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$PE 79032. The method eliminates any guesswork whendetermining how many proving runs are needed.3. The method ensures the desired accuracy of thecalculated meter factor.

Acknowledgments

3.4.5.6.

46.API Manual of Petroleum Measurement Standards, AH,Washington, DC, (May 1978)19.Fiknwarth, A. L.: Remote Supervisory Control IncludesMeter Calibration, Wand GasJ. (June 12, 1967)91-93,Bloser,B, L.: Positive DisplacementLiquid Meters,Measurementsand Control(Sept,-Ott, 1977)80-93.Lilliefors, H. W.: On the Kolmogorov-Srnimov Test forSpecial appreciation to F. H. Sanders Jr. of Sun PipeLine Co. and R. J. McKinley for their contributionto this study. I also appreciate Sun. Co. Inc. forpermission to publish this paper.References1. API Standard 1101,API, Washington,DC,1sted. (1960)21,2. API Standard 2534, AH, Washington,DC,(March1970)16-

NormalitywithMeanand Variance-Unknown,m. Stat,Assn. J. (June1%7)399-402.Shiaw Y. SuSun Co. Inc.Dallas

Original manuscr ipt received in Society of Pefroleum Engineers office Dec. 12,1977. Paper (SPE7113) eccepted for pulslicslionSepf, 27, 197s. Revised msnuscripfreceived June20, 1979.

A Set of Equations for Computing EquilibriumRatios of a Crude Oil/Natural Gas Systemat Pressures Below 1,000 ps!a

Use of equilibrium ratios (K values) to compute thequantity and composition of gas and liquid phases inequilibrium at given temperatures and pressures isdocumented extensively in the petroleum literature.While K values usually come from laboratory experi-mt%ts, the values available to petroleum engineers arepresented most often in the form of chmts. The GasProcessors SuppliersAssn. (GPSA)charts ofK data arewell known in the industry.It long hasbeen recognized that equilibrium ratios aresystem-compositional, temperature, and pressuredepen-dent. Composition dependency usually is indicated bythe apparent convergence pressure value (for example,5,000 psia, 10,000 psia). However, at pressures belowabout 1,000 psia, the effect of the systemcomposition issmall and often may be neglected.A computer program package for evaluating GPSAratios is available from the association. However, useofthe GPSA programs requires a large computer. Thfiequations presented here are simple enough to behandled by small programmable calculators, such as theHP-67, TI-52, and TI-59 machines. It is myopinionthatK values developed from these equations are moreappropriate than GPSA K values for calculating flashvaporizations at conditions usually found in oilfieldgas/oil separation processes.The basicK data involvedhere are those developedbyKatz and Hachmuth2on recombined samples of gasandoil from the Wilcox sand of the Oklahoma City Field.Crude gravity was 38.4API. Based on the reportedviscosity of the crude oil, 43.5 Saybolt SecondsUniversal (SSU) at IOOF,the Universzi Oil ProductsCharacterizationFactor (UOPK) of this crude isjudged0149.2136/i9/0CQ9-7Q0334W.25@1979 soc iety o f Petro leum Engineers o f AlMES~PTEMBER 1979

to be about 12.2. While 22 sets of experimental datawere determined at three terxpratures (up to 3,422psia), the K values used herewere smoothedvalues readfrom 11- X 17Yz-in. charts prepared by Katz andJ-Iachmuth. The K values corresponded to pressures of14, 200,400, 600, 800, and 1,000 psia, at temperaturesof 40, 120, and 200F.The basic equation used to correlate the Katz andHachmuth data was that propcsed by Hoffman et aL:3logKp=~[b(l/TB l/T)], . . . . . . . . . . . . . . . . . (1)where:K = equilibrium ratio, y/x, of the compoundp = pressure, psia (MPa)T= temperature, R (K)b = slope of the straight line connecting thecritical point and the atmospheric boilingpoint on a log vapor pr~ssure vs l/T plot= log (p= /143(l/TB - I/Tc)

