Abstract
Hydraulic fracture modeling has progressed into a high impact decision-making tool for the unconventional petroleum industry. However, the main influence on the model results are the rock mechanical inputs, typically derived from field logs and supplemented by core measurements, and the uncertainty associated to these. The strongly layered nature of unconventional mudstones, however, requires representation of the high contrast in properties between layers, and their anisotropic elastic behavior. This investigation provides an integrated method for experimentally measuring elastic mechanical properties from new anisotropic ultrasonic measurements at sufficiently high resolution (cm scale) to honor the rock fabric along with triaxial compressional data on sample plugs. These results are analyzed, compared, and integrated using a newly developed methodology, based on St. Venant’s reduced symmetry approximation, to develop a continuous representation of the elastic properties and their associated uncertainties. For cases where core is not available, we provide a method to reconstruct anisotropic properties at cm resolution using standard resolution field logs and a borehole image log. A case study on a core from the Permian basin is presented and verified against a standard workflow. Additionally, the methodology to propagate from the cored well to nearby regions (e.g., formations above the cored interval) is demonstrated for cases where logs are available, but core data are not.
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Abbreviations
- \({C}_{ij}\) :
-
Stiffness tensor terms (Voigt notation)
- \({S}_{ij}\) :
-
Compliance tensor terms (Voigt notation)
- \({E}_{i}\) :
-
Young’s modulus
- \({\nu }_{ij}\) :
-
Poisson’s ratio
- \(\nu\) :
-
Poisson’s ratio—Saint Venant 3-term
- \({\nu }_{i}\) :
-
Poisson’s ratio—Saint Venant 4-term
- \({G}_{ij}\) :
-
Shear modulus
- \(\rho\) :
-
Density
- \({\sigma }_{i}\) :
-
Stress
- \({K}_{0}\) :
-
Horizontal to vertical stress ratio
- \({V}_{\mathrm{P}\mathrm{i}}\) :
-
P-wave velocity
- \({V}_{\mathrm{s}\mathrm{i}}\) :
-
S-wave velocity
- \({x}_{i}\) :
-
Model parameters (i = 1…N)
- \(m({x}_{i})\) :
-
Model results as function of x
- \(d\) :
-
Observed data (i = 1…N)
- \({\Sigma }\) :
-
Data covariance matrix
- \(L({x}_{i})\) :
-
Unnormalized log-likelihood
- \(|\psi |\) :
-
Structural constraint
- \(H\) :
-
Point spread function
- z :
-
Latent model parameters
- − 1 :
-
Matrix inverse
- T :
-
Transpose
- *:
-
Convolution
- U :
-
Left singular matrix
- V :
-
Right singular matrix
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Sassen, D., Abell, B. Characterizing Anisotropic Rocks Using a Modified St. Venant Method and High-Resolution Core Measurements with Extension to Field Logs. Rock Mech Rock Eng 55, 2949–2963 (2022). https://doi.org/10.1007/s00603-021-02531-x
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DOI: https://doi.org/10.1007/s00603-021-02531-x