PRESSURE BUILDUP. Figure 1: Schematic of an ideal buildup test


 Lucy Morris
 1 years ago
 Views:
Transcription
1 Tom Aage Jelmer NTNU Dearmen of Peroleum Engineering and Alied Geohysics PRESSURE BUILDUP I is difficul o kee he rae consan in a roducing well. This is no an issue in a buildu es since he well is closed. The rae is zero. This es may be conduced any ime. The disadvanage is ha he well has o be closed for a eriod. Since he well is closed, i will no generae income during his eriod. Hence he shuin ime should be as shor as ossible. Procedure 1. Produce he well a a consan (sabilized) rae. A ime close he well. 2. Measure he las flowing ressure which we call wf and he shuin ressure ws. 3. Make inerreaion. Figure 1: Schemaic of an ideal buildu es In he above figure, and denoe roducion ime and shuin ime resecively. Infinieacing reservoir For a new well, he ressure wave associaed wih he flow eriod may no have reached he ouer boundary. Then he following equaion alies: 1
2 ws B 1.15 = i log + This is he Horner equaion. + The above equaion shows u as a sraigh line on a ws vs. log lo. Deerminaion of ermeabiliy Noe ha he rae rofile of Fig. 1 is idealized. Insananeous shuin is no ossible. There will always be some aferflow (see wellbore sorage). As a consequence he measured ressure will no obey he Horner equaion iniially. Figure 2: Schemaic of a Horner lo of a well wih aferflow and skin. Hr is used o denoe he Horner raio: Hr = + Observe ha he shuin ime,, increases o he lef in he Horner lo, Fig. 2. The Horner raio Hr will decrease as increases.. The sloe of he sraigh line is given by: m = B1.15 Hence he ermeabiliy may be deermined from he following equaion: Tom Aage Jelmer PRESSURE BUILDUP 2
3 k = B πmh The sloe is also defined by wo oins on he sraigh line m = log Hr log Hr 2 which simlifies o: when Hr 1 and Hr 2 are one decade aar. m = 1 2 Deerminaion of he reservoir iniial reservoir ressure The Horner equaion may be wrien: Noe ha: ws = i  B 1.15 log Hr ws = i for Hr = 1 The Horner raio will aroach 1 for infinie shuin ime. Hence he iniial reservoir ressure may be obained by exraolaing he sraigh line back o Hr = 1. The echnique is illusraed in Fig.2. Deerminaion of he skin facor The skin is no included in he Horner equaion. To involve his arameer, he las flowing ressure wf is subraced from boh sides of he Horner equaion. The las flowing ressure is given by he drawdown equaion. On he righ hand side of he Horner equaion we subrac he mahemaical model and on he lef hand side he observed ressure. The resul is: B 1.15 = kh log 2π + k log ϕµ c r ws wf w Usually he shuin ime is small in comarison wih he roducion ime. Hence S + Then he above equaion will simlify since he roducion ime disaears. Tom Aage Jelmer PRESSURE BUILDUP 3
4 The modified Horner equaion may be solved for he skin facor once he shuin ime is secified. The radiional choice is = 1h. This choice leads o: S = 1.15 ws = 1h m wf k log 2 ϕµ c r w 3.91 Observaions: 1. The skin facor is conrolled by he disance = ws = 1h  wf 2. The skin facor S will increase wih increasing difference. 3. The measured wellbore ressure a 1 hour may no be on he sraigh Horner line. Then he line is exraolaed unil i inersecs he Hr = 1h verical line. This is illusraed in he below figure. The Horner raio a 1 hour may be comued from Hr = 1h = + 1 Figure 3: The skin deends on he disance. Bounded reservoir Sooner or laer he ressure wave associaed wih he flow eriod will hi he ouer boundary. Suose his is of noflow ye. If he well is closed during seudoseady flow, hen he ressure will build u owards he average ressure raher han he iniial ressure. This is illusraed below. Tom Aage Jelmer PRESSURE BUILDUP 4
5 Figure 4: Pressure versus disance, seudoseady flow The effec of he ouer boundary aears a he lae ar of he Horner lo while he early ar essenially remains unchanged. The boundary effec will show u as a break off from he sraigh line. Figure 5: Horner lo, bounded reservoir The Horner equaion for he sraigh line secion may be wrien: ws B = * log where * is he inersecion wih he Hr =1 axis. The inersecion has been called he false ressure. I has no hysical inerreaion bu i is relaed o he average ressure, Tom Aage Jelmer PRESSURE BUILDUP 5
