Society of Petroleum Engineers

SPE 30316

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

Copyright 1995, Society of Petroleum Engineers, Inc.

This paper was prepared for presentation at the International Heavy 011 Symposium held in Calgary, Alberta, Canada, 19-21 June1995.

This paper was selected for presentation by an SPE Program Committee following review of Information contained In an abstract submitted by theauthor(s). Contents of the paper, as presented,have not been reviewed by the Society of Petroleum Engineers and are subjected to correction by the author(s). The material, as presented, does not necessarily reflect any position of theSociety of Petroleum Engineers, its officers, or members. Papers presented at SPE meetings are SUbject to publication review by Editorial Committees of the Society of Petroleum Engineers.Permission to copy Is restricted to an abstract of not more than 300 words. Illustrations may not be copied. The abstract shouid contain conspicuous acknowledgment of where and by whomthe paper Is presented. Write Librarian, SPE, P,O. Box 833836, Richardson, TX75083-3836, U.S.A. (Facsimile 214-952-9435).

ABSTRACT: The paper evaluates the reliability of the most common empirical correlations used for determining reservoir fluid propertieswhenever laboratory PVT data are not available: bubblepoint pressure, solution GaR, bubblepoint OFVF, isothermal compressibility, dead-oilviscosity, gas-saturated oil viscosity and undersaturated oil viscosity,The reliability has been evaluated against a set of about 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:

Oil samples have been divided in two different API gravity classes: extra-heavy oils for 0 API:S:; 10, heavy oils for 10< 0 API:S:; 22.3.The best correlations for each class of API gravity have been evaluated for each oil-property,The functional forms of the correlations that gave the best results for each oil property have been used for finding a better correlation 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 proposed.

647

INTRODUCTION

The calcuiation of reserves in an oil reservoir or the determination ofits performance and economics, requires a good knowledge of thefluid's physical properties. Bubblepoint pressure, GaR, OFVF andcompressibility are of primary importance in material balancecalculation, whereas viscosity plays an important role in productiontest interpretation and in well problem analysis. Ideally, theseproperties are determined from laboratory stuclies on samplescollected from the bottom of the well bore or from the surface. Suchexperimental data are however not always available because of one ormore of these reasons: a) samples collected are not reliable, 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

References and illustrations at end of papaer

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 particularfor oils with gravity less than 22 0 API the literature is very poor andnearly absent for oils with gravity less than 10 0 API.This work is aimed at analysing the reliability of literaturecorrelations, listed in table I, relevant to heavy and extra~heavy

Agip's reservoir fluid samples, shown in table 2.This will make it possible to evaluate the use of some correlations inranges of API gravity in which no correlations have been proposedyet (except for viscosity): for oils with density lower than 10 0 API.

LITERATURE REVIEW

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.

2 PRESSURE-VOLUME.TEMPERATURE CORRELATIONS FOR HEAVY AND EXTRA HEAVY OILS SPE30316

In 1947 Standlng/ll2/31 published two correlations for determining, analyses of bottomhole fluid samples were available for therespectively,. thebubblepoint pressure (Pb) and the oil-formation development of correlations. Only the correlation for Pb has beenvolume factor (OfiVF) at bubblepoint, from known values of, considered in this work.reservoir. temperature (Tr), solution gas-oil ratio (GOR) at bubble In 1988 Asgarpour, McLauchlin, Wong and Cheungll11 presentedpoint, oil gravity ('Yo) and gas gravity ('Yg). In all, 105 experimentally a new set of correlations to estimate Pb, OFVF and GOR (atanddetermined data points on 22 different crude-oil/natural-gas mixtures below bubblepoint) as a function of 'Yg, 'Yo, Tr and GO~. Thefrom California were used. correlations were based on more than 310 different crude oil samplesIn 1958 Lasater/41 presented a new correlation for Pb. In all, 158 from Western Canada. Because the physical properties of eachexperimentally measured bubblepoint pressures from 137 geological formation in Western Canada exhibited differentindependent crude oil systems from Canada, western and mid- behaviour, It was necessary to. develop correlations for 3. differentcontinental U.S" and South America were used in his work. geological formations. Although the average errors of the correlationsIn 1959 Chew and Connally/51 proposed a correlation to predict the are very low, the paper has not been considered In this work sincegas-saturated' oil viscosity (1101) as a function of dead.oil viscosity information about the geological formation of crude oil samples Were

not available, and because this information is not easy to gain on(/-lod) and GOR. The correlation was developed from 457 crude oil field.samples from Canada, USA and South America. The study showedthat at a fixed GOR, the relation between 1101and the corresponding 11 In 1989 Labedl/121 published a new set of equations for estimatingod is a straight line on logarithmic co-ordinates. OFVF, oil density at and below bubblepoint, and Co of the African

reservoir fluids, as a function of easily-measurable field data as first-In 1975 Beggs and Roblnson/61 published two new correlations for stage separator pressure and GOR, API, PI' and Tr. PVT data for 128calculating /lodand llot. The equations resulted from a study of 2533 samples were collected from Libya, Nigeria and Angola reservoirs.viscosity measurements involving 600 different crude oil systems. An Only the compressibility correlation has been considered in thisaccuracy of -0.64% for the dead-oil viscosity correlation was found stUdy.when tested against the data used for its work. When tested against II ~I .93 cases from literature, the average error increased to 114,27%. The In 1990.Kartoatrnodjo . presented' new empirical correlations (orAuthors did not explain the reason for the large errors but simply predicting OFVF, Pb, llod, /lol, 110 and Co asa function ofwarned that the extrapolation outside the range of the data used to measurable parameters such as Tr, separator gas gravity (GGPsp),develop the correlation should be done. with care. API and GOR. A total of about 1400 different samples were used to

develop the correlations. Most of them were extracted byPVTIn 1977 Vasquez and Beggs/7/ presented correlations for predicting reports from South East Asia, California and Alaska and a reason.ableGORand OFVF of a gas-saturated crude oil, as a function of crude group from literature. The new correlations were developed using theoil API gravity, 'Yg, reservoir temperature and pressure (Pr). In total, functional form ofthe previously published ones which gavethe best

