Tom BLASINGAME Texas A&M U. Slide 1
|
|
- Giles Small
- 5 years ago
- Views:
Transcription
1 Fundamental Flow Lecture 3 Materal Balance Concets Slde 1
2 Fundamental Flow Lecture 3 Materal Balance Concets Slde 2
3 Fundamental Flow Lecture 3 Materal Balance Concets Materal Balance Notes from Deartment of Petroleum Engneerng Course Notes (2012) Slde 3
4 Fundamental Flow Lecture 3 Materal Balance Concets Materal Balance Reservor Engneerng Asects "Accountng" Concet of Materal Balance: Requre all nflows/outflows/generatons. (Average) reservor ressure rofle s REQUIRED. Requre rock, flud, and rock-flud roertes (at some scale). Ol Materal Balance: Less common than gas materal balance (ressure requred). Gas Materal Balance: Volumetrc dry gas reservor (/z versus G (straght-lne)). Abnormally-ressured gas reservors (varous technques). Waterdrve/water nflux cases (always roblematc) (.e., we don't know the nflux, so we use a model). Materal Balance yelds RESERVOIR VOLUME! (Materal Balance Notes from Deartment of Petroleum Engneerng Course Notes (2012)) Slde 4
5 Fundamental Flow Lecture 3 Materal Balance Concets Materal Balance Concet Dagram General Concet of Materal Balance... a. Intal reservor condtons. b. Condtons after roducng N STB of ol, and G SCF of gas, and W STB of water. From: Petroleum Reservor Engneerng Amyx, Bass, and Whtng (1960). Materal Balance: Key Issues Must have accurate roducton measurements (ol, water, gas). Estmates of average reservor ressure (from ressure tests). Sutes of PVT data (ol, gas, water). Reservor roertes: saturatons, formaton comressblty, etc. (Materal Balance Notes from Deartment of Petroleum Engneerng Course Notes (2012)) Slde 5
6 Fundamental Flow Lecture 3 Materal Balance Concets Materal Balance Average Reservor Pressure Average Reservor Pressure From: Engneerng Features of the Schuler Feld and Unt Oeraton Kaveler (SPE-AIME, 1944). Average Reservor Pressure: Key Issues Must "average" ressures over volume or area (aroxmaton). Pressure tests must be reresentatve ( avg extraolaton vald). Can average usng cumulatve roducton (surrogate for volume). (Materal Balance Notes from Deartment of Petroleum Engneerng Course Notes (2012)) Slde 6
7 Fundamental Flow Lecture 3 Materal Balance Concets Materal Balance Examle Black Ol From: Alcaton of the Materal Balance to a Partal Waterdrve Reservor van Everdngen (SPE, 1953). Black Ol Materal Balance Case: (Examle) Note that all flud functons are gven: N, W, and GOR (for G ). Average reservor ressure s resumed correct. Authors cte "artal waterdrve" remans a contentous ssue. (Materal Balance Notes from Deartment of Petroleum Engneerng Course Notes (2012)) Slde 7
8 Fundamental Flow Lecture 3 Materal Balance Concets Materal Balance Relatons Black Ol Ol Materal Balance Relatons: "Black Ol" Materal Balance: (> b ) 1 B o N Nct Bo "Soluton Gas Drve" (Ol) Materal Balance: (all ) N B o ( R R s ) B g W B w (Wthdrawal (RB)) N ( B o B o ) ( R s R s ) B g (Ol Exanson (RB)) mnb W B e o (1 m) NB w B B g g o 1 ( c S w w (1 S c w ) f ) ( ) (Gas Ca Exanson (RB)) (Water Ex./Pore Vol. Com. (RB)) (Water Influx (RB)) (Materal Balance Notes from Deartment of Petroleum Engneerng Course Notes (2012)) Slde 8
9 Fundamental Flow Lecture 3 Materal Balance Concets General Gas Materal Balance: "Dry Gas" Materal Balance: (no reservor lquds ) "Abnormal Pressure" Materal Balance: (c f =f()) e w nj g sw nj e W B W W B R W G G G z z c z ) ( ) )( ( 1 G G z z 1 1 G G c z z e 1 ) )( ( 1 1 ) ( ) (1 1 ) ( f w R AQ R NNP f w w w e c c V V V V c c S S c Gas Materal Balance Relatons: (Materal Balance Notes from Deartment of Petroleum Engneerng Course Notes (2012)) Materal Balance Relatons Dry Gas Slde 9
10 Fundamental Flow Lecture 3 Materal Balance Concets Materal Balance Relatons Volumetrc Dry Gas "Dry Gas" Materal Balance: Normally Pressured Reservor Examle Volumetrc reservor no external energy (gas exanson only). /z versus G yelds unque straght-lne trend. Lnear extraolaton yeld gas-n-lace (G). (Materal Balance Notes from Deartment of Petroleum Engneerng Course Notes (2012)) Slde 10
11 Fundamental Flow Lecture 3 Materal Balance Concets Materal Balance Relatons "Abnormal Pressure" Dry Gas "Dry Gas" Materal Balance: Abnormally Pressured Reservor Examle Volumetrc reservor no water nflux or leakage. /z versus G yelds unque quadratc trend (from aroxmated MBE). Quadratc extraolaton yeld gas-n-lace (G). (Materal Balance Notes from Deartment of Petroleum Engneerng Course Notes (2012)) Slde 11
