Citation
Acoustic determination of the critical point of methane utilizing a variable volume spherical resonator under isothermal conditions

Material Information

Title:
Acoustic determination of the critical point of methane utilizing a variable volume spherical resonator under isothermal conditions
Creator:
Rentz, D. C., 1957-
Publication Date:
Language:
English
Physical Description:
xii, 100 leaves : ill. ; 29 cm.

Subjects

Subjects / Keywords:
Acoustic data ( jstor )
Acoustic resonance ( jstor )
Acoustic spectra ( jstor )
Bellows ( jstor )
Calibration ( jstor )
Critical points ( jstor )
Critical temperature ( jstor )
Methane ( jstor )
Pressure ( jstor )
Sound pressure ( jstor )
Genre:
bibliography ( marcgt )
theses ( marcgt )
non-fiction ( marcgt )

Notes

Thesis:
Thesis (Ph. D.)--University of Florida, 1994.
Bibliography:
Includes bibliographical references (leaves 95-99).
General Note:
Typescript.
General Note:
Vita.
Statement of Responsibility:
by D.C. Rentz.

Record Information

Source Institution:
University of Florida
Holding Location:
University of Florida
Rights Management:
Copyright [name of dissertation author]. Permission granted to the University of Florida to digitize, archive and distribute this item for non-profit research and educational purposes. Any reuse of this item in excess of fair use or other copyright exemptions requires permission of the copyright holder.
Resource Identifier:
001973112 ( ALEPH )
AKE9904 ( NOTIS )
31743882 ( OCLC )

Downloads

This item has the following downloads:


Full Text








i



ACOUSTIC DETERMINATION OF THE CRITICAL POINT OF METHANE
UTILIZING A VARIABLE VOLUME SPHERICAL RESONATOR
UNDER ISOTHERMAL CONDITIONS



















By


RENTZ


A DISSERTATION PRESENTED TO THE GRADUATE SCHOOL
flT- mrTTr TT TrTlnf lTmr m7 r' r'T flr1l7\ Ti Tia fln mTrTfl T rTTYT rTT T T.NLATFTm


































Copyright

by


1994


Rentz






































To Ashley,


believed


could


anything.
















ACKNOWLEDGEMENTS


impossible


acknowledge


people


have


helped


production


this


work.


However,


there


are


several


teachers


have


been


instrumental


in propelling me


completion


my graduate


studies.


There


my wife,


Ashley


Rentz,


taught


me of


matters


heart.


My parents,


and Marilyn


Rentz,


have


taught


me how to


live


among


others.


friends,


Patti


and Pierre


Robitaille,


who have always been


the example of how


would wish


to treat


others.


My mentor,


Samuel


Colgate,


who has


taught me how


work


out


within


above


craft.


rest.


There


those


are


others,


mentioned


these


those


that


stand


have


gone


unsung,


thank


you.
















TABLE


OF CONTENTS


ACKNOWLEDGEMENTS


. IV


LIST


OF TABLES


. a a 1Vll


LIST


OF FIGURES


Viii


ABSTRACT


CHAPTER


INTRODUCTION


a S a aXl


Motivation


Examining


Critical


Point


Methane


. 1


CHAPTER


HISTORICAL


OVERVIEW


. a. 5


First Thought
Background
Critical


point


action


from


sotherm


studies


Critical


point


location


from


sochore


studies


Criti
Speed
Point


point
Sound


location


from i


Probe


sobar


the


studies
Critic


CHAPTER


THEORY


Wave
Acou


Mechanics


stics


Acoustic


Spectrum Analys


CHAPTER


EXPERIMENTAL


Procedure
Initial


Attainment
Data Acquisition
Calibration


Loading
f System


* a a a
S S S


Criti


* a a a a a a
* a a a a a a
* S C a p 5 S a


Density


a a a a a a a a a a a


S1










48


Transducers


System RTD Placement .
Bellows Construction Detail


CHAPTER


RESULTS


Spherical Resonator
Acoustic Spectra
Data Manipulation
Curve Fitting


* a a a
* a a


Critical pressure
Critical temperature
Thermodynamic Surface


* a a a a a a a
a a a a a S a a
* a a a a a a a a a


CHAPTER 6


DISCUSSION
The Critical Point of Methane


* a a a S a a a
* a a a a a a


Gas Impurity
System RTD


Heis


Pressure Gauge


Precision of Technique


Personal Note

REFERENCE LIST


BIOGRAPHICAL SKETCH
















LIST OF TABLES


Table


3-1. ei, eigenvalues
function of order m.


spherical


Besse
* S t


Table 4-1.


Instrumentation Summary.


S54


Table 4-1.


Table 4-1.


(continued)


(continued)


55


56


Table


5-1.


System


dependent


variables


fitted to experimental data.


equation
. 80


Table


6-1.


Methane critical point parameters


found in


the literature.
















LIST OF FIGURES


Figure


2-1.


Typical P,


and T


associated two dimensional pi


surface construct
ots. .


Figure


2-2.


Pressure-volume isotherms of carbon dioxide


in the critical region.


Figure


2-3.


Pressure-temperature


isochores


in the critical region.


of benzene
.* .


Figure


2-4.


Determination


critical


point


hydrogen from measurements of the liquid density pi
and gaseous density p .


Figure


3-1.


Acoustic


spectrum


methane


from


spherical cavity,


(three inch radius)


Figure


3-2.


Typical detail of individual gas resonance


frequencies,


(excerpts from fig.


3-1)


Figure 4-1.


Figure 4-2.


Experimental apparatus schematic.


Control instrumentation schematic.


Figure


4-3.


Calibration


plot


the Heise gauge


vs.


ADC units.


. 42


Figure 4-4.


Pressure calibration setup.


Figure


4-5.


Response


RTD under identical


system RTD
conditions.


and precalibrated
S. 44


Figure


4-6.


Plot


exhibiting


System RTD


strong


linear


Precalibrated RTD


response


temperatures.


Figure 4-7.


Triple point


of water calibration


for the


precalibrated RTD.


4 n.. -.a 0 1 rnetf rk nm LI t


45


46


n7


u


r?:,,,,, /1_0









Figure 4-10.
shroud.


Figure 4-11.


Construction detail of system temperature


Construction detail of bellows assembly.


Figure


5-1.


Typical


acoustic


spectrum


recorded


well


away from the critical point.


S. .59


Figure


5-2.


Typical acousti


critical point.


spectrum recorded near the
S 60


Figure


5-3.


Excerpt from an acousti


spectrum near the


critical point.


Figure


5-4.


time


Excerpt
volume


from
has


acoustic


changed,


spectrum


(frequencies


after
are


shifted toward zero frequency)


Fiaure


5-5.


Superposition


two


acoustic


spectra


excerpts
frequency


illustrating the rapid change in resonant


amplitude


that


accompanies


small


change


in volume near the critical point.


Figure
of


5-6.


Typical


sound


relationship between system speed


system


volume


near


critical


temperature.


Figure


5-7.


Typical


relationship


between


speed of sound and the system density.


the system
S 65


Figure


5-8.


Typical


relationship


between


system


speed of sound and the system pressure


Figure 5-9.


Plot of all data sets of pressure and speed


of sound on a common set of axes.


Figure 5-10.
data run.


Largest temperature variation for a


single


Figure


5-11.


Pressure


dependence


temperature


data


run


that


deviates


most


from


isothermal


conditions.


S73 73


Figure


5-12.


Frequency


dependence


temperature


data


set


that


deviates


most


from


isothermal


conditions.


, in, ,-r~ 1Q n-I .-~4- -11 r11 A~r4- n vrerFrtr0 -a er CaA


63


64


c; nrrrh E,17


~rrn C nm innn~ nF


nlnt nC









Figure


5-14.


variables;


Three c
pressure,


dimensional


temperature


plot


and


c system
speed of


sound.


Figure


5-15


system

Figure 5-16.


Plot
pressure


Plot


system


speed


sound


versus


with fitted equation overlaid.


system temperature versus system


pressure corresponding to minimum values for system


speed


sound for each data run.


Figure


point


7. Thermodynamic
of methane.


surface


critical


Figure 6-1.


Sub critical pressure data taken near the


critical density.


. .a 89


Figure


6-2.


Above critical pressure data taken near the


critical density.


Figure 6-3.


Sound velocity at selected temperatures


a function of pressure


Figure


6-4.


Graph


sound velocity


function


pressure containing all twenty data runs from this


experiment.


83


92















Abstract


of Dissertation


:he University
Requirements j


ACOUSTIC


UTILIZING A


of Florida


Degree


DETERMINATION


VARIABLE VOLUME


ISOTHERMAL


Presented


in Partial
!e of Doctor


the Graduate


School


Fulfillment of
r of Philosophy


CRITICAL POINT


OF METHANE


SPHERICAL RESONATOR


UNDER


CONDITIONS


Rent


April


1994


Chairperson:


Major


Samuel


Department:


Colgate


Chemistry


novel


apparatus


study


thermodynamic


properties


fluids


been


fabricated


utilized


examine


critical


point


of methane.


A spherical


acoustic


resonator


assembly


with


variable


volume


was


used


sensitive


probe


examining


thermodynamic


surface


methane


critical


region.


resonator


was


built


operate


over


broad


ranges


pressure


and


temperature


4000psi


77-525K)


unique


stainless


steel


bellows


arrangement was incorporated to allow a variable system volume


which


first


time


permitted


acoustic


phase


mapping


under


isothermal


conditions.


frequency


third


radially


symmetric


normal


mode


vibration


was


measured and









measured


reported


4.60810. 0015MPa


189.695z0.021K


respectively.


plot


system


pressure,


temperature


sonic


speed


was


constructed


delineate


thermodynamic


surface


critical


region


of methane.
















CHAPTER


INTRODUCTION


Motivation


Examining


the Critical


Point


of Methane


Methane


principal


component


natural


gas.


such,


used


extensively


fuel


many


different


processes.


demand


this


natural


resource


established methane


a commodity


of great


economic


as well


as political


importance.


As a result


of this demand,


methane


has been made


available on an increasing scale


throughout


twentieth century.


This availability and importance have made


methane


attractive


material


scientific


study.


Consequently


, a wealth


of summarized data can be


found in


scientific


literature.


ready


methane


unified


equation


availability


made


numerous


appealing


state.


tabulations


theoretical


equation


data


work


state


mathematical


model


system


that


relates


pressure,


temperature


specific


volume


density


analytical


way.


history


efforts


to establish


reliable


equations


of state


rich dating back


to the work


of Boyle


as early


nr'm~ ~ r t- I ma~ mt~ rc~ nhnt h~7 bcP c'


4nt rndiinrr


1 G; Gt 1


nrn


th rr t


time


I











No general


analytic


density.


equation of


practical


This


state,


values


been


however,


pressure,


particularly


yet proven to


temperature


detrimental


equations


exist


which


are


reasonable


agreement


with


experiment


under


limited


conditions


that


are


toward the extremes


of the


three


variables.


Since


great


majority


scientific


activity


involves


matter


states


which


are


removed


from


outermost


conditions,


major


efforts


toward


achieving


more


unified


equation


state


slowed


to a crawl


many


years.


Recent


developments


chemistry,


physics


and


astronomy


have


involved


studies


matter under


conditions


well


beyond


those


addressed


established


equations


state.


Those


temperatures and pressure


exhibited by


laser induced plasmas


observable


celestial


bodies


were


accessible


time


when


traditional


equations


state


were


being


formulated.


Consequently,


new


equations


applicable


over


broader


ranges


are


needed,


activity


generating


such


equations


growing.


critical


region


proven


especially


difficult


characterize analytically because it exhibits unusually


large


fluctuations


in the


local


density.


Typically,


a gas


is much


less


dense


than


its


corresponding


liquid.


critical












vapor molecules


tend


aggregate


small


clusters.


Some


thermodynamic


relationships


become


discontinuous


critical point.


The ability to describe such behavior is very


difficult mathematically.

The most fruitful treatment of discontinuities associated


with


critical


region


utilizes


scaling


laws


link


thermodynamic behavior on either side of the critical point.

Thermodynamic properties on one side of the critical point are


dealt


with


almost


separate


entities


from


same


properties on the other side.

in thermodynamic behavior, i


Because of this drastic change


t has become common practice to


base


equation


state


formulations


beginning


critical point.


Thermodynamic detail is then viewed in terms


of its distance from the critical point.


Mathematically,


extensive


use


made


reduced


variables such


as4'o


TI~


- T-T_


~red


P-Pc

Pc


and


P led


P-Pc
Pc


where


temperature


, P


pressure,


density


and


symbols


with


subscript


c represent


same variables at the critical point.


It is apparent that for


any theoretical model based on this approach to be successful,


r. ~ ~ ~ ~ ~ ~ ~ ~ n 4-1, rr t; r naa iI


- 4 r .-.-


I


n rr; ~?1


tkl~


Ckn n~r~mnt~r cl


%--


Ir ~u











methane.


Such a


question calls


a reexamination of


critical point parameters for methane.
















CHAPTER


HISTORICAL OVERVIEW


First


Thoughts


In order to put the current work


in proper context,


it is


important


acquainted


with


past


efforts


examine


critical region and identify the critical point


The relative


merits


and drawbacks of


eac


h method must be evaluated in order


illustrate


novelty


and


utility


work


presented


here.


Ideally


current


work


should


represent


advance


in experimental


technique and yi


eld result


of high precision


accuracy.


Final


judgement


extent


current


work achieves these goals


left


to the reader,


it is the


burden


author


illustrate


they


were


pursued and


what


been


accomplished.


Background


single


component


system


critical


point


typically


identified


some


type


phase


diagram.


pressure,


molar


volume


temperature


relationship


can


represented


a three


dimensional


construct.


surface


1


-. *


C.~~~~~ *: -n-r '*l~ -F' -rN


-4 h D m n


~n rC i nn


II


r~rn I-









6

the highest temperature on the coexistence line and is defined


critical


point.


Figure 2-1. Typical


and


surface


construct


associated


two dimensional


plots.


three


dimensional


construct


figure


cumbersome


projections


difficult


figure


visualize.


represents


Each


simpler


three


view


thermodynamic


surface.


upper


left


view


shows


versus


plotted


various


values


constant


volume.


Each


line











data


taken


a unique


constant


temperature


termed


isotherm.


Similarly,


lower


center


view


data


plotted


while


maintaining


constant


pressure.


Each


line


represents data


taken at


a different


constant


pressure and is


termed an isobar.


Any of the three projections has suffic


lent


information


reconstruct


three


dimensional


surface.


Several


established methods


for determining the location


critical


point


exist.


Traditional


methods


correspond


to production of one of the three projections mentioned above.

A short discussion of each is illustrative of the difficulties


faced


experimentalist


yields


insight


into


problems


that


must


addressed


achieve


accurate


measurement


critical


point.


Critical


point


location


from


isotherm


studies


This method requires the temperature to


be held constant


while


molar


volume


the density)


slowly


varied.


series


pressure


vs.


volume


plots


2 IS


reproduced


figure


change


2-2.


becomes


molar


depressed


volume


and eventually


varied,


reaches


pressure


a stationary


value


as the critical point


approached and surpassed.


8 The


slope


of the


isotherm


(aP/av


T approaches


and becomes


zero


and below


critical


point.









8

the critical point it is quite apparent that the slope of the


line never reaches


zero


over


a range of


volumes.


Likewise,


well below the critical point it is apparent that the slope of


the line


zero over a range of volumes.


However,


near the


critical point


, it becomes a subjective matter to determine at


what values of the state variables the slope of the line first


becomes


zero


and not


just merely close to zero.


Figure


2-2.


Pressure-volume


isotherms of


carbon dioxide


the critical region.





Critical point location from isochore studies


75.0 ---- -- ..-- --

742 ---- ------ ...- --- ---


73.8
Z 734. ,.o-.o.. ..,..,, _



;,.2-------F----^^ -------
B\
'I12


71.8----

71.6 _-l-- _-----3-----------29S-


31 35 39 43 47 51 55 59 63 67
v, x 104 = volume (amagat units) x 104











loaded


with


predetermined


density


material


under


study.


temperature


varied


pressure measured.


plot


pressure


vs.


temperature


constructed.


average


density


within


containment


vessel


lower


than


critical


density,


then


a downward


deflection


observed


graphed


data.


onset


deflection


occurs


corresponding


point.


Conversely,


average


density


within


containment


vessel


higher


than


criti


cal density,


then an upward deflection is observed in the


graphed


data


precisely


corresponding


bubble


point.


Only when the average density is equal to the critical density


does


deflection


occur.


Figure


illustrates


typical


results


method


benzene.


This


technique


straightforward


perform


, but


precision


density


accuracy


required


are

even


poor.

a modest


Substantial


break


change


or discontinuity


plot.


Even


use


curve


fitting


differentiation


techniques


still


fails


yield


high


precision.

The second method dealing with isochores is equivalent to


the first,


but takes advantage of


a peculiarity that occurs at


critical


point,


namely,


disappearance


liquid/gas


separator,


meniscus


critical


point,







































Figure 2
critical


3. Pressure-temperature isochores of benzene
region.


in the


disappears


middle


containment


vessel


uniform


horizontal


cross


section.


average


density


system


less


than


critical


density,


meniscus


will


appear to fall

with gas. If


slowly and eventually the vessel


on the other hand,


will be filled


the average system density


greater


than


critical


density,


meniscus


will


slowly


rise


eventually


vessel


will


filled


with


liquid.


temperature,


pressure


density


which


meniscus


disappears


precisely


halfway


vessel


are


taken


62 -
S CURVE 4 _____
____9 -5- -i I ---
I _BENZENE ____,______
I } ^ 70 cc CHA GE I s
-
2 c c i30b CAGE _____ ,:
- 1500= t50 cc CHA GEI _____ __
46
-- 38 --1504 ce CHAC-E "-


S34 I

30 0 I
f26 --


I8r
14, -I-
10 '-
215 220 225 230 235 240 245 250 255 280 265 270 275 280 285 290 295 300 305 310
Temperature C











critical


point,


however,


difference


between


thermodynamic properties of the liquid and gas becomes minute.


Therefore,

a result,


the meniscus becomes more difficult to observe. As

the reported values of the critical point parameters


eventually become dependant on the subjective


judgement of the


experimentalist.


Critical


point


location


from


isobar


studies


This


technique


known


method


rectilinear


diameter


plotting


illustrated


densities,


figure


(related


11,12


molar


requires


volume),


liquid


saturated


vapor


over


wide


range


temperatures


extending


close


possible


critical


point.


average


densities


calculated


also


plotted


on the


same


graph.


The average density


and the temperature are


fitted to an


equation

extended


form


until


2(pq+P'


=po+aT.


intersects


analytical


coexistence


line


curve.


values


obtained


from


intersection


are


taken


critical


point


parameters.


density


liquid


change


very


rapidly


near the critical


point and defining the shape of


the density


curves


becomes


very


difficult.


Also,


line


representing












more


than


reasonable


estimate


critical


point


parameters


this


method.


Figure 2
hydrogen
gaseous


from


Determination
measurements


critical


liquid


point


density


density


Speed


Sound as


a Probe


the Critical


Point


Each


above


mentioned


techniques


probing


critical


point


requires


certain


amount


subjectivity.


Considering


measurement


isotherms,


example,


ability


distinguish


between


line


slopes


almost


equal


zero


actually


equal


zero


typically


subject


nvn;mn 1nrna ni- -~ rxrr rrrh4av +-h 1n +ha 1 n4


0.08

0.07

0.06

0.05

0.04

0.03

0.02

0.01

0.00


-258 -256 -254 -252 -250 -248 -246 -244 -242 -240
T(C)--


n f: rlnra rt~; nt~~ tl; th


L^











accuracy.


Examination


projection


figure


corresponding


isotherms


P-V


plane


shows


critical


isotherm


passes


through


point


where


isotherm


slope


first


becomes


equal


zero.


A function


which


depends


on the


slope of


the critical


isotherm can have


a very rapidly


changing value at


point


dependent


slope of


T and


will


such a


also


function will


zero


critical


point.


Consequently,


such a


function


exists


would have


rapidly


changing


slope


that


goes


zero


critical point

in the critical


may be more


instead of a very slowly changing slope


isotherm in figure 2-1.


readily


as seen


This type of behavior


identifiable experimentally than deciding


when


virtually


flat


line


actually


becomes


completely


flat.


Thermodynami


explores


many


relationships


between


state


variables.


13 These


include


density,


enthalpy,


the free energy and others.


Heat capacity


is such a variable.


One equation


that


relates


heat


capacity


system at


constant


volume


to other


state


variables


av 8v
r~s arp


Where


is the molar heat capacity
Cis the system entropy
S is the system entropy


ap
9^


ap2/av











Since


approaches


and


becomes


zero


critical


point,


while


other


terms


have


nonzero


finite


values,


heat


capacity


critical


state


also


becomes


zero.


A three-dimensional plot of this state function against


temperature


molar


volume


would


observed


a spike


depression


that


extends


asymptotically


towards


zero


from


relatively


gently


curved


surface.


This


type


behavior


very


well


suited


locating


critical


point


thermodynamic


system,


spike


depression


much


more


readily


observable


than


the change


in slope of


an almost


flat


line.


