Soo&ty of Petroleum Engineers

SPE 30316

Pressure-Volume-Temperature Correlations for Heavy and Extra Heavy OilsGiambattista De Ghetto*, Francesco Paone, and Marco Villa*, AGIP S.p.A.* SPE Member

fXWght 1Ss5, Sdety Of Petmfeum Engineers, Inc.

This papar was prepared for praaametion et the Infematiwml tiaavy Oil Sympmium held in Calgsry, Albarta, CenaOs, 1S-21 JunelSS5

This peper was aektad for pmsantarion by an SPE Progrsm CommMae fallowing reviaw of inforrnatii mnteinad in an atstrsct submiied by the author(s). contents of the paper, es praaentsdZ~*~~tk M~of Pet*~E_maMam_tim~ by ttw sufhor(s), Tha meteriel, aa prasentad, does not neceeserily reflecf any position of the

SOdOty of Petrobum Engineers, its ofkers, or members. Papars presntad ai SPiE tirrgs are aubjacf io piibbtifii iti* bjj E.WI.I ..1,,,0001-..,... .-*,,... .- .. .. . . . ..a.-..4 . . . . . ..”.... *-. ., h e,,,., 1“ ., D*,* GMi-m

Pwmiaeh to oopy is reetrktad to an abstrect of not rmra than S00 words. Ifluatrafions mey not be mpiad. The ebatrmt should mntain ooneR@uwsUta paper is pmaanted. Write Libmrfsn, SPE, PO. Sox SSSSSS, Riirdaon, TX 7S0SS-SS2S, U.S.A. (Facsimile 214-S52-94S5).

SdmowMgmenf orwhereandtywhom

ABSTRACT: Thepaper evaluates the reliability of the most common empirical correlations used for determining reservoir fluid properties

whenever laboratory PVT data are not available: bubblepoint pressure, solution GOR, bubblepoint OFVF. isothermal compressibility, dead-oilviscosity, gas-saturated oil viscosity and undersaturated oil viscosity.

The reliability has been evaluated against a set of shout 65 heavy and extra-heavy oil samples. About 1200 measured data points have beencollected and investigated. All measured data points are reported in the paper. For all the correlations, the following statistical parameters havebeen calculated: a) relative deviation between estimated and experimental values, b) average absolute percent error, c) standard deviation;

011 samples have been divided in two different API gravity ciasses: extra-heavy oils for ‘API< 10, heavy oils for 10< “API< 22.3.The kst correlations for each class of API gravity have been evaluated for each oil-property.

The functional forms of the comelations that gave the best results for each oil property have been used for finding a better comelation with errorsreduced, on average. by 10%. In particular, for extra-heavy oils, since no correlations are available in literature (except for viscosity), a specialinvestigation has been performed and new equations are propmed.

INTRODUCTION

The calculation of reserves in an oil reservoir or the determination ofits performance and economics, requires a good knowledge of thefluids physical properties. Bubblepoint pressure, GOR, OFVF andcompressibility are of primary importance in material balancecalculation, whereas viscosity plays an important role in production

test interpretation and in well problem analysis. Ideally. theseproperties are determined from laboratory studies on samples

collected from the bottom of the wellbore or from the surface. Suchexperimental data am however not always available because of one or

more of these reasons: a) sampies coiiecWi are not reiiabie. b)samples have not been taken because of cost saving. c) PVT analysesare not available when needed. This situation often occurs inproduction-test interpretation in exploration wells.

In such cases PVT properties must be determined by using empiricalderived correlations. Obviously the accuracy of such correlations iscritical for the above mentioned calculations and it is not oftenknown in advance.

Despite the great number of work performed in the past 50 years onPVT correlations. each of them seems to be applicable with a good

reliability only in a well-defined range of reservoir fluidcharacteristics. This is due to the fact that each correlation has beendeveloped by using samples belonging to a restricted geographicalarea, with similar fluid compositions and API gravity. In particular

for oils with gravity less than 22 ‘API the literature is very poor andnearly absent for oils with gravity less than 10 ‘API.

This work is aimed at anaiysing tiie reliability of literature

correlations, listed in table 1, relevant to heavy and extra-heavyAgip’s reservoir fluid samples, shown in table 2.

This will make it prwible to evaluate the use of some correlations in------ _C A 1 —.,:.., ;.. . . . :,.I. ... fi,.-,,l *;-”. h .,. ha” “9.mraIIgCS UI nPI ~IWI1y l!! whl~ll IIU ~,,, i~,a,,”,,. tia.- -,, ~,+osedyet (except for viscosity): for oils with density lower than 10 ‘API.

LITERATUREREVIEW

The following presents a review of the most known correlationspublished in literature. The range of input data used by each Authorin developing his correlation are provided in tables 3 and 4.

References and illustrations at end of papaer 647

2 PRESSURE-VOLUME-TEMPERATURE CORRELATIONS FOR HEAVY AND EXTRA HEAVY OILS SPE 30316

In 1947 Standi&my published two correlations for determining,respectively, the bubblepoint pressure (Pb) and the oil-formationvolume factor (OFVF) at bubblepoint, from known values ofreservoir temperature (T’r), solution gas-oil ratio (GOR) at bubblepoint, oil gravity (w) and gas gravity OS). In ail. 105 ex~~nt~lydetermined data points on 22 different cmde-oil/naturzl-gas mixturesfrom California were used.

In 195S Laaate#a presented a new correlation for Pb. In all, ! 58experimentally measured bubblepoint pressures tlom 137

independent crude oil systems from Canada, western and mid-continentrd U. S., and South America were used in his work.

In 1959 Chew and ConttaU#5/ proposed a correlation to predict thegas-saturated oil viscosity (pol) as a function of dead-oil viscosity

(,pod) and GOR. llte correlation was developed from 457 crude oilsamples tkom Canada, USA and South America. ‘fire study showed

that at a fixed GOR, the relation between wol and the corresponding pod is a straight line on logarithmic co-ordhtates.

In 1975 Begga and RobIrtao# published two new correlations for

calculating pod and pol. The equations resulted tiurrt a study of 2533viscosity measurements involving 600 different crude oil systems. Anaccuracy of -0.64% for the dead-oil viscosity correlation was foundwhen tested against the data used for its work. When tested against93 cases from literature, the average error increased to 114.27%. ‘f?teAuthors did not explain the reason for the large errors but simplywarned that the extrapolation outside the range of the data mwd todevelop the correlation should & done with care.

In 1977 Vasqaez and BeggsY’ presented correlations for pre&ctingGOR and OFVF of a gas-saturated crude oil, as a function of cmde

oil API gravity, ?g, reservoir temperature and pressure (R). In total,6004 data points were used. distributed into two groups (less than 30“API and greater than 30 “API) because ofvariations in the volatility

of crude oil. The Authors found w to be a strong correlating

parameter in the development of the GOR correlation. Because w isdependent on the conditions under which the gas is separated from

oil, a correlation to normalise ~ to a separation pressure of 114.7psia was also developed by the Authors and tested against 124 datapoints from 27 different fluids. Vasquez and Beggs also investigated

the viscosity (PO) and the isothermal compressibility (Co) of undersaturated oils. using 4486 data points for the Co correlation and 3593

data points for the po correlation.

