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ILLINOIS INSTITUTE OF TECHNOLOGY NORMAN L. CARR* CHICAGO, ILL. RIKI KOBAYASHI THE RICE INSTITUTE MEMBER AIME HOUSTON, TEX. Downloaded from http://onepetro.org/JPT/article-pdf/6/10/47/2238156/spe-297-g.pdf by guest on 28 September 2021 DAVID B. BURROWS CONTINENTAL CO. MEMBER AIME PONCA CITY, OKLA.

T.P.3915

ABSTRACT as a function of reduced and , i.e. : The viscosity of hydrocarbon , whether in (1) the or , is a function of pressure, tem­ perature, and phase composition. This paper presents T _ , absolute units where: methods for the prediction of the viscosity of the gas R - critical temperature, absolute units or less dense phase over the practical range of pressure, temperature, and phase compositions encoun­ pressure, absolute units n tered in surface and subsurface production P = critical pressure, absolute units operations. The correlation necessary to predict the /1. = viscosity of gas at reduced temper­ effect of pressure on is presented in Part I. ature Tn and reduced pressure Pn Serious discrepancies in high pressure gas viscosity data in the literature are discussed. /1., = viscosity of gas at atmospheric pressure and at temperature Tn The application of the correlation to predict absolute v,iscosities is discussed in Part II. Auxiliary correlations Serious discrepancies in the viscosity of pure hydro­ are presented to enable calculations of viscosities from carbon gases at high pressures have been called to a knowledge of the pressure, temperature, and gravity our attention by Comings, Mayland, and Egly. They of the gas phase. made a careful analysis of the following methods com­ monly used to measure gas viscosities:

4 INTRODUCTION 1. Oscillating disc " 2. Rolling ball viscometer,,7 A knowledge of the viscosity of hydrocarbon is needed to study the dynamical or flow behavior of 3. Capillary tube viscometer" these mixtures through pipes, porous media, or more generally wherever transport of occurs in On the basis of their analysis of the problem and fluid motion. Since flow is predominantly in the laminar their experimental data on the viscosities of , region in petroleum reservoirs, the influence of fluid , , and , they preferen­ viscosity on this flow is especially important. tially selected data obtained by the capillary tube viscometer to develop their viscosity correlation. Since As early as 1894, Onnes' and Onnes and de Haas' then a need has existed to verify the experimental noted that the viscosities of homologs under correspond­ technique of Comings, Mayland, and Egly for the ing states could be correlated. The theorem of cor­ determination of viscosities at high p}essure; to extend responding states has been further developed and applied the data to mixtures of ; and to extend to the viscosity of pure, nonpolar gases under pressure the range of their correlation to include higher pressures. by Comings, Mayland, and Egly.' It was demonstrated that the viscosity ratio could be expressed rather closely Using the correlation procedure of Comings, May­ land, and Egly, the prediction of gas viscosities is resolved into the correlation of the effect of pressure, Manuscript received in Petroleum Branch Offices Oct. 18, 1953. temperature, and composition on the viscosity of hydro­ Paper presented at Petroleum Branch Fall Meeting in Dallas. Oct. 18-21, 1953. carbons and their mixtures and the prediction of vis­ 'References given at end of paper. SPE 297-G cosities of mixtures of hydrocarbons and other natural 'Present address: Pure on Co., Lake, Ill. gas components at one pressure.