Unfortunately,


accurately measuring the heat capacity for


a system is an arduous task.


What


is needed now is a property


with similar behavior but one which is easily measured.


Such


a state


function


propagation


speed


a pressure


wave


through


system


speed


sound.


thermodynamic


equation


speed


sound i


V M


lp-
Byv


Eqn.


this equation,


7 is


ratio


heat


capacity at


constant


pressure to


the heat


capacity


at constant


volume and


Molecular


weight


specie


s under


study.


1!5


(ap/av


ap











should


very


sensitive


probe


critical


point.


Several methods are known


for measurement


of the sonic


speed.


The method


employed


this


work


is extremely


sensitive.


involves measurement


of standing acoustic wave


frequencies of


cavity


bound


systems.


Virtually


type


containment


vessel


thermodynamic


well


fluid


characterized and


used


wave


long


equation


geometry


solvable


allowed


cavity


resonator


resonant


been


utilized


frequencies.


with


Often


sound


a cylindrical


generator


sound


receiver


located


opposite


ends


cylinder.


However,


propagation of sound through a cylinder is subject to


a bothersome perturbation


to viscous drag on the


cylinder


walls


which


complicates


final


analysis.


more


satisfactory


technique


utilization


spherical


resonator


that


accommodates


some


purely


radial


modes


vibration.


Such


vibrations


correspond


sound


wave


emanating from the center of the sphere and travelling outward


symmetrically to


the chamber wall


and rebounding back toward


the center.


These radial modes


are


free


from viscous effects


which


arise


when


sound


waves


have


components


motion


laterally


along


vessel


walls.


more


detailed


look


theory of


spherical acoustic resonators and their use is found















CHAPTER
THEORY


Wave


Mechanics


transmission


wave


through


fluid


medium


governed by


general


wave


equation18


V2T


Eqn.


Where


Laplacian,


the wave


function


time


wave


velocity.


Laplacian


spherical


coordinates


= --r-
r2 arr


9+
8r


1 a .
r1n sin6e +
r 2sine d 6


1 82
r2sin2O a2


wave


equation


assumed


standing


wave,


that


wave


whose


amplitude


does


depend


time,


then


possible


assume


separable


wave


function


such


that


SWe-ieEt
Eqn.


Where


= -1,


= 2xv,


= frequency.


azlY












Substitution


eqn.


into


eqn.


yields


v2w


r-2
= G
C2


Eqn.


Further,


each


assumed that


spherical


the wave


coordinates,


function


then


is separable


equation


spatial


wave


function


can be


written


= R(r


9(0) (4, )


Eqn.


Substitution of


eqn.


into eqn.


and utilizing the


Laplacian


yields


1 1 d 2dR(r)
R(r) r2 dr dr


1 1 1 d de(0)
(9) r2 sin dOsi dO
8(0) r2 sin0 de de


1
0(,


Eqn.


d2 ()


r2Sin28


task


of finding the wave


function


that


satisfies


eqn.


daunting


appearance.


However,


possible


separate eqn.


into


three


factors each of which deals with


only


one


three


spherical


coordinates.


Once


this


accomplished,


each


factor


separately


zero


rae~' 1 ~ C' fl A-i mane i nn 2 1 ffo arot orln ; n n YC


c2
C2


~ n 1 tr a r"j


~;mnnc;nn~l


rn ~r r 1 t ; n n


P~11=lt inne


;1 rP


/-\Tn












d 2 dR(r)
dr dr


+( 2 2r-A)R(r)
c2


Eqn.


sind sine dO (0)
dO d6


d20 ($)


+ (Asin2e -B) 8 (8)


+B0 (4)


Eqn.


Eqn.


Where


are


separation


constants.


Equation


represents


axial


angle


contribution


the overall


wave


function and


the easiest


to solve.


allow


separation


constant


equal


, then


general


solution


would be


= sin(n )


cos (nt)


Eqn.


Since


each


these


functions


periodic


boundary


condition requires they be single valued


as phi changes by any


multiple


Therefore,


separation


constant


constrained


have


integral


value.


That


Substitution


eqn.


rewriting


yields


sind sine dO
dO d6


+ (Asin2 -n2) (8)


(9,











Since


separation


constant


squared,


new


information


values.


gained


Making the change of


considering


variable,


negative


= cos


integer


yields the


following


(1-12) d2)


dO (ii)


-'IA-


n2
1-T12


6(n)


Eqn.


3-10


Eqn.


3-10


recognizable


as a Legendre function,


provided the


separation


constant


equal


m(m+l)


and


constrained


integer


equal


greater


than


zero.


notation


Legendre


function


written


because


solution


differential


equation


assumed


to be


a polynomial.


general


solution


eqn.


3-10


ecrl


= Pm(r1)


= (1-2)n/2 dn Pm()
dn P


Eqn.


3-11


where P,


the associated Legendre polynomial derived from


following


recursion


formulas


(-m) (1+m) 2
-' .+


(-m) (2-m) (1+m) (3+m


TI4 +.'.


+ (-m)(2-m)(4-m)-.(2s-2-m) (1+m) (3+m) .-(2s-l+m) 28z+..
2s!


= a[l+


P," (rl


Pm











For m


P, (rl)


(1-m) (2+m) 2+
3!


(1-m) (3-m) (2+m) (4+m) 4+..
5!


+ (1-m) (3-m) -(2s-1-m) (2+m) (4+m)---(2s+m) 2s+...
(2s+l) !


value


chosen


also


equal


highest


value


power


independent


variable


found


Legendre


polynomial


obtained


from


above


recursion


formulas.


Consequently,


chosen


such


that


less


than


then


an


From this,


it follows that the general solution stated in eqn.


3-11


additional


constraint


that


0

The combination of


eqn.


and 3-11


yields


the solution


angular


portion


overall


wave


equation.


Traditionally,


this


combination


functions


been


termed


spherical


harmonics,


Ym.n (1,) ,


takes


form


=e(Ti) (


=(1-12) 2


Eqn.
dan COS
dn ()sin(n)
nr


3-12


arl[l


Y,. n(rl











Substituting


= m(m+l)


into


eqn.


yields


d 2 dR(r)
dr dr


+ (k2r 2-m (m+1)


R(r)


Where k


Expanding


derivative


and


making


change


variable


r=kr


leads


d 2R(()


2 dR(C)
C dC


+[2 -m (m+l) R()
C2


Eqn.


3-13


This


equation


s a


general


solution


R(r)


known


spherical


Hankel


function


of order m,


m, ()


Rm (C)


-= h,(C)


combination


= i-m (m+s) !
i( s! (m-s)!


eqns.


3-2,


3-12


.
2(


3-14


Eqn.


3-14


gives


overall


solution


wave


function


defined


eqn.


=Rm (C)Ym,(n (i, )e- t


n
iC

(1i12 )2


m+s) 1


(m-s


dii


I i
2C I


Eqn.


3-15


sin (C') e- it


Acoustics











most


easily


related


thermodynamic


variables.


constraints


wave


function


provide


bridge


between


theory


practicality.


first


constraint


is that


the sound introduced inside


spherical


cavity


allowed


propagate


throughout


cavity.


spherical


Hankel


function,


eqn.


can


separated into two portions;


a real part and an imaginary part


follows


real


part


this


separated


function,


j,((),


known


spherical


Bessel


function


order


while


imaginary


part,


For


is known as a


example,


spherical


first


Neuman


spherical


function


Hankel


of order


functions


corresponding to


and m=l


are


Ro )


R (C)


e iC


e i
-i
C2


substituting


identity


ei =cos


and


rearranging


yields


= ho(C)


= 0 (C) +ino (C)


SEan


3-16


C


j,(C)+in, (C)


h, (C)


n, (r)


(r)+isin(r)


Y\












Ri (C)


= j ((C)+in,()


Ssin(()
C2


cos(C) -sin(C)
c C -- -


Scos(C)
C2


Eqn


3-17


While


either


real


part,


, or


imaginary


part,


are


solutions


radial


contribution


wave


equation,


only


real


part


also


property


of having


finite

just


Once


value

j ( ) :


first


when


standing


spherical


Therefore,


waves


inside


Bessel


can be


an enclose


functions


are


simplified

d chamber.


known,


subsequent


function


j,(


can


derived


from


recursion


formula


= C (2m+l


C) -j (,m-) (c)


second constraint


is that


as the acoustic wave meets


wall


chamber


must


cease


forward


motion.


Writing this


constraint


in mathematical


terms


leads


dRm(()
dr ra


inside
dj m (() resonator
dr r=a


Eqn.


3-18


where a is


radius of


spherical


cavitv. A


Lpplyinq this


nm(U),


h, (C)


R,(r


L^ A


-- A













dj
d


C inside
() resonator
r=a


= Tan(C)-C


Eqn.


3-19


dj1
d


\ inside
1) resonator
Ira


sin(C)


+ 2cos (C)


2sin(C)


Eqn.


3-20


There are an


infinite number of


solutions or eigenvalues


that


satisfy


either


eqns.


3-19


3-20


Separate


eigenvalues


are


designated by


general


symbol


5t,mrn


where


represents


where


infinite


series


solutions


particular


solution


falls.


analogous


manner


naming


more


familiar


hydrogen


atomic


orbitals,


termed


eigenvalue,


3 iS


termed


eigenvalue


forth.


owest


twenty-three


eigenvalues


were


calculated


Lord Rayl


eigh


187221


and H.


Ferris


extended


list


include


lowest


eighty-four


eigenvalues.


22 The


list


recreated


table


Each


eigenvalue


represents


distinct


normal


mode


acoustic vibration of


an elastic


fluid constrained by a rigid


spherical


wall.


Drawing discussion results together


leads


= kr r


Eqn.


3-21


= oa
C


2-91i-,c


1- rn ntr hay


'.4h~ I~ II i


fln1li nf fnf


2tra
V


nn


c


IIL i. I


I I I -


|











Table
order


3-1.


U( -,


eigenvalues


spherical


Bessel


function


.08158


Name


.4079
.9473


Name


4.49341 1 0 is 18.1276 2 11 2n
4.51408 1 3 if 18.3565 3 8 3k
5.64670 1 4 ig 18.4527 1 16 lu
5.94036 2 1 2p 18.4682 5 3 5f
6.75643 1 5 lh 18.7428 6 1 6P
7.28990 2 2 2d 19.2628 4 6 4i
7.72523 2 0 2s 19.2704 2 12 2o
7.85107 1 6 li 19.4964 1 17 iv
8.58367 2 3 2f 19.5819 3 9 31
8.93489 1 7 lj 19.8625 5 4 5g
9.20586 3 1 3p 20.2219 6 2 6d
9.84043 2 4 2g 20.3714 6 0 6s
10.0102 1 8 1k 20.4065 2 13 2q
10.6140 3 2 3d 20.5379 1 18 lw
10.9042 3 0 3s 20.5596 4 7 4j
11.0703 2 5 2h 20.7960 3 10 3m
11. 0791 1 9 11 21.2312 5 5 5h
11.9729 3 3 3f 21.5372 2 14 2r
12.1428 1 10 im 21.5779 1 19 ix
12.2794 2 6 2i 21.6667 6 6f
12.4046 4 1 4p 21.8401 4 8 4k
13.2024 1 11 in 21.8997 7 1 7p
13.2956 3 4 3g 22.0000 3 11 3n
13.4721 2 7 2j 22.5781 5 6 5i
13.8463 4 2 4d 22.6165 1 20 ly
14.0663 4 0 4s 22.6625 2 15 2t
14.2580 1 12 lo 23.0829 6 4 6g
14.5906 3 5 3h 23.167 4 9 41
14.6513 2 8 2k 23.1950 3 12 3o
15.2446 4 3 4f 23.3906 7 2 7d
15.3108 1 13 lq 23.5194 7 0 7s
15.5793 5 1 5p 23.6534 1 21 Iz
15.8193 2 9 21 23.7832 2 16 2u
15.8633 3 6 3i 23.9069 5 7 5j
16.3604 1 14 ir 24.3608 4 10 4m
16.6094 4 4 4g 243824 3 13 3q
16.9776 2 10 2m 24.4749 6 5 6h
17.0431 5 2 5d 24.6899 1 22 la
1 "1 1 "7 "i "7 ", 0 7












Acoustic


Spectrum Analysis


acoustic


resonance


spectrum


will


typically


show


series


freauencies


that


represent


resonances


allowed


eqn.


3-21.


However,


acoustic


spectrum


may


also


contain


other


frequencies


which


are


extraneous


noise.


Consequently,


necessary


employ


stratagem


distinguishing


propagating medium


acoustic


from


spectrum


other


sound


features.


Assume


that


given moment


isolated


system,


speed


sound


a constant.


Then,


eqn.


taken


different


eigenvalues


yields


2xa


v1


Eqn.


2xa


3-22


From


equation


3-22


, it


can


seen


that


ratio


V9 ,m/5i, m


should


constant


resonances


which


involve


only


vibration


contained


fluid.


A typical


acoustic


spectrum


shown


figure


3-1.


particular


peak


thought


fluid


resonance


frequency,


division


correct


eigenvalue


followed


multiplication by subsequent eigenvalues should provide values


Cl .l .


--~A n


Cuhrr~hnn a


- ~ I I as PI-~~ -,nr r n, rt r F Hil' rJ T 4Ir I I -af II i I I


- -2l


. q


I













fluid normal


mode.


such


fashion,


acoustic


spectrum


fluid medium


can


always


'singled


out'


from the


background


noise.


Figure
cavity


Acoustic


three


inch


spectrum


methane


from


spherical


radius)


Figure


shows


typical


resonance


peaks


more


detail.


Peaks


correspond


, 2d


r a a r n fl a


racflflr. Ira -I1


'72 Ilioc


r~tin


via.


I %I f rv N rV" .f L.J irv 1 Iu II LUt rv .. VL t L. At 2 1.U .. .I.. *L.L *% .


3.5E+006 -
-4
-4
I
3 OE+006 -

3.5E+006 --

.E+006 -
-e
3 2.OE+006 ,

F-

I
S 1.5E+006


l.OE+006 -

1
5.0E+005 -


O.OE+0O00 H-------- UI
0 1000 2000 3000 4000 5000 6000 7000 8000 9000 10000
Frequency, Hz













2E*005


1E-005i


4E+0051


4E+0051
1


1 -005
-J
E
S


5E-004


2E-+-OO&


2E+005


OE000---
2447


2547


OE 0 -~OOO


2577


2677


OE+0001-
3174


3274


OEc00-i-O --
47712


Figure 3
frequency i


Typical
(excerpts


detail


individual


resonance


from


perturb


observed


frequencies.


Mehl


Moldover23',4


have


considered


most


prominent


these


and suggest


that


equation


should be


expanded


following manner


2xa


+ Avs
s


+ Avel


+ALv,


+ Vgeom


added


terms


represent


perturbations


thermal


boundary


layer


effect


resonator


wall,


finite


elastic compliance


resonator wall,


the effects of


filling


tubulations


connected


resonator


wall


and


deviations


from


perfect


sphericity


resonator


wall.


carefully


designed


fabricated


apparatus,


these


perturbations


can


quite


small.


Corrections


can


made


either


theoretical


treatments


or by


calibration.


-- -- -- a


- CCh n


A4 'F.Fr~rrnn


mrn rl A


TT


rIo rlar II' f1-d ,-. Ir 111 Ir" I rrIIIV~izn


vibration


4872


I II I


s











modes


involve


tangential


motion


fluid


resonator walls and are not subject to the effects of viscous


drag.


Such resonances


are


generally very


well


defined and


resolved from other allowed resonances.


This facilitates easy


identification and subsequent tracking.
















CHAPTER


EXPERIMENTAL



Procedure


A spherical


acoustic


resonator


assembly


with


a variable


volume was utilized


as a probe to


locate the critical point of


methane.


Temperature


pressure


sonic


speed


were


primary


variables


that


were


tracked,


volume


was


also


followed


non


analytical


manner.


None


variables


was measured directly,


but each was followed as a more readily


measurable


related


parameter.


Figures


are


schematic


representations


represents


physical


overall


apparatus


experiment.


while


Figure


figure


represents the control


instrumentation.


later reference,


the tubulations,


are


referred


pump,


resonator,


sealed methane


inner bellows and RTD shroud


'system


Several


Sections


apparatus


have


unique


features


that


must


addressed


separately


highlight


construction


detail.


Calibrations


temperature


pressure


measuring


devices are


included by necessity.


Also,


instrumentation and


accuracy


are


documented


illustrate


level































































- e-


-


;t

-A



















































rn

77


,nK


'I'


___


i












Initial


Loading


A brief


overview


experimental


procedure


allows


working


insight


into


technique.


Research


grade


methane


assayed


99.99%


pure


from


Scott


Specialty


Gas,


Inc.


was


utilized


experimental


fluid.


entire


system


contact


with


methane


was


stainless


steel


construction


minimize


the potential


for chemical


reaction with containment


walls.


To ensure


initial methane


purity within the


system,


regimen


system


purges


was


conducted


following


manner...


valves


were


closed


except


bellows


bypass


valve,


system


shut


valve


the methane


shut


valve.


The mechanical


shut


vacuum pump


valve


was


started.


mechanical


vacuum


pump


was


opened.


entire


system


was


evacuated


period


of several


hours to ensure the system pressure


fell


below


10-3


torr.


shut


valve


the


mechanical


vacuum


pump


was


closed.


leak


valve


methane


tank


was


opened


ymn nut ci


Snt- rn ri


c1nw hr


I \ I I


mPth;lnP


I / 1











leak valve to the methane tank was closed.


The system pump was started and allowed to run


about


twenty minutes.


entire


procedure


was


repeated starting


step


three


a total


iterations.


The charging procedure required a period of approximately


thirty


hours.


bellows


bypass


valve


was


then


closed


duration


experiment


isolating


one


side


bellows


from the other.


liquid nitrogen tank was attached


constant


temperature


environment


and


system


was


cooled.


The constant temperature environment RTD,


(Resistance


Temperature


Device),


was


monitored


until


system


temperature


fell


near


temperature


anticipated


was


then kept


critical


constant


value.


within


Environment


millikelvin


through


use


a computer


control


algorithm.


methane


leak


valve


shut


valve


were


reopened


minutely


bring the


system pressure


to a value


close


possible to the anticipated critical pressure


The argon leak


valve


shut


valve


were


similarly


opened


maintain


comparable


pressure


both


sides


fragile


bellows.


prevent


rupture


bellows


excess


pressure,


bellows


position


was


constantly


monitored


through


the use of an LVDT


, (Linear Variable Differential


Transformer,











Ap70psi.


order


safeguard


system


the event


dangerous


pressure


gradient,


copper


rupture


disc


lower


strength


was


utililized.


Once


system


pressure


was


near


anticipated


critical


value,


valves


except


system shut


valve,


the argon


shut


valve


argon


leak


valve


were


closed.


Argon


gas continued


to be introduced to the back side of the bellows


order


minimum posit


compress


ion,


slowly.


the argon shut


reaching


bellows


valve and the argon


leak


valve


were


closed


argon


bleed


valve


was


opened


atmosphere.


system pump was put


into operation


to assure


system


homogeneity.


Sufficient


time


was


allowed


temperature


equilibrium


established.


argon


leak


valve


was


reopened


allow


a slow


bleed


of bellows


back


pressure.


The movement


of the bellows from minimum to maximum


position provided a variable volume capability.


Sweep time of


the bellows


full


range of


motion was typically


slow


ten to


twelve hours to ensure only small departures from equilibrium.


During the volume sweep,


the temperature was followed with the


system RTD,


pressure


was


followed


with


Heise


digital


Bourdon gauge and the acoustic


spectrum was


followed with


sonic transducers.


All three instruments were serially polled


results


recorded


periodically


one


two


minute












Attainment


System


Critical


Density


Unfortunately,


a proper


system


loading


methane


could not be obtained simply by filling and cooling the system


to the anti


cipated critical pressure and temperature and then


sealing


off.


Even


small


error


attempting


match


system pressure and temperature to critical


values was greatly


magnified


out


proportion


pressure


change


approaching


zero


critical


point.


purpose


this


rese


arch was to use sonic


speed


as a sensitive detector of the


critical


state.


therm


dynamic


speed


sound approaches


zero


rapidly


temperature


the critical

density, (or


point

molar


where


volume),


the

are


pressure,


their


critical


values,


system density


(see


were


chapter


below


two)

critical


Subsequently,


value,


each new value


system


speed


sound


would


increase


bellows


was


swept


outwards.


Conversely


system


density


were


above


critical


density,


each


new


value


system


speed


sound


would


decrease


bellows


was


swept


outwards.


Only


when


system


density matched


critical


density


somewhere


middle


the bellows


sweep did


speed


sound


first


decrease,


reach


a minimum


and


finally


increase.


,*~~~~~~'t 0 I-r 7 0 nlI I


cnnc&


c~lniir


c~tct nm


I I J


nrnnh~


r i i


'I' nn


~ rnr


r- n i _











bleed


above


argon


tank


was


opened


atmosphere and the argon leak valve was opened sufficiently to


allow


course


bellows


ten


sweep


twelve


from


hours.


high


Temperature,


volume


pressure


over


and an


acoustic


spectrum


were


taken


about


every


two


minutes.