In 19S0 Glttw@ presented correlations for estimating Pb, OFVF and

pod, as a function of Tr, total surface gas gravity, GOR and APIgravity. Because the first two correlations were developed using datafrom 45 oil samples with paraftinicities equivalent to North sea oils,an adjustment to the API gravity term WZ.. suggested for using thecorrelations with oils of a different compositional nature. Gkso alar)provided a method for correcting the predicted Pb for the presence of

C02, N2 and H2S in the total surface gases. The correlation for podwas developed from data obtained from 26 crude oil samples.

In 198S Egbogah and Jackml proposed two different correlations for

estimating pod. ‘fire first one was a nrorMied Beggs and Robinsoncorrelation obtained by using 394 oil systems from laboratories ofAGAT Engineering, Ltd. llre second one introduced a new parameter

to estimate the Kod: the pour point temperature (Tp) which is, bydefinition, the lowest temperature at which the oil is observed toflow. Because Tp seemed to be related to crude oil paraffin content (itincreases with the paraffin content), the Authors believed thatimportant chemical compositional aspects of crude oil could beconsidered in the viscosity correlation by introducing this parameter.‘llw average error of the equation with Tp was slightly lower than themodified Beggs and Robinson correlation (-4.3% vs. -5. 13%). SinceTp is not an ez..ily-measurable parameter on field the lattercorrelation has not been investigated in this study.

in 19SS Marhou#w published empirical correlations for estimatingPb, OFVF at bubblepoint and total OFVF for the Middle Bast crude

oils, as a function of Tr. yg, GOR and API. A total of 69 PVT

analyses of bottomhole fluid samples were available for thedevelopment of congelations.Only the correlation for Pb has beenconsidered in this work.

In 1988 Asgarpour, McLauchlinj Wong and Cheum#” presenteda new set of correlations to estimate Pb, OFVF and GOR (at and

below bubblepoint) as a function of yg, W, Tr and GOR. ‘firecorrelations were baaed on more than 310 different crude oil sampksfrom Western Canada. Because the physical properties of eachgeological formation in Western Canada exhibited differentbehaviottr, it was necessary to develop correlations for 3 differentgeological formations. Although the average errors of the correlationsare very low, the paper has not been considered in this work sinceinformation about the geological formation of crude oil samples wemnot available, and because this information is not easy to gain onfiPiIi. ....”.

In 1989 Labedi/lv published a new set of equations for estimatingOFVF, oil density at and below bubblepoint, and Co of the Africanm.mtir fl.i;~ ss ~ fimetinn of eYW~!v.nMM.RU~~etkld @@ ss first-.“-, .“,. ,.”. , - “ . ... . .. .. -. — , .. .—stage separator pressure and GOR, API, R and Tr. PVT data for 128samples were collected from IJbya, N@eria and Angola reservoirs.Only the compressibility correlation has bum considered in thisstudy.

In 1990 Kartoatmodjt4’3’ presented new empirical correlations for

predicting OFVF, Pb, vod, wI, KO and Co as a timction ofmeasurable parameters such as Tr, separator gas gravity (OOPsp),API and GOR. A total of about 1400 different samples were used todevelop the correlations. Most of them were extmcted by PVTreports from South East Asia, California and Alaska and a reaaonabkgroup from literature. The new correlations were developed using thefunctional form of the previously published ones which gave the bestestimate. Ilre Author also presented a correlation to convert OFVFand GOR from differential to flash liberation process at the separatorcondition. The OFVF, GOR and Pb correlations were developedusing both flash vaporisation data and differential vaporisation data,(the latter converted to flash using the above mentioned conversionfactor). Kartoatmodjo stated that these correlations are applicable to aflash process only. Applying these equations to a differential processmight lead to errors of up to 20%.

in 1990 Mti Kattan and Salnm#4 proposed a new general

correlation for estimating po as a function of R, Pb, vol. GOR andAP1. ‘flu correlation was developed using 253 experimentallydetermined oil viscosity values on 41 different oil sampb fromNorth Africa and Middle-East oil reservoirs. The correlation is

derived from plotting (R-Pb) Vs (po+tol) on a log-log paper. ‘Wplot shown a series of straight lines of a constant slope whoseintercepts could bz represented as a function of APl and GOR.

!n M)90 RoUi~ McCaht Jr. and Creage#y developed anempirical equation to estimate stock-tank GOR as a limction ofseparator pressure and temperature {Psp, Tsp), API and GGPsp. llwcorrelation was obtained using a logarithmic model on a total of 301black oil samples. The solution GOR, obtained by addhg the stock-tznk GOR from equation to the field-determined separator GOR, hasbeen affected by an average error of less than 3%.

In 1992 Labedi/l& published a new set of correlations to predict pod,

pol and po. The data-bank for the development of correlationsconsisted of about one hundred laboratory analyses, representing thefluids of the entire producing reservoirs in Libya Each equationdeveloped is a function of easily-obtainable datz such as API, R andTr. In particular, with regard to the pol correlation, all equations

previously published correlate @to pod and GOR. In this study ptrl

is a direct fimction of pod, API and R, pararnetem more easily-measurable in the field than GOR. Lzbed also published arelationship between differential and flash API. Even if the API usedin all of the oil viscosity correlations developed in this study wasobtained by flashing the fluid sample to the atmospheric pressure.which can be easily done in the field by flashing the well dirtxxly tothe stock-tank, this relation makes it possible to utilise the viscosity

648

SPE30316 G. DE GHEITO, F. PAONE, M. VILLA 3

dsta from the samples that are not flashed to the atmosphericpressure, but differentially liberated. The new correlations can beapplied to other geographical areas such as the Middle East, theNorth Sea and some pats of North and South America, but theyshould be used within the limit of input ds~, in particular theyshould not be extrapolated for crudes of less than 32 ‘APL In thisstudy it was decided to extent the Labedi’s correlations to heavy andextra heavy oils. This was made because no literature correlations areavailable for oils with API < 14.4 (see tables 3 and 4), except fordead-oil viscosity (Egbogsh-Jack correlation). For this reason all theanalysed correlations were applied over the range of input datareported by the Author’s.

in 1993 Petraaky asd Farshad/’7’ presented new empirical PVTcorrelations for estimating Pb, GOR, OFVF and Co, as a function of

m-l” wd~hl- G-IA I+=tn A h-d Of ~ I !~bo~tory PVT analysis,rvm,,l-ll, a.-- .. . .. ---- ----made on crude oils extracted from reservoirs offshote Texas andLouisiana were used to deveiop tiie correlations. Audhors fount+tiiaithdr correlations could predict the PVT properties with averageabsolute errors ranging tlom 0.64% for OFVF to 6.66% for Co. Thecorrelations were developed specifically for Gulf of Mexico crudeoils but Authors said that the same equations could be used in otherregions of the world. Od y the compressibility correlation has beenconsidered in this work.

