reservoir-fluid property correlations

solution GOR results in values that are low by 10% or more. The stock-tank GOR can be estimated with3

log RST=A¡ +A2 log -y0+A3 log "Ygsp+A4 log PsP +As log Tsp, (1)

where A1=0.3818, A2=-5.506, A3=2.902, A4=1.327, and As= -0.7355. Eq. 1 should not be used if the separator temperature is > 140ºF.

Addition of the estimate of stock-tank GOR from Eq. 1 to the separator GOR results in an estímate of solution GOR accurate to within 3%.

Bubblepoint Pressure, p b. The bubblepoint pressure of the oil at reservoir conditions can be estimated with4

Pb = 18.2(Cpb-1.4), (2) where cpb=<Rsl'Yg)º·83 X 1Q(0.00091T-0.012S"(AP¡) (3)

to an accuracy of 15 % . The specific gravity of the separator gas can be used for -y8; however, R5 should include stock-tank vent gas. The equations are valid to 325ºF.

A more accurate estímate of bubblepoint pressure can be obtained if reservoir pressure is measured regularly. Plot reservoir pressure and producing GOR vs. cumulative production. For a volumetric solution-gas-drive reservoir, pressure will decline rapidly initial- ly, then flatten when reservoir pressure drops below the oil bubblepoint pressure (the pressure at which the line changes slope). The producing GOR will begin to increase shortly after bubblepoint pressure is reached.

Solution GOR, R,. Eqs. 2 and 3 can be used to estímate solution GOR for pressures below the bubblepoint. Enter any pressure below bubblepoint in place of P» in Eq. 2 and calculate the corresponding value of solution GOR with Eq. 3. The results should be within 15% of measured values.

If a field-derived bubblepoint pressure has been obtained from pressure measurements as described above, the accuracy of the estimates of solution GOR can be improved. s Start by creating a table of pressures and solution GOR's. Subtract the field-derived bubblepoint pressure from the bubblepoint pressure calculated with Eqs. 2 and 3 to obtain a "delta pressure." Subtract this "delta pressure" from ali pressures in the R5 vs. p table. This procedure works very well for pressures near the bubblepoint. 1t is less accurate at low pressures.

Oil FVF, 80• The oil FVF for use at pressures equal to or below bubblepoint can be estimated with+

Bob =0.9159+ 12(10-S)CBob 1.2, , (4) where CBob =R,(-y gl-y0)0.s + 1.25T (5) The equations can be used for any pressure equal to or below the bubblepoint by inserting the corresponding value of solution GOR estimated as discussed above. The resulting FVF value will be within 5 % of laboratory-measured values if accurate values of solution GOR are used. If solution GOR's are obtained with Eqs. 2 and 3, the accuracy of the resulting FVF values will be sorne unlrnown combination ofthe 15% accuracy ofEqs. 2 and 3 and the 5% accuracy of Eqs. 4 and 5. Do not use at temperatures above 325ºF.

SPE Reservoir Engineering, May 1991 266

Solutioli GOR at Bubblepoint, R,b· The initial producing GOR provides a good estimate of solution GOR for use at pressures equal to and above bubblepoint pressure. This will not be true if free gas from a gas cap or another formation is produced with the oil. Field data often exhíbit a great deal of scatter; however, a trend of constant GOR usually can be discemed before reservoir pressure drops below the bubblepoint.

Often the reported values of producing GOR do not include stock- tank vent gas. In this case, the use of initial producing GOR for 'Now wlth S.A. Holdhch & Asaocs.

Copyright 1991 Soclety of Petroleum Englneers

Propertl•• of Reservolr Uqulds The physical properties discussed next apply only to black oils. En- gineering a volatile-oil reservoir requires a special laboratory study not discussed here.

ldentlflcatlon of R•••rvolr-Fluld Type Surprisingly accurate "rules of thumb" are available 1 to identify reservoir-fluid type from field data. When the initial producing GOR is < 3 ,300 scf/STB, the fluid is a liquid at reservoir conditions. Possible exceptions occur if the stock-tank liquid is colorless or has a gravity higher than about 50º API.

Reservoir liquids are either black oils or volatile oils; the general material-balance equatíons- work only for black oils. The behavior of volatile oils does not fit the assumptions inherent in the derivation of the material-balance equations. Black oils are identified as having initial producing GOR's below 2,000 scf/STB and deeply colored stock-tank oil with gravities below 45º API.

Reservoir gases are classified as retrograde gases (often called condensate gases or gas condensare), wet gases, and dry gases. Retrograde gases have initial producing GOR's > 3,300 scf/STB. The few exceptions of oils that have ratios higher than this are identified as having deeply colored stock-tank liquids with gravities < 40º API. Retrograde behavior occurs for gases with initial producing GOR's of 150,000 scf/STB or higher; however, as a practica! matter, gases with initial producing GOR's ;.::50,000 scf/STB can be treated as wet gases.

The term wet gas is used for a gas that does not release condensate in the reservoir but does form hydrocarbon liquid at the surface. The term dry gas is used for a gas that does not form any hydrocarbon liquid at the surface. In this context, the terms "wet" and "dry" do not refer to water or water vapor, which is always present to some extent.

lntroclucUon V alues of reservoir liquid and gas properties are often needed when laboratory PVT data are not available. This paper shows how to use normally available field data to estimate fluid properties.

While at Texas A&M U., 1 had access to a data base of hundreds of reservoir-fluid studies provided by Core Laboratories Inc. The geographical and geological origins of the reservoir samples had been carefully removed from the data but the samples were lrnown to represent ali areas of the free world in which petroleum exploitation was active during the first 6 years of the 1980's.

Ali reservoir-fluid property correlations available in the petroleum engineering literature were compared with this data base. This paper gives the best correlations.

