appendix
Do Manages Do Good With Othe People s Money? Online Appendix Ing-Haw Cheng Haison Hong Kelly Shue Abstact This is the Online Appendix fo Cheng, Hong and Shue 2013) containing details of the model. Datmouth
More informationGeneral Railgun Function
Geneal ailgun Function An electomagnetic ail gun uses a lage Loentz foce to fie a pojectile. The classic configuation uses two conducting ails with amatue that fits between and closes the cicuit between
More informationResearch Article EXPERIMENTAL STUDY OF HEAT TRANSFER CHARACTERISTICS OF STAINLESS STEEL FIBROUS FLOW INSULATOR
Tansactions of the TSME (16) Vol. 4, No. 2, 148 155 Jounal of seach and Applications in Mechanical Engineeing Copyight 16 by TSME ISSN 2229-2152 pint DOI: 1.14456/jame.16.15 seach Aticle EXPERIMENTAL STUDY
More informationMotithang Higher Secondary School Thimphu Thromde Mid Term Examination 2016 Subject: Mathematics Full Marks: 100
Motithang Highe Seconday School Thimphu Thomde Mid Tem Examination 016 Subject: Mathematics Full Maks: 100 Class: IX Witing Time: 3 Hous Read the following instuctions caefully In this pape, thee ae thee
More informationFW Laboratory Exercise. Survival Estimation from Banded/Tagged Animals. Year No. i Tagged
FW66 -- Laboatoy Execise uvival Estimation fom Banded/Tagged Animals Conside a geogaphically closed population of tout (Youngs and Robson 97). The adults ae tagged duing fall spawning, and subsequently
More information