GEOPHYSICS, VOL. 57, NO. 11 (NOVEMBER 1992); P. 1396-1408, 17 FIGS., 1 TABLE.

Seismic properties of pore fluids

Michael Batzle* and Zhijing Wang:j:

ABSTRACT

Pore fluids strongly influence the seismic propertiesof rocks. The densities, bulk moduli, velocities, andviscosities of common pore fluids are usually oversim-plified in geophysics. We use a combination of ther-modynamic relationships, empirical trends, and newand published data to examine the effects of pressure,temperature, and composition on these important seis-mic properties of hydrocarbon gases and oils and ofbrines. Estimates of in-situ conditions and pore fluidcomposition yield more accurate values of these fluidproperties than are typically assumed. Simplified ex-pressions are developed to facilitate the use of realisticfluid properties in rock models.

Pore fluids have properties that vary substantially,but systematically, with composition, pressure, and

INTRODUCTION

Primary among the goals of seismic exploration are theidentification of the pore fluids at depth and the mapping ofhydrocarbon deposits. However, the seismic properties ofthese fluids have not been extensively studied. The fluidswithin sedimentary rocks can vary widely in compositionand physical properties. Seismic interpretation is usuallybased on very simplistic estimates of these fluid propertiesand, in turn, on the effects they impart to the rocks. Porefluids form a dynamic system in which both composition andphysical phases change with pressure and temperature.Under completely normal in-situ conditions, the fluid prop-erties can differ so substantially from the expected valuesthat expensive interpretive errors can be made. In particular,the drastic changes possible in oils indicate that oils can bedifferentiated from brines seismically and may even producereflection bright spots (Hwang and Lellis, 1988; Clark, 1992).

temperature. Gas and oil density and modulus, as wellas oil viscosity, increase with molecular weight andpressure, and decrease with temperature. Gas viscos-ity has a similar behavior, except at higher tempera-tures and lower pressures, where the viscosity willincrease slightly with increasing temperature. Largeamounts of gas can go into solution in lighter oils andsubstantially lower the modulus and viscosity. Brinemodulus, density, and viscosities increase with in-creasing salt content and pressure. Brine is peculiarbecause the modulus reaches a maximum at a temper-ature from 40 to 80C. Far less gas can be absorbed bybrines than by light oils. As a result, gas in solution inoils can drive their modulus so far below that of brinesthat seismic reflection bright spots may develop fromthe interface between oil saturated and brine saturatedrocks.

We will examine properties of the three primary types ofpore fluids: hydrocarbon gases, hydrocarbon liquids (oils)and brines. Hydrocarbon composition depends on source,burial depth, migration, biodegradation, and production his-tory. The schematic diagram in Figure 1 of hydrocarbongeneration with depth shows that we can expect a variety ofoils and gases as we drill at a single location. Hydrocarbonsform a continuum of light to heavy compounds ranging fromalmost ideal gases to solid organic residues. At elevatedpressures, the properties of gases and oils merge and thedistinction between the gas and liquid phases becomesmeaningless. Brines can range from nearly pure water tosaline solutions of nearly 50 percent salt. In addition, oil andbrine properties can be dramatically altered if significantamounts of gas are absorbed. Finally, we must be concernedwith multiphase mixtures since reservoirs usually have sub-stantial brine saturations.

Manuscript received by the Editor August 3, 1990; revised manuscript received March 3, 1992.*ARCO Exploration and Production Technology, 2300 W. Plano Parkway, Plano, TX 75075.tFormerly CORE Laboratories, Calgary, Alberta T2E 2R2, Canada; presently Chevron Oil Field Research Co., 1300Beach Blvd., La Habra,CA 90633. 1992 Society of Exploration Geophysicists. All rights reserved.

1396

Dow

nloa

ded

11/1

4/13

to 1

99.6

.131

.16.

Red

istrib

utio

n su

bject

to SE

G lic

ense

or co

pyrig

ht; se

e Term

s of U

se at

http:/

/librar

y.seg

.org/

Seismic Properties of Pore Fluids 1397

GAS

fluids, etc.) Even though our analyses can be further com-plicated by rock-fluid interactions and by the characteristicsof the rock matrix, the gas, oil, and brine properties pre-sented here should be adequate for many seismic explorationapplications.

The gas phase is the easiest to characterize. The com-pounds are relatively simple and the thermodynamic prop-erties have been examined thoroughly. Hydrocarbon gasesusually consist of light alkanes (methane, ethane, propane,etc.). Additional gases, such as water vapor and heavierhydrocarbons, will occur in the gas depending on the pres-sure, temperature, and history of the deposit. Gas mixturesare characterized by a specific gravity, G, the ratio of the gasdensity to air density at 15.6C and atmospheric pressure.Typical gases have G values from 0.56 for nearly puremethane to greater than 1.8 for gases with heavier compo-nents of higher carbon number. Fortunately, when only arough idea of the gas gravity is known, a good estimate canbe made of the gas properties at a specified pressure andtemperature.

The important seismic characteristics of a fluid (the bulkmodulus or compressibility, density, and sonic velocity) arerelated to primary thermodynamic properties. Hence, forgases, we naturally start with the ideal gas law:

Numerous mathematical models have been developed thatdescribe the effects of pore fluids on rock density andseismic velocity (e.g., Gassmann, 1951; Biot, 1956a, band1962; Kuster and Toksoz, 1974; O'Connell and Budiansky,1974; Mavko and Jizba, 1991). In these models, the fluiddensity and bulk modulus are the explicit fluid parametersused. In addition, fluid viscosity has been shown to have asubstantial effect on rock attenuation and velocity dispersion(e.g., Biot, 1956a, band 1962; Nur and Simmons, 1969;O'Connell and Budiansky, 1977; Tittmann et al., 1984;Jones, 1986; Vo-Thanh, 1990). Therefore, we present den-sity, bulk modulus, and viscosity for each fluid type. Manyrock models have been applied directly in oil exploration,and expressions to calculate fluid properties can allow thesemore realistic fluid characteristics to be incorporated.

The densities, moduli (or velocities), and viscosities oftypical pore fluids can be calculated easily if simple esti-mates of fluid type and composition can be made. Wepresent simplified relationships for these properties validunder most exploration conditions, but must omit most ofthe mathematical details. The most immediate applicationsof these properties will be in bright spot evaluation, ampli-tude versus offset analysis (AYO), log interpretation, andwave propagation models. We will not examine the role offluid properties on seismic interpretation; neither will weexplicitly calculate the effects of fluids on bulk rock proper-ties, since this topic was covered previously (Wang et al.,1990). Nor will we consider other pore fluids that areoccasionally encountered (nitrogen, carbon dioxide, drilling

_ RTaV=-p' (1)

FIG. 1. A schematic of the relation of liquid and gaseoushydrocarbons generated with depth of burial and tempera-ture (modified from Hedberg, 1974; and Sokolov, 1968). Ageothermal gradient of 0.0217C/m is assumed.

6 ..L..------------ -L.150

(3)

(4)

(2)

2 1 RTaVT=-=--/3TP M

/3T = ~1 C~T'where the subscript T indicates isothermal conditions.