Only


about t

whether


;hirty

system


:otal


data


density


points


was


high


were


required


low,


data


determine


acquisition


was


halted


after


about


hour.


bleed


valve


above


argon


tank


was


then


closed


argon


tank


shut


valve


was


opened.


Argon


was


fed to


the back side of


the bellows


order to


recompress


that


point


argon


valves were


shut


system


was


allowed


sufficient


time


resume


constant


temperature.


mean


time,


raw


data


were


transferred


data


manipulation


computer


where


acoustic


from


signals


time


could


domain


undergo


into


fast


Fourier


frequency


transformation


domain,


(i.e.,


acoustic resonance spectrum)


Each acoustic


spectrum was then


viewed


and


resonance


peaks


identified.


Individual


peaks


were


then


tracked


from


one


spectrum


next.


Once


system


density


.rend i

was


the speed of


adjusted


sound was


accordingly


identified,


either


adding


methane


bleeding


methane


from


system.


entire


process


was


then


repeated


until


elusive


minimum












Data Acquisition


actual


acquisition


data


after


loading


system


proper


procedures


density


required


was


largely


data


uneventful.


acquisition


had


already


the

been


enabled.


Initially,


bellows


began


stationary


minimum


position,


master


data


computer


was


brought


monitoring state,


and sufficient


time was allowed for thermal


equilibrium


established


throughout


the


system.


argon bleed valve


was vented to atmosphere


and the argon


leak


valve


was


adjusted


achieve


total


bellows


sweep


time


ten


twelve


hours.


When


initial


bellows


movement


passed


certain


preset


value


just


above


its


starting


point,


monitoring


master


dat a


computer


switched


active


dat a


acquisition


state.


The master


data


computer


triggered


function


generator to


produce

over a


sine


period


wave


with


about


six


frequency

seconds.


sweep

The fi


from


Junction


10kHz


generator


also

the


produced


Analog


synchronized


Digital


Converter,


square


wave


(ADC),


that


and


triggered

Slock-in


amplifier to begin


data acquisition.


swept


sine wave was


utilized as an acoustic excitation source


for the


input sonic


transducer.


acoustic


signal


was


transmitted


from


one


- .. I


C' l


S- I 4- -


I-- l 'S -r~r.A ~*1- 1t' n mntn n rt nn nr flr TTfi fC I iiIII'.l


Cu~nn rj~rnnu


I-- A A -


nn *r~h









39

pass filter which allowed only the transmitted frequency that

matched the excitation frequency to pass on to the ADC. The


acoustic spectrum was converted from an analog to a digital

signal by the ADC and recorded by the master data computer.


Immediately


afterward,


DMM


(Digital


Multi


Meter)


that


tracked the system RTD,


the DMM that tracked the LVDT


, and the


ADC that tracked the


Heise gauge were serially polled and the


results recorded by the master data computer.


The master data


computer then returned to its monitoring state and awaited the


bellows


movement


pass


next


preset


position


that


triggered the next iteration of the acquisition procedure.


this


way,


data


sets


were


acquired


about


every


minutes until the bellows movement reached a final value just


below


bellows


maximum


position.


dat a


acquisition


program then self terminated and sounded an alarm to alert the


operator that the bellows movement needed to be arrested.


argon bleed


valve


was


closed


and


argon


shut


valve


reopened


long


enough


recompress


the bellows


slowly


to a


minimum


adjusted


position.


achieve


temperature


different


control


working


program


temperature


was


and


sufficient


time


was


allowed


thermal


equilibrium


reestablish.


The entire procedure was reiterated at different


temperatures to span the critical point parameters.












seventeen bit


fast Fourier transform was performed on each raw


acoustic


signal.


The acoustic data


were transformed from the


time


domain


frequency


domain.


Each


spect rum


was


individually


examined


identify


acoustic


resonance


peaks.


individual


peak


frequencies


were


then


tracked


from


one


spectrum


next


order


follow


system


speed


sound.


A data bank was constructed which contained the system


speed


sound,


system


pressure,


system


temperature


system


volume.


Finally,


entire


data


bank


was


saved


on tape


storage


media


future


reference.


table


4-1 at


the end of this chapter for an instrumentation summary.


Calibration


Heise


Pressure


Gauge


Calibration


order


locate


critical


pressure,


was


essential


utilize


accurate


pressure


gauge.


Heise


pressure gauge that was used in this experiment was calibrated


just


before


immediately


after


data


sets


were


acquired.


Since


was


located


in proximity


cooled,


constant


temperature


environment,


final


calibration


was


performed


with


constant


temperature


environment


same


temperature


which


experiment


was


run.


fl ^ n v 1 n


IA7~C I I iiti i~i 7fCT C


nprfn rmmr


d~aci


wei aht


TA? l C


/^


I )









41

was floated atop the piston and provided an absolute pressure,


(p=mg/area,


to gravity)


where m


, on the


the mass and g


fluid within


the acceleration due


the calibration system.


weights


were


loaded


under


vacuum,


correction


pressure


air


was


necessary.


Heise


gauge


output


was


analog


voltage


which


was


converted


digital


format


that


could


acquired

weight p


pressure


master

gauge


data

was c


computer.


compared


The

the


mass

ADC o


dead


>utput


equation was generated that

an absolute pressure measure]


converted ADC units directly


The actual


into


calibration plot


shown


figure


4-3.


The calibration plot for the Heise gauge was incapable of


being


extended


pressure


ranges


involved


this


experiment.


Each


weights


used


dead


weight


pressure


gauge


was


certified


manufacturer,


calibration range extended only to


psia while experimental


pressure


ranges


extended


approximately


fifty


higher


However


extreme


linearity


calibration


line


(chi


squared


lends


a linear


confidence


regression


to extrapolation


data


over this


was


small


.99999952),


range.


The e

calibration


experimental


arrangement


illustrated


figure


used

4-4.


for

The


the

high


pressure

pressure










42


The values given by the ADC and the masses/absolute pressures


dead


weight


pressure


gauge


were


used


generate


figure


4-3.


- ~Sii r


roti


,eI'S


-r
x/ '


2000


-~ r r0 r


* fC'C


1000


I i i i i I II I i1 [ t 1 I .. I I I I I


400


600


Pres


sure,


p510.


Figure 4-3.


Calibration


plot


Heise


gauge


vs.


units.





System RTD Temperature Calibration


RTD'


were


utilized


experiment.


isothermal environment RTD was used as a feedback device for


thc t-mnrrnaitir rnnt-rnl cnmnut pr


The svstem RTD was used to


T












The system RTD


recei


ved the closest scrutiny and underwent the


most


stringent


calibration


process.


Figure


4-4.


Pressure


calibration


setup.


A single platinum RTD was purchased precalibrated by


manufacturer


complied


with


guidelines


set


International


Temperature


Scale


1990.


25 It


came


complete


with a,


p and 6 coefficients


for substitution


into a standard


rna1-Tinn r atl-ina the


temoprature


to measured RTD values.


Constant
Temper at ur e
Env Ironment
Argon Tank Envronen


Ruska
Dead We eight N
Pressure Gaude I


To Vaccuum


Rus ka Pu.p


Heise Gauge


- -












:em


-Te


- -T
9 C~I I


v-qt


te(i


NB


-
~


System


: vibratedd RTD


' 7T1Iii1iT7 TiiT1I:iiIiTiI rl iiTIII Fij ii T '


:o00


Time,


1200


secs.


Figure
under


4-5.


Response


identical


system RTD


precalibrated RTD


condition


ensure


close


temperature


experimental


calibration


conditions


conditions


possible,


were


both


environment


system


were


placed


alongside


precalibrated


constant


temperature


environment.


temperature


control


computer


was


used


drop


temperature to the range of this experiment.

the response of both the system RTD and the


Figure 4-5 shows


precalibrated RTD












precalibrated


RTD.


slight


departure


from


linear


dependence


is easi


ly accounted for by a simple polynomial fit.


S t em


KT TD
KTC:


-- -4
(Vtj~ aaI6L


ca ibrated


TD.


0 80
o 8o


110


i I T120
120


recal


ibrated


RTD


Resistan


Ohms.


Figure 4-6


Plot


System


vs.


Precalibrated


exhibiting strong linear response at low temperatures.


precalibrated RTD


was


electrically


connected


Keithley


196A DMM.


As a check of the DMM,


the resistance of


the precalibrated RTD was measured within a water triple point

cell to ensure a resistance value that corresponded to a true


temperature


value.


triple


point


water


been


established


as equal to


73.1600K.


!2C2
-
-;
-4
r~-4


I









46


Any difference between this lowest resistance value and the

manufacturer's precalibrated value for the same temperature


was treated as an offset due to DMM miscalibration.


offset amounted to a subtraction of 0.3529K from each recorded


temperature


value


was


accounted


data


tabulations.


~~t -l
~1 S -r


'.3T


21 1 ~~i C G r:


212
I.- '-


("C)



?1 99C5C





99.9~C



- t.- ., V


~1
-1
-4


-4
t
2
H
-4


Triple point of water
= 273.1600K
- 99.8460ohms 0 022chms


V I F TV


"note


400.00 600.00 800.00 1000.00 1200.00 1400.00


Time,


secs.


Figure 4-7.


Triple


point


water


calibration


for the


precalibrated RTD.


SOiC~


7


: 1 i 1 i 1 1 ? i i I i 1 1 1 'T1 I I TT r T ~n? 7~rr ij j 1 I i 1 i i TT i i i 5 i T i i i i i I I











Apparatus


Detail


Resonator


Figure


4-8.


Spherical


resonator


schematic.


heart


apparatus,


spherical


resonator was


machined


with


highest


possible


accuracy


available.


inch


diameter


resonator


had


total


diametral


runout


.0001


inches.


construction


was


type


stainless


+t- a -1 -hynrriinhnit-


- nirm 4-Rt


i a sc hematic of the resonator.


K~j~


(___________Lu











being


system


refilled,


pressure


apparatus


climbed


was


high


allowed


eighty


warm


atmospheres


prevent


experimental


apparatus


from


behaving


bomb,


upper


lower


collars


shown


figure


were


clamped


together with


twenty


-24 bolts each torqued to one hundred


foot


pounds.


thin piece of


material


in the center


of the


drawing represents a


copper gasket


that


sealed the two


halves


chamber


together


being


swaged


into


a groove


in the


upper


lower


hemisphere.


shown


figure


are


small


holes,


one


top of the chamber and one in the bottom of the chamber


which


allowed fluids


to enter


experiment


was


and exit


pumped


the chamber.


continuously


fluid used


throughout


system to ensure good blending and prevent


the development


temperature


gradients


actual


system


pump


details


have


been


documented


elsewhere27


pump


circulated


system


fluid


without


generating


strong pressure


gradients.


Transducers


transducers


themselves


were PZT bimorph


oscillators


.400


inches


diameter


.050


inches


thick.


Oscillation


frequency


electric


variation


potential


were


across


the


induced


excitation


placing


transduce


variable

r. The











sender,


does not


interfere with


the spherically symmetric


radial modes,


which are often the most favored signals.


Since


radial


modes


vibration


are


affected by


tangential


interaction


with


chamber


walls,


they


are


often


most


attractive for scientific scrutiny.


A transducer placement of


ninety degrees gave the highest probability of


clear reception


of the most


unperturbed modes of vibration


within the sphere.


Proper


mounting


transducers


within


chamber


required


careful


attention.


electric


signal


applied


transducer.


electric


had to be


received


stainless


potential


electrically


from


steel


return.


shielded


least


chamber


one


itself


electric


from


rest


side


could act


potential


input


chamber


and had to be mounted so as to withstand a pressure as high as


100 atmospheres.


Also,


the electrical


and mechanical


contact


with


transducer


had


have


dampening


effect


else


vibrational


signal


strength


would be


poor.


A machinable


ceramic,


MACOR,


was


used


fabricate


part


of the transducer assembly.


This material


was elected for its


structural


strength,


fluid


impermeability


and


electrical


insulating


quality.


tapered


ram


plug


was


prepared


from


MACOR


match


tapered


seat


machined


into


spherical


chamber


wall.


A sheath


of malleable


copper with


an integral













into a


tapered hole


formed coaxially


in the ceramic MACOR


plug.


Copper




MACOR


*1


Sheat h




Ceram c


s St.


Pin


With


~'wa


sweat e d


gea
ath


ble Copper

Seal


Copper


Sheath


PZT


Electr


Osc i 1 1 ator


. Connect


Open


allow

Sound


sage


Tens ion


Chamber


CrSr.- m c


Gr o und


Figure


4-9.


Construction


detail


transducer mount.


metal


sheath


MACOR


plug


and


centerline


pin


were


assembled


applied


and pressed


pressure


into


greater


the matching


than


tapered seat


maximum


with


pressure


generated


experiment.


action


pressing


*, ,-~~ Y- C' r r~ ~ nfln fl 1 c fY2C CC i-IIk


+- ,hnara


f.i nP


mpl-al


~
/ ~J7


cw~np~


*


1 V T


I nnn mk itr


I 6--


I 1 LJ


h fnn











Once an electrically


isolated


contact


was provided,


each


transducer


was


supported


bottom


electrical


contact


its center.


Center transducer support


was a novel


mounting


technique


previous


workers


had


used


more


common


edge


mounting


technique.


Center mounting


allowed


transducer


float


unconstrained


except


point


contact.


A vibrating circular membrane has a vibrational node


directly


center.


Therefore,


transducer


contact


with


electrical


connectors


center


transducer


caused very


little dampening effect.


This arrangement proved


give


better


performance


terms


enhanced


sensitivity


and prolonged


oscillator


life.


System RTD


Placement


system


RTD


was


placed


within


shroud


that


was


direct


contact


with


system


fluid.


system


fluid


was


continuously moved through the shroud to ensure disruption of


any potential


temperature gradients.


The shroud wall was made


thin


system


pressures


would


allow


provide


rapid


thermal


equilibration across the shroud barrier.


Construction


detail


illustrated


figure


4-10.


Bellows


Construction


Detail























Figure
shroud


4-10.


Construction


detail


system


temperature


experiment.


The bellows


itself,


however


was


fabricated from


very


thin


material


allow


flexibility.


keep


relatively fragile bellows intact at extreme pressures,


fluids


were


introduced to both sides


of the bellows at approximately


equal pressures.


System pressure was


isolated on


one


side of


the bellows while argon balancing pressure was isolated on the


other


side


bellows.


thin material


the bellows


walls


was


sufficient


to contain


fluids


on opposite


sides


provided


pressure


difference


never


exceeded seventy


psi.


Approximately


a thirty


pressure


difference


from


one


side


of the bellows to the other was enough to compress the bellows


to its minimum position.


System volume variation was achieved


slowly


redu


cing


argon


balancing


pressure


back


side


bellows.


system


pressure


was


then


able


push


back


bellows


achieve


increased


volume.


Temper at ure
Shroud


RTD


SyC ill


j---
V;















TV1


illll~lLllllbhll~lhhmliT~~i

Ki
H-


I I


~-TT-=Ii


i


IIYYIYY''Y'1 5 __________irrr


C-:


L L2


I


~ "


r


-











54



Cd



V c),E 42 ()- .4 4 (1) 0 d
c~ka C Wr C WC 0' -H )k )k I
C r r o C I) 0) 00) 4~l I II) ~
EC4E Sd SC Sb CCS Cebl 0Ir ,





cOtW> OUWe-d)-d



>1 4 0) 4,a a

C r i-H CC W~O CA rH' 4 (i
fl r-Hr-4,-c aAt S, U r6r 0
U W c ccra -Hd CO4 dJ WC4t
U~~a O3W' 00) -HCi 0'WliC S







rHW.CO C wCC: 0




da aW-H-flE W-H02 C>UE 4-J.QE ,
WWc (dO OJW~rd0 WIk rHOb l O
k~SLR k$SO~ I ,klr O


rl II II I fl


o LC) '.0 LC >IIr cI
rH n-i r I Cd




7 rHC rHC r-H g



c, -H -H4 -H cv



4d C
C, dc (0c I-
0), U)( 0) 0) 0LHI











55






U) S-r CoQ

C, C W0 COG) 0"' 0) c
4JH4J-cl d-r (dO G)OU HHdCOrb

U) 4( i U) -CI I -H Ck C) tmC01 Ir Q.1 U)

C, 0I U~ >, i- > C, Ct Q. 0"' Cd~k a, r-4 cu $.If-
WouXOH3eC(d 53inr HCd-Wr..JWfO4-






o" -Ht oi

O U d -I U
c i) r- 04(/)3 c
o 0r1W7EdW 4




+Id>4- +104-4 H



'T' O)NN-Hr-1Q
>)3 ZI3:rH0 Q


a, ~rH(d O
pr;)~ c X3
0 Co '0 tr noO
*HSkO40CW( W
f-44-3(00Q4 Or-Ior


H-
w Iml
Ti to H
o NI tOI r
>2 ('1
(' U)C

4-3 tr




U'c rr
COU


Cd 0) 4WW0 r
>2 (0 >c C


5 0
P) U
C
(1) nN O 5- 4kI











56






0)- >1 -Ha
UI) 4-) C COO r
a) -ric HC 0~ rH 4J c


40(RC)-HaCo ( '04 -O C) 4Jr

Oa trd C4-' COCCI) COc)
CWCUWXO HXWx~d






C4 rHOJ
0i -rlrHl
SC C d U)I Ir
U U N
U '0-H HQI ) WrH
Q~~O WC0 0>
rH~ >(drj Z'0

C)o w ~ 1




U>-HN C N0E

CC) Nc, ?Z;O rWI ,

Cr(1 -Hocd 3 a


S $- ct -ri co o- Q.





o to N4c


s-Im



C)



0H iE s- --

C C~f- -ci C)
4-c)> WC C d Cr
C

r-I 0

CUr
















CHAPTER
RESULTS


Spherical


Resonator


Spherical


resonator


development


study


fluid


speed


sound


related


properties


been


successful


activity


workers


this


research


group.


29-38


There


were,


however,


limitations


previous


work


primarily


construction


spherical


spherical


resonator


resonators.


construction was of


earliest


aluminum and designed


operate


primarily


near


ambient


temperature


pressure.


Later,


stainless steel


was used as a construction material


order


study


natural


mixtures


which


contained


small


amounts

designed


corrosive gases.


operate


These


moderate


spherical


temperatures


resonators


and


were


pressures.


They


suffered


from


imperfect


spherical


geometry


fabrication methods


used by the


outside manufacturers.


current


apparatus


found on earlier


incorporates


instruments.


Newly


several


added are


features


thick wall


design


high


pressure


work


exacting


tolerances


ensure spherical


geometry


Operating temperatures can be from


- ~ w- -% 4. -% -r T -f .- %.


-,, -.L


C~Ctr


~r uA~nIYlnn


J


II L


nc~n











stainless


steel


construction


used


throughout


closed


resonator


system.


In addition


to the extremes


in operating


conditions,


apparatus


also


incorporates


a unique


feature


that


allows


system


volume


varied.


expandable


bellows


assembly


that varies the system volume up to 20


is an integral


part


the apparatus.


The addition of the bellows for the first time


make


s isothermal


or isobaric studies practical.


If isochoric


work


system


operating


desired,

with c


bellows


constant


pressures


and


can


volume


easily


still


temperatures.


bypassed


capable


For


this


to yield

extreme


report,


work


was


done


under


controlled


isothermal


conditions.


Acoustic


Spectra


typical


complete


data


acquired


isothermal


volume


scan


included


approximately


80-150


data


points.


Each


datum


point


consisted


a value


temperature,


pressure,


volume


plus


entire


acoustic


spectrum.


acoustic


spectrum consisted of a plot of signal amplitude versus signal


frequency.


Range


and


resolution


for these


variable


was


0-65535

Figure


units


unit


contains


a typical


-10000Hz

acoustic


+ 0.15Hz


respectively.


spectrum taken


from a


data


collected


well


away


from


critical


point.














4.5E+ 006

4E+006


3.5E+ 006

3E+006

2.5E + 006

2E+006

1.5E + 006


1E+006

500000

0


2500


5000 7500


10000


Frequency, Hz .


Figure


5-1.


critical


Typical acoustic spectrum recorded well away from
point.


Each

resonant


spectrum

vibrations


was


visually


method


checked

outlined


identify


chapter


three.


Once


identified,


third


radial


mode


vibration


was


tracked


from


spectrum


spectrum


follow


changing


system speed


Figure


sound.


is an acoustic spectrum recorded very near the


critical


point.


Notice


significant


reduction


signal


compared


figure


5-1.


most


prominent


signals











been


dampened


dispersion


proximity


critical


depressed


point


sonic


Further


speed.


analysis


Both


consistent


reduction


with


resonance


amplitude


and


sonic


speed


are


consistent


with


anticipated


behavior


near


critical


state.


Figure 5-2. Typical acoustic spectrum recorded near the


critical


point


Figure 5-3 and figure 5-4


are excerpts


from two acoustic























ii ii
- -*AA"- --


* -


- --e

Vb


4000


4500


5060


Frequency, Hz.

Figure 5-3. Excerpt from an acoustic spectrum near the
critical point.















