A constitutive model that couples elastic-plastic and damage theories is developed to predict the mechanical behavior of a shale from the Mont Terri rock laboratory (Opalinus Clay). The framework of continuum damage mechanics allows to predict the degradation of the elastic parameters with strains, while the coupling with plasticity correctly reproduces the irreversible strains typical of hard clayey materials. The yield surfaces (one for damage and one for plasticity) are postulated and the evolution equations of the internal variables are derived throughout the application of normality rule. Thermodynamic consistency of the model is investigated. The plastic behavior is described with a non-linear strain hardening function and is coupled with an isotropic damage model suitable for brittle and quasi-brittle geomaterials. The model is integrated with an implicit scheme that guarantees convergence and accuracy. Numerical simulations carried out with the proposed model in triaxial conditions well reproduced observed behavior from experiments.
Permeability evolution in intact rock as a result of micro-crack propagation is fundamental in understanding fluid flow within the excavation damage zone (EDZ) around underground openings. A 2D grain-based discrete element method incorporating Voronoi joint model is used to simulate the permeability evolution with progressive damage in intact rock when it is subjected to incremental mechanical loading. The rock response during uniaxial and triaxial loadings is simulated with and without taking into account the hydro-mechanical interactions between fluid and solid part of the rock. The numerical experiment results show that when modeling the rock behavior under compression, ignoring the coupled damage-flow processes results in an inaccurate prediction of mechanical properties of rock such as the peak strength and the post-peak response. The stress-strain response of the sample indicates that an increase in the applied confining stresses increases both the strain hardening range and the peak strength. In addition, the Permeability of models during triaxial loading increases by up to 2.5 orders of magnitude prior to rupture of rock. Progressive development of fractures as a result of crack accumulation leads to over 3 orders of magnitude increase in post-failure permeability compared to the permeability at the peak stress. These changes have been reported from laboratory testing results as well as in-situ permeability measurements carried out in the damaged zones in tunnel boundary. It has been demonstrated that Voronoi joint model incorporated in a DEM-based code has capability to simulate stress-induced permeability change in the brittle rocks as a result of processes such as initiation, propagation, and accumulation of cracks.
The present work initially presents an overview and the theoretical background of the Material Point Method (MPM) and details of its numerical implementation for coupled fluid-mechanical problems. This method is particularly useful when analyzing large strain problems in solid/fluid media including coupled problems, in particular, for geomechanical and geological media. The method possesses both Eulerian and Lagrangian characteristics which makes it suitable for the solution of a number of problems especially when compared to the usual techniques such as the Finite Element Method (FEM). Using the FEM, sometimes remeshing can make the analysis of certain problems particularly cumbersome. In particular, in the present work the MPM is used firstly for the determination of the complete failure pattern of openings, from the initiation until its complete closure, in two different scales, laboratory and tunnel lengths. This problem may involve large strains and contact situations. The last example includes fluid-mechanical coupling under dynamic conditions. Here, the dynamic effects associated with the impact of a rock block in a saturated porous media in a slope is evaluated.
Dynamic loading methods promise new modes for stimulating geological resources, as the fracture patterns they produce can be tailored by the shape and nature of the pressure pulse employed. However, selecting the type of load is a difficult task: too slow and the stimulatory effect is reduced; too fast and the resource may be negatively impacted by wellbore damage, fines creation or permeability reduction. Moreover, modeling these systems proves challenging due to the myriad of length and timescales involved, combined with the need to accommodate both the generation of new fractures and propagation of preexisting fracture networks.
GEODYN-L is a massively-parallel multi-material Lagrangian code that includes advanced contact models to simulate nonlinear wave propagation through heavily-jointed rock masses, along with material model libraries specifically developed to capture the dynamic response of geologic media. We present results using GEODYN-L to simulate dynamic stimulation of geologic resources with pre-existing fracture networks and discuss the implications of these results for enhancing fracture networks with dynamic loading techniques.
Lavrov, A. (SINTEF Petroleum Research) | Torsæter, M. (SINTEF Petroleum Research) | Albawi, A. (Norwegian University of Science and Technology) | Todorovic, J. (SINTEF Petroleum Research) | Opedal, N. (SINTEF Petroleum Research) | Cerasi, P. (SINTEF Petroleum Research)
Integrity of the near-well area is crucial for preventing leakage between geological horizons and towards the surface during CO2 storage, hydrocarbon production and well stimulation. The paper consists of two parts. In the first part, a finite-element model of earlier laboratory tests on thermal cycling of a casing/cement/rock assemblage is set up. It is demonstrated that radial tensile stresses contributing to annular cement debonding are likely to develop during cooling of such an assemblage. The results of the modeling are in agreement with the results of the earlier laboratory experiments, with regard to the temperature histories, CT data, and location of acoustic emission sources. In the second part of the paper, a computational procedure is developed for upscaling of data about rock damage obtained from CT, to a finite-element model of flow in porous media around a well. The damaged zone is shown to dominate the flow along the axis of a compound specimen (a hollow cylinder of sandstone filled with cement). Implications for leakage along an interface between cement and rock in-situ are discussed.
