Advanced reservoir imaging using frequency-dependent ... Berkeley.pdf · Our proposal is to develop...
Transcript of Advanced reservoir imaging using frequency-dependent ... Berkeley.pdf · Our proposal is to develop...
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Advanced reservoir imaging using frequency-dependent seismic
attributes
Funding opportunity number: DE-PS26-04NT15450-2A [Subsurface Imaging]
CFDA Code: 81.089
CFDA Title: Fossil Energy Research and Development
Area of Interest 2A: Subsurface Imaging
Principal Investigator: Fred Hilterman, Distinguished Research Professor
504 Science and Research Bldg 1
Department of Geosciences, University of Houston
Houston, TX 77204-5006
Tel.: 713-743-5802
Fax: 713-748-7906
E-mail: [email protected]
URL: http://www.geosc.uh.edu/people/faculty/hilterman/index.html
Co-PI: Tad W. Patzek, Professor, Civil and Environmental
Engineering, 210 Ericsson Building, MC 1716
University of California
Berkeley, CA 94720-1716
Tel: 510-643-5834
Fax: 510-642-3805
E-mail: [email protected]
URL: http://petroleum.berkeley.edu/patzek/index.htm
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Advanced reservoir imaging using frequency-dependent seismic attributes
Abstract 3 I. Introduction 4
A. Benefits
II. State of Art 6 A. Physical Modeling B. Field Verification C. Theoretical analysis III. Proposed Technology 17 A. Frequency Dependent Reflectivity
B. Frequency Dependent Reflectivity Issues C. Frequency Preservation Processing D. Frequency Preservation Issues
IV. Project Management and Facilities 29 A. Management and Personnel B. Available Equipment and Resources
C. Available Oil-Industry Data D. Available Physical Laboratory Models V. Statement of Project Objectives 35 A. Objectives B. Scope of Work C. Tasks Theory development Physical modeling Frequency-dependent seismic imaging D. Milestones and decision points Year 1 Year 2 Year 3 E. Deliverables F. Technical transfer Plan G. Budget Request VI. References 43
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Abstract
A technology is proposed that quantifies seismic amplitude attributes in terms of reservoir
properties such as the rock permeability and fluid viscosity and also increases the accuracy and
resolution of the imaged reservoir. The seismic attributes are frequency and incident-angle
dependent. The technology also includes target-oriented processing to preserve the frequency
content of the propagating wavelet for wide-angle reflections.
Our confidence in the proposed approach is supported by several facts. First, we have
documented procedures for processing low-frequency seismic reflection data for the accurate
delineation of oil reservoirs. Second, we have recently developed an elastic fluid-flow model
that accounts for the physical phenomena associated with anomalous low-frequency reflectivity.
Besides theoretical calculations, observations from field and laboratory data indicate that
reflectivity is strongly related to reservoir flow properties. Finally, results from target-oriented
processing of wide-angle reflections show increased resolution and image quality of reservoir
heterogeneities over conventional processing. This unique combination of quantified frequency-
dependent reflectivity measurements and robust frequency processing provides an excellent
opportunity for reservoir characterization regarding the location of the most productive zones
before drilling a well.
Our proposal is to develop an advanced imaging and interpretation technology based on
frequency and incident-angle dependent seismic attributes. The proposed work includes
development of theory and processing algorithms, laboratory experiments and verification of
results using field data provided by industrial partners. To accomplish these challenging tasks,
we have gathered a unique multidisciplinary team including geophysicists, geologists,
petrophysicists, reservoir engineers and applied mathematicians.
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I. Introduction
The Department of Energy has several focus areas for developing technologies relevant to
oil exploration and production. Here, we have a dual proposal to advance the technology of
high-resolution seismic imaging and to advance the prediction of reservoir composition based on
the frequency and angle-dependent analysis of signals associated with oil and/or gas reservoirs.
This proposal is our response to a relatively new and pressing demand for more accurate seismic
predictions of fluid-saturation properties and distribution in matrix- and fracture-porosity rocks.
By incorporating both 3-D physical and numerical modeling, we expect to evaluate
quantitatively the effects of liquid and gas hydrocarbon phases, and to evaluate the impact of the
microscopic pore-scale geometry on seismic reflectivity and attenuation at different frequencies.
Recently, it has been found that low-frequency seismic signals can be successfully used for
accurate delineation of hydrocarbon reservoirs even in cases of very thin fluid-bearing layers.
The results of such low-frequency seismic imaging were confirmed by drilling and production
data. This frequency dependence of seismic reflections from fluid-saturated porous media has
been detected in different geologic environments, both in field and laboratory experiments.
Our accumulated experience in frequency-dependent data processing, along with recently
obtained theoretical results, lead us to the conclusion that new imaging and interpretation
technologies can be developed to improve oil and gas reservoir characterization. In particular,
the flow mechanics between the reservoir rock and fluids, such as the reservoir fluid mobility
will be characterized.
As a means of verifying the technology with real data, processing and interpretation of
seismic data from well-documented oil fields will be an important part of our activity. It will
include interpretation of 3-D seismic data and generation of seismic attributes. The pre-stack
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seismic data will be processed to generate frequency-dependent and angle-dependent attributes
(AVO). We will integrate these data to build a geologic reservoir model. The seismic attributes
will be calibrated and validated against the geologic model and reservoir parameters determined
from petrophysical and engineering data. We expect that analysis of frequency-dependent AVO
attributes and low-frequency imaging will lead to more accurate predictions of pore-fluid
production by mapping fluid contacts and mobility.
A. Benefits
Most U.S. onshore and continental-shelf oil and gas fields are now mature, and new
technologies are needed to extend their production lives. Most large oil companies are focusing
their limited research dollars on the international and deep-water capital-intensive projects.
Onshore exploration and development is increasingly becoming an arena for small independent
oil and gas companies with limited capital and limited experience in developing geophysics-
based technologies. This DOE initiative will enable us to (1) develop new seismic processing
and imaging techniques, (2) calibrate the new frequency-dependent seismic attributes with
geologic and engineering data from intensely drilled West Texas and Gulf of Mexico fields, (3)
develop new tools and methodologies to identify and quantify permeability variation and/or
production rate of hydrocarbons, (4) transfer these new technologies to a wide audience of
independents, and (5) catalyze re-exploitation of important, but mature, onshore U.S. plays.
Two major oil-industry companies are active research participants in this proposal. They are
Shell Oil Company and Fairfield Industries, Inc.; Schlumberger also expressed its interest in the
proposed research.
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II. State of the Art
There are numerous laboratory and field examples where low-frequency components of
reflected seismic waves show surprising imaging capabilities. Ironically, such components are
often filtered out as useless in conventional data processing. However, as we demonstrate
below, this part of the signal contains the most important information about the reservoir.
A. Physical Modeling
We begin with laboratory experiments performed by G.Goloshubin et al., 1996; Goloshubin
and Bakulin, 1998; Goloshubin et al., 2002. The laboratory setup is shown in Fig. 1. A 7 mm-
thick layer of artificial sandstone is squeezed between two thick layers of Plexiglas. Three
different portions of the layer were saturated with different fluids as shown in Figure 1a. An
acoustic signal was generated by a source on the top of the Plexiglas and the reflection was
recorded by a series of receivers. The presence of the fluid-saturated layer is clearly seen as an
anomalously high amplitude and phase shift of the reflected signal. Moreover,
WaterDry Oil
S R
Dry Water Oil
ℵS
Dry Water Oil
S
Dry Water Oil
S
(a) 50 kHz 15 kHz 5 kHz
Fig. 1 Physical modeling experimental setup (left panel) for porous layer with different fluid content (air, water, oil) and common offset gather images of reflection from the layer at different frequencies (from Goloshubin et al., 2002). Note the reflection for liquid-saturated layer dominate at low frequencies with an increasing phase delay.
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the oil-saturated part is more visible at very low (~5 kHz) frequencies, whereas water and air
saturated parts are well detected at 15 kHz and 50 kHz, respectively. These observations cannot
be explained by the differences between the layer impedances or by the tuning effect.
