borehole lecture03 rock physics

8/2/2019 Borehole Lecture03 Rock Physics

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EPS-550 / Winter-2008 Professor Michael Riedel ([email protected]) Slide S3-1

Borehole Geophysics

A little bit on rock physics

The aim of logging (including acoustics) is to determine subsurface properties of the

rocks/sediments. However, acoustic logs themselves are a poor indicator of lithologyitself, if not combined with other logs (density, porosity, resistivity).

The reason for this is that most lithologies have a large natural range in acoustic velocitieswith significant areas of overlap between the dominant types encountered in reservoir rocks

(sandstone, carbonate, shale).However, the by far largest effects on acoustic velocity are from the changes in the pore-fluid filling, i.e. brine, gas, gas hydrates, or oil.

The theory that combines elastic properties of the rock matrix and pore fluid filling is known

as rock-physics modeling. Since the early 1950ies, with the onset of the increasinghydrocarbon industry, several theories have been brought forward to predict acousticreservoir velocities and how they change under different in situ conditions. Going throughthese rock-physics models is beyond the scope of this work, and only a few are explainedand introduced.


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The probably most famous model in reservoir rock physics is the Gassmann (1951) equation,which is still used today (or with various types of modifications). Because of the manyassumptions involved, the Gassmann theory is effectively a 0-Hz, fully elastic, isotropic theory. It

does not predict attenuation or involves any interaction of the pore-fluid with the rock matrix.

To overcome this problem in the Gassmann theory, another set of equations was introduced by

Biot (1952, 1961). This theory allows for attenuation and wave dispersion, but cannot fullypredict the magnitude of field observations.

A further development was achieved by the introduction of the squirt-flow (local flow) theory byMavko and Nur (1975) to accommodate pore-scale flow and compressibility heterogeneities.This theory is able to handle partial pore-fluid filling, especially in the presence of some freegas. The Biot and squirt-flow theory was unified by Dvorkin et al. (1993), known as the BISQmodel.

Another type of approach is achieved using effective medium modeling (Dvorkin and Nur,1993). This theory treats rocks as a pack of spheres (i.e. grains) and includes various types ofinteractions between pore-fluid filling and grains. The effective bulk and shear modulus are thenderived as a mixture of the various mineral constituents weighted by their volume fractions. Theeffective medium theory is especially attractive to rocks that may include cementation effects

(e.g. in case of gas hydrates or in carbonates).

None of these theories deals with anisotropy, fractures, and the effects of shale (clay)!


Borehole Geophysics

A short historic overview


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Borehole Geophysics

The Gassmann equation

2

2

*

1

1

m

d

mf

m

d

d

K

K

KK

KK

KK

+

+=

dGG =*

Gassmann (1951) derived an equation to calculate the effective bulk modulus (K*) of a fluid-saturated porous medium using the known bulk moduli of the solid rock matrix (Km), the dry rock-

frame (Kd), and the pore fluid (Kf).

(EQ 3-1)

The effective shear modulus is not altered by the presence of any pore-fluid, so that it is equal to thedry-frame modulus:

(EQ 3-2)

The density of a fluid saturated rock is simply (as we saw in the 1st lecture)

(EQ 3-3)

The dry-frame and rock matrix moduli and pore-fluid modulus are simply derived from laboratorymeasurements or empirical relationships.

fd +=*


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Borehole Geophysics

The Gassmann equation

The basic assumptions in the Gassmann equation are as follows:

(1) The porous medium is macroscopically homogenous and isotropic(a)

;(2) All pores are interconnected or communicating (c);

(3) The pores are filled with a frictionless fluid; Thats a problem for heavy oil!

(4) The rock-fluid system is closed (undrained);

(5) The relative motion between matrix and fluid is negligible (b);

(6) The pore fluid does not interact with the matrix in a way to either soften or harden theframe (c).

(a) To overcome the isotropic limitation, Backus (1962) derived an averaging method for long-wavelength inhorizontally finely layered elastic media, known as the Backus-average. The Backus-average was later extendedto include attenuation effects, saturated, and partially saturated media. The same averaging technique was alsoused to predict anisotropic rock properties of fractured media.

