Kinetic Modeling of Methanol to Olefins (MTO) Process on SAPO-34 Catalyst
|
|
- Bryan Brooks
- 7 years ago
- Views:
Transcription
1 Simultion nd Optimiztion Chin Petroleum Processing nd Petrochemicl Technology 203, Vol., No. 3, pp September 30, 203 Kinetic Modeling of Methnol to Olefins (MTO) Process on SAPO-34 Ctlyst Pu Jinglong; Weng Huixin (Est Chin University of Science nd Technology, Shnghi ) Abstrct: A kinetic model of MTO process over the SAPO-34 ctlyst considering the effect of ter nd coke deposition hs been proposed. The model tkes into ccount three steps of the MTO rection in hich the products cover lumped components. The ter in the feed not only reduces the concentrtion of methnol but lso llevites the dectivtion of SAPO-34 ctlyst. The kinetic prmeters hve been estimted by the lest squre method. It hs been proved tht the clculted vlues in the kinetic model re in good greement ith the experimentl vlues. Key ords: methnol to olefin process (MTO); kinetic modeling; SAPO-34; dectivtion Introduction The rpid development of the ntionl economy leds to rising demnd for ethylene nd propylene, hich re the bsic chemicl r mterils. The methnol to olefins (MTO) process provides ne route for the production of ethylene nd propylene. Compred ith the trditionl ethylene nd propylene production process (stem crcking of NGL or nphth), MTO hs some dvntges, becuse MTO cn provide ide nd flexible rnge of ethylene nd propylene rtios to meet the mrket needs []. The industril implementtion of MTO process t high methnol conversion hs been possible thnks to the high ctivity nd selectivity of the SAPO-34 ctlyst [2]. The kinetic model for MTO process hs been studied by mny reserchers becuse of the importnce of MTO process in the production of loer olefins. Considering the effect of coke on the MTO process, Bos, et l. proposed kinetic model consisting of 2 rections involving 6 component lumps plus coke [3]. The kinetic model grees ell ith the crbon pool mechnism proposed by Dhl nd Kolboe [4]. Gyubo, et l. simplified the model of Bos by eliminting the sloer steps nd studied the effect of ter in the rection in order tht the model could be esily used in the design of the rector for optimized production of loer olefins []. In this pper, the kinetic model for the MTO process is studied on SAPO-34 ctlyst in fixed bed rector, hich hs tken into considertion the effects of ctlyst dectivtion by ter nd coke deposition. The ne kinetic model, hich covers 3 steps for the formtion of olefins in the MTO process, hs lumped products. The rection rte equtions hve been introduced ccording to the proposed rection netork, nd the prmeters of the model re estimted by the lest squre method. 2 MTO Kinetic Modeling 2. MTO rection netork The rection of MTO process is composed of three steps, viz.: () dehydrtion of methnol to dimethyl ether (DME); (2) formtion of intermedite species, [CH 2 ]; nd (3) formtion of olefins nd other prffins [4]. The overll rection pth my be represented by: CH OH CH OCH [ CH ] olefins Since the source of the olefins is uncertin, the methnol nd DME re regrded s one lumped component clled oxygentes [6]. The products ethylene, propylene nd butene re lumped s C2, C3, nd C4, respectively. Since the mount of methne, CO, nd CO 2 in the products is smll, they re lumped s C. The ne proposed kinetic Recieved dte: ; Accepted dte: Corresponding Author: Prof. Weng Huixin, Telephone: ; E-mil: hxeng@ecust.edu.cn. 86
2 Pu Jinglong, et l. Kinetic Modeling of Methnol to Olefins (MTO) Process on SAPO-34 Ctlyst model for MTO process grees ell ith the Hydrocrbon Pool mechnism [4] hich is shon in igure. igure Rection netork for MTO process over SAPO-34 The kinetic scheme includes 6 first-order nd one secondorder rections. Rection 6 is the second order one, in hich the formtion rte of ethylene from propylene depends on the concentrtion of propylene nd methnol in the medium [3]. Upon considering both the ccurcy nd simplicity of the model, the secondry rection of butene is ignored becuse of the smll mount of butene compred ith propylene in the products. According to the kinetic scheme shon in igure, the rection rte equtions cn be obtined esily, hich re formulted s function of the mss frction (expressed on ter-free bsis, i ) of the corresponding rectnts. A d W = ( ki ) i= () d W = k (2) 2 d W = ( k2 A + k6 A 3) θ (3) 3 d W = ( k3 A k6 A 3 k7 3) θ (4) 4 d W = k4 () d W = ( k A + k7 3) θ (6) In the model, θ is function tht quntifies the effect of ter in the rection medium; is the ctivity of SAPO- 34 ctlyst; k i is the rection rte constnt of ech rection, hich follos the reltionship of Arrhenius eqution: k i = k e 0i Ei RT 2.2 Dectivtion of SAPO-34 ctlyst Coke deposition is extrordinrily rpid in the MTO process, becuse under more severe conditions coke deposition rte equting to 3 4% of the methnol mount in the feed is mesured in the first minute of time on strem []. The ctivity of the SAPO-34 ctlyst declines ith increse of the time on strem. Moreover, the ctivity of SAPO-34 ctlyst chnges ith the rection temperture, spce velocity, nd the degree of methnol dilution by ter in the feed. Consequently, the coke induced dectivtion of ctlyst cnnot be overlooked especilly ith respect to the fresh SAPO-34 ctlyst. The ctivity of SAPO-34 ctlyst is defined by the rtio beteen the rection rte of ctlyst t given time on strem, r, nd the rection rte tht the fresh ctlyst ould hve t tht time under the sme rection conditions, r f : r = r f (8) The dectivtion rte eqution cn be expressed by the folloing reltionship, hich indictes tht the dectivtion of SAPO-34 ctlyst complies ith the prllel dectivtion mechnism: d = dt d kd A θ d (9) In this eqution, k d is the dectivtion rte constnt hich follos the reltionship of Arrhenius eqution, nd θ d is function tht quntifies the ttenuting effect of ter in the rection medium on coke deposition of SAPO-34 ctlyst. 