Summary. This paper presents correlations to determine reservoir-fluid properties from field data. The best available correlations were selected by comparison with a data base of hundreds of reservoir-fluid s~dies of sampl~s representing ~ areas o~ the free world involved in active petroleum exploitation from 1980 to 1986. Also, correlations of formation-water propertíes are given.

Reservoir-Fluid Property Correlatio.ns-State of the Art W.D. McCaln Jr.,• SPE, Cawley, Gillespie & Assocs. lnc.

267

Compressibility Equation of State. The equation of state most often used by petroleum engineers is

pV=znRT. . (20) The Standing-Katz12 correlation of z factors has stood the test

of time. Their graphical correlation may be represented by 13,14

z= 1 +(A 1 +A2/Tpr +A3/Tpr3 +A4/Tpr 4 +As!Tpr5)Ppr

+(A6 +A7/Tpr+Ag/Tpr2)Ppr2 -A9(A7/Tpr+Ag/Tp/)Ppr5

+A1o(l +A 11Ppr2)(ppr2/Tpr3)exp(-A 11Ppr2) (21) and Ppr=0.21[pprl(ZTpr)J, (22) where A 1 =0.3265, A2 = -1.0700, A3 = -0.5339, A4 =0.01569, As= -0.05165, A6 =0.5415, A1 = -0. 7361, Ag =0.1844, A9 = 0.1056, A10=0.6134, and A11 =0.7210. Eq. 21 represents the Standing-Katz correlation to within 1 % for 0.2<Ppr< 15 and 0.1<Tpr<3.0 and to within 3% for 15<Ppr<30.

The pseudoreduced properties are defined as Tpr=T/Tpc (23a)

and Ppr=PIPpc• (23b) where the pseudocritical properties may be calculated with15

Ppc =756.8-131.0-y g -3.6-y g2 (24) and Tpc= 169.2+349.5-y g -14.0-y g2 (25) Eqs. 21 through 25 produce z factors that are well within 2% of experimental for temperatures to 360ºF, pressures to 12,500 psia, and gas specific gravities to 1.6.

If the gas composition is known, gas specific gravity for use in Eqs. 24 and 25 should be calculated with

'Y g=Ma/Mair =Ma/29, (26)

where Ma= EYjMj (27) j

This will improve accuracy over direct calculation of the pseudocritical properties with composítíon.P

When H2S and C02 are present, the pseudocritical properties are adjusted by 16

r;c=Tpc-E (28)

Propertl•• of Reaervolr Gasea Properties of dry gases will be considered first. Toen, the calculations necessary for estimating properties of reservoir wet gases will be discussed. Retrograde gases will not be considered because a special laboratory report is required for these gases.

Toen, the effect of solution GOR corresponding to the pressure of interest is taken into account with 11

P.o =Aµ.oDB, (15)

where A=l0.715(Rs+lOO)-O.S!S (16) and B=5.44(Rs + 150)-0.338 (17)

Eqs. 15 through 17 were derived with data to295ºF and5,250psig. Oil viscosity at pressures above the bubblepoint is estimated by

first calculating viscosity at the bubblepoint with Eqs. 14 through 17 from the solution GOR at the bubblepoint and then adjusting viscosity to higher pressures with 7

P.o =p.01,(plp1,)8, · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · (18) where B=C1pC2 exp(C3 +C4p), (19) and C1 =2.6, C2 =1.187, C3 = -11.513, and C4 =-8.98x 10-s. Eqs. 18 and 19 were developed from a data base with pressures to 9 ,500 psig; the applicable temperatures were not given. 8

lt appears that the relationships of oil viscosity to other properties of the oil are too complicated to be explained by the limited field data normally available. Thus, the values of oil viscosity calculated with Eqs. 14 through 19 should be considered to be "order- of-magnitude'' estimates only.

SPE Reservoir Engineering, May 1991

Oil Viscosity, p.0• Estimation of oil viscosity at pressures below the bubblepoint is a two-step procedure. First, the viscosity of the oil without dissolved gas (dead oil), P.oD• is estimated at reservoir temperature 10:

log log(p.oD+ 1)= 1.8653-0.025086-y API-0.5644 log T. ................................... (14)

Eq. 14 is based ondata with rangesof5 to 58º APiand 60to 175ºF.

c0=-;J(º~ )7-B/º;s )J (10)

At pressures above the bubblepoint, 7

co=(A¡ +A2Rs+A3T+A4-yg+As'YAP1)IA6P, (11) where a¡ =-1,433.0, A2=5.0, A3=17.2, A4=-1,180.0, As= 12.61, and A6 = 105.

Values of oil compressibility calculated with Eq. 11 are general- ly low, by as muchas 50% at high pressures. Accuracy is improved at pressures near the bubblepoint. The data set used to develop this equation included pressures as high as 9,500 psig; however, the author did not give a temperature range. 8

At pressures below the bubblepoint, 9

ln(c0)=-7.633-l.497 ln(p)+l.115 ln(T)+0.533 lnhAPI) +0.184 ln(Rs1,) (12)

The results are accurate to within 10% at pressures above 500 psia. Below 500 psia, the accuracy is within 20%. Ifthe bubblepoint pressure is known, the accuracy of estimates of oil compressibility at pressures below bubblepoint can be improved by using?

ln(c0)= -7.573-1.450 ln(p)-0.383 ln(p1,)+ 1.402 ln(T) +0.256 ln('YAP1)+0.449 ln(Rs1,) (13)

Eqs. 12 and 13 are valid to 330ºF and 5,300 psia.

Oil Density at Reservoir Conditions, PoR· Eq. 7 may be used to calculare> the density of the oil in the reservoir at bubblepoint pressure (and below) from estimated values of B0 and Rs.