PETROLEUM TRANSACTIONS,AIME 47 PART I CORRELATION of the EFFECT of PRESSURE, TEMPERATURE, and COMPOSITION on the VISCOSITY of HYDROCARBONS and their MIXTURES

BY NORMAN L. CARR

METHODS OF DETERMINING GAS VISCOSITY data involves the capillary tube or Rankine type viscometer. The coefficient of viscosity, /L, may be defined as the Fig. 1 shows a comparison of the curves for the ratio of the unit shear acting at a point in a viscosity of methane at 86°F and 203 OF determined fluid which is necessary to maintain a unit by means of the capillary tube viscometer and by gradient perpendicular to the plane of shear. Viscosity, means of a rolling ball viscometer. A comparison of the for the fluid, is somewhat analogous to the resistance to shear in . Only in the laminar the viscosity data for propane is shown in Fig. 2. region can the viscosity be defined simply as: Invariably, the values of viscosities obtained by the rolling ball viscometer fall above those obtained by the /L = w/du/dy (2) capillary tube viscometer. The influence of pressure on the discrepancies may be studied in the light of

where: w = per unit the influence of pressure on the dimensionless Reynolds Downloaded from http://onepetro.org/JPT/article-pdf/6/10/47/2238156/spe-297-g.pdf by guest on 28 September 2021 du/dy = velocity gradient perpendicular to number'o defined as: the plane of shear DVp Re No. (3 ) The relationship between pressure and flow of fluids through a smooth-walled, cylindrical, straight where tube may be expressed simply by means of the well D = diameter or effective diameter of the known Poiseuille's law,' provided prevails channel through which flow occurs in the tube and end effects can be made negligible. V = mean velocity of flow ,'o the criterion of dynamc similarity, may be used to define the region of laminar and p = of fluid turbulent flow in smooth-walled cylindrical, straight f1. = viscosity of fluid tubes. Since the flow relations encountered in the oscil­ lating disc viscometer and the rolling ball viscometer Silice the ratio p / /L increases very rapidly with in­ are complicated, they provide means of determining creased pressure, high Reynolds numbers and hence viscosities by comparative methods. The rolling ball is favored by high pressures for a given viscometer was designed primarily to measure the vis­ instrument. Figs. 1 and 2 indicate a rise in the dis­ cosities of liquid where laminar flow can easily be crepancies with increased pressures. The Reynolds num­ obtained. For gas viscosity determinations, it is difficult, ber may be shown to reach a maximum with respect if not impossible to conduct experimental measurements to pressure for some isotherms so that the degree of entirely in the laminar region using a rolling ball vis­ turbulence in the rolling ball viscometer may also reach cometer. If the condition of flow in the tube is laminar, a maximum value with respect to pressure. These points then the viscosity is nearly linear in of roll multi­ of consistency are demonstrated in Figs. 1 and 2. plied by a factor which takes into account The Benedict, Webb, and Rubin '" the density of the rolling ball and the gas." If the has been applied in an analogy to predict the effect of condition of flow is turbulent (this in itself is difficult pressure on the viscosity of methane, , and two to define in a rolling ball viscometer), then the rolling complex mixtures. The results of the computations indi­ ball viscometer must be calibrated for turbulence. Com­ cated close agreement between the computed and ings, Mayland, and Egly list the difficulties and uncer­ experimental values. The results for methane are pre­ tainties attending such calibrations. On the basis of sented in Fig. 5. their analysis, they concluded that: (1) the rolling ball viscometer has been misused in the determination of / the viscosity of gases at high pressures and (2) the / / / rolling ball viscometer is not a suitable instrument for / / / V / the study of the viscosity of gases under pressure. ,// / I / / i On the other hand, experimental determinations of / / I gas viscosities may be made entirely in the laminar /~ Y . I I / " region by means of a capillary tube viscometer. Ran­ / V / i kine"'" developed the theory of a capillary tube vis­ / " / /// ;/ I cometer and con~ructed an instrument for low pressure studies. Comings, Mayland, and Egly adapted the I Rankine viscometer for high pressure studies and deter­ 2~3.1$ ;;?-;/I / mined viscosities for carbon dioxide, methane, and I~ / ethylene up to 2,500 psia. The viscosity of propane /1 86-F. j // I was determined to 615 psia. RANI

