VISCOSITY of HYDROCARBON GASES under PRESSURE 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 OIL CO. MEMBER AIME PONCA CITY, OKLA. T.P.3915 ABSTRACT as a function of reduced pressures and temperatures, i.e. : The viscosity of hydrocarbon mixtures, whether in (1) the gas or liquid phase, is a function of pressure, tem­ perature, and phase composition. This paper presents T _ temperature, absolute units where: methods for the prediction of the viscosity of the gas R - critical temperature, absolute units or less dense fluid phase over the practical range of pressure, temperature, and phase compositions encoun­ pressure, absolute units n tered in surface and subsurface petroleum production P = critical pressure, absolute units operations. The correlation necessary to predict the /1. = viscosity of gas at reduced temper­ effect of pressure on viscosities 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 viscometer " 2. Rolling ball viscometer,,7 A knowledge of the viscosity of hydrocarbon fluids 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 momentum 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 methane, region in petroleum reservoirs, the influence of fluid ethylene, carbon dioxide, and propane, 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 hydrocarbons; 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., Crystal Lake, Ill. gas components at one atmosphere 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 stress acting at a point in a viscosity of methane at 86°F and 203 OF determined fluid which is necessary to maintain a unit velocity 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 shear modulus for the fluid, is somewhat analogous to the resistance to shear in solids. 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 = shear stress per unit area 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 drop 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 laminar flow prevails channel through which flow occurs in the tube and end effects can be made negligible. V = mean velocity of flow Reynolds number,'o the criterion of dynamc similarity, may be used to define the region of laminar and p = density 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 turbulence 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 time of roll multi­ of consistency are demonstrated in Figs. 1 and 2. plied by a buoyancy factor which takes into account The Benedict, Webb, and Rubin Equation of State'" 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, nitrogen, 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<INE VISCOMETER - COMINGS, £T AL ~ GENERAL ~f/ CORRELATION US(.O "BOV! 2500PW. Basic viscosity data for methane and three mul­ ROLLING BAU vISCOMETER -- - BlCHER AND KATZ' i 000 ticomponent gas mixtures have recently been ob­ '000 1000 .~ ,~ <000 ° "'" """PRESSURE t PSIA ""'" tained",15,,, up to 10,000 psia and 220°F. The experi­ mental technique used in the accumulation of these FIG. I - COMPARISON OF METHANE VISCOSITY DATA, 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.