. 6004 data points were use", distributed into two groups (less than 30 estimate. The Author also presented a correlation to .convert OFVFoAPI and greater than 30 0 API) because ofvarilltions in the voilltility lIOd GOR from differentilll to flash liberation process at the separatorof crude oil. The Authors found 'Yg to be a strong correlllting condition. The OFVF, GOR .1Ind Pbcorrelatlons were developedpllrameter in the development of the GOR correlation. Because 'Yg is using both f1l1sh vllporlsation data and differentilll vllporislltiondatll,dependent on the conditions under which theglls is separated from (the latter converted to f1l1sh using tile above mentioned conversionoil, a correlation to normalise 'Yg to a separation pressure of 114.7 factor). KlIrtoatmodjostated that these correlations are applicable to apsia was also developed by the Authors and tested agllinst 124 data flash process only. Applying these equations to a differentilll processpoints from 27 different fluids, Vasquez and Beggs' also investigated might lelld to errors of up to 20%.the viscosity (f.lo) and the isothermal compressibility (Co) of under In 1990 Majeed, Kattan arid SaIman/141 proposed a newgenetalsaturllted oils. using 4486 data points for the Co correlation lind 3593 corre1lltion for estimating /l0 liS 1I function of PI', Pb, 1101, GOR anddata points for the 110 correlation. API. The correlation was developed using 253 experimentallyIn 1980 GIaso/81 presented correlations for estimating Pb, OFVF find determined oil viscosity values on 41 different oil samples fromllod, as a function of Tr, total surface gas grllvity, GOR and API North Afrlcll and Middle-East oil reservoirs. The correlation isgravity. Because the first two correlations were developed using datll derived from plotting (Pr-Pb) VS(/lo·ll0l) on 1I 10g,.log pllper. Thefrom 45 oil samples with parafflnicities equivalentto North Sea oils, plot shown a s~ries of strllig\1.t lines of a constant slope whosean adjustment to the API gravity term was suggested for using the interpepts could be represerted as a function of API lind GOR.correllltions with oilsofa different compositional nature, Olaso 1I1so In 1990 R~l1ins, McCain Jr. and CreegerllSI devel,oped anprovided a method for correcting the predicted Pb for the presence of empirical equation to estimllte stock-tank GOR liS a function .ofC02, N2 and H2S in the totlll surface gllSes. The correlation for /lod separator pressure lind temperature (Psp, Tsp), API lind G(}Psp. Thewas developed from data obtained from 26 crude 011 samples! correlation was obtained using a logarithmic model on a totlll of 301In 1988 Egbogah and ,}acW91 proposed two different correlations for blllck oilsampll)s. The solution GOR, obtllined by lidding the stock-estimating /lod, The first one was a modified Beggs and Robinson tank GOR from equlltion to the field-determined separator GOR, hascorrellltion obtained by using 394 011 systems from Illboratories of been affected by an average error of less than 3%.AGAT EngIneering, Ltd. The second one introduced a new pammeter In 1992 Labedj/161 published a new set of correIlItlons to predict /lod,to estimate the llod: the pour point temperature (Tp) which is, by /lol and 110. The data-bank for the development of correlationsdefinition, the lowest temperature at which the oil is observed to consisted of lIbout one hundred Illboratory lInalyses, rep~esenting theflow. Because Tp seemed to be related to crude oil paraffin content (it fluids of the entire producing reservoirs in Libya. Each equationincreases with the pamffin conten!), the Authors believed that developed is a function of easily"obtainable dlltll, such as API,Pr andimportant chemical compositional lIspects of crude 011 could be Tr. In particulllr, with regard to the 1101 correilltion, all equationsconsidered in the viscosity correlation by introdUcing this parameter. previously published correlate /lol to llod lind GOR In this study /lolThe average error of the equation with Tp was slightly lower thlln the is a direct function of llod, API and PI', parameters more easily-'modified Beggs lind Robinson correlation (-4,3% vs. -5.13%). Since measurllble in the field than GOR. Labedi also publishedllTp is not an easlly-mellsurable pllrameter on field the latter relationship between differential and flash API. Even if the API usedcorrelation has not been investigated in this study. in all of the oil viscosity correlations developed in this study WllSIn 1988 Marhoun/lOI published empirical correlations for estimllting obtained by flashing the fluid sample to the atmospheric pressure,Pb, OFVF lit bubblepoint and totlll OFVF for the Middle East crude which can be easily done in the field by flashing the well directly tooils, as 1I function of Tr, 'Yg, GOR. and API. A total of 69 PVT the stock-tank, this reilltion makes it possible to. utiliSe the viscosity

648

SPE 30316 G. DE GHETI'O, F. PAONE, M. VILLA 3

(3)

(2)

RESULTS OF RELIABILITV ANALYSIS PERFORMED ON AGiP'S SAMPLES

L i:,[EI - Em]2SD =,,-==.J.:=..__---=:....N-I

The correlation providing the smallest Em value was judged to be thebest. When equal Em was found for more correlations, the loweststandard deviation value defined the best one. Table 6 provides thebest results obtained from the statistical analysis, for the differentparameters estimated, for the two API gravity classes.Below is a discussion of the results obtained for each propertyestimated.

• in the past few years, oil companies have become increasinglyinterested in reservoirs with the extra-heavy oils/35/37/,

• there are no correlations in literature which cover the range of oilswith 0 API S; 10, except for viscosity.

The reliability of each correlation and for each parameter wastherefore tested for each API gravity class. No analyses were madefor the whole group because it is plausible that samples belonging tothe same class are physically and chemically more comparable thansamples from different classes,The reliability study was carried out using graphic and statisticalinstruments. Calculated (Ci) vs. measured (Mi) - value diagrams werecreated for each parameter 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, relativeto each correlation, have been included in this paper. Instead, it wasdecided to show a single diagram which gathers the best resultsobtained for individual classes of oil . The diagrams for each propertyestimated 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 point wasthe relative deviation between estimated and experimental value (Ei),thus defined:

EI=lq~IMII'IOO (1)

After having calculated the Ei for all the available samples, resultswere subjected to a statistical analysis calculating the averagearithmetical value (Em) of the Ei and their standard deviation (SD),i.e., the dispersion ofthe Ei around their average value Em' using thefollowing equations:

E=~N§.m £""i~1 N

All the results are discussed with reference to Table 6 and to figures1,3,5,7,9, II, 13 and 14.

Bubblepoint pressureStanding's correlationIl/2/3/ has given the best results with averageerrors of 9.1% for extra-heavy oils and 15.1% for heavy oils.Solutio" gas-oil ratioThe best results are provided by the Standing and Vasquez-Beggscorrelations with errors of 13.7% for extra-heavy oils and 25.7% forheavy oils.Oil formatio" volume factor at bubhlepointOf the seven properties analysed, this one was estimated in the bestway. The highest errors did not exceed 1.5%. Vasquez-Beggs'scorrelatt.17? gave errors of less than half of those indicated by theAuthors .[sot/,ermal compressibilityThe estimation errors range from 25.5% for heavy oils to 38,7 forextra-heavy oils. Vasquez-Beggs's correlation gave the bestperformance for the both classes,Dead-oil viscosityThe estimation of this property exhibited the highest error, the lowesterrors being greater than 30%. The errors are very high, especially

649

RELIABILITY ANALYSIS ON LITERATURE CORRELATIONS

This 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 include'those correlations which require, as input data, parameters which arenot easily measurable on field or not obtainable from PVT reports.Table I 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 Mediterranean Basin, Africa and thePersian Gulf. Table 2 lists the range of input and output parameters ofall Agip's oil samples While Table 5 reports the experimentally­measured PVT data involved in the present study (about 1200 datapoints).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).The density of an oil is a fundamental characteristic as it reflects itschemical composition, on which all the fluid's main propertiesdepend. For this reason, the API gravity was chosen in this studyamong all the different parameters used for classifying oils; thereforeAgip's oil sample was divided into 2 different classes of API gravityas follows:• extra-heavy oils 0 API S; 10• heavy oils 10< 0 API S; 22.3The second class correspond to a standard classification ofoils/30/3110n the basis of the API gravity; the extremes of the rangeswhich identify the class can vary as there is no universally recognisedclassification. Even if the class of "extra heavy oils" does notcompare in the standard classifications,. in this study it was decided toanalyse separately oils with API < 10 mainly for the followingreasons:• variations in the properties of crudes depend chiefly on the

presence of the most heavy hydrocarbons126127/:18/39/40/

data 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 parts of North and South America, but theyshould be used within the limit of input data; in particular theyshould not be extrapolated for crudes of less than 32 °API. 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 (Egbogah-Jack correlation). For this reason all theanalysed correlations were applied over the range of input datareported by the Author's,In 1993 Petrosky and Farshad/17/ presented new empirical PVTcorrelations for estimating Pb, GOR, OFVF and Co, as a function ofcommonly available field data. A total of 81 laboratory pvr analysis,made on crude oils extracted from reservoirs offshore Texas andLouisiana were used to develop the correlations, Authors found thattheir correlations could predict the PVT properties with averageabsolute errors ranging from 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. Only the compressibility correlation has beenconsidered in this work.

