1

Estimation of Fracture Porosity Using Azimuthal P-Wave AVO: A Case

Study in the Austin Chalk, Gonzales County, Texas

Abdullatif A. Al-Shuhail

King Fahd University of Petroleum and Mineral, Dhahran, Saudi Arabia

2

ABSTRACT

The fracture porosity (Φc) is an important property that needs to be known prior to

developing any naturally fractured reservoir. It is directly proportional to the anisotropic

AVO gradient (GA), which can be estimated from multiazimuthal seismic data. The

proportionality coefficient (D) depends on the properties of the fracture geometry, pore

fluid, and background medium. Although several parameters are needed to calculate D,

modeling shows that only three are important: the pore-fluid phase, P-wave/S-wave

velocity ratio (α/β), and the crack aspect ratio (a). The method is applied to estimate the

background fracture porosity in the Austin Chalk of Southeast Texas. Using the

multiazimuthal seismic data and well-log data, I calculate GA = 0.6008. For calculating

D, I use oil-water pore fluid, which is the main fluid actually produced in the study area.

Furthermore, I use the average reported values of α/β = 1.75 and a = 0.000675

commonly measured in the Austin Chalk; while I use average values for the other

insignificant properties. I calculate D = 276.6, which is used together with GA to estimate

a background Φc = 0.22%. This value lies within the range of fracture porosities

commonly measured in Austin Chalk cores.

KEY WORDS: azimuthal AVO, Austin Chalk, reservoir characterization, fracture

porosity

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INTRODUCTION

The properties of seismic waves are often affected by the presence of anisotropy

in the medium. The dominant alignment of vertical fractures in a reservoir induces

azimuthal anisotropy. A simple representation of azimuthal anisotropy is given by

horizontal transverse isotropy (HTI), where the medium has a single horizontal axis of

symmetry. Amplitudes at the top and bottom of the reservoir vary as a function of

azimuth as a result of the fractures. Ruger and Tsvankin (1997) presented expressions for

the AVO gradient of multiazimuthal P-wave seismic data using Thomsen’s (Thomsen,

1986) anisotropic parameters in HTI media. They used Shuey’s (1985) approximation of

Zoeppritz equations for the reflection coefficient and Hudson’s (1981) for the fracture

model. They found that at least three azimuths are needed to compute the fracture strike.

They emphasized also that using this method would give, ambiguously, two

perpendicular directions: the fracture strike and fracture symmetry axis. To distinguish

which of these two directions was the fracture strike, extra seismic or non-seismic data

was needed.

Al-Shuhail and Watkins (2000) developed this approach and applied it to estimate

quantitatively the principal fracture orientations in the Austin Chalk in Southeast Texas

using a multiazimuthal 2-D seismic dataset. The data was processed using a processing

sequence that preserved the relative change of amplitudes with offset and azimuth. The

AVO gradient, at every CDP, was calculated and the median of all AVO gradients for

CDPs in a line was used to represent the AVO gradient along the azimuth of that line.

Previous studies (Becker and Perelberg, 1986) showed that the overburden in the study

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area was isotropic. In addition, well-log data in the study area showed that the Austin

Chalk and its underlying Eagleford Shale were fairly homogeneous across the study area.

Therefore, any difference in the median AVO gradients was assumed to be due to the

azimuthal effect of fractures. The median AVO gradients of the lines and their

corresponding azimuths were used to solve for the fracture strike (ψ0) repeatedly using

three different lines at a time. The result was a set of solutions that clustered about two

principal directions, N60°E and S30°E. Since other data indicated the presence of

predominantly NE-SW trending fractures, in the subsurface, they concluded that the

N60°E direction was the predominant fracture strike in the study area. The objective of

this study is to describe a method for estimating the fracture porosity from

multiazimuthal seismic data. The method is applied then to estimate the background

fracture porosity in the Austin Chalk of Southeast Texas

AZIMUTHAL P-WAVE AVO IN HTI MEDIA

The P-P reflection coefficient R(θ,φ) in an HTI medium can be approximated as

(MacBeth, 2002; Ruger, 2002):

,sin)sin(),( 22

0 θφφθ AI GGRR ++= (1)

where θ is the incidence angle and φ is the azimuthal angle between the seismic line and

the fracture strike (Fig. 1). R0 is the isotropic normal incidence reflection coefficient or