IO!LIABILITVANALYSISm LITERATUREcortstmmorm

Ttds work analyses the most well-known correlations described inliterature for estimating PVT properties such as bubblepoint pressure,oil formation volume factor and solution gas-oil ratio at bubblepoint,dead-oil viscosity, gas-saturated oil viscosity, under saturated oilviscosity and isothermal compressibility. It does not however includethose correlations which require. as input dst& psrametem which atenot easily measurable on field or not obtsinsbie from PVT reports.Table 1 shows schematically the Authors and the relative correlationsconsidered for each property examined.

Starting exclusively with the PVT studies carried out over the last 30years on Agip oils, a selection was made excluding those lacking allthe input data necessary to use PVT correlations. In this way, a veryheterogeneous sample of 63 crude oils was set up, representative ofdiverse reservoir conditions, in order to ensure that the conclusionsobtained from this analysis would be generally valid and have anextensive applicability to wide range of operative situations.

The 63 oils come from the Meditemanean Basin, Africa and thePersian Gulf. Table 2 lists the range of input and output pamneters of-*! AJ.-1. -:1 --—.-1 . ..,I.:1- .r..l.la <all Aslp S Ull 511111@% WIIIIG I autG J ,+.,. ,,,- wmw,,,rn,,w.y=

—. A. -.+—tall

measured PVT data involved in the present study (about 1200 datapohta).

Tables 3 and 4 list the range of input and output parameters uponwhich each Author based the development of his correlation(Author’s defined range).- ..__,... _* __ _,, ,- - &.-#-_--.”,I ne aemmy or an UII IS u IUIWIHIUI CMSCCG*AC its R dktt itschemical composition, on which all the fluids main propertiesdepend. For this reason, the API gravity was chosen in this studyamong all the different parameters used for classifying oil% tberefomAgip’s oil sample was divided into 2 different classesof API gravityas follows

● extra-heavy oils ‘API s 10s heavy dla 10< “API ~ 22.3‘l%e second class correspond to a standard classification ofOil/-w”on the basis of the API gravi~, the extremes of the rangeswhich identify the class can vary as there is no univerwdly recognisedclassification. Even if the class of “extra heavy oils” does notcompare in the standard classifications, in this study it was decided tomal yse separately oils with API < 10 mainly for the followingreason5

. variations in the properties of crudest2%%%i9iTfly ‘n ‘kpreame of the most heavy hydrocarbons

. in the past few years, oil companies have become increasinglyinterested in reservoirs with the extra-heavy oilsnsn”.

. there am no correlations in literature which cover the range of oilswith ‘API S 10,except for viscosity.

The reliability of each correlation and for each parameter wastherefore tited for each API gravity class. No analyses were madefor the whole group because it is plausible that samples belonging tothe asme class are physically and chemically more comparable thansamples tlom dtfferent classes.

‘l%e reliability study was carried out using graphic and statisticalinstruments. Calculated (~) vs. meawm%l (Mi) - value diagrams wetecreated for each pmmeter studied in order to have a clear andimmediate view of the behaviour of each correlation. For reasons ofspace, not all the calculated-value vs. measured-value graphs, relative

I- ..- G—.. :...AA.AA :. ●I.,:. -— I..* a,.1 ;, w .to c%chCOfRi~tiWi, nave ucm mmmwu III W. ptp,. .,,.t~, ,. _&

decided to show a single diagram which gathers the beat redsobtained for in&idual classesof oil . The diagrams for each proprxtyestimated are shown in figures 1,3,5,7,9, 11, 13 and 14.

The qualitative analysis carried out by means of diagrams wasaccompanied by a statistical analysis, of which the starting Pint wasthe dative deviation between estimated and experimental value (Ei),thus defined

(1)

After having calculated the Ei for all the available samples, resultswtne subjected to a statistics] analysis calculating the averagearithmetical value (Q of the I+ and their standard deviation (SD),i.e., the dispersion of the ~ around their average value ~, using thefollowing equations

(2)

{SD= ~i~,[Ei - %]’

N-1(3)

l%e correlation providing the smallest ~ value was judged to be thebest. When equal ~ was found for more correlations, the loweststandard deviation value defined the best one. Table 6 provides thebest results obtdned from the statistical analysis, for the differentparameters estimated, for the two API gravity classes.

Below is a discussion of the rtaulta obtained for each propertyestimated.

kWLTS OFRELIABILITYANALYSISPSIWORMEDON AGIP’SSAMPLES

All the results are discussed with reference to Table 6 and to figures1,3,5,7,9, 11,13 snd14c

BnbblepointpressrmStsndhrg’s correlatiodlw has given the best results with averageerrors of 9.1% for extra-heavy oils and 15.1% for heavy oils.

Sofstdan gas-oil ratio~ best results are provided by the Standing and Vasquez-Beggscorrelations with errors of 13.7% for extra-heavy oils and 25.7% forheavy oils.

OUfmttation vohtme factor at bubblepointOf the seven propenies anslysed, tlds one was estimated in the bestway. The highest errors did not exceed 1.5%. Vasquez-Beggs’s

yu~#~ f?ve -m of tin.? than half of those indicated by the

Isothermal C-Sdbif@‘IRe estimation errors nmge from 25.5% for heavy oils to 38.7 forextra-heavy oils. Vasqrtez-Beggs’s correlation gave the bestperformance for the both classes.

mad-d Viseos@The estimation of this property exhibited the highest ewor, the Ioweaterrors bektg greater than 30% . Ilre errors are very high, especially

649

4 PRESSURE-VOLUME-TEMPERATURE CORRELATIONS ~R HEAVY AND EXTRA HEAVY OILS SPE 30316

with regard to the cla..s of heavy oils. This behaviour is justifiablebearing in mind that the correlations estimate this property with onlytwo input variables: “API and reservoir temperature. ‘f?re correctmeasurement of this property is difficult to achieve even in thelaboratory.

Gas-safrrmted oil viscosityThe average errors of the best correlations range between 14% attd16%. The best results were provided by Kartoatmodjo’s correlations,:v~~rs comparable with those found by the Author in his own

Figure 9 shows the distribution of the @“nts calculated with tire bestcorrelations where the input variables (dead-oil viscosity and solutiongas-oil ratio) are measured values obtained from PVT repnrts.

Figure 14 shows the results of the same correlations where thecalculated value was used as input data of the dead-oil viscosity.Noteworthy is the increase in dispersions of the points around thebisector which corresponds to an average error increase of more than15 percentage points. The difference is due to the fact that byincltrdlng a calculated rather than a measured input in an equation,the estimation error of the equation in some way combines with thatmade on the calculated input even if the latter has been calculatedwith the best correlation. lle greater the error on this input, thegreater the correlation error. Since the correlations which estimate theviscosity values at different presstrms are all inter-connected, thelower the estimation error of the dead-oil viscosity, the better theestimation of the gas-saturated oil viscosity. The same applies to thecorrelations relative to the undersatttrated oil viscosity which havethe gas-saturated oil viscosity among the inputs. This proves theimportance of correctly determining the dead-oil viscosity, which onthe other hand, is the property calculated in the worst way. Theobservations made can be naturally and easily extended to all theother Ptopertie% in fact. a quantity estimated by using measured inputvariables will undoubted y be more reliable than one estimated with~~i~~l~fd inputs.

