SOCIETYOF PETROLEUMENGINEERS6200 North CenCralExpresswayDallas,Texas 75206

THIS

PREDICTION

OF AIME PAPERNUMBER SPE 2383

IS A PREPRINT--- SUBJECTTO CORRECTION

OF SPONTANEOUSIGNITIONIN IN-SITUCOMBUSTION

By

Roger J. Schoeppel,MemberAIME, OklahomaStateUniversity,Stillwater,OklahomaDemir Ersoy,Jr, Member ADIE, StanfordUniversity,Stanford,California

0 Copyright 1968Amerimm Institute of !Mining, Metallurgical and Petroleum Engineers, Inc.

This paperwas presentedat the OklahomaRegionalMeeting of the Societyof PetroleumEngineeof AIM, to be held at OklahomaStateUniversity,Stillwater,Oklahoma,October25, 1968, Permis-sion to copy is restrictedto an abatractof not more than 300 words. Illustrationsmay not becopied. The abstractshouldcontainconspicuousacknowledgmentof where and by whom the paper ispresented. Publicationelsewhereafter publicationin the JOURNALOF PETROLEUMTECHNOLOGYor theSOCIETYOF PETROLEUMENGINEERSJOURNALis usuallygrantedupon requestto the Editorof the appro-priate journalprovidedagreementto give propercredit is made.

Discussionof this paper is invited. Three copiesof any discussionshouldbe sent to theSocietyof PetroleumEngineersoffice. Such discussionmay be presentedat the abovemeetingand,with the paper,may be consideredfor publicationin one of the two SPE magazines.

ABSTRACT.— INTRODUCTION

This paper presentsa theoreticalstudy In-situcombustionconsistsof injectingof spontaneousignitionas it could inten- ambient temperature air into the reservoirtionallyor unintentionallyoccur duringthe and burninga portionof the oil to improveignitionstageof an in-situcombustionpro- recoveryefficiency. To start this processitject. The study is based on a combinedheat is firstnecessaryto ignitethe oil in theand mass transferanalysisof this low tem- formationand then to sustaincombustionbyperatureoxidationsituationwhereinchemical continuousair injection, Severalmethodsreactionis also present. The mathematical have been used to initiatethe combustionpro-approachapproximatesfieldconditionsby cess. These have used electricalandlorchemusing a radialmodel and determinestempera- icalmeans to raise the immediatewell boreture and oxygenconcentrationsas a function surroundingsto a temperaturelevelsufficienof radiusand time. to sustaincombustion.

From the study, it can be predicted Spontaneousignitionis a phenomenonwhether the well will ignitespontaneously wherein ignitionoccursspontaneouslyas awithoutuse of an outsideheat source,the resultof air injectioninto the reservair.distancefrom the well bore where ignition In the initialstagesheat releaseddue tooccurs,the time requiredto obtainignition, low temperatureoxidationaccumulatesfasterand the effectof controllingvariablessuch than can be dissipatedresultingin an in-as the chemicalactivityof the crude, inter- creasein temperature. If heat continuestofacialarea, initialtemperature,oxygenen- be generatedat a rate greaterthan can be disrichmentof injectedair, pressure,and the sipated,a temperatureconditionis sooninfluenceof chemicalagentsused to promote reachedwhich is generallyacceptedas thelow temperatureoxidation. “ignitiontemperature!’Utilizationof this

tcReferenc@sare given at end of paper.

t

TUTC TC A DRFDRTNT . . . CIIRTRVP TA CflR12UPTTOhl Cnu 9’2Q2

naturalphenomenonwhere applicableoffers cer- that the order of reactionwith respecttotain advantagesover artificialmeans of obtain- fuel concentrationis generallyzerowhich im-ing ignitionof in-situcombustionprojects. plies that fuel contentis in excessand the

rate of reactionis independentof fuel con-The purposeof this paper is to describe centration. If theseconditionsare assumed,

a radial-flowmodel that has been used in pre- then the rate of low temperatureoxidationdietingspontaneousignition. The influence takesthe formof six differentvariableswhich affect radialtemperaturedistributions- resultingfrom con- . y=k,ctinuedair injectionwill be evaluated at

(3)