If we calculate the isothermal compressional wave veloc-ity V T we find

where P is pressure, V is the molar volume, R is the gasconstant, and Ta is the absolute temperature [Ta = T CC) +273.15]. This equation leads to a density p of

Hence, for an ideal gas, velocity increases with temperatureand is independent of pressure.

To bring this ideal relationship closer to reality, twomitigatingfactors must be considered. First, since an acous-tic wave passes rapidly through a fluid, the process isadiabatic not isothermal. In most solid materials, the differ-ence between the isothermal and adiabatic compressibilitiesis negligible. However, because of the larger coefficient ofthermal expansion in fluids, the temperature changes asso-ciated with the compression and dilatation of an acousticwave have a substantial effect. Adiabatic compressibility isrelated to isothermal compressibility through "y, the ratio of

where M is the molecular weight. The isothermal compress-ibility /3 T is

50

~UJa::::::>f-0:(a:UJe,

~UJf-UJ

100 ~~X0a:n,n,0:(

RELATIVE QUANTITY OFHYDROCARBONS GENERATED

llIi ca\ Mathar!f:'0~q,{j.

....

:

2

O'T"""--~=~--~-------r

5

....Ia::::::>CDu.o

iE0.UJoUJ

~xoa:0.0.0:(

Dow

nloa

ded

11/1

4/13

to 1

99.6

.131

.16.

Red

istrib

utio

n su

bject

to SE

G lic

ense

or co

pyrig

ht; se

e Term

s of U

se at

http:/

/librar

y.seg

.org/

1398 Batzle and Wang

heat capacity at constant pressure to heat capacity at con-stant volume; i.e.,

Under reasonable exploration pressure and temperatureconditions, the isothermal value can differfrom the adiabaticby more than a factor of two (Johnson, 1972).

The heat capacity ratio (difficult to measure directly) canbe written in terms of the more commonly measured con-stant pressure heat capacity (Cp), thermal expansion (ex),isothermal compressibility, and volume (Castellan, 1971, p.219)

(lOc)

(lOa)28.8GPP == ZRT 'a

E = 0.109(3.85 - Tpr)2 exp {-[0.45 + 8(0.56

- lITpr)2]P~//Tpr}'

and

Z = [0.03 + 0.00527(3.5 - Tpr)3]p pr + (0.642Tpr- O.OO7T;, - 0.52) + E (lOb)

but only for pure compounds. The approach using pseu-doreduced values is preferable for mixtures, and compo-nents such as CO2 and N 2 can even be incorporated by usingmolar averaged Tpc and Ppc :

Gas densities derived from the Thomas et aI., (1970)relations are shown in Figure 2. Alternatively, for thepressures and temperatures typically encountered in oilexploration, we can use the approximation

where

(5)

(6)

-yf3s = f3T'

1 Ta Vex 2-= 1---.-y Cp f3 T

These properties, in turn, can be derived from an equation ofstate of the fluid and a reference curve of Cp at some givenpressure.

The second and more obvious correction stems from theinadequacies of the ideal gas law [equation (1)]. A morerealistic description includes the compressibility factor Z;

Following the same procedure as in equations (3) to (5), weget the relationship for adiabatic bulk modulus K s ,

Ppr = P/Ppc = P/(4.892 - 0.4048 G), (9a)Tpr = Ta/Tpc = Ta/(94.72 + 170.75 G), (9b)

where P is in MPa. They then used these pseudoreducedpressures and temperatures in the Benedict-Webb-Rubin(BWR) equation of state to calculate velocities. The BWRequation is a complex algebraic expression that can besolved iteratively for molar volume and thus modulus anddensity . Younglove and Ely (1987) developed more preciseBWR equations and tabulated both densities and velocities,

300200

TEMPERATURE ("C)100

0.0

FIG. 2. Hydrocarbon gas densities as a function of tempera-ture, pressure, and composition. Densities are plotted for alight gas (Pgas/Pair = G = 0.6 at 15SC and 0.1 MPa). andheavy gas (G = 1.2). Values for light and heavy gasesoverlay at 0.1 MPa.

.""""".. G. 0.6--G.l.2

0.6 -r-------------------.....,

0.1

0.5

~ 0.3enzwo~ 0.2o

This approximation is adequate as long as Ppr and Tpr arenot both within about 0.1 of unity. As expected, the gasdensities increase with pressure and decrease with temper-ature. However, Figure 2 also demonstrates how the densi-ties are strongly dependent on the composition of the gasmixture.

The adiabatic gas modulus K s is also strongly dependenton composition. Figure 3 shows the modulus derived fromThomas et aI., (1970). As with the density, the modulusincreases with pressure and decreases with temperature.The impact of composition is particularly dynamic at lowtemperatures. Again, a simpler form can be used to approx-imate Ks under typical exploration conditions, but with thesame restriction as for equation (10).

M 0.4E.gC>

(7)

(8)

_ ZRTaV=--.P

1 -yP

x, = f3s = (1 _ ~ az)zap T

The modulus can be obtained, therefore, if Z can be ade-quately described.

The variable composition of natural gases adds a furthercomplication in any attempt to describe their properties. Forpure compounds, the gas and liquid phases exist in equilib-rium along a specific pressure-temperature curve. As pres-sure and temperature are increased, the properties of the twophases approach each other until they merge at the criticalpoint. For mixtures, this point of phase homogenizationdepends on the composition and is referred to as the pseudo-critical point with pseudocritical temperature Tpc and pres-sure Ppc : The properties of mixtures can be made moresystematic when temperatures and pressures are normalizedor "pseudoreduced" by the pseudocritical values (Katz etaI., 1959). Thomas et aI., (1970) examined numerous naturalgases and found simple relationships between G and thepseudoreduced pressure Ppr and pseudoreduced tempera-ture Tpr.

Dow

nloa

ded

11/1

4/13

to 1

99.6

.131

.16.

Red

istrib

utio

n su

bject

to SE

G lic

ense

or co

pyrig

ht; se

e Term

s of U

se at

http:/

/librar

y.seg

.org/

Seismic Properties of Pore Fluids 1399

almost no pressure dependence for viscosity, but rather anincrease in viscosity with increasing temperature. This be-havior is in contrast to most other fluids. At atmosphericpressure, gas viscosity can be described by

(lla)--,--------- 'Yo,P, := ( Pp r aZ)

1 - Z app r

T

Values for aZlappr are easily obtained from equations (lOb)and (JOe).

The velocities calculated by Thomas et a!., (1970) from theequation of state show several percent error when comparedto direct measurements of velocity in methane (Gammon andDouslin, 1976) or the tabulated values of Younglove and Ely(l987). Small errors in the volume calculations of the BWRequation transform into much larger errors in the calculatedvelocity. In spite of this, the Thomas et al., (1970) relation-ships have the advantage of applicability to a wide range inhydrocarbon gas composition.

