## 5 Geomechanics
### Static and Dynamic Geomechanics  
Due to the impact of varying facies on geomechanical properties, the Vaca Muerta formation exhibits a wide range of values for both Young's modulus and Poisson's ratio. As illustrated in the following figure, Young's modulus varies from 1 to 8 GPa, while Poisson's ratio ranges from 0.18 to 0.38. This demonstrates significant heterogeneity within the formation (Figure 8).  
In a dynamically active tectonic environment, precise stress characterization is essential for optimizing hydraulic fracturing operations. Elevated treatment pressures in hydraulic  
Figure 8: Distribution of [PERSON]’s modulus and Poisson’s ratio in the Vaca Muerta formation. Reprinted with permission from Ref. [42]. Copyright 2014, Society of Petroleum Engineers.  
Figure 7: Logging data and variations in closure pressure/net pressure at various depths in Vaca Muerta, covering upper, middle, and Cocina sections. Reprinted with permission from Ref. [70]. Copyright 2018, Society of Petroleum Engineers.  
fracturing can induce additional rock rigidity and broaden the influence of stress shadows, thus necessitating meticulous stress state assessments for successful fracturing.  
[PERSON] et al. collected core samples from two boreholes in the Neuquen Basin, specifically targeting the Vaca Muerta formation, in order to conduct both static and dynamic rigidity evaluations. For static rigidity assessments, the rock specimens are subjected to creep conditions for an adequate duration to mitigate their influence on the resulting elastic metrics. These measurements are taken during both the loading and unloading stress phases at roughly a third of the peak deviatoric stress level. Traditional analyses employ a triaxial approach, utilizing horizontal, vertical, and 45-degree oriented samples from the same depth to compute all rigidity coefficients. Dynamic rigidity, on the other hand, is ascertained from P- and S-wave velocities in both the horizontal and vertical specimens and is also less susceptible to variations in confining pressures. In terms of dynamic rigidity, mudstones exhibit clear anisotropy, while andesites are nearly isotropic and display 30 to 60% greater rigidity than any mudstone.  
The examined rock categories include mudstone, calcareous mudstone--which has fluctuating carbonate levels and constitutes the bulk of the stratigraphic sequence--and andesite, a silica-rich igneous rock. The findings indicate that mudstones display anisotropy in both static and dynamic conditions, whereas andesites exhibit limited anisotropy but possess high rigidity. The static Young's modulus demonstrates considerable sensitivity to stress changes, with peak variations of +32% for mudstone, +38% for calcareous mudstone, and 31% for andesite as the confining pressure increases (Figure 9).  
The results of the dynamic testing indicate a strong correlation between stiffness and density, with andesite exhibiting greater values than calcareous mudstone, which in turn is greater than mudstone. In the same set of tests, differences between loading and unloading were observed. The Young's modulus values obtained during loading were found to be 50-75% of those obtained in dynamic conditions. The unloading values should be used for predicting the stress shadow during hydraulic fracturing, given the rapid nature of this process. Additionally, the ratio between unloading and loading is an important parameter for quantifying plastic deformation. Static results show that, for all samples, the ratio of [PERSON]'s modulus during horizontal unloading to loading is approximately 1.4. For vertical samples, the values for the two types of mudstone and and andesite are 2 and 1.3, respectively (Figure 10).  
Figure 9: Young’s modulus during loading and unloading vs. mass density in horizontally and vertically oriented samples. Reprinted with permission from Ref. [71]. Copyright 2014, Society of Petroleum Engineers.