We have recently developed an inverse method to infer anisotropic fracture geometry from disparate geophysical measurements by combining forward models for fracture properties with a maximum entropy inversion criterion. We have tested and verified the resulting procedure for robustness and internal consistency by using idealized cases and photographic image data from natural fracture networks.
Flow and transport of fluids through fractured rock is of primary importance for oil and gas exploration and development, environmental analysis and remediation, and many aspects of geotechnical engineering. Improvements in our ability to extract information about fracture system characteristics from geophysical measurements and in the ability to use that information for prediction would be widely useful.
In theory, fractures are detectable by remote means due to their effects on geophysical properties. For example, the high compressibility of fractures and the anisotropic and heterogeneous character of their geometry give rise to strong anisotropy and spatial heterogeneity of seismic velocities. Similarly, fracture systems can have a profound influence on directional permeabilities and electrical conductivities.
In the context of this problem, forward modeling is the process of predicting measured values from knowledge of the distribution of fracture lengths, orientations, apertures, etc; inverse modeling is the process of inferring the nature of the fracture system from its effect on observables. We have developed both forward and inverse modeling algorithms as well as software to examine the connection between fracture systems and several important types of geophysical measurements (in particular permeability, electrical conductivity, and elastic wave speed and polarization). Due to space limitations we discuss only the connections among fracture geometry, fluid permeability, and electrical conductivity in this paper.
Our forward modeling is based upon an elegant and extensive body of theory by M. Oda and his coworkers. In previous work, we have extended these models to include the dependence of fracture aperture and thus fracture permeability on changes in either tectonic stress or pore pressure (Brown & Bruhn 1998) and to relate electrical conductivity to fracture geometry (Tripp et al. 1999). Our inverse modeling is based upon the application of geophysical inverse theory, a rich and well-developed body of work (e.g. Parker 1995), to this suite of forward models. Inverse modeling proceeds by repeated forward computations and thus is based entirely upon the physical theory incorporated in the forward modeling.
In the following, we present the details of our forward and inverse fracture modeling technique in more detail. We then discuss an example test of the algorithm with photographic image data from a natural fracture network.