12 Fundamental Flow Lecture 3 Materal Balance Concets Materal Balance Relatons "Water Influx" Dry Gas a. Gas Materal Balance Plot: /z vs. G smulated erformance. Note effect of aqufer ermeablty on feld erformance. b. Gas Materal Balance Plot: /z vs. G smulated erformance. Note effect of dslacement effcency (E ). Gas Materal Balance: Water Drve Gas Reservor Pressure (hence /z) s mantaned durng roducton va communcaton wth an unsteadystate aqufer (ths study). Unsteady-State Performance of Water Drve Gas Reservors, Agarwal (Texas A&M Ph.D., 1967). (Materal Balance Notes from Deartment of Petroleum Engneerng Course Notes (2012)) Slde 12
13 Fundamental Flow Lecture 3 Materal Balance Concets Volumetrc Ol Reservors Materal Balance Notes from Deartment of Petroleum Engneerng Course Notes (1984) Slde 13
14 Fundamental Flow Lecture 3 Materal Balance Concets [Volumetrc Ol Reservors] (Materal Balance Notes from Deartment of Petroleum Engneerng Course Notes (1984)) Slde 14
15 Fundamental Flow Lecture 3 Materal Balance Concets [Volumetrc Ol Reservors] (Materal Balance Notes from Deartment of Petroleum Engneerng Course Notes (1984)) Slde 15
16 Fundamental Flow Lecture 3 Materal Balance Concets [Volumetrc Ol Reservors] (Materal Balance Notes from Deartment of Petroleum Engneerng Course Notes (1984)) Slde 16
17 Fundamental Flow Lecture 3 Materal Balance Concets Gas Reservors Materal Balance Notes from Deartment of Petroleum Engneerng Course Notes (1984) Slde 17
18 Fundamental Flow Lecture 3 Materal Balance Concets [Gas Reservors] (Materal Balance Notes from Deartment of Petroleum Engneerng Course Notes (1984)) Slde 18
Petroleum Engineering 324 Reservoir Performance. Material Balance 16 February 2007
Petroleum Engineering 324 Reservoir Performance Material Balance 16 February 2007 Thomas A. Blasingame, Ph.D., P.E. Deartment of Petroleum Engineering Texas A&M University College Station, TX 77843-3116
More informationA Quadratic Cumulative Production Model for the Material Balance of Abnormally-Pressured Gas Reservoirs F.E. Gonzalez M.S.
Formaton Evaluaton and the Analyss of Reservor Performance A Quadratc Cumulatve Producton Model for the Materal Balance of Abnormally-Pressured as Reservors F.E. onale M.S. Thess (2003) T.A. Blasngame,
More informationA Quadratic Cumulative Production Model for the Material Balance of Abnormally-Pressured Gas Reservoirs F.E. Gonzalez M.S.
Natural as Engneerng A Quadratc Cumulatve Producton Model for the Materal Balance of Abnormally-Pressured as Reservors F.E. onale M.S. Thess (2003) T.A. Blasngame, Texas A&M U. Deartment of Petroleum Engneerng
More informationPetroleum Engineering 324 Well Performance Daily Summary Sheet Spring 2009 Blasingame/Ilk. Date: Materials Covered in Class Today: Comment(s):
Petroleum Engineering 324 Well Performance Daily Summary Sheet Sring 2009 Blasingame/Ilk Date: Materials Covered in Class Today: Comment(s): Petroleum Engineering 324 (2009) Reservoir Performance Material
More informationStatistical Material Balance Analysis of Water Drive Reservoirs
Abstract Research Journal of Chemcal Scences E-ISSN 2231-606X Res. J. Chem. Sc. Statstcal ateral Balance Analyss of Water Drve Reservors Adeloye Olalean chael 1*, Ejofor Chnonso Declan 2 and Abu Robn Nyemenm
More informationWater-drive gas reservoir: sensitivity analysis and simplified prediction
Lousana State Unversty LSU Dgtal Commons LSU Master's Theses Graduate School 00 Water-drve gas reservor: senstvty analyss and smlfed redcton Juneng Yue Lousana State Unversty and Agrcultural and Mechancal
More informationAssignment 4. Adsorption Isotherms
Insttute of Process Engneerng Assgnment 4. Adsorpton Isotherms Part A: Compettve adsorpton of methane and ethane In large scale adsorpton processes, more than one compound from a mxture of gases get adsorbed,
More informationNon-Ideality Through Fugacity and Activity
Non-Idealty Through Fugacty and Actvty S. Patel Deartment of Chemstry and Bochemstry, Unversty of Delaware, Newark, Delaware 19716, USA Corresondng author. E-mal: saatel@udel.edu 1 I. FUGACITY In ths dscusson,
More informationA New Analytical Method for Analyzing Linear Flow in Tight/Shale Gas Reservoirs: Constant-Flowing-Pressure Boundary Condition
A New Analytcal Method for Analyzng Lnear Flow n Tght/Shale Gas Reservors: Constant-Flowng-Pressure Boundary Condton Morteza Nobakht, * SPE, Unversty of Calgary and Fekete Assocates, and C.R. Clarkson,
More informationLecture # 02: Pressure measurements and Measurement Uncertainties