B. Field Verification
Now, let us consider three examples of field data processing. In all of them, the
hydrocarbon-rich zones of the reservoir were localized using low-frequency analysis. These
zones were confirmed a posteriori by well-production data. The imaging analysis was
performed without well data. Note that conventional methods of data processing could not
detect the hydrocarbon zones.
The first example demonstrates that oil-rich zones in natural reservoirs augment reflective
properties at low frequencies. The data for this example were obtained from the Ai-Pim oil field
in the central region of Western Siberia. The log and core measurements in this field indicate the
presence of two types of oil reservoirs. The first oil reservoir is at a depth of 2300 m (twt ~ 1.9 s)
and consists of a 11 – 15 meters thick productive layer (AC11) of coarse sandy Cretaceous
siltstone. Below, there is the second oil reservoir (Ju0), which is 15 – 20 meters thick and
consists of fractured bituminous Jurassic argillites. Conventional processing yielded the seismic
time cross-section shown in Fig. 2a. The seismic section is of high resolution, which makes it
possible to map the local small-amplitude structures and stratigraphic nonconformities. A
comparison of the seismic cross-section and test results shows no correlation between the
reflective properties of layers AC11 and Ju0, and the character of fluid saturation. Neither the
amplitude nor the shape of the signal changes along the seismic horizon. Fig. 2b shows the
result of low-frequency processing with a wavelet transform of 12 Hz. The oil content of both
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a
b
AC11
Ju0
Fig. 2 A seismic line from Ay-Pim Western Siberia oil field was used to image two different types of oil-saturated reservoirs. The well data indicate that the upper reservoir AC11 consist of an 11-15 m thick sandstone with varying fluid content. The lower reservoir Ju0 is represented by 15-20 m thick fractured shale. There is no evident correlation between well content and high-frequency standard seismic imaging (a). In contrast, the oil-saturated domains of the both sandstone reservoir AC11 and fractured shale reservoir Ju0 create high amplitude low-frequency (<15 Hz) reflections (b). The data for processing and analysis are courtesy of Surgutneftegas.
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strata (AC11 and Ju0) is depicted as an amplitude anomaly in the low-frequency component. It
should be noted that the lithologic properties of strata AC11 and Ju0 are considerably different.
Fig. 2a also shows the locations of the wells, whose production data were used for
verification of the imaging. The black circles depict the intervals of successful oil production,
whereas the white circles mark the intervals where the produced fluid was mostly water. There
is a strong correlation between the locations of the black circles and bright spots on the low-
frequency image Fig. 2b, whereas the locations of the white and black circles are not
distinguishable from the point of view of conventional analysis, Fig. 2a.
In the second example, a 3 km-deep Jurassic sandstone reservoir is investigated (J1, Fig. 3).
The reservoir thickness is approximately 8-10 m with mean porosity of 17-18%. From the 15
available wells, 7 produced oil and 6 produced water. The remaining two wells produced equal
mixture of oil and water. Shown are four calibration wells, three of which (76, 91, 95) produced
oil whereas the fourth one (9) produced water. In a blind test, the data from the other 11 wells
were used only for a posteriori verification of the mapping. Fig. 3 shows a time map of the
target horizon J1.
Fig. 3 Structural time map of the reservoir surface with location of 4 calibration wells, three of which (76, 91, 95) produce oil whereas the fourth one (9) produces water. Note a poor correlation between medium structure and fluid.
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Fig. 4 A blind test of the ability of frequency-dependent processing and interpretation to map the oil-water contact using the low-frequency part of seismic data. The seismic and well data recorded in Central Siberia. The seismic image shows the difference of low-frequency reflectivity at 12 Hz to the one at 40 Hz centered frequency, the predicted oil-water contact, and the locations of the calibration wells and the wells used for testing purposes. (Goloshubin, et al., 2002)
Fig. 4 shows the results of frequency-dependent processing of this dataset. The seismic
imaging map includes the variation of the amplitude of the target reflected wave at a low
frequency (12 Hz) relative to the amplitude of the same wave at a high frequency (40 Hz). The
imaging results predicted the location of oil-water contact. These results were confirmed by the
well data. All wells producing water are outside of the oil-saturated region. The wells with the
highest oil production rate (e.g., wells 91 and 86) are found close to the zones of the high
deviation of the map attribute at low frequencies.
The third example is based on 3D seismic data from the South Marsh Island oil field in the
Gulf of Mexico. The reservoir is about 3 km deep. It consists of 8-10 m thick sandstone layer of
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porosity about 0.35. The rock permeability is relatively high, 1-2 Darcy. The low-frequency
analysis was performed “blindly”. The well locations were provided only after the seismic
imaging of the reservoir zones. Even along the same line, the seismic sections of AVO attributes
at different frequencies produce different images (Fig. 5a,b).
a b
Fig. 5 The vertical seismic sections present the AVO attributes (intercept x gradient) at both high frequencies (a) and low frequencies (b). The low frequency (10 Hz) AVO attributes section (b) contains a bright anomaly at reservoir depth (twt ~ 2.7 s). The seismic and well data are the courtesy of Fairfield Industries.
There is no visible anomaly displayed in the lower part of the section (Fig. 5a) that
represents conventional AVO attributes. In contrast, the low-frequency (10 Hz) AVO attribute
section (5b) contains a bright anomaly around the reservoir depth (twt ~ 2.7 s.).
Fig. 6 shows an amplitude map of the low frequency AVO attributes along the reservoir
surface. The low-frequency AVO attribute map correlates well with the known production.
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Fig. 6 Blind test result for the Gulf of Mexico data. The well data indicate that the oil and gas reservoir consists of an 8-10 m thick sandstone at about 3 km depth with porosity about 0.35 and very high permeability (1-2 Darcy). 3D seismic data were used for recognition of the reservoir zones and imaging of the oil saturated areas. The plan view map includes the AVO attributes of low frequency reflectivity at about 10 Hz. Well data show the reservoir saturation and production activity. The seismic and well data for processing and interpretation are the courtesy of Fairfield Industries.
C. Theoretical Analysis
The examples presented above clearly demonstrate that anomalously high-reflection signal
at low frequencies cannot be explained with tuning effects. Here we will demonstrate that the
high reflection amplitude from a reservoir layer is a consequence of the diffusive character of the
wave attenuation in that layer. The low value of the quality factor Q for the low-frequency
waves is a characteristic feature of the permeable fluid-bearing layers. Consequently, the
amplitudes and the phase delays of the low-frequency reflected waves increase in comparison
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with the high-frequency modes (Korneev et al., 2004). The measured values of Q along with
their diffusion theory approximations are shown in Fig. 7, where the dry layer produces a smaller
attenuation of the signal. It is interesting to note the very low (below 5) values of Q, as well as a
very distinctive decrease of Q as the frequency approaches zero.
Fig. 7. Experimental (solid lines) and theoretical (dashed lines) values of apparent Q vs. frequency for air (red) and water saturated (blue) porous material (from Korneev et al., 2004).
Following Korneev et al. (2004), consider a generic scalar wave-propagation equation of the
form
2 22
2 2 0u u u uvt t x t x
χ γ∂ ∂ ∂ ∂ ∂2
2+ − −∂ ∂ ∂ ∂ ∂
= (1)
where is displacement. The second term in equation (1) characterizes the diffusive
dissipation, whereas the third one describes the viscous damping. We call the coefficients
u
χ
and γ the diffusive and the viscous attenuation parameters, respectively. is the phase velocity
in a non-dissipative medium. Equation (1) has a solution in the form of a harmonic wave
v
exp( ) exp( )u ikx i tω= −% , k k iα= +% (2)
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where ω is the angular frequency, and
vsq
α = , qkvω
= (3)
are the attenuation coefficient and the wave number, respectively. Calculations yield
2
2
1 12 4 2
s vq s χγ γω
⎛ ⎞= − + + −⎜ ⎟
⎝ ⎠,
2 2
4 2
12
vsv 2
ω γ χω γ+
=+
(4)
At low frequencies, i.e., for 0ω → one gets
2vωχ
α κ= = and 12 2kQα
= = (5)
The “apparent” Q depends on frequency as / 2Q ω χ= . A comparison between the theoretical
results and the ultrasonic measurements of Q is presented in Fig. 7. The corresponding values of
the attenuation parameters in the air-saturated case were estimated as 12000χ = Hz and 0.3γ =
, whereas in the water-saturated case, the result was 2 /m s 24000χ = Hz and 1.0γ = .