2.3 Effect of ter in the kinetic model The presence of ter in feed hs gret effect on the rection rte in the MTO process. Compred ith the methnol in the ter-free feed, the presence of ter decreses the rte of rection becuse of the dilution of the methnol concentrtion in feed. The effect of ter resistnce cn be quntified by the function θ: θ = + K (0) In the eqution, K is prmeter tht quntifies the ter resistnce for the rection rte, nd is the ter content in the rection medium hich is the eight frction (on (7) 87
3 Chin Petroleum Processing nd Petrochemicl Technology 203,(3):86-90 ter-free bsis) of ter in the rection medium. On the other hnd, the presence of ter in feed lso hs significnt effect of ttenuting coke induced dectivtion of ctlyst. This result cn be ttributed to the competition of ter ginst coke deposition on the cid sites of SAPO-34 ctlyst. Wter cn be dsorbed on the cid sites of SAPO-34 ctlyst prior to the coke deposition becuse ter is polr molecule [7]. The inhibition effect of ter on coke deposition llevites the dectivtion of the SAPO-34 ctlyst hich cn be quntified by the function θ [8] d : θ d n Kd = + () here K d is prmeter tht qulifies the ter resistnce ginst the coke deposition on SAPO-34 ctlyst. The ter content in the rection medium,, is sum of the ter in feed, 0, nd the ter formed, f. = 0 + f (2) The ter formed in the rection medium hs reltionship ith the oxygente content, A, hich cn be expressed by the folloing eqution [9] : 2 3 = (3) f A A A 3 Estimtion of Kinetic Prmeters 3. Experimentl dt on SAPO-34 The experimentl dt on the prmeter estimtion ere obtined from Qi [0], hose experiments ere conducted in fixed bed rector using the fresh SAPO-34 ctlyst. The temperture of the rection s 37, 400, 42, 40, nd 47, respectively, nd the spce velocity over the ctlyst vried from 3.84 h - to 3.9 h - (grms of methnol fed into the rector in n hour versus grms of ctlyst), hile the totl rection pressure s kept t tmospheric pressure. The rtio of ter nd methnol in feed s 0 nd in order to investigte the effect of ter on the rection. The time on stem of the process s equl to. minutes. 3.2 Estimtion procedure The procedure for estimting the kinetic model involves non-liner prmeter estimtion problems. The ordinry differentil equtions ere solved by the fourth-order method of Lung-Kutt, in hich the initil conditions ere: (W/) 0 =0, A0 =, nd i0 =0 (i=, 2, 3, 4, ). After the concentrtion of ech component t the outlet s clculted, the prmeters in the kinetic model ere estimted by the lest squre method in order to minimize the objective function, EO. nl nexp 2 i j i= j = ( i clc j ),, EO = (4) nlnex p here i,j is the experimentl vlue of eight frctions for i lump in the experimentl point j, nd i(clc),j is the clculted vlue, heres n l is the number of lumps, nd n exp is the number of experimentl points. 4 Results nd Discussion 4. Kinetic prmeters The prmeters of the kinetic model re estimted nd re presented in Tble, in hich the corresponding vlue of the objective function, EO, is Tble Prmeters of the kinetic model of MTO over SAPO-34 ctlys Kinetic constnts, h - k i0, h - E i, J/mol Prmeters of dectivtion nd functions of ttenution by ter k d=.0 k K =.0 k k k k k k d θ = + K The verge reltive errors nd the mximum reltive errors of clculted vlues re listed in Tble 2. Since the desired products in the MTO process minly cover ethylene nd propylene, the emphsis of the study is to predict the ethylene nd propylene yields. As shon in Tble 2, the mximum reltive error of ethylene yield is.83% nd its verge reltive error is 4.0%. The mximum reltive error of propylene yield is.8%, ith the verge reltive error reching 3.4%. The verge reltive errors of ll the lumped components re less thn 0%. Consequently, the clculted vlues of the kinetic model θ d = +. 88
4 Pu Jinglong, et l. Kinetic Modeling of Methnol to Olefins (MTO) Process on SAPO-34 Ctlyst re relible. Tble 2 Reltive errors of ech lumped component Lumped components C C2 C3 C4 C Averge reltive error, % Mximum reltive error, % Sttisticl test of the model The sttisticl tests of the kinetic model, including the decisive index, the ρ 2 tests nd the tests, re conducted. The significnt level, α in the test is %, hich evlutes the devition for the men regression. The results of the sttisticl tests confirm tht ρ 2 >0.9 nd >0 t, s shon in Tble 3. Consequently, the kinetic model nd the estimted prmeters re relible. Tble 3 Sttisticl test of the kinetic model ρ 2 t 0 t The clculted vlues of ech lumped component re compred ith the experimentl vlues s shon in igure 2. It cn be seen from igure 2 tht the dt points re lmost symmetriclly distributed on both sides of the digonl line. It is proved tht the clculted vlues re in good greement ith the experimentl vlues. igure 2 Comprison beteen clculted vlues nd experimentl vlues 89
