ABSTRACT
Petrophysics and Geophysics have not always worked in the
past as closely together as one might expect. This paper discusses
current advances, and sketches future developments. The major
objective of Geophysical Research was to obtain sharper pictures.
With the advent of 3-D seismic, there is a strong trend to make
displays both in time and depth, and to convert seismic attributes
into rock properties. Conversions based on seismic data alone
give non-unique results. Further progress hinges on calibration
of acoustic attributes with parameters measured on cores. For
time lapse seismic, the situation is even more complicated, due
changing effects of temperature, pressure, and compaction. All
these effects have to be properly quantified if we want to couple
4-D seismic interpretations to dynamic reservoir models and realize
the situation where all geoscientists work on one "unified"
3-D earth model. Biot - Gassman fluid substitution algorithms
were successfully applied for decades, but suffer like all mixing
laws from non-uniqueness. Recent investigations demonstrate that
dispersion in the low frequency band could have strong implications
on seismic attribute analysis. Further experimental work is warranted
to find out which relations measured at high frequencies can
be used for seismic, and which require additional laboratory
work. The shock-tube is well suited for this task, because it
handles large rock samples, and obtains acoustic responses down
to a few hundred Hz.
KEYWORDS : Formation evaluation, reservoir characterization,
rock properties
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INTRODUCTION
Petrophysics and Geophysics have in the past not worked as
closely together as one might expect. Both disciplines measure
subsurface rock properties, albeit one near the borehole, and
the other far away from the surface. While Petrophysics is, or
more correctly was restricted to the vicinity of the borehole,
Geophysics covered the entire subsurface. Petrophysics looks
near the borehole with high resolution, and Geophysics far from
the surface with a low resolution. Why was there not more interaction?
There are several reasons:
- Geophysics concentrated on the big picture, and imaging became
sometimes a goal in itself. Many papers prove the superiority
of a new method with an improvement of the seismic picture. Whether
this was the best representation of the physical reality often
received less attention.
- Petrophysics, as the name implies, aimed from its inception
at obtaining the physical properties, which are related to vital
production parameters such as porosity, saturation and permeability.
Petrophysics often evaluated one well at the time, compensating
for complicated borehole and invasion effects, but in this process
sometimes forgetting the big picture.
- The scales on which the two disciplines are working are very
different. Logs and cores give a resolution better than a foot,
while seismic resolution is less than 50 feet at the depth where
many hydrocarbon accumulations are found. This is illustrated
by projecting a wireline log (white), and half a cycle of a seismic
wave (black), on a sequence of sand and shale layers (Figure
1).
Fig.1 Comparison resolution core
/ logs / seismic
(P. Enbers, 1997)
 |
FORCES THAT FORGE THE FUSION
There has been a dramatic improvement in definition and quality
of seismic sections, due to the 3-D seismic revolution. Enhanced
images give better stratigraphy and reservoir architecture, but
is it enough? To tie the "former" exploration and production
communities together one needs to position geological features
in time and in depth. This is self evident, but the implication
is that more accurate relations between seismic attributes and
rock properties are required. We have to put flesh on the bones
i.e. display rock properties together with seismic horizons.
In a paper fittingly titled: "Seismic lithology - the integration
of Seismology and Petrophysics" White (1995) stated, "Just
as seismic stratigraphy united seismic interpretation and sedimentary
geology, so too will seismic lithology inevitably entail integration
of seismology and petrophysics. The results rely on petrophysical
modeling and collaboration between seismologists and petrophysicist
is needed to understand a seismic response of a large volume
of rock." Some impressive innovations have been made over
the last decade to satisfy this need.
WIRELINE LOGGING TOOLS
- Logging tools which can accurately measure both compressional
and shear wave velocities (Tang, 1998)
- Measuring while drilling (MWD) instruments that record compressional
wave velocity became recently available (Heysse et al, 1996)
and measuring shear wave velocities is probably a matter of time.
Single well seismic tools that measure reflections some 10
m away from the borehole, with transmitters and receivers in
one tool, are being proto-typed. (Chang et al 1998)
SEISMIC ACQUISITION
- Ocean bottom cables (OBC) which make direct contact with
the sea-bottom, and measure compressional and shear waves are
gaining ground (Soubaras, 1996).