48 OCTOBER, 1~,i4 • JOURNAL OF PETROLEUM TECHNOLOGY ·022 ,------,--,.------,---.,----r-----,--,..------,

.020

--l-----~

.016

.014

RANI(INE VISC. - -- SAGE ANO LACEY . I I I I

FIG. 2 - COMPARISON OF PROPANE VISCOSITY DATA , AT 220°F. , , Downloaded from http://onepetro.org/JPT/article-pdf/6/10/47/2238156/spe-297-g.pdf by guest on 28 September 2021 CORRELATION OF GAS VISCOSITY DATA I Table 1 gives the composition of the gas mixtures 1 i on which viscosity determinations were made. In addi­ r i "~ -- tion, viscosity determinations were made on pure me­ thane. These data and the data previously obtained by Comings, Mayland, and Egly and by Michels and Gibson" on nitrogen have been correlated as functions §ill~B!lolI~IIIIIIIIIII~n~I-ID 10.1 2.3.4 .5.6.7.8.91.0 3 4 5 6 789100 200 of reduced pressures and temperatures. Fig. 3 presents PSEUOOREDUCED PRESSURE 1 PR the final correlation of iLl iLl as functions of pseudo­ reduced pressure for various values of pseudoreduced FIG. 3 - VISCOSITY RATIO VS PSEUDOREDUCED temperatures. The viscosity ratios for pseudoreduced PRESSURE. pressures below 1.0 have been obtained from the of Comings, Mayland, and Egly. Fig. 4, a crossplot of Il Fig. 3, may be used to interpolate between the isotherms of Fig. 3. For mixtures of hydrocarbons, the pseudo­ PPc = ) X, Pc, (5) critical concept of Kay" is applied. Thus, in place of i= 1 the critical temperature in Equation (1) the pseudo­ critical temperature, were used. In the above equations: x, = mol fraction of component i in the n TOI = critical temperature of component i, absolute pTe = L x,Tc, (4) scale i= 1 Pc, = critical pressure of component i, absolute :;cale and the pseudocritical pressure, The average deviation of the predicted viscosity ratio from experimental points used in the correlation was TABLE 1 - COMPOSITION OF GAS MIXTURES USED IN VISCOSITY RATIO CORRELATION found to be approximately 1.5 per cent. The maximum deviation occurred at reduced pressures in excess of A. HIGH CONTENT GAS 10 for the high nitrogen content gas mixture. The Mol maximum deviation was 5.4 per cent. Component Per Cent The success with which the viscosity ratios may be 0.6 correlated as unique functions of reduced temperatures 73.4 Gas Gravity = .6B44 25.6 and pressures is intimately related to the success with 0.2 which the volumetric behavior of the pure components 0.2 and mixtures can be correlated as a unique function of reduced temperatures and pressures. Thus, in the region B. HIGH NITROGEN CONTENT near Tn = 1 and P R = 1 where correlation of volumetric He 0.8 properties becomes difficult, the representation of vis­ N, 15.8 cosity ratios may be expected to have the greatest CH, 73.1 C,HG 6.1 Gas Gravity = .6903 uncertainty. On the other hand, in the region of high C,Hs 3.4 reduced temperatures, the accuracy of representing vis­ i - C~HlO 0.2 cosity ratios of hydrocarbon mixtures in general may n - C4HIU 0.6 be expected to be good. It should be emphasized that Figs. 3 and 4 apply to the viscosity of a single phase C. LOW ETHANE CONTENT GAS mixture, more particularly to the gas or less dense phase. N, 0.3 Phase equilibria calculations may be necessary to insure CH, 95.6 Gas Gravity := .5776 C2H, 3.6 the existence of a single phase or to obtain the com­ CoH, 0.5 of the equilibrium gas phase.