TB= boiling point of the compound at 14.7 psia,R (K)Tc= critical temperature of the compound, R(K)

P. = critical pressure of the compound, psia(MPa)The function insidebrackets is the componentcharacter-ization factor, designated by the symbol F.Several authors4-Ghave shown that plots of log Kp vsF, at a given pressure, often form essentially straightlines. Also, the effect of increasing pressure has beenshown to raise the position of the line on the plot and toyield a line of lesser slope. Actually, there are no

1193

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a

theoretical reasons for the isobar lines to be straight orfor them to converge at a commonpoint, as indicated byBrinkman and Sicking4 (see their Fig. 2). However,wlien straight lines are indicated by the data, simplerequations for K result.Correlation of Katz and HachmuthK DataSince the Katz and Hachmut5 charts gave K values forlumped butanes, pentanes, andhexanes, it wasnecessaryto use lumped F values in ihe correlative work. Thebutanes f~acti~n was treated as being composed of 25%i.:+butanti arii 75% n-butanq the pentanes fraction as35% isopm tane and 65% n-pentane; and the hexanes as25% 2-me?nylpentane, 25% 3-methylpentane, and 50%rwrmal hexane. These butanes and pentanes splits wereindicated by the authors; the hexanes split is myassumption. The resulting b and TB values for thelumped fractionswere: butanes, b = 2124, TB= 486k,pentanes, b = 2441, TB= 552R;hexanes, b = 2738,TB = 61OR.Early in the research, values of b md TB listed byHoffman et al.3 for methrmeand ethane were found to

- give undesirable results. Fig, 1 is a plot of log Kp vscomponent characterization factors, F, at 800 psia,While the propane and heavier compounds form anadequate straight line, the methane values, and to alesser degree, the ethane values, do not align with thegeneral trend, Behavior similar to that shown in Fig. 1was found at other pressures. This behaviorwasrectifiedby determining values of b and TB that caused themethane and ethane points to align with aud fall on theline formed by the heavier compounds. T~e overall bestadjusted values for methane were found to be b =10,!IOO5,009

10

I I I Ido 40 fn WI FA 200OF /!c!$0 _/2

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76

/-1 0 1 2 3COHPONENTHARACTERIZATIONACTOR.

FI . 1L kp vs F, relatlonahipof Ka~ and Ilaohnuth&l!-paia ate at temperaturesof 40, 120, and 200F.1194

300, TB = 94R, for ethane the values were b = 1145,TB= 303R.Note that using these adjustedvalues ratherthr& values proposed by Hoffman et al. reduced theaverage difference between methane equation K valuesand chart K values from 16.2 to 2,370.Use of adjustedbagd TBvalues for ethane reduced the average differencefrom 8.5 to 2.1%.It is not surprising that this spurious behavior wasfound for methane and ethane. Valuesof b and TBlistedby Hoffman et al. originate from vapor pressure valuesof pure compounds. It long has been known7*8thatequilibrium ratios of methane and ethane depend onthe character of the heavy components (UOP K, forexample) in the mixture, as well as on temperature,pressure, and total composition, Thus, the adjustedvalues of b and TBabove shouldbe considered specifictothe Oklahoma City cmde oil systems. However, theyalso pr~bably represent other crude oil systems ofcomparable paraffinicity very well.Six isobw plots of logKp vs F were made for.the 18sets of chart K values using b and TBvalues from Table1. The best straight-line fit to the points was made byinspection, and the slope and intercept value at F = Owas determined. The slope and intercept values thenwere plotted vs pressure, and the best fit by a quadraticequation was determined. Results of this study aresurnnmized by the following four equations.K= l/p @J+c19. . . . . .. . . . . . . . . . . . . . . , . .,, (2)F = b(l/TB - lIT). . . . . . . . . . . . . . . . . . . . . . . (~)a (intercept) = 1,2 t 4.5(10-4) p + 15(10-*) pz.

. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . #, (4)c (slope) = 0.890- 1.7(10-4) p - 3.5(10-5) pz.

