PARALLEL NUMERICAL SIMULATION OF SONIC LOGGING IN ANISOTROPIC VISCOELASTIC MEDIA

Abstract eng:
The key objective of acoustic logging is to receive detailed knowledge on mechanical properties of adjacent rocks based on the measurement of a wave field generated by a downhole source. The simplest statement of this problem (borehole within homogenous elastic medium) was studied at the first time in (Biot 1952). Thereafter, many authors made contributions to analysis of this problem. However, to present time there is a lack of a comprehensive description of sonic wave fields for realistic 3D heterogeneous media with anisotropy and attenuation. Meanwhile, from the practical application viewpoint these features are of particular importance nowadays. It is worth mentioning that advanced high performance computers available today make it possible to proceed to the study of complete wave fields which are generated during acoustic logging for mentioned above 3D heterogeneous media with realistic mechanical properties such as anisotropy and attenuation. Note, that anisotropy is rather wide-spread property of a reservoir as it may be caused by thin-layering (Backus 1962) or systems of oriented fractures (Berryman 2008), (Grechka and Kachanov 2006), (Hudson 1980), while attenuation may indicate fluid saturation and a type of fluid. We present a new approach to finite difference simulation of sonic log for anisotropic viscoelastic media on the base of Lebedev scheme in cylindrical coordinates. In order to deal with an elastic anisotropic medium with attenuation one needs to construct a model for the first of all. In our study we follow (Crampin 1981) and consider the stiffness tensor being complex-valued in phase space,where real part of the tensor defines propagation while the imaginary one entries correspond to attenuation of wavesgoverned by a model. This representation is easy to treat and allows constructing a generalized standard linear solid model or GSLS (Christensen 1982) which is actually the most widely-used one for simulation of waves in viscoelastic media. On the other hand the correspondence between the complex-valued tensor and a quality factor (attenuation) of a particular wave is not trivial for anisotropic media, see (Zhu and Tsvankin 2006) and (Vavrycuk 2008). At the same time the common way to define media with attenuation is by means of quality factors as they are available for measurements. Because of this reason we construct an algorithm to compute the tensor from measured data – quality factors of particular waves along particular directions, see (Lys et al. 2008) for the details.

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