PETROLEUM TRANSACTIONS. AIM~~ 49 PART II APPLICATION of CORRELATION to the PREDICTION of VISCOSITIES of NATURAL GAS MIXTURES

BY NOMAN L. CARR, RIKI KOBAYASHI, AND DAVID BURROWS

The usefulness of Figs. 3 and 4 in predicting the The agreement in all cases over the concentration range viscosities of complex hydrocarbon mixtures is de­ is within 1 per cent. Either the molecular weight or pendent on the prediction of the atmospheric viscosities gas gravity may be applied to Fig. 6 to determine of mixtures by relatively simple means. Methods for the atmospheric viscosities. Throughout this paper the the prediction of the atmospheric viscosities of natural gas gravity is defined as: gases which have been developed by past workers'!'~' are discussed. Density of Gas at 60'F, 14.7 psi a (6) G = Density of Air at 60'F, 14.7 psia VISCOSITY AT ONE ATMOSPHERE PRESSURE Nonhydrocarbon components occur quite frequently BY INTERPOLATION OF PURE COMPONENT in natural mixtures of hydrocarbons. The atmospheric Downloaded from http://onepetro.org/JPT/article-pdf/6/10/47/2238156/spe-297-g.pdf by guest on 28 September 2021 VISCOSITIES viscosities of some of the more common nonhydrocarbon components are plotted on Fig. 7. The molecular weight­ Fig. 6 is a plot of viscosity versus molecular weight viscosity relationship of these components cannot be which is essentially the plot proposed by Bicher and expected to correlate with the hydrocarbons, since the' Katz2! to determine the viscosity of hydrocarbon gas kinetic behavior of these differs considerably mixtures at atmospheric pressure. It was developed from from hydrocarbons of the same molecular weight. The the viscosities of natural mixtures containing a moderate viscosity of i-, n-butane, n-, and n-nonane, amount of isomers. Bicher and Katz observed that the which were computed by the method of Hirschfelder;,,25 viscosities of methane-propane mixtures at one at­ are also plotted on Fig. 7. The values for n- were mosphere pressure read from a plot of viscosity versus obtained by extrapolation. The viscosity of i-butane is molecular weight checked the experimental values shown to be higher than that of n-butane, whereas obtained by Trautz and Sorg." Fig. 9 shows this com­ Sage, Yale, and Lacey'" report the viscosity of n-butane parison graphically for the methane-propane system. to be greater than that of i-butane.

6.0

1\ 5.0

4.0

3.5

3.0 , ..<>s~V 1$ 'DO~ ~ 2.5 ~Du. 1\ C~D 0 II I- 10 ,o,o?~S 1\ 1.5 i'- r-- I" ~ r-- r-- r-- \ i'- I", 1\ t--t-- r- I l-

1.q).8 1.0 1.2 1.4 1.6 1.8 2.0 2.2 2.4 2.6 2.8 3.0 3.2 PSEUDOREDUCED TEMPERATURE, TR

FIG. 4 - VISCOSITY RATIO VS PSEUDOREDUCED TEMPERATURE.

50 OCTOBER,19;>4 • JOURNAL OF PETROLEUM TECHNOLOGY .040 nonhydrocarbons. The insert plots were obtained from the viscosity of the pure components and Fig. 6. The presence of each of the nonhydrocarbons is to increase the viscosity of the hydrocarbon mixtures . .O~5 The accuracy with which the viscosities of mixtures W of methane and higher molecular weight hydrocarbons III <5 .OSO at one atmosphere may be predicted from Fig. 6 is not '"f= known with certainty, since experimental data are ~ \oJ unavailable. Methods used to calculate viscosities seem " to indicate that Fig. 6 may be extended to complex >- .025 I- mixtures involving components heavier than propane. iii 0 III ;;" .020 CALCULATION OF VISCOSITY AT LOW PRESSURE Heming and Zipperer" proposed the following mi \.­ .015 L-- .-+- ---~--'4 '. - EXPERIMENTAL '1 ture rule for the viscosity of a mixture of gaseous com­ ---- KINETIC PRESSURE ANALOG ponents: --- FIGS. 3 AND 4 ! I n 10,000