The theoretical curves for both cases are shown in Fig. 8 along with the physical modeling
experimental data. The theoretical formulation with diffusive term matches the physical model
2 /m s
Fig. 8. The reflection coefficient ratios (water saturated/dry) vs. frequency: (a) computed from data (red), and theory (blue). The theoretical curve for a half-space is shown in black. Travel time delays (b) of
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the wave reflected from a dry layer relative to a water-saturated layer. Experimental data shown in red, the theoretical curve is in blue.
data reasonably well. At the same time, computations without incorporating the diffusive
attenuation terms do not match the observed frequency dependence.
Korneev et al. (2004) and Goloshubin et al. (2001) analyzed the VSP data recorded at a
natural gas storage field in Indiana operated by the Northern Indiana Public Service Company
(NIPSCO). This VSP survey was a time-lapse study. Due to gas injection in the summer and
withdrawal in the winter, the reservoir fluid changed seasonally between predominantly gas to
predominantly water. While the data demonstrated good repeatability, the conventional VSP
travel-time measurements interpreted by Daley et al. (2000) did not reveal changes in the
reservoir gas saturation. At low frequencies, using frequency-dependent analysis, a clear
signature of the variations in water saturation was detected in the reflected waves (Fig. 9). The
spectral amplitude ratios and the travel-time delays in the reservoir reflection are shown as the
solid blue lines in Fig. 10. For comparison, the same functions were computed for a time-
window centered at the event, which arrives 100 ms later. Apparently, it is a reflection signal
from a boundary located far below the bottom of the reservoir. This reflection event has been
transmitted through the reservoir twice before reaching the receivers.
The plots in Fig. 10 show a clear frequency-dependent amplitude response. The reservoir
reflection amplitude ratio increases as the frequency decreases. Fig. 10 also shows a frequency
dependent travel-time delay, which increases as the frequency decreases. The spectral ratio for a
later arrival, which was transmitted through the reservoir, increases with the frequency. These
results are consistent with the opposite characters of the frequency dependencies for the reflected
and transmitted energy.
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a
b
Tapering windows for selection of the reflected phase
Fig. 9. Upgoing wave fields (a) for 1996 (left) and 1997 (right) reveal the low-frequency changes for reflections from the Trenton dolomite. The zoomed section (b) shows the reflections from the reservoir. Changes are clearly seen in the circled area.
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10 20 30 40 50Frequency [Hz]
0.0
0.5
1.0
1.5
2.0
Ref
lect
ion
ampl
utud
e 97
/96
ratio
s Target layer reflectionsDeeper layer reflections
10 20 30 40 50
Frequency [Hz]
-4
0
4
8
12
16
Rel
ativ
e 97
- 96
trave
l tim
e de
lay
[ms] Target layer reflections
Deeper layer reflections
a b
Fig. 10. The reflection amplitude ratios (1997/1996) vs. frequency (a) computed for the target reflection (solid line), and a later phase (dashed line). Also shown are the relative (1997/1996) travel time delays (b) of the target reflection (solid line) and later phases (dashed line). These results agree with theoretical predictions when comparing gas- and water-saturated conditions (Fig. 3).
The fact that reflection, transmission, and attenuation in fluid-saturated solids are frequency-
dependent was discussed in the literature (Geertsma and Smith, 1961, Dutta and Ode, 1983;
Santos et al., 1992; Denneman et al., 2002; Pride et al., 2003). Castagna et al. (2003) report the
“low-frequency shadows” associated with hydrocarbons. The authors admit that this can be an
artifact of the numerical data processing. We note, however, that such late arrivals of the low-
frequency reflected signal are consistent with the results shown in Figures 8, 10.
III. Proposed Technology
A. Frequency Dependent Reflectivity
Recently, we have obtained an asymptotic representation of the seismic reflection from a
fluid-saturated porous medium in the low-frequency domain. It turned out that the frequency-
dependent component of the reflection coefficient is proportional to the square root of the
product of frequency of the signal and the mobility of the fluid in the reservoir.
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In our argument, we apply a somewhat nontraditional approach. Namely, we have derived
the elastic wave propagation equations in fluid-saturated porous medium from the basic
principles of the theory of filtration (Polubarinova-Kochina, 1962; Bear, 1972; Barenblatt et. al.,
1990). In particular, we verify that the main poroelasticity equations (Gassmann, 1951; Biot,
1956ab, 1962), and the pressure diffusion equation, which is routinely used in well test analysis
(Earlougher, 1977), have the same roots.
Below, we briefly overview our derivation and formulate the principle conclusions. The
details can be found in (Silin et. al., 2004).
Here, we focus only on planar p-waves. Hence, we consider only the one-dimensional
displacements of the skeleton and fluid flow. Let t denote time and x, the spatial coordinate.
The balance of forces yields the following equation of motion for the coupled rock-fluid system
2 2
2
1b f
u W ut t xβ
∂ ∂ ∂+ = −
∂ ∂ ∂ñ ñ 2
px∂∂
(6)
Here p and fñ are the pressure and the density of the fluid, and is the bulk density of the
fluid-saturated medium,
bñ
(1 )b g f fφ φ= − + = +ñ ñ ñ ñ φñ where φ is the porosity and gñ is the grain
density of the reservoir rock. The small u denotes the displacement of the solid skeleton,
whereas the capital W is the Darcy velocity of the fluid. The coefficient β is the respective
uniaxial elastic coefficient. In equation (6), the Darcy velocity is measured relative to the porous
medium, that is, the Darcy velocity in a fixed coordinate system is equal to uWt
φ ∂−
∂.
To characterize fluid flow relative to the skeleton, we apply a dynamic version of Darcy’s
law. Darcy’s law was originally established for steady-state flow (Darcy, 1856). To account for
inertial and non-equilibrium effects in transient flow, we replace Darcy’s law with a relationship
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WWt x
κτη
∂ ∂Φ+ = −
∂ ∂ (7)
where τ is a characteristic redistribution time, κ is the permeability of the rock, η is the
viscosity of the fluid, and is the flow potential (Hubbert, 1940, 1956). Such a modification of
Darcy’s law was proposed by Alishaev (1974) and Alishaev and Mirzadzhanzadeh (1975). In
multiphase flow, similar considerations were used to model non-equilibrium effects at the front
of water-oil displacement and in spontaneous imbibition (Barenblatt, 1971, Barenblatt and
Vinnichenko, 1980), see also Barenblatt et. al. (2003) and Silin and Patzek (2004). Some results
on estimation of the relaxation time based on experiments were reported by Molokovich et. al.
(1980), Molokovich (1987) and Dinariev and Nikolaev (1990). The relaxation time is a function
of the pore-space geometry, fluid viscosity
Φ
η and compressibility fβ . Dimensional
considerations suggest that 2(f F Lτ ηβ κ )/ , where L is the characteristic size of an elementary
representative volume of the medium and is some dimensionless function. When the
obtained equations are compared with Biot’s wave equations, the time
F
τ and the tortuosity factor
(Biot, 1962) are involved in such a manner to suggest that they are linearly related to each other
through the reservoir fluid mobility. Thus, accounting for the accelerated motion of the skeleton,
we obtain
2
2fW pWt x
κ κτη η
ut
∂ ∂ ∂+ = − −
∂ ∂ ∂ñ (8)
Finally, mass conservation can be expressed in the following way:
2
1 (1 ) (1 )gsf gf
u p Wx t t
βφ φβ φ β
β⎛ ⎞⎜ ⎟⎝ ⎠
⎛ ⎞x
∂ ∂ ∂+ − + + − = −⎜ ⎟ ∂ ∂ ∂⎝ ⎠ ∂
(9)
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Here, gsβ and gfβ are, respectively, the coefficients of compressibility of the grains with respect
to the variations of the skeleton stress and the fluid pressure. In many cases, these two
coefficients are close to zero.