6 . The sraigh line on he horner lo may be used o deermine he ermeabiliy and skin facor as discussed reviously. The rocedure will no be reeaed here. Deerminaion of he average ressure Mahews, Brons and Hazebroek resened chars ha relae he false ressure o he average ressure for various geomeries. Figure 6: Schemaic of a Maews,Brons and Hazebroek lo Index D is used o denoe dimensionless variables. The average ressure may be calculaed as follows: 1. Obain he sloe m and he false ressure * from he Horner lo. 2. Esimae he shae and size of he drainage area. 3. Comue he dimensionless roducion ime from he formula: k DA = ϕµ c A 4. Look u he MBHcurve ha corresonds o he esimaed shae of he drainage area, and find P DMBH. 5. Calculae he average ressure from he formula: m DMBH = * The difficul ar in his calculaion rocedure is oin 2. Esimaion of he size and shae of he drainage area is beyond he scoe of hese noes. The average ressure is used in maerial balance calculaions. Also i is used o calculae he flow efficiency, FE. wf FE = wf S Tom Aage Jelmer PRESSURE BUILDUP 6
7 wf is he las flowing ressure. For seudoseady flow, he difference wf is indeenden of ime. This condiion leads o a consan value of he flow efficiency. Oherwise i will deend on ime. * wf S Someimes he flow efficiency is aroximaed by FE =. ( * wf ) The resul is no as accurae bu easier o obain. Horner ime As menioned reviously i is difficul o kee he flow rae consan for any lengh of ime. The rae may have flucuaed significanly during he roducion eriod. Horner roosed he following correcion: N = qlast where N is he cumulaive roducion since he las major shuin eriod and q LAST is he las sabilized rae. Tom Aage Jelmer PRESSURE BUILDUP 7
THE PRESSURE DERIVATIVE
Tom Aage Jelmer NTNU Dearmen of Peroleum Engineering and Alied Geohysics THE PRESSURE DERIVATIVE The ressure derivaive has imoran diagnosic roeries. I is also imoran for making ye curve analysis more reliable.
More informationLecture 2: Telegrapher Equations For Transmission Lines. Power Flow.
Whies, EE 481 Lecure 2 Page 1 of 13 Lecure 2: Telegraher Equaions For Transmission Lines. Power Flow. Microsri is one mehod for making elecrical connecions in a microwae circui. I is consruced wih a ground
More informationAppendix A: Area. 1 Find the radius of a circle that has circumference 12 inches.
Appendi A: Area workedou s o OddNumbered Eercises Do no read hese workedou s before aemping o do he eercises ourself. Oherwise ou ma mimic he echniques shown here wihou undersanding he ideas. Bes wa
More informationCapacitors and inductors
Capaciors and inducors We coninue wih our analysis of linear circuis by inroducing wo new passive and linear elemens: he capacior and he inducor. All he mehods developed so far for he analysis of linear
More information1. The graph shows the variation with time t of the velocity v of an object.
1. he graph shows he variaion wih ime of he velociy v of an objec. v Which one of he following graphs bes represens he variaion wih ime of he acceleraion a of he objec? A. a B. a C. a D. a 2. A ball, iniially
More informationSection 7.1 Angles and Their Measure
Secion 7.1 Angles and Their Measure Greek Leers Commonly Used in Trigonomery Quadran II Quadran III Quadran I Quadran IV α = alpha β = bea θ = hea δ = dela ω = omega γ = gamma DEGREES The angle formed
More information#A81 INTEGERS 13 (2013) THE AVERAGE LARGEST PRIME FACTOR
#A8 INTEGERS 3 (03) THE AVERAGE LARGEST PRIME FACTOR Eric Naslund Dearmen of Mahemaics, Princeon Universiy, Princeon, New Jersey naslund@mahrinceonedu Received: /8/3, Revised: 7/7/3, Acceed:/5/3, Published:
More informationcooking trajectory boiling water B (t) microwave 0 2 4 6 8 101214161820 time t (mins)
Alligaor egg wih calculus We have a large alligaor egg jus ou of he fridge (1 ) which we need o hea o 9. Now here are wo accepable mehods for heaing alligaor eggs, one is o immerse hem in boiling waer
More informationRC, RL and RLC circuits
Name Dae Time o Complee h m Parner Course/ Secion / Grade RC, RL and RLC circuis Inroducion In his experimen we will invesigae he behavior of circuis conaining combinaions of resisors, capaciors, and inducors.
