Esteban Rougier

Understanding hydraulic fracturing: a multi-scale problem

Despite the impact that hydraulic fracturing has had on the energy sector, the physical mechanisms that control its efficiency and environmental impacts remain poorly understood in part because the length scales involved range from nanometres to kilometres. We characterize flow and transport in shale formations across and between these scales using integrated computational, theoretical and experimental efforts/methods. At the field scale, we use discrete fracture network modelling to simulate production of a hydraulically fractured well from a fracture network that is based on the site characterization of a shale gas reservoir. At the core scale, we use triaxial fracture experiments and a finite-discrete element model to study dynamic fracture/crack propagation in low permeability shale. We use lattice Boltzmann pore-scale simulations and microfluidic experiments in both synthetic and shale rock micromodels to study pore-scale flow and transport phenomena, including multi-phase flow and fluids mixing. A mechanistic description and integration of these multiple scales is required for accurate predictions of production and the eventual optimization of hydrocarbon extraction from unconventional reservoirs. Finally, we discuss the potential of CO2 as an alternative working fluid, both in fracturing and re-stimulating activities, beyond its environmental advantages. This article is part of the themed issue ‘Energy and the subsurface’.

Seismic source functions from free-field ground motions recorded on SPE: Implications for source models of small, shallow explosions

Reduced displacement potentials (RDPs) for chemical explosions of the Source Physics Experiments (SPE) in granite at the Nevada Nuclear Security Site are estimated from free-field ground motion recordings. Far-field P wave source functions are proportional to the time derivative of RDPs. Frequency domain comparisons between measured source functions and model predictions show that high-frequency amplitudes roll off as ω− 2, but models fail to predict the observed seismic moment, corner frequency, and spectral overshoot. All three features are fit satisfactorily for the SPE-2 test after cavity radius Rc is reduced by 12%, elastic radius is reduced by 58%, and peak-to-static pressure ratio on the elastic radius is increased by 100%, all with respect to the Mueller-Murphy model modified with the Denny-Johnson Rc scaling law. A large discrepancy is found between the cavity volume inferred from RDPs and the volume estimated from laser scans of the emplacement hole. The measurements imply a scaled Rc of ~5 m/kt1/3, more than a factor of 2 smaller than nuclear explosions. Less than 25% of the seismic moment can be attributed to cavity formation. A breakdown of the incompressibility assumption due to shear dilatancy of the source medium around the cavity is the likely explanation. New formulas are developed for volume changes due to medium bulking (or compaction). A 0.04% decrease of average density inside the elastic radius accounts for the missing volumetric moment. Assuming incompressibility, established Rc scaling laws predicted the moment reasonable well, but it was only fortuitous because dilation of the source medium compensated for the small cavity volume.

A generalized anisotropic deformation formulation for geomaterials

In this paper, the combined finite-discrete element method (FDEM) has been applied to analyze the deformation of anisotropic geomaterials. In the most general case geomaterials are both non-homogeneous and non-isotropic. With the aim of addressing anisotropic material problems, improved 2D FDEM formulations have been developed. These formulations feature the unified hypo-hyper elastic approach combined with a multiplicative decomposition-based selective integration for volumetric and shear deformation modes. This approach is significantly different from the co-rotational formulations typically encountered in finite element codes. Unlike the co-rotational formulation, the multiplicative decomposition-based formulation naturally decomposes deformation into translation, rotation, plastic stretches, elastic stretches, volumetric stretches, shear stretches, etc. This approach can be implemented for a whole family of finite elements from solids to shells and membranes. This novel 2D FDEM based material formulation was designed in such a way that the anisotropic properties of the solid can be specified in a cell by cell basis, therefore enabling the user to seed these anisotropic properties following any type of spatial variation, for example, following a curvilinear path. In addition, due to the selective integration, there are no problems with volumetric or shear locking with any type of finite element employed.

High-stress triaxial direct-shear fracturing of Utica shale and in situ X-ray microtomography with permeability measurement: SHALE FRACTURE, μCT, AND PERMEABILITY

The challenge of characterizing subsurface fluid flow has motivated extensive laboratory studies, yet fluid-flow through rock specimens in which fractures are created and maintained at high-stress conditions remains under-investigated at this time. The studies of this type that do exist do not include in situ fracture geometry measurements acquired at stressed conditions, which would be beneficial for interpreting the flow behavior. Therefore, this study investigates the apparent permeability induced by direct-shear fracture stimulation through Utica shale (a shale gas resource and potential caprock material) at high triaxial-stress confinement and for the first time relates these values to simultaneously acquired in situ X-ray radiography and microtomography images. Change in fracture geometry and apparent permeability was also investigated at additional reduced stress states. Finite element and combined finite discrete element modeling were used to evaluate the in situ observed fracturing process. Results from this study indicate that the increase in apparent permeability through fractures created at high-stress (22.2 MPa) was minimal relative to the intact rock (less than 1 order of magnitude increase) while fractures created at low stress (3.4 MPa) were significantly more permeable (2 to 4 orders of magnitude increase). This study demonstrates the benefit of in situ X-ray observation coupled with apparent permeability measurement to analyze fracture creation in the subsurface. Our results show that the permeability induced by fractures through shale at high stress can be minor and therefore favorable in application to CO2 sequestration caprock integrity but unfavorable for hydrocarbon recovery from unconventional reservoirs.