To complete our description of gas properties, we need toexamine viscosity. The viscosity of a simple, single compo-nent gas can be calculated using the kinetic theory ofmolecular motion. This procedure would be similar to ourderivation of modulus from the ideal gas law. When thecompositions become complex however, more empiricalmethods must be used. Petroleum engineers have madeextensive studies of gas viscosity because of its importancein fluid transport problems (see, for example, Carr et al.,1954; Katz et al., 1959). We will include some simplerelationships here although more precise calculations can bemade, particularly if there is detailed information on the gascomposition.

The viscosity of an ideal gas is controlled by the momen-tum transfer provided by molecular movement betweenregions of shear motion. Such a kinetic theory predicts

where

(13)

.,.""m G. 0.6

-- G,1.2

2.5.. "''''..""''''''..".."..,,..,,,, ,,''',, ,,'''''.,..."'...,,,..~;;"'..,,"''''..---,,....,....'''..._.,,,,,'',..'''-,,,'-,,.._,,.._.

0.1 MPa

1]1 = 0.0001[Tp r(28 + 48 G - 5G 2) - 6.47 G-2

+ 35 G~l + 1.14 G - 15.55], (12)

0.08

0.02

j'8. 0.06E..

~ 0.04iii8(f)s

- 3.24T" - 38].Figure 4 shows the calculated viscosities for light (G = 0.6)and heavy (G = 1.2)gases under exploration conditions. Therapid increase in viscosity of the heavy gas at low tempera-ture is indicative of approaching the pseudocritical point. Aswith many of the other physical properties, if gas from aspecific location is very well characterized, the viscosityusually can be more accurately calculated by our associatesin petroleum engineering.

OIL

0.0 +--r---'--""T--"'T'"--r---,---f

where 1] 1 is in centipoise. The viscosity of gas at pressure 1]is then related to the low pressure viscosity by

Crude oils can be mixtures of extremely complex organiccompounds. Natural oils range from light liquids of lowcarbon number to very heavy tars. At the heavy extreme arebitumen and kerogen which may be denser than water andact essentially as solids. At the light extreme are conden-sates which have become liquid as a result of the changingpressures and temperatures during production. In addition,light oils under pressure can absorb large quantities ofhydrocarbon gases, which significantly decrease the moduliand density. Under room conditions, oil densities can varyfrom under 0.5 g/crn' to greater than 1 g/cm", with mostproduced oils in the 0.7 to 0.8 g/cm' range. A referencedensity that can be used to characterize an oil Po is measured

[1057 - 8.08Tp r 796 p~~2 - 704

1]11] 1 = 0.001Ppr P + -(T----1-:,)0:-;.7:-(P--+-l-)pr pr pr

(II b)

300

--......."" G ~ 0.6

--G.l.2

200100

5.6 27.1'Yo = 0.85 + + 2(Ppr + 2) (Pp r + 3.5)

- 8.7 exp [-0.65(P pr + 1)].

e (0.1MPa)

600

500

100

te 400'":3::;)co~ 300

"..J::;)CD

~ 200e

TEMPERATURE (0C) 100 200 300

FIG. 3. The bulk modulus of hydrocarbon gas as a function oftemperature, pressure, and composition. As in Figure 2, thevalues for the light and heavy gases overlay at 0.1 MPa.

TEMPERATURE (0C)

FIG. 4. Calculated viscosity of hydrocarbon gases.

Dow

nloa

ded

11/1

4/13

to 1

99.6

.131

.16.

Red

istrib

utio

n su

bject

to SE

G lic

ense

or co

pyrig

ht; se

e Term

s of U

se at

http:/

/librar

y.seg

.org/

1400 Batzle and Wang

where V 0 is the initial velocity at the reference temperatureand b is a constant for each compound of molecular weightM.

at 15.6C and atmospheric pressure. A widely used classifi-cation of crude oils is the American Petroleum Institute oilgravity (API) number and is defined as

(18)

(20b)

Or, in terms of API

V= 15450(77.1 + API)-1I2 - 3.7T+ 4.64P

+ 0.01l5(0.36API I /2 - l)TP,

and temperature has been examined in detail by petroleumengineers (e.g., McCain, 1973). For an oil that remainsconstant in composition, the effects of pressure and temper-ature are largely independent. The pressure dependence iscomparatively small and the published data for density atpressure Pp can be described by the polynomial

pp = Po + (0.00277P - 1.71 x 1O-7p 3)(po - 1.15)2

The effect of temperature is larger, and one of the mostcommon expressions used to calculate the in-situ densitywas developed by Dodson and Standing (1945).

P = pp/[0.972 + 3.81 x lO-\T + 17.78) 1.175] (19)

where V is velocity in mls. Using this relationship with thedensity from equation (19), we get the oil modulus shown inFigure 7.

As an alternative approach, we could derive the velocityand adiabatic modulus using pressure-volume-temperaturerelationships, such as in equations (18) and (19). Heatcapacity ratios may be estimated using generalized charts.This procedure can yield fairly good estimates as shown in

V= 2096( Po )112 _ 3.7T+ 4.64P2.6 - Po

+ 0.0115[4.12(1.08po l _1)112 - I]TP. (20a)

The results of these expressions are shown in Figure 5.Wang (1988) and Wang et aI., (1988) showed that the

ultrasonic velocity of a variety of oils decreases rapidly withdensity (increasing API) as shown in Figure 6. A simplifiedform of the velocity relationship they developed is

(15)

(14)

V(T) = Vo - bAT,

141.5API = -- - 131.5.

PoThis results in numbers of about five for very heavy oils tonear 100 for light condensates. This API number is often theonly description of an oil that is available. The variablecompositions and ability to absorb gases produce widevariations in the seismic properties of oils. However, thesevariations are systematic and by using Po or the API gravitywe can make reasonable estimates of oil properties.

If we had a general equation of state for oils, we couldcalculate the moduli and densities as we did for the gases.Numerous such equations are available in the petroleumengineering literature; but they are almost always stronglydependent on the exact composition of a given oil. Inexploration, we normally have only a rough idea of what theoils may be like. In some reservoirs, adjacent zones willhave quite distinct oil types. We will, therefore, proceed firstalong empirical lines based on the density of the oil.

The acoustic properties of numerous organic fluids havebeen studied as a function of pressure or temperature. (e.g.,Rao and Rao, 1959.) Generally, away from phase bound-aries, the velocities, densities, and moduli are quite linearwith pressure and temperature. In organic fluids typical ofcrude oils, the moduli decrease with increasing temperatureor decreasing pressure. Wang and Nur (1986) did an exten-sive study of several light alkanes, alkenes, and cycloparaf-fins. They found simple relationships among the density,moduli, temperature, and carbon number or molecularweight. The velocity at temperature V(T) varies linearlywith the change in temperature AT from a given referencetemperature.

Similarly, the velocities are related in molecular weight by

V(T, M) = Vo - bAT - am(~ - ~J, (17)where V(T, M) is the velocity of oil of molecular weight Mat temperature T, and V0 is the velocity of a reference oil ofweight Moat temperature To. The variable am is a positivefunction of temperature and so oil velocity increases withincreasing molecular weight. When compounds are mixed,velocity is a simple fractional average of the end compo-nents. This is roughly equivalent to a fractional average ofthe bulk moduli of the end components. Pure simple hydro-carbons, therefore, behave in a simple and predictable way.