Equations (6), (8) and (9) form a complete system that can be solved with appropriate initial
and boundary conditions. Depending on the assumptions, this system can be reduced either to
Biot’s equations (Biot, 1956a, 1962; Dutta and Ode, 1979, 1983), or to the pressure diffusion
equation (Muscat, 1937; Barenblatt et. al., 1990).
Let us consider propagation of a planar elastic compression wave of an angular frequency
ω . Note, that within a reasonable range of rock and fluid properties, the dimensionless
parameter bκε ωη
=ñ is small at low (below 1 kHz) seismic frequencies. If we consider the
reflection of a wave of angular frequency ω from the planar boundary between dry and fluid-
saturated elastic media, then the asymptotic (with respect to ε ) expression of the reflection
coefficient R has the following form:
( )0 1 1 bR R R i κ ωη
= + +ñ (10)
Here R1 and R2 are real coefficients and i is the imaginary unit. The coefficients R1 and R2 are
dimensionless functions of the mechanical properties of the fluid and rock, which include the
porosity, the densities, and the elastic coefficients. At 0ε = the absolute value of the reflection
coefficient attains its low-frequency maximum. If the relaxation time is large, i.e., τ > 1/ω , then
scaling relationship (10) must be replaced with
10bR R R i κτω
η= + −
ñ ω (11)
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The explicit formulae for the coefficients are given in (Silin et. al., 2004).
The obtained results lead to important conclusions and suggest the following action items to
be investigated:
1. The reflection coefficient from a plane interface between dry and fluid-saturated rocks is
frequency-dependent.
2. At low frequencies, the dependence of the reflection coefficient on the frequency admits
an asymptotic representation (10). In particular, this means that the reservoir fluid flow
properties can be evaluated based on analysis of the reflection signal. The most
productive reservoir zones can be accurately mapped with the new method proposed
here.
3. The proposed theory explains the results obtained in the frequency-dependent analysis of
field and laboratory data (Goloshubin et. al., 1996, 2002; Goloshubin and Bakulin, 1998;
Goloshubin and Korneev, 2000; Korneev et. al., 2004).
4. The relaxation time is closely related to the tortuosity factor. The values of tortuosity
reported in the literature range from one to infinity (Molotkov, 1999). If the tortuosity is
large, it enters the asymptotic scaling (11). A rock/fluid classification by the respective
characteristic values of the relaxation times and tortuosity will enhance the high-quality
delineation of the hydrocarbon reserves and recovery processes. This enhancement will
come from characterizing the rock and fluids and from mapping the most productive
zones. Recent advances in the modeling of fluid flow at a microscopic scale (Patzek,
2001, Jin et. al., 2003, Silin et. al., 2003a) show how to estimate the tortuosity factor for
different types of rocks and different displacement processes.
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5. The proposed new imaging technology can be used for tracking propagation of the
injected fluid and for investigation of the cap rock integrity in CO2 geologic sequestration
projects and at liquid waste disposal sites.
6. The analysis carried out in (Silin et. al., 2004) should be extended to more general
situations where the incidental wave is not necessarily normal to the interface. The
dependence of the asymptotic relations (10) and (11) on the incident angle should be
investigated.
7. The mechanism of reflection leading to relations (10) and (11) is different from the
classical tuning effect. However, the role of the reservoir thickness in the frequency-
dependent reflection analysis should be investigated.
8. The impact of local heterogeneities, such as fractures, on the asymptotic relations (10)
and (11) should be taken into account. Recent preliminary studies of diffusive fluid
waves propagating in double-porosity and double-permeability media (Silin et. al.,
2003bc) suggest that the dependence of the reflected signal on the frequency should have
similar, but yet different asymptotics.
For the data in Fig. 4, the imaging attribute ( , )A x y was proportional to the first derivative
over the frequency of the reflected amplitude at a fixed (low) frequency. This implies that the
following relationship:
A(x,y) ≈ C (κ/η)1/2 (12)
holds true, and the imaging attribute is therefore proportional to square root of fluid mobility.
Using well data we can find the unknown constant C which is a complex function of porous rock
parameters. Assuming that the well production rate is proportional to mobility we can compute
the theoretical curve for the production rate vs. the imaging attribute. Figure 11 shows the
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measured production rates for the oil field from Fig. 4, and the theoretical curve, which was
calibrated using just one well data point. The field data and theory correlate quite well.
Fig. 11 The oil production rate vs. the imaging attribute. Data taken from oil field shown on Fig. 4. The theoretical blue line is computed using the low-frequency asymptotic solution (12).
504000 506000 508000 510000 512000 514000 516000 518000 520000
692000
694000
696000
698000
700000
702000
704000
5
15
25
35
45
5565
75
85
95
105
115
125
135
Production rate [m3/day]
Fig. 12. The oil production rate vs. the imaging attribute. The input data are taken from oil field shown in Fig. 4.
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This agreement allows one to convert the attribute map from Fig. 4 into the production rate
map. The result is shown in Fig. 12. This map is the first of its kind; it predicts spatial
distribution of the productivity of an oil field.
The double porosity–double permeability model (Pride and Berryman, 2003ab; Pride et al.,
2003) suggests that fracture flow is critical for seismic frequencies, and this dependence can
resolve the scaling issues. The presence of fractures also explains the same low-frequency effect
observed for reservoirs with negligible pore flow (examples 1 and 2 in Section II B and NIPSCO
example in Section II C).
B. Frequency Dependent Reflectivity Issues
It is clear that low-frequency seismic imaging has great potential since it allows the
characterization of the subsurface fluid reservoirs in situations when other approaches fail. Still
several important problems must be addressed before the robust and effective imaging
technology is ready for routine use. These problems are the following:
1. To date, the low frequency imaging approach was applied to only 20 different data sets. It
turned out that it worked well in about 75% of the cases, while in other cases the
interpretation outcome was uncertain. The limits and conditions of the applicability of
the method need to be formulated, so that the imaging procedure can be adapted to each
case depending on the situation (geology, data quality, frequency content, etc.).
2. Current imaging procedure needs well data for calibration. Well information can be very
helpful, but is not always available. A theory is needed to relate the imaging attributes to
reservoir parameters, which might enable us to convert the images into the hydrological
reservoir properties in absence of well data.
25
3. Since the pore sizes are the same, there is a scaling problem that seems to disallow a
direct relationship between laboratory and field data. The available theory describes
laboratory data, and we have to find how it can be downscaled to seismic frequencies.
Several important clues to the solution of this problem come from the fact that the
frequency-dependent effect was observed in nonporous but fractured reservoirs. This
suggests that fluid flow in fractures might play a major role at low seismic frequencies
and the double porosity–double permeability model is critical for seismic frequencies,
and this dependence can resolve the scaling issues.
4. In the recently developed theory (Silin et al., 2004) it is shown that the tortuosity of a
porous medium might reach values that change the low-frequency asymptotic character
of the imaging attribute dependence on the medium parameters. The rock tortuosity
varies from 1 to infinity and, therefore, should be studied for different types of porous
rocks. Furthermore, it is likely that the fracture tortuosity and permeability dominates the
low seismic frequency effects.
5. There is a parameter reduction problem. Biot’s theory and its modifications currently
give the most comprehensive descriptions of elastic waves in fluid-saturated porous
media. The major problem in application of this theory is the necessity of using about a
dozen parameters that describe the porous saturated rock. Most of these parameters are
unknown in real situations, creating a high degree of ambiguity in interpreting the data.
Some of the parameters, such as fluid mobility, are of special interest in gas and oil
prospecting applications. Extraction of those seismic attribute dependencies that are
related to the main hydrological parameters is of special importance. The fluid mobility
parameter can be retrieved from the seismic reflected signal at low frequencies.