AerE 3L & AerE343L Lecture Notes Lecture # 0: Pressure measurements and Measurement Uncertantes Dr. Hu H Hu Deartment of Aerosace Engneerng Iowa State Unversty Ames, Iowa 500, U.S.A Mechancal Pressure
More informationA Quadratic Cumulative Production Model for the Material Balance of Abnormally-Pressured Gas Reservoirs
A Quadratic Cumulative Production Model for the Material Balance of Abnormally-Pressured as Reservoirs F.E. onale, M.S. Thesis Defense 7 October 2003 Deartment of Petroleum Engineering Texas A&M University
More informationAdvanced Topics in Optimization. Piecewise Linear Approximation of a Nonlinear Function
Advanced Tocs n Otmzaton Pecewse Lnear Aroxmaton of a Nonlnear Functon Otmzaton Methods: M8L Introducton and Objectves Introducton There exsts no general algorthm for nonlnear rogrammng due to ts rregular
More informationPETE 310 Lectures # 24 & 25 Chapter 12 Gas Liquid Equilibrium
ETE 30 Lectures # 24 & 25 Chapter 2 Gas Lqud Equlbrum Thermal Equlbrum Object A hgh T, Object B low T Intal contact tme Intermedate tme. Later tme Mechancal Equlbrum ressure essels Vale Closed Vale Open
More informationEN40: Dynamics and Vibrations. Homework 4: Work, Energy and Linear Momentum Due Friday March 1 st
EN40: Dynamcs and bratons Homework 4: Work, Energy and Lnear Momentum Due Frday March 1 st School of Engneerng Brown Unversty 1. The fgure (from ths publcaton) shows the energy per unt area requred to
More informationMATERIAL BALANCE CALCULATIONS FOR PETROLEUM RESERVOIRS
MATERIAL BALANCE CALCULATIONS FOR PETROLEUM RESERVOIRS Hassan S. Naji, Professor, hnaji@kau.edu.sa In 1936, Schilthuis develoed a general material balance equation that can be alied to all reservoir tyes.
More informationOPTIMISATION. Introduction Single Variable Unconstrained Optimisation Multivariable Unconstrained Optimisation Linear Programming
OPTIMIATION Introducton ngle Varable Unconstraned Optmsaton Multvarable Unconstraned Optmsaton Lnear Programmng Chapter Optmsaton /. Introducton In an engneerng analss, sometmes etremtes, ether mnmum or
More informationLecture 3 Examples and Problems
Lecture 3 Examles and Problems Mechancs & thermodynamcs Equartton Frst Law of Thermodynamcs Ideal gases Isothermal and adabatc rocesses Readng: Elements Ch. 1-3 Lecture 3, 1 Wllam Thomson (1824 1907) a.k.a.
More informationCHE-201. I n t r o d u c t i o n t o Chemical E n g i n e e r i n g. C h a p t e r 6. Multiphase Systems
I n t r o d u c t o n t o Chemcal E n g n e e r n g CHE-201 I N S T R U C T O R : D r. N a b e e l S a l m b o - G h a n d e r C h a t e r 6 Multhase Systems Introductory Statement: Phase s a state of
More informationME 440 Aerospace Engineering Fundamentals
Fall 006 ME 440 Aerosace Engneerng Fundamentals roulson hrust Jet Engne F m( & Rocket Engne F m & F ρ A - n ) ρ A he basc rncle nsde the engne s to convert the ressure and thermal energy of the workng
More informationLinear system of the Schrödinger equation Notes on Quantum Mechanics
Lnear sstem of the Schrödnger equaton Notes on Quantum Mechancs htt://quantum.bu.edu/notes/quantummechancs/lnearsstems.df Last udated Wednesda, October 9, 003 :0:08 Corght 003 Dan Dll (dan@bu.edu) Deartment
More informationPID Controller Design Based on Second Order Model Approximation by Using Stability Boundary Locus Fitting
PID Controller Desgn Based on Second Order Model Aroxmaton by Usng Stablty Boundary Locus Fttng Furkan Nur Denz, Bars Baykant Alagoz and Nusret Tan Inonu Unversty, Deartment of Electrcal and Electroncs
More informationApplication of Material Balance Equations of Multicompartment Gas Reservoirs in YC Gas Reservoir
Internatonal Conference on Manufacturng Scence and Engneerng (ICMSE ) Applcaton of Materal Balance Equatons of Multcompartment as Reservors n YC as Reservor Quan-Hua Huang, a, Chong Chen, b, Lang Yn, c,
More informationEstimation of the composition of the liquid and vapor streams exiting a flash unit with a supercritical component
Department of Energ oltecnco d Mlano Va Lambruschn - 05 MILANO Eercses of Fundamentals of Chemcal rocesses rof. Ganpero Gropp Eercse 8 Estmaton of the composton of the lqud and vapor streams etng a unt
More informationThe Ordinary Least Squares (OLS) Estimator
The Ordnary Least Squares (OLS) Estmator 1 Regresson Analyss Regresson Analyss: a statstcal technque for nvestgatng and modelng the relatonshp between varables. Applcatons: Engneerng, the physcal and chemcal
More information( ) 2 ( ) ( ) Problem Set 4 Suggested Solutions. Problem 1