We need to extend this analysis to include crude oilswhich are generally much heavier and have more complexcompositions. The general density variation with pressure

1.05'T""------------------.......,

300

po -1.00-- (10 dog. API)po _0.88-- (30 dog. API)po _0.78 ....... (50 dog. API)

200

TEMPERATURE (oc)100

::::iiifiI:::::::::::::::::::::.... so~s I.!: IIP~~ :::::::::::::::::::::::::::0.65

0.95

~enffi 0.75o..J(5

;)5 0.85'"

FIG. 5. Oil densities as a function of temperature, pressure,and composition.

0.55 +---'T"'""--r---.....,--..,.--""T'"--...---!

(16)7.6b = 0.306 --.M

Dow

nloa

ded

11/1

4/13

to 1

99.6

.131

.16.

Red

istrib

utio

n su

bject

to SE

G lic

ense

or co

pyrig

ht; se

e Term

s of U

se at

http:/

/librar

y.seg

.org/

Seismic Properties of PoreFluids 1401

Figure 6. However, the analysis is further complicated bythe drastic changes in oil composition typical under in-situconditions.

Large amounts of gas or light hydrocarbons can go intosolution in crude oils. From the hydrocarbon generationindicated in Figure 1, large dissolved gas contents should betypical at depth. In fact, very light crude oils are oftencondensates from the gas phase. We would expect gassaturated oils (live oils) to have significantly different prop-erties than the gas-free oils (dead oils) commonly measured.As an oil is produced, the original single phase fluid willseparate into a gas and a liquid phase. The original fluidin-situ is usually characterized by RG, the volume ratio ofliberated gas to remaining oil at atmospheric pressure and15.6C. The maximum amount of gas that can be dissolved inan oil is a function of pressure, temperature, and composi-tion of both the gas and oil.

ficients by more than a factor of two. Hwang and LelIis(1988) showed the substantial decrease in moduli and densi-ties of numerous oils with increasing gas content. Theyattributed several seismic bright spots to the reduced rockvelocities resulting from gas-saturated oils. Similarly, Clark(1992) measured the ultrasonic velocity reduction in severaloils with increasing gas content. She demonstrated howthese live oils can produce dramatic responses in bothseismic sections and sonic logs. Because such strong effectsare possible, analyses based on dead oil properties can begrossly incorrect.

Seismic properties of a live oil are estimated by consider-ing it to be a mixture of the original gas-free oil and a lightliquid representing the gas component. Velocities can still becalculated using equation (20) by substituting a pseudoden-sity p' based on the expansion caused by gas intake.

(22)RG = 0.02123G[P exp (

4poon

- 0.00377 T) ],205,(21a)

, Po -1P = - (I + O.OOIR G ) ,Bowhere Bo is a volume factor derived by Standing (1962),

or, in terms of API

RG = 2.03G[P exp (0.02878 API - 0.00377T)] 1.205,

(2Ib)where R G is in Liters/Liter (1 L/L = 5.615 cu ft/BBL) andG is the gas gravity (after Standing, 1962). Equation (21)indicates that much larger amounts of gas can go into thelight (high-API number) oils. In fact, heavy oils may precip-itate heavy compounds if much gas goes into solution. Wehave found this equation to occasionally be a more reliableindicator of in-situ gas-oil ratios than actual productionrecords: if a reservoir is drawn down below its bubble point,gas will come out of solution and be preferentially produced.

The effect of dissolved gas on the acoustic properties ofoils has not been well documented. Sergeev (1948) noted thatdissolved gas reduces both oil and brine velocities. Hecalculated this would change some reservoir reflection coef-

Figure 8 shows the live and dead oil velocities measured byWang et al., (1988) along with calculated values using p'. Thegas induced decreases in velocity are substantial. Below thesaturation pressure (bubble point) of the live oil at about 20MPa, free gas exsolves, and calculated velocities departgreatly from measured values.

True densities of live oils are also calculated using B0, butthe mass of dissolved gas must be included.

(24)where PG is the density at saturation. At temperatures andpressures that differ from those at saturation, PG must beadjusted using equations (18) and (19). Because of this gas

1.1 +.I--+--""""T--'-.,.......-T-....L......,r-----'L.r---i'J

po .1.00-- (10 dog. API)po .0.88-- (30 dog. API)po 0.78 ....... (SO dog. API)

2500

3000

500

'i~ 2000'":3::;)8 1500::;

'"..Jill 1000..J5

0.7

60

0.750.8

40

~oPo ...~0.85

20

....

-.-,

....

......

".-,

'.

1.05 1.0 0.95 0.9

1.8

1.7

U 1.6Ql

~~ 1.5

~~ 1.4W> 1.3

1.2

API GRAVITY100 200 300

FIG. 6. Oil acoustic velocity as a function of referencedensity, Po (or API), using equation (20) (solid line) versusvalues derived from empirical phase relations (dashed line).Data (0) are at room pressure and temperature.

TEMPERATURE (oe)

FIG. 7. The bulk modulus of oil as a function of temperature,pressure, and composition.

Dow

nloa

ded

11/1

4/13

to 1

99.6

.131

.16.

Red

istrib

utio

n su

bject

to SE

G lic

ense

or co

pyrig

ht; se

e Term

s of U

se at

http:/

/librar

y.seg

.org/

1402 Batzle and Wangeffect, oil densities often decrease with increasing pressureor depth as more gas goes into solution.

The viscosity of oils increases by several orders of mag-nitude when Po is increased (lower API) or temperature islowered. As temperatures are lowered, oil approaches itsglass point and begins to act like a solid. The velocityincreases rapidly and the fluid becomes highly attenuating(Figure 9). In the seismic frequency band, this effect can besignificantfor tar, kerogen, or heavy organic-rich rock (e.g.,Monterey formation). For logging, and particularly for lab-oratory ultrasonic frequencies, this effect can be a problemfor produced heavy oils. Even for oils where bulk velocity isstill low, the viscous skin depth can be sufficient within the

confines of a small pore space to increase the rock compres-sional and shear velocities. This particular topic was coveredin detail by Jones (1986).

Unlike gases, oil viscosity always decreases rapidly withincreasing temperature since the tightly packed oil moleculesgain increasing freedom of motion at elevated temperature.Beggs and Robinson (1975) provide a simple relationship forthe viscosity, in centipoise, of gas-free oil as a function oftemperature, 1]T'

LOg lO(1] T + 1) = 0.505y(l7.8 + n-1.163 (25a)with

LoglO(y) = 5.693 - 2.863/po(25b)

FIG. 8. Acoustic velocity of an oil both with gas in solution(live) and without (dead). Oil reference density, Po = 0.916(API = 23), gas-oil ratio, R G , is about 85 L/L. Measure-ments were made at 22.8 and 72.0C.As the "bubble point"at 20 MPa is passed with decreasing pressure, free gas beginsto come out of solution from the gas charged oil.

