Idar Larsen

Rayleigh wave propagation in intact and damaged geomaterials

Abstract An analytical model of an elastically deforming geomaterial with microstructure and damage is assumed to be a material where the second spatial gradients of strain are included in the constitutive equations. Based on this assumption, a linear second gradient (or grade-2) elasticity theory is employed, to investigate the propagation of surface waves in either intact or weathered—–although homogeneous and isotropic at the macroscale—materials with microstructure such as soils, rocks and rock-like materials. First, it is illustrated that in contrast to classical (grade-1) elasticity theory, the proposed higher-order elasticity theory yields dispersive Rayleigh waves, as it is also predicted by the atomic theory of lattices (discrete particle theory), as well as by viscoleasticity theory. Most importantly, it is demonstrated that the theory: (a) is in agreement with in situ non-destructive measurements pertaining to velocity dispersion of Rayleigh waves in monumental stones, and (b) it may be used for back analysis of the test data for the quantitative characterization of degree of surface cohesion or damage of Pendelikon marble of the Parthenon monument of Athens.

Static and dynamic behaviour of compacted sand and clay: Comparison between measurements in Triaxial and Oedometric test systems

In rock mechanics and rock physics, like in many other branches of research, it is important to compare results obtained in different kinds of apparatus that are meant to measure the same properties. Differences may in general be due to differences in samples, or in test procedures. Here we compare uniaxial compaction experiments in oedometric and triaxial tests systems, using brine-saturated samples made from pure kaolinite or from Ottawa sand. Small differences in sample manufacturing or in initial loading of the specimens were found to cause significant differences in static behaviour and in ultrasonic velocities during the tests. The influence of differences in sample geometry (wide and thin samples in the oedometer versus long and slim samples in the triaxial set-up) and the influence of different boundary conditions caused by the confining medium (steel in the oedometer, thin soft sleeve in the triaxial system) were studied, amongst others with the use of discrete particle modelling. Although the boundary conditions may have an influence, the most significant sources of discrepancy in our experiments were associated with the manufacturing and preparation of the samples to be tested. The test data show that the drained static compaction modulus for sand is close to its dynamic counterpart, while for kaolinite, the dynamic modulus is significantly larger than the static one.

Laboratory Observation and Micromechanics-Based Modelling of Sandstone on Different Scales

The mechanical properties of sandstone are, to a large extent, controlled by its microstructure. When sandstone is loaded, the stress conditions and stress history can influence the sandstone in terms of the deformation parameters, strength parameters, failure modes, as well as acoustic properties and other petrophysical parameters. In this paper, we show how we may use a discrete element model to compute the mechanical behaviour based on the microstructure of the rock, as obtained from micro-computed tomography. The model is calibrated with triaxial test data obtained with three different sandstones. The key element in the model is a contact law, attempting to capture deformation and failure at the level of the grain scale. A micromechanics-based core-scale model was also suggested using the same contact law but without explicitly mimicking the rock microstructure. The simulation results from both the microscale model and the macroscale model were in reasonably good agreement with the laboratory measurements on sandstone specimens.

Rock Mechanics Aspects of Well Productivity in Marginal Sandstone Reservoirs: Problems, Analysis Methods, and Remedial Actions

Rock mechanics may directly or indirectly affect productivity decline; however, remediation in sandstone reservoirs may be possible. Several mechanisms are linked to rock-mechanics aspects through local pore-pressure changes and induced deformations of the formation rock. Plugging may further induce rock mechanical failure around the well. Two principles of direct sand control are discussed [i.e., borehole reinforcement (expandable screens, gravel packing, propped fracturing, and chemical consolidation) and filtering (standalone screens, gravel packs, frac packs, and prepacked screens)] along with their effects on productivity and, therefore, reservoir depletion, scaling, sand production, filter-cake mobilization, and fines migration.

