ABSTRACT

Undulating wells are routinely drilled to improve reservoir exposure across hydrocarbon-bearing zones. Although conventional acoustic-log interpretation methods are reliable in vertical wells, they often yield inaccurate results when applied to high-angle or horizontal wells due to azimuthal asymmetry, spatial averaging effects, and wave-mode interference. Three-dimensional finite-difference and finite-element algorithms are typically used to quantify the aforementioned effects on acoustic logs, but they are extremely demanding on the central processing unit’s (CPU) time and memory. We develop a fast algorithm to simulate flexural slownesses acquired in high-angle wells using 3D linear spatial sensitivity functions. Spatial sensitivity functions quantify the variation of phase slowness measured by the sonic tool due to spatial perturbations of elastic properties. First, we construct 3D frequency-dependent sensitivity functions of flexural modes using the product of 1D axial, radial, and azimuthal sensitivity functions obtained from first-order approximations. Then, we simulate frequency-domain flexural logs acquired with wireline tools and dipole sources in isotropic and vertical transversely isotropic (VTI) formations penetrated by high-angle wells. For the examined examples, simulated flexural logs exhibit root-mean-square errors less than 0.4  μs/ft when compared with those calculated with a 3D time-domain finite-difference (3D-TDFD) algorithm. We found that in isotropic formations with layers thinner than the length of the receiver array, flexural slownesses acquired separately with cross dipoles are different because of geometric asymmetry, whereas in VTI formations we observed differences between cross-dipole slownesses because of effective anisotropy. Furthermore, the flexural logs are affected by spatial averaging introduced by the acoustic wireline tool, especially in the vicinity of layer boundaries. Three-dimensional sensitivity functions reduce the computation time of the flexural logs from an average of 15 h of CPU time per depth (using 3D-TDFD methods) to less than 3 min. The fast simulation algorithm disregards wave reflections, wave-mode conversion, and wave-mode interference occurring at layer boundaries.

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