The crack damage progression in crystalline rocks is approximated in laboratory by means of rigorous strain measurement and/or monitoring of Acoustic Emission (AE) activity. When both means are used, they are treated independently for quantification of damage in the rock. This paper is investigating a new method to combine the AE and strain data in a unified function to calculate the balance of stored and released energy in the rock due to loading (strain energy) and micro-cracking respectively. This method introduces a new solution for measurement and quantification of crack damage in rock and also provides a tool to investigate the brittleness of different rock types. Unconfined Compressive Strength (UCS) testing of six different rock types with strain measurement and AE monitoring was performed for this study. The application of the new method to the data collected from the UCS tests indicates the difference between the behaviour of the various rock types in terms of sudden energy release at the onset of CI threshold and the difference in the storability of strain energy before and after CI and CD thresholds.
Laboratory experiments have been performed to simulate in situ and core compaction behavior of soft reservoir sandstones. Fine-grained synthetic sandstones have been manufactured under simulated in situ stress conditions with various cement contents. A systematic study shows that in situ compaction is close to elastic only under initial conditions, and that plasticity develops gradually during compaction. Two mechanisms control rock alteration as a result of stress release during coring: Cement bond breakage, which leads to softer and more stress sensitive core material at low stresses, and grain rearrangement into a denser packing, leading to permanently reduced porosity and hence increased stiffness compared to in situ behavior. The relative importance of these mechanisms depends on the degree of cementation, on the coring stress path, and on the stress level. Ultrasonic velocities have been measured and linked to time lapse seismic response of soft reservoirs and to the feasibility of predicting it with core material. Time dependent (creep) deformation has been observed, and appears related to the evolution of plastic strain.
A robust understanding of the thermal stress development due to injection of cold fluids is crucial when developing the Åsgard field on the Norwegian Continental Shelf (NCS) offshore Norway. To get a better and more direct estimation of the stress reduction, a series of triaxial tests under uniaxial strain control were conducted with cooling on reservoir core samples. The purpose of the testing program was to find elastic properties, thermal expansion coefficients and change in confining stress due to temperature reduction. The results show that the cooling related stress effect is strongly stress path dependent. As the sample is subjected to more cooling the stress state tends to approach an elasto-plastic formulation leading to a more soft response of the material. As a consequence the measured stress effect is lower than the estimated which was based on elastic state assumptions.
Deep saline aquifers have a great potential for geologic carbon dioxide (CO2) sequestration and proper assessment of host and cap rock is needed to guarantee that the procedure is safe. Temperatures and pressures at which most of the possible host rocks exist dictate that CO2 is present in a supercritical condition, having both gas and liquid properties. Hence, rock-fluid interaction has to be studied and measurements of poroelastic parameters are necessary. Sandstone formations are mostly considered as the possible host rock. However, in some countries only calcite-rich formations can satisfy the requirements for safe geologic CO2 sequestration.
This paper deals with measurements of poroelastic parameters of calcarenite (or Apulian limestone), which is 95-98% calcite. Jacketed and unjacketed hydrostatic compression experiments and undrained plane strain compression tests provided the full set of poroelastic parameters. Additionally, the specific storage coefficient was calculated. Inability to obtain constant values of Skempton B coefficient even at high pore pressures (~ 4 MPa) and the decrease in P-wave velocity with water injection revealed partial dissolution of calcarenite in water at high pressures. This phenomenon, as well as the mechanical behavior of rock in contact with supercritical CO2, are currently under consideration.
This paper presents an experimental investigation on both monotonic strength and fatigue crack kinetics for Berea sandstone. It is found that for all specimens the Paris-Erdogan law is applicable for a wide range of the amplitudes of the stress intensity factor. The fatigue tests also indicate that there is a small-crack growth regime at the beginning stage, where the growth rate decreases as the crack propagates. The fracture kinetics for both the small-crack growth and the Paris regimes is subjected to a strong size effect. During the strength and fatigue tests, the damage process is examined by the digital image correlation method, and it is shown that the length of the fracture process zone under cyclic loading is about 60% larger than that under monotonic loading. In parallel with the experiments, a theoretical model is developed to explain the observed size effect on fatigue crack kinetics.