2000 4000 6000 8000 Downloaded from http://onepetro.org/JPT/article-pdf/6/10/47/2238156/spe-297-g.pdf by guest on 28 September 2021 PRESSURE, PSI A. L JJ.jXI YM. FIG. 5 - COMPARISON OF EXPERIMENTAL VISCOSITIES i = 1 t.tm == (7) OF METHANE WITH KINETIC THEORY CALCULATIONS. n xiyM, Fig. 10 presents the viscosity of nitrogen-ethane and L carbon dioxide-propane mixtures at one atmosphere. i = 1 Both lines show a nearly linear relationship of the effect In which: 1-'. viscosity of component i of concentration on viscosity. Insert plots on Fig. 6 = show corrections to the hydrocarbon viscosity values 1-'", = viscosity of mixture which may be applied to account for the presence of x, = mol fraction of component i sulfide, nitrogen, and carbon dioxide. A linear M, = molecular weight of component i effect of concentration has been assumed to apply over the concentration range from 0 to 15 mol per cent of Equation (7) affords a simple and reliable means

GAS GRAVITY ~0IR" 1.0001 05 10 '5 25 3.0 35 .016 -'L L'I .1' l'1. I' .I L.ILIJ .. N2 h''9 CO 2 .015 .0015 ,c; .0015 T 0 0w w 0 ., go.; 0<>: 1-1 "-I .014 , -r " 0.0010 001 o zl "°.I , 00 : .0 -=11> II> , .,... 0- > , .013 ~ >.00 J .0005 , III 0: 0 0 0'" .... en 0 0 .012 0 0 a.. 0 5 10 15 0 5 10 I~ i= MOL % N2 MOL % CO z 2 III 0 .011 - . ~~ , 1

ft .010 ,

.~ - .

. .. I­ j rl <{ -+'. H 5 ~ ~ .008 ~o .0015 , >­ .... I UJn: ,-l- g..; - ~ .e107 -"1.0010 z· !> o 0 0 en .... II>- 0 :> .006 [il>.0005 0: 0:0 0 .... 0 - .005 00 10 15 MOL % H:!S .. UI III II , 11'ITln"'" .004 10 " 20 30 40 50 60 70 80 90 100 MOLECULAR WEIGHT

FIG. 6 - VISCOSITY OF PARAFFIN HYDROCARBON GASES AT ONE ATMOSPHERE.

PETROLEUM TRANSACTIONS,AIME 51 .024 r-r.....,--r-,--,--r--.-r.. ..."-,- ..--r-r-r-T7r-,-r-r-.,..,.-,-T"" ...... ,..,,.-...,,-,-,-' analysis is known, the pseudocriticals used to compute f-++-l++-+-H++-+-H,c-+, ' --+-....-1'-"'. 4-+-+-h-'H--1y~H-+,++-+-1 , VT . 'i-- the pseudoreduced pressure and temperature may be computed using Equations (4) and (5). f-t--,---t-+-+-+-+-+ t +-¥:'f '.-f .-:. I-I I-! -+ --t:; .~2~-H++-+-H++-+y~f-++-+~f-+~~~-H~+-++-++~ Katz" showed that the pseudocritical temperatures and f-++-+~+-+ ~~~~+~~~~~'H-+-f-+~-+-+-+-H~,r+-+-H-I f-+--+-+-~~.~~v~+-+--1j/~/+4~y~~I-+-f-+~-+-~~-+-+-++-l--1 pressures of natural gases could be correlated with gas gravity. The pseudocritical gas gravity relation for various gas streams from a given gas field showed an even higher degree of correlation. The correlation ob­ tained by Bicher and Katz: Fig. 8, may be used to obtain the pseudocritical pressure and temperature and thence the pseudo reduced pressure and temperature of natural gases. Again, insert plots are provided to indicate the direction and magnitude of errors introduced in the pseudo critical predictions by the presence of nonhydro­ carbon constituents. These corrections are hypothetical in and assume that the hydrocarbon distribution remains unaffected by the presence of the nonhydro­ carbons. This assumption is, of course, open to question. Downloaded from http://onepetro.org/JPT/article-pdf/6/10/47/2238156/spe-297-g.pdf by guest on 28 September 2021 PROCEDURE TO DETERMINE GAS VISCOSITIES OF NATURAL GASES FROM GAS GRAVITY The gas viscosities of naturally occurring gases may be obtained in the following manner: 1. From the experimental specific gravity of the gas phase, determine the pseudocritical temperature and pressure from Fig. 8. Corrections to these pseudocritical