4 PRESSURE-VOLUME-TEMPERATURE CORRELAnONS FOR HEAVY AND EXTRA HEAVY OILS SPE 30316

with regard to the class of heavy oils. This behaviour is justifiablebearing in mind that the correlations estimate this property with onlytwo input variables: 0 API and reservoir temperature. The correctmeasurement of this property is difficult to achieve even in thelaboratory.Gas.sahtrated oil viscosityThe average errors of the best correlations range between 14% and16%. The best results were provided by Kartoatmodjo's correlations,with Nfprs comparable with those found by the Author in his ownwork .Figure 9 shows the distribution of the points calculated with the beStcorrelations where the input varlables (dead-oil viscosity and solutiongas~oi1 ratio) are measured values obtained from PVT reports.Figure 14 shows the results of the same corr('llations where theCalculated value was used as input data of the' dead-oil viscosity.Noteworthy is the increase in dispersions ofthe points around thebisector which corresponds to an average error increase of morethlln15 percentage points. The difference is due to the fact that byincluding 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. The greater the error on this inpllt,thegreater the correlation error. Since the correlations which estimate theviscosity values at different pressures are all inter-connected~ thelower the estimation error of the dead-oil viscosity, the better theestimation ofthe gas-saturated oil viscosity. The same applies to thecorrelations. relative to the undersaturated oil viscosity which havethe gas-saturated oll viscosity among the inputs. This proves' theimportance ofcorrectly 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 al1 theother properties; in fact, a quantity estimated by using measured inputvariables will undoubtedly be more reliable than one estimated withcalculated inputs.

Undersaturated oil viscosityThe best correlations showed a maximum error of 12.3% (Labedi,extra-heavy oils). Note that Labedi'scorrelation/16/which had in factbeen gauged with oils with °API >32 (Tab. 4), showedexcel1entresults even for the other classes of oil. It should also be pointed outthat the error in estimating the viscosity normally beCOmes smallerand smal1er 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 pressureand GOR), characterise the phenomenon better than the inputs of thedead-oil viscosity COAPI and reservoir temperature).

DEVELOPMENT OF MODIFIED CORRELATIONS

The results obtained from the above-explained reliability analysisshows that, except for the OFVF correlation, 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 reliability 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 been used as models for a best-fit activity aimedat improving the accuracy of literature correlations in predicting PVTproperties for typical Agip's oils.Maintaining the same Junctional pattern of the starting model, thenumerical coefficients of the different equations were re-calculatedby applying multiple, linear and non-linear regressions by means ofthe SAS program which carries out these regression analyses usingthe minimum squared m(lthod.The modified correlati~ns were obtained for (lach class ofd(lnsity intowhich the Agip's oil sample was divided. In fact oils from the sameclass are more comparable than oils from different 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 wereproposed only for each API gravity class and not for all the group ofAgip'soils. 'In order to test the reliability of the modified,equations, the samegrap!\ic-statistical .instruments as those in the previous stpdy wereused. The results obtained are shown in Table 7 and in fig. 2, 4, 6,8,10, and 12, prepared in the same way as those for the analysis on thelitlJrature equations, in order to be able to compare the two sets ofgraphs, more adequately. In some cases, it was necessary to eliminatesome samples from the class being analysed in order to make theregression more reliable; however, the exclusions never exceeded 5%of the entire group. The study did not take into consideration thecOt1:(llations which estimate the oil formation volume factor at bubblepoint .as the estimation of t'1is property carried out using theequations chosen(rom literature was felt to be very satisfactory..Appendix A shows the analytical form o( the new correlations.

RESUJ"TS OF RELIAPIl,lTY ANALYSIS Pf;RFORMED ON MODIFIEDCORRELATIONS.

The resultsof Tab. '7 obtained for the different properties are shownbelow, and are Compared with those of Table 6.Bubblepoint pressureThe starting models used for improving the estimate of this propertywas Standing's correlations for the both classes of oils. The newcorrelations reduced the estimation errors of 4.9 percentage points(see 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 was ,consideredslJf,ficiently reliable, for estimating oils' bubblepoint pressure withoAPI < 10. Comparing th~ diagrams in fig. I and 2 it Can be seen thatthe most significant improvement in the new correlation is in thepressure range below 2000 psia.In order to allow an easy interpretation of the results obtained withthe reliability.studies performed in this work, the best results of thestatistical analyses, are compared in a histogram for each PVTproperty (see fig.15 to 20).Each histogram shows the value of the most important statisticalparameter (Em' average absolute error) for the two classes of oil·' intowhich the sample was divided.Solution gas-oil ratioThe equl;ltions used ,as model were those of Standing for extra-heavyoils and Vasqu~z"Beggs for heavy oils. The regression of Vasquez­Beggs' equation was carried out keeping fixed the equation of the'Ygcorr. provided by the Authors; this was done every time the startingmodel was a Vasquez-Beggs correlation. The new equations redl1cedthe estimation error from a minimum of 7.,2 to a maximum of 8.7percentage points. The comparison between the diagrams in fig.3 and4 shows that the most obvious improvements were in the GOR rangebeJow2?0 scf/STB.l,vothermal compressibilityThe mode] to regress was Vasquez-Beggs' correlation for both theclasses of oils. This set of new equations provided the mostsignificant improvements. Theerror decre.ased 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 greatestimprovements were obtained for compressibility between 5 and I0 x10"6 psia" I.Dead-oil viscosityThe 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 percentage points with, (he new, equations (extra heavy oils),values higherthan30% (heavy oils), are 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 GHETTO, F. PAONE, M. VILLA 5

of this kind using equations which only use two input variables (0APIand reservoir temperature) becomes even more difficult. In any case,not even laboratory measurements of viscosjty 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 equipment, gauged in the same way, arenormal. The diagrams in figures 7 and 8 compare the trend betweenthe old and the new equations. They reveal that the most significantimprovements are to be found in the range of viscosity greater than10cp.Gas-saturated 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 equationsupplied by the Author fixed for the input variable ygcorr. Thisprocedure was also followed for the other properties whenever thestarting model was one of Kartoatmodjo's equations. The regressionreduced the estimation error from a minimum of 2.1 (extra heavyoils) to a maximum of 403 (heavy oils) percentage points (see Tables6 and 7). Diagrams in fig. 9 and 10 show that the new correlationsimprove the estimate in the range between 10 and J00 cpoUndersaturated oil Vi.fcosityThe models to regress were Labedi's correlation for extra heavy oilsand Kartoatmodjo's correlation for heavy oils. The new equationsbrought the maximum estimation error to 6% (Tab. 7). The diagramsin fig. 1I and 12, which compare the trend of the old and newequations, show that the improvements are distributed along theentire viscosity range.

CONCLUSIONS

• The reliability analysis of the literature PVT correlations carriedout 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, !loland ~lO exhibited maximum errors of about 15%, 16% and 12%respectively. The GOR, Co and !lod estimates were less precise:the maximum errors were about 26%, 39% and 42% respectively.