'I "







*=.- -
?c f ;- .........











second spectrum shows


shift


toward zero


frequency


well


an overall decrease in signal amplitude.


The frequency of vibration for a resonant peak is related


system


speed


sound


according


3-21.


addition,


the thermodynamic speed of sound becomes zero at the


critical


point.


Therefore


acoustic


spectrum


with


lowest


frequency


vibration


given


resonant


peak


corresponds


experimental


conditions


closest


critical point for that data set.


In figure


and figure


4, the peaks at 4612Hz and at 4517Hz respectively are each due


third radial mode of


vibration.


information


both spectra was recorded just two minutes apart at a change


system


volume


only


0.1%.


Clearly,


shift


third radial


mode


vibration


frequency


both


dramatic and


quantifiable


Figure 5-5


is a superposition


of both spectra excerpts


illustrates


not


only


frequency


shift


third


radial


mode


also


loss


signal


amplitude


that


accompanies the approach of the critical point .


The placement


chamber


transducers


was


designed


maximize


ability to identify the radial modes of vibration.


Since the


radial modes of vibration correspond to symmetric passage of


sound toward and away


from the chamber walls,


they


are




































Figure 5-5. Superposition of two acoustic spectra excerpts


illustrating


amplitude
critical


that


rapid


accompanies


change


a small


resonant


change


frequency


volume


near the


point


third


radial


mode


vibration


was


utilized


throughout


the experiment


for calculating the


system speed of


sound for two


reasons.


First,


readily


identifiable and


well

large


resolved

height


from


neighboring


width


ratio,


signals.


value)


Second,

which


makes


relatively


easy


track


from


one


acoustic


spectrum


next.


Data


Manipulation












frequency


vibration


was


converted


system


speed


sound,


(see


eqn.


3-21),


combined


with


other


system


variables.


plot


system


speed


sound


versus


system


volume


illustrates


relationship


that


exists


between


two


variables.


Plot


versus


system


speed


approximate


sys temu


sound


volumee.


Pt-t


Q1OAIO


2(10 Ut


190.00


jIUt. Ut


170.00


1BU.UO


Approximate


Volume,


Figure
sound


5-6
and


Typical


system


volume


relationship


near


between


critical


system


speed


temperature.


allowed


modes


vibration


shift


their


frequencies


strongly


critical


downward


density.


While at


system


density


or near the critical


approaches


temperature,


the v.c;stm seed of sound exhibits a similar behavior as


it is













system


speed


sound


system


volume


under


these


conditions.


Plot


versuS


system speed
proportional s


sound


;ystemi


density


A-u ~


l 91


170 U

11-A
160 -


/Volume,
1/Volume,


(Proportional


.density)
density)


Figure 5-
sound and


Typical
; system


relationship between the system speed of
density.


closed


system,


molar


density


inversely


related


system


volume


moles/V.


Furthermore,


molar


volume


defined


volume


occupied by


a mole,


= V/moles.


Therefore,


the molar volume and molar density


are


inversely


graphically


related,


terms


1/p,


density


data


figure


shown


5-7.


C --.


.r-~r~ ni"1


In nn 'T1 r I 'tll'l r f ll Ir 11 Afl In lf & l I VtJII tl~lc.uL A.


a1rnr


U.31T


0.40


1-4-i


r7]ntta~











the amount


of methane introduced to the system was devised and


fabricated.


calibration


scheme


metering


exact


system


volume


a function


bellows


position


was


also


devi


and


into


practice.


Unfortunately,


feature


the bellows that


responsible


the experiment


defeating


was built


ability


to exploit


measure


was also


system


density


accurately.


walls


bellows


were


quite


thin


flexible.


such,


they


thereby


bellows


allowed the

change the


was


bellows

overall


position,


move


system

walls


freely

volume.


were


When


compressed


down

the

and


quite


rigid.


However,


when


bellows


was


high


position,


the walls


were uncompressed and had some freedom of


movement


temperature


expand


was


changed,


bulge


outwards.


stiffness


system


compliance


bellows


walls


also


changed.


Therefore,


amount


bellows outward bulge and the change


in system volume changed


dependent


temperature.


extra


degree


freedom


bulge outward combined with changing wall

temperature made it impossible to find an


properties based on


exact system density


by monitoring


bellows


position.


Consequently,


while


volume measurements illustrated in various graphs in this work


are


highly


accurate,


they


have


uncertainty











system


volume


was


precisely


quantifiable,


desirable


focus


system


parameter


that


was


more


accurately measured.


constant temperature environment was


held


within


ten millikelvin


each


set


temperature


under


study.


system


volume


was


increased


a nearly


constant


rate


and


system


pressure


and


system


speed


sound


were


tracked


analytically.


Figure 5-8. Typical relationship between the system speed of


sound and


system pressure.











Figure


plot


system


speed


sound


versus


system


pressure.


minimum


that


appears


center


the graph corresponds to


the closest


approach


to the critical


point recorded by the system parameters;


that


is the pressure,


volume,


temperature and the speed of sound within the enclosed


methane.


Figure


may be roughly divided into two parts.


To the


left


minimum,


system


pressure


less


than


critical

phase fl


pressure


uid.


and

this


system


region,


exists


system


single


speed


gaseous

sound is


inversely


proportional


system


pressure.


pressure


increased,


speed


sound


decreased.


the right


the minimum,


the system pressure


is greater than


critical


fluid


pressure


liquid


system


equilibrium.


exists


this


phase


region,


system


sonic


speed


directly


proportional


system


pressure.


As the pressure


is increased,


the speed of


sound is


also


increased.


Each plot


of system speed of sound versus system pressure


can


examined


location


minimum.


ince


thermodynamic


speed


sound


goes


zero


critical


point,


individual


plot


with


minimum


that


extends


lowest


system


speed


sound


corresponds











plot


that


most


closely


approaches


critical


point


conditions.


At the same time,


an indication of the precision


of the overall technique can be demonstrated.


Plot


all


data


runs


on


common


set


axes.


n r~ -'


190 00

180.00

170.00


S1r60 00


T T I -i i i T I I


;~~ I 7jT


4 5500


4 6000


a 6500


4.7000


4.7500


Pressure


, MPa.


Figure 5-9.
sound on a


Plot of


common set of


data sets of pressure and speed of


axes.


Figure 5-9


illustrates


the asymptotic nature of


system


speed


sound


experimental


conditions


approach


critical


point


conditions.


Combined


plot


shown


- I


-_i











exhibits


'spike'


pointing


pressure


that


corresponds


critical


pressure.


While


true


that


system


speed


sound


never


reaches


zero,


the inaccuracy of identifying the critical point


is very small.


The asymptotic behavior exhibited by the speed


of sound at


critical


the critical


pressure


point


that


provides a


precludes


strong


indicator of


necessity


attain


zero


speed


sound-


data


this


experiment


were


to be collected


under


isothermal


conditions.


constant


temperature


environment


was


kept


at a set


point


temperature


to within


ten millikelvin


for each data


run.


However,


temperature within


the fluid


system itself


did not


remain nearly


so constant.


Even


though


it was possible to maintain a very constant temperature around


sealed


spherical


resonator,


fluid


inside


system


was


isolated enough


that


temperature variation was as much as


several


hundred millikelvin


over the


course


of a single


data


run.


Figure 5-10 illustrates the temperature variation within


the sealed spherical


resonator


as a function of


time during a


data


collection


run.


apparent


from figure 5-10 that


it was difficult


maintain


isothermal


conditions


during


a data


collection


run.


Again,


one


of the


strengths


of the


system was


also one of














Typical


over


the


variation
course


temperature


entire


data


run.


190.000


r180.750
Q


189.500


*89.250


0.00


100.00


- i--- I


200.00


300.00


400.00


500.00


800,00


Time,


mins.


Figure


5-10.


Largest


temperature variation for


a single data


run.


work


against


surroundings.


process


essentially


adiabatic


since


exchange


heat


across


phase

slow.


boundary


lC


represented by

)ss of internal


solid


l


energy


system

that a<


walls


Companies


very

the


expansion


thermodynamic


fluid


reflected


overall


such


drop


a phenomena


system


temperature.


would be


to provide


only


sufficient


to prevent


amount


I II


I i i i


mi











conditions.


Consequently,


experiments were carried out


under


approximate


isothermal


conditions


only.


more


efficient heat exchange system would have to be provided for

future work to approximate isothermal working conditions more

closely.


Such


situation


does


negate


results


experiment,


because


system


temperature


was


recorded


throughout


data


collection.


plot


system


pressure


system speed of


sound versus temperature should appear


vertical


line


true isothermal


conditions are maintained.


Figures 5-11 and 5-12 illustrate the departure from isothermal

conditions typically encountered in this work.


Figures


5-11


5-12


represent


worst


case


departure


from


isothermal


run


conditions.


general,


drift in temperature during a run averaged approximately 0-1K,


even


this


made


ability


zero


critical


temperature very difficult.


Typically,


a temperature had to


be selected for the constant temperature environment that was


about


tenth


degree


higher


than


temperature


interest


order


assured


being


near


proper


temperature when the system expanded sufficiently to be at the


critical density.


A task that was difficult at best and one


that


required


some


trial


and


error


produce


reasonable















Pressure
for least


isothermal


data


dependence
run.


4.7000




4 6700




4.6400




4.6100


4r.til30


4.5fi0O


1*** F


Sr I i


;1*** I I I


189.400


189.500


189.600


189.700


189.800


Temperature,


189.900
K.


190.000


190.100


I-
Figure 5-11. Pressure dependence on temperature for data run
that deviates most from isothermal conditions.


Speed of Sound Temperature dependence
for least isothermal data run.

220.00 -



170.00 -




-











170.00 -
I


Temperature











vertical lines,


provided the system was truly operating under


isothermal conditions.


A slight drift


in temperature should


produce


a series


shaped


curves


system speed of


sound


decreases,


reaches a minimum and then increases when the


critical


density


approached,


passed and moved away


from.


Figure 5-13


is a plot of system speed of


sound versus system


temperature


:or


data runs.


Inspection shows that every


data run experienced a temperature drift during the course of


experiment.


No amount


time


was


sufficient


to ensure


true


thermal


equilibrium


with


constant


temperature


environment.


Plot


all


data


runs


on


common


set


axes.


-'O O10-''


' } .O0
.00 -









D93QC




*^.~00


C ~ liii. I I 1' I hi IL


1?


"" I


I


I i i I i r r i !1 ii 1 i i i I i i i : I i r i 1 I i 1 i i.i i I 1 I l.i











A three-dimensional


plot


three


system


parameters


clearly


demonstrates


in this experiment.


precision


Figure


5-14


is a plot


technique


employed


of system speed


sound,


system


temperature


system


pressure.


plotted


figure


looks


strikingly


like


head


arrow


pointing


directly


such


striking


critical


point.


indicator


No other technique


location


provides


critical


point.


V niiro


c-li rn n i nn. 1


nl nt- n


c~wst pm


vari a les:


27-0



0m0
"taoo



7 ItoO'0oQ


b id~'a~;


'Phr rs P


5114











Curve Fitting


attain


parameters


critical


point


methane,


is possible to draw the limiting slope asymptotes


on figures 5-9 and 5-13 and identify their intersection as the


critical


point.


However,


such a


technique


is graphical


nature and subject


individual


interpretation.


Since


overall


experimental


technique


based


a mathematical


singularity,


a much more satisfying method of


critical point


identification would involve a fit of the experimental data to


appropriate


mathematical


relationship


from


which


critical parameters may be analytically inferred.

Critical pressure


A model


for describing the behavior of the


latent


heat of vaporization


as a function of temperature was proposed


Stell


Torquoto.40


Their


mathematical


model


subsequent


equation


was


modified by


41,42


Sivaraman


relate the speed of


sound to temperature.


The equation was


derived


from


renormalization


group


theory


Wegner43


later refined by Ley-Koo and Green.


The mathematical model


treats behavior similar to that exhibited by the experimental


data


gathered from


this


work.


The basic equation


relating


speed of sound to temperature is











Where


Speed


Sound,


= Ideal


Constant,


J/ (K)mole


= Critical


Temperature,


= Molecular


Weight,


Kg/mole


= Coefficients


= Reduced


Temperature


IT0)


Equation


critical


utilized


temperature


data


equation


either


contains


side


system


dependent


variables


that


must


found such


that


overall


deviation


function


from


experimental


values


minimized.


The quantity represented by the square root


symbol


in equation


has units


of m/


s and renders


left


side of


equation


unitless.


since


reduced


temperature


units


associated


with


each


variables


right


side


equation


also


unitless.


For work


conducted under


isothermal


conditions,


Eqn.


can be modified to work with pressure instead of temperature.

Wherever the reduced temperature appears, the reduced pressure


can


substituted.


What


constants


should


appear


under


square


root


symbol


left


side


equation


unclear,


they


must


combine


yield


quantity


that


units


s to


assure


that


left


side


new











allow


coefficients


right


side


equation


have


UnJ-zs


of m/


Equation


can


then be


rewritten


= AP


+ A2P$


+ A3P -1 p


Eqn.


A4Pr


+ A2P 2
SA5 P


Equation


only nine system dependent


variables to


be searched instead of


of equation 5-1.


Equation


will not

the nine


yield a value for the critical pressure directly,


syst


em dependent parameters can be found utilizing an


estimated


value


critical


pressure.


critical


pressure


can


then


varied


nine


system


dependent


parameter


s recalculated.


Overall


equation


deviation


can


compared


from


one


iteration


next


until


error


been


reduced


a minimum.


final


value


critical


pressure


taken


that


value


which


produces


minimal


deviation


fitted


equation


from


measured


experimental


results


visible


cross


hatches


figure


5-15


are


actual


experimental


data


a single data


run while


the smooth


line


represents


results


fitting


equation


data.


can


readily


seen


that


fitted


equation


reproduces actual


experimental results very


closely.


The nine


+ APr3







































Figure 5-15. Plot of system speed of sound versus system


pressure


with


fitted


equation


overlaid.


experimental


results,


(chi


squared


from


regression


analysis


was


.9972)


close


examination


exponents


eqn.


indicates


that


However,


another


exponent


already


Thus,


both


terms


can


combined


simplify


equation


two


5-2.


variables


Yet,

are


the

equal


coefficients


magnitude


front


these


opposite


same

sign


suggests


they


cancel


each


other


out.


Consequently,


orni~t- 1 nf


r1 -l II-S


<:i mn1 i f ip


PXnrSS ion


shown


r is


S-


p+s=1


. I I -











Table


5-1.


experimental


System dependent
data.


variables


for equation fitted to


Critical


temperature


begin


search


critical


temperature,


temperature


pressure


can


sought


which


correspond


minimum


plot


speed


system


sound


temperature


each


versus


individual


system


data


pressure


run.


can


constructed


illustrate


dependence


two


system


variables.


Such


a plot


below


critical


point


would be


A~~ ~ ~ a~ 1 r 4 n nt ; F 4- n, nn r r rt~ r c4 a nt r~a ni ryat.Of


i t-rnii ri anH xrnrr


Variable Low Pressure High Pressure
Side Side

A, 2.5834904 m/s 3.5191821 m/s

A, -A4 -A4

A3 300.59068 m/s 286.50994 m/s

A4 -A2 -A2

A, 639132.87 m/s 102031.60 m/s

A6 -77601569 m/s -5604354.6 m/s
a 0.66666667 0.66666667

P -0.25000000 -0.25000000
6 1.2500000 1.2500000

Pc 4.6081493 MPa


:,,, c ,, h F












5-16


plot


system


temperature


versus


system


pressure


where each


individual


point


is at


the minimum system speed of


sound


indi


vidual


data


run.


Plot


corres
for ea


Pressure


ponding
ch data


vs. Temperature


minimum


Speed


Sound


run.


4.7000


4.6750


4.6500


4.6250


Critical point
4.6081 MPa.


189.695 K.


4.6000


189.600


189.775


189.950


190.125


190.200


Temperature,


Figure


press
sound


ure


16.
corres


each


Plot


ponding to


data


system
minimum


temperature
values for


versus
system


system
speed of


run.


line drawn


in figure 5-16


straight


However,


coexistence


curve


between


liquid


and


vapor


states


4-ha~~~ r rAn n ~ i nn -r' ch rn no- t n P~tTIi n ct r~ I'h


all1


F111; cl nnt


C ~ n rn\ h ~J ~ t n 7 M ;











interval.


The temperature value for the critical point lies


somewhere along the line drawn in figure 5-16.

The value for the critical pressure found earlier can be

substituted into the equation of the line shown in figure 5-16


and the critical temperature can be calculated directly.


equation


line


(0.150768MPa/K) T


- 2


3. 9918MPa.


From this equation,


the critical temperature is 189.695K.


Thermodvnamic Surface


The existence of


results


equations that model


in an analytical manner


the experimental


leads to the possibility of


illustrating the thermodynamic surface at the critical point.


Figure 5-17


is an extrapolation of the analytical equations up


through and beyond the critical point of Methane.






















loN
'50


Figure 5-17. Thermodynamic surface of the critical point of
methane.
















CHAPTER 6
DISCUSSION


The Critical Point of Methane


The final critical


values determined from this work are


as follows...


4. 6081MPa.

189.695K


.0015MPa.

.021K


Critical parameters gathered from work published in the

past are listed in table 6-1 along with the present values to


facilitate comparison.


Scrutiny of the values in table 6-1


illustrates


that


this


work


will


rest


controversy

methane.


over

Ample


location


precedence


exists


the

for


critical


higher


point of

critical


pressure


than


latest


value


obtained


Kleinrahm


coworkers.


However,


there is no earlier indication that the


value for the critical


temperature should be as


that


found during the course of this work.


Such


situation


leaves


author


horns


dilemma.


It would be the height of hubris to claim offhand


that this current


piece of work is correct


and all previous


-~~ -r. -: 1L 2 1~ -1 .. -r 2 .. I.-.n ---.


1,,,.,.,,,L




















-. S I j I ~I~~**~A I I I


~I 1 I II I- I I I I'I-I-


-. I- I I-. I I I- I- I~


- b I I -.-- I I_ 1 1 t'"1 I


aI at *I .I SI *I .I -I -I *i II -I I I


I I I I I I I ._I I -











difficult.


possible,


however,


look


potential


systematic errors


search


that might


complete,


exist


in this


precision


this


work.


Once such a


technique


can


favorably


demonstrated


a comparison


this


data


that


obtained


from previous


work


can


be made.


Impurity


reference


cited


just


previous


this


work


table


6-1,


quality


methane


utilized


Kleinrahm


coworkers


was


stated


99.9995


pure.


methane


utilized


for this work was only


99.99% pure.


addition


certain


gases,


most


notably


hydrogen


helium,


could


definitely


affect


results


s experiment


and


yield


inaccurate critical


parameters


Both Hydrogen and Helium gas


typically accompany natural


gas in its native state.


However,


identify


initial


source


possibly


inaccurate


results


inadequate


without


some


type


instrumental


verification.


Such verification was unavailable


time


this


experiments


performance.


System RTD


Keithley


system


196A DMM


was


used


purchased


measure


precalibrated


resistance


from











been


obtained less than six months


previous


to performance of


this experiment,


calibration was deemed unnecessary.


Also,


precision


resistor


was


required,


unavailable.


precaution,


Keithley


196A


was


checked


against


precalibrated


RTD.


Resistance


values


corresponding


temperature


values


were


supplied


manufacturer.


DMM


was


properly


calibrated,


should always


produce


resistance


values


that


matched


resistance


values


supplied by


manufacturer


specific


temperature.


precalibrated


value


was


triple


checked


point


against


of water.


known


temperature


difference


between


resistance


reading


and


stated


manufacturer'


resistance


value


was


treated


offset


throughout


experiment.


reconcile


necessity


the DMM to actual


using


temperature


resistance


values might


offset


indicate


that


DMM


further


systematic


errors


that


went


undetected.


Finally,


physical


location


system


was


above


spherical


resonator.


flow


of methane


was


into


the bottom of the resonator and out


the top.


Placement of the


system


close


point


which


methane


was


being examined by acoustic excitation was essential.


However,


constant


temperature


environment


was


kept


cool











environment


directly


through


blades


circulating


fans.


Potentially,


temperature


directly


adjacent


circulating


fans


might


have been


colder


than


rest


environment.


fans


were


located


near


constant


temperature


environment


one


side


and


near


bottom on the other side to provide maximum


cross


circulation.


possible


that


location


system


near


top of the


constant temperature environment might have been an


error.


shield


physical


barrier


was


placed


between


circulating


fans


and the RTD


shroud during all


experiments


help alleviate


this potential


error


, but


it must be mentioned


order


Heise


to be


Pressure


thorough.


Gauge


The

absolute


Heise

dead w


pressure


eight


gauge


pressure.


was ca

However,


librated


against


calibration


did not


extend


into


region


pressure


necessary


this


experiment.


It was assumed that extrapolation of the pressure


calibration to higher pressures was


legitimate because of the


extreme linearity


of the calibration plot


lower pressures.


Such


assumption


have


been


appropriate.


Still,


great


care


was


exercised


calibration


Heise


pressure


gauge


well


the measurement


devices.