Undkrsatnmted oil viscosftyThe best correlations showed a maximum error of 12.3% (Labe&extm-heavy oils). Note that Labedi’s correlationllw which had in factbeen gauged with oils with ‘API >32 (Tab. 4), showed excellentresults even for the other classes of oil. It should also be pointed outthat the ertur in estimating the viscosity normally becomes smallerattd smaller as we go from atmospheric pressure viscosity to reservoirpressure viscosity. It is likely that the input variables which estimatethe reservoir oil viscosity (bubble point pressure. reservoir pressureattd 00R), characterise the phenomenon better than the inputs of thedead-oil viscosity (“API attd reservoir temperature).

~VELOPMENT OF MODIFIEDCORRELATIONS

‘fhe results obtained from the atmve-explained reliability analysisshows that, except for the OFVF comelation, the average errors indetermining PVT properties are still high, especially when oils arebeyond the Author’s defined range. For this reason the need toimprove the reliabilityy of the literature correlations has beenrecognised.

The functional forms of the correlations that in the previousreliability analysis on Agip’s samples gave the best results, for eachPVT property, have heen used as models for a best-fit activity aimedat improving the accuracy of literature correlations in predcting PVT

properties for typical Agip’s oils.

Maintaining the same functional pattern of the starling model, thenumerical Ctrefflcients of the different quations were m-calculatedby applying multiple. linear and non-linear regressions by means ofthe SAS program which carries out these regression analyses usingthe minimum squared method.

The modified correlations were obtained for each class of density intowhich the Agip’s oil sample was divided. In fact oils from the sameclass are more comparable than oils from dKferent classes, and thenthe availability of two different equations, one for each class, to

estimate the same property, is certainly more reliable than a singlecorrelation for all the sample. For this reason, new equations werepruposed only for each API gravity class and not for all the group ofAgip’s oils.

In order to test the reliability of the modified quations, the samegraphic-statistical instruments as those in the previous study wereused. The results obtained are shown in Table 7 and in fig. 2,4,6, 8,10 attd 12, prepared in the same way as those for the analysis on theliterature equations, in order to be able to compare the two sets ofgraphs more adequately. In some cases, it was necemry to eliminate..— . . . . ...1. #’.-n- *h.= ml. . bin. n..l”$&~ ~~ o*~ @ rn&~ !a~W,,lc Uwn,yrd ,,”,,, .,.- -s..s.. -,.,~ “..”.,

regression more reliabl~ however, the exclusions never exceeded 5%of the entire group. The study did not take into consideration thecorrelations which estimate the oil formation volume factor at bubblepoint as the estimation of this prrpwty carried out using theequations chosen from literature was felt to be very satisfactory.Appendix A shows the analytical form of the new correlations.

~LTS OF RIZLIABILITYANALYSJSPERFORMED ON MODJFIEDCORRELAITONS.

‘llreresults of Tab. 7 obtained for the different properties are shownbelow, and are compared with those of Table 6.

Bubblepoint pressure

‘fire starting models used for improving the estimate of this propertywas Standing’s correlations for the both classes of oils. Tire newcorrelations twduced the estimation errors of 4.9 percentage points(aes Tab. 6 and 7) for the class of heavy oils. Regression in the classof extra-heavy oils, having given results worse than the startingmodel, “is not shown. Standing’s correlation WM c~si~

sufficiently reliable for atimating oils’ bubblepoint pressure with“API c 10. Comparing the diagrams in fig. 1 and 2 it can be seen thatthe most significant improvement in the new correlation is in thepressurerange below 20(N paia.

In order to allow an easy interpretation of the results obtained withthe reiiabilit y studies perfomred in this work, the best results of thestatistical analyses are compared in a histogram for each PVT

Prowy (= fig.15 to 20).Each histogram shows the value of the most important statisticalparameter (~. average absolute error) for the two classesof oil intowhich the sample was divided.Sofulibn gus-ail #a‘flte quations used as model were those of Standing for extra-heavyoils and Vasqtrez-Beggs for heavy oils. ‘llre regression of Vasquez-Beggs’ qttation was carried out keeping fixed the quation of the

~orr provided by the Authors; this was done every time the startingmodel was a Vaaquez-Beggs correlation. llre new quations reducedthe estimation error from a minimum of 7.2 to a maximum of 8.7percentage points. The comparison between the diagrams in iig.3 and4 shows that the most obvious improvements wete in the 00R rangebdOW 250 scf/STB.isothermal eonrpressibilityIlre model to regress was Vasquez-Beggs’ correlation for both theclasses of oils. IIds setof new quations provided the mostsignificant improvements. The error decreased from a minimum of10 to a maximum of 30 percentage points for extra-heavy oils,Comparing the diagrams in fig.5 and 6 it can seen that the greatest:-— .----* - ...— Mid %. M -a.lh” lit” WW-n %sm.-l i Q ~llllPIU+GIIlclIcm“=, = OU.=lJW ,V, -vmY. worn.vs,..J -. .. W.. - ..,,.,10-6 paia-t.

Dead-d viscosftyThe models chosen was Egbogah-Jack’s correlation for the bothclasses.The dead-oil viscosity is the most critical property to estimatewith empirical equations. In fact, although the errors dropped downto 13 pementage points with the new quatiorrs (extra heavy oils),values higher than 30% (heavy oils), me still present. On the otherhand, the viscosity, not being a state property also depends on thebehaviour of the fluid. All the correlations assume that the fluid canbe considered Newtonian, but this is not always true, especiallywhere high viscosity are concerned. To attempt to estimate a quantity

650

SPE 30316 G. DE GHEITG, F. PAONE, M. VILLA 5

of this kind using equations which only use two input variables (“APIand reservoir temperature) becomes even more difficult. In any case.not even laboratory measurements of viscosity can be consideredcompletely reliable: in fact. particularly in the range of high viscosity,differences of 10% between two measurements taken on the samesample by two different quipment, gauged in the same way, arenormal. The diagrams in figures 7 and 8 compare the trend betweenthe old and the new quations. They reveal that the most significantimprovements are to be found in the range of viscosity greater thanIocp.

Gsw-sotrmrted oil viscosityThe starting model for the regression was Kartoatmodjo’s correlationfor the both classes. For the Kartoatmodjo’s correlation. the multiplenon-linear regression was carried out by keeping the quation

supplied by the Author fixed for the input variable ~corr. Thisprocedure was also followed for the other properties whenever thestarting model was one of Kartostrnmljo’s equations. me regressionreduced the estimation error from a minimum of 2.1 (extra heavyoils) to a maximum of 4.3 (heavy oils) percentage Pints (see Tables6 and 7). D~agrams in fig. 9 and 10 show that the new correlationsimprove the estimate in the range between 10 and 100 cp.