More informationANALYTIC PROOF OF THE PRIME NUMBER THEOREM
ANALYTIC PROOF OF THE PRIME NUMBER THEOREM RYAN SMITH, YUAN TIAN Conens Arihmeical Funcions Equivalen Forms of he Prime Number Theorem 3 3 The Relaionshi Beween Two Asymoic Relaions 6 4 Dirichle Series
More informationCALCULATION OF OMX TALLINN
CALCULATION OF OMX TALLINN CALCULATION OF OMX TALLINN 1. OMX Tallinn index...3 2. Terms in use...3 3. Comuaion rules of OMX Tallinn...3 3.1. Oening, realime and closing value of he Index...3 3.2. Index
More information11/6/2013. Chapter 14: Dynamic ADAS. Introduction. Introduction. Keeping track of time. The model s elements
Inroducion Chaper 14: Dynamic DS dynamic model of aggregae and aggregae supply gives us more insigh ino how he economy works in he shor run. I is a simplified version of a DSGE model, used in cuingedge
More informationCointegration: The Engle and Granger approach
Coinegraion: The Engle and Granger approach Inroducion Generally one would find mos of he economic variables o be nonsaionary I(1) variables. Hence, any equilibrium heories ha involve hese variables require
More informationChapter 2 Problems. 3600s = 25m / s d = s t = 25m / s 0.5s = 12.5m. Δx = x(4) x(0) =12m 0m =12m
Chaper 2 Problems 2.1 During a hard sneeze, your eyes migh shu for 0.5s. If you are driving a car a 90km/h during such a sneeze, how far does he car move during ha ime s = 90km 1000m h 1km 1h 3600s = 25m
More informationChapter 8 Copyright Henning Umland All Rights Reserved
Chaper 8 Copyrigh 19972004 Henning Umland All Righs Reserved Rise, Se, Twiligh General Visibiliy For he planning of observaions, i is useful o know he imes during which a cerain body is above he horizon
More informationMathematics in Pharmacokinetics What and Why (A second attempt to make it clearer)
Mahemaics in Pharmacokineics Wha and Why (A second aemp o make i clearer) We have used equaions for concenraion () as a funcion of ime (). We will coninue o use hese equaions since he plasma concenraions
More informationChapter 2 Problems. s = d t up. = 40km / hr d t down. 60km / hr. d t total. + t down. = t up. = 40km / hr + d. 60km / hr + 40km / hr
Chaper 2 Problems 2.2 A car ravels up a hill a a consan speed of 40km/h and reurns down he hill a a consan speed of 60 km/h. Calculae he average speed for he rip. This problem is a bi more suble han i
More information4.8 Exponential Growth and Decay; Newton s Law; Logistic Growth and Decay
324 CHAPTER 4 Exponenial and Logarihmic Funcions 4.8 Exponenial Growh and Decay; Newon s Law; Logisic Growh and Decay OBJECTIVES 1 Find Equaions of Populaions Tha Obey he Law of Uninhibied Growh 2 Find
More informationRevisions to Nonfarm Payroll Employment: 1964 to 2011
Revisions o Nonfarm Payroll Employmen: 1964 o 2011 Tom Sark December 2011 Summary Over recen monhs, he Bureau of Labor Saisics (BLS) has revised upward is iniial esimaes of he monhly change in nonfarm
More informationChapter 2 Kinematics in One Dimension
Chaper Kinemaics in One Dimension Chaper DESCRIBING MOTION:KINEMATICS IN ONE DIMENSION PREVIEW Kinemaics is he sudy of how hings moe how far (disance and displacemen), how fas (speed and elociy), and how
More informationRepresenting Periodic Functions by Fourier Series. (a n cos nt + b n sin nt) n=1
Represening Periodic Funcions by Fourier Series 3. Inroducion In his Secion we show how a periodic funcion can be expressed as a series of sines and cosines. We begin by obaining some sandard inegrals
More informationChapter 8: Regression with Lagged Explanatory Variables
Chaper 8: Regression wih Lagged Explanaory Variables Time series daa: Y for =1,..,T End goal: Regression model relaing a dependen variable o explanaory variables. Wih ime series new issues arise: 1. One
More informationOptimal RealTime Scheduling for Hybrid Energy Storage Systems and Wind Farms Based on Model Predictive Control
Energies 2015, 8, 80208051; doi:10.3390/en8088020 Aricle OPEN ACCESS energies ISSN 19961073 www.mdi.com/journal/energies Oimal RealTime Scheduling for Hybrid Energy Sorage Sysems and Wind Farms Based
More informationTECHNICAL REPORT: BONDS VALUATION MUNEER AFZAL EP BS. ACTUARIAL SCIENCES AND RISK MNAGEMENT EVENING PROGRAM UNIVERSITY OF KARACHI.