REVIEWAND DEVELOPMENT where C is oxygenconcentrationand k’ is aconstant,

Gates and Rameyl have reportedthat com-bustionspontaneouslyoccurredafter three Accordingto Arrheniua’prediction,themonths of continuousinjectionto establish reactionrate is given byair permeabilityin the South BelridgeFieldthermalrecoveryexperiment. The phenomenon . ac‘=A exp(-E/RT)was firstnoticedby an increasedin formation 3t

(4)

temperaturein an observationwell located20feet from the injectionwell. Within a week where A = constantor so the injectionwellborereachedtempera- E = activationenergytures in excessof 1000°F. Combustionhad R = universalgas constantapparentlybegun spontaneouslyat some dis- T = absolutetemperaturetance from the injectionwell and proceededinboth forwardand reversedirectionsin propor- The amountof heat releasedduring lowtion to the temperature,and fuel and oxygen temperatureoxidationdependson a numberofavailable. After reverseburningto the in- factorsincludingthe chemicalactivityofjectionwell, and consumingall availablefuel, the oil and its rate of reaction. Sincethe rear combustionzone ceasesto exi.s”tand changesin oxygenconcentrationprovidea con-its heat becomesdissipated. The net result venientmeans for followingthe rate of reac-is the auto-ignitionof an in-situcombustion tion,an estimateof the heat releaseperprojectwith a slightlylargerthan usual cubic foot of air utilizedcan be usedwithinitialheat bank. reasonableaccuracyto determinethe heat

generatedby the chemicalreaction. Thus,ChemicalKinetics

dCThe chemicalkineticswhich govern sponta- -Z=Q = skC exp(-E/RT) (5)

neous ignitiondependon the low temperatureoxidationcharacteristicof the crude oil. where s = surfaceto voiume ratioIf it is assumedthat oxidationof crude oil k = reactionrate constantis a simplereaction,such aa C = oxygenconcentration.

OXYGEN+ HYDROCARBONS+ PRODUCTSPhysicalModel

{aA -1-bB*pP (1)

The physicalmodel, consideredin thisanalysis$consistsof a typicalinjectionwell

where a, b, and p are the stoichiometriccoef-in an invertedfive-spotin-situcombustion

ficientsof A, B and P, then the rate of oxy-project,in which the injectedair flowsradi-

gen consumptionisally into a horizontaland homogeneoussectionof the reservoir, The model assumesa con-

aCA - ~stant pressuresystamwith’negligibletempera-

o CBture and oxygenconcentrationvariationsalong

~=kcA(2) the verticalaxis. Heat transferis assumed

to be by conductionand convection. It iswhere GA and CB are CO’nCeTttratiOIM $f reac- furtherassumedthat an infiniteheat trans-tantsA and B, respectively,6 and 13are their fer coefficientexistsbetweenthe gas andreactionorders,and k is the reactionrate rock matrix. The chemicalreactionis consi-constant. dered to followArrhenius’relationship.

Oxygen loss,by chemical.reaction,ia offsetWarren,Reed and Price(3considerthat the by the processesof diffusionand continued

orderof reactionwith respectto oxygencon- injection. The diffusioncoefficient,as wellcentrationmay vary betweenzero and one butis closerto one in this case. They also noted

as other physicalparameters,are consideredto be independentof temperature.

,- ..-” - ..”a-* w . “-.. ”-w”w* -,. ” ““..*** -.-”,*

Heat BalanceEauation method, the distanceand time derivativescanbe approximatedby:

By applyinga heat balanceto a differen-tial radialelementof unit thickness,the ~=~

(‘i-l-1,1+1- ‘i-1,1+1

followingequa~ion ar 2 2 Ar

aaTF

!l&!)+g+ (1 - 2nK * ‘i+l,j - ‘i-1‘i)2Ar ‘ (8)

‘tct aT+ # skC exp(-E/RT) = ——

K at(6) a

~=+ ‘Ti+l,j+l(

- 2Ti,j+l+‘1.1,1+1~

can be derivedas shown in App&dix 1,

+ ‘il-l,j- 2Ti + Ti-lOxygen BalanceEauation s

Ara “)(9)

For the same differentialradialelement, andoxygenconcentrationis governedby an oxygenbalance,where concentrationwithin the sys- @T= ‘i,jl-l- Ti,$tem are functionsof both time and radial at At “ (10)

location, Applyingthis “ Ilanceover theelementgives, For one mesh point,the equationcan be

writtenby finitedifferencerepresentationa,

=+(S 1 ac.—.— where the left 8ide of the equationcontains~r 2;) r & threeunknownsand the right side contains