• The new PYT correlations proposed in the paper gave errorslower, on average, than 10 percentage points when compared withthe best literature correlation for each PVT property. 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 sufficiently extendibleas they were obtained on a very heterogeneous sample of oils.

• A deep literature review has shown that, except for viscosity, thereare no PVT correlations for extra-heavy oils (0API :s; 10). Theproposed new equations for such oils provide average error of6.5% for solution GOR, 8.5% for isothermal 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 (from literatureand Agip's reports), has shown that the results obtained with thenew equations have a general validity. This analysis involved onlythe viscosity correlation because of lack of literature data aboutthe estimation of the others PVT properties.

FURTHER INVESTIGATtON ON THE NEW MODIFIED CORRELATION

THAT ESTIMATE THE VISCOSITY

The new modified correlations have been obtained analysing Agip'soils sample. For a more general validity of the results obtained in theprevious analysis, it was decided to test the new equations using anew group of oils collected from 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 from literature only 10 oil samples, with dataavailable for the only viscosity correlation analysis. To make morerepresentative the results of this analysis, a group of 45 oils samples,collected from the Agip's viscosity measurements reports, has beenadded to the oils from literature. In this wayan heterogeneous sampleof 55 oils has been obtained. The complete data bank is given inTable 8. Since the extra heavy oils are only 5, results obtained in thisclass have to be considered not as representatives 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,are given in Table 9. Comparing this results with those listed in Table7 and, secondly, Table 6, we can say that:

• Dead 011 viscosity : the Em increased by about 9 percentagepoints for extra heavy oils and decreased by 2.4 points for heavyoils. The 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.

• Saturated oil viscosity: Em increased by 7,2 percentage pointsfor extra heavy oils and by 8.7 points for heavy oils.

• Undersaturated oil viscosity : an increase of 1.9 percentagepoints for the Em in the class of extra heavy and a decrease of OJpoints in the class of heavy oils confirm the general validity ofthe new corresponding correlations.

NOMENCLATURE

APICiCo

Ei

Em,AAEGOR, Rs, RtotLogLnMiN

OFYF, Bo, Bofb

PbPr, PPspRstRspS.DTr, TTpTspYC02

YH2S

YN2

yg, GG(av)

ygcorr, GGcorr

651

Stock-tank oil gravity, °APICalculated valueIsothermal compressibility of undersatutated oil,psia- I

Relative deviation between estimated andexperimental value, %Average absolute error, %Solution gas-oil ratio from flash'test, scf/STB.Logarithm on base 10Natural logarithmExperimental valueNumber of data pointsBubblepoint oil formation volume factor.bbl/STBBubblepoint pressure, psia.Reservoir pressure, psia.Separator pressure, psia.Stock-tank gas-oil ratio, scf/STB.Separator gas-oil ratio, scf/STB.Standard deviationReservoir temperature, OF.Poor point temperature, OFSeparator temperature, OF.Mole fraction of C02 in total surface gases, %mol: Glaso's/4/ bubblepoint correlation.Mole fraction of H2S in total surface gases, %mol: G1aso's/4/ bubblepoint correlation.Mole fraction of N2 in total surface gases, %mol: Glaso's/4/ bubblepoint correlation

Average specific gravity of total surface gases.

Gas Specific gravity at separator pressure of114.7 psia.

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

ygPsp, GG(Psp),ysp Gas Specific gravity at any separator pressure.yo, yost Stock-tank 011 specific gravity.~o, Vo Unqersalurated oil viscosity, cp.!-lod, Vod Dead-oil or gas-free oil viscosity, cp..!-lol, Vol Gas-saturated oil viscosity, cp.

81 MET~IC CONVE~SION FACTORS

• '( 141.5) =g/cm3

131.5+° API ,

• Nm3/m3 x 5.5519 = scf/STB

• KPa x 0.14504= psia

• psia - 14.7 = psig

• °C x 1.8 +32 =OF

• KPa -Ix 6.894757 = psia -I

• cp x 1,0 = mPa x s.

• bbl x 0: 1589873 = m3

REFERENCES,

Standing MR: "Volumetric and Phase Behaviour of Oil FieldHydrocarbon System", SPE-A.IMB, Ninth Printing (1981).

2 Standing M.B.: "Oil-System Correlations" PetrQl!Jwn Pro,d"ctionHandhQok, Frick 1'.C.(ed.), SPE, Richardson, TX (1962) Vol. 2,Cap 19.

3 Standing M.B.: "A Pressure-Volume-Temperature Correlation forMixtures of California Oils and Gases," Drill & Prod, Prac:t., API(1947), pp 275-87.

4 Lasater J,A.: "Bubble Point Pressure Correlation," TransactionAIME (1958) 21.3, pp 379-81.

5 Chew J. & Connally C.A.:i'A Viscosity Correlation for Gas­Saturatecl Crude Oils" Transactions AIMS, (1959) Vol. 216, pp23-25. ,

6 Beggs RD. & Robinson J.R.:"Bstimating the Viscosity of CrudeOil Systems" JPT, (September 1975), pp 1140-41.

7 Vasquez M.E. & Beggs H,D::"Correlations for Fluid PhysicalProperty Prediction," SPE 6719, (1977).

8 Glaso 0,: "Generalised Pressure-Volume-TemperatureCorrelations" JPT (May 1980), pp 785-95.

9 Egbogah E.O. & Jack T.Ng: "An Improved Temperature-Visc~sityCorrelation for Crude Oil Systems," Journal of Petroleum Sc,enceand Engineering,S (1990), pp 197-200.

10 AI-Marhoun M.A.: "PVT Correlations for Middle East CrudeOils," JPT (May 1988), pp 650-66.

II Asgapur S., McLauchlin L., Wong D., Cheung V,: "Pressure­Volume-Temperature Correlations for Western Canadian Gasesand oils" Petroleum Society of CIM, paper No 88-39-62 (1988),pp 62-1/62-24.

12 Labedi 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 Kartoatmodjo T. "New Correlations for Estimating HydrocarbonLiquid Properties" (Thesis), The University of Tulsa, TheGraduate School, (1990)

14 Majeed G.H.A., Kallan R.Rand Salman N.H.: "New correlationfor estimating the viscosity of under saturated crude oils", Journalof Canadian Petroleum Technology, (May-June 1990), Vol 29,No.3, pp 80-85.

15 Rollins J.B., McCain W.DJr., Creeger J.T.: "Estimation ofSOlution GORof Black Oils", JPT (January 1990), pp 92-94.

16 Labedl R "Improved correlations for predicting the viscosity oflight crudes", Journal of Petroleum Science and Engineering, 8(1992), pp 221-234.

17 Petrosky G.B. Jr., Farshad F,F.: "Pressure-Volume-TemperatureCorrelations for Gulf of Mexico Crude Oils," SPB 26644, (1993),pp 395-406.

18 Beal C.: "The Viscosity of Air, Water, Natural Gas, Crude Oil andIts Associated Gases at Oil. Field Temperatures and Pressures," Oiland Gas Property Evaluation and Reserve Estimates, ReprintSeries, SPE, Richardson, TX, (1970).