EHNIAL REOR: BONDS VALUAION MUNEER AFZAL E49 BS. AUARIAL SIENES AND RISK MNAGEMEN EVENING ROGRAM UNIVERSIY OF KARAHI. BONDS: Bonds are securiies ha esablish a credior relaionshi beween he urchasers (credior)
More informationFourier Series Solution of the Heat Equation
Fourier Series Soluion of he Hea Equaion Physical Applicaion; he Hea Equaion In he early nineeenh cenury Joseph Fourier, a French scienis and mahemaician who had accompanied Napoleon on his Egypian campaign,
More informationDYNAMIC MODELS FOR VALUATION OF WRONGFUL DEATH PAYMENTS
DYNAMIC MODELS FOR VALUATION OF WRONGFUL DEATH PAYMENTS Hong Mao, Shanghai Second Polyechnic Universiy Krzyszof M. Osaszewski, Illinois Sae Universiy Youyu Zhang, Fudan Universiy ABSTRACT Liigaion, exper
More informationUnderstanding Sequential Circuit Timing
ENGIN112: Inroducion o Elecrical and Compuer Engineering Fall 2003 Prof. Russell Tessier Undersanding Sequenial Circui Timing Perhaps he wo mos disinguishing characerisics of a compuer are is processor
More informationRotational Inertia of a Point Mass
Roaional Ineria of a Poin Mass Saddleback College Physics Deparmen, adaped from PASCO Scienific PURPOSE The purpose of his experimen is o find he roaional ineria of a poin experimenally and o verify ha
More informationThe Transport Equation
The Transpor Equaion Consider a fluid, flowing wih velociy, V, in a hin sraigh ube whose cross secion will be denoed by A. Suppose he fluid conains a conaminan whose concenraion a posiion a ime will be
More informationA PRODUCTION INVENTORY MODEL WITH DETERIORATING ITEMS AND SHORTAGES
Yugoslav Journal of Oeraions Research 4 (004), Number, 930 A PRODUCTION INVENTORY MODEL WITH DETERIORATING ITEMS AND SHORTAGES G.P. SAMANTA, Ajana ROY Dearmen of Mahemaics Bengal Engineering College (D.
More informationReturn Calculation of U.S. Treasury Constant Maturity Indices
Reurn Calculaion of US Treasur Consan Mauri Indices Morningsar Mehodolog Paper Sepeber 30 008 008 Morningsar Inc All righs reserved The inforaion in his docuen is he proper of Morningsar Inc Reproducion
More informationCircuit Types. () i( t) ( )
Circui Types DC Circuis Idenifying feaures: o Consan inpus: he volages of independen volage sources and currens of independen curren sources are all consan. o The circui does no conain any swiches. All
More informationCHARGE AND DISCHARGE OF A CAPACITOR
REFERENCES RC Circuis: Elecrical Insrumens: Mos Inroducory Physics exs (e.g. A. Halliday and Resnick, Physics ; M. Sernheim and J. Kane, General Physics.) This Laboraory Manual: Commonly Used Insrumens:
More informationMTH6121 Introduction to Mathematical Finance Lesson 5
26 MTH6121 Inroducion o Mahemaical Finance Lesson 5 Conens 2.3 Brownian moion wih drif........................... 27 2.4 Geomeric Brownian moion........................... 28 2.5 Convergence of random
More informationEntropy: From the Boltzmann equation to the Maxwell Boltzmann distribution
Enropy: From he Bolzmann equaion o he Maxwell Bolzmann disribuion A formula o relae enropy o probabiliy Ofen i is a lo more useful o hink abou enropy in erms of he probabiliy wih which differen saes are
More informationA Mathematical Description of MOSFET Behavior
10/19/004 A Mahemaical Descripion of MOSFET Behavior.doc 1/8 A Mahemaical Descripion of MOSFET Behavior Q: We ve learned an awful lo abou enhancemen MOSFETs, bu we sill have ye o esablished a mahemaical
More informationComplex Fourier Series. Adding these identities, and then dividing by 2, or subtracting them, and then dividing by 2i, will show that
Mah 344 May 4, Complex Fourier Series Par I: Inroducion The Fourier series represenaion for a funcion f of period P, f) = a + a k coskω) + b k sinkω), ω = π/p, ) can be expressed more simply using complex
More informationTable of contents Chapter 1 Interest rates and factors Chapter 2 Level annuities Chapter 3 Varying annuities
Table of conens Chaper 1 Ineres raes and facors 1 1.1 Ineres 2 1.2 Simple ineres 4 1.3 Compound ineres 6 1.4 Accumulaed value 10 1.5 Presen value 11 1.6 Rae of discoun 13 1.7 Consan force of ineres 17
More informationWeek #9  The Integral Section 5.1
Week #9  The Inegral Secion 5.1 From Calculus, Single Variable by HughesHalle, Gleason, McCallum e. al. Copyrigh 005 by John Wiley & Sons, Inc. This maerial is used by permission of John Wiley & Sons,
More informationAcceleration Lab Teacher s Guide
Acceleraion Lab Teacher s Guide Objecives:. Use graphs of disance vs. ime and velociy vs. ime o find acceleraion of a oy car.. Observe he relaionship beween he angle of an inclined plane and he acceleraion
More informationand Decay Functions f (t) = C(1± r) t / K, for t 0, where
MATH 116 Exponenial Growh and Decay Funcions Dr. Neal, Fall 2008 A funcion ha grows or decays exponenially has he form f () = C(1± r) / K, for 0, where C is he iniial amoun a ime 0: f (0) = C r is he rae
More informationEconomics 140A Hypothesis Testing in Regression Models
Economics 140A Hypohesis Tesing in Regression Models While i is algebraically simple o work wih a populaion model wih a single varying regressor, mos populaion models have muliple varying regressors 1
More informationRelative velocity in one dimension
Connexions module: m13618 1 Relaive velociy in one dimension Sunil Kumar Singh This work is produced by The Connexions Projec and licensed under he Creaive Commons Aribuion License Absrac All quaniies
More informationChapter 7. Response of FirstOrder RL and RC Circuits
Chaper 7. esponse of FirsOrder L and C Circuis 7.1. The Naural esponse of an L Circui 7.2. The Naural esponse of an C Circui 7.3. The ep esponse of L and C Circuis 7.4. A General oluion for ep and Naural
More informationDuration and Convexity ( ) 20 = Bond B has a maturity of 5 years and also has a required rate of return of 10%. Its price is $613.