Q known values. If there are (I) internalmesh

-WC exp(- E/RT) =~~ (7)pointsalong each time row, and the equationis written for every point,one may obtain(1) simultaneousequationsin termsof ini-

as similarlyderivedin”Appendix.1. tial and limitingconditions. These calcula-tion can then be forwardedto successive

Initialand boundaryconditionsfor the time rows.systemare aa follows:

NumericalHeat BalanceEquationHeaC Balance ~gen Balance

Initia1 The heat balanceequationshownabove can

Condition: t=O !C=TL C=c~ be simplifiedby definingthe constants

Limiting ~=l. ii?&Conditions:r=rwT=To C=co

aT-o g=o i3:=--sk‘=reZ - ar

(no flow (no flow Pt =t

boundary) boundary) Y =—K

lMPLICITSOLUTION to give:

As previouslyshown,the mathematical a2T+alaTanalysiaof this systemyields two parabolic ~ YSpartialdifferentialequationswhich arecoupledby rate-of-reactionterms. Theseequationsmay be solvednumericallyusing the

+9 C exp(- E/RT) = y% (11)

Crank-Nicolaon3methodwhich is applicablefor all rangesof time (j) and distance(i) By applyingthe Crank-Nicolsonimplicitincrements. In thismethod the derivative method to derivativeterms and rearrangingsotermsare replacedby the mean of its finite that unknownsappearon the leftand knownsdifferencerepresentationson the (j 1-1) and appearon the right,we obtain(j) time row, where thevaluee on the (j)time row are known and the valuea on the x(z) Ti-l,j+l+y(I) Ti,j+l(j + 1) time row are tobe calculated.

Accordingto the Crank-Nicolsonimplicit + 2(1) %l,j+l = W(I) ( 12)

t

TUTS TS A PRl?PRTNT --- S1lR.TI?CT T(3 C(3RRI?CTTON GDP 92Q’1

where

X(I) =21 At-~At

Y(I) = - 41 At - 4Ar2 I y

Z(I) =21 At+ aAt

W(I) = 21 A t(- Ti+l,j+ 2Ti,j - Ti-l,j~

-t-At Q(- Ti+l,j + ‘i-l,j)

-4 Ara IAt$C i,j+l‘Xp(- E’RTi,j+l)

“4Ar= 1yTiY3”

NumericalOxygenBalanceEquation

II

‘(1) = 21At(-ci+l,j+ ‘i,j- Ci.l,j)

+ ‘tar(-ci+l,j+ Ci-l,j)

- 4Ara I A t Sr Ci 3+1 exp(- E/RT9 i,j+l)

‘4Arz 1 ‘rci}j’

If initialand limitingconditionsforthe heat and oxygenbalanceequationsare de-fined$it is possibleto caLculatetempera-ture profilesand correspondingoxygencon-centrationsafter every time row, Limitingconditionsassumedfor numericalsolutionofthe heat and oxygenequationsare as follows:

I Heat Balance:

The numericalsolutionof the oxygenInitialcondition: T(i,l)= Ti lsi<I

balanceequationcan be simplifiedin a mannersimilarto the heat balanceequationto give:

j~=1

l=Araac MC+p~+arrar r C exp(-E/RT) Limitingconditions: T(l,j)=TO i= 1

where

( 13) ‘total1 s j SJ J=~

T(I-l,j)= T(I+l,j) lsjsJ,v

CYr ‘1-%5 OxygenBalance:

@r= -y

yr = Q/l.

Initialcondition: C(i,l)= Ci 1<1<1

Replacingderivativetermsby their finite Limitingconditions: C(i,j)= Codifferenceapproximationsand regrouping

j.sl

gives:

‘(1) Ci-l,j+l+ yy(I) Ci,j+l l<jsJ ~ = ‘totalAt

+ ZZ(I) Ci+l,j+l= W(I) (14) C(I-l,j)= C(I+l,j) lsjsJ.

where

XX(I) =21At-@rAt

‘iY(I)= -41At- 4AraIyr

The heat and oxygenbalanceequationscanthen be written in numericalform for everyradialpositionin the secondtime row result-ing in (I-1)equationswith (1-1)unknowns.Becauseof the nature of theseequations,Gaussianeliminationtechniquesare useful intheir simultaneoussolution.