. . . . . . . . . . . . . . . . . . . . . . . . . . . ,, ... (5)Use of these equations to compute Katz and HachmuthK vaiues should be restricted to pressures below 1,000psia and temperatures between 40 and 200F. One alsomust use the b and TBvalues listed in Table 1, Withinthese restraints, one may expect a standard deviation of

TABLE l-VALUES OF b and T@FOR USE INCOMPUTING KAIZ AND HACHMUTH EQUILIBRIUMRATtOS BELOW 1,000 pEiaCompound (cyc~ R).Nitrogen 470Carbon dioxide 652Hydrogen iwlfioe 1136Methane 300!Zthane 1145Propime 1799

iso-B@w 2037n.Butane 2153ieo-Pantene 2368n-Pentane 2460iso-tiexanee 2696n-Hexane 2780n-Heptane 3066n&tane 3335n+lonane 3590n.Cmcane 3828Hexanee (lumped) 2738Heptanes and heavier= 7.3 + 00075 T(OF)+ 0.00:3 P (peia):= 1013 + 324 n - 4.258 neTB= 301 + 59.85 n -0.971 ng

(%)G1943313%416471491542557803616889718783805610

:...-~.

JOURNALF PETROLEUMECHNOLOCv

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about 3.5% between equation-generated K values andthe original Katz and Hachmuth chart K values.Ks for Heptanes-and-Heavier FractionWhen making flash calculations, the question of the Kvalue to use for the lumped plusfractionalways arises.One rule of thumb proposed by Katz and Hachmuth2isthat the K value for CT+ can be taken as 15%of the Kof C7,The correlation method that involves a semilog plot ofKPvs F offers an answer to this question, at least for theOklahoma City crude oil/natural gas systems Katz andHachmuth studied. In this portion of the work, plots oflog KP vs F were made from the hexanes and lightercomponent experimentaldata and the best straight line fitof the data determined by least-squares method. Know-ing the expwimental valueof theC7+ K, itwas theneasyto compute the corresponding CT+ F value, and fromthis to specify the pure normal parraffinhydrocarbonthatwould have the K value of the C7+ fraction.Results of this analysis were somewhat ragged, butdefinitely indicated that the effective K of the C7+fraction varied with temperature and pressure. If thesymbol n is used to designate the number of carbonatoms of the normal paraffinhydrocarbon that has theKvalue of the C7+ fraction, the relationship of n,temperature, and pressure is:n(C7+) ~ 7.3 + 0.0075 7(F)+ 0.0016 p(psia).

. . . . . . . . . . ,,, ..,,... . . . . . . . . . . . . (6)Thus, in the temperatureandpressureranges studied, theC7+ K can be characterized as equivalent to Ks ofnormal paraffin compounds ranging from C7.3H16.6toGo.4 H22.LI.To use this information to calculate K values for C7+fractions requires relationships between 1 and n, and TBand n. For n values between 7 (normal heptane) and 20(~ormaleicosane), the band TBvalues listed by Hoffmane~ al. are fit very closely by the equations:

b(n) =1013 -t-324 n-4.256n2. . . . . . . . . (7)TB(n) =301 + 59.85 n 0.971 n2. . . . . . . . (8)

Thus, b and TB values for the C7+ fraction in theOklahoma City crude oilhatural gas system can beevaluated by substituting the value of n from Eq. 6 intoEqs. 7 and 8.Ks for Nonhydrocarbon CompoundsMany naturally occurring systems contain variousamounts of N2, C02, and H2S, as well as the usualhydrocmbons. For maximum utility, some provisionshou!d be made for computing Ks for these nonhydro-cartm compounds.Equilibrium ratios of N2,C02, andH2Sinmixture~ofnatural gas and absorber oil and mixtures of natural gasand crude oil have been reported by Jacoby and Rzasa.9Poettmann10also has reported K values for C02 inmixtures of natural gas and crude oil. API gravities ~fthe Oklahoma City crude oil and those used in Poett-manns studies were essentially the same (&38API),while the crude oil Jacoby and Rzasa used was lowerCMglnalrnanuaer lpt rwlved in the Soclaly of Petroleum@neerafficect.S,19?S,qmr (SPE 7SOL) ampf ed f or publicationJuly 1, 1879.

