Advanced reservoir imaging using frequency-dependent seismic attributes

8/14/2019 Advanced reservoir imaging using frequency-dependent seismic attributes

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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
mailto:[email protected]://www.geosc.uh.edu/people/faculty/hilterman/index.htmlmailto:[email protected]://petroleum.berkeley.edu/patzek/index.htmhttp://petroleum.berkeley.edu/patzek/index.htmmailto:[email protected]://www.geosc.uh.edu/people/faculty/hilterman/index.htmlmailto:[email protected]


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Advanced reservoir imaging using frequency-dependent seismic

attributes

Abstract 3

I. Introduction 4A. Benefits

II. State of Art 6A. Physical Modeling

B. Field Verification

C. Theoretical analysis

III. Proposed Technology 17

A. Frequency Dependent ReflectivityB. Frequency Dependent ReflectivityIssues

C. Frequency Preservation Processing

D. Frequency Preservation Issues

IV. Project Management and Facilities 29A. Management and PersonnelB. Available Equipment and Resources

C. Available Oil-Industry Data

D. Available Physical Laboratory Models

V. Statement of Project Objectives 35A. ObjectivesB. Scope of Work

C. Tasks

Theory developmentPhysical modeling

Frequency-dependent seismic imaging

D. Milestones and decision pointsYear 1

Year 2

Year 3

E. DeliverablesF. 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

S

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 (


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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 resultspredictedthe 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 ofQ 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 ofQ, as well as a

very distinctive decrease ofQ 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 20

u u u uv

t t x t x

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

and 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 t = % , k k i= +% (2)


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where is the angular frequency, and

vs

q = ,

qk

v

= (3)

are the attenuation coefficient and the wave number, respectively. Calculations yield

2

2

1 1

2 4 2

s vq s

= + +

,

2 2

4 2

1

2

vs

v 2

+=

+(4)

At low frequencies, i.e., for 0 one gets

2v

= = and

1

2 2

kQ

= = (5)

The apparent Q depends on frequency as / 2Q = . A comparison between the theoretical

results and the ultrasonic measurements ofQ is presented in Fig. 7. The corresponding values of

the attenuation parameters in the air-saturated case were estimated as 12000 = Hz and 0.3 =

, whereas in the water-saturated case, the result was2/m s 24000 = Hz and 1.0 = .

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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a

b

Tapering windows for selectionof 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 50

Frequency [Hz]

0.0

0.5

1.0

1.5

2.0

Reflectionamplutude97/96ratios Target layer reflections

Deeper layer reflections

10 20 30 40 50

Frequency [Hz]

-4

0

4

8

12

16

Relative97-96traveltimedelay[ms]

Target layer reflections

Deeper layer reflections

a b

Fig. 10. Thereflection 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 thetarget 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 tdenote 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 u

t t x

+ =

2

p

x

(6)

Here p and are the pressure and the density of the fluid, and is the bulk density of the

fluid-saturated medium,

b

(1 )b g f f = + = + where is the porosity and g 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 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 tou

W

t

.

To characterize fluid flow relative to the skeleton, we apply a dynamic version of Darcys

law. Darcys law was originally established for steady-state flow (Darcy, 1856). To account for

inertial and non-equilibrium effects in transient flow, we replace Darcys law with a relationship


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WW

t x

+ =

(7)

where is a characteristic redistribution time, is the permeability of the rock, is the

viscosity of the fluid, and is the flow potential (Hubbert, 1940, 1956). Such a modification of

Darcys 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

and compressibility f . Dimensional

considerations suggest that 2(fF L )/ , 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 Biots wave equations, the time

F

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

2f

W pW

t x

u

t

+ =

(8)

Finally, mass conservation can be expressed in the following way:

2

1 (1 ) (1 )gs

f gf

u p W

x t t

x

+ + + =

(9)


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Here, gs and gf 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

Biots 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

. Note, that within a reasonable range of rock and fluid properties, the dimensionless

parameter b

=

is small at low (below 1 kHz) seismic frequencies. If we consider the

reflection of a wave of angular frequency from the planar boundary between dry and fluid-

saturated elastic media, then the asymptotic (with respect to ) expression of the reflection

coefficientR has the following form:

( )0 1 1bR R R i

= + +

(10)

HereR1 andR2 are real coefficients and i is the imaginary unit. The coefficients R1 andR2 are

dimensionless functions of the mechanical properties of the fluid and rock, which include the

porosity, the densities, and the elastic coefficients. At 0 = the absolute value of the reflection

coefficient attains its low-frequency maximum. If the relaxation time is large, i.e., > 1/ , then

scaling relationship (10) must be replaced with

10bR R R i

= +

(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). Arock/fluid classification bythe 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 anddifferent 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 (/)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 Cwhich 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).

5 04 00 0 5 06 00 0 5 08 00 0 5 10 00 0 5 12 00 0 5 14 00 0 5 16 00 0 5 18 00 0 5 20 00 0

692000

694000

696000

698000

700000

702000

704000

5

15

25

35

45

55

65

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 theproductivity of an oil field.

The double porositydouble 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.


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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 porositydouble 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. Biots 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.


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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 doesnt 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.


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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. Datawere flattened to top of structure. (Bottom) Conventional 35-50 angle stack of high-amplitude structuredisplayed 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.


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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
http://www.geosc.uh.edu/info/research/research.htmhttp://www.geosc.uh.edu/info/research/research.htm


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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
http://www.geosc.uh.edu/people/faculty/hilterman/index.htmlhttp://www.geosc.uh.edu/people/faculty/hilterman/index.html


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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.
http://www.geosc.uh.edu/info/research/research.htm#computationalhttp://www.agl.uh.edu/research_fac.shtml#Laboratoryhttp://www.agl.uh.edu/research_fac.shtml#Laboratoryhttp://www.agl.uh.edu/research_fac.shtml#Laboratoryhttp://www.agl.uh.edu/research_fac.shtml#Laboratoryhttp://www.geosc.uh.edu/info/research/research.htm#computational


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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


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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


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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 Poissons ratio of 0.38 and 0.39 for the layers above and the layer

below the channel respectively.


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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.


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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.


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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.


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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).


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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)


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2. Low-frequency asymptotic formula for a reflection coefficient of seismic waves for

porous fluid saturated half space model.


double-porosity-double permeability half space model.


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.


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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, 166174.

Alishaev, M.G. and A. Kh. Mirzadzhanzadeh, 1975, On retardation phenomena in filtration

theory (in Russian), Neft i Gaz, no. 6, 7174.

Barenblatt, G. I., Filtration of two nonmixing fluids in a homogeneous porous medium, Soviet

Academy Izvestia. Mechanics of Gas and Fluids (1971), no. 5, 857864.

Barenblatt, G .I., Entov, V. M., and Ryzhik, V. M., 1990, Theory of Fluid Flows through Natural

Rocks: Dordrecht, Kluwer Academic Publishers.


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Barenblatt G. I. and Vinnichenko, A. P., Non-equilibrium seepage of immiscible fluids,

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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

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Daley, T.M., Feighner, M.A., and Majer, E.L., 2000, Monitoring Underground Gas Storage in a

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Dutta, N. C. and Ode, H., 1983, Seismic reflections from a gas-water contact, Geophysics 48, no.

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Advanced reservoir imaging using frequency-dependent seismic attributes

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