Problem Set 4 Suggested Solutons Problem (A) The market demand functon s the soluton to the followng utlty-maxmzaton roblem (UMP): The Lagrangean: ( x, x, x ) = + max U x, x, x x x x st.. x + x + x y x,
More informationGasometric Determination of NaHCO 3 in a Mixture
60 50 40 0 0 5 15 25 35 40 Temperature ( o C) 9/28/16 Gasometrc Determnaton of NaHCO 3 n a Mxture apor Pressure (mm Hg) apor Pressure of Water 1 NaHCO 3 (s) + H + (aq) Na + (aq) + H 2 O (l) + CO 2 (g)
More informationOn incorporating time-lapse seismic survey data into automatic history matching of reservoir simulations
ontents On ncorporatng tme-lapse sesmc survey data On ncorporatng tme-lapse sesmc survey data nto automatc hstory matchng of reservor smulatons Laurence R. Bentley BSTRT orosty, permeablty and other parameters
More informationEvaluating Thermodynamic Properties in LAMMPS
D. Keffer ME 64 Det. of Materals cence & Engneerng Unversty of ennessee Knoxvlle Evaluatng hermodynamc Proertes n LAMMP Davd Keffer Deartment of Materals cence & Engneerng Unversty of ennessee Knoxvlle
More informationNormally, in one phase reservoir simulation we would deal with one of the following fluid systems:
TPG4160 Reservor Smulaton 2017 page 1 of 9 ONE-DIMENSIONAL, ONE-PHASE RESERVOIR SIMULATION Flud systems The term sngle phase apples to any system wth only one phase present n the reservor In some cases
More informationFall 2012 Analysis of Experimental Measurements B. Eisenstein/rev. S. Errede
Fall 0 Analyss of Expermental easurements B. Esensten/rev. S. Errede We now reformulate the lnear Least Squares ethod n more general terms, sutable for (eventually extendng to the non-lnear case, and also
More informationChapter 11: Simple Linear Regression and Correlation
Chapter 11: Smple Lnear Regresson and Correlaton 11-1 Emprcal Models 11-2 Smple Lnear Regresson 11-3 Propertes of the Least Squares Estmators 11-4 Hypothess Test n Smple Lnear Regresson 11-4.1 Use of t-tests
More information290 IEEE TRANSACTIONS ON CIRCUITS AND SYSTEMS I: FUNDAMENTAL THEORY AND APPLICATIONS, VOL. 45, NO. 3, MARCH H d (e j! ;e j!
9 IEEE TRANSACTIONS ON CIRCUITS AND SYSTEMS I: FUNDAMENTAL THEORY AND APPLICATIONS, VOL. 45, NO. 3, MARCH 998 Transactons Brefs Two-Dmensonal FIR Notch Flter Desgn Usng Sngular Value Decomoston S.-C. Pe,
More informationModel Reference Adaptive Temperature Control of the Electromagnetic Oven Process in Manufacturing Process
RECENT ADVANCES n SIGNAL PROCESSING, ROBOTICS and AUTOMATION Model Reference Adatve Temerature Control of the Electromagnetc Oven Process n Manufacturng Process JIRAPHON SRISERTPOL SUPOT PHUNGPHIMAI School
More informationLesson 16: Basic Control Modes
0/8/05 Lesson 6: Basc Control Modes ET 438a Automatc Control Systems Technology lesson6et438a.tx Learnng Objectves Ater ths resentaton you wll be able to: Descrbe the common control modes used n analog
More informationOn New Selection Procedures for Unequal Probability Sampling
Int. J. Oen Problems Comt. Math., Vol. 4, o. 1, March 011 ISS 1998-66; Coyrght ICSRS Publcaton, 011 www.-csrs.org On ew Selecton Procedures for Unequal Probablty Samlng Muhammad Qaser Shahbaz, Saman Shahbaz
More information#64. ΔS for Isothermal Mixing of Ideal Gases
#64 Carnot Heat Engne ΔS for Isothermal Mxng of Ideal Gases ds = S dt + S T V V S = P V T T V PV = nrt, P T ds = v T = nr V dv V nr V V = nrln V V = - nrln V V ΔS ΔS ΔS for Isothermal Mxng for Ideal Gases
More informationRELIABILITY ASSESSMENT
CHAPTER Rsk Analyss n Engneerng and Economcs RELIABILITY ASSESSMENT A. J. Clark School of Engneerng Department of Cvl and Envronmental Engneerng 4a CHAPMAN HALL/CRC Rsk Analyss for Engneerng Department
More informationChapter Eight. Review and Summary. Two methods in solid mechanics ---- vectorial methods and energy methods or variational methods
Chapter Eght Energy Method 8. Introducton 8. Stran energy expressons 8.3 Prncpal of statonary potental energy; several degrees of freedom ------ Castglano s frst theorem ---- Examples 8.4 Prncpal of statonary
More informationCOMPOSITE BEAM WITH WEAK SHEAR CONNECTION SUBJECTED TO THERMAL LOAD
COMPOSITE BEAM WITH WEAK SHEAR CONNECTION SUBJECTED TO THERMAL LOAD Ákos Jósef Lengyel, István Ecsed Assstant Lecturer, Professor of Mechancs, Insttute of Appled Mechancs, Unversty of Mskolc, Mskolc-Egyetemváros,
More informationLogistic regression with one predictor. STK4900/ Lecture 7. Program
Logstc regresson wth one redctor STK49/99 - Lecture 7 Program. Logstc regresson wth one redctor 2. Maxmum lkelhood estmaton 3. Logstc regresson wth several redctors 4. Devance and lkelhood rato tests 5.