PoR =(psTO +0.01351R/y g)IB0, (7) where p oR is the density of the reservoir liquid at the pressure and temperature at which B0 and R, were estimated. A weighted aver- age of separator and stock-tank-gas specific gravities should be used for 'Yg; however, the use of separator gas gravity gives adequate results. The accuracy of this .calculation should be sorne unlcnown combination of the accuracy of the estimates of B0 and Rs; however, in practice, the calculated density is within 5% oflaboratory- measured values.

Density of reservoir oil at pressures above the bubblepoint can be calculated with

Po =p01, exp[c0(p-p1,)] (8)

Coefflcient of lsothermal Compressibility of Oil, c0• The coefficient of isothennal compressibility of oíl, often called oil compressibility, is defined for pressures above the bubblepoint as

Co = -(llV)(iW/op)r, (9a) c0= -(l!B0)(0B0)/op)r, (9b)

Or C0 =(1fp0)(op0/op)r (9c) At pressures below the bubblepoint, oil compressibility is definedf as

At pressures above bubblepoint pressure, the oil FVF is calculated with

B0=Bob exp[c0(p,,-p)], (6)

where FVF at the bubblepoint is estimated as discussed above. Es- timation of the coefficient of isothennal compressibility of oil, e O, is discussed later.


Wet Gases. Toe key to the estimation of the properties of a wet gas is that the composition of the reservoir gas is not the same as the composition of the surface gas. Hydrocarbon liquid condenses from the reservoir gas as it moves from reservoir conditions to surface conditions. Toe surface gas and surface liquid must be recom- bined by calculation to detennine the specíñc gravity of the reservoir gas. Correlations given above can be used once the specific gravity. of the reservoir gas is known.

Specific Gravily o/ Wet Gas. Wet gases are processed through two or more stages of separation at the surface. U nfortunately, the quantity and specific gravity ofthe stock-tank gas are rarely known. The specific gravity of a reservoir wet gas can be estimated when only the properties of the gas from the primary separator are known.20

RspJ'YSPI +4,600-yo+Gpa 'Y gR = . . .. , . , . , . . . . . . . . .. . ( 42)

Rsp¡ +Veq

Toe equivalent volume, Veq• is the volume of stock-tank gas and second separator gas, ifpresent, plus the volume in standard cubic feet that would be occupied by a barrel of stock-tank liquid if it were gas. Toe additional gas produced, Gpa, is related to the mass of gas produced from the stock tank and the second separator, if present.

For three stages of separation,

Veq =Ao +A 1 (p5p¡)A2 (-y5p¡)A3 (-y AP1)A4 (Tsp1)A5 (Tsn)A6' ................................... (43)

whereA0=535.916, A1 =2.62310, A2 =0.793183, A3 =4.66120, A4 = 1.20940, As= -0.849115, and A6 =0.269869, and

Gpa=A 1 (Psp1 -14.65)A2('Ysp1)A3(-y AP1)A4 (Tsp1)As(Tsn)A6, ................................... (44)

where x¡ =2.99222, A2 =0.970497, A3 =6.80491, A4 = l.07916, As= -1.19605, and A6 =0.553669.

For two stages of separation, Veq=Ao+.A¡ (p5p¡)A2('Y5p)A3(-y API)A4(Tsp)As, (45)

whereA0=635.530, A 1 =0.361821,A2=1.05435, A3 =5.08305, A4=1.58124, A5=-0.791301, and

Gpa =A¡(Psp¡ -14.65)A2('Ysp)A3(-y API)A4(Tsp)As, ..... (46) where A 1 = 1.45993, A2 = 1.33940, A3 =7 .09434, A4 = 1.14356, and A5=-0.934460.

Values of specific gravity of reservoir gas calculated with Eq. 42 and the appropriate pair of Eqs. 43 and 44 or Eqs. 45 and 46 will be within 2 % of laboratory-detennined values. This accuracy degenerates to about 6% when the total nonhydrocarbon content of the gas is between 5 and 25 mol% . Toe equations are not rec- ommended when total nonhydrocarbon content of the gas exceeds 25 mol%. Toe results are independent of reservoir temperature and pressure. Reservoir gases with specific gravities between 0.8 and 1.55 were used in the development of the equation.

FVF o/ Wet Gas. Eqs. 31 and 32 apply only to a dry gas. Toe FVF of a wet gas is usually defined as the volume of reservoir gas

Gas Viscosily. Gas viscosity may be estimated with 19

µ.8=A exp(Bp8C)(l0-4), (38)

(9.379+0.01607Ma)Tl.5 where A = , (39)

209.2+ 19.26Ma+T

B=3.448+(986.4/T)+0.01009Ma, (40) and C=2.447-0.2224B (41)

Toe results of Eqs. 38 through 41 agree with the limited published data of gas viscosity to within 2 % at low pressure and to within 4 % at high pressure when the specific gravity of the gas is < 1.0. Toe equations are less accurate for gases of higher specific gravities, usually giving low estimates by up to 20% for retrograde gases with specific gravities over 1.5.