Full Text

PAGE 1

W $&2867,& '(7(50,1$7,21 2) 7+( &5,7,&$/ 32,17 2) 0(7+$1( 87,/,=,1* $ 9$5,$%/( 92/80( 63+(5,&$/ 5(621$725 81'(5 ,627+(50$/ &21',7,216 %\ & 5(17= $ ',66(57$7,21 35(6(17(' 72 7+( *5$'8$7( 6&+22/ 2) 7+( 81,9(56,7< 2) )/25,'$ ,1 3$57,$/ )8/),//0(17 2) 7+( 5(48,5(0(176 )25 7+( '(*5(( 2) '2&725 2) 3+,/2623+< 81,9(56,7< 2) )/25,'$

PAGE 2

&RS\ULJKW E\ & 5HQW]

PAGE 3

7R $VKOH\ ZKR EHOLHYHG FRXOG GR DQ\WKLQJ

PAGE 4

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

PAGE 5

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

PAGE 6

&+$37(5 7UDQVGXFHUV 6\VWHP 57' 3ODFHPHQW %HOORZV &RQVWUXFWLRQ 'HWDLO 5(68/76 6SKHULFDO 5HVRQDWRU $FRXVWLF 6SHFWUD 'DWD 0DQLSXODWLRQ &XUYH )LWWLQJ &ULWLFDO SUHVVXUH &ULWLFDO WHPSHUDWXUH 7KHUPRG\QDPLF 6XUIDFH &+$37(5 ',6&866,21 7KH &ULWLFDO 3RLQW RI 0HWKDQH *DV ,PSXULW\ 6\VWHP 57' +HLVH 3UHVVXUH *DXJH $ 3HUVRQDO 1RWH 5()(5(1&( /,67 %,2*5$3+,&$/ 6.(7&+ YL

PAGE 7

/,67 2) 7$%/(6 7DEOH TQ HLJHQYDOXHV IRU VSKHULFDO %HVVHO IXQFWLRQ RI RUGHU P 7DEOH ,QVWUXPHQWDWLRQ 6XPPDU\ 7DEOH FRQWLQXHGf 7DEOH FRQWLQXHGf 7DEOH 6\VWHP GHSHQGHQW YDULDEOHV IRU HTXDWLRQ ILWWHG WR H[SHULPHQWDO GDWD 7DEOH 0HWKDQH FULWLFDO SRLQW SDUDPHWHUV IRXQG LQ WKH OLWHUDWXUH f f 9OO

PAGE 8

/,67 2) ),*85(6 )LJXUH 7\SLFDO 3 9 DQG 7 VXUIDFH FRQVWUXFW DQG DVVRFLDWHG WZR GLPHQVLRQDO SORWV )LJXUH 3UHVVXUHYROXPH LVRWKHUPV RI FDUERQ GLR[LGH LQ WKH FULWLFDO UHJLRQ )LJXUH 3UHVVXUHWHPSHUDWXUH LVRFKRUHV RI EHQ]HQH LQ WKH FULWLFDO UHJLRQ )LJXUH 'HWHUPLQDWLRQ RI WKH FULWLFDO SRLQW IRU K\GURJHQ IURP PHDVXUHPHQWV RI WKH OLTXLG GHQVLW\ S DQG JDVHRXV GHQVLW\ SJ )LJXUH $FRXVWLF VSHFWUXP RI PHWKDQH IURP D VSKHULFDO FDYLW\ WKUHH LQFK UDGLXVf )LJXUH 7\SLFDO GHWDLO RI LQGLYLGXDO JDV UHVRQDQFH IUHTXHQFLHV H[FHUSWV IURP ILJ f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f f f 9OOO

PAGE 9

)LJXUH &RQVWUXFWLRQ GHWDLO RI V\VWHP WHPSHUDWXUH VKURXG )LJXUH &RQVWUXFWLRQ GHWDLO RI EHOORZV DVVHPEO\ )LJXUH 7\SLFDO DFRXVWLF VSHFWUXP UHFRUGHG ZHOO DZD\ IURP WKH FULWLFDO SRLQW )LJXUH 7\SLFDO DFRXVWLF VSHFWUXP UHFRUGHG QHDU WKH FULWLFDO SRLQW )LJXUH ([FHUSW IURP DQ DFRXVWLF VSHFWUXP QHDU WKH FULWLFDO SRLQW )LJXUH ([FHUSW IURP DQ DFRXVWLF VSHFWUXP DIWHU WLPH DQG YROXPH KDV FKDQJHG IUHTXHQFLHV DUH VKLIWHG WRZDUG ]HUR IUHTXHQF\f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

PAGE 10

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

PAGE 11

$EVWUDFW RI 'LVVHUWDWLRQ 3UHVHQWHG WR WKH *UDGXDWH 6FKRRO RI WKH 8QLYHUVLW\ RI )ORULGD LQ 3DUWLDO )XOILOOPHQW RI WKH 5HTXLUHPHQWV IRU WKH 'HJUHH RI 'RFWRU RI 3KLORVRSK\ $&2867,& '(7(50,1$7,21 2) 7+( &5,7,&$/ 32,17 2) 0(7+$1( 87,/,=,1* $ 9$5,$%/( 92/80( 63+(5,&$/ 5(621$725 81'(5 ,627+(50$/ &21',7,216 %\ & 5HQW] $SULO &KDLUSHUVRQ 6DPXHO &ROJDWH 0DMRU 'HSDUWPHQW &KHPLVWU\ $ QRYHO DSSDUDWXV IRU WKH VWXG\ RI WKHUPRG\QDPLF SURSHUWLHV RI IOXLGV KDV EHHQ IDEULFDWHG DQG XWLOL]HG WR H[DPLQH WKH FULWLFDO SRLQW RI PHWKDQH $ VSKHULFDO DFRXVWLF UHVRQDWRU DVVHPEO\ ZLWK D YDULDEOH YROXPH ZDV XVHG DV D VHQVLWLYH SUREH IRU H[DPLQLQJ WKH WKHUPRG\QDPLF VXUIDFH RI PHWKDQH LQ LWV FULWLFDO UHJLRQ 7KH UHVRQDWRU ZDV EXLOW WR RSHUDWH RYHU EURDG UDQJHV RI SUHVVXUH DQG WHPSHUDWXUH SVL DQG .f $ XQLTXH VWDLQOHVV VWHHO EHOORZV DUUDQJHPHQW ZDV LQFRUSRUDWHG WR DOORZ D YDULDEOH V\VWHP YROXPH ZKLFK IRU WKH ILUVW WLPH SHUPLWWHG DFRXVWLF SKDVH PDSSLQJ XQGHU LVRWKHUPDO FRQGLWLRQV 7KH IUHTXHQF\ RI WKH WKLUG UDGLDOO\ V\PPHWULF QRUPDO PRGH RI YLEUDWLRQ ZDV PHDVXUHG DQG UHODWHG WR WKH VRQLF VSHHG RI PHWKDQH ZLWKLQ WKH VSKHULFDO FDYLW\ 7KH FULWLFDO YDOXHV IRU SUHVVXUH DQG WHPSHUDWXUH ZHUH [L

PAGE 12

PHDVXUHG DQG UHSRUWHG DV s03D DQG U. UHVSHFWLYHO\ $ SORW RI V\VWHP SUHVVXUH WHPSHUDWXUH DQG VRQLF VSHHG ZDV FRQVWUXFWHG WR GHOLQHDWH WKH WKHUPRG\QDPLF VXUIDFH RI WKH FULWLFDO UHJLRQ RI PHWKDQH ‘ f ;OO

PAGE 13

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

PAGE 14

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

PAGE 15

YDSRU PROHFXOHV WHQG WR DJJUHJDWH LQ VPDOO FOXVWHUV 6RPH WKHUPRG\QDPLF UHODWLRQVKLSV EHFRPH GLVFRQWLQXRXV DW WKH FULWLFDO SRLQW 7KH DELOLW\ WR GHVFULEH VXFK EHKDYLRU LV YHU\ GLIILFXOW PDWKHPDWLFDOO\ 7KH PRVW IUXLWIXO WUHDWPHQW RI GLVFRQWLQXLWLHV DVVRFLDWHG ZLWK WKH FULWLFDO UHJLRQ XWLOL]HV VFDOLQJ ODZV WR OLQN WKHUPRG\QDPLF EHKDYLRU RQ HLWKHU VLGH RI WKH FULWLFDO SRLQW 7KHUPRG\QDPLF SURSHUWLHV RQ RQH VLGH RI WKH FULWLFDO SRLQW DUH GHDOW ZLWK DV DOPRVW VHSDUDWH HQWLWLHV IURP WKH VDPH SURSHUWLHV RQ WKH RWKHU VLGH %HFDXVH RI WKLV GUDVWLF FKDQJH LQ WKHUPRG\QDPLF EHKDYLRU LW KDV EHFRPH FRPPRQ SUDFWLFH WR EDVH HTXDWLRQ RI VWDWH IRUPXODWLRQV DV EHJLQQLQJ DW WKH FULWLFDO SRLQW 7KHUPRG\QDPLF GHWDLO LV WKHQ YLHZHG LQ WHUPV RI LWV GLVWDQFH IURP WKH FULWLFDO SRLQW 0DWKHPDWLFDOO\ H[WHQVLYH XVH LV PDGH RI UHGXFHG YDULDEOHV VXFK DV 77FA 7 & 33Ff 9 3& ZKHUH 7 LV WKH WHPSHUDWXUH 3 LV WKH SUHVVXUH S LV WKH GHQVLW\ DQG WKH V\PEROV ZLWK WKH VXEVFULSW F UHSUHVHQW WKH VDPH YDULDEOHV DW WKH FULWLFDO SRLQW ,W LV DSSDUHQW WKDW IRU DQ\ WKHRUHWLFDO PRGHO EDVHG RQ WKLV DSSURDFK WR EH VXFFHVVIXO LW LV YLWDO WKDW WKH SDUDPHWHUV IRU WKH FULWLFDO SRLQW EH XQGLVSXWHG 5HFHQWO\ KRZHYHU D SDSHU ZDV SXEOLVKHG WKDW TXHVWLRQV WKH ODWHVW 3 7 DQG S YDOXHV IRU WKH FULWLFDO SRLQW RI

PAGE 16

PHWKDQH 6XFK D TXHVWLRQ FDOOV IRU D UHH[DPLQDWLRQ RI WKH FULWLFDO SRLQW SDUDPHWHUV IRU PHWKDQH

PAGE 17

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

PAGE 18

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

PAGE 19

GDWD WDNHQ DW D XQLTXH FRQVWDQW WHPSHUDWXUH DQG LV WHUPHG DQ LVRWKHUP 6LPLODUO\ WKH ORZHU FHQWHU YLHZ LV 7 DQG 9 GDWD SORWWHG ZKLOH PDLQWDLQLQJ FRQVWDQW SUHVVXUH (DFK OLQH UHSUHVHQWV GDWD WDNHQ DW D GLIIHUHQW FRQVWDQW SUHVVXUH DQG LV WHUPHG DQ LVREDU $Q\ RI WKH WKUHH SURMHFWLRQV KDV VXIILFLHQW LQIRUPDWLRQ WR UHFRQVWUXFW WKH WKUHH GLPHQVLRQDO VXUIDFH 6HYHUDO HVWDEOLVKHG PHWKRGV IRU GHWHUPLQLQJ WKH ORFDWLRQ RI WKH FULWLFDO SRLQW H[LVW 7UDGLWLRQDO PHWKRGV FRUUHVSRQG WR SURGXFWLRQ RI RQH RI WKH WKUHH SURMHFWLRQV PHQWLRQHG DERYH $ VKRUW GLVFXVVLRQ RI HDFK LV LOOXVWUDWLYH RI WKH GLIILFXOWLHV IDFHG E\ WKH H[SHULPHQWDOLVW DQG \LHOGV LQVLJKW LQWR WKH SUREOHPV WKDW PXVW EH DGGUHVVHG WR DFKLHYH DQ DFFXUDWH PHDVXUHPHQW RI WKH FULWLFDO SRLQW &ULWLFDO SRLQW ORFDWLRQ IURP LVRWKHUP VWXGLHV 7KLV PHWKRG UHTXLUHV WKH WHPSHUDWXUH WR EH KHOG FRQVWDQW ZKLOH WKH PRODU YROXPH RU WKH GHQVLW\f LV VORZO\ YDULHG $ VHULHV RI SUHVVXUH YV YROXPH SORWV IRU & LV UHSURGXFHG LQ ILJXUH $V WKH PRODU YROXPH LV YDULHG WKH SUHVVXUH FKDQJH EHFRPHV GHSUHVVHG DQG HYHQWXDOO\ UHDFKHV D VWDWLRQDU\ YDOXH DV WKH FULWLFDO SRLQW LV DSSURDFKHG DQG VXUSDVVHG 7KH VORSH RI WKH LVRWKHUP SFf9fW DSSURDFKHV DQG EHFRPHV ]HUR DW DQG EHORZ WKH FULWLFDO SRLQW 7KH PHWKRG ZRUNV ZHOO HVSHFLDOO\ IRU V\VWHPV ZLWK 7F QHDU URRP WHPSHUDWXUH EXW VXIIHUV IURP DQ LQDELOLW\ WR GHWHUPLQH WKH FULWLFDO SRLQW ZLWK KLJK SUHFLVLRQ :HOO DERYH

PAGE 20

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

PAGE 21

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

PAGE 22

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

PAGE 23

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f RI WKH OLTXLG DQG VDWXUDWHG YDSRU JDV RYHU D ZLGH UDQJH RI WHPSHUDWXUHV H[WHQGLQJ DV FORVH DV SRVVLEOH WR WKH FULWLFDO SRLQW 7KH DYHUDJH RI WKH WZR GHQVLWLHV LV FDOFXODWHG DQG DOVR SORWWHG RQ WKH VDPH JUDSK 7KH DYHUDJH GHQVLW\ DQG WKH WHPSHUDWXUH DUH ILWWHG WR DQ HTXDWLRQ RI IRUP SfSf SD7 7KH DQDO\WLFDO OLQH LV H[WHQGHG XQWLO LW LQWHUVHFWV WKH FRH[LVWHQFH FXUYH 7KH YDOXHV REWDLQHG IURP WKH LQWHUVHFWLRQ DUH WDNHQ DV WKH FULWLFDO SRLQW SDUDPHWHUV 7KH GHQVLW\ RI WKH JDV DQG OLTXLG FKDQJH YHU\ UDSLGO\ QHDU WKH FULWLFDO SRLQW DQG GHILQLQJ WKH VKDSH RI WKH GHQVLW\ FXUYHV EHFRPHV YHU\ GLIILFXOW $OVR WKH OLQH UHSUHVHQWLQJ WKH DYHUDJH GHQVLW\ KDV VRPH FXUYDWXUH DQG D OLQHDU ILW LV TXHVWLRQDEOH 7KHVH WZR DPELJXLWLHV PDNH LW GLIILFXOW WR PDNH

PAGE 24

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

PAGE 25

DFFXUDF\ ([DPLQDWLRQ RI WKH SURMHFWLRQ LQ ILJXUH FRUUHVSRQGLQJ WR WKH LVRWKHUPV LQ WKH 39 SODQH VKRZV WKH FULWLFDO LVRWKHUP SDVVHV WKURXJK SRLQW & ZKHUH WKH LVRWKHUP VORSH ILUVW EHFRPHV HTXDO WR ]HUR $ IXQFWLRQ ZKLFK GHSHQGV RQ WKH VORSH RI WKH FULWLFDO LVRWKHUP FDQ KDYH D YHU\ UDSLGO\ FKDQJLQJ YDOXH DW SRLQW & 7KH VORSH RI VXFK D IXQFWLRQ ZLOO EH GHSHQGHQW RQ SYfW DQG ZLOO DOVR EH ]HUR DW WKH FULWLFDO SRLQW &RQVHTXHQWO\ LI VXFK D IXQFWLRQ H[LVWV LW ZRXOG KDYH D UDSLGO\ FKDQJLQJ VORSH WKDW JRHV WR ]HUR DW WKH FULWLFDO SRLQW LQVWHDG RI D YHU\ VORZO\ FKDQJLQJ VORSH DV VHHQ LQ WKH FULWLFDO LVRWKHUP LQ ILJXUH 7KLV W\SH RI EHKDYLRU PD\ EH PRUH UHDGLO\ LGHQWLILDEOH H[SHULPHQWDOO\ WKDQ GHFLGLQJ ZKHQ D YLUWXDOO\ IODW OLQH DFWXDOO\ EHFRPHV FRPSOHWHO\ IODW 7KHUPRG\QDPLFV H[SORUHV WKH PDQ\ UHODWLRQVKLSV EHWZHHQ VWDWH YDULDEOHV 7KHVH LQFOXGH WKH GHQVLW\ WKH HQWKDOS\ WKH IUHH HQHUJ\ DQG RWKHUV +HDW FDSDFLW\ LV VXFK D YDULDEOH 2QH HTXDWLRQ WKDW UHODWHV WKH KHDW FDSDFLW\ RI WKH V\VWHP DW FRQVWDQW YROXPH WR RWKHU VWDWH YDULDEOHV LV :KHUH & LV WALH PrODU KHDW FDSDFLW\ 6 LV WKH V\VWHP HQWURS\

PAGE 26

6LQFH 3Yf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f r / OLQH n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

PAGE 27

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

PAGE 28

&+$37(5 7+(25< :DYH 0HFKDQLFV 7KH WUDQVPLVVLRQ RI D ZDYH WKURXJK D JRYHUQHG E\ WKH JHQHUDO ZDYH HTXDWLRQ IOXLG PHGLXP LV O) F DW (TQ :KHUH 9 LV WKH /DSODFLDQ n) LV WKH ZDYH IXQFWLRQ W LV WLPH DQG F LV WKH ZDYH YHORFLW\ 7KH /DSODFLDQ LQ VSKHULFDO FRRUGLQDWHV LV D L D VAQJ BGB L DAB U U VLQ U VLQ Mf ,I WKH ZDYH HTXDWLRQ LV DVVXPHG WR EH IRU D VWDQGLQJ ZDYH WKDW LV IRU D ZDYH ZKRVH DPSOLWXGH GRHV QRW GHSHQG RQ WLPH WKHQ LW LV SRVVLEOH WR DVVXPH D VHSDUDEOH ZDYH IXQFWLRQ VXFK WKDW :KHUH L &R WWY (TQ IUHTXHQF\

PAGE 29

6XEVWLWXWLRQ RI HTQ LQWR HTQ \LHOGV (TQ )XUWKHU LI LW LV DVVXPHG WKDW WKH ZDYH IXQFWLRQ LV VHSDUDEOH LQ HDFK RI WKH VSKHULFDO FRRUGLQDWHV WKHQ WKH HTXDWLRQ IRU WKH VSDWLDO ZDYH IXQFWLRQ FDQ EH ZULWWHQ DV L_U 5 U f f !f (TQ 6XEVWLWXWLRQ RI HTQ LQWR HTQ DQG XWLOL]LQJ WKH /DSODFLDQ \LHOGV O O G UFO5Uf A ML] A 5 U U GU GU F G LGf f U VLQ G G G!Wff 4 !f UVLQ G-! (TQ 7KH WDVN RI ILQGLQJ WKH ZDYH IXQFWLRQ WKDW VDWLVILHV HTQ LV GDXQWLQJ LQ DSSHDUDQFH +RZHYHU LW LV SRVVLEOH WR VHSDUDWH HTQ LQWR WKUHH IDFWRUV HDFK RI ZKLFK GHDOV ZLWK RQO\ RQH RI WKH WKUHH VSKHULFDO FRRUGLQDWHV 2QFH WKLV LV DFFRPSOLVKHG HDFK IDFWRU LV VHSDUDWHO\ VHW WR ]HUR DQG WKH UHVXOWLQJ RQH GLPHQVLRQDO GLIIHUHQWLDO HTXDWLRQV DUH VROYHG VXEMHFW WR UHDVRQDEOH ERXQGDU\ FRQGLWLRQV 7KH WKUHH HTXDWLRQV WR EH VROYHG DUH

PAGE 30

G G5Lf GU GU VLQVLQ GHOf G G M F U $f 5 Uf $VLQ%f f (TQ (TQ G! IWf %S A` B (TQ G-f :KHUH n$n DQG n%n DUH VHSDUDWLRQ FRQVWDQWV (TXDWLRQ UHSUHVHQWV WKH D[LDO DQJOH FRQWULEXWLRQ WR WKH RYHUDOO ZDYH IXQFWLRQ DQG LV WKH HDVLHVW WR VROYH ,I ZH DOORZ WKH VHSDUDWLRQ FRQVWDQW n%n WR HTXDO Q WKHQ WKH JHQHUDO VROXWLRQ ZRXOG EH -! !f VLQQ-!f RU FRV Q_!f (TQ 6LQFH HDFK RI WKHVH IXQFWLRQV LV SHULRGLF WKH ERXQGDU\ FRQGLWLRQ UHTXLUHV WKH\ EH VLQJOH YDOXHG DV SKL FKDQJHV E\ DQ\ PXOWLSOH RI W 7KHUHIRUH WKH VHSDUDWLRQ FRQVWDQW Q LV FRQVWUDLQHG WR KDYH DQ LQWHJUDO YDOXH 7KDW LV Q s 6XEVWLWXWLRQ RI Q IRU n \LHOGV Q G Q G f V L Q V L Q G G %n LQ HTQ DQG UHZULWLQJ $VLQQf f

