Anisotropic Poroelastic Modelling of Depletion-Induced Pore Pressure Changes in Valhall Overburden

Abstract

Stress and pore pressure changes due to depletion of or injection into a reservoir are key elements in stability analysis of overburden shales. However, the undrained pore pressure response in shales is often neglected but needs to be considered because of their low permeability. Due to the anisotropic nature of shales, the orientation of both rock and stresses should be considered. To account for misalignment of the medium and the stress tensor, we used anisotropic poroelasticity theory to derive an angle-dependent expression for the pore pressure changes in transversely isotropic media under true-triaxial stress conditions. We experimentally estimated poroelastic pore pressure parameters of a shale from the Lista formation at the Valhall field. We combined the experimental results with finite element modelling to estimate the pore pressure development in the Valhall overburden over a period of nearly 40 years. The results indicate non-negligible pore pressure changes several hundred meters above the reservoir, as well as significant differences between pore pressure and effective stress estimates obtained using isotropic and anisotropic pore pressure parameters. We formulate a simple model approximating the undrained pore pressure response in low permeable overburden. Our results suggest that in the proximity of the reservoir the amplitude of the undrained pore pressure changes may be comparable to effective stresses. Combined with the findings of joint analysis of locations of casing deformation and total and effective stresses, the results suggest that pore pressure modelling may become an important element of casing collapse and caprock failure risk analysis and mitigation.

Third‐order elasticity of transversely isotropic field shales

“…This indicates a globally optimized set of TOE coefficients. For D shale, we bootstrapped the inversion of the TI TOE coefficients by using subsets of experimental data including only two stress paths, resulting in six subsets, as also discussed by Duda et al (2020) with a hexagonal TOE model. Except for the subset that included the isotropic stress path and the uniaxial-strain path, all bootstrapped TOE coefficients remained within the 95% confidence interval obtained in the complete inversion.…”

“…This preservation technique enables the cores to be stored for a long time while retaining their suitability for subsequent testing, as it minimizes the loss of pore fluid that would otherwise cause irreversible damage to the shales. The experimental data from these shales are also discussed by Bakk, Holt, Bauer et al (2020 and Duda et al (2020). The key characteristics of the shales are summarized in Table 1.…”

“…By minimizing the sum of square deviations between the predicted group velocities and the measured group velocities, 𝐶 13 was determined (Duda et al, 2020). The theory involved in this routine is valid for arbitrary (not just weak) TI anisotropy.…”

“…This model has been cali-brated to ultrasonic data obtained from different lithologies (Prioul & Lebrat, 2004; and has been utilized to predict the seismic response (Asaka, 2023;Herwanger & Koutsabeloulis, 2011;MacBeth et al, 2018). Apart from Duda et al (2020) and Bakk, Holt, Duda et al (2020), who studied a model with hexagonal symmetry of the TOE tensor, restricted to isotropic horizontal strains, only isotropic TOE tensors have been employed in the modelling of sedimentary rocks (Asaka, 2023;Donald & Prioul, 2015;Prioul & Lebrat, 2004;Rasolofosaon, 1998;Sarkar et al, 2003;Sinha & Kostek, 1996;Winkler & Liu, 1996). To our knowledge, a transversely isotropic (TI) symmetric TOE tensor has not been previously proposed for any application.…”

The Anisotropic Behavior of a Clay Shale: Strength, Hydro‐Mechanical Couplings and Failure Processes

“…For shales and similar rocks, many laboratory studies have investigated the anisotropic mechanical and hydro‐mechanical properties including the elastic constants (e.g., Kim et al., 2012; Sarout et al., 2017), the poroelastic behavior (Duda et al., 2021; Horsrud et al., 1998; Islam & Skalle, 2013), and the compressive shear strength (Ambrose et al., 2014; Attewell & Sandford, 1974; Bonnelye et al., 2017b; Chenevert & Gatlin, 1965; Horsrud et al., 1998; Ibanez & Kronenberg, 1993; Islam & Skalle, 2013; McLamore & Gray, 1967; Minardi et al., 2021; Niandou et al., 1997; Wild & Amann, 2018a). Many previous studies conducted uniaxial compressive and indirect tensile strength tests under various loading configurations (e.g., Ajalloeian & Lashkaripour, 2000; Cho et al., 2012; Debecker & Vervoort, 2009; Karakul et al., 2010) and have shown that rocks exhibit strength anisotropies.…”