, 100 150 200 250 300 350 400 properties for the presence of the nonhydrocarbon TEMPERATURE 'F gases (CO" N" and H,S) should be made if they are present in concentrations greater than 5 mol per cent. FIG. 7 - VISCOSITY OF NATURAL GASES As mentioned previously, if the compositions of the gas AT Low PRESSURES. phase are available, the calculated pseudocriticals are recommended over this procedure. for calculating the viscosity of natural gas mixtures whose analyses are known. This equation was applied 2. Divide the known pressure (psia) by the pseudo­ to synthetic mixtures and compared with the results critical pressure to obtain the pseudo reduced pressure. obtained from Fig. 6. For both binary and complex In like manner, divide the known temperature (OR) by the pseudo critical temperature to obtain the pseudo­ mixtures, the calculated values were found to be in reduced temperature. close accord with Fig. 6. Table 2 shows comparison of some of the mixtures calculated. 3. From the pseudo reduced temperature and pressure, obtain the corresponding viscosity ratio from Figs. 3 and 4. CALCULATIONS BASED ON MOLECULAR THEORY 4. Obtain the viscosity of the gas at one atmosphere from Fig. 6 and convert the viscosity ratio to the Outstanding theoretical work has been published by absolute gas viscosity. Corrections of the atmospheric 24 25 Hirschfelder et al • on the viscosity and other trans­ viscosities for the presence of high contents of non­ port properties of gases. Basic equations and procedures hydrocarbon gases may be made from the insert plots for calculating the temperature dependence of viscosity in Fig. 6. . for 45 pure gases are given." Curtiss and Hirschfelder developed relations to calculate the viscosities of mix­ TABLE 2 - COMPARISON OF EXPERIMENTAL AND CALCULATED tures at low pressures. Their relations have been applied VISCOSITY AT ONE ATMOSPHERE to binary, ternary, and multi component systems with Cal· culated amazing accuracy. This calculation of viscosity, which by is based upon molecular theory, probably gives the Temp. Experi- Mixture Per Cent Fiq. Per Cent OF 22 most accurate means of computing temperature and Gas mental Rule Dev. 6 Dev. composition dependence of viscosity. The computational A' 79 .01040 .01055 + 1.44 .01042 -I- 0.19 methods of Hirschfelder et al have been adapted to 150 .01180 .01185 -I- 0.42 .01158 - 1.86 graphical and nomographic by Bromley and B' 150 .01326 .01333 -I- 1.29 .01299 - 2.04 Wilke." 200 .01420 .01419 - 0.07 .01375 -- 3.17 50% C 1-500/0C:I * * 68 .00906 .00911 -I- .55 .00908 -I- .22 392 .01386 .01382 .29 .01391 -I- .36 PSEUDOCRITICAL PRESSURES AND 50% C1·50% C,*' 68 .00984 .00983 .10 .00981 - .30 TEMPERATURES OF NATURAL GASES 392 .01496 .01490 .40 .01480 - 1.07 50% C,·50% C3*' 68 .00854 .00865 -I- .12 .00855 -I- 1.17 In order to obtain the effect of pressure on viscosity 392 .01326 .01322 .30 .01320 .45 from Fig. 6, it is necessary to know the pseudo reduced ~See Table 1 for composition pressure and temperature of the mixture. If the gas **Mol Per Cent

52 OCTOBER. 1954 • JOURNAL OF PETROLEUM TECHNOLOGY ~50 ~IOO , +100 ie z ie ~ 0 z Z ;: § 0 :oJ .0.6 -1.5 "0.6 -2.0 t; G-0.6 -2.0 - t IIJ- .. 0 0 0 - _. .. .. 3 8 4 (/) 8 I vi (/) vi G- .. IIJ III ..::! g:

>= -r-+- OTHER GASES I § 6 o CONDENSATE WUL FLUID o pPe ::> , IIJen 11. u "­ Q.