26
C. Frequency Preservation Processing
The calibration of seismic frequency-dependent reflectivity measurements to reservoir
properties is based on the assumption that robust amplitudes are obtained for individual
frequency components of the propagating wavelet. However, the frequency content of the
seismic wavelet is distorted by conventional data processing with NMO providing the most
significant distortion. In a conventional CMP gather, the trace associated with an offset equal to
depth has a wavelet frequency that is nominally 12 percent lower than the wavelet frequency
associated with the normal-incident reflection. With the introduction of anisotropic NMO
processing, the wavelet frequency content on the very far-offset trace can be almost one-half that
of the normal-incident wavelet. This is not an acceptable condition when calibrating loss
mechanisms to reservoir properties as a function of frequency. In addition, AVO attributes are
suspect when appreciable NMO stretch is generated. Hilterman and Van Schuyver (2003)
introduced a novel processing scheme based on a migration algorithm that doesn’t perform NMO
corrections followed by a target-oriented NMO correction. The CDP gather on the right side of
Fig. 13 illustrates the retention of wavelet frequency when target-oriented processing is applied.
Fig. 13. CMP gathers illustrating target-oriented processing (right side) versus conventional processing. The frequency content of the propagating wavelet within the dashed target interval has not been distorted by target-oriented processing.
27
Besides the preservation of frequency, the quality of the seismic image is improved
significantly with target-oriented processing. Figures 14-16 illustrate this point with an obvious
improvement in the structural interpretation. The structure shown in Fig. 14 is a faulted anticline
and on the angle stack (26°-35°), there is an indication of fault blocks near the apex of the
structure. In order to observe the frequency content of the signal, the upper surface of the high
amplitude reflection was flattened to a constant time and the result is shown in Fig. 15. The fault
location is illustrated with a green line on both the angle stacks.
Fig. 14 Pre-stack time migrated sections with conventional angles (0°-26°) and far-offset angles (26°-35°). Structure is faulted anticline with some indication of fault blocks near apex. Potential reservoirs are within the large amplitude band.
With conventional processing, the 35°-50° angle stack has excessive wavelet stretch and the
interpretative value of section becomes questionable. However, with target-oriented processing,
the 35°-50° angle stack in Fig. 16 exhibits excellent quality. In fact, there are fault blocks
illustrated on the 35°-50°angle in Fig. 16 that are difficult to observe in the 0°-16° angle stack.
This better definition of faults on oblique reflection data is an expected result once wavelet
stretch is removed. With target-oriented processing and interpretation, the reservoir time
horizon is picked first. Then, the final NMO is applied to block shift the offset traces within a
CMP gather to the horizon time of the specified CMP gather. Because of the block shift,
28
interpretation and data analyses are normally limited to a time window about 100 ms on either
side of the reservoir event.
Fig. 15. (Top) Conventional 0°-16° angle stack of high-amplitude structure displayed in Fig. 14. Data were flattened to top of structure. (Bottom) Conventional 35°-50° angle stack of high-amplitude structure displayed in fig. 14. The CDP offset ranges in this section contain incident angles beyond critical angle.
Fig. 16. These two sections are similar to those displayed in Fig. 15 except target-oriented processing has been applied.
29
D. Frequency Preservation Issues
It is clear that NMO stretch needs to be avoided if quantitative analyses of amplitudes as a
function of frequency are to be conducted. The target-oriented approach provides an avenue to
avoid stretch, however, there are several problems that need to be resolved.
1. Currently, the migration algorithms are designed for 2D processing and need to be
expanded to 3D. No conventional seismic processing software has target-oriented
processing.
2. Processing requires anisotropy in NMO and migration. NMO corrections for very large
offset traces are difficult to stabilize in time and suggest that depth imaging should be
examined.
3. Target-oriented processing requires the migrated t0 times for the target horizon.
Numerous algorithms for interpretation need to be developed to handle this change in
processing and interpretation philosophy.
IV. Project Management and Facilities
A. Management and Personnel
The Department of Geosciences at University of Houston has assembled an integrated team
of faculty and research staff including geophysicists, petrophysicists, geologists, and computer
scientists, capable of addressing a wide range of problems in seismic imaging and reservoir
characterization. ( http://www.geosc.uh.edu/info/research/research.htm) We have gathered a
unique multidisciplinary team including geophysicists, geologists, petrophysicists, reservoir
30
engineers and applied mathematicians from University of Houston, University of California, and
Lawrence Berkeley National Laboratory.
Dr. Fred Hilterman, the project PI is Distinguished Research Professor at the Department of
Geosciences at University of Houston, and has 40 years experience in R&D and management:
http://www.geosc.uh.edu/people/faculty/hilterman/index.html
Dr. Tad Patzek, a co-PI on this project, is Professor of Geoengineering at the Department of
Civil and Environmental Engineering, University of California, Berkeley. He has 20 years of
experience in petroleum-related research in industry and academia. He has studied multiphase
flow at microscopic and microscopic scales, worked on the microseismic methods of
hydrofracture imaging, on lossy-transmission-line modeling of hydrofracture dynamics, rock
damage propagation, etc.
Dr. Gennady Globoshubin, Research Professor of Department of Geosciences at the University
of Houston, is geophysicist with 30 years experience in seismic experiments, data processing,
imaging and interpretation, rock physics and wave propagation.
Dr. Robert Wiley, Research Associate Professor of Department of Geosciences at the
University of Houston, has worked in the oil industry for over 27 years, with particular expertise
in numerical and physical seismic modeling, seismic processing and interpretation, and imaging.
Dr. Charlotte Sullivan, Research Assistant Professor of Department of Geosciences at the
University of Houston, is a petroleum geologist with 30 years experience in carbonates and the
integration of geologic, engineering and geophysical data.
Dr. Valeri Korneev, Staff Geological Scientist in Earth Sciences Division (LBNL) where
he works since 1991. He has broad theoretical knowledge and experience in seismic wave
31
propagation theory and data inversion. He is a co-author of several latest publications related to
low-frequency effects.
Dr. Dmitriy Silin, Associate Researcher at the University of California, Berkeley and
Geological Scientist at LBNL. His background is in applied mathematics. His expertise is in
single-phase and multiphase flow in porous media, asymptotic analysis of reservoir fluid flow, in
modeling of elastic wave propagation in fluid-saturated rocks.
This project will provide support and data for MS.- and Ph.D.-level research by graduate
students.
B. Available Equipment and Resources
Computational network of the Department of Geosciences at the University of Houston
includes a 48-node Xeon Beowulf cluster, and 5 Tbytes of Raid-5 disk linked to a Sun V-880
server and 25 Sparc workstations, and access to a 98-node Sun Starfire supercomputer. The
Department of Geosciences has state-of-the-art commercial software in seismic interpretation,
processing, imaging, inversion, modeling, visualization, reservoir calibration, and reservoir
simulation (URL http://www.geosc.uh.edu/info/research/research.htm#computational).
During recent years, a new 2 m x 4 m x 1.5 m physical modeling tank in the basement of
Science and Research Building 1 was constructed. This equipment boasts state-of-the-art model
calibration and measurement electronics (URL: http://www.agl.uh.edu/research_fac.
shtml#Laboratory). We have recently developed the capability to construct physical models that
incorporate heterogeneous, permeable zones, as well as the capacity to inject different fluids and
gasses into those zones. Recent developments in the hardware and software controlling the
acquisition system enable us to control the frequency of the signal transmitted through the
model.
32
Center of Computational Seismology (CCS) at the Earth Science Division in LBNL has a
modern network of computers and a Linux computer cluster with 48 nodes. If needed, LBNL
projects can access the local supercomputing center NERSC, and use massively parallel
supercomputers. LBNL has several seismic processing packages including PROMAX and
Focus.
C. Available Oil-Industry Data
The existing in-house dataset covers 50 km2 of 3-D seismic data from the reservoirs of the
Central Basin Platform (Crane County) in West Texas (Figure 17). These reservoirs include
deepwater chert-turbidite channels and karsted ramp platform dolomites. The surveys cover data-
rich mature and super mature oil and gas fields, and are ideally located to test and calibrate
frequency-dependent seismic attributes against the porous reservoir model, fractured reservoir
model, and double porosity – double permeability reservoir model.