19 Siotle ill Frick T.C.: "Petroleum Production Handbook" SPE­AIME, (1962), Vol 2.

20 Calhoun J.e. Ir: "Fundamental of Reservoir Engineering,"University of Oklahoma Press, Norman, OK (1947) 35.

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

22 Majeed G.H.A. & Salman N.H.: "An empirical Correlation for OilFVF Prediction," Joamal ofPetroleum Technology.

23 Obomanu DA & Okpobori GA: "Correlating the PVTProperties of Nigerian Crudes," Transaction ASME (987) Vol109, pp 214-16.

24 Ali J.K.: "Evaluation of Correlation for Estimating the Viscosityof Hydrocarbon. Fluids," Jo/lmal of Petroleum Science andEngineeting, 5 (1991), pp 351-69.

25 Sutton RP. and Farshad F.: "Evaluation of Empirically DerivedPVT Properties for Gulf of Mexico Crude Oils," SPB Reser:voirEngineering, (February 1990), pp 79-86.

26 Callegari A., De Ghetto G.:"Studio di Affidabilita di Correlazioniper la Stima delle Proprieta di Oli di Giacimento," Agip (internalreport), (Gennaio 1992).

27 Lang KoR., Donohue D.AT., P.H.D., J.D" Senior SeriesEditor:"PE 406-PetroleumEngineering IHRDC E and P VideoLibrary" edizione in Lingua Italiana a cura di G.Fiammengo(LACH) e ADFO.M.R

28 Davis J,C.:"Statistics and Data Analysis in Geology", JoIln Wiley& Sons, New Yark (1973), pp 54-127

29 Spiegel: "Statistics", Coliana Schaum, (May 1976).30 Chierici G.t.; Ciucci G,M., Sclocchi G.:"Two~Phase Vertical

Flow in Oils Wells-Prediction of pressure Drop," JPT (August1974), pp 927-38, Transaction AIMS, 257. .

3rChierici G.L.:"Principi di Ingegnerla deiOiacimenti Petroliferi,"Vol I, Agip-S.P.A, (settembreI 99l).

32 Paone F.: "Studio di Affidabilita delle Correlazioni che Stimano IePraprietadegli Oli di Giacimento", Tesidi Laurea in IngegneriaMinerarla, Universita degli Studi di Bologna, (13 ottobre 1993).

33 Closmann PJ., Seba R.D.: "A correlation of viscosity andmolecular weight," The Journal of Canadian PetroleumTechnology, (July-August 1990), Vol. 29, No.4, pp 115-116.

34 McCain W.D. Jr., "Reservoir-fluid property correlations-State ofthe Art," SPE Reservoir Engineering, (May 1991), pp 266-272.

35 PUllagunta V.R., Miadonye A, B. Singh : "Simple .conceptpredicts viscosity of heavy oil and bitumen," Oil & Gas Journal(Mar. I, 1993), pp 71-73.

36 AI-Blehed M.S., Sayyouh M.H., Desouky S.M.: "API Gravity andViscosity Determine. Crude Oil Sulphur Concentration,"Petroleum Engineer International, (June 1993), pp 56-60.

37 Singh B., Miadonye A, Puttagunta V.R.: "Heavy oil viscosityrange from one test," Hydrbcarbon Processing, (August 1993), pp157-162.

38 McCain W,D. Jr.: "Chemical Composition Determines Behaviourof Reservoir Fluids," Petroleum Engineer International, (October1993), pp 18-25,

39 McCain W.D. Jr.: "Black Oils and Volatile Oils-What's theDifference?" Petroleum Engineer Intemational, (November 1993),pp 24-27.

652

SPE 30316 G. DE GHElTO, F, PAONE, M, VILLA 7

(A - 10)

• Heavy oils: Modified Kartoatmodjo's correlation~o = 0.9886, llol +0,002763' (p - Pb),

-( -0,01153' ~~i7933 +0,0316, ~~i5939) (A - II)where

YI?COI'r = YI?Prp '[1 + 0.1595, API 0.4078 '(TIPr 0.2466, WI? ( P.rp J], '114,7

• Heavy oils: Modified Kartoatrnodjo'scorreJation2!-tol =-0,6311+1.078·F-O.003653·P (A-9)

where

F = (0.2478+ 0.6114 .10-0.000845' Rs), ~~dO.4731+0.5158· Y)

Y = 10-0.00081, Rs

[0.4078 ( )- 0.2466 (Psp )]Yl?corr=YI?Prp' 1+0.1595·API . TIp ·!.AII? --

, '114,7

6-Undersaturated oil viscosity:

• Extra-heavy oils: Modified Labedi's correlation

= _[(I_~)' [10-2

.19

. ~ ~'d055 ,PbO,3132]]~o ~ol Pb 10°,0099' API

2- Solution GOR:

• Extra-heavy oils: Modified Standing's correlation

(Pb I (O,OI69'API-O,00156'T))1.1128

Rs =Y . --, ° (A - 2)g 10.7025

• Heavy oils: Modified Vasquez-Beggs correlation1.2057

Rs= Ygcorr,Pb ,10 1O.9267 ,API/(T+460) (A-3)

56.434where

YI?corr = YI?PSP' [I +0.59t2' APT ·T.rp 'wI? (I ~:7 }0-4 ]

3-Isothermal CompressiblIity:

• Extra-heavy oils: Modified Vasquez-Beggs correlation- 889,6+ 3, 1374, Rs+ 20, Tg - 627,3' YgcolT -81.4476· API (A _4)

Co = -----------:;----""''''''-----Pg .105

t-Bubblepoint Pressure:

• Heavy oils: Modified Standing's correlation

[

0.7885

Y

R

g

S 100,0020'TPb = 15.7286, --..,...,-,.,....,..,-::- (A - 1)

I00,0 I42,API

APPENDIX A - MODIFIED CORRELATIONS

40 McCain W.O. Jr.. Bridges B.: "Volatile oils and RetrogradeGases-What's the Difference?" Petroleum Engineer International,(January 1994), pp 35-36,

~ol = 2,3945+0,8927'F+O,001567'F2 (A - 8)

where

( 1 1-0,000845.RS) (0.5798+0.3432'y)

F= -0.0335+ .0785, 0 '!-tod====================

y = 10-0,00081, Rs

YI?corr = YI?Prp '[I + 0, 1595, API 0.4078 , (Trpr 0,2466 , [..<II? ( Psp

)], '114,7

where

[ (Poll' ) -4]YI?COl'r = YI?PSP' 1+ 0.5912· API .T,rp . LOI? 114.7 10

• Heavy oils: Modified Vasquez-Beggs correlation-2841.8 +2, 9646· Rs+ 25.5439' Tg -1230.5· YgeOff +41.91· API

Co =-----------:;-----"':.::..:...---Pg'10

5(A - 5)

where

[ ( P.w J -4]YI?COl'r = YI?Psp' 1+ 0,5912, API· T.rp . UII? 114.7 10

4-Dead-oil viscosity

• Extra-heavy oils: Modified Egbogah-.Tack's correlation

log .Iog(rl od + I) = I. 90296 - 0.012619· API - 0. 61748, log(Tg)

(A- 6)• Heavy oils: Modified Egbogah-.Jack's correlation

log' log(1lod + I) = 2.06492 - 0.0179, API - 0, 70226.log(Tg) (A - 7)