5 Chin Petroleum Processing nd Petrochemicl Technology 203,(3):86-90 Conclusions In this study, ne kinetic model for MTO process in fixed bed rector s built by considering the effect of ter nd coke deposition. The effect of ter in the feed on the rection is relted ith dilution of methnol nd ttenution of the SAPO-34 ctlyst dectivtion. Since the increse of the coke deposition on fresh SAPO-34 ctlyst is rpid t the beginning of the rection, the dectivtion of the SAPO-34 ctlyst must be considered. The prmeters of the kinetic model re estimted by the lest squre method nd the clculted vlues re compred ith the experimentl vlues. The result hs verified tht the clculted vlues re in good greement ith the experimentl vlues, ith the verge reltive errors of ll lumped components being less thn 0%. So the kinetic model hs good cpbility to predict the performnce of the lumped components in fixed bed rector. Nomenclture ctivity of the SAPO-34 ctlyst d order of dectivtion k i rte constnt of the rection, h - k d rte constnt of dectivtion, h - A mss frction of methnol (ter-free bsis) i mss frction of component i (ter-free bsis) W eight of SAPO-34 ctlyst, g mss flo rte of methnol in the feed, g/h K prmeters tht quntifies the ter resistnce mss frction of ter in the rection medium (ter-free bsis) k 0i pre-exponentil fctor, h - E i ctivtion energy, J R molr gs constnt, J mol - K - t time on strem, min T thermodynmic temperture, K f mss frction of ter formed in the rection medium (ter-free bsis) 0 mss frction of ter in the feed (ter-free bsis) EO the objective function θ function of ttenution by ter responsible for the min rection θ d function of ttenution by ter responsible for the dectivtion References [] Njfbdi A T, temi S, Sohrbi M, et l. Kinetic modeling nd optimiztion of the operting condition of MTO process on SAPO-34 ctlyst[j]. Journl of Industril nd Engineering Chemistry, 202, 8 (): [2] roment G, Dehertog W J H, Mrchi A J. Zeolite ctlysis in the conversion of methnol into olefins[j]. Ctlysis, 992, 9 (): -64 [3] Bos A N R, Tromp P J J, Akse H N. Conversion of methnol to loer olefins kinetic modeling, rector simultion nd selection[j]. Ind Eng Chem Res, 99, 34(): [4] Dhl I M, Kolboe S. On the rection mechnism for propene formtion in the MTO rection over SAPO-34[J]. Ctl Lett, 993, 20: [] Gyubo A G, Aguyo A T, Sánchez del Cmpo A E, et l. Kinetic modeling of methnol trnsformtion into olefins on SAPO-34 ctlyst[j]. Ind Eng Chem Res, 2000, 39(2): [6] Chen D, Grønvold A, Moljord K, et l. Methnol conversion to light olefins over SAPO-34: rection netork nd dectivtion kinetics[j]. Ind Eng Chem Res, 2007, 46(2): [7] Wng Geng, Tng Yu, ue Zhenxin. Recent progress in methnol to olefins technology[j]. Lioning Chemicl Industry, 20, 40 (7): (in Chinese) [8] Gyubo A G, Aguyo A T, Alonso A, et l. Rection scheme nd kinetic modelling for the MTO process over SAPO- 8 ctlyst[j]. Ctlysis Tody, 200, 06: 2-7 [9] Sánchez del Cmpo A E. Kinetic modelling of the trnsformtion of methnol into light olefins on SAPO-34 ctlyst[d]. University of the Bsque Country, Bilbo, Spin, 997 [0] Qi Guozhen, ie Ziku, Chen Qingling. Kinetics of methnol to olefins over fresh SAPO-34 ctlyst[j]. Chemicl Rection Engineering nd Technology, 202, 28 (6): 06-2 (in Chinese) 90
The International Association for the Properties of Water and Steam. Release on the Ionization Constant of H 2 O
The Interntionl Assocition for the Properties of Wter nd Stem Lucerne, Sitzerlnd August 7 Relese on the Ioniztion Constnt of H O 7 The Interntionl Assocition for the Properties of Wter nd Stem Publiction
More informationRate and Activation Energy of the Iodination of Acetone
nd Activtion Energ of the Iodintion of Acetone rl N. eer Dte of Eperiment: //00 Florence F. Ls (prtner) Abstrct: The rte, rte lw nd ctivtion energ of the iodintion of cetone re detered b observing the
More information** Dpt. Chemical Engineering, Kasetsart University, Bangkok 10900, Thailand
Modelling nd Simultion of hemicl Processes in Multi Pulse TP Experiment P. Phnwdee* S.O. Shekhtmn +. Jrungmnorom** J.T. Gleves ++ * Dpt. hemicl Engineering, Ksetsrt University, Bngkok 10900, Thilnd + Dpt.hemicl
More informationStudy on enzyme-assisted aqueous extraction of oil from soybean
8 Journl Scientific & Industril Reserch J SCI IND RES VOL 69 NOVEMBER 2010 Vol. 69, November 2010, pp. 8-865 Study on enzyme-ssisted queous extrction oil from soyben Jun-Qing Qin*, De-Hui Qin, Xing-Mo
More informationPSYCHROMETRICS: HEATING & HUMIDIFYING or COOLING & DEHUMIDIFYING
PSYCHROMETRICS: HEATING & HUMIDIYING or COOLING & DEHUMIDIYING I) Objective The objective of this experiment is to exmine the stte of moist ir s it enters nd psses through the ir hndling unit. When ether
More informationOperations with Polynomials
38 Chpter P Prerequisites P.4 Opertions with Polynomils Wht you should lern: Write polynomils in stndrd form nd identify the leding coefficients nd degrees of polynomils Add nd subtrct polynomils Multiply
More informationEconomics Letters 65 (1999) 9 15. macroeconomists. a b, Ruth A. Judson, Ann L. Owen. Received 11 December 1998; accepted 12 May 1999
Economics Letters 65 (1999) 9 15 Estimting dynmic pnel dt models: guide for q mcroeconomists b, * Ruth A. Judson, Ann L. Owen Federl Reserve Bord of Governors, 0th & C Sts., N.W. Wshington, D.C. 0551,
More informationExperiment 6: Friction
Experiment 6: Friction In previous lbs we studied Newton s lws in n idel setting, tht is, one where friction nd ir resistnce were ignored. However, from our everydy experience with motion, we know tht
More informationTreatment Spring Late Summer Fall 0.10 5.56 3.85 0.61 6.97 3.01 1.91 3.01 2.13 2.99 5.33 2.50 1.06 3.53 6.10 Mean = 1.33 Mean = 4.88 Mean = 3.