AVO intercept, GI is the isotropic AVO gradient in the background (unfractured)

medium, and GA is the anisotropic AVO gradient due to the presence of fractures. The

total AVO gradient along the jth line (Gj) that has an azimuth of φj can be written as:

5

)(sinsin 0

22 ψψφ −+=+= jAIjAIj GGGGG . (2)

Three measurements G1, G2, and G3 along three different azimuths φ1, φ2, and φ3 can be

used to solve equation (2) uniquely for ψ0 (Al-Shuhail, 1998). Using this fracture strike,

GA is calculated through the following relation (Al-Shuhail, 1998):

)].(sin)(/[sin)( 01

2

02

2

12 ψψψψ −−−−= GGGA (3)

Therefore, with each calculation of ψ0, a new value of GA is calculated. The median of

these repeatedly estimated GA values is selected as GA in the location where the azimuthal

AVO analysis is carried out.

The anisotropic AVO gradient GA is related to Φc as:

cA DG Φ= , (4)

where D is a coefficient given by:

−−+

−−

−−=

)1)(1(

21

)1)(23(

42/3

0432/3

043 AaFAa

Dn ηηπ

ηηπ

η . (5)

The derivation of equations (4) and (5) as well as the definition of the parameters , A0,

and Fn are given in Appendix A. Therefore, if GA is estimated from multiazimuthal

seismic data and D is calculated from the properties of the background medium, pore

fluid, and fracture geometry; then, it is possible to invert equation (4) for the Φc. This

method is used here to estimate the background fracture porosity in the Austin Chalk.

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APPLICATION TO THE AUSTIN CHALK

Calculation of GA

The data used in this study consisted of eight 2-D seismic lines, well logs from

several vertical wells, and production data from many horizontal wells in the study area,

which is Gonzales County, Texas (Fig. 2). The azimuths and median AVO gradients of

the eight seismic lines are shown in Table 1. Combining these azimuths and median

AVO gradients three at a time gave 336 solutions for ψ0 and GA. The dominant fracture

strike (ψ0) was calculated by Al-Shuhail (1998) to be N60°E, while the median GA is

calculated here to be 4.8764. This median GA is used to estimate the background fracture

porosity after the scaling procedure described next.

Well logs are used to estimate the median densities and P-wave velocities in the

Austin Chalk and the underlying Eagleford Shale across the study area. These median

densities and velocities are used then to calculate the median normal incidence reflection

coefficient R0 at the interface between the Austin Chalk and Eagleford Shale where the

AVO analysis is carried out. Furthermore, because the seismic amplitudes are essentially

reflection coefficients amplified by the recording instruments, the computed value of GA

needs to be scaled to its original magnitude. The ratio between the median R0 computed

from the well logs and the median R0 computed from the seismic data is used to scale GA.

Table 2 shows the calculation of the scaling factor along with the median GA before and

after scaling.

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Estimation of D and ΦΦΦΦc

In order to estimate D from equation (5), information about the fracture geometry,

pore fluid, and background medium has to be determined. The fracture geometry

information is represented by A0 and a. Since the effect of A0 on D is relatively small

(Fig. 3), an average value of A0 = 0.2 is selected because this parameter has not been

estimated in the Austin Chalk. On the other hand, a has a remarkable inverse effect on D

(Fig. 4). Therefore, it has to be estimated from field data. Average crack apertures (c)

are 0.01 – 0.4 mm (Snyder and Craft, 1977; McKiernan, 1993), while average crack

lengths (d) are 30 – 50 cm (Wiltschko et al., 1991) giving aspect ratios (a = c / d) of

0.00002 – 0.00133. The average value of a = 0.000675 is selected for the calculation of

D.

The pore fluid information is contained in Fn, which depends on the density and

P-wave velocity of the fluid. The effect of pore-fluid properties on D is illustrated in Fig.

5. Changing the pore fluid from oil to water has a negligible effect on D, while replacing

the pore liquid with gas reduces D dramatically (MacBeth, 2000). This shows that the

pore-fluid phase (gas versus liquid) is important while the properties of the pore liquid

are insignificant. Therefore, pore-fluid phase has to be established from field data.