(b) The relative motion between fluid and rock is the basis of the Squirt-flow theory.(c) The effect of a cement on the frame-modulus can be incorporated in the effective medium theory (see gas hydrate

examples later). A cement can also effectively seal a reservoir.


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In the following we will learn more about various factors than canchange acoustic velocity, and how we can exploit thesedependencies in interpretation of acoustic log data.

Lithology: mud-rock line

Porosity

Pressure

Saturation

Temperature (oil)

Attenuation (Qp, Qs)

At the end we will have a more closer look into gas hydrates.


Borehole Geophysics


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Effect of lithology the mud-rock line


Borehole Geophysics

Source: Well logging for physical properties, Hearst et al.,2000, page 268

Acoustic velocity is NOT a very

strong function of lithology, so thatvelocity logs alone are difficult touse in differentiating lithology.

However, an important advance inthe use of acoustic logs came withthe use of cross-plots, mainlyplots of Vp versus Vs. It is foundthat the Vp/Vs ratio issystematically increasing withslowness, defining the so-calledmud-rock line (Castagna et al.,

1985). Departures from the lineartrend are attributed to effects ofsaturation, i.e. a change in thepore-fluid filling (e.g. from brine togas/oil).


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Effect of porosity


Borehole Geophysics

The last image of P- versus S-wave velocity, we already saw that the mud-rock line has a porosity-effect built-in. E.g. rocks such as Basalt or Granite have a much higher velocity (P and S) than shale

or sandstone. From simple observations of hand specimens one can see that the igneous rocks Basaltand Granite are much more dense and less porous than the sedimentary rocks Shale and sandstone.

So, in simple terms, a reduction in porosity increases P- and S-wave velocity.

A famous equation that relates porosity (), matrix (Vma) and pore-fluid (Vf) velocity to the effectivebulk-rock velocity (Vb) was suggested by Wyllie et al (1956, 1958):

(EQ 3-4)

This equation is often only called the time-average equation.

Equation (3-4) is the most commonly used equation in acoustic logging to e.g. obtain porosity and thenvarious empirical corrections are applied to the result to account for e.g. shale fractions. Gassmannsequation is also applied to the result to carry out a fluid-substitution to define the type and amount ofpore-fluid saturation.

mafb VVV

+=11


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Effect of porosity


Borehole Geophysics

However, the use of the Wyllie equation is technically restricted to porosities below 35% and fully-saturated sediments. Often these conditions are ignored or modifications are applied to make the theory

work again for different conditions (e.g. higher porosities).

A different approach was carried out by Geertsma (1961) who showed that for small (


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Effect of porosity


Borehole Geophysics

All the above examples are commonly used in commercial reservoir rocks, which typically do nothave porosities above 35%. But what to do if we have unconsolidated, high porosity sediments?

One approach is to introduce a weighted time-average equation, such as Lee et al. (1996)combining various theories or simply just go with your own empirical function.

Source: Yuan et al., 1996

Those empirical functions (e.g. like the one on the

right) are derived by cross-plotting log and/or coredata and thus serve a local range only.

They should not be extrapolated too far awayfrom the geological/regional source environmentfrom which the data originally were acquired.

Although, if desperate some researchers arestill forced to do so but all you need to do isfind an excuse for doing such a thing and statethe limitations and expected uncertainties


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Effect of pressure compaction and porosity reduction


Borehole Geophysics

Source: Wyllie et al., 1958

Source: Schmitt, 2004

Simplified diagram illustrating effects ofconfining pressure (Pc) on a rocksample for scenarios involving pore-pressure Pp=0 (red curve) and various

differential pressures (P = Pc - Pp).

The left image showssome data from Wyllieet al. (1958) where adry Berea sandstone issubject to various types

of confining pressure. Inall scenarios tested,velocity goes upsignificantly until asaturation level isachieved, beyond whichvelocity does notincrease with pressureany longer. Themaximum compactionfor the matrix isachieved at that level(i.e. minimum porosity)

An increase in pressure increases velocity. However, localpore-pressures can alter the effect significantly. The drivingfactor is then the differential pressure between confiningpressure (e.g. the weight of the overburden) and pore-pressure.