The nlysis of vrince (ANOVA) Although the t-test is one of the most commonly used sttisticl hypothesis tests, it hs limittions. The mjor limittion is tht the t-test cn be used to compre the mens of only
More informationGraphs on Logarithmic and Semilogarithmic Paper
0CH_PHClter_TMSETE_ 3//00 :3 PM Pge Grphs on Logrithmic nd Semilogrithmic Pper OBJECTIVES When ou hve completed this chpter, ou should be ble to: Mke grphs on logrithmic nd semilogrithmic pper. Grph empiricl
More informationPHY 222 Lab 8 MOTION OF ELECTRONS IN ELECTRIC AND MAGNETIC FIELDS
PHY 222 Lb 8 MOTION OF ELECTRONS IN ELECTRIC AND MAGNETIC FIELDS Nme: Prtners: INTRODUCTION Before coming to lb, plese red this pcket nd do the prelb on pge 13 of this hndout. From previous experiments,
More informationRotating DC Motors Part II
Rotting Motors rt II II.1 Motor Equivlent Circuit The next step in our consiertion of motors is to evelop n equivlent circuit which cn be use to better unerstn motor opertion. The rmtures in rel motors
More informationTHERMAL EXPANSION OF TUNGSTEN
. THERMAL EXPANSION OF TUNGSTEN S515 By Peter Hidnert nd W. T. Sweeney ABSTRACT This pper gives the results of n investigtion on the therml expnsion of tungsten (99.98 per cent) over vrious temperture
More informationHelicopter Theme and Variations
Helicopter Theme nd Vritions Or, Some Experimentl Designs Employing Pper Helicopters Some possible explntory vribles re: Who drops the helicopter The length of the rotor bldes The height from which the
More informationSimulation of operation modes of isochronous cyclotron by a new interative method
NUKLEONIKA 27;52(1):29 34 ORIGINAL PAPER Simultion of opertion modes of isochronous cyclotron y new intertive method Ryszrd Trszkiewicz, Mrek Tlch, Jcek Sulikowski, Henryk Doruch, Tdeusz Norys, Artur Srok,
More informationExponential and Logarithmic Functions
Nme Chpter Eponentil nd Logrithmic Functions Section. Eponentil Functions nd Their Grphs Objective: In this lesson ou lerned how to recognize, evlute, nd grph eponentil functions. Importnt Vocbulr Define
More informationHow To Study The Effects Of Music Composition On Children
C-crcs Cognitive - Counselling Reserch & Conference Services (eissn: 2301-2358) Volume I Effects of Music Composition Intervention on Elementry School Children b M. Hogenes, B. Vn Oers, R. F. W. Diekstr,
More information1. Find the zeros Find roots. Set function = 0, factor or use quadratic equation if quadratic, graph to find zeros on calculator
AP Clculus Finl Review Sheet When you see the words. This is wht you think of doing. Find the zeros Find roots. Set function =, fctor or use qudrtic eqution if qudrtic, grph to find zeros on clcultor.
More informationDlNBVRGH + Sickness Absence Monitoring Report. Executive of the Council. Purpose of report
DlNBVRGH + + THE CITY OF EDINBURGH COUNCIL Sickness Absence Monitoring Report Executive of the Council 8fh My 4 I.I...3 Purpose of report This report quntifies the mount of working time lost s result of
More informationPolynomial Functions. Polynomial functions in one variable can be written in expanded form as ( )
Polynomil Functions Polynomil functions in one vrible cn be written in expnded form s n n 1 n 2 2 f x = x + x + x + + x + x+ n n 1 n 2 2 1 0 Exmples of polynomils in expnded form re nd 3 8 7 4 = 5 4 +
More informationUnderstanding Life Cycle Costs How a Northern Pump Saves You Money
Understnding Life Cycle Costs How Nrn Pump Sves You Money Reference: Hydrulic Institute (www.s.g) Introduction Wht Life Cycle Cost (LCC) Clculting Totl LCC LCC Components Wht Life Cycle Cost Life Cycle
More informationQuality Evaluation of Entrepreneur Education on Graduate Students Based on AHP-fuzzy Comprehensive Evaluation Approach ZhongXiaojun 1, WangYunfeng 2
Interntionl Journl of Engineering Reserch & Science (IJOER) ISSN [2395-6992] [Vol-2, Issue-1, Jnury- 2016] Qulity Evlution of Entrepreneur Eduction on Grdute Students Bsed on AHP-fuzzy Comprehensive Evlution
More informationEffect of viscosity on C sugar in Beet sugar factories
ANNUAL TRANSACTIONS OF THE NORDIC RHEOLOGY SOCIETY, VOL. 16, 2008 Effect of on C sugr in Beet sugr fctories Mohmmd Hojjtoleslmy 1, Rez Shokrni 2 nd Ahmd Krsi 3 1 Deprtment of food technology, College of
More informationAll pay auctions with certain and uncertain prizes a comment
CENTER FOR RESEARC IN ECONOMICS AND MANAGEMENT CREAM Publiction No. 1-2015 All py uctions with certin nd uncertin prizes comment Christin Riis All py uctions with certin nd uncertin prizes comment Christin
More informationUnit 6: Exponents and Radicals
Eponents nd Rdicls -: The Rel Numer Sstem Unit : Eponents nd Rdicls Pure Mth 0 Notes Nturl Numers (N): - counting numers. {,,,,, } Whole Numers (W): - counting numers with 0. {0,,,,,, } Integers (I): -
More informationBasic Analysis of Autarky and Free Trade Models
Bsic Anlysis of Autrky nd Free Trde Models AUTARKY Autrky condition in prticulr commodity mrket refers to sitution in which country does not engge in ny trde in tht commodity with other countries. Consequently
More informationSmall Business Networking
Why network is n essentil productivity tool for ny smll business Effective technology is essentil for smll businesses looking to increse the productivity of their people nd processes. Introducing technology
More informationHow To Network A Smll Business
Why network is n essentil productivity tool for ny smll business Effective technology is essentil for smll businesses looking to increse the productivity of their people nd processes. Introducing technology
More informationDistributions. (corresponding to the cumulative distribution function for the discrete case).