IIJ It: ::> OTHER GASES I­« It: IIJ 11. ::;; IIJ Downloaded from http://onepetro.org/JPT/article-pdf/6/10/47/2238156/spe-297-g.pdf by guest on 28 September 2021 I- pTe ...J 4 +50 +50 +50 « I ~ ~ '" ~ z z !::: z 0 0 0:: 0 ;:: G-O.6-1.5 o t <> o t -a6-2.0 o \I! 0 ~o ::!o 0-2.0 ::> -os-•. Of ...... 0 0 IIJ CONDENSATE WELL FLUID <> <> en 8 0: .. .. "- :IE ...:IE ~ u I- ~ l- I- 50 -5q) 0. 0 10 5 '0 15 • MOL.• '!Co N. •• MOL~ co. MOL.. "" "rS ••

i5 0.6 0.7 0.8 0.9 LO U L2 L3 1.4 L5 L6 L7 L8 L9 2 o GAS GRAVITY

FIG. 8 - PREDICTION OF PSEUDOCRITICAL PRE3SURE AND TEMPERATURE FROM GAS GRAVITY.

EXAMPLE CALCULATION from gas specific gravity measurements are plotted in Fig. 11. Viscosity values which were calculated using The following example calculation is presented to compositions obtained by spectrometer fractional illustrate the use of the correlation to obtain gas vis­ analyses from which pseudocritical pressures and tem­ cosities from reservoir fluid data. The gas used in this peratures were obtained by the use of Equations (4) iUustration was collected during one oper­ and (5) are also presented on the same plot. It is seen ation in the stepwise pressure reduction during the that the viscosity values computed from the fractional analysis of a bottom-hole sample. This procedure is analyses (which is considered the most accurate method) followed to simulate differential liberation of gas from and those obtained from gas gravity measurements a reservoir fluid. The reservoir temperature was 195°F, are in close agreement. and the test pressure was 1,800 psig (1 ,815 psi a ). The gravity of the liberated gas was determined by the use of a tared weighing balloon. The gas gravity was EXPERIMENTAL 23 found to be .7018 (air = 1.000). The calculations pro­ o FROM FIG. 6 ceed in the following manner: .016 t-.----+---+---,-----t----I 1. Molecular weight = (.7018 X 28.95) = 20.31 2. From which: LtJ Pseudo critical pressure = 667 (Fig. 8) 6.014 Q. 92 oF. Pseudo critical temperature = 390 (Fig. 8) t­ Z W Pseudoreduced pressure = 1,815/667 = 2.721 o Pseudo reduced temperature = (460 + 195)/390 ;.012 t- = 1.679 iii o 212' F. o 3. From Figs. 3 and 4: (f) 1'/1'1 = 1.28 >.010 ~--~~~--+_-----+_-----+_----=~ 4. From Fig. 6: 68' F. Viscosity at one atmosphere (iLl) = .0 I 223 cp 5. Therefore: .0080~----~20~-----40~----~60~----~8~0--~~OO~ The viscosity at 1,800 psig and 195°F = MOL. % PROPANE 1.28 X .01223 = .01565 cp FIG. 9 - VISCOSITY OF METHANE-PROPANE MIXTURES This and other points computed in the same manner AT ONE ATMOSPHERE: EXPERIMENTAL VS FIG. 6.