SEPTEMBER 1979

(t 27API). Poettmanns systems contained 6 and 11%C02, while Jacoby and Rzasas systems contained 5%N2, 5% C02, and 5% H2S. Katz and lIachmuthssystems had none of these compounds.Thegeneral procedureusedto develop b andTBvaluesfor the nonhydrocr@on gases was: (1) it vas firstassumed that at a given temperature and pressure, therelative volatility of the nonhydrocarbon and methane(ratio of their Ks) measure in the Jacoby/Rzasa and inthe Poettmann systems could be applied directly to theKatz and Hachmuth systems, (2) using the measuredrelative volatilities and the methane K values indicatedby the Katz and Hachmuth data, equivalent Ks werecomputed for the nonhydrocarbon in the Katz andHachmuth systems, (3) having computed the equivalentnonhydrocarbonKs, the appropriate log KPvs F chartwas entered from the KPaxis, and a corresponding Fvalue determined for the nonhydrocarbon, and (4) fromthe F values at various temperatures, the correspondingvalues of b and TBwere computed.Results of conducting this procedure at 100, 150, and200F and at 200,400,600,800, and 1,000 psiawereN2values of b = 470, TB = 109R;C02 values of b =652, TD= 194R,and H2Svalues of b = 1,136, TB=331R. These should be properly labled as adjustedvalues because they originated from multicomponentsystem behavior, not vapor pressure measurements, andhave been adjusted to fit equations for Katz andHachmuths hydrocarbons equilibrium ratios.References1.

2.

3.

4.5.

6,

7.

8.

9.

10.

EngineeringData ~ook, Gas Processors SuppliersAssn., Tulsa(1972).Katz, D. L. and Hachmuth, K. H.: Vaporization EquilibriumConstants in a Crude OLNatural Gas System: Ind. Eng. Chem(1937) 29, 1072.Hoffman, A. E., Crump, J. S., and Hocott, C. R.: T?quilibriumConstants for a Gas-CondensateSystem, Trans., AIME(1953)198, 1-10.Brinkman, F. H. and Sicking, J. N.: *EquilibriumRatios forReservoir Studies: Trans., AIME (1960) 219, 313-319.Kehn, D. M.: *Rapid Analysis of Condensate Systems byChromatogrsphyfl J. Pe/. Tech. (April 1964) 435-440; Trans.,AIME, 231.Dykstra, H, andMueller, T. D.: Calculationof PhaseComposi-tion and Properties for Lean- or Enriched-GasDrivev Sot. Per.Eng. J. (Sept. 1965) 239-246 Trans., AIME, 234.Sage, B. H., Hicks, B. L., and Lacey, W. N.: TentativeEquilibriumConstants for IJght Hydrocarbons,Dri/LandProd.Prac., W1 (1938) 386.Solomon, Emesc Liquid-VaporEquilibriumin LightHydrocar-kon-Absorber 011 Systems: Chem. Eng. Prog. Sym. Ser. 48(1952) No. 3, 93.Jacoby, R. H. andRzasa, M. J.: EquilibriumVaporizationRatiosfor Nitrogen, Methane, Carbon Dioxide, Ethane, and HydrogenSulfidenAbsorberil-NaturalasandCrudeOil-NaturalasSystemsYTrans., AIME (1952) 195, 99-110.Poettmann,, H.:Vaporizationhdrscteristicsf CarbonDioxide iri a Natural G&/Crude Oil Sy&em~ Trans., AIME(1951) 192, 141-144.

S1 Metric Conversion FactorsAPI 141.5/131.5 + API = kglm3F (F-32)/l .8 = cpsia x 6.894757 E-03 = MPaR 0R/1.8 =K

M. B. Standing, sPE-AIMEStanfordU.Stanford,CA1195