The deepwater chert-turbidite reservoirs are Devonian and belong to the Thirtyone
Formation. The combined Silurian-Devonian deepwater carbonates and cherts of West Texas and
New Mexico have produced over 2 billion barrels of oil equivalent and are still a viable play.
The Thirtyone reservoirs have over 500 million barrels of remaining moveable oil. The chert
reservoirs consist of a mixture of biogenic shallow-water carbonates and silicious sponge
spicules. The cherts extend north of the survey area to southern Andrews County, where they
produce from thick tabular beds and thin, continuous channelized deposits (Saller, et al., 2001).
These reservoirs, interpreted to proximal to the paleo-shelf margin, are compartmentalized by
complex faulting, and are heterogeneous as a result of fracturing, and depositional and diagenetic
variability (Montgomery, 1998; Ruppel and Hovorka, 1995). In contrast, thin, vertically stacked,
laterally discontinuous chert bodies dominate the reservoirs in the distal, southern part of the
33
basin, covered by our 3-D surveys. The distal chert reservoirs are compartmentalized by faults
and stratigraphic architecture; flow units are thin (3-8 m) and their development appears to be
influenced by basin geometry, slope stability, and sea-level cyclicity (Ruppel and Barnaby,
2001).
Crane Co. Seismic data
Fig. 17. Location of the Dollarhide and Crane County Devonian fields of the Central Basin Platform in the Permian
Basin. (After Saller et al., 2001)
The second type of reservoir consists of Ordovician and Permian karsted platform carbonates.
These reservoirs typically have little porosity expression on wireline logs, but they produce from
a combination of low matrix porosity and well-connected fracture systems. The chert reservoirs
have up to 40% porosity (generally microporous) and are encased in extremely low porosity
(3%) limestones (Fig. 18)
In addition to the available West Texas data, Fairfield Industries will provide 3D data from
their extensive long-offset seismic-acquisition database. This database covers the shelf area of
the Gulf of Mexico from shoreline to 200-ft water depth. There are several questions that need
to be resolved before any data from the Tertiary basins of the Gulf of Mexico are re-processed
34
for attenuation analyses. From previous studies, only 75 percent of the hydrocarbon reservoirs
examined had reflections that exhibited anomalous frequency content that suggested an
attenuation mechanism. With the possibility of selecting sand reservoirs from AVO
environments in Class 3 to Class 1, a method to qualitatively defined potential reservoir
candidates for this study needs to be defined.
Fig. 18. Type log of the Thirtyone Formation. Note the contrasting log signature between the high-porosity microporous cherts and the encasing low-porosity limestones. (After Saller et al 2001).
D. Available Physical Model Data
We have two existing models related to our tasks. The first model is a 3D porous channel
that was designed to calibrate seismic attributes for time-lapse experiments. The channel model
is a sandstone analog built from sintered glass beads (10-mm thickness) and it has a synclinal
shape that gradually decreases in thickness near the edge of the model. It is a simple bifurcated
channel imbedded between two shale layers. The shale layers were modeled with two different
resins. These resins have a Poisson’s ratio of 0.38 and 0.39 for the layers above and the layer
below the channel respectively.
35
The second model represents a 3D fractured carbonate reservoir imbedded in clastic layers.
To simulate the anisotropic effects of a fracture swarm, glass microscope slide covers were used.
We placed three sets of 50 slides (0.5-mm thick) on edge in sets between two glass blocks. By
placing the slides end-to-end with the long edge down, long vertical fractures were simulated.
The sets were staggered to prevent the spaces between adjacent slide covers from aligning. This
assembly was embedded in resins to simulate the shale layers above and below the fractured
reservoir. The material properties of the glass blocks and the glass slide covers are very similar
and produce an anisotropic layer that simulates a vertically fractured carbonate.
V. Statement of Project Objectives
A. Objectives
The main objective of this project is the development and application of a new advanced
technology of hydrocarbon reservoir imaging supported by a frequency-dependent reflectivity
model. Based on this model, we will develop a methodology to determine the reservoir
properties using the frequency dependence of seismic reflections. Also, the low-frequency
asymptotic analytical solutions for seismic waves reflected from fluid-saturated layers will be
developed and validated. Scalability relations between field and laboratory model parameters
will be investigated. The new technology will be validated by processing field data provided by
industry partners and comparing the predicted fluid-saturation model to the one derived from
well data. Because of the wave-propagation theory is dependent on the seismic frequency
content, wide-angle processing of the seismic data will be incorporated.
36
B. Scope of Work
Recent experiments and specialized processing of seismic data, based on the theory of wave
propagation in a double-porosity double-permeability fluid-saturated medium, demonstrate that
the frequency dependence of seismic response can be used to not only provide high-resolution
hydrocarbon reservoir images, but also predict the reservoir and fluid properties. For prediction
of the reservoir and fluid properties, a low-frequency seismic response of the medium plays an
important role.
We propose to investigate the physical mechanisms that control low-frequency seismic
attenuation within the reservoir and frequency-dependent reflectivity of the reservoir zones. We
will evaluate and develop the principle concepts of wave propagation in porous, fluid-saturated
media taking into account the diffusion waves.
We propose to exploit both 3-D physical and numerical modeling approaches in the
Proposal. Allied Geophysical Laboratories at University of Houston have recently developed a
capability to construct physical models that incorporate heterogeneous, permeable zones, as well
as the capacity to inject different fluids and gasses into those zones. Recent developments in the
hardware and software controlling the seismic acquisition systems enable control of the
frequency of the signal transmitted through the model. 3-D numerical modeling will allow us to
evaluate whether some of the frequency-dependent reflection may be associated with the subtle
mode conversion and tunneling phenomena associated with thin bed reservoirs. The results of
two modeling approaches, using the same AVO and spectral decomposition analysis tools were
found to be successful in analyzing 3-D field data. By exploiting both these tools, we expect to
quantify the effects of liquid and gas hydrocarbon phases, as well as the effects of reservoir
geometry on seismic reflectivity at different frequencies.
37
The processing and interpretation of real seismic data for well-documented oil fields will be
an important part of our activity. Our processes will include the seismic interpretation of 3-D
seismic data, and the generation of the seismic attributes. We will integrate these data to build a
geologic reservoir model. The pre-stack seismic data will be processed to generate frequency-
dependent AVO attributes. These attributes will be calibrated against the geologic model and
reservoir parameters determined from petrophysical and engineering data, taking into account the
principle concepts of wave propagation in porous media, and the results of 3-D physical and
numerical modeling. We expect that by frequency-dependent AVO and low-frequency imaging
we will be able more accurately to predict fluid products and map fluid contacts and mobility.
C. Tasks
Theory development
Task 1. Develop the asymptotic model and governing equations describing the low-frequency
wave propagation in fluid-saturated porous and fractured rocks. Investigate the interaction
between the solid skeleton and the fluid at the transition between permeable and impermeable
zones.
Task 2. Describe the reflectivity equations that can be used in frequency-dependent seismic
imaging of reservoir properties for the cases of porous (micro porous) rock model, fractured rock
model, and double porosity – double permeability model and oblique angle of reflections.
Develop the computer codes for numerical modeling.
Task 3. Formulate the algorithms and develop computer codes for the frequency-dependent
seismic imaging and quantitative analysis of the frequency dependent images.
38
Physical modeling
Task 4. Utilize 3D isotropic porous physical model for investigation of wave attenuation within
porous material and frequency-dependent reflectivity of the porous model surfaces. Acquire
seismic data with wide frequency band (10-300 kHz) for different offsets over the model filled
with air, water, and glycerin.
Task 5. Utilize 3D anisotropic fractured physical model for investigation of wave attenuation
within fractured material and azimuth- and frequency-dependent reflectivity of the porous model
surfaces. Acquire seismic data with wide frequency band (10-300 kHz) for different azimuths
and offsets over the model filled with air, water, and glycerin.