PAGE 31

6LQFH WKH VHSDUDWLRQ FRQVWDQW nQn LV VTXDUHG QR QHZ LQIRUPDWLRQ LV JDLQHG E\ FRQVLGHULQJ LWV QHJDWLYH LQWHJHU YDOXHV 0DNLQJ WKH FKDQJH RI YDULDEOH 7f FRV -f \LHOGV WKH IROORZLQJ 7f G U_f B GUf U G W_f GQ $ Q mf WOf (TQ (TQ LV UHFRJQL]DEOH DV D /HJHQGUH IXQFWLRQ SURYLGHG WKH VHSDUDWLRQ FRQVWDQW n$n LV VHW HTXDO WR PPOf DQG P LV FRQVWUDLQHG WR EH DQ LQWHJHU HTXDO WR RU JUHDWHU WKDQ ]HUR 7KH QRWDWLRQ RI WKH /HJHQGUH IXQFWLRQ LV ZULWWHQ DV 3P f EHFDXVH WKH VROXWLRQ RI WKH GLIIHUHQWLDO HTXDWLRQ LV DVVXPHG WR EH D SRO\QRPLDO 7KH JHQHUDO VROXWLRQ IRU HTQ LV 7f 3PQ7Of 7LfQ f§ 3PQ! (TQ GU_ Q ZKHUH 3PUS LV WKH DVVRFLDWHG /HJHQGUH SRO\QRPLDO GHULYHG IURP WKH IROORZLQJ UHFXUVLRQ IRUPXODV )RU P 3Qf D / Pf OPf A Pf Pf Pf Pf A Pf Pf Pf VPf WPf Pf VOPf H V A fff

PAGE 32

)RU P 3}7f OW OPf Pf ABLB Pf Pf Pf Pf A OPf Pf VOPf Pf Pf VPf VOf 7 7KH YDOXH FKRVHQ IRU nPn LV DOVR HTXDO WR WKH KLJKHVW YDOXH IRU WKH SRZHU RI WKH LQGHSHQGHQW YDULDEOH IRXQG LQ WKH /HJHQGUH SRO\QRPLDO REWDLQHG IURP WKH DERYH UHFXUVLRQ IRUPXODV &RQVHTXHQWO\ LI n Pn LV FKRVHQ VXFK WKDW nPn LV OHVV WKDQ n Qn WKHQ )URP WKLV LW IROORZV WKDW WKH JHQHUDO VROXWLRQ VWDWHG LQ HTQ KDV WKH DGGLWLRQDO FRQVWUDLQW WKDW QP 7KH FRPELQDWLRQ RI HTQ DQG \LHOGV WKH VROXWLRQ RI WKH DQJXODU SRUWLRQ RI WKH RYHUDOO ZDYH HTXDWLRQ 7UDGLWLRQDOO\ WKLV FRPELQDWLRQ RI IXQFWLRQV KDV EHHQ WHUPHG WKH VSKHULFDO KDUPRQLFV


PAGE 33

6XEVWLWXWLQJ n$n PPOf LQWR HTQ \LHOGV G UG5Uf NUBPPA` f5Uf GU GU :KHUH N f§ F ([SDQGLQJ WKH GHULYDWLYH DQG PDNLQJ WKH FKDQJH RI YDULDEOH e NU OHDGV WR O >&P P f @ 5 A (TQ G& & G& & 7KLV HTXDWLRQ KDV D JHQHUDO VROXWLRQ IRU 5Af NQRZQ DV WKH VSKHULFDO +DQNHO IXQFWLRQ RI RUGHU P KPef] LaP \ PVf L ? VHLF (TQ L& V PVf ? & 7KH FRPELQDWLRQ RI HTQV DQG JLYHV WKH RYHUDOO VROXWLRQ IRU WKH ZDYH IXQFWLRQ GHILQHG LQ HTQ r 5P


PAGE 34

PRVW HDVLO\ UHODWHG WR WKHUPRG\QDPLF YDULDEOHV 7ZR FRQVWUDLQWV RQ WKH ZDYH IXQFWLRQ SURYLGH WKH EULGJH EHWZHHQ WKHRU\ DQG SUDFWLFDOLW\ 7KH ILUVW FRQVWUDLQW LV WKDW WKH VRXQG LQWURGXFHG LQVLGH D VSKHULFDO FDYLW\ LV DOORZHG WR SURSDJDWH WKURXJKRXW WKH FDYLW\ 7KH VSKHULFDO +DQNHO IXQFWLRQ HTQ FDQ EH VHSDUDWHG LQWR WZR SRUWLRQV D UHDO SDUW DQG DQ LPDJLQDU\ SDUW DV IROORZV KP MP&fLQP&f 7KH UHDO SDUW RI WKLV VHSDUDWHG IXQFWLRQ MPef LV NQRZQ DV D VSKHULFDO %HVVHO IXQFWLRQ RI RUGHU P ZKLOH WKH LPDJLQDU\ SDUW QPef LV NQRZQ DV D VSKHULFDO 1HXPDQ IXQFWLRQ RI RUGHU P )RU H[DPSOH WKH ILUVW WZR VSKHULFDO +DQNHO IXQFWLRQV FRUUHVSRQGLQJ WR P DQG P O DUH VXEVWLWXWLQJ \LHOGV WKH LGHQWLW\ HL" FRV ef LVLQ ef 5&f K&f M &f LQ f B B VLQ&f FRV 4 F F DQG UHDUUDQJLQJ (TQ

PAGE 35

5&f 02 M D LQ&f B VLQ&f B FRV&f 9MI VLQ&f B FRV&f f n> F F M O F F M (TQ :KLOH HLWKHU WKH UHDO SDUW MPef RU WKH LPDJLQDU\ SDUW QPef DUH VROXWLRQV IRU WKH UDGLDO FRQWULEXWLRQ WR WKH ZDYH HTXDWLRQ RQO\ WKH UHDO SDUW DOVR KDV WKH SURSHUW\ RI KDYLQJ D ILQLWH YDOXH ZKHQ Uf§! 7KHUHIRUH 5f FDQ EH VLPSOLILHG WR MXVW MPef IRU VWDQGLQJ ZDYHV LQVLGH DQ HQFORVHG FKDPEHU 2QFH WKH ILUVW WZR VSKHULFDO %HVVHO IXQFWLRQV DUH NQRZQ DOO VXEVHTXHQW IXQFWLRQV IRU MPef FDQ EH GHULYHG IURP WKH UHFXUVLRQ IRUPXOD MfLI! M POfMPLf M PB[ 2 7KH VHFRQG FRQVWUDLQW LV WKDW DV WKH DFRXVWLF ZDYH PHHWV WKH ZDOO RI WKH FKDPEHU LW PXVW FHDVH LWV IRUZDUG PRWLRQ :ULWLQJ WKLV FRQVWUDLQW LQ PDWKHPDWLFDO WHUPV OHDGV WR ? LQVLGH MUHVRQDWRU U D (TQ ZKHUH D LV WKH UDGLXV RI WKH VSKHULFDO FDYLW\ $SSO\LQJ WKLV FRQVWUDLQW WR WKH UHDO SDUW RI HTQ DQG HTQ OHDYHV

PAGE 36

f LQVLGH UHVRQDWRU U D 7DQ & (TQ LQVLGH UHVRQDWRU n L D VLQ&f A FRV&f B VLQ&f & & & (TQ 7KHUH DUH DQ LQILQLWH QXPEHU RI VROXWLRQV RU HLJHQYDOXHV WKDW VDWLVI\ HLWKHU RI HTQV RU 6HSDUDWH HLJHQYDOXHV DUH GHVLJQDWHG E\ WKH JHQHUDO V\PERO }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f 7KH HLJHQYDOXHV DUH ZHOO NQRZQ DQG WKH UHVRQDWRU UDGLXV DQG VRXQG IUHTXHQFLHV FDQ EH DFFXUDWHO\ PHDVXUHG

PAGE 37

7DEOH RUGHU P P P HLJHQYDOXHV IRU VSKHULFDO %HVVHO IXQFWLRQ RI P 1DPH P P _ ,W K Q N _ OX I 3 L 1DPH

PAGE 38

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 Ff§ a / (TQ ( WD Y e (n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

PAGE 39

IOXLG QRUPDO PRGH ,Q VXFK D IDVKLRQ WKH DFRXVWLF VSHFWUXP GXH WR WKH IOXLG PHGLXP FDQ DOZD\V EH nVLQJOHG RXWn IURP WKH EDFNJURXQG QRLVH ( ( A ( M ( 6 ( ( ( f§ ( nn, L L )UHTXHQF\ +] )LJXUH $FRXVWLF VSHFWUXP RI PHWKDQH IURP D VSKHULFDO FDYLW\ WKUHH LQFK UDGLXVf )LJXUH VKRZV W\SLFDO JDV UHVRQDQFH SHDNV LQ PRUH GHWDLO 3HDNV FRUUHVSRQG WR WKH OJ S G DQG V UHVRQDQFHV UHVSHFWLYHO\ 9DOXHV IRU WKH UDWLR RI YAI IRU WKHVH VDPH SHDNV DUH DQG 'HYLDWLRQV LQ LQGLYLGXDO UDWLRV DUH GXH WR QRQLGHDOLW\ LQ WKH VSKHULFDO UHVRQDWRU ,Q D UHDO DSSDUDWXV VHYHUDO IDFWRUV FDQ

PAGE 40

SHUWXUE WKH REVHUYHG IUHTXHQFLHV 0HKO DQG 0ROGRYHUnA KDYH FRQVLGHUHG WKH PRVW SURPLQHQW RI WKHVH DQG VXJJHVW WKDW HTXDWLRQ VKRXOG EH H[SDQGHG LQ WKH IROORZLQJ PDQQHU Y LW P $Y f $Y $ Y $Y V HO W JHRP 7KH DGGHG WHUPV UHSUHVHQW SHUWXUEDWLRQV GXH WR WKH WKHUPDO ERXQGDU\ OD\HU HIIHFW DW WKH UHVRQDWRU ZDOO WKH ILQLWH HODVWLF FRPSOLDQFH WKH UHVRQDWRU ZDOO WKH HIIHFWV RI ILOOLQJ WXEXODWLRQV FRQQHFWHG WR WKH UHVRQDWRU ZDOO DQG GHYLDWLRQV IURP SHUIHFW VSKHULFLW\ RI WKH UHVRQDWRU ZDOO )RU D FDUHIXOO\ GHVLJQHG DQG IDEULFDWHG DSSDUDWXV WKHVH SHUWXUEDWLRQV FDQ EH TXLWH VPDOO &RUUHFWLRQV FDQ EH PDGH HLWKHU E\ WKHRUHWLFDO WUHDWPHQWV RU E\ FDOLEUDWLRQ 7KH SHUWXUEDWLRQV DIIHFW GLIIHUHQW PRGHV RI YLEUDWLRQ GLIIHUHQWO\ 7KH SXUHO\ UDGLDO PRGHV DUH JHQHUDOO\ OHDVW SHUWXUEHG DQG FRQVHTXHQWO\ RQH RU PRUH RI WKH VSKHULFDOO\ V\PPHWULF UHVRQDQFHV IRU ZKLFK P DUH RIWHQ VHOHFWHG 5DGLDO

PAGE 41

PRGHV LQYROYH QR WDQJHQWLDO PRWLRQ RI WKH IOXLG DW WKH UHVRQDWRU ZDOOV DQG DUH QRW VXEMHFW WR WKH HIIHFWV RI YLVFRXV GUDJ 6XFK UHVRQDQFHV DUH JHQHUDOO\ YHU\ ZHOO GHILQHG DQG UHVROYHG IURP RWKHU DOORZHG UHVRQDQFHV 7KLV IDFLOLWDWHV HDV\ LGHQWLILFDWLRQ DQG VXEVHTXHQW WUDFNLQJ

PAGE 42

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n V\VWHPn 6HYHUDO 6HFWLRQV RI WKH DSSDUDWXV KDYH XQLTXH IHDWXUHV WKDW PXVW EH DGGUHVVHG VHSDUDWHO\ WR KLJKOLJKW FRQVWUXFWLRQ GHWDLO &DOLEUDWLRQV RI WHPSHUDWXUH DQG SUHVVXUH PHDVXULQJ GHYLFHV DUH LQFOXGHG E\ QHFHVVLW\ $OVR LQVWUXPHQWDWLRQ DQG LWV DFFXUDF\ DUH GRFXPHQWHG WR LOOXVWUDWH WKH OHYHO RI UHVHDUFK WKDW KDV EHHQ XQGHUWDNHQ

PAGE 43

/9'7 TX L L 1 L W URFRQ 7DQ N %OHHG 9DOYH 0HWKDQH 6KXW 2I I 9 D Y H 0HW KDQH 7DQN )LJXUH ([SHULPHQWDO DSSDUDWXV VFKHPDWLF X!

PAGE 44

, QVW L PQHOLW 5DFN & ; 77/ 6TXDUH :DYH 7U L JJH U/ $? '00 &RQVW 7HPS &RQW UX '00 6YVWHP 7HPS '00 /9'7 3XV LW LRQ $'& )XQFW L RQ 6ZHSW *HQHUDW RU 6LQH :DYH /RFN LQ $PSOLILHU 3UH $PSOLI LHU ( ! ? 1 I 7HPSH UDW OLUH &RQWURO &RPSXWHU 23 ,% WLQV nnn > DLU]L ’ /L 'DW D 0DQ LSX DW L RQ &RPSXW HU F ‘ 7DSH 'DWD 6W RUDJH & 0DVWHU 'DWD &RPSXWHU ‘ G ’ (W KHU QHW )LJXUH &RQWURO LQVWUXPHQWDWLRQ VFKHPDWLF X! 1!

PAGE 45

,QLWLDO *DV /RDGLQJ $ EULHI RYHUYLHZ RI WKH H[SHULPHQWDO SURFHGXUH DOORZV D ZRUNLQJ LQVLJKW LQWR WKH WHFKQLTXH 5HVHDUFK JUDGH PHWKDQH DVVD\HG DW b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n WRUU 7KH VKXW RII YDOYH WR WKH PHFKDQLFDO YDFXXP SXPS ZDV FORVHG 7KH OHDN YDOYH WR WKH PHWKDQH WDQN ZDV RSHQHG PLQXWHO\ WR LQWURGXFH PHWKDQH VORZO\ WR WKH V\VWHP 6\VWHP SUHVVXUH ZDV EURXJKW WR DERXW WHQ DWPRVSKHUHV DV PRQLWRUHG E\ WKH +HLVH *DXJH

PAGE 46

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f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f 7KH SUHVVXUH GLIIHUHQFH DFURVV WKH EHOORZV ZDV QRW DOORZHG WR H[FHHG D IHZ SRXQGV SHU VTXDUH LQFK SVLf ,UUHYHUVLEOH GDPDJH ZRXOG KDYH RFFXUUHG

PAGE 47

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

PAGE 48

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f DUH DW WKHLU FULWLFDO YDOXHV VHH FKDSWHU WZRf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

PAGE 49

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f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

PAGE 50

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f DQG WKH ORFNLQ DPSOLILHU WR EHJLQ GDWD DFTXLVLWLRQ 7KH VZHSW VLQH ZDYH ZDV XWLOL]HG DV DQ DFRXVWLF H[FLWDWLRQ VRXUFH IRU WKH LQSXW VRQLF WUDQVGXFHU 7KH DFRXVWLF VLJQDO ZDV WUDQVPLWWHG IURP RQH VRQLF WUDQVGXFHU WR WKH RWKHU E\ PHDQV RI IOXLG YLEUDWLRQ ZLWKLQ WKH VSKHULFDO UHVRQDWRU 7KH SUHDPSOLILHU LQFUHDVHG WKH RXWSXW VRQLF WUDQVGXFHU VLJQDO DQG IHG LW WR WKH ORFNLQ DPSOLILHU 7KH ORFNLQ DPSOLILHU FRQWUROOHG D IUHTXHQF\ EDQG

PAGE 51

SDVV ILOWHU ZKLFK DOORZHG RQO\ WKH WUDQVPLWWHG IUHTXHQF\ WKDW PDWFKHG WKH H[FLWDWLRQ IUHTXHQF\ WR SDVV RQ WR WKH $'& 7KH DFRXVWLF VSHFWUXP ZDV FRQYHUWHG IURP DQ DQDORJ WR D GLJLWDO VLJQDO E\ WKH $'& DQG UHFRUGHG E\ WKH PDVWHU GDWD FRPSXWHU ,PPHGLDWHO\ DIWHUZDUG WKH '00 'LJLWDO 0XOWL 0HWHUf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

PAGE 52

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

PAGE 53

ZDV IORDWHG DWRS WKH SLVWRQ DQG SURYLGHG DQ DEVROXWH SUHVVXUH S PJDUHD ZKHUH P LV WKH PDVV DQG J LV WKH DFFHOHUDWLRQ GXH WR JUDYLW\f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f OHQGV FRQILGHQFH WR H[WUDSRODWLRQ RYHU WKLV VPDOO UDQJH 7KH H[SHULPHQWDO DUUDQJHPHQW XVHG IRU WKH SUHVVXUH FDOLEUDWLRQ LV LOOXVWUDWHG LQ ILJXUH 7KH KLJK SUHVVXUH SXPS ZDV XVHG WR LQFUHDVH RU GHFUHDVH WKH SUHVVXUH RI WKH FDOLEUDWLRQ V\VWHP XQWLO WKH SLVWRQ RI WKH GHDG ZHLJKW SUHVVXUH JDXJH IORDWHG DW PLGSRLQW RI LWV OHQJWK RI WUDYHO

PAGE 54

7KH YDOXHV JLYHQ E\ WKH $'& DQG WKH PDVVHVDEVROXWH SUHVVXUHV RQ WKH GHDG ZHLJKW SUHVVXUH JDXJH ZHUH XVHG WR JHQHUDWH ILJXUH 6\VWHP 57' 7HPSHUDWXUH &DOLEUDWLRQ 7ZR 57'nV ZHUH XWLOL]HG LQ WKH H[SHULPHQW 7KH LVRWKHUPDO HQYLURQPHQW 57' ZDV XVHG DV D IHHGEDFN GHYLFH IRU WKH WHPSHUDWXUH FRQWURO FRPSXWHU 7KH V\VWHP 57' ZDV XVHG WR PHDVXUH WKH WHPSHUDWXUH RI WKH IOXLG LQVLGH WKH UHVRQDWRU ,WV UHVSRQVH ZDV UHFRUGHG E\ WKH PDVWHU GDWD FRPSXWHU DORQJ ZLWK GDWD UHODWHG WR SUHVVXUH YROXPH DQG DFRXVWLF VLJQDO

PAGE 55

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r& WR r& 7KLV 57' ZDV XWLOL]HG DV D ODERUDWRU\ VWDQGDUG DJDLQVW ZKLFK RWKHUV ZHUH FDOLEUDWHG

PAGE 56

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

PAGE 57

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

PAGE 58

$Q\ GLIIHUHQFH EHWZHHQ WKLV ORZHVW UHVLVWDQFH YDOXH DQG WKH PDQXIDFWXUHUnV SUHFDOLEUDWHG YDOXH IRU WKH VDPH WHPSHUDWXUH ZDV WUHDWHG DV DQ RIIVHW GXH WR '00 PLVFDOLEUDWLRQ 7KH RIIVHW DPRXQWHG WR D VXEWUDFWLRQ RI IURP HDFK UHFRUGHG WHPSHUDWXUH YDOXH DQG ZDV DFFRXQWHG IRU LQ DOO GDWD WDEXODWLRQV

PAGE 59

$SSDUDWXV 'HWDLO 5HVRQDWRU 7KH KHDUW RI WKH DSSDUDWXV WKH VSKHULFDO UHVRQDWRU ZDV PDFKLQHG ZLWK WKH KLJKHVW SRVVLEOH DFFXUDF\ DYDLODEOH 7KH VL[ LQFK GLDPHWHU UHVRQDWRU KDG D WRWDO GLDPHWUDO UXQRXW RI LQFKHV 7KH FRQVWUXFWLRQ ZDV RI W\SH VWDLQOHVV VWHHO WKURXJKRXW )LJXUH LV D VFKHPDWLF RI WKH UHVRQDWRU 5HVRQDWRU ZDOOV DQG WKH HQWLUH GHYLFH ZHUH RI TXLWH VXEVWDQWLDO WKLFNQHVV DV RSHUDWLQJ SUHVVXUHV ZHUH QHDU IRUW\ ILYH DWPRVSKHUHV (DFK WLPH WKH OLTXLG QLWURJHQ WDQN ZDV