More information36.1 Why is it important to be able to find roots to systems of equations? Up to this point, we have discussed how to find the solution to
ChE Lecture Notes - D. Keer, 5/9/98 Lecture 6,7,8 - Rootndng n systems o equatons (A) Theory (B) Problems (C) MATLAB Applcatons Tet: Supplementary notes rom Instructor 6. Why s t mportant to be able to
More informationCinChE Problem-Solving Strategy Chapter 4 Development of a Mathematical Model. formulation. procedure
nhe roblem-solvng Strategy hapter 4 Transformaton rocess onceptual Model formulaton procedure Mathematcal Model The mathematcal model s an abstracton that represents the engneerng phenomena occurrng n
More informationLecture 13 APPROXIMATION OF SECOMD ORDER DERIVATIVES
COMPUTATIONAL FLUID DYNAMICS: FDM: Appromaton of Second Order Dervatves Lecture APPROXIMATION OF SECOMD ORDER DERIVATIVES. APPROXIMATION OF SECOND ORDER DERIVATIVES Second order dervatves appear n dffusve
More informationSTUDY ON TWO PHASE FLOW IN MICRO CHANNEL BASED ON EXPERI- MENTS AND NUMERICAL EXAMINATIONS
Blucher Mechancal Engneerng Proceedngs May 0, vol., num. www.proceedngs.blucher.com.br/evento/0wccm STUDY ON TWO PHASE FLOW IN MICRO CHANNEL BASED ON EXPERI- MENTS AND NUMERICAL EXAMINATIONS Takahko Kurahash,
More informationName: SID: Discussion Session:
Name: SID: Dscusson Sesson: Chemcal Engneerng Thermodynamcs 141 -- Fall 007 Thursday, November 15, 007 Mdterm II SOLUTIONS - 70 mnutes 110 Ponts Total Closed Book and Notes (0 ponts) 1. Evaluate whether
More informationNote 10. Modeling and Simulation of Dynamic Systems
Lecture Notes of ME 475: Introducton to Mechatroncs Note 0 Modelng and Smulaton of Dynamc Systems Department of Mechancal Engneerng, Unversty Of Saskatchewan, 57 Campus Drve, Saskatoon, SK S7N 5A9, Canada
More informationCALCU THIRD EDITION. Monfy J. Strauss. Texas Tech University. Gerald L Bradley. Claremont McKenna College. Karl J. Smith. Santa Rosa Junior College
CALCU THIRD EDITION Monfy J. Strauss Texas Tech Unversty Gerald L Bradley Claremont McKenna College Karl J. Smth Santa Rosa Junor College Prentce Hall, Upper Saddle Rver, New Jersey 07458 Preface x 1 Functons
More informationFuzzy approach to solve multi-objective capacitated transportation problem
Internatonal Journal of Bonformatcs Research, ISSN: 0975 087, Volume, Issue, 00, -0-4 Fuzzy aroach to solve mult-objectve caactated transortaton roblem Lohgaonkar M. H. and Bajaj V. H.* * Deartment of
More informationScatter Plot x
Construct a scatter plot usng excel for the gven data. Determne whether there s a postve lnear correlaton, negatve lnear correlaton, or no lnear correlaton. Complete the table and fnd the correlaton coeffcent
More informationAnalytical calculation of adiabatic processes in real gases
Journal of Physs: Conferene Seres PAPER OPEN ACCESS Analytal alulaton of adabat roesses n real gases o te ths artle: I B Amarskaja et al 016 J. Phys.: Conf. Ser. 754 11003 Related ontent - Shortuts to
More informationThermal-Fluids I. Chapter 18 Transient heat conduction. Dr. Primal Fernando Ph: (850)
hermal-fluds I Chapter 18 ransent heat conducton Dr. Prmal Fernando prmal@eng.fsu.edu Ph: (850) 410-6323 1 ransent heat conducton In general, he temperature of a body vares wth tme as well as poston. In
More informationAdsorption: A gas or gases from a mixture of gases or a liquid (or liquids) from a mixture of liquids is bound physically to the surface of a solid.
Searatons n Chemcal Engneerng Searatons (gas from a mxture of gases, lquds from a mxture of lquds, solds from a soluton of solds n lquds, dssolved gases from lquds, solvents from gases artally/comletely
More informationOutline. Unit Eight Calculations with Entropy. The Second Law. Second Law Notes. Uses of Entropy. Entropy is a Property.