Indeed, production data from horizontal wells in the Austin Chalk of the study area

indicates that the major fluids produced are oil and water. This observation agrees with

the results obtained from core analysis (Snyder and Craft, 1977). Therefore, a liquid is

assumed as the pore-fluid phase. Since the properties of the pore liquid do not affect D

significantly, the specific values of these properties are assumed using common values

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for oil and water (Mavko et al., 1998). Specifically, the water saturation (Sw) is set to

20% with the rest being oil (So = 80%). The oil has a αο and ρο of 1,400 m/s and 0.75

gm/cm3, respectively, while the water has a αw and ρw of 1,600 m/s and 1.10 gm/cm

3,

respectively.

The properties of background medium that enter into the calculation of D are α/β,

α, and ρ. Fig. 5 shows that D has a relatively strong inverse relation with α/β, while Fig.

6 shows that both α and ρ have small effects on D. Therefore, of the three parameters

related to the background medium, only α/β has a significant effect on D. Hence,

α/β has to be determined from field data. Johnston (1986) measured α/β along the

isotropic plane of the Austin Chalk using VSP P- and S-wave measurements. He found

that α/β had a fairly constant value of 1.75. Since α/β along this plane essentially

represents that for the background unfractured Austin Chalk, I use it for calculating D.

For α and ρ in the background medium, I select the median values estimated from

vertical well logs namely α = 5,350 m/s and ρ= 2.60 gm/cm3. Inserting these values for

the parameters of fracture geometry, pore fluid, and background medium into equation

(5), I calculate D = 276.6. Using this value for D and GA = 0.6008, I use equation (4) to

calculate a background fracture porosity Φc = 0.2172% in the Austin Chalk in the study

area. This value lies within the range of average fracture porosities (0.10 – 0.25%)

commonly measured in the Austin Chalk cores (Snyder and Craft, 1977). It should be

noted that the fracture porosity value calculated here represents a background value

because the seismic lines do not intersect at a point. For lines that intersect at a point, the

procedure outlined here should estimate the fracture porosity at the intersection point.

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CONCLUSIONS

The fracture porosity (Φc) is an important parameter of any naturally fractured

reservoir because it determines the extent of fracturing in the reservoir. The anisotropic

AVO gradient (GA) is linearly related to Φc through a coefficient (D) that depends on the

properties of the fracture geometry, pore fluid, and background medium. If GA is

estimated from multiazimuthal seismic data and D from information about the relevant

reservoir parameters; then, it is possible to calculate Φc. In this study, I use this approach

to estimate the background Φc in the Austin Chalk of Southeast Texas. The data

consisted of eight 2-D, P-wave seismic lines, supported by production data from

horizontal wells and well logs from vertical wells. GA was estimated from the

multiazimuthal seismic data and scaled using well-log data. Using this procedure, I

estimated GA to be 0.6008.

To calculate D, I needed several parameters, some of which were not known in

the study area. However, modeling showed that only three parameters had significant

effects on D: the pore-fluid phase, P-wave/S-wave velocity ratio (α/β), and the crack

aspect ratio (a). The pore-fluid phase was determined from the production data to be

mainly oil with little water. a and α/β were determined from average values in the

Austin Chalk commonly reported in the literature, which were 0.000675 and 1.75,

respectively. The rest of the parameters were relatively insignificant and, therefore,

average values were assumed for these parameters. Using these values, D was calculated

to be 276.6 and the background Φc was estimated to be 0.2172%. This value lies within

the range of fracture porosities (0.1 – 0.25%) commonly measured in Austin Chalk cores.

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ACKNOWLEDGEMENT

I would like to thank KFUPM and the British Council for supporting this project.

I would like to thank also the Petroleum Engineering Department of Heriot-Watt

University in Edinburgh, UK for their help and support while I was working on this

project there.

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REFERENCES

Al-Shuhail A. A., 1998. Seismic characterization of fracture orientation in the Austin

Chalk using azimuthal P-wave AVO. Texas A&M University, College Station, 78 pp.

Al-Shuhail, A. A. and Watkins J. S., 2000. Using azimuthal P-wave AVO to

determine the principal fracture orientations in the Austin Chalk, Gonzales County,

Texas. Expanded Abstracts, 70th Ann. Internat. Mtg. SEG, Calgary: 206-209.

Becker, D. F., and Perelberg, A. I., 1986, Seismic detection of subsurface fractures.

Expanded Abstracts, 56th Ann. Internat. Mtg. SEG, Dallas: 466-468.

Hudson J. A., 1981. Wave speeds and attenuation of elastic waves in a material

containing cracks. Geophysical Journal of the Royal Astronomical Society, 64: 133-

150.