268

1 0.27 [ (éJz/éJpp,)rp, J cp,= Ppr - z2 Tp, 1 +(JJp,lz)(éJz/éJpp,)rp, (36)

An expression for (éJz/éJpp,) can be derived- from Eq. 21:

(éJzléJpp,)rp, =A 1 +A2/Tp, +A31Tp,3 +A4/Tp, 4

+As!Tp,s +2pp,(A6 +A7/Tp,+AglT,,,2) -5pp, 4A9(A7/Tp,+A8/Tp,2)

2A JOPpr 2 2 4 2) (37) + (1 + A 11Ppr -A II Ppr )exp( -A 11Ppr , · · · · Tp,3

where the values of the constants are given with Eq. 21. lsothenns ofthe z factor plotted vs. pseudoreduced pressure have

rather sharp minima at low temperatures. Eq. 21 follows the shape ofthese isothenns rather well. However, the slopes ofthe isothenns calculated with Eq. 37 are not particularly accurate near these míni ma, where the slope changes sharply from negative to positive. Thus, Eqs. 36 and 37 should not be used at Tp, < 1.4 for 0.4<p ,<3.0. Toe accuracy ofthese equations is unknown; however, ~ results should be suitable for engineering calculations.

cp,=cgppc=-1- -~e-~) (34) Ppr Z éJpp, T pr

Eq. 34 can be combinedt'' with the definition of pseudoreduced gas density,

Pp,=0.21[pp,l(zTp,)J, (35) where the z factor of the gas at the critical point is assumed to be 0.27, to arrive at

Dry Gases. Dry gases are easy to deal with because no liquid condenses from the gas as it moves from the reservoir to the surface. Thus, the specific gravity ofthe surface gas can be used in correlations to determine the properties of the gas in the reservoir.

When the gas is associated and produced with a black oil, it may be assumed to be a dry gas with specific gravity equal to the specific gravity of the gas from the primary separator.

Gas FVF. The FVF of a dry gas is defined as B8=VR!Vsc- (31)

If standard conditions are taken to be 14.65 psia and 60ºF, 88 =0.0282(zT/p) =0.00502(zT/p). . (32)

Toe equations are exact, and the calculated values of gas FVF are directly related to the accuracy of the values of z factor used.

Coefficienl o/ lsothermal Compressibilily o/ Gas. Toe coefficient of isothermal compressibility of gas is defined as

c8 = -(llV)(iW/éJp)7 : (33a) or Cg=(llBg)(éJBgléJp)r (33b) Eqs. 33 and 20 can be combined and placed on a pseudoreduced basis>:

, PpcT/,c and Ppc = , (29) Tpc +YH2s0-YH2s)E

where17 E=l20(f~~!d+ f~1d)+(fi2s-f~25) (30)

Eqs. 28 through 30 result in z factors within 5 % of experimental 16 for C02 concentrations to 55 mol% and H2S conditions to 74 mol% at temperatures to 300ºF and pressures to 7 ,000 psia.

z-factor values are not greatly affected by the presence of nitrogen. z-factor increases by about 1 % over the values calculated with Eqs. 21 and 22 for each 5 mol% of nitrogen in the gas.s

Toe z-factor values calculated as described above are about as accurate as can be measured in the laboratory. This is true even for wet gases and retrograde gases with specific gravities as high as 1.6.

269

log[ (Rsw)brine J = -0.0840655S7-0.285854. . (57) (Rsw)pure water

Eq. 57 fits the existing graphical correlation23 to within 3% for salinities up to 30% and temperature from 70 to 250ºF.

Coefflcient oflsothermal Compressibllity ofFonnation Water, cw. At pressures above the bubblepoint, water compressibility is defined as

Cw = (1/V w)(é}V wfé}p)r, (58a)

Solution Gas/Water Ratio ofFonnation Water, Rsw· The solution gas/water ratio of pure water may be calculated with 5

Rsw=A+Bp+cp2, (53) where A=8.15839-6.12265(10-2)T+ 1.91663(10-4)72

-2.1654(10-7)73, (54) B= 1.01021(10-2)-7.44241(10-5)7+3.05553(10-7)72 -2.94883(10-10)73, (55)

and C= -(l0-7)[9.02505-0.1302377+8.53425(10-4)72 -2.34122(10-6)73 +2.37049(10-9)74]. . (56) These equations fit the original graphical correlatíon-é to within 5% at pressures from 1,000 to 10,000 psia and temperatures from 100 to 340ºF. Do not use at pressures below 1,000 psia.

Eq. 57 gives a salinity adjustment factorS that is multiplied by the result of Eq. 53 to give the solution gas/water ratio of formation water.

Density of Fonnation Water, Pw. The density of fonnation water at standard conditions may be calculated with5

Pw=62.368+0.438603S+ l.60074x 10-3S2. . (52) The results are as accurate as laboratory measurement through-

out the full range of solids contents. Density at reservoir conditions is calculated by dividing density at standard conditions by FVF for the pressure and temperature of interest.

Values from this correlation agree with the lirnited published experimental data to within 2 % . The correlation is valid throughout the full range of solids contents, temperatures to 260ºF, and pressures to 5,000 psia. An increase in solids content causes a slight increase in '1 V wT and a slight decrease in '1 V wp that are offsetting to within l % . ·

Cppm•Cwx104


FVF of Formation Water, Bw. The FVF of brine may be calculated withS

Bw=(l +'1V wp)(l +.,ffwr), (49) where '1Vwr= -1.0001(10-2)+ 1.33391(10-4)7+

5.50654(10-7)T2 (50) and '1V""= - l.95301(10-9)p7- l.72834(10-13)p27

-3.58922(10-7)p-2.25341(10-IO)p2 (51)

Bubblepoint Pressure of Formation Water, Pb· The bubblepoint pressure of formation water is the same as the bubblepoint pressure of the coexisting oil. If the water is in contact with gas, its bubblepoint pressure is equal to initial reservoir pressure. Both of the above are the result of thermodynamic equilibrium in the reservoir at discovery.

Solids Content. Ali formation waters contain dissolved solids, primarily NaCl. The quantity and distribution ofthe ions are differ- ent in every formation water. Solids contents have been reported from as little as 200 ppm to saturation, whichjust exceeds 300,000 ppm.

Solids contents are reported in various sets of units. Table 1 gives the relationships between these units.

