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Journal of Applied Geophysics 44 2000 103–113 www.elsevier.nlrlocaterjappgeo
Predicting the transport properties of fractured rocks from seismic information: numerical experiments
Fred Kofi Boadu
Department of CiÕil and EnÕironmental Engineering, Duke UniÕersity, P.O. Box 90287, Durham, NC 27708-0287, USA Received 15 June 1998; accepted 21 May 1999
Abstract
The hydraulic properties including porosity and permeability of fractured rock masses are estimated from seismic velocities derived from controlled numerical experiments. Models of fractured media are developed to represent fractures
embedded in an otherwise intact rock. Fracture porosity and permeability are computed using a hydraulic model that accounts for fracture length, aperture and orientation. Seismic attributes are used as a guide to detect the onset of reflections
from the fractured medium. Seismic velocities of the fractured layers are computed from the transit times of seismic waves propagating through the layer. The study shows that the velocity ratio between the fractured and the intact rock correlates
with the hydraulic properties. Low velocity ratios are associated with high fracture porosity and permeability. Empirical least-squares regression relationships are developed to describe the correlations for practical use. q 2000 Elsevier Science
B.V. All rights reserved.
Keywords: Fractured medium; Seismic velocities; Porosity; Permeability
1. Introduction
Most rocks in the earth’s crust are fractured to some extent in response to tectonic and other
in situ stresses. These fractures are pervasive and range in size from microcracks to crustal
faults. In civil engineering, geotechnical, hydro- geological and geo-environmental practice, frac-
tures play a central role. They enhance porosity and permeability and thereby increase the reten-
Tel.: q1-919-660-5432;
fax: q1-919-660-5219;
E-mail: boaduakoto.egr.duke.edu
tional and production capabilities of a reservoir or an aquifer. Fractures can control the transport
of contaminants in the subsurface and therefore characterizing them is vital in remediation
strategies. Retentional and fluid flow properties of fractured aquifers are of enormous concern in
remediation efforts. The stability of the founda- tion of engineered structures and excavations
are degraded when fractures are present in the subsurface. Fractured reservoirs with large re-
serves of hydrocarbons exist throughout the
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world Van Golf-Racht, 1982 . Thus, presently in the hydrocarbon and environmental industry,
fracture-related fluid flow imposes increasing challenges to reservoir and site characterization.
0926-9851r00r - see front matter q 2000 Elsevier Science B.V. All rights reserved. Ž
. PII: S 0 9 2 6 - 9 8 5 1 9 9 0 0 0 2 0 - 8
Oil exploration and exploitation efforts are in recent times being redirected toward fractured
reservoirs. Though the transport properties and the productive capabilities of fluid filled reser-
voirs are undoubtedly influenced by fractures, quantification of fracture systems remains a
formidable task. The hydraulic properties are normally measured through localized and ex-
pensive operations such as borehole drilling and fluid flow experiments. It is of utmost impor-
tance to develop cost-effective techniques to characterize fractures quantitatively, and relate
these characteristics to the production capabili- ties of the reservoir.
An important question that often arises and remains unsolved is: How can fractures that are
significant in controlling the transport or reten- tion of fluids in the subsurface be identified,
located and characterized? A relatively inexpen- sive way to characterize a fractured reservoir
remotely and on a much larger volume or scale is through the use of geophysics specifically
seismic methods. The question addressed here is: Can we relate the non-invasively and easily
measured seismic parameters to hydraulic prop- erties of fractured media? Information about
fracture porosity and permeability obtained re- motely would be particularly useful to engineers
and hydrogeologists involved in assessment of production and transport potential of aquifers
and development of remediation strategies. It would be an important development if informa-
tion about the transport properties of a fractured reservoir can be obtained from seismic data.
The same parameters that contribute to the vari- ations in hydraulic properties such as effective
permeability or discharge also contribute to the variations in seismic velocity and attenuation
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. Cook, 1992 .
The elastic and hydraulic parameters as well as the travel times and amplitudes of seismic
waveforms propagating through such fractured Ž
medium are modified Walsh and Grosenbaugh, 1974; Goodman, 1976; Brown and Scholz,
. 1986 . Generally, the effect of fractures on seis-
mic wave velocities is modeled by deriving the effective elastic moduli of the fractured rock
mass and subsequently relating these moduli to the velocities via the elastodynamic equations.
For relatively large, sparsely distributed frac- tures, the effective moduli approach to calculat-
Ž ing velocities may not be appropriate Pyrak-
. Nolte et al., 1990 . Furthermore, this approach
cannot account for the effect of fractures on seismic wave attenuation. For seismic measure-
ments to be useful in characterizing the mechan- ical and transport properties, a physical model
that describes the geometric properties of the fracture which incorporates the dynamics of the
fracture upon interaction with a seismic wave is needed.
An alternative, more versatile model, for de- scribing the effect fractures have on both seis-
mic velocity and attenuation is the displacement discontinuity model. The basic premise of this
model is that the displacement of seismic waves that propagate across a fracture becomes discon-
tinuous while the stresses are continuous. The displacement discontinuity concept is originally
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due to Mindlin 1960 and first applied to seis- Ž
. mic wave propagation by Schoenberg 1980 .
Several experimental studies have confirmed this Ž
model Lutsh, 1959; Morris et al., 1964; Pyrak- Nolte et al., 1987; Pyrak-Nolte et al., 1990;
. Cook, 1992 . The modified displacement dis-
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continuity model MDD developed by Boadu Ž
. Ž
. 1997a; b and Boadu and Long 1996 includes
the fracture size, fraction of surface area in contact, viscosity of infilling material and the
fracture aperture. This advancement is achieved by incorporating the dynamics of the fracture
into the equations of motion and exploiting the analogy between electrical properties and me-
chanical properties to obtain the reflection Ž
. scattering and transmission coefficients. The
MDD model has been substantiated with experi- mental data and compared with existing models
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in Boadu 1997a; b and Boadu and Long 1996 . The intent of this study is to explore the
relationship between seismic velocity and the permeability and porosity of fractured media
through numerical experiments. These experi-
ments would provide the theoretical base neces- sary for field scale interpretation of relations
between seismic and hydraulic parameters.
2. Theoretical formulations