Graduae School of Business Adminisraion Universiy of Virginia UVAF38 Duraion and Convexiy he price of a bond is a funcion of he promised paymens and he marke required rae of reurn. Since he promised
More informationChabot College Physics Lab RC Circuits Scott Hildreth
Chabo College Physics Lab Circuis Sco Hildreh Goals: Coninue o advance your undersanding of circuis, measuring resisances, currens, and volages across muliple componens. Exend your skills in making breadboard
More informationHANDOUT 14. A.) Introduction: Many actions in life are reversible. * Examples: Simple One: a closed door can be opened and an open door can be closed.
Inverse Funcions Reference Angles Inverse Trig Problems Trig Indeniies HANDOUT 4 INVERSE FUNCTIONS KEY POINTS A.) Inroducion: Many acions in life are reversible. * Examples: Simple One: a closed door can
More informationModule 3 Design for Strength. Version 2 ME, IIT Kharagpur
Module 3 Design for Srengh Lesson 2 Sress Concenraion Insrucional Objecives A he end of his lesson, he sudens should be able o undersand Sress concenraion and he facors responsible. Deerminaion of sress
More informationChapter 2: Principles of steadystate converter analysis
Chaper 2 Principles of SeadySae Converer Analysis 2.1. Inroducion 2.2. Inducor volsecond balance, capacior charge balance, and he small ripple approximaion 2.3. Boos converer example 2.4. Cuk converer
More informationSection 5.1 The Unit Circle
Secion 5.1 The Uni Circle The Uni Circle EXAMPLE: Show ha he poin, ) is on he uni circle. Soluion: We need o show ha his poin saisfies he equaion of he uni circle, ha is, x +y 1. Since ) ) + 9 + 9 1 P
More informationVoltage level shifting
rek Applicaion Noe Number 1 r. Maciej A. Noras Absrac A brief descripion of volage shifing circuis. 1 Inroducion In applicaions requiring a unipolar A volage signal, he signal may be delivered from a bipolar
More informationEDEXCEL NATIONAL CERTIFICATE/DIPLOMA UNIT 67  FURTHER ELECTRICAL PRINCIPLES NQF LEVEL 3 OUTCOME 2 TUTORIAL 1  TRANSIENTS
EDEXEL NAIONAL ERIFIAE/DIPLOMA UNI 67  FURHER ELERIAL PRINIPLE NQF LEEL 3 OUOME 2 UORIAL 1  RANIEN Uni conen 2 Undersand he ransien behaviour of resisorcapacior (R) and resisorinducor (RL) D circuis
More informationINVESTIGATION OF THE INFLUENCE OF UNEMPLOYMENT ON ECONOMIC INDICATORS
INVESTIGATION OF THE INFLUENCE OF UNEMPLOYMENT ON ECONOMIC INDICATORS Ilona Tregub, Olga Filina, Irina Kondakova Financial Universiy under he Governmen of he Russian Federaion 1. Phillips curve In economics,
More informationRandom Walk in 1D. 3 possible paths x vs n. 5 For our random walk, we assume the probabilities p,q do not depend on time (n)  stationary
Random Walk in D Random walks appear in many cones: diffusion is a random walk process undersanding buffering, waiing imes, queuing more generally he heory of sochasic processes gambling choosing he bes
More informationMachine Learning in Pairs Trading Strategies
Machine Learning in Pairs Trading Sraegies Yuxing Chen (Joseph) Deparmen of Saisics Sanford Universiy Email: osephc5@sanford.edu Weiluo Ren (David) Deparmen of Mahemaics Sanford Universiy Email: weiluo@sanford.edu
More informationAP Calculus BC 2010 Scoring Guidelines
AP Calculus BC Scoring Guidelines The College Board The College Board is a noforprofi membership associaion whose mission is o connec sudens o college success and opporuniy. Founded in, he College Board
More informationA Robust Exponentially Weighted Moving Average Control Chart for the Process Mean
Journal of Modern Applied Saisical Mehods Volume 5 Issue Aricle 005 A Robus Exponenially Weighed Moving Average Conrol Char for he Process Mean Michael B. C. Khoo Universii Sains, Malaysia, mkbc@usm.my
More informationAn empirical analysis about forecasting Tmall airconditioning sales using time series model Yan Xia
An empirical analysis abou forecasing Tmall aircondiioning sales using ime series model Yan Xia Deparmen of Mahemaics, Ocean Universiy of China, China Absrac Time series model is a hospo in he research
More informationContents. Preface P5. Syllabus Reference P7. Flow Chart P10
Preface P1 Conens Preface P5 Syllabus Reference P7 Flow Char P10 Chaer 1 Survival Disribuions C11 1.1 Ageadeah Random Variables C11 1.2 Fuure Lifeime Random Variable C14 1.3 Acuarial Noaion C16
More informationFullwave rectification, bulk capacitor calculations Chris Basso January 2009
ullwave recificaion, bulk capacior calculaions Chris Basso January 9 This shor paper shows how o calculae he bulk capacior value based on ripple specificaions and evaluae he rms curren ha crosses i. oal
More informationChapter 6. First Order PDEs. 6.1 Characteristics The Simplest Case. u(x,t) t=1 t=2. t=0. Suppose u(x, t) satisfies the PDE.