Understslnmted oil viscosi@Ilre models to regress were Labedi’s correlation for extra heavy oilsand Kssrtoatmodjo’s correlation for heavy oils. Ilre new quationsbrought the maximum estimation error to 6% (Tab. 7). The diagramsin fig. I I and 12, which compare the trend of the old and newquations, show that the improvements are distributed along theentire viscosity range.

FURTNER INVESTIGATIONON TNE NEW MOBWIED CORRELATIONTNAT ESTTMATETHE VISCOSSTV

The new modified correlations have been obtdned analysing Agip’soils sample. For a snore general validity of the results obtained in theprevious analysis. it was decided to test the new quations using asww group of oi Is collected tlom literature. A deep literature reviewhas shown that the Author’s are usually reluctant to publish the oildata bank used for testing their correlations. For this reason it waspossible to collect thm Iiteratum only 10 oil samples. with dstaavailable for the ordy viscosity correlation analysis. To make morerepresentative the results of this analysis. a group of 45 oils samples,collected from the Agip’s viscosity meawrements reports, has beenadded to the oils from literature. In this way an heterogeneous sampleof 55 oils has been obtained. Ilse complete data bank is given inTable 8. Since the extra heavy oils are only 5, results obtained in thisclass have to be considered not asrepresentatives as those of theheavy oils class (50 samples). The results of the statistical analysis,performed on this sample using the same statistical index as before,am given in Table 9. Comparing this results with those listed in Table7 and, secondly, Table 6, we can say that:

●

●

●

Dead dl viscosity : the Em increased by about 9 percentagepoints for extra heavy oils and decreased by 2.4 points for heavyoils. ‘l%e result for the heavy oils is very good and confirm thegeneral validity of the new corresponding correlation. For theextra heavy oils the poor number of samples makes the resultsless representatives. However results by Table 9 for extra heavyoils are better than the corresponding by Table 6, relatives to thebest literature correlations.

Sdssrded dl viacoaity : Em increased by 7.2 percentage pointsfor extra heavy oils and by 8.7 point.. for heavy oils.

Usdesmtssratsd dl viscosity : an increase of 1.9 percentagepoints for the Em in the clRssof extra heavy and a &crease of 0.3points in the class of heavy oils confirm the general validity ofthe new corresponding correlations.

The reliability analysis of the literature PVT correlations earnedout on 63 oil samples from Mediterranean Basin, Africa andPersian Gulf, gave the best results for the estimate of the OFVF.with maximum errors lower than 1.5%. The estimates of Pb, pol

and VO exhibited maximum errors of about 15%, 16% and 12%respective y. The GOR, Co and pod estimates were less precisethe maximum errors were about 26%, 39% and 42% respectively.

Ilse new PVT correlations proposed in the paper gave errorslower, on average, than 10 percentage points when compared withthe best literature correlation for each PVT propefiy. In particular.for the isothermal compressibility of extra-heavy oils. the newcorrelation revealed an error lower than 30 percentage points.

It is believed that the new correlations are sutlkiently extendibleas they were obtained on a very heterogeneous sample of oils.

A deep literature review has shown that, except for viscosity, there

are no PVT correlations for extra-heavy oils (“API S 10). Theproposed new equations for such oils provide average error of6.5% for solution GOR, 8.5% for isothermrd compressibility,17.4% for dead-oil viscosity, 12.6% for gas-saturated oil viscosityand 4% for undersaturated oil viscosity.

A further investigation of the new modified correlations,performed on a new different group of oil samples (ftum literatureand Agip’s reports), has shown that the results obtained with thenew equations have a general validity. lWs analysis involved onlythe viscosity correlation because of lack of literature data aboutthe estimation of the others PVT properties.

NOMENCLATURE

API

a

co

Ei

Em, AAE

GOR, ft$, Rtot

LQ8Ln

Mi

N

OFVF, Bo, Botb

Pb

Pr, P

Psp

Rst

Rsp

S.D

Tr, T

Tp

Tsp

YC02

YH2S

YN2

~. GG(av)

ygcorr, GGcorr

651

Stock-tank oil gravity, “API

Calculated value

Isothermal compressibility of undersatursted oil,psia- 1

Relative deviation between estimated andexperimental value, %

Average absolute error, %

Solution gas-oil ratio from flash test, scf/STB.

Logarithm on base 10

Natural logarithm

Experimental value

Number of data points

Bubblepoint oil formation volume factor.bblls’m

Bubblepoint prwssure,psia.

Resewoir pressure, psia.

Separator pressure, psia.

Stock-tank gas-oil ratio, scf/STB.

Separator gas-oil ratio, scf/STB.

Standard deviation

Reservoir temperature, ‘F.

Poor point temperature, “F

Separator temperature, “F.

Mole tkaction of C02 in total surface gases, %mol: Glaso’slw bubblepoint correlation.

Mole tiadon of H2S in total surface gases, %mol: Glaso’sW bubblepoint correlation.

Mole fraction of N2 in total surface gases, %mol: Glaso’~ bubblepoint correlation

Average S@fiC gSWity Of total SU&2C @eS.

Gas Specific gravity at separator pressure of114.7 psia.