5-Gas-saturated oil viscosity

• Extra-heavy oils: Modified Kartoatmodjo's correlation653

TABLE 1: FLUIO PROPERTY CORRELATIONS

Fluid Property Correlation

BUbblepoint pressure Standing III"'~/, Lasater/'ll, Glaso /~/

Kartoatmodjo 113/,Al_Marhoun1101

Solution GOR Standing, Vasquez-Beggs I'f/,

Kartoatmodjo,Rollins-McCain-Creeger 1151

OFVFStanding, Vasquez-Beggs, Glaso,Kartoatmodjo

Isothennalcompressibility

Dead-oil viscosity

Gas-saturated oilviscosity

Undersaturated oilviscosity

Vasquez-Beggs, Kartoatmodjo,Labedi 1121, Petroslcy-Farsha<y171

Slotte flY/, Beggs-Robinson /l>!,

Glaso, Kartoatmodjo,Egbogah-Jack!91, Labedi 116/

Chew-C01mally /~/, Beggs-Robinson,Kartoatmodjo, Labedi /161

Vasquez-Beggs, Kartoatmodjo,Majeed-Kattarl-Sahnan 1141,

Labedi 1161

TABLE 2: AGIP'S RANGE FOR PVf PROPERTIES SAMPLE

Tank-oil gravity (0API) 6t022.3

Reservoir prl$$ure (psia) 1038.49 to 7411.54

Reservoir temperature (OF) 131.4 to 250.7

Solution GOR (sofYSTB) 17.21 to 640.25

Bubblepoint pressure (psia) 208.86 to 4021.96

Separator p~ure (psia) 14.5 to 752.2

SeparatQr temperature (OF) 59 to 177.8

Separator GOR (sofYSTB) 1I.l to $7$.62

Stock-tank GOR (set/STB) 4.39 to 311.41

Total sulface gas gravity (alr=l) 0.675 to 1.517

Separator gas gravity (alr=1) 0.623 to 1.517

Mole fraction ofCOz in total gases (% mol.) 0.5 to 98.8

Mole fraction ofNz in total gases (% mol.) Ot063.32

Mole fraction ofHZS in total gases (% mol.) Oto 1.99

Oil formation volume fact9r (bbl/STB) 1.057 to 1.362

Isothermal comp~ibility (psia-1x 10 6) 3.02· to 42.9

Dead-oil viscosity (cp) 7.7 to 1386.9

Gas-saturated oil viscosity (cp) 2.1 to 295.9

Undersaturated oil viscosity (cp) 2.4 to 354.6

654

0)C1I(]I

TABLE 3: AUTIIOR'S DEFlNED RANGE FOR BUBBLEPOINT PRESSURE, SOLUTION GOR, OFVF AND COMPRESSffiILITY CORRELATIONS

Standing Lasater Glas<> Kanoatmocljo Vasquez-Beggs Al-Mamoun Rollins-McCain Petrosky-Farsbad LabediCreeger

Tank-oil gravity (0API) 16.5 to 63.8 17.9 to 51.1 22.3 to 48.1 14.4 to 58.95 15.3 to 59.5 19.4to 44.6 18 to 53.5 16.3 to 45 32.2 to 48

Bubb1epoint pressure (Psia) 130 to 7000 48 to 5780 165 to 7142 Oto6040 15 to 6055 130 to 3573 - 1574to 6523 520 to 6358

Reservoir temperature (OF) 100 to 258 82 to 272 80 to 280 75 to 320 170 (mean) 74to 240 - 114 to 288 128 to 306

OFVF at bubblepoint (bbl/STB) 1.024 to 2.15 - 1.025 to 2.588 1.022 to 2.747 1.028 to 2.226 1.032 to 1.997 - 1.1178 to 1.6229 1.088 to 2.92

Solution GOR (scf7STB) 20 to 1425 3 to 2905 90 to 2637 Oto2890 Oto2199 26 to 1602 - 217to 1406 -Separator gas gravity (air-1) - - - 0.4824 to 1.668 0.511 to 1.351 - 0.579 to 1.124 - -Total surface gas gravity (air-1) 0.59 to 0.95 0.574 to 1.223 0.65 to 1.276 - - 0.752 to 1.367 - 0.5781 to 0.8519 -Separator pressure (psia) 265 to 465 15to 60S 415 (mean) 100 60 to 565 - 29.7 to 314.7 - 34.7 to 789.7

Separator temperature (OF) 100 (mean) 34to 106 125 (mean) 38 tQ 294 76 to 150 - 60 to 150 - 60 to 220

Reservoir pressure (psia) - - - 10 to 6000 141 to 9515 20 to 3573 - 1700 to 10692 -Stock-tank GOR (scf7STB) - - - - - - 4to220 - -Separator GOR (scf7STB) - - - - - - 12 to 1742 - -

TABLE 4: AUfHO~SDEFlNED RANGE FOR VISCOSITY CORRELATIONS

Beggs-Robinson Glas<> Kartoatmodjo Eg1>Ogah-Jack Labedi Chew-connany Vasquez-Beggs Majeed-KattanSalman

Tank-oil gravity (OAPI) 16 to 58 20.1 to 48.1 14.4 to 58.95 5to58 32.2 to 48 - 15.3 to 59.5 15 to 51

Reservoir temperature (OF) 70 to 295 50 to 300 80 to 320 59 to 176 100 to 306 72 to 292 - -Reservoir pressure (psia) 15 to 5265 - 15 to 7171 - - - 141 to 9515 711 to 7112

Solution GOR(scf1STB) 20 to 2070 - Ito 2044 - - 51 to 3544 9.3 to 2199 60 to 1334

Bubblepoint pressure (psia) - - - - 60 to 6358 132 to 5645 498 to 4864

Dead-oil viscosity (cp) - 0.616 to 39.1 0.5062 to 682 - 0.66 to 4.79 0.38 to 50 -Gas-saturated oil viscosity (cp) - - 0.096 to 586 - 0.115 to 3.72 - 0.117to 148 0.093 to 20.5

TABLE 5: EXPERIMENTALLY MEASURED PVTDATA

18.0'2l,215,82,14,;0j8,8:

6,118.l!2,61

295,9190,3

171,412D8,S'

1Sl,8]106.1:2.40.0:U8,Olu,ol116;3185,6

106,S1~

49~

:119.11

81.7

8.3119.8!2l,3'

3S,3

2l,8,23,3,30,8

:165.469,469,9,43,3'14.~

Vol

0,000.10

0.0010,000.0010,001,0.001

0.000;00,O.OOi0;00

0.0010.00;0.000,0010.00,0.00

0.0010.001.0.000,00

0.001O.OO!0.000.000.000.000,000.0010;00'0,000.0010.000,00

0.001

0,0010,00.0,00

0.0010.001,82

0.10

0.41\0,00'0,000,0010.00'0;000,0010.41,0.00'

0,011

.0,00.

1

'0,320,000,91,

0.000;000.101

l.99'0.000.001

YIi2s

0.65]2,611

YII2

1,1311,09

79.1980,311803182,38'

29.1198U41u.so8,20

25.93113,61'

47.0114,56164,56'22,SO

4.89,O.SO

66,49

13.8613.751

66,01'8l.64"81.so76,33'19,59'46,40'

55.119

G.411

0.48

2,90

49.7410,53'

G.41IG.95

1

0.6011,51so.04131,83'

14.0822,41,12.511

=112,15,

:~I:8,11

98,88

~~38.78'3l.3S69.781

v_

59,0

104.0

90.0

133.51

lS8.0,

::1',129,2

lS8.0'1S8,O158,0

118,8162,~

115.51

116,016,1

IS8,O161,0161.0'161.0

122,01

134.6,18.8

116,6

86,01

122,0

IP4.0

68,~1100.4!100.4

:':r69.81

69.818M69.81

10G,484,2

122,01,5,2

1l,6

80.61100,4'15,669.8

104;0:68,0,

100.486,0

0.69610;615:l,429'

1,13410;156

l.4'0.7.