PAGE 60

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

PAGE 61

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

PAGE 62

ILW LQWR D WDSHUHG KROH IRUPHG FRD[LDOO\ LQ WKH FHUDPLF 0$&25 SOXJ 7KH PHWDO VKHDWK 0$&25 SOXJ DQG FHQWHUOLQH SLQ ZHUH DVVHPEOHG DQG SUHVVHG LQWR WKH PDWFKLQJ WDSHUHG VHDW ZLWK DQ DSSOLHG SUHVVXUH JUHDWHU WKDQ WKH PD[LPXP SUHVVXUH WR EH JHQHUDWHG LQ DQ H[SHULPHQW 7KH DFWLRQ RI SUHVVLQJ WKH DVVHPEO\ LQWR WKH WDSHUHG RSHQLQJ VZDJHG WKH ILQH PHWDO ULE EDFN LQWR WKH VLGHV RI WKH DVVHPEO\ DQG SURGXFHG D VWURQJ KHUPHWLF VHDO )LJXUH LOOXVWUDWHV WKH WUDQVGXFHU DQG IHHGWKURXJK FRPSRQHQWV

PAGE 63

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

PAGE 64

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

PAGE 65

)LJXUH &RQVWUXFWLRQ GHWDLO RI EHOORZV DVVHPEO\

PAGE 66

,QVWUXPHQW 0DQXIDFWXUHU 0RGHO 5DQJH 2SHUDWLRQ $FFXUDF\ 8VH LJLWDO .HLWKOH\ 0XOWL0HWHU '00f ,QVW UXPHQW V ,QF $ WHUPLQDO UHVLVWDQFH PHDVXUHPHQW IURP L4 0e 5DQJH GHSHQGHQW 2ZQHUnV PDQXDO OLVWV GHWDLOV 3ODWLQXP UHVLVWDQFH WHPSHUDWXUH GHYLFH PHDVXUHPHQW 'LJLWDO 0XOWL0HWHU '00f .HLWKOH\ ,QVW UXPHQW V ,QF WHUPLQDO UHVLVWDQFH PHDVXUHPHQW IURP L4 0 $OVR UDQJH GHSHQGHQW EXW RQH GLJLW WKDQ PRGHO $ 6\VWHP 3ODWLQXP UHVLVWDQFH WHPSHUDWX GHYLFH PHDVXUHPHQW 'LJLWDO .HLWKOH\ $ 0XOWL0HWHU '00f ,QVW UXPHQW V ,QF WHUPLQDO UHVLVWDQFH PHDVXUHPHQW IURP O4 04 5DQJH GHSHQGHQW 2ZQHUnV PDQXDO OLVWV GHWDLOV /9'7 SRVLWLRQ UHVLVWDQFH PHDVXUHPHQW $QDORJ 'LJLWDO &RQYHUWHU $'&f ,27HFK sPYROWV YROWV LR ELW LR +HLVH JDXJH DQG $FRXVWLF VSHFWUXP YROWDJH GLJLWL]DWLRQ 7DEOH ,QVWUXPHQWDWLRQ 6XPPDU\ FQ

PAGE 67

,QVWUXPHQW 0DQXIDFWXUHU 0RGHO 5DQJH RI 2SHUDWLRQ $FFXUDF\ 8VH :DYHIRUP 6\QWKHVL]HU t )XQFWLRQ *HQHUDWRU +HZOHWW 3DFNDUG % 6LQH ZDYH IURP OIO+] WR 0+] DQG DPSOLWXGH RI YROWV SHDN WR SHDN s[Oa WLPHV D VHOHFWHG YDOXH DW QRUPDO URRP WHPSHUDWXUH JHQHUDWHV DFRXVWLF H[FLWDWLRQ VLQH ZDYH DQG 77/ VTXDUH ZDYH WULJJHU V\QFK /RFN LQ $PSOLILHU 6WDQIRUG 5HVHDUFK 6\VWHPV ,QF 65 +] WR .+] s YROW RXWSXW DW IXOO VFDOH LQSXW 6LQH ZDYH FDSWXUH 6LJQDO PHDVXUHPHQW GRZQ WR O2QY IXOO VFDOH 6SXULRXV VWURQJ VLJQDO UHMHFWLRQ E\ XVLQJ OLQH QRWFK DQG VHOIWUDFNLQJ EDQGSDVV ILOWHUV 7DEOH FRQWLQXHGf FQ FQ

PAGE 68

, ,QVWUXPHQW 0DQXIDFWXUHU 0RGHO 5DQJH RI 2SHUDWLRQ $FFXUDF\ 8VH 3UH $PSOLILHU 6WDQIRUG 5HVHDUFK 6\VWHPV ,QF 65 WR PY UPV LQSXW b JDLQ ,QSXW QRLVH UHGXFWLRQ DQG IXOO VFDOH VHQVLWLYLW\ H[WHQVLRQ WR O2QY 2VFLOORn VFRSH /HDGHU ,QF WR .+] I UHTXHQF\ DQG YROW SS DPSOLWXGH GLVSOD\ 9HUWLFDO DQG KRUL]RQWDO GULYHUV sb 9LVXDO H[FLWDWLRQ RU UHVSRQVH VLQH ZDYH IROORZHU '\QDPLF 6 L J Q D $QDO\]HU +HZOHWW 3DFNDUG + 3 $ M+] WR .K] IRU VLQJOH FKDQQHO VSHFWUXP 1R GHWDLOV DYDLODEOH UHDO WLPH IDVW )RXULHU VSHFWUXP GLVSOD\ 7DEOH FRQWLQXHGf WBQ 22

PAGE 69

&+$37(5 5(68/76 6SKHULFDO 5HVRQDWRU 6SKHULFDO UHVRQDWRU GHYHORSPHQW IRU WKH VWXG\ RI IOXLG VSHHG RI VRXQG DQG UHODWHG SURSHUWLHV KDV EHHQ D VXFFHVVIXO DFWLYLW\ RI ZRUNHUV LQ WKLV UHVHDUFK JURXSn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

PAGE 70

VWDLQOHVV VWHHO FRQVWUXFWLRQ LV XVHG WKURXJKRXW WKH FORVHG UHVRQDWRU V\VWHP ,Q DGGLWLRQ WR WKH H[WUHPHV LQ RSHUDWLQJ FRQGLWLRQV WKH DSSDUDWXV DOVR LQFRUSRUDWHV D XQLTXH IHDWXUH WKDW DOORZV WKH V\VWHP YROXPH WR EH YDULHG $Q H[SDQGDEOH EHOORZV DVVHPEO\ WKDW YDULHV WKH V\VWHP YROXPH XS WR b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s XQLW DQG +] s +] UHVSHFWLYHO\ )LJXUH FRQWDLQV D W\SLFDO DFRXVWLF VSHFWUXP WDNHQ IURP D GDWD VHW FROOHFWHG ZHOO DZD\ IURP WKH FULWLFDO SRLQW 2I SDUWLFXODU LQWHUHVW LV WKH DSSDUHQW ZHDOWK RI LQIRUPDWLRQ FRQWDLQHG ZLWKLQ WKH VSHFWUXP 6LJQDO DPSOLWXGH LV VWURQJ DQG IUHTXHQF\ LGHQWLILFDWLRQ LV VWUDLJKWIRUZDUG

PAGE 71

' 7 3 f+ 2* 2n f+ : ( ( ( ( ( ( ,( ( L_ r f @ f ‘ f O/ n L r DL + f r OL L f f W O L f Y_ f f cL )UHTXHQF\ +] )LJXUH 7\SLFDO DFRXVWLF VSHFWUXP UHFRUGHG ZHOO DZD\ IURP WKH FULWLFDO SRLQW (DFK VSHFWUXP ZDV YLVXDOO\ FKHFNHG WR LGHQWLI\ WKH UHVRQDQW YLEUDWLRQV E\ WKH PHWKRG RXWOLQHG LQ FKDSWHU WKUHH 2QFH LGHQWLILHG WKH WKLUG UDGLDO PRGH RI YLEUDWLRQ ZDV WUDFNHG IURP VSHFWUXP WR VSHFWUXP WR IROORZ WKH FKDQJLQJ V\VWHP VSHHG RI VRXQG )LJXUH LV DQ DFRXVWLF VSHFWUXP UHFRUGHG YHU\ QHDU WKH FULWLFDO SRLQW 1RWLFH WKH VLJQLILFDQW UHGXFWLRQ LQ VLJQDO FRPSDUHG WR ILJXUH 7KH PRVW SURPLQHQW VLJQDOV LQ WKH VSHFWUXP DSSHDU DW +] LQWHUYDOV WKHVH FRUUHVSRQG WR QRLVH JHQHUDWHG E\ WKH HOHFWULF FXUUHQW VXSSOLHG DW WKH SRZHU RXWOHW +RZHYHU WKH DFRXVWLF VSHFWUXP LV VWLOO SUHVHQW EXW

PAGE 72

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

PAGE 73

)UHTXHQF\ +] )LJXUH ([FHUSW IURP DQ DFRXVWLF VSHFWUXP QHDU WKH FULWLFDO SRLQW Q )UHTXHQF\ +] )LJXUH ([FHUSW IURP DQ DFRXVWLF VSHFWUXP DIWHU WLPH DQG YROXPH KDV FKDQJHG IUHTXHQFLHV DUH VKLIWHG WRZDUG ]HUR IUHTXHQF\f

PAGE 74

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b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

PAGE 75

)LJXUH 6XSHUSRVLWLRQ RI WZR DFRXVWLF VSHFWUD H[FHUSWV LOOXVWUDWLQJ WKH UDSLG FKDQJH LQ UHVRQDQW IUHTXHQF\ DQG DPSOLWXGH WKDW DFFRPSDQLHV D VPDOO FKDQJH LQ YROXPH QHDU WKH FULWLFDO SRLQW 7KH WKLUG UDGLDO PRGH RI YLEUDWLRQ ZDV XWLOL]HG WKURXJKRXW WKH H[SHULPHQW IRU FDOFXODWLQJ WKH V\VWHP VSHHG RI VRXQG IRU WZR UHDVRQV )LUVW LW LV UHDGLO\ LGHQWLILDEOH DQG ZHOO UHVROYHG IURP QHLJKERULQJ VLJQDOV 6HFRQG LW KDV D ODUJH KHLJKW WR ZLGWK UDWLR 4 YDOXHf ZKLFK PDNHV LW UHODWLYHO\ HDV\ WR WUDFN IURP RQH DFRXVWLF VSHFWUXP WR WKH QH[W 'DWD 0DQLSXODWLRQ (DFK DFRXVWLF VSHFWUXP LQ WKH GDWD VHWV ZDV H[DPLQHG WR ILQG WKH SHDN FRUUHVSRQGLQJ WR WKH WKLUG UDGLDO PRGH 7KH

PAGE 76

IUHTXHQF\ RI YLEUDWLRQ ZDV FRQYHUWHG WR WKH V\VWHP VSHHG RI VRXQG VHH HTQ f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

PAGE 77

WKH V\VWHP VSHHG RI VRXQG DQG WKH V\VWHP YROXPH XQGHU WKHVH FRQGLWLRQV ,Q D FORVHG V\VWHP WKH PRODU GHQVLW\ LV LQYHUVHO\ UHODWHG WR V\VWHP YROXPH E\ S PROHV9 )XUWKHUPRUH WKH PRODU YROXPH LV GHILQHG DV WKH YROXPH RFFXSLHG E\ D PROH 9 9PROHV 7KHUHIRUH WKH PRODU YROXPH DQG PRODU GHQVLW\ DUH LQYHUVHO\ UHODWHG 9 S DQG WKH GDWD PD\ EH VKRZQ JUDSKLFDOO\ LQ WHUPV RI GHQVLW\ DV LQ ILJXUH ,Q ERWK ILJXUH DQG WKH YDULDEOH SORWWHG DORQJ WKH [D[LV LV LQH[DFW 2ULJLQDOO\ WKH H[SHULPHQW ZDV GHVLJQHG WR PHDVXUH WKH V\VWHP GHQVLW\ DQDO\WLFDOO\ DV ZHOO DV WKH RWKHU V\VWHP SDUDPHWHUV $Q HODERUDWH PHWKRG IRU ZHLJKLQJ

PAGE 78

WKH DPRXQW RI PHWKDQH LQWURGXFHG WR WKH V\VWHP ZDV GHYLVHG DQG IDEULFDWHG $ FDOLEUDWLRQ VFKHPH IRU PHWHULQJ WKH H[DFW V\VWHP YROXPH DV D IXQFWLRQ RI EHOORZV SRVLWLRQ ZDV DOVR GHYLVHG DQG SXW LQWR SUDFWLFH 8QIRUWXQDWHO\ D IHDWXUH RI WKH EHOORZV WKDW WKH H[SHULPHQW ZDV EXLOW WR H[SORLW ZDV DOVR UHVSRQVLEOH IRU GHIHDWLQJ WKH DELOLW\ WR PHDVXUH WKH V\VWHP GHQVLW\ DFFXUDWHO\ 7KH ZDOOV RI WKH EHOORZV ZHUH TXLWH WKLQ DQG IOH[LEOH $V VXFK WKH\ DOORZHG WKH EHOORZV WR PRYH IUHHO\ XS DQG GRZQ DQG WKHUHE\ FKDQJH WKH RYHUDOO V\VWHP YROXPH :KHQ WKH EHOORZV ZDV DW D ORZ SRVLWLRQ WKH ZDOOV ZHUH FRPSUHVVHG DQG TXLWH ULJLG +RZHYHU ZKHQ WKH EHOORZV ZDV DW D KLJK SRVLWLRQ WKH ZDOOV ZHUH XQFRPSUHVVHG DQG KDG VRPH IUHHGRP RI PRYHPHQW WR H[SDQG RU EXOJH RXWZDUGV $V WKH V\VWHP WHPSHUDWXUH ZDV FKDQJHG WKH VWLIIQHVV RU FRPSOLDQFH RI WKH EHOORZV ZDOOV DOVR FKDQJHG 7KHUHIRUH WKH DPRXQW RI WKH EHOORZV RXWZDUG EXOJH DQG WKH FKDQJH LQ V\VWHP YROXPH FKDQJHG GHSHQGHQW RQ WHPSHUDWXUH 7KH H[WUD GHJUHH RI IUHHGRP WR EXOJH RXWZDUG FRPELQHG ZLWK FKDQJLQJ ZDOO SURSHUWLHV EDVHG RQ WHPSHUDWXUH PDGH LW LPSRVVLEOH WR ILQG DQ H[DFW V\VWHP GHQVLW\ E\ PRQLWRULQJ WKH EHOORZV SRVLWLRQ &RQVHTXHQWO\ ZKLOH WKH YROXPH PHDVXUHPHQWV LOOXVWUDWHG LQ YDULRXV JUDSKV LQ WKLV ZRUN DUH QRW KLJKO\ DFFXUDWH WKH\ GR QRW KDYH DQ XQFHUWDLQW\ RI PRUH WKDQ D IHZ PLOOLOLWHUV RXW RI DSSUR[LPDWHO\ D WKUHH OLWHU V\VWHP

PAGE 79

$V WKH V\VWHP YROXPH ZDV QRW SUHFLVHO\ TXDQWLILDEOH LW LV GHVLUDEOH WR IRFXV RQ D V\VWHP SDUDPHWHU WKDW ZDV PRUH DFFXUDWHO\ PHDVXUHG 7KH FRQVWDQW WHPSHUDWXUH HQYLURQPHQW ZDV KHOG WR ZLWKLQ WHQ PLOOLNHOYLQ RI HDFK VHW WHPSHUDWXUH XQGHU VWXG\ 7KH V\VWHP YROXPH ZDV LQFUHDVHG DW D QHDUO\ FRQVWDQW UDWH DQG WKH V\VWHP SUHVVXUH DQG V\VWHP VSHHG RI VRXQG ZHUH WUDFNHG DQDO\WLFDOO\ L LQ ;R FQ 2 4M Ur LQ 7\SLFDO SORW RI V\VWHP VSHHG RI VRXQG YHUVXV V\VWHP SUHVVXUH 9 ? ? Lf§Lf§U r } f§U W f§,f§U 7f§U Lf§U Lf§f§U 3UHVVXUH 03D )LJXUH 7\SLFDO UHODWLRQVKLS EHWZHHQ WKH V\VWHP VSHHG RI VRXQG DQG WKH V\VWHP SUHVVXUH

PAGE 80

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

PAGE 81

SORW WKDW PRVW FORVHO\ DSSURDFKHV WKH FULWLFDO SRLQW FRQGLWLRQV $W WKH VDPH WLPH DQ LQGLFDWLRQ RI WKH SUHFLVLRQ RI WKH RYHUDOO WHFKQLTXH FDQ EH GHPRQVWUDWHG T A 2n FQ 8 8 aL r* & *RR &2 + + 3ORW RI DOO GDWD UXQV RQ D FRPPRQ VHW RI D[HV WWf§Lf§U ‘ L ‘ W V WaL L L L L L L L L L L L L  L L L L Lf§Lf§L L L L L 3UHVVXUH 03D )LJXUH 3ORW RI DOO GDWD VHWV RI SUHVVXUH DQG VSHHG RI VRXQG RQ D FRPPRQ VHW RI D[HV )LJXUH LOOXVWUDWHV WKH DV\PSWRWLF QDWXUH RI V\VWHP VSHHG RI VRXQG DV WKH H[SHULPHQWDO FRQGLWLRQV DSSURDFK WKH FULWLFDO SRLQW FRQGLWLRQV &RPELQHG LQ WKH SORW VKRZQ LQ ILJXUH DUH D WRWDO RI WZHQW\ GDWD UXQV FRQVLVWLQJ RI WRWDO GDWD SRLQWV $V WKH FULWLFDO SRLQW LV DSSURDFKHG WKH FRPELQHG SORW UDSLGO\ IDOOV RII WRZDUG ]HUR VSHHG RI VRXQG DQG

PAGE 82

H[KLELWV D nVSLNHn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

PAGE 83

7\SLFDO YDULDWLRQ RI WHPSHUDWXUH RYHU WKH FRXUVH RI DQ HQWLUH GDWD UXQ W f§ W U f L M L L M U c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

PAGE 84

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

PAGE 85

WKDW GHYLDWHV PRVW IURP LVRWKHUPDO FRQGLWLRQV

PAGE 86

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

PAGE 87

$ WKUHHGLPHQVLRQDO SORW RI DOO WKUHH V\VWHP SDUDPHWHUV FOHDUO\ GHPRQVWUDWHV WKH SUHFLVLRQ RI WKH WHFKQLTXH HPSOR\HG LQ WKLV H[SHULPHQW )LJXUH LV D SORW RI V\VWHP VSHHG RI VRXQG V\VWHP WHPSHUDWXUH DQG V\VWHP SUHVVXUH 7KH SORWWHG ILJXUH ORRNV VWULNLQJO\ OLNH WKH KHDG RI DQ DUURZ SRLQWLQJ GLUHFWO\ WR WKH FULWLFDO SRLQW 1R RWKHU WHFKQLTXH SURYLGHV VXFK D VWULNLQJ LQGLFDWRU RI WKH ORFDWLRQ RI WKH FULWLFDO SRLQW )LJXUH 7KUHH GLPHQVLRQDO SORW RI V\VWHP YDULDEOHV WHPSHUDWXUH DQG VSHHG RI VRXQG

PAGE 88

&XUYH )LWWLQJ 7R DWWDLQ WKH SDUDPHWHUV IRU WKH FULWLFDO SRLQW RI PHWKDQH LW LV SRVVLEOH WR GUDZ WKH OLPLWLQJ VORSH DV\PSWRWHV RQ ILJXUHV DQG DQG LGHQWLI\ WKHLU LQWHUVHFWLRQ DV WKH FULWLFDO SRLQW +RZHYHU VXFK D WHFKQLTXH LV JUDSKLFDO LQ QDWXUH DQG VXEMHFW WR LQGLYLGXDO LQWHUSUHWDWLRQ 6LQFH WKH RYHUDOO H[SHULPHQWDO WHFKQLTXH LV EDVHG RQ D PDWKHPDWLFDO VLQJXODULW\ D PXFK PRUH VDWLVI\LQJ PHWKRG RI FULWLFDO SRLQW LGHQWLILFDWLRQ ZRXOG LQYROYH D ILW RI WKH H[SHULPHQWDO GDWD WR DQ DSSURSULDWH PDWKHPDWLFDO UHODWLRQVKLS IURP ZKLFK WKH FULWLFDO SDUDPHWHUV PD\ EH DQDO\WLFDOO\ LQIHUUHG &ULWLFDO SUHVVXUH $ PRGHO IRU GHVFULELQJ WKH EHKDYLRU RI WKH ODWHQW KHDW RI YDSRUL]DWLRQ DV D IXQFWLRQ RI WHPSHUDWXUH ZDV SURSRVHG E\ 6WHOO DQG 7RUTXRWR 7KHLU PDWKHPDWLFDO PRGHO DQG VXEVHTXHQW HTXDWLRQ ZDV PRGLILHG E\ 6LYDUDPDQ HW DO WR UHODWH WKH VSHHG RI VRXQG WR WHPSHUDWXUH 7KH HTXDWLRQ ZDV GHULYHG IURP UHQRUPDOL]DWLRQ JURXS WKHRU\ E\ :HJQHU DQG ODWHU UHILQHG E\ /H\.RR DQG *UHHQ 7KH PDWKHPDWLFDO PRGHO WUHDWV EHKDYLRU VLPLODU WR WKDW H[KLELWHG E\ WKH H[SHULPHQWDO GDWD JDWKHUHG IURP WKLV ZRUN 7KH EDVLF HTXDWLRQ UHODWLQJ VSHHG RI VRXQG WR WHPSHUDWXUH LV $M7I $7USrD $7M r3 $7U $7M $J7M (TQ