Task 6. Analyze the attenuation and the frequency-dependent reflectivity for different angles and
azimuths of reflections. Verify the numerical modeling and the seismic imaging algorithms by
comparison with the physical modeling data.
Frequency-dependent seismic imaging
Task 7. Reprocess the existing 3D seismic data with preserved amplitudes and frequencies data
from intensely drilled West Texas and Gulf of Mexico fields. Estimate seismic attributes.
Task 8. Build the geologic models of (1) chert-turbidite (generally microporous) reservoir, (2)
carbonate (generally fractured) reservoir of the Devonian age and belonging to the Thirtyone
Formation of the Central Basin Platform in West Texas. Generate the frequency-dependent
seismic images of the reservoirs.
Task 9. Calibrate the frequency-dependent seismic attribute against the geologic models and
reservoir parameters determined from petrophysical and engineering data. Map fluid contacts
and permeability variation and/or production rate of hydrocarbons for the chert-turbidite
reservoir and the carbonate reservoir.
39
Task 10. Analyze conventional 3D across various GOM hydrocarbon fields from the Fairfield
database to develop a qualitative method of predicting reservoirs that are good candidates for
frequency-dependent reflections studies.
Task 11. Analyze the results. Submit papers for publications. Package reports, publications,
algorithms, and software in a digital format.
D. Milestones and Decision Points
Year 1 (10/2004 - 9/2005)
• Development of algorithms for low-frequency information extraction from seismic
data (UH, LBNL, 10/2004 - 02/2005).
• Development of asymptotic model and governing equations describing low-
frequency wave propagation in porous media (UCB, LBNL, 10/2004 - 02/2005).
• Tortuosity parameter evaluation for typical porous reservoir rocks (UCB, 10/2004 -
02/2005).
• Numerical and analytical analysis of dependence of reflection amplitudes on
tortuosity and formulation of correspondent imaging algorithms (UH, UCB, LBNL,
03/2005 - 09/2005).
• Formulation of reflectivity equations, development of algorithms and computer
codes for numerical modeling and frequency-dependent seismic imaging for porous
permeable layered medium (UCB, LBNL, UH, 03/2005 - 09/2005).
40
• Acquisition of seismic data with different observation system designs for the existing
3D porous channel physical model filled with different fluids (UH, 02/2005-
06/2005).
• Reprocessing of the existing 3D seismic data with preserved amplitudes and
frequencies. Estimation of the AVO and other seismic attributes (UH, 02/2005-
09/2005).
• Construction of the geologic models of the chert turbidite reservoir. Computation of
the frequency-dependent seismic images of the reservoirs (UH, 04/2005-09/2005).
• Analysis of the results. Preparation of the report (UH, UCB, LBNL, 08/2005-
09/2005).
Year 2 (10/2005 - 9/2006)
• Calibration of the frequency-dependent seismic attribute against the geologic models
of the chert turbidite reservoir. Mapping of the fluid contacts for the reservoir.
Progress of the computer codes for analysis of the frequency-dependent images.
(UH, UCB, LBNL, 10/2005-03/2006).
• Analysis of the frequency-dependent reflectivity for different angles of reflections.
Verification of the numerical modeling and the seismic imaging algorithms by
comparison with the physical modeling data (UH, UCB, LBNL, 10/2005-04/2006).
• Acquisition of seismic data with different observation system designs for the existing
3D fractured physical model filled with different fluids (UH, 02/2006-06/2006).
• Construction of the geologic models of the fractured carbonate reservoir. Estimation
of the frequency-dependent seismic images of the reservoir. Progress of the
frequency-dependent seismic imaging computer codes. (UH, 03/2006-09/2006)
41
• Analysis of the results. Preparation of the report and papers for publications. (UH,
UCB, LBNL, 07/2006-09/2006)
Year 3 (10/2006 - 9/2007)
• Development of asymptotic model describing low-frequency wave propagation in
double porosity – double permeability media. Formulation of reflectivity equations,
development algorithms and computer codes for numerical modeling and frequency-
dependent seismic imaging of double porosity – double permeability media (UCB,
LBNL, 10/2006-02/2007).
• Analyzing of the frequency-dependent reflectivity for different azimuths and angles
of reflections in double porosity – double permeability media. (UH, UCB, LBNL,
10/2006-02/2007).
• Extension of the previous results for the cases of purely fractured fluid-saturated
media. Verifying of the numerical modeling and the seismic imaging algorithms by
comparison with the physical modeling data (UH, UCB, LBNL, 10/2006-02/2007)..
• Calibration of the frequency-dependent seismic attribute against the geologic models
of the fractured carbonate reservoir. Mapping of the fluid contacts and permeability
variation and/or production rate of hydrocarbons for the fractured carbonate
reservoir. Analysis of the results, preparation of the papers and final report (UH,
UCB, LBNL, 03/2007-09/2007).
E. Deliverables
1. Low-frequency asymptotic formula for a reflection coefficient of seismic waves for
porous fluid saturated layer model (small angle oblique incidence).
42
2. Low-frequency asymptotic formula for a reflection coefficient of seismic waves for
porous fluid saturated half space model.
3. Low-frequency asymptotic formula for a reflection coefficient of seismic waves for
double-porosity-double permeability half space model.
4. Low-frequency asymptotic formula for a reflection coefficient of seismic waves for
double-porosity-double permeability layer model (small angle oblique incidence).
5. Algorithm of low-frequency component extraction from seismic data
6. Low-frequency fluid mobility imaging algorithm for porous layers and zero-offset
amplitude attribute.
7. Low-frequency fluid mobility imaging algorithm for fractured layers and zero-offset
amplitude attribute.
8. Low-frequency fluid mobility imaging algorithm for porous layers and AVO attribute.
9. Low-frequency fluid mobility imaging algorithm for fractured layers and AVO attribute.
Deliverables will be presented in form of annual reports, SEG Meeting talks and
professional papers.
F. Technical Transfer Plan
By the end of each year, a paper will be submitted to a peer-reviewed journal. The results will
be also reported at the annual Society of Exploration Geophysicists Meetings and will be
available on the web. The work on the project will be performed in a close contact with the
industrial partners: Shell Int. and Fairfield Industries. Upon completion of the project, a
workshop for all interested parties will be organized.
43
G. Budget Request
BUDGET Year 1 Year 2 Year 3
UH 141K 111K 58K
UCB 110K 110K 70K
LBNL 75K 75K 50K
Shell 70K 70K 70K
Fairfield 56K 56K 56K
Total 452K 422K 304K
Grand total: 1178K
University of Houston (UH), University of California at Berkeley (UCB) and Lawrence
Berkeley National Laboratory (LBNL) apply for DOE funding (total: 800K). Participation of
Shell and Fairfield Industries Inc. staff will be supported by the respective companies as
contribution to the project.
VI. References
Alishaev, M.G., 1974, Proceedings of Moscow Pedagogy Institute, 166–174.
Alishaev, M.G. and A. Kh. Mirzadzhanzadeh, 1975, On retardation phenomena in filtration
theory (in Russian), Neft i Gaz, no. 6, 71–74.
Barenblatt, G. I., Filtration of two nonmixing fluids in a homogeneous porous medium, Soviet
Academy Izvestia. Mechanics of Gas and Fluids (1971), no. 5, 857–864.
Barenblatt, G .I., Entov, V. M., and Ryzhik, V. M., 1990, Theory of Fluid Flows through Natural
Rocks: Dordrecht, Kluwer Academic Publishers.
44
Barenblatt G. I. and Vinnichenko, A. P., Non-equilibrium seepage of immiscible fluids,
Advances in Mechanics 3 (1980), no. 3, 35–50.
Barenblatt, G. I., Patzek, T. W., and Silin, D. B. 2003, The Mathematical Model of Non-
Equilibrium Effects in Water-Oil Displacement. SPE Journal, Dec, p. 409-416
Bear, J. Dynamics of fluids in porous media, Elsevier, N.Y., 1972.