Unt Eght Calculatons wth Entropy Mechancal Engneerng 370 Thermodynamcs Larry Caretto October 6, 010 Outlne Quz Seven Solutons Second law revew Goals for unt eght Usng entropy to calculate the maxmum work
More informationPage 1. Physics 131: Lecture 14. Today s Agenda. Things that stay the same. Impulse and Momentum Non-constant forces
Physcs 131: Lecture 14 Today s Agenda Imulse and Momentum Non-constant forces Imulse-momentum momentum thm Conservaton of Lnear momentum Eternal/Internal forces Eamles Physcs 201: Lecture 1, Pg 1 Physcs
More informationLINEAR REGRESSION ANALYSIS. MODULE IX Lecture Multicollinearity
LINEAR REGRESSION ANALYSIS MODULE IX Lecture - 30 Multcollnearty Dr. Shalabh Department of Mathematcs and Statstcs Indan Insttute of Technology Kanpur 2 Remedes for multcollnearty Varous technques have
More informationLOGIT ANALYSIS. A.K. VASISHT Indian Agricultural Statistics Research Institute, Library Avenue, New Delhi
LOGIT ANALYSIS A.K. VASISHT Indan Agrcultural Statstcs Research Insttute, Lbrary Avenue, New Delh-0 02 amtvassht@asr.res.n. Introducton In dummy regresson varable models, t s assumed mplctly that the dependent
More informationPrinciples of Food and Bioprocess Engineering (FS 231) Solutions to Example Problems on Heat Transfer
Prncples of Food and Boprocess Engneerng (FS 31) Solutons to Example Problems on Heat Transfer 1. We start wth Fourer s law of heat conducton: Q = k A ( T/ x) Rearrangng, we get: Q/A = k ( T/ x) Here,
More informationIonization fronts in HII regions
Ionzaton fronts n HII regons Intal expanson of HII onzaton front s supersonc, creatng a shock front. Statonary frame: front advances nto neutral materal In frame where shock front s statonary, neutral
More informationNote: Please use the actual date you accessed this material in your citation.
MIT OpenCourseWare http://ocw.mt.edu 6.13/ESD.13J Electromagnetcs and Applcatons, Fall 5 Please use the followng ctaton format: Markus Zahn, Erch Ippen, and Davd Staeln, 6.13/ESD.13J Electromagnetcs and
More informationChapter 2. Volumetric Gas Reservoir Engineering
Chater 2 Volumetrc as Reservor ngneerng References (B) Dake, L.P., Fundamentals of Reservor ngneerng, revsed edton, lsever Scentfc B.V., Amsterdam, the Netherlands, 200. (C) Craft, B.C., and Hakns, M.F.,
More informationa for save as PDF Chemistry 163B Introduction to Multicomponent Systems and Partial Molar Quantities
a for save as PDF Chemstry 163B Introducton to Multcomponent Systems and Partal Molar Quanttes 1 the problem of partal mmolar quanttes mx: 10 moles ethanol C 2 H 5 OH (580 ml) wth 1 mole water H 2 O (18
More informationLimited Dependent Variables
Lmted Dependent Varables. What f the left-hand sde varable s not a contnuous thng spread from mnus nfnty to plus nfnty? That s, gven a model = f (, β, ε, where a. s bounded below at zero, such as wages
More information(1985), Reddy and venkateswarlu (1988) are some of the authors who have investigated various aspects of the four di-
Internatonal Journal of Scentfc & Engneerng Research, Volume 5, Issue 3, March-14 99 Wet dark flud Cosmologcal Model n Lyra s Manfold.S.Nmkar, M.R.Ugale.M.Pund bstract : In ths aer, we have obtaned feld
More informationThe Tangential Force Distribution on Inner Cylinder of Power Law Fluid Flowing in Eccentric Annuli with the Inner Cylinder Reciprocating Axially
Open Journal of Flud Dynamcs, 2015, 5, 183-187 Publshed Onlne June 2015 n ScRes. http://www.scrp.org/journal/ojfd http://dx.do.org/10.4236/ojfd.2015.52020 The Tangental Force Dstrbuton on Inner Cylnder
More informationExercises of Fundamentals of Chemical Processes
Department of Energ Poltecnco d Mlano a Lambruschn 4 2056 MILANO Exercses of undamentals of Chemcal Processes Prof. Ganpero Gropp Exercse 7 ) Estmaton of the composton of the streams at the ext of an sothermal
More informationIn this section is given an overview of the common elasticity models.
Secton 4.1 4.1 Elastc Solds In ths secton s gven an overvew of the common elastcty models. 4.1.1 The Lnear Elastc Sold The classcal Lnear Elastc model, or Hooean model, has the followng lnear relatonshp
More informationTopic 5: Non-Linear Regression
Topc 5: Non-Lnear Regresson The models we ve worked wth so far have been lnear n the parameters. They ve been of the form: y = Xβ + ε Many models based on economc theory are actually non-lnear n the parameters.
More information( ) 1/ 2. ( P SO2 )( P O2 ) 1/ 2.
Chemstry 360 Dr. Jean M. Standard Problem Set 9 Solutons. The followng chemcal reacton converts sulfur doxde to sulfur troxde. SO ( g) + O ( g) SO 3 ( l). (a.) Wrte the expresson for K eq for ths reacton.