Distributions Recll tht n integrble function f : R [,] such tht R f()d = is clled probbility density function (pdf). The distribution function for the pdf is given by F() = (corresponding to the cumultive
More informationThe Velocity Factor of an Insulated Two-Wire Transmission Line
The Velocity Fctor of n Insulted Two-Wire Trnsmission Line Problem Kirk T. McDonld Joseph Henry Lbortories, Princeton University, Princeton, NJ 08544 Mrch 7, 008 Estimte the velocity fctor F = v/c nd the
More informationANALYSIS OF THERMAL STRATIFICATION IN THE PRIMARY CIRCUIT WITH THE CFX CODE
ANALYSIS OF THERMAL STRATIFICATION IN THE PRIMARY CIRCUIT WITH THE CFX CODE Ildikó Boros, Dr. Attil Aszódi Budpest University of Technology nd Economics, Institute of Nucler Techniques Abstrct The therml
More informationSpace Vector Pulse Width Modulation Based Induction Motor with V/F Control
Interntionl Journl of Science nd Reserch (IJSR) Spce Vector Pulse Width Modultion Bsed Induction Motor with V/F Control Vikrmrjn Jmbulingm Electricl nd Electronics Engineering, VIT University, Indi Abstrct:
More informationModule 2. Analysis of Statically Indeterminate Structures by the Matrix Force Method. Version 2 CE IIT, Kharagpur
Module Anlysis of Stticlly Indeterminte Structures by the Mtrix Force Method Version CE IIT, Khrgpur esson 9 The Force Method of Anlysis: Bems (Continued) Version CE IIT, Khrgpur Instructionl Objectives
More informationCOMPARISON OF SOME METHODS TO FIT A MULTIPLICATIVE TARIFF STRUCTURE TO OBSERVED RISK DATA BY B. AJNE. Skandza, Stockholm ABSTRACT
COMPARISON OF SOME METHODS TO FIT A MULTIPLICATIVE TARIFF STRUCTURE TO OBSERVED RISK DATA BY B. AJNE Skndz, Stockholm ABSTRACT Three methods for fitting multiplictive models to observed, cross-clssified
More informationSmall Business Networking
Why network is n essentil productivity tool for ny smll business Effective technology is essentil for smll businesses looking to increse the productivity of their people nd processes. Introducing technology
More informationTITLE THE PRINCIPLES OF COIN-TAP METHOD OF NON-DESTRUCTIVE TESTING
TITLE THE PRINCIPLES OF COIN-TAP METHOD OF NON-DESTRUCTIVE TESTING Sung Joon Kim*, Dong-Chul Che Kore Aerospce Reserch Institute, 45 Eoeun-Dong, Youseong-Gu, Dejeon, 35-333, Kore Phone : 82-42-86-231 FAX
More informationExample A rectangular box without lid is to be made from a square cardboard of sides 18 cm by cutting equal squares from each corner and then folding
1 Exmple A rectngulr box without lid is to be mde from squre crdbord of sides 18 cm by cutting equl squres from ech corner nd then folding up the sides. 1 Exmple A rectngulr box without lid is to be mde
More information9 CONTINUOUS DISTRIBUTIONS
9 CONTINUOUS DISTIBUTIONS A rndom vrible whose vlue my fll nywhere in rnge of vlues is continuous rndom vrible nd will be ssocited with some continuous distribution. Continuous distributions re to discrete
More informationUplift Capacity of K-Series Open Web Steel Joist Seats. Florida, Gainesville, FL 32611; email: psgreen@ce.ufl.edu
Uplift Cpcity of K-Series Open Web Steel Joist Sets Perry S. Green, Ph.D, M.ASCE 1 nd Thoms Sputo, Ph.D., P.E., M.ASCE 2 1 Assistnt Professor, Deprtment of Civil nd Costl Engineering, University of Florid,
More informationLecture 3 Gaussian Probability Distribution
Lecture 3 Gussin Probbility Distribution Introduction l Gussin probbility distribution is perhps the most used distribution in ll of science. u lso clled bell shped curve or norml distribution l Unlike
More informationThe Acoustic Design of Soundproofing Doors and Windows
3 The Open Acoustics Journl, 1, 3, 3-37 The Acoustic Design of Soundproofing Doors nd Windows Open Access Nishimur Yuy,1, Nguyen Huy Qung, Nishimur Sohei 1, Nishimur Tsuyoshi 3 nd Yno Tkshi 1 Kummoto Ntionl
More informationand thus, they are similar. If k = 3 then the Jordan form of both matrices is
Homework ssignment 11 Section 7. pp. 249-25 Exercise 1. Let N 1 nd N 2 be nilpotent mtrices over the field F. Prove tht N 1 nd N 2 re similr if nd only if they hve the sme miniml polynomil. Solution: If
More informationReasoning to Solve Equations and Inequalities
Lesson4 Resoning to Solve Equtions nd Inequlities In erlier work in this unit, you modeled situtions with severl vriles nd equtions. For exmple, suppose you were given usiness plns for concert showing
More informationHow To Set Up A Network For Your Business
Why Network is n Essentil Productivity Tool for Any Smll Business TechAdvisory.org SME Reports sponsored by Effective technology is essentil for smll businesses looking to increse their productivity. Computer
More informationAn Undergraduate Curriculum Evaluation with the Analytic Hierarchy Process
An Undergrdute Curriculum Evlution with the Anlytic Hierrchy Process Les Frir Jessic O. Mtson Jck E. Mtson Deprtment of Industril Engineering P.O. Box 870288 University of Albm Tuscloos, AL. 35487 Abstrct
More informationA generic Decision Support System for integrated weed management
A generic Decision Support System for integrted weed mngement By: Per Rydhl, IPM Consult, Denmrk nd: Nicols Munier-Jolin (INRA), Frnce Robert Msin, University of Pdov, Itly Murizio Sttin (IBAF-CNR), Itly
More informationEE247 Lecture 4. For simplicity, will start with all pole ladder type filters. Convert to integrator based form- example shown
EE247 Lecture 4 Ldder type filters For simplicity, will strt with ll pole ldder type filters Convert to integrtor bsed form exmple shown Then will ttend to high order ldder type filters incorporting zeros
More informationProbability m odels on horse-race outcomes
Jour nl of Applied Sttistics, Vol. 25, No. 2, 1998, 221± 229 Probbility m odels on horse-rce outcomes M UKHTAR M. ALI, Deprtment of Economics, University of Kentucy, USA SUMMARY A number of models hve
More informationImplementation Evaluation Modeling of Selecting ERP Software Based on Fuzzy Theory
Implementtion Evlution Modeling of Selecting ERP Softwre Bsed on Fuzzy Theory Xukn Xu 1, Ydong Jing 1 nd Zheng Shi 2 1 Informtion Mngement Deprtment, Chngzhou Cmpus, Hohi University, Chngzhou 213022, Jingsu,