6 PRESSURE-VOLUME-TEMPERATURE CORRELATIONS FOR HEAVY AND EXTRA HEAVY OILS SPE 30316

n~p, GG(Psp),wp G= Specific grWity Zi amy*~ZiiiGi pressiim.! c L~H_~ R, “lm~ved correlations for predicting the viscosity of

~~~~.@q~ Q~!Spific gravity.-fo, jtxtlight crudes”, Journal of Petroleum Science and Engineering, 8

po, Vo Undersaturatcd oil viscosity, cp.(i992k pp 22i -234.

17 Petrosky G.E. Jr.. Farshad F.F.: “Pressrrre-Volume-Tempemtumpod, Vod Dead-oil or gas-free oil viscosity, cp. Correlations for Gulf of Mexico Crude oils,” SPE 26644, (1993),

pol, Vol Gas-saturated oil viscosity, cp. pp 395-406.

18 Beat C.: ‘The Viscosity of Air, Water, Natural Gas, Crude Oil and

S1 METRIC CONVERSION FACI’ORS

●

●

●

●

●

●

(*)=gcm3Nm3/m3 x 5.5519= SCf/STB

KPa x O.14504= psia

psia - 14.7= psig

‘C XI.8+32=”F

KPa -1 x 6.894757= psia -1

cpxl.O=mPaxs.

bbl x 0.1589873= m3

Its Associated Gases at 011 Field Temperature and pressures; Oiland Gas Property Evaluation and Resewe Estimates, ReprintSeries, SPE, Richardson, TX, (1970).

19 Slotte in Frick T.C.: “petroleum production Handbook” SPE-AIME, ( 1%2), Vol 2.

20 Calhoun J.C. JC “Fundamental of Reservoir Engineering:University of Oklahoma Press, Norman, OK (1947) 35.

21 Trube A. S.: “Compressibility of Under saturated HydrocarbonReservoir Fluids,” Transaction AIME (1957) 210, pp 341-44.

22 Majeed G.H.A. & Salman N. H.: “An empirical Correlation for OilFVF Prediction,” Journal of Petroleum Technology.

23 Obomanu D.A. & Okpobori G. A.: “Correlating the PVTproperties of Nigerian CrudesU Transaction ASME (1987) Vol

lo9, pp214-16.

24 Ali J.K.: “Evaluation of Correlation for Estimating the Viscosity

REFERENCES of Hydrocarbon Fluids: Journal of Petroleum- Science and

1 Standing M. B.: “Volumetric and Phase Behaviour of Oil FieldEngineering, 5 (1991),pp351-69.

Hydrocarbon System”, SPE-AIME, Ninth Printing (1981).25 Sutton R.P, and Farahad F.: “Evaluation of Empirically Derived

PVT Pmoetties for Gulf of Mexico Crude Oils,” SPE Reservoir

3

4

5

Standing M. B,: “Oil-System Correlations” Petroleum Pmd~#ctionHandbook, Frick T.C.(ed.), SPE, Richardson, TX (1%2) Vol. 2,Cap 19.

Standing M. B.: “A Pressure-Voirrme-Temperature Comeiation forMixtures of Crdifomia Oils and Gases,” Drill& Prod. Pmct., API(1947), pp 275-87.

Laaater J.A.: “Bubble Point Pressure Correlation,” TransactionAIME (1958) 213, pp 379-81.

Chew J. & Connally C.A.:”A Viscosity Correlation for Gas-Saturated Cmde Oils” Transactions AIME, (1959) Vol. 216, pp23-25.

6 Begga H.D. & Robinson J.R.:”Estimating the Viscosity of CrudeOil Systems” JPT, (September 1975), pp 1140-41.

7 Vaaquez M.E. & Beggs H. D.:’’Comelations for Fluid PhysicalProperty Prediction,” SPE 6719, (1977).

8 Glaao O.: “Generalised Pressrrre-Volrrme-Temperature

Correlations” JPT (May 1980), pp 785-95.

9 Egbogah E.O. & Jack T.Ng “An Improved Tempemtrrre-ViscosityCorrelation for Crude Oil Systems,” Journal of Petroleum Scienceand Fxgineering, 5 (1990). pp 197-200.

10 A1-Marhorrn MA.: “PVT Correlations for Middle East Cmdeoils? JPT (May 1988), pp 650-66.

11 Asgapur S., McLaughlin L., Wong D., Cheung V.: “Pressrrre-Voiume-Tem~mm Correlations for Western Canadian GSSCSand oils” Petroleum Sochsty of CIM, paper No 88-39-62 (1988),pp ~~- i i~~-~&

I z W! R.: “use of Production Data to Estimate Volume Factor,

Density and Compressibility of Reservoir Fluids,” Journal ofPetroleum Science and Engineering, 4 (1990), pp 375-90.

13 Kattoatrnodjo T. “New Correlations for Estimating HydrocarbonLiquid Pmperdes” (71eaki), ‘Ilte University of Tul~ TheGraduate School. (1990)

!A Maj~ G.B,A,: Kattan R.R. and Sahnan N.H.: “New correlation

for estimating the viscosity of under saturated crude oils”, Journalof Canadian Pettolerun Technology, (May-June 1990), Vol 29.No.3, pp 80-85.

15 Rollins J.B., McCtdn W.D.Jr., Creeger J.T.: “Estimation of80hltiOllGOR of Black OilS”, JPT (Jfmu?u’Y1990), w 92-94.

En~nee~ng, (February 1990), pp 79-86.

26 Callegari A., De Ghetto G.:”Studio di Affidabilit~ di Correlazioniper la Stima delle Pmprieth di Oli di Giacinrento,” Agip (internalreport), (Gennaio I 992).

27 Lang K.R., Donohue D.A.T., P.H.D., J.D., Senior SeriesEdito~”PE 406-Petroleum Engineering IHRDC E and P VideoLibrary” edizione in Lingua Italiana a curs di G.Flarnmengo(LACH) e ADFO.M.R.

28 Davis J.C.:”Statistics and Data Analysis in Geology”, John Wiley& Sons, New York (1973), IJP54-127

29 Spiegel:”Statistics”, Collana kchaum, (May 1976).

30 Chierici G.L., Ciucci G. M., Sclocchi G.: ‘Two-Phase VerticalFlow in Oils Wells-Mlction of Pressure Drop,” JVT (August1974), pp 927-38, Transaction AIME, 257.

31 Chierici G.L.:”Principi di Ingegneria dd Giacirnenti Petroliferi,”Vol 1, AgipS.P.A, (aettembrz 1991 ).

32 Paone F.: “Studio di Affidabilitk delle Correlazioni che Stimano IePmprietk degli Oli di Gktcimento”, Tesi di Laurea in IngegneriaMineraria, Univeraiti degli Studi di Bologn& (13 ottobre 1993).