(26a)1] = 1]T + 0.145PI,

Pressure has a smaller influence, and a simple correlationwas developed by Beal (1946) to obtain the corrected vis-cosity 1] at pressure.

where

LoglO(l) = 18.6[0.1 LOglO(1]T )+ (Log lO(1]T ) + 2)-0.1 - 0.985]' (26b)

The results of this relationship are plotted in Figure 10.Gas in solution also decreases viscosity. In a typical

engineering procedure, viscosity at saturation, or bubblepoint temperature and pressure, is calculated first thenadjustments are made for pressures above saturation. Alter-natively, a simple estimate can be made by using live oildensity. First, Bo is calculated for standard conditions(0.1 MPa, 15.6C). Then the resulting value found for PG isused in equations (25)and (26)in place of Po. Such estimatesare usually adequate for general exploration purposes, butthe more precise engineering procedures should be used ifthe exact oil composition is known.

40

+

I

30

CAlCULATED - - - - - --

{Gas saturated (Live) 0

MEASUREDGas IlBe (Dead) +

I

20

PRESSURE (MPa)10

I

------

---

---

------ +22.80C~_------ +---------- : +

+ --------- +72.0~_------ + _0..-_- - -'\' - - + _.0- _0.--

------- + .o---~--Q.-.s->: + + ..o-II~- ...........

+ + 0 grJCR e~ II ~22.8---- 0 _-2--

72.0~ 9----'""'" "\ .0---

.J)- ---0----O~D~

_........ --

1.0

1.6

~1.4 - +~~~~ 1.2W>

2.4o

300200

po .1.00 --- (10 dog. API)po 0.88--- (30dog. API)po 0.78 ~,.,. .. (SO dog. API)

100o

10

1000

..J 1.0

Seismic Properties of Pore Fluids 1403

(28)

(27a)

300200

TEMPERATURE (0C)

100

4 3

V w = 2: 2: wijTipj,i=O)=O

pressure over a limited temperature range. Additional dataon sodium chloride solutions were provided by Zarembo andFedorov (1975), and Potter and Brown (1977). Using thesedata, a simple polynomial in temperature, pressure, andsalinity can be constructed to calculate the density of sodiumchloride solutions.

Pw = 1 + I X 1O-6(-80T- 3.3T2 + 0.00175T3 + 489P

- 2TP + 0.016T2p - 1.3 X 1O- 5T3P - 0.333p 2

2.0~-------------------...,

where constants W ij are given in Table 1. Millero et aI.,(1977) and Chen et aI., (1978) gave additional factors to beadded to the velocity of water to calculate the effects of

0.5 +---~--T"""--r--.....,r__-__r--.......--~

1.S

and

PB = Pw + S{0.668 + 0.44S + I x 1O-6[300P - 2400PS

+ T(80 + 3T - 3300S - 13P + 47PS)]}, (27b)where Pwand PB are the densities of water and brine ing/cm ', and S is the weight fraction (ppm/loooooO) of sodiumchloride. The calculated brine densities, along with selecteddata from Zarembo and Fedorov (1975) are plotted inFigure 13. This relationship is limited to sodium chloridesolutions and can be in considerable error when othermineral salts, particularly those producing divalent ions, arepresent.

A vast amount of acoustic data is available for brines, butgenerally only under the pressure, temperature, and salinityconditions found in the oceans (e.g., Spiesberger andMetzger, 1991). Wilson (1959) provides a relationship for thevelocity V w of pure water to 100C and about 100 MPa.

FIG. 12. The sonic velocity of pure water. These values werecalculated from the data of Helgeson and Kirkham (1974)."Saturation" is the pressure at which vapor and liquid are inequilibrium.

xx

~X~X~~XX

X

RODESSAo HOSSTON.to COTTON VALLEYX SMACKOVER

I I I

100 200 300SALT CONCENTRATION (x 1000 ppm I

~.,

,,..

".,,.,

,

,

" a~, ~.9-'f '2,." III..

,

a

0 ......--------------------,

3

:rf-a.wo 2

BRINE

FIG. 11. Salt concentration in sand waters versus depth insouthern Arkansas and northern Louisiana (after Price,1977; and Dickey, 1966). These Gulf Coast data are forbasins in which bedded salts are present. The relationship ofincreasing formation water salinity with increasing depthwithin the normally pressured zone generally holds forpetroleum basins. However, in basins with only clasticsediments and no bedded salts, the maximum salinities willbe much less. The California petroleum basins (Ventura, LosAngeles, Sacramento Valley, San Joaquin, etc.) rarely ex-ceed 35000 ppm salt and the bulk are well below 30000 ppm.

The most common pore fluid is brine. Brine compositionscan range from almost pure water to saturated saline solu-tions. Figure 11 shows salt concentrations found in brinesfrom several wells in Arkansas and Louisiana. Gulf ofMexico area brines often have rapid increases in salt con-centration. In other areas, such as California, the concentra-tions are usually lower but can vary drastically amongadjacent fields. Brine salinity for an area is one of the easiestvariables to ascertain because brine resistivities are rou-tinely calculated during most well log analyses. Simplerelationships convert brine resistivity to salinity at a giventemperature (e.g., Schlumberger log interpretation charts,1977). However, local salinity is often perturbed by groundwater flow, shale dewatering, or adjacent salt beds anddomes.

The thermodynamic properties of aqueous solutions havebeen studied in detail. Keenen et aI., (1969) gives a relationfor pure water that can be iteratively solved to give densitiesat pressure and temperature. Helgeson and Kirkham (I974)used these and other data to calculate a wide variety ofproperties for pure water over an extensive temperature andpressure range. From their tabulated values of density,thermal expansivity, isothermal compressibility, and con-stant pressure heat capacity, the heat capacity ratio "y forpure water can be calculated using equation (6). Using thisratio with the tabulated density and compressibility yieldsthe acoustic velocities shown in Figure 12. Water and brinesare unusual in having a velocity inversion with increasingtemperature.

Increasing salinity increases the density of a brine. Roweand Chou (I970) presented a polynomial to calculate specificvolume and compressibility of various salt solutions at

Dow

nloa

ded

11/1

4/13

to 1

99.6

.131

.16.

Red

istrib

utio

n su

bject

to SE

G lic

ense

or co

pyrig

ht; se

e Term

s of U

se at

http:/

/librar

y.seg

.org/

1404 Batzle and Wang

Table 1. Coefficients for water properties computation.

salinity. Their corrections, unfortunately, are limited to 55Cand 1 molal ionic strength (55000ppm). We can extend theirresults by using the data of Wyllie et aI., (1956) to 100C and150000 ppm NaC!. We could find no data in the hightemperature, pressure, and salinity region.

As with the gases, since we have an estimate of the heatcapacity ratio and the density relation of equation (27)provides us with an equation of state, we could calculate thevelocity and modulus at any pressure, temperature, andsalinity. However, equation (27) is so imprecise that thecalculated values are in considerable disagreement with thelow temperature data that exists. A more accurate procedureis to start with the lower temperature and salinity data anduse the pure water velocities calculated from Helgeson andKirkham (1974), and then let the general trend of velocitychange indicated by equation (27) provide estimates athigher temperatures and salinities. We can use a simplifiedform of the velocity function provided by Chen et al., (1978)with the constants modified to fit the additional data.