More informationSmall Business Cloud Services
Smll Business Cloud Services Summry. We re thick in the midst of historic se-chnge in computing. Like the emergence of personl computers, grphicl user interfces, nd mobile devices, the cloud is lredy profoundly
More informationEcon 4721 Money and Banking Problem Set 2 Answer Key
Econ 472 Money nd Bnking Problem Set 2 Answer Key Problem (35 points) Consider n overlpping genertions model in which consumers live for two periods. The number of people born in ech genertion grows in
More informationENHANCING CUSTOMER EXPERIENCE THROUGH BUSINESS PROCESS IMPROVEMENT: AN APPLICATION OF THE ENHANCED CUSTOMER EXPERIENCE FRAMEWORK (ECEF)
ENHNCING CUSTOMER EXPERIENCE THROUGH BUSINESS PROCESS IMPROVEMENT: N PPLICTION OF THE ENHNCED CUSTOMER EXPERIENCE FRMEWORK (ECEF) G.J. Both 1, P.S. Kruger 2 & M. de Vries 3 Deprtment of Industril nd Systems
More informationc. Values in statements are broken down by fiscal years; many projects are
Lecture 18: Finncil Mngement (Continued)/Csh Flow CEE 498 Construction Project Mngement L Schedules A. Schedule.of Contrcts Completed See Attchment # 1 ll. 1. Revenues Erned 2. Cost of Revenues 3. Gross
More informationFirm Objectives. The Theory of the Firm II. Cost Minimization Mathematical Approach. First order conditions. Cost Minimization Graphical Approach
Pro. Jy Bhttchry Spring 200 The Theory o the Firm II st lecture we covered: production unctions Tody: Cost minimiztion Firm s supply under cost minimiztion Short vs. long run cost curves Firm Ojectives
More informationPROF. BOYAN KOSTADINOV NEW YORK CITY COLLEGE OF TECHNOLOGY, CUNY
MAT 0630 INTERNET RESOURCES, REVIEW OF CONCEPTS AND COMMON MISTAKES PROF. BOYAN KOSTADINOV NEW YORK CITY COLLEGE OF TECHNOLOGY, CUNY Contents 1. ACT Compss Prctice Tests 1 2. Common Mistkes 2 3. Distributive
More informationApplication of Analytical Hierarchy Process (AHP) Technique To Evaluate and Selecting Suppliers in an Effective Supply Chain
Appliction of Anlyticl Hierrchy Process (AHP) Technique To Evlute nd Selecting Suppliers in n Effective Supply Chin Shhroodi 1*, Kmbiz, Industril Mngement Deprtment, Islmic Azd University (Rsht Brnch),
More informationModule Summary Sheets. C3, Methods for Advanced Mathematics (Version B reference to new book) Topic 2: Natural Logarithms and Exponentials
MEI Mthemtics in Ection nd Instry Topic : Proof MEI Structured Mthemtics Mole Summry Sheets C, Methods for Anced Mthemtics (Version B reference to new book) Topic : Nturl Logrithms nd Eponentils Topic
More informationPhysics 43 Homework Set 9 Chapter 40 Key
Physics 43 Homework Set 9 Chpter 4 Key. The wve function for n electron tht is confined to x nm is. Find the normliztion constnt. b. Wht is the probbility of finding the electron in. nm-wide region t x
More informationSPECIAL PRODUCTS AND FACTORIZATION
MODULE - Specil Products nd Fctoriztion 4 SPECIAL PRODUCTS AND FACTORIZATION In n erlier lesson you hve lernt multipliction of lgebric epressions, prticulrly polynomils. In the study of lgebr, we come
More informationFactoring Polynomials
Fctoring Polynomils Some definitions (not necessrily ll for secondry school mthemtics): A polynomil is the sum of one or more terms, in which ech term consists of product of constnt nd one or more vribles
More informationWeek 11 - Inductance
Week - Inductnce November 6, 202 Exercise.: Discussion Questions ) A trnsformer consists bsiclly of two coils in close proximity but not in electricl contct. A current in one coil mgneticlly induces n
More informationSmall Business Networking
Why network is n essentil productivity tool for ny smll business Effective technology is essentil for smll businesses looking to increse the productivity of their people nd business. Introducing technology
More informationORBITAL MANEUVERS USING LOW-THRUST
Proceedings of the 8th WSEAS Interntionl Conference on SIGNAL PROCESSING, ROBOICS nd AUOMAION ORBIAL MANEUVERS USING LOW-HRUS VIVIAN MARINS GOMES, ANONIO F. B. A. PRADO, HÉLIO KOII KUGA Ntionl Institute
More informationINVESTIGATION OF THE EXTINGUISHING FEATURES FOR LIQUID FUELS AND ORGANIC FLAMMABLE LIQUIDS ATOMIZED BY A WATER FLOW
EPJ Web of Conferences 110, 01083 (2016) DOI: 10.1051/ epjconf/ 201611001083 C Owned by the uthors, published by EDP Sciences, 2016 INVESTIGATION OF THE EXTINGUISHING FEATURES FOR LIQUID FUELS AND ORGANIC
More informationEQUATIONS OF LINES AND PLANES
EQUATIONS OF LINES AND PLANES MATH 195, SECTION 59 (VIPUL NAIK) Corresponding mteril in the ook: Section 12.5. Wht students should definitely get: Prmetric eqution of line given in point-direction nd twopoint
More informationUnit 29: Inference for Two-Way Tables
Unit 29: Inference for Two-Wy Tbles Prerequisites Unit 13, Two-Wy Tbles is prerequisite for this unit. In ddition, students need some bckground in significnce tests, which ws introduced in Unit 25. Additionl
More informationMathematics. Vectors. hsn.uk.net. Higher. Contents. Vectors 128 HSN23100
hsn.uk.net Higher Mthemtics UNIT 3 OUTCOME 1 Vectors Contents Vectors 18 1 Vectors nd Sclrs 18 Components 18 3 Mgnitude 130 4 Equl Vectors 131 5 Addition nd Subtrction of Vectors 13 6 Multipliction by
More informationSection 7-4 Translation of Axes
62 7 ADDITIONAL TOPICS IN ANALYTIC GEOMETRY Section 7-4 Trnsltion of Aes Trnsltion of Aes Stndrd Equtions of Trnslted Conics Grphing Equtions of the Form A 2 C 2 D E F 0 Finding Equtions of Conics In the
More informationSmall Business Networking
Why network is n essentil productivity tool for ny smll business Effective technology is essentil for smll businesses looking to increse the productivity of their people nd business. Introducing technology
More informationAN ANALYTICAL HIERARCHY PROCESS METHODOLOGY TO EVALUATE IT SOLUTIONS FOR ORGANIZATIONS
AN ANALYTICAL HIERARCHY PROCESS METHODOLOGY TO EVALUATE IT SOLUTIONS FOR ORGANIZATIONS Spiros Vsilkos (), Chrysostomos D. Stylios (),(b), John Groflkis (c) () Dept. of Telemtics Center, Computer Technology
More informationWhy is the NSW prison population falling?