Johnston D. H., 1986. VSP detection of fracture-induced velocity anisotropy. Expanded

Abstracts, 56th Ann. Internat. Mtg. SEG, Dallas: 464-466.

MacBeth C., 2000. Using P-wave data to distinguish gas from water in fractures. In:

Ikelle, L. and Gangi, F. (Eds.), Anisotropy 2000 - Fractures, converted waves and

case studies, Open File Publications, No. 6, SEG: 223-237.

MacBeth, C., 2002. Multi-component VSP analysis for applied seismic anisotropy.

Pergamon Press, London.

McKiernan D. E., 1993. Extrapolation of fracture orientation and spacing in Austin

Chalk outcrops to corresponding petroleum reservoirs. Texas A&M University,

College Station.

Ruger, A., 2002. Reflection coefficients and azimuthal AVO analysis in anisotropic

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media. SEG, Tulsa.

Mavko, G., Mukerji, T. and Dvorkin, J., 1998. The rock physics handbook – tools for

seismic analysis in porous media. Cambridge University Press, Cambridge.

Shuey, R. T., 1985. A simplification of the Zoeppritz equations. Geophysics 50: 609-614.

Snyder, R. H. and Craft, M., 1977. Evaluation of Austin and Buda Formations from core

and fracture analysis. Gulf Coast Association of Geological Societies Transactions 27:

376-385.

Thomsen, L., 1986. Weak elastic anisotropy. Geophysics 51: 1954-1966.

Wiltschko, D. V., Corbett, K. P., Friedman, M. and Hung, J., 1991. Predicting fracture

connectivity and intensity within the Austin Chalk from outcrop fracture maps and

scanline data. Gulf Coast Association of Geological Societies Transactions 41: 702-

718.

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APPENDIX A

DERIVATION OF EQUATIONS (4) AND (5)

In equation (1), R0 is defined as:

),(2

10

ρρ

αα ∆+

∆=R (A-1)

and GI is defined as:

),2

(22 β

βρρ

ηαα ∆

+∆

−∆

=IG (A-2)

where α is the P-wave velocity, ρ is the density, β is the S-wave velocity, and η = (β/α)2.

In equations (A-1) and (A-2), ∆ represents the difference while a bar above represents the

average in a property across the interface. GA is defined as:

),( ntA eeG ζη −= (A-3)

where ζ =1-2η and en and et are the normal and tangential fracture compliances, which

are dimensionless scalars that depend on the fracture geometry, pore fluid, and properties

of the background medium. It should be noted here that η in equation (A-3) is estimated

in the background medium that contains the fractures.

The fracture model used here is a fracture with two surfaces that are pushed

together into welded contact except at a series of small, randomly distributed cracks. The

cracks are assumed to be thin oblate spheroidal in shape (MacBeth, 2002). Using this

model, the tangential compliance is given as:

,1 2/3

043 A

be tc

t −

Φ= (A-4)

where Φc is the total fracture porosity due to all cracks on that fracture surface. A0 is the

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fractional area of open space on the fracture surface (i.e., A0 = 0 indicates a completely

closed fracture). Typical values of A0 are 0.1, 0.2, and 0.3. bt is the tangential crack

factor, which is given by:

,)23(

4

ηπ −=a

bt (A-5)

where a is the average aspect ratio of the cracks. The normal compliance is:

,1 2/3

043 AbF

be

nn

ncn −+

Φ= (A-6)

where bn is the normal crack factor given by:

)1(

1

ηηπ −=a

bn , (A-7)

nF is the pore-fluid factor given by:

,2

2

ρα

αρ ff

nF =

(A-8)

and ρf and αf are the density and P-wave velocity of the fluid filling the cracks, while ρ

and α are the density and P-wave velocity of the background (unfractured) medium. In

the case of more than one fluid filling the cracks, the total normal compliance will be a

function of the individual normal compliances and their respective saturations, provided

that the fluids remain immiscible and each crack is filled with only one fluid (MacBeth,

2000).

Equation (A-3) can be rewritten to facilitate the calculation of Φc from GA as:

cA DG Φ= , (A-9)

where D is a coefficient that depends on the properties of the background medium, pore

fluid, and fracture geometry as:

15

−−+

−−

−−=

)1)(1(

21

)1)(23(

42/3

0432/3

043 AaFAa

Dn ηηπ

ηηπ

η . (A-10)

Equation (A-9) is equation (4) in the text, while equation (A-10) is equation (5) in the

text.