ZZ(I)=21At-t-urAt I CALCULATIONPROCEDURE

Two second-orderparabolicpartialdif-ferentialequations,one for heat balanceandone for oxygenbalance,were approximatedbyCrank-Nicolsonimplicitmethodco a numericalform. By applytngan implicitequationto

— a.-. !?noor .1. %-hmennel sand Tkmlr ErsovF /*xl ..v~-. “ . --..--rF-. ----- - ------ ----

everypoint Oi. the same time row and defining RESULTSAND CONCLUSIONSrk.elimitingconditions,a set of simultaneouseyuationshave been obtainedwhich were solved Use of Arrhenius’relationto coupleby Gaussianeliminationtechniques. By this heat and oxygenbalanceequationsdescrip-procedure,temperatureand oxyg$nd$~~$$nt,f~,,%~f

[tive of low temperatureoxidationin a

tion valueswere calculatedfor ‘&Jeryt me A fieldmodel offersa mean~forincrements, predictingspontaneousignitionin an in-

situ combustionor otherair injectionpro-A computerprogramwas written to per- ject. (An alternateapproachwhich combines

form thesecalculations.Inthe program, 60 dimensionlessgroupswith experimentalre-sistanceincrementswere used where each in- sultshas been presentedby Caruthers4forcrementequaled5 feet. Calculations were predictingthe spontaneous.ignitionof lab-carriedout successivelyto 90 time increments oratoryexperiments.) The methodas devel-where each time incrementequaled24 hours. oped hereinpredictsthat a substantial

Assumeddata for a typicalfieldcasetemperatureincressemay occurwhen air isinjectedinto a reservoiras has been ob-

are preeentedin Table 1, An exampleof the servedin practice. This temperaturerisetempe~ ures and

tioxygenconcentrati,onscom- msy vary from minuteamountsto quite sig-

pute At e data of Table 1 and Run 1 of Table2 are presentedin Figure 1 for 15, 30, 45,

nificanttemperatureincreases,depending

60, 65 and 70 day periods,for all radial lo-upon the nature of the fuel and the otherfactorswhich controlthe spontaneousig-

cations. The peak temperaturemay be observ- nitionprocess,ed to move away from the well bore with con-tinuedair injection. Ignitionin this ex- it has been shownthat activationample occurredspontaneouslyat 26-27 feetfrom the injectionwell.

energyis an importantfactorin controllingspontaneousignitionwhere a smalldecrease

EFFECTOF PROCESSVARIABLESin she activationenergygreatlyincreasesthe rate of low temperatureoxidationandthus, spontaneousi~ni,tion.Initial forma-

The effectof heat generationon the rate tion temperatureis also shownto be an im-of spontaneousignitionhas been examinedfor portantfactorin auto-ignition,This var-processvariables. The resultsare presented iablehas a more effectiveinfluence ifin Figures2-6. consideredjointlywith loweractivation

energies. OxygenconcentrationeffectsdueThe effectof surfaceto volumeratio &a to eitherincreasedpressureor enrichment

shown in Figure2, where variationsfrom 10,000 are also importantin governingspontaneousto 30,000squarefeet per cubic foot az? con- ignition. Other parametershave smalleffectssidered. This parameteris shownto have a in comparisonwith activationenergy.directeffecton both the peak temperaturerise due to spontaneouscombustionand the Propagationof the locationof the peak8hapeof the temperatureprofile. temperatureaway from the well bore depends

Figure 3 showsthe effectof the reactionupon the rate of temperatureincreaseandthe distancetransvezaed. Movementof the

rate constantoverf!ten-foldchange. As shown, peak temperaturelocationis predictedtoan increasein the reactionrate constanthas reach a steadystate locationat a fixeda considerableeffecton spontaneousignition. distancefromth: well bore% The specific

distancedependAagupon proceseparameters.The activationenergywas found to have

the most pronouncedeffectson the low temp-eratureoxidationbehaviorof the system.The NOMENCLATUREeffectof nearlya ten percentdecreaseinotl activityis shownin Figure4 after 70 A Proportionalityconstantdays of continuousinjection. c Oxygen concentration,lb-mole

o~ / ft=The effectof initialoxygenconcentration

CfHeat capacityof matrix,

is consideredas a functionof pressureandlor Btu/lb ‘Foxygenenrichment.inFigure 5. Three differ- Heat capacityof ga~, Btu/lb