NSW Bureu of Crime Sttistics nd Reserch Bureu Brief Issue pper no. 80 September 2012 Why is the NSW prison popultion flling? Jcqueline Fitzgerld & Simon Corben 1 Aim: After stedily incresing for more thn
More informationAir-Conditioning PID Control System with Adjustable Reset to Offset Thermal Loads Upsets
11 Air-Conditioning PID Control System with Adjustble Reset to Offset Therml Lods Upsets Tknori Ymzki 1, Yuji Ymkw 2, Kzuyuki Kmimur 3 nd Shigeru Kurosu 4 1 Oym Ntionl College of Technology, 2 Univ. of
More information2006 IPCC Software for National Greenhouse Gas Inventories: Application and use for India
2006 IPCC Softwre for Ntionl Greenhouse Gs Inventories: Appliction nd use for Indi Presenttion for NGGIP Side Event Bonn, June 8, 2013 Prof. Amit Grg (mitgrg@iimhd.ernet.in), INDIA GHG Inventory Softwre
More informationSTATUS OF LAND-BASED WIND ENERGY DEVELOPMENT IN GERMANY
Yer STATUS OF LAND-BASED WIND ENERGY Deutsche WindGurd GmbH - Oldenburger Strße 65-26316 Vrel - Germny +49 (4451)/9515 - info@windgurd.de - www.windgurd.com Annul Added Cpcity [MW] Cumultive Cpcity [MW]
More informationIncreasing Q of Waveguide Pulse-Compression Cavities
Circuit nd Electromgnetic System Design Notes Note 61 3 July 009 Incresing Q of Wveguide Pulse-Compression Cvities Crl E. Bum University of New Mexico Deprtment of Electricl nd Computer Engineering Albuquerque
More informationPROBLEMS 13 - APPLICATIONS OF DERIVATIVES Page 1
PROBLEMS - APPLICATIONS OF DERIVATIVES Pge ( ) Wter seeps out of conicl filter t the constnt rte of 5 cc / sec. When the height of wter level in the cone is 5 cm, find the rte t which the height decreses.
More informationCost Functions for Assessment of Vehicle Dynamics
Cost Functions for Assessment of Vehicle Dynmics Dzmitry Svitski Automotive Engineering Deprtment Ilmenu University of Technology Ilmenu, Germny dzmitry.svitski@tu-ilmenu.de Pvel Nedom, Jroslv Mchn Skod
More informationMath 135 Circles and Completing the Square Examples
Mth 135 Circles nd Completing the Squre Exmples A perfect squre is number such tht = b 2 for some rel number b. Some exmples of perfect squres re 4 = 2 2, 16 = 4 2, 169 = 13 2. We wish to hve method for
More informationImproving Library Users' Perceived Quality, Satisfaction and Loyalty: An Integrated Measurement and Management System
Improving Librry Users' Perceived Qulity, Stisfction nd Loylty: An Integrted Mesurement nd Mngement System by Anne Mrtensen nd Lrs Gr0nholdt This rticle describes the development nd ppliction of structurl
More informationThe Effect of Crumb Rubber Modifier (CRM) on the Performance Properties of Rubberized Binders in HMA pavements
The Effect of Crum Ruer Modifier (CRM) on the Performnce Properties of Ruerized Binders in HMA pvements Soon-Je Lee* Ph.D. Grdute Student Deprtment of Civil Engineering Clemson University Clemson, SC 29634-0911
More information15.6. The mean value and the root-mean-square value of a function. Introduction. Prerequisites. Learning Outcomes. Learning Style
The men vlue nd the root-men-squre vlue of function 5.6 Introduction Currents nd voltges often vry with time nd engineers my wish to know the verge vlue of such current or voltge over some prticulr time
More informationExample 27.1 Draw a Venn diagram to show the relationship between counting numbers, whole numbers, integers, and rational numbers.