Chaper 6 Firs Order PDEs 6.1 Characerisics 6.1.1 The Simples Case Suppose u(, ) saisfies he PDE where b, c are consan. au + bu = 0 If a = 0, he PDE is rivial (i says ha u = 0 and so u = f(). If a = 0,
More informationMotion Along a Straight Line
Moion Along a Sraigh Line On Sepember 6, 993, Dave Munday, a diesel mechanic by rade, wen over he Canadian edge of Niagara Falls for he second ime, freely falling 48 m o he waer (and rocks) below. On his
More informationYEN FUTURES: EXAMINING HEDGING EFFECTIVENESS BIAS AND CROSSCURRENCY HEDGING RESULTS ROBERT T. DAIGLER FLORIDA INTERNATIONAL UNIVERSITY SUBMITTED FOR
YEN FUTURES: EXAMINING HEDGING EFFECTIVENESS BIAS AND CROSSCURRENCY HEDGING RESULTS ROBERT T. DAIGLER FLORIDA INTERNATIONAL UNIVERSITY SUBMITTED FOR THE FIRST ANNUAL PACIFICBASIN FINANCE CONFERENCE The
More information23.3. Even and Odd Functions. Introduction. Prerequisites. Learning Outcomes
Even and Odd Funcions 23.3 Inroducion In his Secion we examine how o obain Fourier series of periodic funcions which are eiher even or odd. We show ha he Fourier series for such funcions is considerabl
More information( ) in the following way. ( ) < 2
Sraigh Line Moion  Classwork Consider an obbec moving along a sraigh line eiher horizonally or verically. There are many such obbecs naural and manmade. Wrie down several of hem. Horizonal cars waer
More informationGraphing the Von Bertalanffy Growth Equation
file: d:\b1732013\von_beralanffy.wpd dae: Sepember 23, 2013 Inroducion Graphing he Von Beralanffy Growh Equaion Previously, we calculaed regressions of TL on SL for fish size daa and ploed he daa and
More informationRISKBASED REPLACEMENT STRATEGIES FOR REDUNDANT DETERIORATING REINFORCED CONCRETE PIPE NETWORKS
RISKBASED REPLACEMENT STRATEGIES FOR REDUNDANT DETERIORATING REINFORCED CONCRETE PIPE NETWORKS Bryan Adey, Olivier Bernard 2 and Bruno Gerard 2 Division of Mainenance and Safey, Faculy of Archiecure,
More informationThe naive method discussed in Lecture 1 uses the most recent observations to forecast future values. That is, Y ˆ t + 1
Business Condiions & Forecasing Exponenial Smoohing LECTURE 2 MOVING AVERAGES AND EXPONENTIAL SMOOTHING OVERVIEW This lecure inroduces imeseries smoohing forecasing mehods. Various models are discussed,
More informationSensor Network with Multiple Mobile Access Points
Sensor Newor wih Mulile Mobile Access Poins Parvahinahan Veniasubramaniam, Qing Zhao and Lang Tong School of Elecrical and Comuer Engineering Cornell Universiy, Ihaca, NY 4853, USA Email: v45@cornell.edu,{qzhao,long}@ece.cornell.edu
More informationTribology International
Tribology Inernaional 53 (2012) 61 67 Conens liss available a SciVerse ScienceDirec Tribology Inernaional journal homeage: www.elsevier.com/locae/riboin lasic yield inceion of an indened coaed fla and
More information23.3. Even and Odd Functions. Introduction. Prerequisites. Learning Outcomes
Even and Odd Funcions 3.3 Inroducion In his Secion we examine how o obain Fourier series of periodic funcions which are eiher even or odd. We show ha he Fourier series for such funcions is considerabl
More informationStochastic Optimal Control Problem for Life Insurance
Sochasic Opimal Conrol Problem for Life Insurance s. Basukh 1, D. Nyamsuren 2 1 Deparmen of Economics and Economerics, Insiue of Finance and Economics, Ulaanbaaar, Mongolia 2 School of Mahemaics, Mongolian
More informationTerm Structure of Prices of Asian Options
Term Srucure of Prices of Asian Opions Jirô Akahori, Tsuomu Mikami, Kenji Yasuomi and Teruo Yokoa Dep. of Mahemaical Sciences, Risumeikan Universiy 111 Nojihigashi, Kusasu, Shiga 5258577, Japan Email:
More informationChapter 4. Properties of the Least Squares Estimators. Assumptions of the Simple Linear Regression Model. SR3. var(e t ) = σ 2 = var(y t )