VB = V w + S(l170 - 9.6T+ 0.055T2 - 8.5 X to-5T 3

+ 2.6P - 0.0029TP - 0.0476p 2) + S 1.5(780 - lOP (31)KG = 1 + 0.0494RG '

where K B is the bulk modulus of the gas-free brine. Equation(32)shows that for a reasonable gas content, say 10L/L, theisothermal modulus will be reduced by a third. We presumethat the adiabatic modulus, and hence the velocity, will besimilarly affected. Substantial decreases in brine velocityupon saturation with a gas were reported by Sergeev (1948).

We conclude this description of brines with a brieflook atviscosity. Brine viscosity decreases rapidly with tempera-ture but is little affected by pressure. Salinity increases theviscosity, but this increase is temperature dependent. Mat-thews and Russel (1967) presented curves for brine viscosityat temperature, pressure, and salinity. Kestin et al., (1981)developed several relationships to describe the viscosity.The results are shown in Figure 15. For temperatures belowabout 250C the viscosity can be approximated by

where R G is the gas-water ratio at room pressure andtemperature. Dodson and Standing (1945) found that thesolution's isothermal modulus KG decreases almost linearlywith gas content.

The calculated moduli using equations (27) and (29) areshown in Figure 14.

Gas can also be dissolved in brine. The amount of gas thatcan go into solution is substantially less than in light oils.Nevertheless, some deep brines contain enough dissolvedgas to be considered an energy resource. Culbertson andMcKetta (1951), Sultanov et aI., (1972), Eichelberger (1955),and others have shown that the amount of gas that will gointo solution increases with pressure and decreases withsalinity. For temperatures below about 250C the maximumamount of methane that can go into solution can be esti-mated using the expression

LoglO(R G ) = Log 10{0.712P!T - 76.7111.5 + 3676po.64}

- 4 -7.786S(T+ 17.78)-0.306, (30)

(29)

W02 = 3.437 X 10- 3W12 = 1.739 X 10-4wn = -2.135 x 10-6W32 = -1.455 X 10-8w42 = 5.230 X 10- 11W03 = -1.197 X 10- 5W13 = -1.628 X 10- 6W23 = 1.237 x 10- 8W33 = 1.327 X 10- 10w43 = -4.614 X 10- 13

Woo = 1402.85WIO = 4.871W20 = -0.04783W30 = 1.487 X 10-4W40 = -2.197 X 10-7WOl = 1.524Wll = -0.0111W21 = 2.747 X 10-4W31 = -6.503 X 10- 7W41 = 7.987 X 10- 10

TEMPERATURE (0C)300200100

_.!E0 MPa ----- PPM=0.-.............. - PPM .150000_.~.- ..

....... ....... .-._._. PPM. 3000000.1 ........... ....J=> 3.000

~:: 2.0III

1.0

0

300200100

1.3

1.2

1.1

"'E~ 1.0.9~Ci.i 0.9Zw0

0.8

0.720

FIG. 13. Brine density as a function of pressure, temperature,and salinity. The solid circles are selected data from Za-rembo and Fedorov (1975). The lines are the regression fit tothese data. "PPM" refers to the sodium chloride concentra-tion in parts per million.

TEMPERATURE (0G)

FIG. 14. Calculated brine modulus as a function of pressure,temperature, and salinity.

Dow

nloa

ded

11/1

4/13

to 1

99.6

.131

.16.

Red

istrib

utio

n su

bject

to SE

G lic

ense

or co

pyrig

ht; se

e Term

s of U

se at

http:/

/librar

y.seg

.org/

Seismic Properties of Pore Fluids 1405

FLUID MIXTURES

2.0-r--------------------,

TI = 0.1 + 0.3335 + (1.65 + 91.95 3) exp {-[0.42(50 8

(34)

(35b)

(35a)

_ _ (VA)dV A = (-VA I3 AaPls = - ap ,KA swhere K A is the adiabatic bulk modulus and 13 A is thecompressibility of component A. The total volume changefor the mixture will be the sum of these changes.

Hence, for a mixture

1406 Batzle and Wang

ADDITIONAL CONSIDERATIONS

3 "T"""------------------,

(36)2a

PG=PB + - ,r

where P G and P B are the pressures within the gas and brine,respectively, a is the surface tension, and r is the bubbleradius. We see from this equation that as the radius de-creases, the pressure inside the bubble could become sub-stantial. As the gas pressure increases, the gas modulus anddensity increase. At small enough radii, high enough PG' thegas will condense into a liquid. Kieffer (1977) examined thiseffectfor air-water mixtures to evaluate its possible influenceon the mechanics of erupting volcanoes and geysers. Hercalculations indicated that the effect will become pro-nounced when the bubble radii go below about 100 ang-stroms. This is the pore size (and therefore bubble size)found in shales and fine siltstones (Hinch, 1980). To theextent that this equation remains valid at such small radii,the depression of rock velocity expected from partial gassaturation, as was indicated in Figure 16, will be precludedfrom shales. This important topic requires further investiga-tion.

Last, in natural systems, the behavior of the fluids can bemuch more complex than we have described. Other com-pounds are often present, either as components of the gases,oils, or brines, or as separate phases. For example, undercertain pressures and temperatures, hydrocarbon gases willreact with water to form hydrates. The hydrocarbons them-selves are usually complex chemical systems with pseudo-critical points, retrograde condensation, phase composi-tional interaction, and other behaviors that can only bedescribed with a far more detailed analysis than we haveprovided. These subtleties can become important, particu-larly in reservoir geophysics where fluid identification andphase boundary location are primary concerns.

Further, as pore size decreases in a rock, the boundaryconditions of our model change. We had assumed that as awave passes, heat could not be conducted and so the processwas adiabatic (even as the frequency is lowered, the wave-length and distance that heat must travel are proportionatelyincreased). In reality, as a wave passes through a mixture ofgas and liquid phases, most of the work is done on the gasphase but most of the heat resides in the liquid. Most of theadiabatic temperature changes are in the gas phase. If theparticle size of the mixture is small enough, significant heatcan be exchanged between the phases. The process is thenisothermal and not adiabatic. This effect would lead tofrequency dependent rock properties. In any case, sinceadiabatic and isothermal properties are usually so close, theresults of this effect should be small.

Another factor neglected in our analysis is surface tension.If a fluid develops a surface tension at an interface, then aphase in a bubble within this fluid will have a slightly higherpressure. For a gas bubble within a brine,

1.00.8

.........,~ .....