2 Rtionl Numbers Integers such s 5 were importnt when solving the eqution x+5 = 0. In similr wy, frctions re importnt for solving equtions like 2x = 1. Wht bout equtions like 2x + 1 = 0? Equtions of this
More informationDecision Rule Extraction from Trained Neural Networks Using Rough Sets
Decision Rule Extrction from Trined Neurl Networks Using Rough Sets Alin Lzr nd Ishwr K. Sethi Vision nd Neurl Networks Lbortory Deprtment of Computer Science Wyne Stte University Detroit, MI 48 ABSTRACT
More informationModeling POMDPs for Generating and Simulating Stock Investment Policies
Modeling POMDPs for Generting nd Simulting Stock Investment Policies Augusto Cesr Espíndol Bff UNIRIO - Dep. Informátic Aplicd Av. Psteur, 458 - Térreo Rio de Jneiro - Brzil ugusto.bff@uniriotec.br Angelo
More informationWEB DELAY ANALYSIS AND REDUCTION BY USING LOAD BALANCING OF A DNS-BASED WEB SERVER CLUSTER
Interntionl Journl of Computers nd Applictions, Vol. 9, No., 007 WEB DELAY ANALYSIS AND REDUCTION BY USING LOAD BALANCING OF A DNS-BASED WEB SERVER CLUSTER Y.W. Bi nd Y.C. Wu Abstrct Bsed on our survey
More information, and the number of electrons is -19. e e 1.60 10 C. The negatively charged electrons move in the direction opposite to the conventional current flow.
Prolem 1. f current of 80.0 ma exists in metl wire, how mny electrons flow pst given cross section of the wire in 10.0 min? Sketch the directions of the current nd the electrons motion. Solution: The chrge
More informationRadius of the Earth - Radii Used in Geodesy James R. Clynch February 2006
dius of the Erth - dii Used in Geodesy Jmes. Clynch Februry 006 I. Erth dii Uses There is only one rdius of sphere. The erth is pproximtely sphere nd therefore, for some cses, this pproximtion is dequte.
More informationTHE PARAMETERS OF TRAPS IN K-FELDSPARS AND THE TL BLEACHING EFFICIENCY
GEOCHRONOMETRIA Vol. 2, pp 15-2, 21 Journl on Methods nd Applictions of Asolute Chronology THE PARAMETERS OF TRAPS IN K-FELDSPARS AND THE TL BLEACHING EFFICIENCY ALICJA CHRUŒCIÑSKA 1, HUBERT L. OCZKOWSKI
More informationUse Geometry Expressions to create a more complex locus of points. Find evidence for equivalence using Geometry Expressions.
Lerning Objectives Loci nd Conics Lesson 3: The Ellipse Level: Preclculus Time required: 120 minutes In this lesson, students will generlize their knowledge of the circle to the ellipse. The prmetric nd
More informationPerformance analysis model for big data applications in cloud computing
Butist Villlpndo et l. Journl of Cloud Computing: Advnces, Systems nd Applictions 2014, 3:19 RESEARCH Performnce nlysis model for big dt pplictions in cloud computing Luis Edurdo Butist Villlpndo 1,2,
More informationProject Recovery. . It Can Be Done
Project Recovery. It Cn Be Done IPM Conference Wshington, D.C. Nov 4-7, 200 Wlt Lipke Oklhom City Air Logistics Center Tinker AFB, OK Overview Mngement Reserve Project Sttus Indictors Performnce Correction
More informationMulti-Scale Modeling of Nano Scale Phenomenon using CUDA based HPC Setup
Multi-Scle Modeling of Nno Scle Phenomenon using CUDA bsed HPC Setup Rohit Pthk nd Stydhr Joshi Acropolis Institute of Technology & Reserch, Indore, Mdhy Prdesh, Indi Shri Vishnv Institute of Technology
More informationMATH 150 HOMEWORK 4 SOLUTIONS
MATH 150 HOMEWORK 4 SOLUTIONS Section 1.8 Show tht the product of two of the numbers 65 1000 8 2001 + 3 177, 79 1212 9 2399 + 2 2001, nd 24 4493 5 8192 + 7 1777 is nonnegtive. Is your proof constructive
More information2013 Flax Weed Control Trial
2013 Flx Weed Control Tril Dr. Hether Drby, UVM Extension Agronomist Susn Monhn, Conner Burke, Eric Cummings, nd Hnnh Hrwood UVM Extension Crops nd Soils Technicins 802-524-6501 Visit us on the web: http://www.uvm.edu/extension/cropsoil
More informationg(y(a), y(b)) = o, B a y(a)+b b y(b)=c, Boundary Value Problems Lecture Notes to Accompany
Lecture Notes to Accompny Scientific Computing An Introductory Survey Second Edition by Michel T Heth Boundry Vlue Problems Side conditions prescribing solution or derivtive vlues t specified points required
More informationAdvanced Treatment of Wastewater from Food Waste Disposer in Modified Ludzack-Ettinger Type Membrane Bioreactor
Environ. Eng. Res. June,7() : 59-6 Reserch Pper http://dx.doi.org/.449/eer..7..59 pissn 6-5 eissn 5-968X Advnced Tretment of Wstewter from Food Wste Disposer in Modified Ludzck-Ettinger Type Membrne Biorector
More informationNational greenhouse gas inventory data for the period 1990 2010
United Ntions FCCC/SBI/2012/31 Distr.: Generl 16 November 2012 Originl: English Subsidiry Body for Implementtion Thirty-seventh session Doh, 26 November to 1 December 2012 Item 3(b) of the provisionl gend
More informationLINEAR TRANSFORMATIONS AND THEIR REPRESENTING MATRICES
LINEAR TRANSFORMATIONS AND THEIR REPRESENTING MATRICES DAVID WEBB CONTENTS Liner trnsformtions 2 The representing mtrix of liner trnsformtion 3 3 An ppliction: reflections in the plne 6 4 The lgebr of
More informationReview guide for the final exam in Math 233
Review guide for the finl exm in Mth 33 1 Bsic mteril. This review includes the reminder of the mteril for mth 33. The finl exm will be cumultive exm with mny of the problems coming from the mteril covered
More informationEstimating Exchange Rate Exposures:
Estimting Exchnge Rte Exposures: Issues in Model Structure * Gordon M. Bodnr ** Pul H. Nitze School of Advnced Interntionl Studies, The Johns Hopkins University 1740 Msschusetts Avenue NW Wshington, DC
More information