11/28EPS-550 / Winter-2008 Professor Michael Riedel ([email protected]) Slide S3-11

Borehole Geophysics

Effect of saturation water/oil/gas

Source: Murphy et al., 1993

As outlined before, acoustic velocityvaries little with lithology, but changes inpore-fluid filling have pronounced effectsand are exploited in the hydrocarbonindustry.

A change from water (brine) as pore-fluidto oil and/or gas drastically reduced theV

p

/Vs

velocity ratio as shown in the figureon the right.

The change is especially pronounced athigher porosities above 30%.

The replacement of brine in a reservoir

rock (e.g. sandstone) to gas/oil results ina characteristic response in logging andseismic imaging (e.g. bright spot). Thoseresponses are summarized in the termDirect Hydrocarbon Indicator (or DHI).


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The problem with oil is multifold: one has to differentiate the effects of pressure (confining andpore), density and type of the oil in place as well as the local temperature at the reservoir.

Higher temperatures reduce the velocity of oil, it alsoprofoundly changes its viscosity by many orders of magnitude!


Borehole Geophysics

Effect of saturation water/oil

Source: Schmitt 2004


The density of oil can vary from values just above water/brine density forbitumen (1.05 g/cm3), and can be as low as 0.8 g/cm3 for light oil. The diagramto the right is a simplification of the trend for various types of oil as function ofspecific gravity (API units) and mass density.

The higher the API gravity, the lower the density and velocity!


13/28EPS-550 / Winter-2008 Professor Michael Riedel ([email protected]) Slide S3-13

Borehole Geophysics

Source: Clark, 1992

The image below shows an example of a DHI (bright spot) on a seismic section due to the presenceof oil in a sand formation of Pleistocene age in the Gulf of Mexico at a depth of around 4000 ft (1200m). The small circle on the top axis indicates the location of the test well.


DHI


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Borehole Geophysics


Source: Clark, 1992

The image to the left shows the well-logs

acquired through the anomalous zone seenon the seismic data as DHI. The right-most

log is acoustic velocity (in units of s/ft, adeflection of the log to the left is equivalent toa reduction in velocity).

For reference, the four oil-bearing zones andone water-filled zone are colored in as blackareas on the resistivity log (middle panel).

Note that the velocity reduction is coincidentto increases in electrical resistivity especiallyfor the lower-most two oil-bearing zones.

The correlation is not perfect all the time, butoverall the expected reduction in velocity isevident in the oil-rich zones.

100180

?

?


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The effect of free gas on acoustic velocity is extremely pronounced. Gas reduces velocity drastically,even if only 1% of the pore-space is filled with free gas. Practically, most of the effect happens for therange of 0-10% of free gas; for higher saturations, no further change is seen, except for a slight increase

due to the reduction in effective density. The S-wave velocity is unchanged by free gas (gas cannottransmit S-motion!) and the slight increase seen is again the effect of density reduction.


Borehole Geophysics

Effect of saturation water/gas



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Borehole Geophysics

Effect of saturation water/gas

Source: OBrien, 2004

Seismic line over King KongField, which ties the Conoco

Green Canyon Block 473 No. 1well. Yellow/red troughs indicatea decrease in acousticimpedance; blue peaks indicatean increase.

The vertical axis is two-waytravel time (TWT) inmilliseconds. The DHI at 4 sTWT corresponds to a depth of~12,000 ft (~3600 m).

The formation of interest is aTertiary sand in the deep-waterof the Gulf of Mexico.


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Borehole Geophysics

Effect of saturation water/gasExample of well-logsacquired through theanomalous zone seen onthe seismic section. Note

the pronounced reductionin P-wave velocity anddensity due to thepresence of free gas.Accordingly electricalresistivity in increased.Compare the response inthe gas-rich zone (pay-sand) with the wet-sandat the top. The lithologyindicator log (gamma ray)

is reduced in both casesindicating the presence ofreservoir sand, but Vpand density are notreduced in the brine-saturated sand.

Source: OBrien, 2004


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Borehole Geophysics

Attenuation Q/

Throughout the lecture so far we have mentioned non-elastic behavior of materials. Those non-elastic effects can be summarized by a new intrinsic property: attenuation, described by either

Q (Quality factor) or attenuation coefficient.