Combining the modified discrete element method with the virtual element method for fracturing of porous media

Simulation of fracturing processes in porous rocks can be divided into two main branches: (i) modeling the rock as a continuum enhanced with special features to account for fractures or (ii) modeling the rock by a discrete (or discontinuous) approach that describes the material directly as a collection of separate blocks or particles, e.g., as in the discrete element method (DEM). In the modified discrete element (MDEM) method, the effective forces between virtual particles are modified so that they reproduce the discretization of a first-order finite element method (FEM) for linear elasticity. This provides an expression of the virtual forces in terms of general Hook’s macro-parameters. Previously, MDEM has been formulated through an analogy with linear elements for FEM. We show the connection between MDEM and the virtual element method (VEM), which is a generalization of FEM to polyhedral grids. Unlike standard FEM, which computes strain-states in a reference space, MDEM and VEM compute stress-states directly in real space. This connection leads us to a new derivation of the MDEM method. Moreover, it enables a direct coupling between (M)DEM and domains modeled by a grid made of polyhedral cells. Thus, this approach makes it possible to combine fine-scale (M)DEM behavior near the fracturing region with linear elasticity on complex reservoir grids in the far-field region without regridding. To demonstrate the simulation of hydraulic fracturing, the coupled (M)DEM-VEM method is implemented using the Matlab Reservoir Simulation Toolbox (MRST) and linked to an industry-standard reservoir simulator. Similar approaches have been presented previously using standard FEM, but due to the similarities in the approaches of VEM and MDEM, our work provides a more uniform approach and extends these previous works to general polyhedral grids for the non-fracturing domain.

Laboratory experiments on ultrasonic logging through casing for barrier integrity validation

Verification of annular barriers is essential for well integrity, with ultrasonic methods being central in well integrity testing for many decades. By doing ultrasonic pitch-catch measurements on a bench top laboratory setup developed to replicate an oil well casing, we were able to show that the beam width, -6dB, of the leaky Lamb wave propagating in the pipe widens only from 14 to 20.4 mm after 140mm of propagation in the pipe. This indicates that the excited Lamb wave has beam-like features, with litle spreading perpendicular to the propagation direction, hence, can be used to evaluate a limited area of the pipe. When introducing two pipes in the experimental setup, as an extension of a previously conducted simulation study by Viggen et al. [1], we could observe multiple Lamb wave packets being excited in the pipes. By adjusting the setup to replicate casing eccentricity, the effects of this could be observed in the measurements.

Combining the Modified Discrete Element Method with the Virtual Element Method for Fracturing of Porous Media

Simulation of fracturing processes in porous rocks can be divided in two main branches: (i) modeling the rock as a continuum enhanced with special features to account for fractures, or (ii) modeling the rock by a discrete (or discontinuous) modeling technique that describes the material directly as an assembly of separate blocks or particles, e.g., as in the discrete element method (DEM). In the modified discrete element (MDEM) method, the effective forces between virtual particles are modified in all regions without failing elements so that they reproduce the discretization of linear FEM for linear elasticity. This provides an expression of the virtual forces in terms of general Hooks macro-parameters. Previously, MDEM has been formulated through an analogy with linear elements for FEM. We show the connection between MDEM and the virtual element method (VEM), which is a generalization of traditional FEM to polyhedral grids. Unlike standard FEM, which computes strain-states in reference space, MDEM and VEM compute stress-states directly in real space. This connection leads us to a new derivation of the MDEM method. Moreover, it gives the basis for coupling (M)DEM to domains with linear elasticity described by polyhedral grids, which makes it easier to apply realistic boundary conditions in hydraulic-fracturing simulations. This approach also makes it possible to combine fine-scale (M)DEM behavior near the fracturing region with linear elasticity on complex reservoir grids in the far-field region without regridding. To demonstrate simulation of hydraulic fracturing, the coupled (M)DEM-VEM method is implemented in the Matlab Reservoir Simulation Toolbox (MRST) and linked to an industry-standard reservoir simulator. Similar approaches have been presented previously using standard FEM, but due to the similarities in the approaches of VEM and MDEM, our work is a more uniform approach and extends previous work to general polyhedral grids for the non-fracturing domain.