- Compressional to shear converted waves can be recorded with
the OBC and three component (3C) geophones on land. Recent examples
of looking through shallow gas zones and beside saltdomes have
opened up prospective zones. (Ge et al, 1997).
- Vertical Seismic Profiles (VSP) using nine components (Davis,
1998) are now used to detect the position and direction of fracture
zones.
- Time lapse 3-D seismic surveys (4-D) prove that the difference
of attributes recorded in time can be related to changes in saturation
caused by production (Popov, 1998).
COMPUTING POWER
The tempestuous computer hardware and software development
is not only essential for processing the ever increasing amount
of data, but also for the design of new logging by means of modeling
(Strack et al, 1998). If the doubling of computer power every
2 years continues, we soon will see:
- 3D pre-stack depth migration within reach of every operator.
- 3D elastic wave imaging, and inversion.
- Forward modeling of the tool response while logging is already
applied to Stoneley wave permeability prediction (Tang, 1998).
The resolution of the static and dynamic reservoir models
is currently an order of magnitude different, with the dynamic
model limited to about a million grid blocks. The trend sketched
above will shortly enable simulations with several million-grid
blocks, approaching the resolution of seismic data, as predicted
by Gutteridge (1994).
All these developments bring Petrophysics and Geophysics closer
together. The benefits of this trinity of new wireline logging
tools, acquisition techniques, and computer power, can only be
translated in high resolution 3-D earth models, if they are matched
by more accurate relations between rock properties and acoustic
parameters. This is probably the most important driving force
for the integration of Petrophysics and Geophysics.
INTEGRATION
For a static reservoir model, it is difficult enough to relate
porosity, pore-fill, and lithology to seismic attributes. For
a dynamic reservoir model, the situation is exacerbated because
other parameters such as temperature, pressure, fluid saturation
compaction, and changes in pore fluid play a role. This is not
an unambiguous exercise as mentioned by (White, 1992): "A
major aim of seismic interpretation is inference of petrophysical
properties of reservoir rocks. Because [this] inversion is far
from unique, this task requires a range of seismic parameters".
One cannot hope to derive all rock properties simultaneously
from seismic. After all only one physical phenomenon is measured
with a low resolution. There are usually very many configurations,
made up of layers with different porosities, acoustic travel
times, lithologies, and fluid contacts, that all will produce
the same seismic response. Seismic models have to be constrained
by other data to limit the number of physical realizations. A
recent reservoir characterization study by Workman et al (1997)
drew the conclusion :" If no constraints are used, the results
of the characterization will be highly non-unique..."
Eventually one wants to be able to superimpose all relevant
rock properties onto the seismic horizons, and in addition, it
is desirable to follow these parameters as a function of time.
If the trend in computer power continues, a 3-D earth model with
geological, petrophysical, and geophysical data in all grid-blocks
will be available soon. This "unified model" would
have the resolution of cores near the well bore; of logs in most
other places; and will be used for both static and dynamic modeling.
LOG DERIVED SYNTHETIC SEISMIC
A high-resolution acoustic impedance trace in depth is obtained
by simply taking the ratio of density and sonic travel time log
readings. However the process of drilling and associated mud
invasion has a varied and sometimes a devastating effect on log
measurements (Peeters, 1999-1). Corrections for mud invasion
and shale alteration are required. For the density tool, a simple
linear relation exists between bulk density and the contribution
of the rock and fluid volume fractions. Based on firm physical
principles, and assuming that mud filtrate and formation water
have the same density rw, the correction of the density log for
mud filtrate invasion can be expressed as:
In which f is the porosity. Saturations
Sw and Sxo of the virgin and the invaded zone respectively are
derived from the resistivity logs. Hydrocarbon density rh is based on production
samples, and the water density rw from the salinities of mud filtrate and formation
water. For sonic logs, corrections are non-linear and more complicated.
BIOT AND BEYOND
The work by Biot (1956) and Gassman (1951) still forms the
fundament for quantifying the effects of rock and fluid parameters
on acoustic velocities.