More informationChapter 9: Statistical Inference and the Relationship between Two Variables
Chapter 9: Statstcal Inference and the Relatonshp between Two Varables Key Words The Regresson Model The Sample Regresson Equaton The Pearson Correlaton Coeffcent Learnng Outcomes After studyng ths chapter,
More informationThe Finite Element Method
The Fnte Element Method GENERAL INTRODUCTION Read: Chapters 1 and 2 CONTENTS Engneerng and analyss Smulaton of a physcal process Examples mathematcal model development Approxmate solutons and methods of
More informationA Modulated Hydrothermal (MHT) Approach for the Facile. Synthesis of UiO-66-Type MOFs
Supplementary Informaton A Modulated Hydrothermal (MHT) Approach for the Facle Synthess of UO-66-Type MOFs Zhgang Hu, Yongwu Peng, Zx Kang, Yuhong Qan, and Dan Zhao * Department of Chemcal and Bomolecular
More informationMore metrics on cartesian products
More metrcs on cartesan products If (X, d ) are metrc spaces for 1 n, then n Secton II4 of the lecture notes we defned three metrcs on X whose underlyng topologes are the product topology The purpose of
More informationPh.D. Qualifying Examination in Kinetics and Reactor Design
Knetcs and Reactor Desgn Ph.D.Qualfyng Examnaton January 2006 Instructons Ph.D. Qualfyng Examnaton n Knetcs and Reactor Desgn January 2006 Unversty of Texas at Austn Department of Chemcal Engneerng 1.
More informationEXCESS FUNCTIONS MATHEMATICAL EXPLANATION
EXCESS FUNCTIONS Excess functons... 1 Mathematcal exlanaton... 1 Physcal examle: Molar volume of a ure substance... 2 Chemcal otental for a ure substance... 3 Actvty, actvty coeffcent and fugacty (ure
More informationDr. Shalabh Department of Mathematics and Statistics Indian Institute of Technology Kanpur
Analyss of Varance and Desgn of Exerments-I MODULE III LECTURE - 2 EXPERIMENTAL DESIGN MODELS Dr. Shalabh Deartment of Mathematcs and Statstcs Indan Insttute of Technology Kanur 2 We consder the models
More informationMass Transfer Processes
Mass Transfer Processes S. Majd Hassanzadeh Department of Earth Scences Faculty of Geoscences Utrecht Unversty Outlne: 1. Measures of Concentraton 2. Volatlzaton and Dssoluton 3. Adsorpton Processes 4.
More informationReport on Image warping
Report on Image warpng Xuan Ne, Dec. 20, 2004 Ths document summarzed the algorthms of our mage warpng soluton for further study, and there s a detaled descrpton about the mplementaton of these algorthms.
More informationSupplementary Notes for Chapter 9 Mixture Thermodynamics
Supplementary Notes for Chapter 9 Mxture Thermodynamcs Key ponts Nne major topcs of Chapter 9 are revewed below: 1. Notaton and operatonal equatons for mxtures 2. PVTN EOSs for mxtures 3. General effects
More informationAnnouncements EWA with ɛ-exploration (recap) Lecture 20: EXP3 Algorithm. EECS598: Prediction and Learning: It s Only a Game Fall 2013.
Lecture 0: EXP3 Algorthm 1 EECS598: Predcton and Learnng: It s Only a Game Fall 013 Prof. Jacob Abernethy Lecture 0: EXP3 Algorthm Scrbe: Zhhao Chen Announcements None 0.1 EWA wth ɛ-exploraton (recap)
More informationSpectral method for fractional quadratic Riccati differential equation
Journal of Aled Matheatcs & Bonforatcs vol2 no3 212 85-97 ISSN: 1792-662 (rnt) 1792-6939 (onlne) Scenress Ltd 212 Sectral ethod for fractonal quadratc Rccat dfferental equaton Rostay 1 K Kar 2 L Gharacheh
More informationCS 468 Lecture 16: Isometry Invariance and Spectral Techniques
CS 468 Lecture 16: Isometry Invarance and Spectral Technques Justn Solomon Scrbe: Evan Gawlk Introducton. In geometry processng, t s often desrable to characterze the shape of an object n a manner that
More informationNotes prepared by Prof Mrs) M.J. Gholba Class M.Sc Part(I) Information Technology
Inverse transformatons Generaton of random observatons from gven dstrbutons Assume that random numbers,,, are readly avalable, where each tself s a random varable whch s unformly dstrbuted over the range(,).