Chaper 4 Properies of he Leas Squares Esimaors Assumpions of he Simple Linear Regression Model SR1. SR. y = β 1 + β x + e E(e ) = 0 E[y ] = β 1 + β x SR3. var(e ) = σ = var(y ) SR4. cov(e i, e j ) = cov(y
More informationAnswer, Key Homework 2 David McIntyre 45123 Mar 25, 2004 1
Answer, Key Homework 2 Daid McInyre 4123 Mar 2, 2004 1 This prinou should hae 1 quesions. Muliplechoice quesions may coninue on he ne column or page find all choices before making your selecion. The
More informationINTRODUCTION TO FORECASTING
INTRODUCTION TO FORECASTING INTRODUCTION: Wha is a forecas? Why do managers need o forecas? A forecas is an esimae of uncerain fuure evens (lierally, o "cas forward" by exrapolaing from pas and curren
More informationSteps for D.C Analysis of MOSFET Circuits
10/22/2004 Seps for DC Analysis of MOSFET Circuis.doc 1/7 Seps for D.C Analysis of MOSFET Circuis To analyze MOSFET circui wih D.C. sources, we mus follow hese five seps: 1. ASSUME an operaing mode 2.
More informationOn alternative methods of determining Radius of Curvature using Newton s Rings set up
Inernaional Leers of Chemisry, Physics and Asronomy Online: 0035 ISSN: 993843, Vol. 48, pp 731 doi:10.1805/www.scipress.com/ilcpa.48.7 0 SciPress Ld., Swizerland On alernaive mehods of deermining Radius
More informationMicrostructure of Russian stock market and profitability of market making
КОНСОРЦИУМ ЭКОНОМИЧЕСКИХ ИССЛЕДОВАНИЙ И ОБРАЗОВАНИЯ  РОССИЯ И СНГ ECOOMICS EDUCATIO AD RESEARCH COSORTIUM RUSSIA AD CIS G. Kolodyazhny and A. Medvedev Microsrucure of Russian sock marke and rofiabiliy
More information9. Capacitor and Resistor Circuits
ElecronicsLab9.nb 1 9. Capacior and Resisor Circuis Inroducion hus far we have consider resisors in various combinaions wih a power supply or baery which provide a consan volage source or direc curren
More informationPROFIT TEST MODELLING IN LIFE ASSURANCE USING SPREADSHEETS PART ONE
Profi Tes Modelling in Life Assurance Using Spreadshees PROFIT TEST MODELLING IN LIFE ASSURANCE USING SPREADSHEETS PART ONE Erik Alm Peer Millingon 2004 Profi Tes Modelling in Life Assurance Using Spreadshees
More informationFACULTY OF MATHEMATICAL STUDIES MATHEMATICS FOR PART I ENGINEERING. Lectures
FACULY OF MAHEMAICAL SUDIES MAHEMAICS FOR PAR I ENGINEERING Lecures MODULE 3 FOURIER SERIES Periodic signals Wholerange Fourier series 3 Even and odd uncions Periodic signals Fourier series are used in
More informationRC (ResistorCapacitor) Circuits. AP Physics C
(ResisorCapacior Circuis AP Physics C Circui Iniial Condiions An circui is one where you have a capacior and resisor in he same circui. Suppose we have he following circui: Iniially, he capacior is UNCHARGED
More informationNETWORK TRAFFIC MODELING AND PREDICTION USING MULTIPLICATIVE SEASONAL ARIMA MODELS
1s Inernaional Conference on Exerimens/Process/Sysem Modeling/Simulaion/Oimizaion 1s ICEsMsO Ahens, 69 July, 2005 ICEsMsO NETWORK TRAFFIC MODELING AND PREDICTION USING MULTIPLICATIVE SEASONAL ARIMA
More informationThe Experts In Actuarial Career Advancement. Product Preview. For More Information: email Support@ActexMadRiver.com or call 1(800) 2822839
P U B L I C A T I O N S The Eers In Acuarial Career Advancemen Produc Preview For More Informaion: email Suor@AceMadRiver.com or call (8) 8839 Preface P Conens Preface P7 Syllabus Reference P Flow
More informationA closer look at Black Scholes option thetas
J Econ Finan (2008) 32:59 74 DOI 0.007/s29700790008 A closer look a Black Scholes oion heas Douglas R. Emery & Weiyu Guo & Tie Su Published online: Ocober 2007 # Sringer Science & Business Media, LLC
More informationDifferential Equations. Solving for Impulse Response. Linear systems are often described using differential equations.