The low frequency limit of the fast compressional velocity
Vpf in saturated porous rocks is:
(2)
In which rb is the bulk density, H = Kb*
+ 4 G/3 ; G is the shear modulus, and Kb*
is the effective bulk modulus of the saturated rock. Kb*
can be predicted with Gassman's (1951) algorithm.
(3)
The subscripts indicate : "f" for fluid, "s"
for saturated, "d" for dry, and "m" for minerals
/ matrix. The non-linear effect of the gas saturation on the
fast compressional velocity Vpf is contrasted
with density r, and the shear wave
velocity Vs in Figure 2.
Figure 2. Fluid saturation effect
on density, shear & compressional velocities, and the ratio
of the latter.
 |
It is often not realized that the derivation of the Kb* is not unambiguous, but suffers, like other
mixing laws, from non-uniqueness. The ratio of the bulk moduli
of the dry porous rock over the matrix material Kd/Km is used to approximate the ratio of the load
bearing over the total grain area, and is highly compaction dependent
(Spencer, 1994). The combination of Gassman's theory (Xu &
White, 1995) with the difference of aspect ratio's of shales
and sandstone (Toksöz et al, 1976), led to a much better
match between modeled and measured acoustic logs. However, the
better match transferred the problem from unknown mixing parameters
to unknown aspect ratio's (Xu & White, 1995).
That Gassman substitution equations are not universally valid
should not come as a surprise. Petrophysics has been plagued
with a mixing law problem in shaly sand evaluations for decades.
This problem has not been fully solved, despite eminent contributions
form Waxman & Smits (1967), Clavier et al (1972), and Worthington
(1991).
At high frequencies, fluid flow effects at the grain scale
are expected to create velocity dispersion and attenuation. Plona
and Johnson (1982) demonstrated that significant frequency effects
occur at low frequencies, especially for high porosity rocks.
Kelder & Smeulders (1997, 1998) reported experiments over
a frequency range from 10 Hz up to 1 MHz on small samples to
quantify the effect of grainsize, permeability, and lithology.
They measured for the first time the slow wave on natural fluid
saturated sandstone.
The fast & slow compressional waves and the shear wave
are modes that satisfy the dynamic Biot equation. For the fast
compressional wave the fluid in the pores and the matrix material
move in phase, while for the slow compressional wave the fluid
and matrix movements are out of phase. This latter wave is very
dispersive and strongly damped. The velocity of the slow p-wave
Vps is, in contrast with the fast p-wave Vpf, not only dependent
on the moduli of the matrix materials and pore fluids, but also
on the absolute permeability ko
If we assume that the bulk modulus of the matrix material
Ks is much larger than that of the fluid Kf and that the compressibility
of the grains is very small, we can derive a relation between
the ratio of the squares of the compressional waves and the permeability
:
(4)
In which f(w) is a complex function
of the angular frequency w,
rb the bulk density, G the shear
modulus, and h the fluid viscosity.
If rock and fluid moduli, and the viscosity are known, the slow
p-wave velocity can be used to predict permeability (Peeters,
1999-2). Research on rock (Batzle 1992, 1996), and fluid properties
(Alberty 1992) is invaluable for determining these parameters.
However, the understanding of the effects of partial saturations,
lithology, texture, overburden pressure, and especially frequency
is far from complete. The need for extending this work will be
demonstrated in this rest of this paper.
AMPLITUDE VERSUS OFF-SET (AVO)
The reflection of a plane acoustic wave, which arrives at
the interface of two layers under an incident angle q,
has been studied for a long time Zoeppritz (1919). The reflection
is determined by six elastic rock parameters. These six are compressional
velocities Vp1 and Vp2
(average Vpa); shear velocities Vs1 and Vs2 (average
Vsa); the densities r1 and r2 ; and Poisson
ratio's s1 and s2
(average sa) of the two layers. The normal incidence reflectivity
NI (q = 0) is :
(5)
The reflection coefficient RC as a function of reflection
angle q can be simplified by using
Shuey's approximation (1985), the formalism of Verm & Hilterman
(1995), and by dropping terms for q
smaller than 30° (tanq = sinq). Finally by assuming that Vpa/Vsa= 2 we find :
RC(q) @
NI + PR sin^2 (q)
(6)
PR is the far-offset reflectivity, and is not really
a reflectivity and dominated by s. It is therefore convenient
to refer to it as the Poisson reflectivity.