33 Closmann P.J., Seba R.D.: “A correlation of viscosity andmolecular weight,” ‘he Journal of Canadkm PetroleumTechnology, (July-August 1990), VOi. 29, No. 4, PP 115-116.

34 McCain W.D. Jr., “Reservoir-fluid property correlations-State oft~ Afi,” S~ Rmoir Engineering, (May 1991). Op 266-272.

35 Puttagunta V. R., Miadonye A., B. Singh : “Simple conceptpredicts viscosity of heavy Oii and bitumen,” Oii & Gas Joumai(Mar 1. 1993) no 71-73.. ... . . . . . ..- ,3r r.-

36 A1-Blehed M.S., Sayyouh M. H., Deaorrky S.M.: “API Gravity andViscosity Deterndne Cmde Oil Sulphur Concentration.”petroleum Engineer International, (June 1993), pp 5660.

37 singhB.,Mittdmrye A., Puttagunta V.R.: “Heavy Oil ViSCOSity

range from one teat,” Hydrrwarbon processing, (August 1993), pp1<7 16?.-, -..,-.

38 McCain W.D. Jr.: “Chendcal Composition Ddmmkea Behaviourof Reservoir Fluids,” Petroleum Engineer International, (Octoberl@lm nn l&25...=”,, rr -- ---

39 McCain W.D. Jr.: “Black Oils and Volatile Oils-What’s themffercnce?” Petroleum Engineer International, (November 1993),Pp 24-27.

SPE30316 G.DE GHETTG,F.P AONE.M.VILLA 7

40 McCain W.D. Jr., Bridges B.: “Volatile oils and RetrogradeGases-What’s the Diffemnce7° Petroleum Engineer International.

Vol = 2.3945+0.8927.F+0.001567.F2 (A -8)

(January i994j. pp 35-36. Willxe

(-0.0335+1.0785.10-0”-’”%.py~~~~+””’”””’)

)

----- ,F=

-0.00081.R.!y=lo

APPENDIX A - MODIFtEDCORRELATIONS

l-Bubbiepaint Pressure:

● Heavy oikx Modified Stanclktg’s correlation

‘1[)‘]0.7885

,00.0020TPb= 15.7286.K

,00.0142.API(A-1)

Yg

2- solution GOR.

● ExtrR-hezvy oik Modified Stsnding’s correlation

( Pb ,.(O .oiw.An-o.m156. T)) ’””2s—. (#$ . ~)‘s= ‘g ‘[ 10.7025 )

● Hezvy oils: Modifti Vsaquez-Beggs correlation

Rs=%=+’1.2057

,,0lo.9267.AFl/(T+460)(A -3)

56.434. .

where

[ [11‘v ,.-4yRCoW = YKp~p 1+0.5912.API .Tfp LOX —114.7

3-Iaothermd Compressibility:

● Extm-heavy oikx Modified Vaaquez-Begga correlation- 889.6+3.1374. %+ 20Tg -627.3 .ygw= -81.4476. API

co= (A -4)Pg 105

where

Y~corr = YgP.Tp[ (11‘T,.-41+0.5912 APl. Tv. f.oR —

114.7

● Heavy oils: Modifkd Vssquez-lkggs correlation-2M1.8+2.MR s+25.W39Tg-1230.5yg - +41.91 API

co. (A -5)Pg.los

where

~Rcorr = 7RP.VJ[ [11

‘fP ,0-4. 1+0.5912 .APIF~p. Log —114,7

Mkad-oil viscosity

● Extra-heavy ok Modiikcl Egbogah-Jazk’s correlation

Iw”lw(Pd +1]= i,9ij296_- -----<...0,--1 )U.UIXM9 ,4P; -0,01 I*B. IW\Tgf

(A- 6)● Heavy dim Modiiied Egbogah-Jack’s corteiation

()tog iog Pd + i = 2.06492-0.0179 API -0.70226 .iog(Tg) (A- 7)

~gcorr = TRP.rp[

~ 1+0.i595 AP1°’w8

H]

.(7’’)-0”2*.bg *

● Heavy dk Modified Kartoatmodjo’s correlation

Pol = -0.6311 +1.078 .F-0.003653. F2 (A -9)Whete

F=(

0.2478 +0.611410-0 ”000845’m .p~’+05’58”y))

-0.W08 i ~Rsy=io

r

~xcorr = ~gP.sp i+0.i595 APIO’m8 .(Tv)-02%mg (~]~ii4.7

64Jnderaxturated oil viscosity:

. Extra-hexvy oikx Modified Labedi’s correlation

[[ “1[ IIio-2. i9 i.055. m0.3132 -

PPo=Poi - J-; “

“podio0.0099. AFt

(A - 10)

● Heavy oils: Modified Jktoatm@o’s corrziation

P. = 0.988ti. Po, +0.002763 .( P- Fb)

[. -0. Oi i53v~3 +0.03 i6qI~i5939

)(A-ii)

~~corr= YRP,fp[

. I +0, 1595, Ap, 0.4078

[ 11(~fp)-0”2’%*ii4.7

S-Gas-sxtorxteddl 4’kOZity

. Extra-heaw oils: Modified Kartoxtmodio’s correlation. .653

ITABIZ 1: FUJIDPROPER’IY CORRELATIONS I

lpbddProper& 1-IBubblepoint premlrc I Staaiiiiiziii,Las2tcr~,w20@ I

Ibtodmdjo ‘lwJU-Marhounnw

SolutionGOR s- V-- “’,Km@modjo,

Rollinf5-MabCm&r n~

IOFVF S- Vqudkggs, Glaso,htoatmdjo

Vuqucz-13qEW Kart@mdjo,cmqm?siity Lsbali ‘z, Fetros&Fsrsha@7’

un&@Ulmdoil Vasqued3qWSKmt@modjo,Vi2c08ity Majccd-Kattan-Salman’14,

I.abali fl~

ITAB152 AOIP’SRANGE POR PVT PROPERTIESSAMPI.X I

r-ati) ] 1038.49t07411.34 I

‘Lwlirtalmlumm I 131.4ta 230.7 I

Mobhctkmafco2rntdxl gaam(%mal.)

w59 to 177.8 I

11.1 to 575.62 I

4.39 t031L41 i

0.5 to 9RS I

oiifmlldkmvolIlmosdar@bl/sTB) 11.057to 1.362 I

%iliMu&x 10 % I 3.02 to 429 I.-Dedd ViIcody((p) 7.7to 13s6.9

~clilvimaily(cp) 21tow5.9

Udmdmidosviaccdy ((al) 12.4ti334.6 I

TABLE3 AUTHORS DEFINED WOE FOR BUBBLEKXNT PRELSm f

- 1-Tank-d ~vity ~APl) 16.5 to 63.8 17.9to 51.1

BubblepOidpmsum (pllia) 130t07000 48t05780

~~m 100t0258 82t0272

OFVF d Ilubbw (bwsTB) I 1.024 t02.15 I -

SolutionOOR(dSTB) 120to 1425 13t02905

Sto&tmkOOR (sc@STB)

SqmmtorOOR(IC@TB)

Solution00R(acflSTB)

BIMM ~ (W@

De40s ViaxJdy(q)

ouutw@60sviwodh’(cP)

X.LITIONOOR,OFVFAND COMPRESSLBIIIIYCORRELATIONS

O&o K@@-#o vMqurz-Beg@ AIMafhmlll Rolsm-MdhilI -F- ~~

22.3 to 48.1 14.4 to 58.95 15.3 to 59.5 19.4 to 44.6 lsto53.5 16.3 to 45 32.2 to 48

165t07142 oto6040 15t06055 130 to 3!573 - 1574to 6523 520106358

8oto280 75 to 320 170 (Oll!aa) 74to 240 - l14to 288 12810306

1.025 to 2.588 1.022 to 2.747 1.028 to 2.226 1.032 to 1.997 - 1.l178to 1.6229 1.088 to 2.92

90 to 2637 oto2890 oto2199 26 to Mm - 217to 1406 -

0.4824to L668 o.511to L351 - 0.579to 1.124 -