PAGE 89

:KH F 6SHHG RI 6RXQG PV 5 ,GHDO *DV &RQVWDQW -.fPROH 7f &ULWLFDO 7HPSHUDWXUH 0 0ROHFXODU :HLJKW .JPROH $ &RHIILFLHQWV 7 5HGXFHG 7HPSHUDWXUH _77&_7&f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

PAGE 90

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

PAGE 91

H[SHULPHQWDO UHVXOWV FKL VTXDUHG IURP WKH UHJUHVVLRQ DQDO\VLV ZDV f $ FORVH H[DPLQDWLRQ RI WKH H[SRQHQWV RQ 3U LQ HTQ LQGLFDWHV WKDW +RZHYHU DQRWKHU H[SRQHQW RQ 3U LV DOUHDG\ 7KXV ERWK WHUPV FDQ EH FRPELQHG WR VLPSOLI\ HTXDWLRQ
PAGE 92

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

PAGE 93

LV D SORW RI V\VWHP WHPSHUDWXUH YHUVXV V\VWHP SUHVVXUH ZKHUH HDFK LQGLYLGXDO SRLQW LV DW WKH PLQLPXP V\VWHP VSHHG RI VRXQG IRU DQ LQGLYLGXDO GDWD UXQ VRXQG IRU HDFK GDWD UXQ 7KH OLQH GUDZQ LQ ILJXUH LV VWUDLJKW +RZHYHU WKH FRH[LVWHQFH FXUYH EHWZHHQ OLTXLG DQG YDSRU VWDWHV IRU D WKHUPRG\QDPLF IOXLG LV QRW FRQVWUDLQHG WR EH VWUDLJKW DW DOO 6WLOO DQ\ FXUYH FDQ EH DSSUR[LPDWHG E\ D VWUDLJKW OLQH SURYLGHG WKH DUF OHQJWK XQGHU VFUXWLQ\ LV KHOG WR D VPDOO

PAGE 94

LQWHUYDO 7KH WHPSHUDWXUH YDOXH IRU WKH FULWLFDO SRLQW OLHV VRPHZKHUH DORQJ WKH OLQH GUDZQ LQ ILJXUH 7KH YDOXH IRU WKH FULWLFDO SUHVVXUH IRXQG HDUOLHU FDQ EH VXEVWLWXWHG LQWR WKH HTXDWLRQ RI WKH OLQH VKRZQ LQ ILJXUH DQG WKH FULWLFDO WHPSHUDWXUH FDQ EH FDOFXODWHG GLUHFWO\ 7KH HTXDWLRQ RI WKH OLQH LV 3 03D.f 7 03D )URP WKLV HTXDWLRQ WKH FULWLFDO WHPSHUDWXUH LV 7KHUPRG\QDPLF 6XUIDFH 7KH H[LVWHQFH RI HTXDWLRQV WKDW PRGHO WKH H[SHULPHQWDO UHVXOWV LQ DQ DQDO\WLFDO PDQQHU OHDGV WR WKH SRVVLELOLW\ RI LOOXVWUDWLQJ WKH WKHUPRG\QDPLF VXUIDFH DW WKH FULWLFDO SRLQW )LJXUH LV DQ H[WUDSRODWLRQ RI WKH DQDO\WLFDO HTXDWLRQV XS WR WKURXJK DQG EH\RQG WKH FULWLFDO SRLQW RI 0HWKDQH

PAGE 95

)LJXUH PHWKDQH 7KHUPRG\QDPLF VXUIDFH RI WKH FULWLFDO SRLQW RI

PAGE 96

&+$37(5 ',6&866,21 7KH &ULWLFDO 3RLQW RI 0HWKDQH 7KH ILQDO FULWLFDO YDOXHV GHWHUPLQHG IURP WKLV ZRUN DUH DV IROORZV ,03D 03D 7B s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

PAGE 97

7HPSHUDWXUH 3UHVVXUH 'HQVLW\ 5HVHDUFKHU \HDU &DUGRVR f .H\HV f QD %HQQHZLW] t $QGUHHYD %ORRPHU t 3DUUHQW QD 7LPURW t 3DYORYLWFK *ULJRU t 6WHHOH f QD 5LFFL t 6FDIH f r 9HQQL[ HW DOf f -DQVRRQH HW DO f 3RSH HW DOf r *LHOHQ HW DOf .OHLQUDKP HW DO rr QD 7KLV :RUN r %DVHG RQ ,QWHUQDWLRQDO 7HPSHUDWXUH 6FDOH RI rr %DVHG RQ ,QWHUQDWLRQDO 7HPSHUDWXUH 6FDOH RI 7DEOH 0HWKDQH FULWLFDO SRLQW SDUDPHWHUV IRXQG LQ WKH OLWHUDWXUH FR ML

PAGE 98

GLIILFXOW ,W LV SRVVLEOH KRZHYHU WR ORRN IRU SRWHQWLDO V\VWHPDWLF HUURUV WKDW PLJKW H[LVW LQ WKLV ZRUN 2QFH VXFK D VHDUFK LV FRPSOHWH WKH SUHFLVLRQ RI WKLV WHFKQLTXH FDQ EH IDYRUDEO\ GHPRQVWUDWHG DQG D FRPSDULVRQ RI WKLV GDWD WR WKDW REWDLQHG IURP SUHYLRXV ZRUN FDQ EH PDGH *DV ,PSXULW\ ,Q WKH UHIHUHQFH FLWHG MXVW SUHYLRXV WR WKLV ZRUN LQ WDEOH WKH TXDOLW\ RI WKH PHWKDQH XWLOL]HG E\ .OHLQUDKP DQG FRZRUNHUV ZDV VWDWHG DV b SXUH 7KH PHWKDQH XWLOL]HG IRU WKLV ZRUN ZDV RQO\ b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

PAGE 99

EHHQ REWDLQHG OHVV WKDQ VL[ PRQWKV SUHYLRXV WR SHUIRUPDQFH RI WKLV H[SHULPHQW FDOLEUDWLRQ ZDV GHHPHG XQQHFHVVDU\ $OVR D SUHFLVLRQ UHVLVWRU ZDV UHTXLUHG EXW XQDYDLODEOH $V D SUHFDXWLRQ WKH .HLWKOH\ $ ZDV FKHFNHG DJDLQVW WKH SUHFDOLEUDWHG 57' 5HVLVWDQFH YDOXHV FRUUHVSRQGLQJ WR WHPSHUDWXUH YDOXHV ZHUH VXSSOLHG E\ WKH 57'nV PDQXIDFWXUHU ,I WKH '00 ZDV SURSHUO\ FDOLEUDWHG LW VKRXOG DOZD\V SURGXFH UHVLVWDQFH YDOXHV WKDW PDWFKHG UHVLVWDQFH YDOXHV VXSSOLHG E\ WKH 57' PDQXIDFWXUHU IRU D VSHFLILF WHPSHUDWXUH 7KH SUHFDOLEUDWHG 57' ZDV FKHFNHG DJDLQVW WKH NQRZQ WHPSHUDWXUH YDOXH IRU WKH WULSOH SRLQW RI ZDWHU 7KH GLIIHUHQFH EHWZHHQ WKH '00 UHVLVWDQFH UHDGLQJ DQG WKH VWDWHG PDQXIDFWXUHUn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

PAGE 100

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

PAGE 101

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

PAGE 102

ZDV JDLQHG IURP DQ H[SHULPHQW ZKLFK XWLOL]HG DQ LVRFKRULF F\OLQGULFDO UHVRQDWRU LQVWHDG RI DQ LVRWKHUPDO VSKHULFDO UHVRQDWRU DV LQ WKLV ZRUN ,QIRUPDWLRQ UHSUHVHQWHG LQ ILJXUH ZDV QRW LQWHQGHG WR JLYH D SUHFLVH PHDVXUHPHQW RI WKH FULWLFDO SRLQW RI PHWKDQH 5DWKHU LW ZDV LQWHQGHG WR LOOXVWUDWH WKH SRWHQWLDO VHQVLWLYLW\ RI WKH WHFKQLTXH DV D SUREH IRU WKH FULWLFDO SRLQW RI DQ\ WKHUPRG\QDPLF IOXLG )LJXUH LV D JUDSK RI WZHQW\ GDWD VHWV FROOHFWHG IRU WKLV ZRUN SORWWHG LGHQWLFDOO\ WR WKH GDWD FRQWDLQHG LQ ILJXUH ,W FDQ EH UHDGLO\ VHHQ WKDW WKH SUHFLVLRQ RI WKH WHFKQLTXH XWLOL]HG IRU WKLV UHSRUW LV H[WUHPHO\ KLJK 1R RWKHU WHFKQLTXH KDV EHHQ DEOH WR ORRN DW GDWD DV WLJKWO\ FOXVWHUHG DV WKH FXUUHQW ZRUN LV FDSDEOH RI RQ D URXWLQH EDVLV :RUN GRQH E\ UHVHDUFKHUV LQ WKLV JURXS LQ WKH SDVW XWLOL]LQJ UHODWHG VRQLF WHFKQLTXHV KDV URXWLQHO\ EHHQ ZLWKLQ

PAGE 103

b RI SUHYLRXVO\ DFFHSWHG OLWHUDWXUH YDOXHV 6XFK H[FHOOHQW DJUHHPHQW KDV EHHQ DWWDLQHG IRU IOXLGV WKDW ZHUH PXFK OHVVGHPDQGLQJ LQ WHUPV RI WKH DELOLW\ WR ZRUN DW WKH WHPSHUDWXUH DQG SUHVVXUH RI WKHLU FULWLFDO UHJLRQ 7 ; 7 3UHVVXUH 03D )LJXUH 6RXQG YHORFLW\ DW VHOHFWHG WHPSHUDWXUHV DV D IXQFWLRQ RI SUHVVXUH 3HUVRQDO 1RWH 7KH LQLWLDO SUHVVXUH ORDGLQJ RI WKH VSKHULFDO UHVRQDWRU V\VWHP ZLWK PHWKDQH ZDV IROORZHG RQ D '\QDPLF 6LJQDO $QDO\]HU '6$f 2QFH WKH V\VWHP ZDV ORDGHG ZLWK WKH DQWLFLSDWHG FULWLFDO SUHVVXUH WKH '6$ ZDV XVHG WR FKHFN ZKHWKHU RU QRW LW ZDV SRVVLEOH WR ILQG D PLQLPXP LQ WKH VSHHG RI VRXQG RI WKH V\VWHP ZLWKLQ WKH UDQJH RI WKH EHOORZV PRYHPHQW 7KH '6$ ZDV XWLOL]HG EHFDXVH LW ZDV FDSDEOH RI SHUIRUPLQJ D ELW IDVW

PAGE 104

)LJXUH *UDSK RI VRXQG YHORFLW\ DV D IXQFWLRQ RI SUHVVXUH FRQWDLQLQJ DOO WZHQW\ GDWD UXQV IURP WKLV H[SHULPHQW )RXULHU WUDQVIRUP RQ DFRXVWLF GDWD DQG GLVSOD\LQJ WKH UHVXOWLQJ IUHTXHQF\ GDWD DW WLPHV D PLQXWH &KDQJHV RI FRQGLWLRQV ZLWKLQ WKH VSKHULFDO UHVRQDWRU V\VWHP FRXOG EH IROORZHG YHU\ FORVHO\ ,I WKH VSKHULFDO UHVRQDWRU V\VWHP KDG LQVXIILFLHQW RU H[FHVV PHWKDQH ZLWKLQ LW WKH GLVFUHSDQF\ FRXOG EH GLVFRYHUHG TXLWH TXLFNO\ DQG WKH V\VWHP SUHVVXUH FRXOG EH DGMXVWHG DFFRUGLQJO\ $V WKH RYHUDOO V\VWHP FRQGLWLRQV DSSURDFKHG YHU\ QHDU WKH FRQGLWLRQV WKDW H[LVW DW WKH FULWLFDO SRLQW RI PHWKDQH IUHTXHQF\ GDWD GLVSOD\HG RQ WKH '6$ EHFDPH GDPSHQHG DQG PRYHG YHU\ UDSLGO\ WRZDUG ]HUR IUHTXHQF\ (YHQWXDOO\ WKH V\VWHP EHFDPH WRR G\QDPLF DQG WKH '6$ SURYHG LQFDSDEOH RI NHHSLQJ SDFH ZLWK FKDQJLQJ FRQGLWLRQV 7KH GHFLVLRQ ZDV PDGH WR

PAGE 105

VZLWFK WR WKH PRUH DFFXUDWH PHWKRG RI IROORZLQJ IUHTXHQF\ GDWD WKDW WKH PDVWHU GDWD FRPSXWHU DIIRUGHG QDPHO\ D ELW IDVW )RXULHU WUDQVIRUP FDSDELOLW\ %HIRUH WKH FKDQJHRYHU KRZHYHU WHPSHUDWXUH ZDV GURSSHG VWHDGLO\ DQG YROXPH ZDV H[SDQGHG VWHDGLO\ LQ DQ DWWHPSW WR UHDFK WKH FULWLFDO SRLQW FRQGLWLRQV )UHTXHQF\ GDWD GURSSHG VWHDGLO\ XQWLO WKH DQWLFLSDWHG FULWLFDO SRLQW FRQGLWLRQV ZHUH UHDFKHG EXW WKH IUHTXHQF\ GDWD FRQWLQXHG WR PRYH WR ORZHU YDOXHV HYHQ DIWHU WKLV SRLQW ,W ZDV DVVXPHG DW WKH WLPH WKDW IXUWKHU WZHDNLQJ RI WKH V\VWHP YDULDEOHV ZDV UHTXLUHG WR ]HUR LQ RQ WKH FULWLFDO SRLQW FRQGLWLRQV DQG WKDW VXFK DGMXVWPHQW FRXOG EH PDGH RQO\ DIWHU FDUHIXO VWXG\ RI WKH PRUH DFFXUDWH PHWKRGV HPSOR\HG E\ WKH PDVWHU GDWD FRPSXWHU DOJRULWKPV 7HPSHUDWXUH DQG YROXPH FKDQJHV ZHUH DOORZHG WR FRQWLQXH KRZHYHU LQ DQ DWWHPSW WR ILQG WKH SRLQW DW ZKLFK WKH IUHTXHQF\ GDWD ZRXOG EHJLQ WR PRYH WR KLJKHU YDOXHV DV KDV EHHQ REVHUYHG LQ VHYHUDO JUDSKV SUHVHQWHG LQ SUHYLRXV FKDSWHUV RI WKLV UHSRUWf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

PAGE 106

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nV EXW ZLWK WKH UDSLG FKDQJH RFFXUULQJ LQ HOHFWURQLF LQVWUXPHQWDWLRQ VXFK FDSDELOLW\ LV OLNHO\ WR DULVH LQ WKH IXWXUH

PAGE 107

5()(5(1&( /,67 -RVWHQ 0HOYLQ -RKQVWRQ 'DYLG 1HWWHUYLOOH -RKQ 7 :RRG -DPHV / :RUOG RI &KHPLVWU\ 6DXQGHUV &ROOHJH 3XEOLVKLQJ 3KLODGHOSKLD 3D $WNLQV 3 : 3K\VLFDO &KHPLVWU\ UG HG : + )UHHPDQ DQG &RPSDQ\ 1HZ
PAGE 108

$OEHUW\ 5REHUW $ 'DQLHOV )DUULQJWRQ 3K\VLFDO &KHPLVWU\ WK HG -RKQ :LOH\ t 6RQV 1HZ
PAGE 109

0RUVH 3KLOLS 0 ,QJDUG 8QR 7KHRUHWLFDO $FRXVWLFV 0F*UDZ+LOO %RRN &RPSDQ\ 1HZ
PAGE 110

6LYDUDPDQ $ .UDJDV 7 .RED\DVKL 5 )OXLG 3KDVH (TXLOLEULD :HJQHU ) 3KYV 5HY % /H\.RR 0 *UHHQ 0 6 3K\V 5HY $ &DUGRVR ( &KLP 3KYV Y .H\HV ) 6PLWK / % -RXEHUW % 0DWK 3KYV 0 7f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

PAGE 111

-LQ ; 7DQJ 6 6HQJHUV 7KHUPRSK\V MXO\ 9 ,QW -

PAGE 112

%,2*5$3+,&$/ 6.(7&+ 7KH DXWKRU 'DYLG &DVH\ 5HQW] ZDV ERUQ $XJXVW WK +LV SDUHQWV DUH 5D\PRQG DQG 0DULO\Q 5HQW] +LV VLEOLQJV DUH /DXULH (ULF .HYLQ DQG (ULQ +H PDUULHG $VKOH\ (OL]DEHWK /LJKW LQ 0D\ RI +H HDUQHG D %DFKHORU RI 6FLHQFH GHJUHH IURP WKH 8QLYHUVLW\ RI 1RUWKHUQ ,RZD LQ +H FRPSOHWHG KLV JUDGXDWH VWXGLHV DW WKH 8QLYHUVLW\ RI )ORULGD LQ $SULO RI

PAGE 113

, FHUWLI\ WKDW KDYH UHDG WKLV VWXG\ DQG WKDW LQ P\ RSLQLRQ LW FRQIRUPV WR DFFHSWDEOH VWDQGDUGV RI VFKRODUO\ SUHVHQWDWLRQ DQG LV IXOO\ DGHTXDWH LQ VFRSH DQG TXDOLW\ DV D GLVVHUWDWLRQ IRU WKH GHJUHH RI 'RFWRU RI 3KLORVRSK\ $VVRFL &KDLU RI &KHPLVWU\ FHUWLI\ WKDW KDYH UHDG WKLV VWXG\ DQG WKDW LQ P\ RSLQLRQ LW FRQIRUPV WR DFFHSWDEOH VWDQGDUGV RI VFKRODUO\ SUHVHQWDWLRQ DQG LV IXOO\ DGHTXDWH LQ VFRSH DQG TXDOLW\ DV D GLVVHUWDWLRQ IRU WKH GHJUHH RI 'RFWRU RI 3KLORVRSK\ 0LFKDHO =HUQA 3URIHVVRU RIK FHUWLI\ WKDW KDYH UHDG WKLV VWXG\ DQG WKDW LQ P\ RSLQLRQ LW FRQIRUPV WR DFFHSWDEOH VWDQGDUGV RI VFKRODUO\ SUHVHQWDWLRQ DQG LV IXOO\ DGHTXDWH LQ VFRSH DQG TXDOLW\ DV D GLVVHUWDWLRQ IRU WKH GHJUHH RI 'RFWRU RI 3KLORVRSK\ HPLVWU\ J (\OHU VVRU RI &KHPLVWU\ FHUWLI\ WKDW KDYH RSLQLRQ LW FRQIRUPV UHDG WKLV VWXG\ DQG WKDW VWDQGDUGV R DFFHSWDEOH LQ P\ RI VFKRODUO\ SUHVHQWDWLRQ DQG LV IXOO\ DGHTXDWH LQ VFRSH DQG TXDOLW\ D GLVVHUWDWLRQ IRU WKH GHJUHH RI 'RFWRU RI 3KLORVRSK\ 3URIHVVR &KHPLVWU\ FHUWLI\ WKDW KDYH UHDG WKLV VWXG\ DQG VWDQGDUGV WKDW LQ P\ RSLQLRQ LW FRQIRUPV WR DFFHSWDEOH VWDQGDUGV RI VFKRODUO\ SUHVHQWDWLRQ DQG LV IXOO\ DGHTXDWH LQ VFRSH DQG TXDOLW\ D GLVVHUWDWLRQ IRU WKH GHJUHH RI 'RFWRU RI 3KLORVRSK\ =RUDQ 3RS6WRMDQRYLF 3URIHVVRU RI 0DWKHPDWLFV

PAGE 114

7KLV GLVVHUWDWLRQ ZDV VXEPLWWHG WR WKH *UDGXDWH )DFXOW\ RI WKH 'HSDUWPHQW RI &KHPLVWU\ LQ WKH &ROOHJH RI /LEHUDO $UWV DQG 6FLHQFHV DQG ZDV DFFHSWHG DV SDUWLDO IXOILOOPHQW RI WKH UHTXLUHPHQWV IRU WKH GHJUHH RI 'RFWRU RI 3KLORVRSK\ $SULO 'HDQ *UDGXDWH 6FKRRO

PAGE 115

81,9(56,7< 2) )/25,'$


xml version 1.0 encoding UTF-8
REPORT xmlns http:www.fcla.edudlsmddaitss xmlns:xsi http:www.w3.org2001XMLSchema-instance xsi:schemaLocation http:www.fcla.edudlsmddaitssdaitssReport.xsd
INGEST IEID ENY3PMQLC_YITSBK INGEST_TIME 2012-01-27T21:51:02Z PACKAGE AA00003222_00001
AGREEMENT_INFO ACCOUNT UF PROJECT UFDC
FILES