(7)
NI depends on both fluid fill and lithology. A large negative
change in NI produces a bright spot, and is often related
to the presence of a gas sand below a hard shale. A cross-plot
of NI vs. PR is a much better vehicle to separate
pore fill and lithology effects than reflectivity NI alone.
(Engbers, 1997, Figure 3). This figure shows the predominant
effect of fluid type on the normal reflection coefficient, and
the large lithology effect on the Poisson reflectivity PR.
However, a baseline (red line in shaded area) which represents
a brine-filled reservoir is required to quantify the hydrocarbon
effect.
Figure 3. Normal incidence (NI)
vs. Poisson (PR) reflection coefficients (P. Engbers, 1997)
 |
For petrophysicists, the use of cross-plots is standard, and
it is pleasing to see that Geophysicists start to exploit this
technique. By color coding seismic sections, proportional to
the length of the "fluid" arrow shown in Figure 3,
it is now possible to differentiate fluid fill, and lithology
effects (Verm & Hilterman, 1995). This work is an important
step towards the aim of showing rock properties together with
the seismic horizons. For fluid and lithology discrimination
the assumption Vpa/Vsa
equals 2 is often permissible. The danger of using a fixed Vpa/Vsa ratio was recently
discussed by Hornby & Pasternack (1998).
They demonstrated that silts with residual gas, which have
a much smaller Vpa/Vsa ratio, could be erroneously interpreted
as gas bearing sands. This highlights once more that more accurate
shear and compressional velocities as a function of partial saturation,
fluid type, and lithology are required. Modern dipole tools can
provide the Vpa/Vsa ratio with a high spatial resolution. The
great potential of dipole sonic tools is illustrated by measurements
of Vpa/Vsa through casing, which could even be related to oil
saturations (Moos 1995).
CONVERTED WAVE INTERPRETATION
For converted waves, from compressional to shear, the asymmetry
of the ray-path is a fundamental problem. There is no common
measuring point, even for flat reflectors. The ratio of the tangents
of the angel of incidence and the reflection angle are of course
proportional to the Vpa/Vsa
velocity ratio. The lack of a CMP is usually circumvented by
assuming a fixed velocity ratio. However strong vertical variations
as found around saltdomes, and gas chimneys, invalidate this
assumption. An acceptable solution is obtained via prestack depth
migration, but this process can be greatly enhanced if the Vpa/Vsa velocity ratio
as a function of depth is available from dipole sonic logs. It
is surprising that papers that discuss converted waves seldom
mention dipole sonic logs for calibration. The potential of using
converted waves is very high (Simmons, 1994), because they are
expected to provide better lithology and fluid discrimination
than AVO. The discrimination power of the combination of shear
and compressional waves is illustrated in Figure 5. This emphasizes
the importance of 3 component surveys, which record both the
compressional (p) and shear wave (s) velocities, when gas is
present. Gas hampers detection of p-waves and can produce featureless
p-sections (Peeters et al, 1998). The converted wave technique
can be used to image through shallow gas wipeouts. Shear waves
get through relatively unscathed. This effect and the twofold
increase in resolution due too the use of shear waves is shown
in Fig 6.
FUTURE WORK
To reap the full benefits of the techniques discussed above,
and get high resolution seismic sections that show rock and fluid
properties, it will be mandatory to calibrate the real seismic
traces with synthetic traces. These traces should be generated
through forward modeling from accurate rock properties, which
need to be measured at frequencies close to the seismic frequency
band. The large gain in resolution that can be achieved especially
with shear wave synthetics is demonstrated in Figure 9 at the
end of the paper.
A lot of excellent work has been carried out by Plona (1982),
Xu & White (1994), King (1998), but this work was restricted
to high frequencies (100 kHz - 1 MHz) and small samples. Limited
research has been carried out at much lower frequencies due to
the huge difference between a 50 Hz seismic wavelength (~40 m)
and a 10 kHz sonic wireline tool wavelength (~20 cm). Dispersion
can play an important role even for low frequencies (Kelder &
Smeulders 1997). Batzle et al (1996) demonstrated that partially
saturated rocks can have a high dispersion and attenuation in
the 0 to 1 kHz range (Fig. 4).