Propertlea of Reaervolr Water Most of the water correlations presented here require a knowledge of the solids content of the brine of interest. Solids content can be easily measured in the laboratory, or it can be determined-! from measurement of the resistivity of the brine.

required to produce 1 bbl of stock-tank liquid. The units are either standard cubic feet of reservoir gas per stock-tank barrel or bar- reis of reservoir gas at reservoir conditions per stock-tank barrel.

The sum of the primary separator gas and Veq is the standard cubic feet of reservoir gas required to produce 1 bbl of stock-tank liquid:

Vw8=Rsp1 +Veq· (47) This can be converted to reservoir conditions, 5 resulting in Bwg =0.00502(Rsp¡ + Veq)7/p, (48)

where standard conditions of 14.65 psia and 60ºF were used. Eq. 48 will give results within about 6% of laboratory measure-

ment for gases with nonhydrocarbon content < 5 % . The accuracy degenerates badly for higher nonhydrocarbon content.

Term Symbol Definition -- molality Cm g mol solid

1,000 g pure water molarity CM g mol solid

1,000 ml brine normality CN eq wt solid

1,000 ml brine milliequivalents per litar Cmeq/l meq solid

1,000 ml brine weight percent solids Cw g solid

100 g brine parts per million Cppm g solid

106 g brine milligrams per liter Cmg11. g solid

106 ml brine grains per gallon Cgr1ga1 grains solid

gal brine Cgr/gal = 17.1 X Cmg/l • 17.1 XPw X Cppm,

where p w is in g/cm 3 at standard conditions.

'Adapted from Jordan. J.R. and Campball, F.L.: We// Logg/ng /-Rock Proparties, Borehole Envlronmant, Mud, and Temperatura Lor,g/ng, Monograph Serias, SPE, Richardson, TX (1985) 9, 38.

TABLE 1SUMMARY OF NOMENCLATURE ANO UNITS FOR CONCENTRATION OF OISSOLVEO SOLIOS IN FORMATION WATERS *

Equations

Hydrate Formation. Hydrocarbon gas and liquid water will com- bine to form solids called gas hydrates at temperatures above the temperature at which water freezes. Eq. 70 can be used to estímate the temperature at which hydrates will form32:

Th = 1/[2. 77077(10-3)-2. 78224(10-3)(ln 'Y 8)-5.64929(10-4) (In p)- l.29859(10-3)(ln 'Y 8)2 + I.40712(10-3)(ln 'Y 8)(ln p) + I.78574(10-4)(ln p)2 + 1.13028(10-3)(ln 'Y 8)3 +5.97282(1Q-4)(ln -y8)2(Jn p)-2.32792(10-4)(ln -y8)(ln p)2 -2.68408(lQ-5)(ln p)3 +4.66106(10-3)(ln 'Y 8)4 +5.55424(1Q-4)(In -y8)3(ln p)- l.47278(I0-5)(ln -y8)2(ln p)2 + l.39381(10-5)(ln 'Y 8)(ln p)3 + I.48850(10-6)(ln p)4].

................................... (70) The estímate of hydrate-forming temperature could be in error by 5ºF or more. Do not use Eq. 70 at temperatures above 62ºF, pressures above 1,500 psia, or gas specific gravities above O. 9.

Toe presence of H2S and/or C02 in the gas will cause an increase in hydrate-forming temperatures, but data are too limited to quantify this.

Toe presence of dissolved solids in the water will decrease the temperature at which hydrates form. Toe decrease can be calculated with5

ATh=AS+BS2+CS3, (71) where A=2.20919-l0.5746-y8+ 12.1601-y/, (72)

B= -0.106056+0.722692-y8-0.85093-y/, (73) and C=0.00347221-0.0165564-y 8 +0.019764-y g2 (74) Eq. 71 agrees with the existing data30 exactly when the results are rounded to the nearest whole degree Fahrenheit. Eqs. 71 through 74 are based on gas specific gravities < O. 68 and salinities < 20%.

Inhibitor is often added to the water in contact with gas to reduce the hydrate-forming temperature. Toe temperature reduction can be calculated wifu33,34

ATh =2,335w/100M-Mw. . (75) Toe results ofEq. 75 are well within the scatter ofthe experimental data.

Toe presence of liquid hydrocarbons with the gas and liquid water will decrease hydrate-forming temperature. 34 Data are limited, and the temperature decrease has not been quantified.

Nomenclature A,B,C = coefficients

B8 = FVF of dry gas, res ft3/scf or RB/scf B0 = oíl FVF, RB/STB Bw = water FVF, RB/STB

Bwg = FVF of wet gas, RB/STB c8 = coefficient of isothermal compressibility of gas,

psi-1 c0 = coefficient of isothermal compressibility of oíl,

psi "! cp, = pseudoreduced coefficient of isothermal

compressibílity cw = coefficient of isothermal compressibility of

water, psi 1


where S=salinity, wt%. Eq. 69 agrees with the existing graphical correlation-? to within 1 % .

Toe above correlations were developed for dry-gas systems con- taining no nonhydrocarbon components. The presence of heavier hydrocarbons in wet gases or retrograde gases will increase the water content by as muchas 10% at 1,000 psia and 20% at 10,000 psia. Natural gas that contains substantial amounts of C02 and/or H2S will contain more water vapor. 30 Although no data are available, the increase is probably on the order of 5 % . Substantial amounts of nitrogen or helium will lower the moisture content. 31 Limited data are available; the decrease is probably 5 to 10%.

270

W=Alp+B, (66) 18(I06)psc

where A =pv 8 0 (67) '

2 l0.13(459.6+Tsc)Zsc

and log B=-3083.87(1/T)+6.69449 (68) Eqs. 66 through 68 give results that are as accurate as moisture

content can be measured (about 5%) at pressures to 10,000 psia and temperatures to 460ºF.