The offsett&40$”an initialtemperaturein- ;ent oxygenc n~~ t.ationlevelswere studied. “F

Diffusioncoefficient,creaseand a decreaaein the’initialoxygen ft3/hr-ftconcentrationi8 shown in Figure 6. As is E Activationenergy$Btu/lb-moleindicated,the increaaein initialtemperature H Heat of reaction,Btu/lb02more than compensatesfor the decrea8ein ox- h Overallheat transfercoeffi-vgen enrichment. cient,Btu/°F

,

6 THIS IS A PREPRINT--- SUBJECTTO CORRECTTON SPE 23

K

k

flc

qr

RR(C,T)

Pf

‘g

Thermalconductivity,Btu/hr-ft-°F

Reactionrate constant,lb-mole(32/hr-ft2

Oxygen flux, lb-mole0Z/hr-ft2

Heat flux,Btu/hr-ft2

Gas constant,Btu/lb-mole“REffectiverate of reaction,lb-mole 0e/hr-ft3

Surfaceto volume ratio, ft2/ftzAbsolutetemperature,“RAir injectionrate, SCF/hr-ftVolumetricair flux,SCF/hr-ft2Reactionorder of oxygen,dimen-sionless

Reactionorder of fuel, dimen-sionless

Densityof matrix, lb/ft3

Densityof gas, lb/ft3

Porosity,fractional‘g2,?,”V Constants,heat balanceequation

2r,13r,vr Constants,oxygenbalanceequa-tion

X,Y,Z,W Constants,simultaneousequationfor heat balanceequation

XX,YY,ZZ,WW Constants,simultaneousequationfor oxygenbalanceequation

i Radial locationj Time increment

ACKNOWLEDGMENT

The authorswish to recognizethegraduateprogramat the Universityof Tulsawhereinthiswork was completed. The seniorauthoralso wishes to thank the managementof Gulf Researchand DevelopmentCompanyforpermissionto extendand publishthe resultsof a summerwork assignment. Mr. L. A.Wilson is due specialrecognitionfor hisinitialguidancein the problem.

REFERENCES

(1) Gates,C. F., and Ramey,H. J., Jr.,“FieldResults of SouthBelridgeTher-mal RecoveryExperiment,” Trans.AIME(1958),~, 236.

(2) Warren,J, E,, Reed, R. L., and Price,H. S., ‘TheoreticalConsiderationsofReverseCombustionin Tsr Sands,”Trans.

(3) Smith,G. D., NumericalSolutionofPartialDifferentialEquations.OxfordUniversityPresa (1965).

(4) Caruthers,R. M., “SpontaneousIgnitionin PorousMedia,”Ph,D. Dissertation,Universityof Texas (1965),

APPENDIXI

DERIVATIONOF HEAT BALANCEAND OXYGEN

BALANCEEQUATIONS

Heat BalanceEquation

Consideringa differentialradialelementof unit thickness,a heat balanceof this systemcan be writtenas:

Heat in + heat generated

\ = Heat out + Heat accumulated

Heat transferby conductioncan bewrittenas,

Q1 = qrlr . 2,.Tr.t

“ qrlr+& “ 2(r+.r) “t (l-

where flux (qr) is governedby Fourier’slaw.

qr=-K~

Q1=-K *lr ●2.r-t

5J+ ‘~r] tih . 2“’(*ir) .t (1-

Convectionwithin the gas phase is,

Q2 = ‘gcgvT~r “ 2qr;t

- Pgcg~T~~4r ● 21T(*~r)~t (l-

Heat generationby Arrhenius’predictionofthe reactionrate can be shown to be:

Q3 = H s k C exp(-E/RT)o 21rLr~t (1-

Heat accumulationwithin the systemcan be caculatedfrom

%“ %ct’hit

. 2T’rrAr- PtctTlt, 2nrLr (l-

where

=(1- Qg) Pfcf+ Qg Pg Cg ●Ptct

Sl?E2383 Ro~er J. Schoemel and Demir Ernov. . — --- —------ ——-- ,

ICombiningthese terms in the form of a heat

balanceaccordingto

Q+ Q2+Qj=c&

and rearrangingwith differentiationyields:

82T ~LB.%%!~F r ar K M

f’tct aT‘R’(C,T) =~~‘K

(l-6)