Supplementary experiments are required to find out which high
frequency results can be extrapolated to the seismic domain.
Resonant bar experiments on rod shaped rock samples can go down
to 1 kHz, but do not cover all wave modes. (Sothcott et al 1998).
Figure 4: Dispersion of compresional
velocity as a function of partial saturation (Batzle 1996)
 |
Figure 5 : Combination of shear
(r.Vs) , and
compressional (r.Vp) impedances
 |
Figure 6 : Comparison P &
S CMP panels Huesca
Peeters (1999-1)
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In a shock-tube, (Figure 7), it is possible to measure the
progress of a pressure step-function through a sample. (Wisse
1998). The shock tube can accommodate samples of more than 1
m in length, which opens up the possibility to record signals
with frequencies down to 1 kHz, thus approaching the seismic
frequency range. Large samples allow accurate attenuation measurements,
which is important for Q-factor verification. The high power
of the pressure step-function makes it relatively easy to detect
the slow p-wave. Modeling a borehole configuration indicated
that the slow p-wave arrivals could be detected for formations
with permeabilities down to 10 mD. In contrast with methods based
on Stoneley wave logging (Cheng & Tang 1995, Tang et al 1998)
or flow analysis during formation testing, the slow-p wave technique
is in theory insensitive to borehole effects.
Figure 7: Shock-tube experimental
set up
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FUTURE
DEVELOPMENTS
Inversion by comparing the actual measurements (logs, seismic)
with forward modeling results, will rapidly gain in importance
as computer power constraints are diminishing. The distinction
between inversion of an induction log, a wave train from a sonic
tool, or a single seismic trace, will vanish and be performed
by similar software. This trend is expected to blur boundaries
between Petrophysics and Geophysics.
The requirement to approach the physical reality more closely
can only be fulfilled if accurate rock and fluid properties have
been measured on samples. The limitations of the Gassman fluid
substitution algorithms, the lack of proper shear velocities
in unconsolidated sediments, and the uncertainty of the dispersion
effect on acoustic velocities,
all strengthen the need for more fundamental work in this area
Forward modeling and simultaneous inversion of all log data to
find rock properties is currently being investigated. The time
might be near when log data and seismic traces are inverted together
to update the 3-D earth model, without carrying out separate
wireline log and seismic interpretations.
More efforts need also to be spent on increasing the seismic
bandwidth towards higher frequencies both through advanced acquisition
and processing techniques. Downhole sources and "permanent"
geophone strings in observation wells are instrumental to achieve
this goal. Only if both more accurate rock properties and wide
band seismic are available can we expect significant improvements
in reservoir characterization.
Figure 8: Comparison of shear
wave synthetics derived from dipole sonic and density logs with
surface shear seismic (Blaylock, May 1999)
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CONCLUSIONS
1. Geophysics and Petrophysics are drawing together, because
they progressively use common techniques such as forward modeling
and cross-plotting, to determine rock properties.
2. The blurring of disciplinary boundaries is not restricted
to Petrophysics and Geophysics. If the steep trend in computer
power continues, the distinction between static and dynamic reservoir
models will vanish. All geo-scientists will then work on "unified"
3-D earth models.
3. More accurate relations between seismic attributes and rock
properties, underpinned by theoretical work, are required to
realize the full potential of pre-stack depth migration, and
amplitude vs. offset studies.
4. Gassman's fluid substitution algorithm compensates acoustic
velocities for changes in pore fluids. Recent research indicates
frequency dependence not only for high frequencies but also in
the seismic frequency band, which warrants further experimental
research
5. The shock-tube experimental set-up is well suited for this
work, because it handles large rock samples, and obtains responses
down to 1 kHz.
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ACKNOWLEDGEMENTS
This paper is an extract of the address by the author, presented
on the commencement of the Baker Hughes Distinguished Chair.
The support C. Payton, K. Strack, and D. Skerl of the former
Atlas Wireline Logging company, is gratefully acknowledged
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