Biot, M.A., 1956a, Theory of propagation of elastic waves in a fluid-saturated porous solid. I.
Higher frequency range: Journal of the Acoustical Society of America, v. 28, p. 179-191.
Biot, M.A., 1956b, Theory of propagation of elastic waves in a fluid-saturated porous solid. I.
Low-frequency range: Journal of the Acoustical Society of America, v. 28, p. 168-178.
Biot, M.A., 1962, Mechanics of deformation and acoustic propagation in porous media: Journal
of Applied Physics, v. 33, p. 1482-1498.
Castagna, J.P., Sun, S., and Siegfried, R. W., 2003, Instantaneous spectral analysis: detection of
low-frequency shadows associated with hydrocarbons: The Leading Edge, p. 120-127.
Daley, T.M., Feighner, M.A., and Majer, E.L., 2000, Monitoring Underground Gas Storage in a
Fractured Reservoir Using Yime-Lapse VSP: Berkeley CA, LBNL.
Darcy, H., 1856, Les fontaines de la ville se Dijon: Paris, Victor Dalmont.
Denneman, A. I. M., Grijkoningen, G. G., Smeuldres, D. M. J., and Wapenaar, K. 2002,
Reflection and transmission of waves at a fluid/porous medium interface, Geophysics, 67,
no. 1, 1777-1788
Dinariev O. Yu., and Nikolaev, O. V., 1990, On relaxation processes in low-permeability porous
materials, Eng. Phys. Journal 55, no. 1, 78–82.
Dutta, N. C. and Ode, H., 1979, Attenuation and dispersion of compressional-waves in fluid-
filled rocks with partial gas saturation (White model) - Part I: Biot theory, Geophysics 44,
no. 11, 1777–1788.
45
Dutta, N. C. and Ode, H., 1983, Seismic reflections from a gas-water contact, Geophysics 48, no.
02, 148–162.
Earlougher, R.C., 1977, Advances in Well Test Analysis: New York, Society of Petroleum
Engineers.
Gassmann, F., 1951, Uber die Elastizitat poroser Medien: Vier. Natur. Gesellschaft Zurich, v. 96,
p. 1-23.
Geertsma, J., and Smit, D. C., 1961, Some aspects of elastic wave propagation in fluid-saturated
porous solids. Gephysics, 26, no. 2, 169-181
Goloshubin, G.M., and Bakulin, A.V., 1998, Seismic reflectivity of a thin porous fluid-saturate
layer versus frequency, SEG Meeting.
Goloshubin, G.M., Daley, T.M., and Korneev, V.A., 2001, Seismic low-frequency effects in gas
reservoir monitoring VSP data, SEG Meeting: San Antonio, TX.
Goloshubin, G.M., and Korneev, V.A., 2000, Seismic low-frequency effects from fluid-saturated
reservoir, SEG Meeting: Calgary.
Goloshubin, G.M., V.A.Korneev, V.A., and Vingalov, V.M., 2002, Seismic low-frequency
effects from oil-saturated reservoir zones, SEG Meeting,: Salt Lake City.
Goloshubin, G.M., Verkhovsky, A.M., and Kaurov, V.V., 1996, Laboratory experiments of
seismic monitoring, 58th EAEG Meeting: Amsterdam.
Hilterman, F. and Van Schuyver, C., 2003, Seismic wide-angle processing to avoid NMO
stretch, 73rd SEG Meeting: Dallas.
Hubbert, M.K., 1940, The theory of ground-water motion, Journal of Geology 48, 785–943.
Hubbert, M.K., 1956, Darcy's law and the field equations of the flow of underground fluids:
Transactions AIME, v. 207, p. 222-239.
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Jin, G., Patzek, T. W., and D. B. Silin. SPE 83687: 2003, Physics-based reconstruction of
sedimentary rocks. In Proceedings of the SPE Western Regional/AAPG Pacific Section
Joint Meeting, Long Beach, CA, May 19–24,
Korneev, V.A., Goloshubin, G.M., Daley, T., and Silin, D. B. 2004, Seismic low-frequency
effects in monitoring of fluid saturated reservoirs: Geophysics, to appear.
Molokovich, Yu. M. 1987. Problems of filtration theory and mechanics of oil recovery
improvement (in Russian), Nauka, Moscow, 1987.
Molokovich, Yu. M., Neprimerov, N. N., Pikuza, B. I., and A. V. Shtanin, 1980, Relaxation
filtration (in Russian), Kazan University, Kazan.
Molotkov, L. N., 1999,On coefficients of pore tortuosity in an effenctive Biot model (in russian),
Transactions of St.-Petersburg branch of Steklov mathematical institute 257, 157–164.
Montgomery, S.L., 1998, Thirtyone Formation, Permian Basin, Texas: structural and lithologic
heterogeneity in a lower Devonian chert reservoir: AAPG Bulletin, 82, 1-24.
Muskat, M., 1937, The Flow of Homogeneous Fluids through Porous Media: McGraw-Hill, N.Y.
Patzek, T. W., 2001, Verification of a complete pore network model of drainage and imbibition.
Soc. Pet. Eng. J., 6(2):144–156.
Polubarinova-Kochina, P. Ya., 1962, Theory of Groundwater Movement. Princeton University
Press, Princeton, N. J.
Pride, S.R., and Berryman, J.G., 1998, Connecting theory to experiment in poroelasticity: J.
Mech. Phys. Solids, 46, p. 719-747.
Pride, S.R., and Berryman, J.G., 2003a, Linear dynamics of double-porosity dual-pemeability
materials. I. Governing equations and acoustic attenuation: Physics Review E, 68, no. 3
Pride, S.R., and Berryman, J.G., 2003b, Linear dynamics of double-porosity dual-pemeability
materials. II. Fluid transport equations: Physics Review E, 68, no. 3
47
Pride, S. R. Harris J. M., Johnson, D. L., Mateeva, A., Nihei, K. T., Noeack, R. L., Rector, J. W.,
Spelzler, H., Wu, R., Yamomoto, T Berryman, J. G., and Fehler, M. 2003, Permeability
dependence of seismic amplitudes, The Leading Edge (2003), 518--525
Ruppel S. C., and Barnaby, R.J., 2001, Contrasting styles of reservoir development in proximal
and distal chert facies: Devonian Thirtyone Formation, Texas; AAPG Bulletin, 85, 7-33.
Ruppel, S.C., and Hovorka, S.D., 1995, Controls on reservoir development in Devonian chert:
Permian Basin, Texas: AAPG Bulletin, 79, 1757-1785.
Saller, A., Ball, B., Robertson, S., PcPherson, B., Wene, C., Nims, R., and Gogas, J., 2001,
Reservoir characteristics of Devonian cherts and their control on oil recovery: Dollarhide
field, west Texas: AAPG Bulletin, 85, 35-50.
Santos, J. E., Corbero, J. M., Ravazzoli, C. L., and Hensley, J. L., 1992, Reflection and
transmission coefficients in fluid-saturated porous media. Journal of Acoustical Society of
America, 91, no. 1, 1911-1923.
Silin, D. B., Jin, G., and Patzek, T. W. SPE 84296: 2003a, Robust determination of the pore
space morphology in sedimentary rocks. In Proceedings of the SPE Annual Technical
Conference and Exhibition, Denver, CO, October 5–8.
Silin, D. B., Korneev, V. M., and Goloshubin, V. M., 2003b, Pressure diffusion waves in porous
media. 2003 Annual SEG Meeting, Dallas, TX, October 2003
Silin, D. B., Korneev, V. M., and Goloshubin, V. M., 2003c, Diffusion Waves in Seismology?
Eos Trans. AGU, 84(46), Abstract S22B-0454, 2003
Silin, D. B., Korneev, V. M., Goloshubin, V. M., and Patzek, T. W., 2004, A Hydrologic View
on Biot’s Theory of Poroelasticity. LBNL Report 54459
Silin, D.B. and. Patzek, T.W., On Barenblatt’s model of spontaneous countercurrent imbibition,
Transport in Porous Media 54 (2004), no. 3, 297–322.