50 MPa Gas-free~.~.....(Dead)

0.60.40.2

2

O+-"T"""T"'""T"""'II"""'1~~"""T'_r_r_"'T"'""T""_r__r_T"'""r_I"""'1~__t0.0

This analysis of fluid properties has included brines, oils,and gases under pressures and temperatures typically en-countered in exploration. By using these properties in suchmodels as those by Gassmann (1951) or Biot (l956a, band1962) the effects of different pore fluids on rock propertiescan be calculated. However, many factors can intervene toalter the fluid and rock properties estimated under thesimplistic conditions we have assumed.

Rocks are not the inert and passive skeletons usuallyassumed in composite media theory. Considerable amountsof fluid/rock interactions occur under natural circumstances.In particular, water layers become bound to the surface ofmineral grains. Electrical conductivity measurements andexpelled fluid analyses indicate that such bound water willhave significantlydifferent properties than those of bulk porewater. This interaction effect will increase in rocks as thegrain or pore size get smaller and mineral surface areasincrease. Much of the water in a shale may behave more likea gel than like a free-water phase.

The situation is more complex if we examine mixtures ofbrine and oil. As oil absorbs gas, its properties approachthose of the free gas phase. The modulus of a brine-oilmixture is shown in Figure 17both for constant compositionliquids and for gas-saturated liquids at pressure and temper-ature. Increasing gas content decreases K oil with increasingpressure. If we compare Figures 16and 17, we see that, withincreasing pressure (depth) a gas-saturated (live) oil appearsmuch like a gas. Thus, estimates of in-situ pore fluids can bein substantial error when dissolved gas is not considered.Figure 17 indicates how bright spots can be developed offbrine/oil interfaces as observed by Hwang and Lellis (1988)and Clark (1992).

VOLUME FRACTION OFOIL CONCLUSIONS

FIG. 17. The calculated modulus of a mixture of light oil(Po = 0.825, API = 40) and brine (50000 ppm NaCI). Curvesinclude both "live" mixtures saturated with gas in both oiland brine, and "dead" liquids with no gas in solution. Theapproximate in-situ temperatures were used at each pressure(0.1 MPa-20C; 25 MPa-68C; 50 MPa-1l6C).

The primary seismic properties of pore fluids: density,bulk modulus, velocity, and viscosity, vary substantially butsystematically under the pressure and temperature condi-tions typical of oil exploration. Brines and hydrocarbongases and oils are the most abundant pore fluids and their

Dow

nloa

ded

11/1

4/13

to 1

99.6

.131

.16.

Red

istrib

utio

n su

bject

to SE

G lic

ense

or co

pyrig

ht; se

e Term

s of U

se at

http:/

/librar

y.seg

.org/

Seismic Properties of Pore Fluids 1407

properties are usually oversimplified in geophysics. In par-ticular, light oils can absorb large quantities of gas atelevated pressures significantly reducing their modulus anddensity. This reduction can be sufficient to cause reflectionbright spots of oil-brine contacts. With simple estimates ofcomposition and the in-situ pressure and temperature, morerealistic properties can be calculated.

ACKNOWLEDGMENTS

We wish to express our thanks to the ARCO Oil and GasCompany for encouraging this research. John Castagna,Jamie Robertson, Robert Withers, and Vaughn Ball gavemany helpful comments on the manuscript. Matt Greenbergcontributed useful references and ideas. Bill Dillon, AnthonyGangi and others provided very constructive reviews leadingto substantial improvements in the text. Professor Amos Nurprovided valuable support and guidance to Z. Wang on thesetopics at Stanford University. We also wish to thank AtlanticRichfield Corporation and Core Laboratories Canada forpermission to publish this work.

REFERENCES

Beal, C., 1946, The viscosity of air, water, natural gas, crude oil,and its associated gases at oil field temperatures and pressures:Petroleum Trans., Soc. of Petro Eng. of AIME, 165, 95-118.

Biot, M. A., 1956a, Theory of propagation of elastic waves in afluid-saturated porous solid. I. Low-frequency range: J. Acoust.Soc. Am., 28, 168-178.

--- 1956b, Theory of propagation of elastic waves in a fluid-saturated porous solid. II. Higher frequency range: J. Acoust.Soc. Am., 28, 179-191.

--- 1962, Mechanics of deformation and acoustic propagation inporous media: J. Appl, Phys., 33, 1482-1498.

Beggs, H. D., and Robinson, J. R., 1975, Estimating the viscosity ofcrude oil systems: J. Petro Tech., 27, 1140-1141.

Carr, N. L., Kobayashi, R., and Burrows, D. B., 1954, Viscosity ofhydrocarbon gases under pressure: Petroleum Trans .. Soc. ofPetro Eng. of AIME, 201, 264-272.

Clark, V. A., 1992, The properties of oil under in-situ conditions andits effect on the seismic properties of rocks: Geophysics, 57,894-901.

Castellan, G. W., 1971, Physical chemistry, 2nd Ed.: Addison-Wesley Pub\. Co.

Chen, C. T., Chen, L. S., and Millero, F. J., 1978, Speed of soundin NaCI, MgClz, NaZS04, and MgS04 aqueous solutions asfunctions of concentration, temperature, and pressure: J. Acoust.Soc. Am., 63, 1795-1800.

Culbertson, 0. L., and McKetta, J. J., 1951, The solubility ofmethane in water at pressure to 10,000 PSIA: Petroleum Trans ..AIME, 192, 223-226.

Dickey, P. A., 1966, Patterns of chemical composition in deepsubsurface waters: AAPG Bull., 56, 1530-1533.

Dodson, C. R., and Standing, M. B., 1945, Pressure-volume-temperature and solubility relations for natural-gas-water mix-tures: in Drilling and production practices, 1944. Am. Petr. Inst.

Eichelberger, W., 1955, Solubility of air in brine at high pressures:Ind. Eng. Chern., 47, 2223-2228.

Gammon, B. E., and Douslin, D. R., 1976, The velocity of soundand heat capacity in methane from near-critical to subcriticalconditions and equation-of-state implications: J. Chern. Phys., 64.203-218.

Gassmann, F., 1951, Elastic waves through a packing of spheres:Geophysics, 16, 673-685.

Hedberg, H. D., 1974, Relation of methane generation to undercom-pac ted shales, shale diapirs, and mud volcanoes: AAPG Bull .. 58,661-673.

Helgeson, H. C., and Kirkham, D. H., 1974, Theoretical predictionof the thermodynamic behavior of aqueous electrolytes: Am. J.Sci., 274, 1089-1198.

Hinch, H. H., 1980, The nature of shales and the dynamics of

hydrocarbon expulsion in the Gulf Coast Tertiary section, inRoberts, W. H. III, and Cordell. R. J., Eds, Problems of petro-leum migration, AAPG studies in geology no. 10: Am. Assn. PetroGeo!.,1-18.

Hwang, L-F .. and Lellis, P. J . 1988, Bright spots related to highGOR oil reservoir in Green Canyon: 58th Ann. Internat. Mtg.,Soc. Exp\. Geophys. Expanded Abstracts, 761-763.

Johnson, R. C.. 1972, Tables of critical flow functions and thermo-dynamic properties for methane and computational proceduresfor methane and natural gas: NASA SP-3074, National Aeronau-tics and Space Admin.