Dissolved solids in the water reduce the partial pressure of the water, thereby reducing the water content of the gas. Moisture content from Eq. 66 should be multiplied by the salinity-adjustment factor- given in Eq. 69:

wbrine ---=l-4.920(1Q-3)S-l.7672(10-4)S2, ..... (69) wpure water

Moisture Content ofNatural Gas. Toe dewpoint water-vapor content of natural gas in equilibrium with liquid water may be calculated with 29

Viscosity of Fonnation Water, µw. Toe viscosity of formation water at reservoir temperature and atmospheric pressure can be estimated wíth>

µwl =AT-B, (62) where A=109.574-8.40564S+0.313314S2 +8.72213(1Q-3)S3

................................... (63) and B= l .12166-2.63951(10-2)S+6. 79461(10-4)S2

+5.47119(1Q-5)S3 - l.55586(I0-6)S4 (64)

Eq. 62 fits the existing graphical correlatíon-? to within 5% at temperatures between 100 and 400ºF and salinities to 26%.

Water viscosity at 1 atm can be adjusted to reservoir pressure wíth>

µwlµwl =0.9994+4.0295X lQ-5p+3.1062X 1Q-9p2 .... (65) Eq. 65 fits data28 at 86 to 167ºF and pressures below 10,000 psia to within 4%. At pressures between 10,000 and 15,000 psia, the fit is to within 7 % .

cw= -(llBw)(éJBwlop)r, (58b) or Cw=(llpw)(Opwlop)r (58c)

Eq. 59 may be used to estímate values of water compressibility.24

Cw=l/(7.033p+0.5415S-537.0T+403,300), (59) where S=salinity in mg/L.

Eq. 59 is valid only for temperatures between 200 and 270ºF, pressures of 1,000 to 20,000 psia, and salinities up to 200,000 mg/L. Osif24 gave no estímate of accuracy. A graphic correlation-t is available for use at lower temperatures and pressures.

At pressures below the bubblepoint, water compressibility is calculated 26 as

Cw = :w c;w) / :: c:;w t • (60)

Toe first term on the right side of Eq. 60 is related to water compressibility at pressures above the bubblepoint and can be estimated with Eq. 59. Toe derivative in the second term on the right side of Eq. 60 can be estimated with5

(éJRswlop)r=B+2Cp, (61) whereB and Care from Eqs. 55 and 56. Toe result ofEq. 61 should be multiplied by the salinity adjustment factor of Eq. 57. Values of FVF of formation water for use in the second term are estimated as described above, and FVF of gas is estimated with a gas specific gravity of 0.63.

Toe resulting estímate of water compressibility is of unknown accuracy. It should be considered to be • 'order of magnitude'' only.

271

Subscripts acid = C02 + H2S

air = air b = at bubblepoint pressure at reservoir temperature

H2S = hydrogen sulfide j = component j R = reservoir conditions se = standard conditions SP = separator

SPl = primary separator SP2 = second-stage separator ST = stock tank

STO = stock-tank oíl

Acknowledgmenta I am grateful to Core Laboratories Inc. and, in particular, to Phíl Moses for providing the data used to evaluate these correlations. Also, 1 thank Cawley, Gillespie & Assocs. lnc. for permission to publish this paper.

Reterencea l. Moses, P.L.: "Enginccring Applications of Phase Behavior of Crude

Oil and Condensate Systems," JPT (July 1986) 715-23. 2. Schilthuis, R.J.: "Active Oil and Reservoir Energy," Trans., AIME

(1936) 118, 33-52. 3. Rollins, J.B., McCain, W.D. Jr., and Creeger, J.T.: "Estimation of

Solution GOR ofBlack Oils," JPT(Jan. 1990) 92-94; Trans., AIME, 289.

4. Standing, M.B.: Volumetric ami Phase Behavior of Oil Fietd Hydrocar- bon Systems, SPE, Richardson, TX (1977) 124.

5. McCain, W.D. Jr.: The Properties of Petroleum Fluids, second edition, PennWell Books, Tulsa (1989) 120, 175, 214, 318, 322, 513, 525-28.

6. Martin, J.C.: "Simplified Equations of Flow in Gas Orive Reservoirs and the Theoretical Foundation of Multiphase Pressure Buildup Anal- yses," Trans., AIME (1959) 216, 309-11.

7. Vazquez, M. and Beggs, H.D.: "Correlations for Fluid Physical Prop- erty Prediction," JPT(June 1980) 968-70.

8. Vazquez, A.M.E.: "Correlation for Fluid Physical Prediction," MS thesis, U. of Tulsa, Tulsa, OK (1976).

9. McCain, W.D. Jr., Rollins, J.a:, and Villena, A.J.: "The Coefficient oflsothermal Compressibility ofBlack Oils at Pressures Below the Bub- blepoint," SPEFE (Sept. 1988) 659-62; Trans., AIME, 285.

10. Ng, J.T.H. and Egbogah, E.O.: "On Improved Temperature-Viscosity Correlation for Crode Oil Systems," paper CIM 83-34-32 presented at the 1983 Petroleum Soc. of CIM Annual Technical Meeting, Banff, May 10-13.

11. Beggs, H.D. and Robinson, J.R.: "Estimating the Viscosity of Crode Oil Systems," JPT (Sept. 1975) 1140-41.

12. Standing, M.B. and Katz, D.L.: "Density of Natural Gases," Trans., AIME (1942) 146, 140-49.

13. Takas, G.: "Comparisons Made for Computer z-Factor Calculations," Oil &: Gas J. (Dec. 20, 1976) 64-66.

14. Dranchuk, P.M. and Abou-Kassem, J .H.: "Calculations of z-Factors for Natural Gases Using Equations of State," J. Cdn. Pet. Tech. (July- Sept. 1975) 34-36.