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FIGURE CAPTIONS

Fig. 1. A fractured HTI medium (an isotropic background medium with vertical aligned

fractures) overlain by an isotropic medium. The seismic line has an azimuth φ with the fracture strike. Also shown is a vertical plane containing the seismic line and an incident

ray that has an incidence angle θ. On the seismic line, S stands for the source and R for the receiver.

Fig. 2. Seismic lines (represented by line segments and one-letter names) and vertical

well-log locations (represented by diamonds and two-letter names) that were used in the

study. Contours indicate the estimated ultimate recovery (EUR) of oil from horizontal

wells in the Austin Chalk (Al-Shuhail, 1998).

Fig. 3. Effect of A0 on D (a = 0.001, α/β = 1.75, α = 5,350 m/s, ρ = 2.60 gm/cm3, So = 100%, αo = 1,400 m/s, ρ o = 0.75 gm/cm3).

Fig. 4. Effect of a on D (A0 = 0.2, α/β = 1.75, α = 5,350 m/s, ρ = 2.60 gm/cm3, So = 100%, αo = 1,400 m/s, ρ o = 0.75 gm/cm3).

Fig. 5. Effect of pore fluid on D (A0 = 0.2, a = 0.001, α = 5,350 m/s, ρ = 2.60 gm/cm3, αg = 500 m/s, ρg = 0.10 gm/cm3, αo = 1,400 m/s, ρ o = 0.75 gm/cm3, αw = 1,600 m/s, ρ w = 1.10 gm/cm3). Curves are for full saturation with a single pore fluid.

Fig. 6. Effects of ρ and α of the background medium on D (A0 = 0.2, a = 0.001, α/β = 1.75, So = 100%, αo = 1,400 m/s, ρ o = 0.75 gm/cm3).

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LIST OF TABLES

Table 1. Line azimuth (φj), median AVO intercept (R0j), and median total AVO gradient (Gj) for each of the seismic lines used in the solution for ψ0 and GA.

Table 2. Calculation of the scaling factor used to scale the median GA estimated from the

seismic data.

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Fig. 1. (Al-Shuhail)

Fracture strike

Seismic line

θθθθ

S R

HTI

medium

φφφφ

Isotropic

medium

Fractures

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Table 1. (Al-Shuhail)

Line (j) Azimuth (φφφφj) R0j Gj

C-13 N15E -2.8839 6.5642

C-14 S70E -2.5676 3.9978

C-15 S73E -2.1905 3.6715

C-16 S56E -4.6384 6.6121

C-7 S73E -2.6185 -0.1316

C-8 S60E -2.3792 0.8722

C-802 N2E -3.4209 5.1065

N-2 S70E -5.8226 4.1889

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Bastrop Co.

Gonzales Co.

EUR (1,000 BBL)

DF-1

KL-2

KY-1KR-2

JM-1

CK-1

C-8

C-7

C-13C-14

C-15

C-802

C-16

N-2

KL-1GS-1RL-1

GS-2

NN-3TR-1TR-1A

50

150

250

350

100

200

300

400

Fig. 2. (Al-Shuhail)

W97 °° °° 5

2’ 30”

W97 °° °° 7

’ 30”

N29°°°° 7’ 30”

N29°°°° 52’ 30”

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Table 2. (Al-Shuhail)

Parameter Value

Median R0 (calculated from well logs) -0.3390

Median R0 (calculated from seismic data) -2.7512

Median R0 (calculated from well logs)

Scaling factor =

Median R0 (calculated from seismic data)

0.1232

Median GA (calculated from seismic data – before scaling) 4.8764

Median GA (calculated from seismic data – after scaling) 0.6008

22

100

150

200

0.1 0.2 0.3

A 0

D

Fig. 3. (Al-Shuhail)

23

10

100

1000

10000

0.0001 0.001 0.01a

D

Fig. 4. (Al-Shuhail)

24

-250

-200

-150

-100

-50

0

50

100

150

200

250

1.5 1.8 2.1 2.4 2.7 3.0

α/βα/βα/βα/β

D

Gas

Oil

Water

Fig. 5. (Al-Shuhail)

25

Fig. 6. (Al-Shuhail)

170

175

180

185

190

D

1000 2000 3000 4000 5000

αααα (m/s)

6000 7000 8000

2.0 2.2 2.4 2.6 2.8 3.0

ρρρρ (gm/cm 3 )