Jones, T. D.. 1986, Pore fluids and frequency-dependent wavepropagation in rocks: Geophysics, 51, 1939-1953.

Katz, D. L., Cornell, D., Vary, J. A., Kobayashi, R., Elenbaas,J. R.. Poettrnann, F. H., and Weinaug, C. F., 1959, Handbook ofnatural gas engineering: McGraw-Hill Book Co.

Keenen, J. H .. Keyes, F. G., Hill, P. G., and Moore, J. G., 1969,Steam tables: John Wiley & Sons, Inc.

Kestin, J . Khalifa, H. E., and Correia, R. J., 1981. Tables of thedynamic and kinematic viscosity of aqueous NaCI solutions in thetemperature range 20-150C and the pressure range 0.1-35 MPa:J. Phys. Chem. Ref. Data. 10, 71-74.

Kieffer, S. W .. 1977. Sound speed in liquid-gas mixtures: Water-airand water-steam: J. Geophys. Res., 82. 2895-2904.

Kuster, G. T.. and Toksoz, M. N. 1974, Velocity and attenuation ofseismic waves in two-phase media: Part I. Theoretical formula-tions: Geophysics, 39. 587-606.

McCain, W. D., 1973. Properties of petroleum fluids: PetroleumPub. Co.

Millero, F. J .. Ward. G. K .. and Chetirkin, P. V., 1977, Relativesound velocities of sea salts at 25C: J. Acoust. Soc. Am., 61,1492-1498.

Matthews. C. S., and Russel. D. G., 1967, Pressure buildup and flowtests in wells. Monogram Vol. I, H. L. Doherty Series: Soc. PetroEng. of AIME.

Mavko, G. M., and Jizba, D., 1991, Estimating grain-scale fluideffects on velocity dispersion in rocks: Geophysics, 56, 1940-1949.

Nur, A., and Simmons, G., 1969, The effect of viscosity of a fluidphase on the velocity in low porosity rocks: Earth Plan. Sci. Lett.,7,99-108.

O'Connell, R. J., and Budiansky, B., 1974, Seismic velocities in dryand saturated cracked solids: J. Geophys. Res., 79. 5412-5426.--- 1977, Viscoelastic properties of fluid-saturated crackedsolids: 1. Geophys. Res .. 82, 5719-5735.

Potter, R. W., II, and Brown, D. L., 1977, The volumetericproperties of sodium chloride solutions from 0 to 500 C atpressures up to 2000 bars based on a regression of available datain the literature: U.S. Geol. Surv. Bull 1421-C.

Price, L. C.; 1977, Geochemistry of geopressured geothermal wa-ters from the Texas Gulf coast: in J. Meriwether, Ed., Proc. ThirdGeopressured-geothermal Energy Conf., 1, Univ. S. Louisiana.

Rao, K. S.. and Rao, B. R.. 1959. Study of temperature variation ofultrasonic velocities in some organic liquids by modified fixed-path interferometer method: J. Acoust. Soc. Am., 31, 439-431.

Rowe. A. M.. and Chou. J. C. S" 1970, Pressure-volume-tempera-ture-concentration relation of aqueous NaCI solutions: J. Chem.Eng. Data, IS, 61-66.

Schlurnberger, Inc., 1977. Log interpretation charts: Schlurnberger,Inc.

Sergeev, L. A.. 1948, Ultrasonic velocities in methane saturated oilsand water for estimating sound reflectivity of an oil layer, FourthAll-Union Acoust. Conf. Izd. Nauk USSR. (English trans).

Sokolov, V. A .. 1968. Theoretical basis for the formation andmigration of oil and gas: in Origin of petroleum and gas, Nauka,Moscow, (English trans), 4-24.

Spiesberger.T. L.. and Metzger, K., 1991, New estimates of soundspeed in water: J. Acoust. Soc. Am., 89,1697-1700.

Standing, M. B., 1962, Oil systems correlations, in Frick, T. C.,Ed .. Petroleum production handbook, volume II: McGraw-HiliBook Co., part 19.

Sultanov, R. G.. Skripka, V. G., and Namiot, A. Y., 1972, Solubilityof methane in water at high temperatures and pressures: GazovaiaPrommyshlenmost, 17. G-], (English trans).

Thomas, L. K .. Hankinson. R. W., and Phillips, K. A.. 1970,Determination of acoustic velocities for natural gas: J. PetroTech., 22, 889-892.

Tittrnann, B. R., Bulau, J. R.. and Abdel-Gawad, M., 1984, The roleof viscous fluids in the attenuation and velocity of elastic waves inporous rocks, in Johnston, D. L., and Sen, P. S., Eds., Physicsand chemistry of porous materials: AlP Conf. Proc., 107. [31-143.

Vo-Thanh, D.. 1990. Effects of fluid viscosity on shear-wave atten-uation in saturated sandstones: Geophysics, 55. 712-722.

Dow

nloa

ded

11/1

4/13

to 1

99.6

.131

.16.

Red

istrib

utio

n su

bject

to SE

G lic

ense

or co

pyrig

ht; se

e Term

s of U

se at

http:/

/librar

y.seg

.org/

1408 Satzle and WangWang, Z-W., 1988, Wave velocities in hydrocarbons and hydrocar-

bon saturated rocks-with applications to EOR monitoring: Ph.D.thesis, Stanford Univ.

Wang, Z., Batzle, M. L., and Nur, A., 1990,Effect of different porefluids on seismic velocities in rocks: Can. J. ExpI. Geophys., 26,104-112.

Wang, Z., and Nur, A., 1986, The effect of temperature on theseismic wave velocities in rocks saturated with hydrocarbons:Soc. Petr. Eng. (SPE) paper 15646, Proc. 61st Soc. Petr. Eng.Tech. Conf.

Wang, Z., Nur, A., and Batzle, M. L., 1988,Acoustic velocities inpetroleum oils: Soc. Petr. Eng. (SPE) paper 18163, Proc. 63rdSoc. Petr. Eng. Tech. Conf., Formation EvaI. Res. GeoI. Section,571-585.

Wilson, W. D., 1959, Speed of sound in distilled water as a functionof temperature and pressure: J. Acoust. Soc. Am., 31,1067-1072.

Wyllie, M. R. J., Gregory, A. R., and Gardner, L. W., 1956,Elasticwave velocities in heterogenious and porous media: Geophysics,21,41-70.

Younglove, B. A., and Ely, J. F., 1987,Thermophysical propertiesof fluids. II. Methane, ethane, propane, isobutane, and normalbutane: J. Phys. Chern. Ref. Data, 16, 557-797.

Zarembo, V. I., and Fedorov, M. K., 1975, Density of sodiumchloride solutions in the temperature range 25-350Cat pressuresup to 1000kg/ern": J. AppI. Chern. USSR, 48,1949-1953, (Englishtrans).

Dow

nloa

ded

11/1

4/13

to 1

99.6

.131

.16.

Red

istrib

utio

n su

bject

to SE

G lic

ense

or co

pyrig

ht; se

e Term

s of U

se at

http:/

/librar

y.seg

.org/