Differenial Equaions Linear sysems are ofen described using differenial equaions. For example: d 2 y d 2 + 5dy + 6y f() d where f() is he inpu o he sysem and y() is he oupu. We know how o solve for y given
More informationExponentially Weighted Moving Average Control Charts with TimeVarying Control Limits and Fast Initial Response
Exponenially Weighed Moving Average Conrol Chars wih TimeVarying Conrol Limis and Fas Iniial Response Sefan H. Seiner Dep. of Saisics and Acuarial Sciences Universiy of Waerloo Waerloo, Onario N2L 3G1
More informationMACROECONOMIC FORECASTS AT THE MOF A LOOK INTO THE REAR VIEW MIRROR
MACROECONOMIC FORECASTS AT THE MOF A LOOK INTO THE REAR VIEW MIRROR The firs experimenal publicaion, which summarised pas and expeced fuure developmen of basic economic indicaors, was published by he Minisry
More informationA Note on Using the Svensson procedure to estimate the risk free rate in corporate valuation
A Noe on Using he Svensson procedure o esimae he risk free rae in corporae valuaion By Sven Arnold, Alexander Lahmann and Bernhard Schwezler Ocober 2011 1. The risk free ineres rae in corporae valuaion
More informationEconomics Honors Exam 2008 Solutions Question 5
Economics Honors Exam 2008 Soluions Quesion 5 (a) (2 poins) Oupu can be decomposed as Y = C + I + G. And we can solve for i by subsiuing in equaions given in he quesion, Y = C + I + G = c 0 + c Y D + I
More information4kq 2. D) south A) F B) 2F C) 4F D) 8F E) 16F
efore you begin: Use black pencil. Wrie and bubble your SU ID Number a boom lef. Fill bubbles fully and erase cleanly if you wish o change! 20 Quesions, each quesion is 10 poins. Each quesion has a mos
More informationJournal Of Business & Economics Research September 2005 Volume 3, Number 9
Opion Pricing And Mone Carlo Simulaions George M. Jabbour, (Email: jabbour@gwu.edu), George Washingon Universiy YiKang Liu, (yikang@gwu.edu), George Washingon Universiy ABSTRACT The advanage of Mone Carlo
More informationMA261A Calculus III 2006 Fall Homework 4 Solutions Due 9/29/2006 8:00AM
MA6A Calculus III 006 Fall Homework 4 Soluions Due 9/9/006 00AM 97 #4 Describe in words he surface 3 A halflane in he osiive x and y erriory (See Figure in Page 67) 97 # Idenify he surface cos We see
More informationModule 4. Singlephase AC circuits. Version 2 EE IIT, Kharagpur
Module 4 Singlephase A circuis ersion EE T, Kharagpur esson 5 Soluion of urren in A Series and Parallel ircuis ersion EE T, Kharagpur n he las lesson, wo poins were described:. How o solve for he impedance,
More informationTime Series Analysis Using SAS R Part I The Augmented DickeyFuller (ADF) Test
ABSTRACT Time Series Analysis Using SAS R Par I The Augmened DickeyFuller (ADF) Tes By Ismail E. Mohamed The purpose of his series of aricles is o discuss SAS programming echniques specifically designed
More informationWHAT ARE OPTION CONTRACTS?
WHAT ARE OTION CONTRACTS? By rof. Ashok anekar An oion conrac is a derivaive which gives he righ o he holder of he conrac o do 'Somehing' bu wihou he obligaion o do ha 'Somehing'. The 'Somehing' can be
More informationTwo Compartment Body Model and V d Terms by Jeff Stark
Two Comparmen Body Model and V d Terms by Jeff Sark In a onecomparmen model, we make wo imporan assumpions: (1) Linear pharmacokineics  By his, we mean ha eliminaion is firs order and ha pharmacokineic
More informationCLASSICAL TIME SERIES DECOMPOSITION
Time Series Lecure Noes, MSc in Operaional Research Lecure CLASSICAL TIME SERIES DECOMPOSITION Inroducion We menioned in lecure ha afer we calculaed he rend, everyhing else ha remained (according o ha
More informationPHYS245 Lab: RC circuits
PHYS245 Lab: C circuis Purpose: Undersand he charging and discharging ransien processes of a capacior Display he charging and discharging process using an oscilloscope Undersand he physical meaning of
More information