0.65 to 1.276 - . 0.752 to 1.367 - 0.5781 to 0.8519 -

415 (ImaO) 100 6oto565 - 29.7to 3114.7 - 34.7 to 789.7

125 (mean) 3s to 294 76 to 150 - 6oto ml 60 tal220

. loto6000 141t09515 20t03573 - 1700to 10692 -

. 4t0220 .

. 12 to 1742 -

TABLE !k EXPERIMENTALLY NlEASURED PVT DATA

4mdl

-q414M42228,4484.78

14823,23

48264248W2ma4882M

a23,81

28un

mm

ann

1mb7!480SM

4329.4!

4410.6

I-X228t.a2727.2

2m2

43142.O

424

2n8.6122L0741M

7413.2

m47.4

4227.217822

mm.!1448,!m2u

mm!

4m7.mlmm72274

123801

1748/4824,(M

44?2342mu2208J

2mmm

m.m52.22

102.1O84.0438,278L220,27-.33law4nm240.0022L24224.1423L47334,21

24L80mum%mmt,lb17.21

lm.m

43.874U3

sot2L21*U2L48

10L82228.00$732

220.24M4,40m,lallLfimmMm

22M3244.23.

i

11m124

1

114,12o1216,m.e

200.448

2?2.=m

m.u

12.1

%3

w

all

288.

97,1

nW.2824.4227.84mm202m22Lam

4%I

1L44

24.48Ia40U44

7,7727.44

22.37w28.2112.02

%33am

4.22

4,11

24.24lqn7,44

22.8128.484.0s

44.42ma

2aaW31.42

20.43M4804123X4anW2432.802M222,22mu14,44

m

3L42

2L22l,m

423484.42

142,23’

L2242.4mL4m

LI*L2XM124.8280.722L2m4.322wm

0.734

L2m

La3Ll~L3mwL044L2m0288@mL1282.217L281*

LmL2m8.824L4m3,422

3.411L8282.417L143L202Lom23233347L222

Lm2w

22L422L0Im,o2a222L0v7,214L2

=0m.886284.0

12L2m2aoImo

M22ao3s.0228.01248

424IM31%0

Xl1s0247.0MOW1.o

me3.%6m.8

ll&6MO

3Z010Lo

4L0104,4la 4

u o* o4%8

48.820,4m.8

U4.4

3L2m o72.2n 620.6

100.4

73.4e .2

M, o

a ola 4

8Lo28,224.o!

4a04 ‘W#23.02mm82.27 34W

20,83 280222

am 6W,22

22.37 848,427L07 723.20no7 W.a7L87 wW7 287.243$37 424.222L02 847,42

Isa llw,n224.44 lam,m224.44 320217227.71 M18,84

24.s7 m14,72

22L44 224L80124,42 142L22m.m Ilmw

4a04 :-78.22 mL423S7 227,7i

8sS7 lm4,22

224,44 U8M3

U.21 23?S4

20.X 2n&mw Z7.7 1

3a.08 2m,o1

42.22 222.22m 1724.2 1

28am 2m%mm.n 4m.44

m 1074.72

2S37 la8Loo

224.84 -M&a 888,32M644 1047,19

72.07 03?.81Mm nw.28mm 784.2773.07 488,s3lLOl 784.277Lol ms.m

227,n 1034,43

w 784.2722L41 12a wm % n

m, nm3 ,42

n 07847 .421%u 122L04n w 94.22w 823.m

m, n M63N224.44 - .m?a30 2423.22w 33331464 1 Mm ,48483 1424. 33.

4427,44

24.42Lm

44.1I

%’32860 182.4483.S

m.mW53

464032.09M 7wam

e.n

0520.41

10,%

O@12.3I

20.043Ln

ua=4 1

K2 12292Uala 220.02M78,n

88.22S.2341 7

28.n32324s.m

2.92m n2oYl8L23

4a23% w#1#41L20

8.20-73.4747.01

%2444.24Z204.48

w

!!liiI4,924 3,m4LLLL

LLL

Ll Laa L1

4.LL81 L

Lt

—TABLE 6: BEST RESULTS OF STATISTICAL ANAUSYS FERllXIMED ON AOIF’SSAMPUN

(AAE =Aq Abduta k. % SD - *W ~@

Om Sduth QOR — OFVF I&4k01d cuWe&wilY

- T sh&s — ~ ugldk3WJ<-10 “API AAE .

SD 179 1.2 219Aulha 9L vuq0d3q# — vuqufA&y v8qu5Be&8J

10< “m c= 22.3 15.1 25.7 1.4 23.sSD 13.9 45.9 1.1 19.2—

tb6-OilVkOdly Onax@alosl&iiiJ Wdm@mddos-

ygr - ? Labus<-10 “AM 12.3

SD : 13:0 7.8

pgc +—

10 c OAFIC= 22.3 16.1 10.1SD 24:9 16.5 — 10”5

mCn-1

) TABLE 7: STATISTICALANAUSYS PERFORMED fiiiODIFIED CORRELATIONS I(AAE=A

mmAuumr St8adh8

<=10“AM ME 9.1‘“ “ST”-*SD 9.8Author M-StdiOS

10< “AFI c= 22.3 10.2SD S.1

~--:=~

Ba6.oilvi8cdtY Ondm8tdos ViMsy wdanmmdos-Ausmr M-E#mglhJuk M-KarWm@io M-hbcdi

<=1O”AFI 17.4 12.6 4.0 7

I.. .—.

ISD I I 10.0 I 3.4lAutbur lREdWabkk

I]M-hhtmdjo — I M-~ “o I

6.07.2 I— I

1234s678910111213

14

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m

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2s

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w

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33

34

35

36*

3P

3~*

39

40

41

42

43

44

45*

w

47

43

49

so51*

32

530

~.

●API I m(w) I Pr(glh ) lw9dmB)l Pe(jldD) I ?%6(q) 1 Vd(c@ I Vo(Cp)

I I I i7,175

82829,010,210,s1Q61Q611,2113113lN1261*O13.013,01201%013,614.8IZ814#14#14,8M,81481s.01%01$1ISJM,O160164

173

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19.0

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2120moo218,7218.7117.3211,1ls4#2120212,01s4,821Q21s4,8204820&o212,0212,0212021202120215.42113211,3211,3211321132113211,321131%0207,s207.3211,3211.32120193.118Q010QOlnll118.0149.0217.4163.4163,4193,8180,0190.0179,6179,6179,6

m17Q1

4911.0s4s6s,864376.24

2671.64471s.2328SQCU4766,01476&ol28s0,044s89.0728sQln4S09,W480s.1849q73-734993.7349W.734993,734281384281s42a13842a1384281584281s4281384281>84281.S84976,214281,S84281.S84281,S84281S8

3723.184978316400$24978,211182,08

6ss7.261807,201807.203373$65333,8s497821

%89,483430,S04978214978.21

82,172426144.02786.70208.7s189,8734s>s91.6672S,W37692202.093q76m,63

min.42

m47$,63

493.4s768@2q7s228,412!q31315@419,00444,1046s,64753J746%7519s,s9IQ1O1913816s,8221sgl143@73,6226Q1124733xq14lwg3IIm15207229,462s&44W&m197,81437.10

2s2s67w2n)8320618921378@18s.88S21,38412.s1

2283

1Z721.0

S28.o75.0I*413Z0IQ1s,040I&oSo@7.4

S40ao119

2297223.8

2431611221S,69,68,1S2

683” 142’ 14,247 7.1

563 21.8 30985S.6 18.9 23537,0 153 %63%6 13.8 18,3

w 1%7 19.0

703 4Q0 m3,4 44

203 2$4%6 3.6

mo 80.6 N6

543 233 220159 to 161

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