In this equation? = & where V is the volu-

metric injectionrate per foot of bed thicknessVolumetricinjectionrate ia consideredcon-stant so that the volumetricgas fluxwill bea functionof radial location. Thus, R’(C,T)=s k C exp(-E/RT). Rearrangingthe terms givesthe finalheat balanceequation:

~+(1. ~)+~

Ptct aT+#skCexp(-E/RT)= ~ ~. (1-7)

OxygenBalanceEquation

For the same radialdifferentialelementused in derivingthe heat balanceequation,and assumin8an isobaricsystem,an oxygenbalancemust yield an equationwhere ~xygenconcentrationis expressedas a f M-? a.1 ofboth time and radial location, Sta- <ngwiththe overalloxygenbalanceequation

oxygen in = oxygenout

+ oxygen lossby reaction

+ change I.noxygencontent.

The oxygen transferby diffusioncan be des-cribedas,

c1 = qclr . 2nrAt - ‘cIr+Ar

. 2n(rl-Ar)At (1-8)

where

acqc=-D~.

The oxygentransferby convectionis,

C* = TClr “ 2nrAt

. ~Clr+Ar ● 2n(ri-Ar)At. (l-9)

Likewisethe oxygen loss by chemicalreactiocan be describedas:

C3 = R’(C,T)● 2nrArAt

= s k C exp(-E/RT)● 2nr4rAt (1-1

The change in the oxygencontentwithin thedifferentialelementcsn be describedas:

oxygencontentat time (t-!-At)

- oxygencontentat”time (t).

C4 = ‘gClt+At$ 2mrAr

- t’gC(t● 2nr4r (1-1

Combiningthese terms in the net oxygenbalanceequation:

c1 + C2 =C3+C4

gives,with differentiationand rearranging

where

~.1217.r

and

R’(C,T)= s ● k * C exp(- E/RT) .

(1-12)

, 0

THIS IS A PREPRINT --- SUBJECTTO CORRECTION SPE 2383

Parameter

‘g

‘g

v

K

H

Pf

Cf

fig

D

TABLE 1

PROCESS PARAMETERS

Selected Values

.08 lb/ft3

.2 13tu/lb°F

1000 SCF)hr-ft

.8 Btu)hr-ft°F

6000 Btu/lb 02

2.02 lb/ft3

20. Btu/lb°F

.2 fractional

.68 ftslhr-ft

TABLE II

PROCESS VARIABLES

Reaction OxygenRun Surface to Rate Activation Initial Concentra-

Number Volume Ratio Constant Energy Temperature tion

1 10000 .001 10000 540 .2845

S2 20000 ,.001 10000 540 .2845S3 30000 “.001 10000 540 .2845

K4 10000 .0001 10000 540 ,2845K5 10000 ..0005 10000 540 ,2845K6 10000 ● 0050 10000 540 .2845

E7 10000 :001 8000 540 .2845E8 10000 ..001 9000 540 .2845E9 10000 ..001 11000 540 .2845E1O 10000 .001 12000 540 .2845

Tll 10000 *001 10000 58o .2845T12 10000 ..001 10000 62o .2845T13 10000 .001 10000 660 .2845

C14 10000 ..001 10000 540 ,4060C15 10000 ● 001 10000 540 .5420

. ●

TEMPERATURE PROFUES

1208

1100

1000

90

RADIAL 10CATION, FT.

I?ig. 1. Temperature P~ofiles and Peak TemperatureBehavior in Example Calculation

TEMPERA TVRE,”R

●

☛

CHANGE W REACTION RATE’ CONSTANT

,

/,

MDU1 LOCATION, -FT.

Fig. 3. Effect of Reaction Rate Constanton Temperature Behavior

CMAMGE IM ACliivATIOM ENERGY

)

o

,/

&4RtAL DISTANCE, F1.Pig. 4. Effect of Activation Energy on

Temperature Behavior

/ .

.

-..20 40 60 8fl 100 120 140 1S8 188 20Q 22Q 24t? 260 280 300

RALM!4101S7ARWE,FXFig. 5. Effect o-f(lxYEemConcentration on I%nmerature Beha~?im*

. .

.

.

.

CflAM6E 1! IWXJA1 TEMPERATURE

Fig. 6. Effect of

JMMAL DISTANCE. FT.

Initial Temperature on Temperature Behavior

/.