1.4151

1,4911,334!

1,4101

l,419

1.0351

l,Z63,

l,29S1,178l,301l1,344'

1,064

l,Z1610.7880.784!1,188

l,S11:

'aY." T!

1,129l,236]0,81S

0.810

10.735

1,2S3,

0.8~

0.7161

0.1141

l,323:

O~

1,2061,1~

1,292'G.9141,>\021

1.4121

-1,406'1,4111.0591,>\1111,.1691,lilSl1.0921l,336'

. l,3411

1,333:1.2S611,005G.96:1.06.1,>\21:

4,

14,88110,27'

7.44~,

18.491

6;05!

44;421

53,58,

6,111

7,7137.64

33.37136.36,30,3111,0534,53

33.03'

6,721

28,2D,$,94'

4,39

:148,19)

5.11U,0514.49112,60'U,66

11,55311,41

12,8888;83

31,6513O,;6Si

l3,9449,41U,66:

12,TlI16,54

U,6O

3G.1Sl3,2l

93.44110.44,S2,S8

lS,SS

31.65:l3,2l

7.so42,36

96,05'

168.3)116,32

11,10:

Rs

3121,131209,63

3598,446Z12,98

1149.18:

3428,155391,144808,081

4132,66:3563.63'

4143.14

SSl8.114494.79'

4708.001'48S~

4883.so:4996,63

4908.IS]4808.08:4895.10'2850.04'

2916,151

2893.551S139.23'2916.15

28S0,04

1Z8S8.1448U,88'

2916,7;430S,18

4519.4S!4410.61:

2552.10

13684,023121,53,

3121.53'3784.09

=~:.II4281,583328,611lS3,01

741l,S414813,34:1411.54

104.'.49.•11806.416SS1,2j;!

1792,26

1593.121

187l',S41649.98:721l.391934;4OS305,5!i'4238,01!

6921.11187l',S4

ID7.421

1806.411

1149.416856,04

PrI£.-.141.~I165;2Z10,2

~IZ03,9:165;2

215,61

ZI0,2,ZlS.6'

Z12,°1Zl'7.4=0

Zlo.°lZI'.4154.8

~I161.•0152.~

154.81153.1

ZI0,2]

lS2,~

208,0:=.6'Z11,6

183.ZI~,

201~

201.71214.01203;0'

13l,4I'ZI1,3188,1140.0'

250"1194.02.44.4

163.4,

211.4165,2:

l.Sll,0!154.4112,4

2.40.8,171.8,118.71

161.0:231,8 1

17.G.62.44.0163,41lSO.8:231,8:

i~19G,4,188;81179,6134.1

6,

6,3]6;517,37,5.1,911,9:8,0:

8,0

8.318,~

8.99.01

9;6110.0,10.5

1

IG.911,0Il,O!

~~~:I12,412,612,8]

~::I'14,6

14,9,15,1,

21.3:2l,3'

22,0

°API1Z3

456111

910

11121314IS161118192D2122

23

2.425Z6Z1282930

31323334353637

3S39

40414Z43

4445464148

49SO515253

54

5556515859

60616Z63

iPVT

0)010)

0>01.......

TABLE 6: BEST RESULTS OF STATISTICALANAllSYS PERFORMED ON AGIP'S SAMPLES

(AAE =Average AbSolute Error, %; SD = Standard Deviation)

°APIRange Bubbleooint pressure Solution GOR OFVF Isothemla1..

Author Standing Standing Glaso Vasquez-Beggs<=lO OAPI AAE 9.1 13.7 1.3 38.7

SD 9.8 17.9 1.2 21.9Author Standing Vasquez-Beggs Vasquez-Beggs Vasquez-Beggs

10 < °API <= 22.3 AAE 15.1 25.7 1.4 25.5SD 13.9 45.9 1.1 19.2

Dead-oil viscositv Gas-saturated oil viscosi1rv Undersaturated oil viscositvAuthor Egbogah-Jack. Kartoatmodjo Labedi

<=10 oAPI AAE 30.3 14.7 12.3SD 24.4 13.0 7.8Author Egbogah-Jack. Kartoatmodjo Kartoatmodjo

10< °API <=223 AAE 41.8 16.1 10.1SD 24.9 16.5 10.5

TABLE 7 : STATISTICALANAIlSYS PERFORMED ON MODIFIED CORRELATIONS(AAE=AvenI2e Absolute Error,%; SD=StandardDeviatiOD, M = modified)

°APlRange Bubbleoointpressure Solution GOR OFVF Isothemml..

Author Standing M-Standing not investigated M-Vasquez-Beggs<=10 OAPI AAE 9.1 6.5 8.5

SD 9.8 4.5 5.0Author M-Standing M-Vasquez-Beggs not investigated M-Vasquez-Beggs

10 < °API <=22.3 AAE 10.2 17.0 15.6SD 8.1 11.3 10.7

Dead-oil viscositY Gas-saturated oil viscosi1rv Undersatnratedoil viscositvAuthor M-Egbogah-Jack. M-Kartoatmodjo M-Labedi

<=10 oAPI AAE 17.4 12.6 4.0SD 8.9 10.0 3.4Author M-Egbogah-Jack. M-Kartoatmodjo M-Kartoatmodjo

10 <oAPI <=22.3 AAE 37.8 ll.8 6.0SD 21.9 9.9 7.2

TABLE 8 : EXPERIMENTALLY MEASURID DATA IIOR VlSCOSITY INVESTIGATION(. = sample fi'om literature)

PVTRepori °API Tr("J!) Pr(psla) Rs (sdISTB) Pb(psla) Vod(~p) Vol (~p) Vo(~p)

I 7.1 212,0 4911,05 82.17 554.05 278.5 124,7 228.32 7,5 203,0 4565.86 24,26 121,83 451,5 360.13 8.2 218,7 4876.24 144.02 796,27 203,5 77,3 132.74 8,2 218.7 4876,24 786.70 4993,73 222,4 20,1 21.0

5 9,0 117.5 2671.64 208.75 2364,15 3340,0 528.0

6 10.2 211.1 4715,25 189,87 1934.83 125.8 41,7 75.07 10,5 154,8 2850.04 345.55 2574.46 99.0 16,0 16,4

8 10,6 212,0 4766.01 91.66 781,77 130,6 78,9 137.09 10,6 212.0 4766.01 725.08 4993,73 148,8 9,3 10,7

10 11,2 154,8 2850,04 376.92 2858,74 100.2 15,0 15.0

11 !l.3 210,2 4589.07 202,09 2319,19 111.7 42.0 64.0

12 11.3 154,8 2850.04 370.76 2475,83 110,0 17,2 18,0

13 12.3 204,8 4509,29 227.63 2261,17 105,6 37,7 50,0

14 12,6 208,0 4805,18 736.57 4993,73 103.1 7,3 7,4

15 13,0 212,0 4993,73 127,42 1151.62 59.3 30,2 54.0

16 13,0 212,0 4993,73 300,52 2858.74 60.6 . .l7,4 23.0

17 13,0 212.0 4993;73 479,63 4993,73 57,4 11.9 11.9

18 ·13.0 212,0 4993,73 493,45 2858.74 75,0 17.0 22,9

19 13,0 212,0 4993,73 788,04 4993,73 75,3 7.2 7,2

20 13.6 215,4 4281,58 208,75 1650,56 53,4 19,6 .25,8

21 14.8 211,3 4281;58 228,41 2261,17 36,9 16,2 24,5

22 14.8 211,3 4281.58 292,31 2858,74 41,3 13,6 16,1

23 14,8 21l,3 4281,58 315.90 2858,74 40,0 10,5 12,2

24 14,8 2!l,3 4281,58 419.00 2858,74 32,7 9.1 15,6

25 14,8 2U,3 4281,58 444.10 4281,58 37.3 9,6 9.6

26 14,8 211,3 4281,58 465.64 4281,58 39,8 8,1 8,1

27 14,8 21l,3 4281,58 753,17 4281,58 40.9 5,2 5.2

28 15,0 211.3 4281,58 463,75 4281,58 ~8.3 14,2 14,2

29* 15,0 194.0 4978,21 195,59 71'1,13 4,7 7.1

30 15.1 207,5 4281,58 182,10 1763,69 56.3 21,8 30,8

31 15.1 207,3 4281,58 191,98 1834,76 55.6 18,9 25,5

32 16,0 21l,3 4281,58 189,82 1778,19 37,0 15,5 20.6

33 16,0 211,3 4281.58 215,91 1991,40 38.6 13,8 18,3

34 .16,4 212,0 4808,08 143,68 1038,49 24.5 12,7 19.0

35 17;8 193.1 3723,18 73,62 683,14 70.3 40,0 60.336* 17,9 180.0 4978;21 260,11 2417.96 3,4 4,4

37* 18,0 100.0 6400,62 247,23 2450.02 20,5 25,4

38* 18,2 170.1 4978,21 290,14 68,29 2,6 3.639 19,2 118,0 1182,08 109,93 797.72 273,0 80,6 86.640 19,0 149.0 1330.02 113,59 668,63 54,5 23,3 .25.0

41 19,0 217,4 6557,26 152,07 725,20 15,9 8,0 16.1

42 19,0 163,4 1807,20 229,46 1393.83 52.7 13,7 15,6

43 19,0 163,4 1807,20 256,44 1807,20 52,7 11,7 11,7

44 19,6 195,8 3375,08 198,31 1012,38 20,S 7,6 9,6

45* 20,0 180,0 5333,85 197,81 1066,77 5,2 7,7

46* 21.1 190,0 4978,21 437,10 2062,47 2,0 2,547 21,3 179,6 6272,98 252,56 6272,98 12.9 7,8 7.848 21.3 179,6 6272,98 702,70 2104,53 16,1 2,5 3,6

49 21,3 179,6 6272,98 832,06 6272.98 '.12,8 2,2 2,2SO 21,7 202,5 4000,20 189,21 960,16 12,1 4.1 5,4

51* 21,7 170,1 5689,48 378,64 3747,83 1.7 2.152 21;8 201,0 3450,50 185,88 918,10 12,0 5.1 6.6

53* 21,8 177,8 4978,21 521,38 3136,34 \.3 1,554* 22,0 181,0 4978,21 412,51 1422.41 1.7 2,3

55* 22,0 193.8 4978,21 494,45 2560,25 1,9 2,3

TA13LE 9 : Statisticol RQsults ofViscosity Investigation(ME = Avcralle Abs.Error,% SO = Stand. Oev., M = Modified)°APIRonlle Vod Vol Vo

Author M-Egbogah M-Kartoalm. M-Labedi<= 10 ME 26,4 19,8 5,9

SO 17,1 22,3 1,3

Author M-Egbogah M-Kartoalm. M-I<artoolm.10 - 22.3 ME 35,4 20,5 5,7

SO 18,2 13,5 7

658

-

4000

--- --- .. ....

..

--..

1000

..0.JL..---1-----I----+----l-----!

o

..

1000

Fig.!: Bubblepoint pressure, best correlations from literature Fig. 2: Bubblepoint pressure, present work

730,-----------------------;( 730,----------------------Jf

.lOll .lOll

I II " I .

"..250 250

."

730l\I!ASUlID (1.1181'8)

730

Fig. 3: Solution GOR, best correlations from literature Fig. 4: Solution GOR, present work

\l10

MUSUlID(I",I'IA"")

o.JL..------+--------I--------lo

13,----------------------.,(

10

MYABl,JIlID (1",... 11 &t,)

13,.---------------------.,(

! 10 ro

~

"~1

I II

••t

Fig. S: Isothermal compressibility, best correlations from literature

659Fig. 6: Isothennal compressibility, present work

100 100

i i

I • I10 .0

•

100010010

.000,.-------,-------r------'71

100010010I ""--------l------~I__----____l

I

.ooo-r-------,--------,-------,t

Fig. 7: Dead-oil viscosity, best correlations from literature Fig 8: Dead-oil viscosity, presentwork

.00010010

10 +------**'--.------1-------1

looo-r-------,-------,------'71

I

1000'0010

10+-_- -df-L-,..,.-- ~1- __;

lOO-l------+----~~f'!i-----_1

.ooo-r-------,-------,------~

I

Fig. 9: Gas-saturated oil Viscosity, best correlations from literature Fig. 10: Gas-saturated oil viscosity, present work

'00 100

i i

I I10 10

1000100.0

1000 -r-'----I----,-------,------71

'000100'0

.ooo,------..,..------.......-----~

Fig. 11: Undersaturated oil viscosity, best correlations froni literature

660Fig. 12: undersaturated oilviscosity; presentwork

1000

1000,.-------,-------,-------7f

1,41,3

1,4

( I~ • §

Li •• I10

~I

MrABUlDl lWJ$11l) MrMUlDl«,)

Fig. 13: Bubblepoint OFVF, best correlations from literature Fig. 14: Gas-saturated oil viscosity, best correlationsfrom literature (input dead-oil Viscosity calculated)

10-22.3

APIRan ge

< 10

Standing

o 5 10 15 20 25 30

Average absolute error

Fig.15 Bubblepoint pressure correlation: comparlsonofbest results

A PIRange

10-22.3

< 10

V asquoz-B oggs

o 5 10 15 20 25 30 35

Average absolute error

Fig.16 Solution OOR correlation: comparison ofbest results

APIRange

10-22.3

<: 10

V asquoz-B eggs

Vasquoz-Boggs

o 5 10 15 20 25 30 35 40 45 50

Average absolute error

Fig. 17 Isothermal compressibility correlation: comparison ofbest results

661

APIRan ge

10-22.3

< 10

o 10 20 30 40

Bgbogah·lao!<

50

APIR aoge

10-22.3

< 10

Av'e .. age absolute e .... o ..

Fig. 18 Dead"OjJ viscosity correlation: comparison ofbest results

K artoatm odjo

o 5 10 15 20 25 30

A PIRange

10-22.3

< 10

Ave .. age absolute e .... o ..

Fig. 19 Oas-saturated oil viscosif,y correlation: comparison ofbest results

Lobedl

o 2 4 6 8 10 12 14

AVeJ'jlge absolute e .... o ..

Fig. 20 Undersaturated oil viscosity correlation: comparison ofbest results

662