More informationBayesian Decision Theory
No.4 Bayesan Decson Theory Hu Jang Deartment of Electrcal Engneerng and Comuter Scence Lassonde School of Engneerng York Unversty, Toronto, Canada Outlne attern Classfcaton roblems Bayesan Decson Theory
More informationComparative Study of Oil Production Forecast by Decline Curve Analysis and Material Balance
EJERS, European Journal of Engneerng Research and Scence Vol. 3, No. 4, Aprl 2018 Comparatve Study of Ol Producton Forecast y Declne Curve Analyss and Materal Balance Anyadegwu Charley Iyke and Oha Nnaemeka
More informationPattern Classification
attern Classfcaton All materals n these sldes were taken from attern Classfcaton nd ed by R. O. Duda,. E. Hart and D. G. Stork, John Wley & Sons, 000 wth the ermsson of the authors and the ublsher Chater
More informationPattern Classification
Pattern Classfcaton All materals n these sldes ere taken from Pattern Classfcaton (nd ed) by R. O. Duda, P. E. Hart and D. G. Stork, John Wley & Sons, 000 th the permsson of the authors and the publsher
More informationElectrical double layer: revisit based on boundary conditions
Electrcal double layer: revst based on boundary condtons Jong U. Km Department of Electrcal and Computer Engneerng, Texas A&M Unversty College Staton, TX 77843-318, USA Abstract The electrcal double layer
More informationTopology optimization of plate structures subject to initial excitations for minimum dynamic performance index
th World Congress on Structural and Multdsclnary Otmsaton 7 th -2 th, June 25, Sydney Australa oology otmzaton of late structures subject to ntal exctatons for mnmum dynamc erformance ndex Kun Yan, Gengdong
More informationOdd/Even Scroll Generation with Inductorless Chua s and Wien Bridge Oscillator Circuits
Watcharn Jantanate, Peter A. Chayasena, Sarawut Sutorn Odd/Even Scroll Generaton wth Inductorless Chua s and Wen Brdge Oscllator Crcuts Watcharn Jantanate, Peter A. Chayasena, and Sarawut Sutorn * School
More informationA total variation approach
Denosng n dgtal radograhy: A total varaton aroach I. Froso M. Lucchese. A. Borghese htt://as-lab.ds.unm.t / 46 I. Froso, M. Lucchese,. A. Borghese Images are corruted by nose ) When measurement of some
More informationLINEAR REGRESSION ANALYSIS. MODULE IX Lecture Multicollinearity
LINEAR REGRESSION ANALYSIS MODULE IX Lecture - 31 Multcollnearty Dr. Shalabh Department of Mathematcs and Statstcs Indan Insttute of Technology Kanpur 6. Rdge regresson The OLSE s the best lnear unbased
More informationin a horizontal wellbore in a heavy oil reservoir
498 n a horzontal wellbore n a heavy ol reservor L Mngzhong, Wang Ypng and Wang Weyang Abstract: A novel model for dynamc temperature dstrbuton n heavy ol reservors s derved from and axal dfference equatons
More informationHomogeneous model: Horizontal pipe and horizontal well. Flow loops can't duplicate field conditions. Daniel D. Joseph. April 2001
Homogeneous model of producton of heavy ol through horzontal ppelnes and wells based on the Naver-Stokes equatons n the ppelne or the well and Darcy's law n the reservor Homogeneous model: Danel D. Joseph
More informationChapter 8 Balances on Nonreactive Processes 8.1 Elements of Energy Balances Calculations 8.1a Reference States A Review
Chater 8 Balances on Nonreactve Processes 8.1 Elements of Energy Balances Calculatons 8.1a Reference States A Revew We can never know the absolute values of U and H for a seces at a gven state. t Fortunately,
More informationModule 3: The Whole-Process Perspective for Thermochemical Hydrogen
"Thermodynamc Analyss of Processes for Hydrogen Generaton by Decomposton of Water" by John P. O'Connell Department of Chemcal Engneerng Unversty of Vrgna Charlottesvlle, VA 2294-4741 A Set of Energy Educaton
More informationSELECTION OF MIXED SAMPLING PLANS WITH CONDITIONAL DOUBLE SAMPLING PLAN AS ATTRIBUTE PLAN INDEXED THROUGH MAPD AND LQL USING IRPD
R. Samath Kumar, R. Vaya Kumar, R. Radhakrshnan /Internatonal Journal Of Comutatonal Engneerng Research / ISSN: 50 005 SELECTION OF MIXED SAMPLING PLANS WITH CONDITIONAL DOUBLE SAMPLING PLAN AS ATTRIBUTE
More information...Thermodynamics. If Clausius Clapeyron fails. l T (v 2 v 1 ) = 0/0 Second order phase transition ( S, v = 0)
If Clausus Clapeyron fals ( ) dp dt pb =...Thermodynamcs l T (v 2 v 1 ) = 0/0 Second order phase transton ( S, v = 0) ( ) dp = c P,1 c P,2 dt Tv(β 1 β 2 ) Two phases ntermngled Ferromagnet (Excess spn-up
More informationYong Joon Ryang. 1. Introduction Consider the multicommodity transportation problem with convex quadratic cost function. 1 2 (x x0 ) T Q(x x 0 )
Kangweon-Kyungk Math. Jour. 4 1996), No. 1, pp. 7 16 AN ITERATIVE ROW-ACTION METHOD FOR MULTICOMMODITY TRANSPORTATION PROBLEMS Yong Joon Ryang Abstract. The optmzaton problems wth quadratc constrants often
More informationDIELECTRIC MEASUREMENTS OF THE TERNARY MIXTURES OF ALCOHOLS WITH ANILINE IN CARBON TETRACHLORIDE AT 301K
Vol. 1 No. 4 147-15 Octoer - Decemer 17 ISSN: 974-1496 e-issn: 976-83 CODEN: RJCAP http://www.rasayanjournal.com http://www.rasayanjournal.co.n DIELECTRIC MEASUREMENTS OF THE TERNARY MIXTURES OF ALCOHOLS
More informationModeling heat flow across material interfaces and cracks using the material point method
Comutatonal Partcle Mechancs manuscrt No. (wll be nserted by the edtor) Modelng heat flow across materal nterfaces and cracks usng the materal ont method John A. Narn Acceted: July 18 Abstract Heat conducton
More information