PETROLEUM TRANSACTIONS. AIME 53 ·018 .016 l / .016 .015 I I V V .014 .014 /V i >­ f- .013 /, in .012 o /! (,) UJ '">

...>- .011 I 008 0~--2""0:------=4::-0-----;:';60:------:;8::-0 ----:-:!,OO iii 0 I (,) _._------

USING - Downloaded from http://onepetro.org/JPT/article-pdf/6/10/47/2238156/spe-297-g.pdf by guest on 28 September 2021 CARBON DIOXIDE-PROPANE MIXTURE AT I . VISCOSITY VALUES CALCULATED ONE ATMOSPHERE. .009 USING GAS GRAVITY MEASUREMENT I I I I I Additional analyses were performed on experimental data obtained from five separate reservoir fluid samples .0080 200 400 600 8CXI I 000 I200 1400 1600 I eoo 2000 2200 MOOt- to check the two methods of obtaining pseudocritical PRESSURE , PSIA pressures and temperatures. The deviation in gas vis­ cosities did not exceed 3 per cent. FIG. 11 - COMPARISON OF GAS VISCOSITIES OBTAINED USING LIBERATED GAS COMPOSITION AND GAS GRAVITY MEASUREMENTS.

CONCLUSIONS versity of Illinois Experiment Station A correlation of the effect of pressure, temperature, Bulletin No. 354 (1944), 42. and composition on the viscosity of hydrocarbons at 4. Mason, S., and Maass, 0.: "Measurement of the pressures greater than 14.7 psia is presented. The cor­ Viscosity in the Critical Region," Canadian Journal relation employs the theorem of corresponding states of Research (1940), 18B, 128. and may be expected to apply wherever this theorem accurately describes the volumetric behavior of the 5. Naldreth, S. N., and Maass, 0.: "The Viscosity of mixtures in question. The viscosity of complex hydro­ Carbon Dioxide in the Critical Region," Ibid. carbon gas mixtures at one atmosphere may be com­ (1940), 18B, 322. puted from the gas analysis and almost as accurately from the gas gravity. Reliable viscosities of complex 6. Sage, B. H., and Lacey, W. N.: "'Effect of Pressure hydrocarbon gas mixtures at a given pressure and tem­ Upon Viscosity of Methane and Two Natural perature may be rapidly calculated from a knowledge Gases," Trans. AIME (1938), 127, 118. of gas gravity only. 7. Hubbard, R. M., and Brown, G. G.: "Viscosity of n-," Ind. Eng. Chem. (1943), 35, 1276.

ACKNOWLEDGMENTS 8. Bicher, L. B., and Katz, D. L.: "Viscosities of the Methane-Propane System," Ibid. (1943), 35, The authors wish to express their appreciation to 754. R. E. Peck of the Illinois Institute of Technology for 9. Poiseuille, J.: Memoires des Savants Etrangers his helpful suggestions and criticisms and to the man­ (1846), 9, 433. agement of Continental Oil Co. for permission to publish this paper. 10. Reynolds, 0.: "An Experimental Investigation of the Circumstances Which Determine Whether the Motion of Shall Be Direct or Sinous and REFERENCES of the Law of Resistance in Parallel Channels," Phil. Trans. Roy. Soc. (London), (1883),174,935. 1. Onnes, H. K.: "The Coefficient of Viscosity for Fluids in Corresponding States," K. Akad. Wet., 11. Smith, A. S., and Brown, G. G.: "Correlating Fluid versl. van vergad. (1894), 2, 126. Viscosity," Ind. Eng. Chem. (1943), 35, 705. 12. Rankine, A. 0.: "On a Method of Determining 2. Onnes, H. K., and de Haas, M.: "On the Coefficient the Viscosity of Gases," Proc. Roy. Soc. (1910), of Viscosity of in Corresponding States 83A,265. According to Calculations by M. de Haas," Ibid. (1894),3,62. 13. Rankine, A. 0.: "A Simple Viscometer for Gases," .T. Sci. Ins/r. (1924), 1, 105. 3. Comings, E. W., Mayland, B. J., and Egly, R. S.: "The Viscosity of Gases at High Pressures," Uni- 14. Carr, N. L.: 'The Viscosity of Gas Mixtures at

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