15. Sutton, R.P.: "Compressibility Factors for High-Molecular-Weight Reservoir Gases," paper SPE 14265 presented at the 1985 SPE Annu- al Technical Conference and Exhibition, Las Vegas, Sept. 22-25.

16. Wichert, E. and Aziz, K.: "Calculate z's for Sour Gases," Hydrocar- bon Processing (May 1972) 119-22.

17. Wichert, E. and Aziz, K.: "Compressibility Factor of Sour Natural Gases," Cdn. J. Chem. Eng. (April 1971) 267-73.

18. Mattar, L., Brar, G.S., and Aziz, K.: "Compressibility of Natural Gases," J. Cdn. Pet. Tech. (Oct.-Dec. 1975) 14, 77-80.

19. Lee, A.L., Gonzales, M.H., and Eakin, B.E.: "The Viscosity ofNatural Gases," JPT (Aug. 1966) 997-1000; Trans., AIME (1966) 234.

20. Gold, D.K., McCain, W.D .. Jr., and Jennings, J.W.: "An Improved Method for the Determination of the Reservoir-Gas Specific Gravity for Retrograde Gases," JPT(July 1989) 747-52; Trans., AIME, 287.

21. Log Imerpretation Charts, Schlumberger Well Services, Houston ( 1986) 5.

Psro = stock-tank oíl density at standard conditions, lbmfft3

Pw = water density, lbmfft3

SPE Rcservoir Enginccring, May 1991

facid = surn of mole fraction of C02 and H2S in Eq. 30

fH2s = mole fraction of H2S in Eq. 30 Gpa = additional gas produced, Eqs. 42 through 44,

scf/STB times specific gravity m = mass, lbm mol M = molecular weight of solute in Eq. 75, lbm/lbm

mol M0 = apparent molecular weight, lbm/lbm mol

Mm = apparent molecular weight of air, lbm/lbm mol p = pressure, psia

Pb = bubblepoint pressure, psia Ppc = pseudocritical pressure, psia PÍ,C = pseudocritical pressure adjusted for acid-gas

content, psia p pr = pseudoreduced pressure

Pv,HzO = vapor pressure of pure water at temperature of interest, psia

R = universal gas constant, 10.732 (psia-ft3)/(lbm mol- ºR), or producing GOR

R, = solution GOR, scf/STB Rsp¡ = producing GOR from prímary separator,

scf/STB RsT = producing GOR from stock tank, scf/STB Rsw = solubílity of gas in water, scf/STB

S = saliníty, wt% solids or mg/L in Eq. 59 T = temperature, ºF or ºR in Eqs. 12, 13, 20, 23,

32, 39, 40, 48, and 68 Th = hydrate-formation temperature, ºF

llTh = decrease in hydrate-formation temperature, ºF T. e = pseudocritical temperature, ºR

T /c = pseudocritical temperature adjusted for acid-gas content, ºR

Tpr = pseudoreduced temperature V= volume, ft3

Veq = equivalent volurne, scf/STB Vw = volume of water, ft3

V wg = volume of reservoir wet gas, ft3 ll V "P = change in liquid volume during pressure

reduction in Bw correlation ll V wT = change in liquid volume during temperature

reduction in Bw correlation w = weight percent solute in Eq. 75 W = moisture content of gas, lbm/MMscf

Wbrine = moisture content of gas in contact with brine, lbm/MMscf

W pure water = moisture content of gas in contact with pure water, lbm/MMscf

y = composition of gas, mole fraction z = gas compressibility factor, pV!mRT

'Y API = stock-tank oíl gravity, º API 'Y 8 = gas specific gravity 'Y O = stock-tank oíl specific gravity

'YSPI = specific gravity of gas from primary separator E = pseudocritical adjustment factor for acid-gas

content, ºR µ8 = gas viscosity, cp µ0 = oíl viscosity, cp

P.oD = oíl viscosity at 1-atm pressure and reservoir temperature, cp

P.w = water viscosity, cp P.wl = water viscosity at 1-atm pressure and reservoir

temperature, cp p = density, g/cm3 in Eq. 38 or lbm/ft3

Po = oíl density, lbmfft3 PoR = reservoir oíl density at reservoir conditions,

lbmfft3 Ppr = pseudoreduced density


22. Culberson, O.L. and McKetta, J.J. Jr.: "Phase Equilibria in Hydrocarbon-Water Systems m-Solubility of Methane in Water at Pres- sures to 10,000 psia," Trans., AIME (1951) 192, 223-26.

23. McKetta, J.J. and Wehe, A.H.: "Hydrocarbon-Water and Formation Water Correlations," Petroleum Production Handbook, T.C. Frick and, R.W. Taylor (eds.), SPE, Richardson, TX (1962) n, 22-1-22-26.

24. Osif, T .L.: "The Effects of Salt, Gas, Temperature, and Pressure on the Compressibility of Water," SPERE (Feb. 1988) 175-81.

25. Dodson, C.R. and Standing, M.B.: "Pressure, Volume, Temperature and Solubility Relations for Natural Gas-Water Mixtures," Drill. & Prod. Prac., API, Dallas (1944) 173-79.

26. Ramey, H.J. Jr.: "Rapid Methods for Estimating Reservoir Compres- sibilities," JPT (April 1964) 447-54; Trans., AIME, 231.

27. Matthews, C.S. and Russell, D.G.: Pressure Buildup and Flow Tests in Wells, Monograph Series, SPE, Richardson, TX (1967) l.

28. Collins, A.G.: "Properties of Produced Waters," Petroleum Engineer- ing Handbook, H.B. Bradley (ed.), SPE, Richardson, TX (1987) 24-17.