The energy that is stored in a seismic waveform is partially lost if the seismic wave travelsthrough a lossy medium (also called visco-elastic material). The amount of energy lost is

described by Q or .

The attenuation coefficient is related to the seismic velocity (V) and seismic frequency (f) asfollows:

= f / Q V (EQ 3-8)where Q (quality-factor) is defined as:

Q-1 = 2 (EQ 3-9)

with as wavelength.

A different definition of attenuation is given by the loss of energy (E) relative to the total energy(E) per unit wavelength:

2Q-1 = E / E (EQ 3-10)

[A low value of Q means high attenuation; a low value ofmeans low attenuation.]


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Borehole Geophysics

Attenuation Q/

In general attenuation decreases with increasing applied pressure.

Since attenuation is mainly an effect of losses occurred in the pore-space by differential motion

between rock-frame and pore-fluid (squirt-flow), it is simple to understand that attenuation isreduced when porosity is reduced.

Partial saturation (less than 100% of one type of pore-fluid) increases attenuation since there is moreroom for partial motion of the pore-fluid relative to the rock-frame work.

One pronounced effect of free gas on seismic data is a complete wash-out.

Knapp, et al., 2001.


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Borehole Geophysics


Summary matrix of effects of Temperature (T), pressure (P) (confining, pore-pressure)and saturation (Sg) on seismic velocity, density, porosity, and attenuation (Q). Bluearrows down indicate a reduction of the property with an increase in conditions;alternatively a red arrow up indicates an increase in the property with an increase incondition.

Borehole damage


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Gas hydrates: higher VP and VS with hydrates


Borehole Geophysics

As described before, the effective medium theorycan incorporate the effects of cement and grains.

In the case of gas hydrate, the hydrocarbon (=gashydrate) can form in various ways, as shown in theimage on the left.

The effective seismic velocities vary stronglydepending on which formation scenario is used, as

shown on the image below

Source: Dai et al., 2004

Source: Dai et al., 2004

Observations from various fields show that gashydrate mainly forms as a supporting matrix-grain(scenario 3).


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Borehole Geophysics

Gas hydrates: higher VP and VS with hydrates

Example of logs acquired from offshore Vancouver Island, IODP Site U1326. Note the high P- and S-wave velocities in the hydrate bearing zone at 60 100 meter below seafloor. Resistivity is alsoincreased in these zones.


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Attenuation in gas hydrate bearing sediments is higher!


Borehole Geophysics

Source: Guerin and Goldberg, 2001

Hydrate zones

Acoustic Well-logs with full waveform show a pronounced decrease of wave amplitude in hydrate-bearingzones. The example below is from the Mallik well site, Mackenzie delta, NWT.


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What else can an acoustic log be used for?

Impedance inversion!


Borehole Geophysics

Seismic data are technically speaking an image of sub-surface impedance contrasts. Acoustic

impedance is the product of density and velocity. Each time the impedance changes, seismic data getreflected from such an interface and the strength of the reflected wave is a direct function of theimpedance contrast.

Vertical incidence:

Reflection coefficient is function ofimpedances only.

Oblique incidence:

Zoeppritz equations govern reflection coefficients,

AVO-theory (EPSC-551-Seismic data processing)


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Borehole Geophysics

Impedance inversion tries to get a more regional estimate of physical properties that were acquired atone (or more0 well-locations from logging. The inversion first calibrates the regional seismic response(on scales > 10 m) at the well-location before extrapolating away from the borehole.

Acoustic logging and Impedance inversion

Source: Riedel., 2004


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Careful calibration is achieved by matching the synthetic seismogram (calculated from density andvelocity and wavelet estimate) to the regional seismic data at the well-site.


Borehole Geophysics



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Borehole Geophysics


The inversion then calculates a regional impedance response for all seismic traces along a sectionor 3D cube, which allows extraction of velocity values at all locations of the section/3D cube. It canbe used for volume calculations of the hydrocarbon in place (but this still requires equal regionalestimates of porosity).


borehole lecture03 rock physics

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