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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
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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:(
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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.
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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.
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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
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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.
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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
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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.
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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
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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/