29. Bukacek, R.F.: "Equilibrium Moisture Contact ofNatural Gases," re- search bull. IGT, Chicago (1955) 8, 2,11.

30. Katz, D.L. et al.: Handbook of Natural Gas Engineering, McGraw- Hill Book Co. Inc., New York City (1959) 198-200.

31. Deaton, W .M. and Frost, E.M. Jr.: Gas Hydrates and Their Relation to the Operation ofNatural Gas Pipelines, Monograph Series, USBM, Washington, DC (1946) 8.

32. Kobayashi, R., Kyoo, Y.S., and Sloan, E.D.: "Phase Behavior of Water/Hydrocarbon Systems," Petroleum Engineering Handbook, H.B. Bradley (ed.), SPE, Richardson, TX (1987) 25-1-25-28.

33. Hammerschmidt, E.G.: "Formation of Gas Hydrates in Natural Gas Transmission Lines," lnd. & Eng. Chem. (1934) 26, 851-55.

34. Scauzillo, F.R.: "Inhibiting Hydrate Formations in Hydrocarbon Gases," Chem. Eng. Prog. (Aug. 1956) 52, 324-28.

272

Original SPE manuscript received for review June 15, 1988. Paper (SPE 18571) accepted for publlcation Feb. 22, 1989. Revised manuscript received March 17, 1989.

SPERE • Converslon factor is exact.

E+OO E-01

g/cm ' Pa m3 ºC kPa std m3/m3

SI Metrlc Converslon Factora ºAPI 141.5/(131.5+ºAPI)

aun x 1.013 250* E+05 bbl X 1.589 873 E-01 ºF (ºF-32)/1.8 psi X 6.894 757

scf/bbl x 1.801 175

Wllllam D. McCaln Jr. Is an executlve consultant wlth S.A. Holdltch & Assocs. In College Statlon, TIC. He prevlously was a petroleum englneer wlth Cawley, Glllesple & Assocs. lnc. In Fort Worth and taught petroleum englneerlng at Texas A&M U. and Mlsslsslppl State U. He holds a es degree from Mlsslsslppl State U. and MS and PhD degrees from Georgia lnst. of Technology. McCaln was a member of the 1986-89 Career Guldance Commlttee and the 1972-75

Textbook Commlttee. He was 1972 Mlsslsslppl Sectlon chalr· man and a member of the Educatlon and Accredltatlon eom mlttee from 1967 to 1971, chalrlng lt In 1970.

Author

SPE Reservoir Engineering, November 1991

SPERE (SPE 23594)

Referencea l. Moses, P.L.: "Engineering Applications of Phase Behavior of Crude

Oil and Condensate Systems," JPT (July 1986) 715-23. 2. McCain, W.D. Jr.: "Reservoir-Fluid Property Correlations-State of

the Art," SPERE (May 1991) 266-72. 3. McCain, W .D. Jr.: Tñe Properties of Petroleum Fluids, second edition,

PennWell Books, Tulsa (1989) 149-53.

510

Hayworth may have found an example reservoir fluid that does not fit the "rules of thumb" for determining reservoir fluid type.1,2 However, he does not give the color of the stock-tank liquid. Stock- tank oil color is the third rule of thumb and is useful in confirming fluid type.

Composition was not considered because the paper- was written to show how to usefield data to estimate reservoir-fluid properties (see the first sentence of the Summary or the second sentence of the Introduction). Extensive information in the use of field and laboratory data to distinguish between black and volatile oils is available elsewhere. 3

Author's Reply to Discussion of Reservolr-Fluid Property Correlations-State of the Art Wllllam D. McCaln Jr., SPE, S.A. Holditch & Assocs. lnc.

SPERE (SPE 23583)

= g/cm3 ºC std m3/m3

Referenc•• l. Craft, B.C. andHawkins, M.F.:AppliedPetroleumReservoirEngineer-

ing, Prentice-Hall Inc., Englewood Cliffs, NJ (1959) 186. 2. Moses, P.L.: "Engineering Applications of Pbase Behavior of Crude

Oil and Condensate Systems," JPT (July 1986) 715-23.

SI Metrlc Converalon F•ctora º API 141.5/(131.5+ º API)

ºF (ºF ~32)/1.8 scf/bbl X 1.801 175 E-01

McCain's definition of a black oil does not consider reservoir temperature or composition. For the example cited, reservoir temperature and a high concentration of intermediate components have undoubtedly had a significant impact on reservoir-tluid behavior.

Earlier authors t ,2 considered reservoir temperature and compo- sitions as important parameters in classifying reservoir fluid types.

In ''Reservoir-Fluid Property Correlations-State of the Art" (May 1991 SPERE, Pages 266-72), McCain states that "Black oils are identified as having initial producing GOR's below 2,000 scf/STB and deeply colored stock-tank oil with gravities below 45 º API." Unfortunately, defining reservoir fluid type by these parameters alone can result in misinterpretation of the reservoir-tluid behavior.

For example, Field X, a Cretaceous "D" sand reservoir in the Denver basin, has an initial stock-tank gravity of 40º API, an initial producing GOR of 600 scf/STB, and a reservoir temperature of 230ºF. According to the author's classification of black oils, this field would fall well within the black-oil designation. Reser- voir performance, however, has shown that the fluid does not be- have as a black oil.

During primary depletion, the producing GOR increased to more than 13,000 scf/STB. Stock-tank oil gravity coincidentally increased from 40 to 60º API.

Evidently, this reservoir does not fit black-oil assumptions. Black- oil material-balance calculations have proved unrealistic.

W.R. Hayworth, SPE, Divérsified Operating Corp.

Discussion of Reservoir-Fluid Property Correlations-State of the Art

reservoir-fluid property correlations

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