Radionuclide gas transport through nuclear explosion-generated fracture networks

Underground nuclear weapon testing produces radionuclide gases which may seep to the surface. Barometric pumping of gas through explosion-fractured rock is investigated using a new sequentially-coupled hydrodynamic rock damage/gas transport model. Fracture networks are produced for two rock types (granite and tuff) and three depths of burial. The fracture networks are integrated into a flow and transport numerical model driven by surface pressure signals of differing amplitude and variability. There are major differences between predictions using a realistic fracture network and prior results that used a simplified geometry. Matrix porosity and maximum fracture aperture have the greatest impact on gas breakthrough time and window of opportunity for detection, with different effects between granite and tuff simulations highlighting the importance of accurately simulating the fracture network. In particular, maximum fracture aperture has an opposite effect on tuff and granite, due to different damage patterns and their effect on the barometric pumping process. From stochastic simulations using randomly generated hydrogeologic parameters, normalized detection curves are presented to show differences in optimal sampling time for granite and tuff simulations. Seasonal and location-based effects on breakthrough, which occur due to differences in barometric forcing, are stronger where the barometric signal is highly variable.

A non-locking composite tetrahedron element for the combined finite discrete element method

Purpose In order to avoid the problem of volumetric locking often encountered when using constant strain tetrahedral finite elements, the purpose of this paper is to present a new composite tetrahedron element which is especially designed for the combined finite-discrete element method (FDEM). Design/methodology/approach A ten-noded composite tetrahedral (COMPTet) finite element, composed of eight four-noded low order tetrahedrons, has been implemented based on Munjiza’s multiplicative decomposition approach. This approach naturally decomposes deformation into translation, rotation, plastic stretches, elastic stretches, volumetric stretches, shear stretches, etc. The problem of volumetric locking is avoided via a selective integration approach that allows for different constitutive components to be evaluated at different integration points. Findings A number of validation cases considering different loading and boundary conditions and different materials for the proposed element are presented. A practical application of the use of the COMPTet finite element is presented by quantitative comparison of numerical model results against simple theoretical estimates and results from acrylic fracturing experiments. All of these examples clearly show the capability of the composite element in eliminating volumetric locking. Originality/value For this tetrahedral element, the combination of “composite” and “low order sub-element” properties are good choices for FDEM dynamic fracture propagation simulations: in order to eliminate the volumetric locking, only the information from the sub-elements of the composite element are needed which is especially convenient for cases where re-meshing is necessary, and the low order sub-elements will enable robust contact interaction algorithms, which maintains both relatively high computational efficiency and accuracy.

Phenomenology and Modeling of Explosion‐Generated Shear Energy for the Source Physics Experiments

Abstract We present a mechanism for shear‐wave generation from buried explosions as part of the Source Physics Experiment (SPE) series. The SPE series includes sensitized heavy ammonium nitrate/fuel oil sources of various sizes detonated in a borehole in the jointed Climax stock granite. The cylinder‐shaped shots were grouted in the borehole to couple the energy to the rock. A high‐fidelity site model—with explicit inclusion of the cylindrical explosive, the grout‐filled borehole, and site joint sets—was included in a numerical simulation that mimics the near‐field velocity environment measured by an array of in‐ground accelerometers. This approach was accommodated through a coupled Euler–Lagrange code that allows simultaneous solving of a Euler domain to model the high‐deformation source region and a Lagrange domain that includes the complex geology with full contact. Specific laboratory‐measured geomechanical properties for the rock and the joint sets were included in the model. The simulations compare favorably to the data and provide a possible physical mechanism for unexpected shear motion through the release of stored shear strain on the joints. This research will advance our understanding of explosion‐generated shear‐wave energy from low‐yield nuclear tests.

Quantifying Topological Uncertainty in Fractured Systems using Graph Theory and Machine Learning

Fractured systems are ubiquitous in natural and engineered applications as diverse as hydraulic fracturing, underground nuclear test detection, corrosive damage in materials and brittle failure of metals and ceramics. Microstructural information (fracture size, orientation, etc.) plays a key role in governing the dominant physics for these systems but can only be known statistically. Current models either ignore or idealize microscale information at these larger scales because we lack a framework that efficiently utilizes it in its entirety to predict macroscale behavior in brittle materials. We propose a method that integrates computational physics, machine learning and graph theory to make a paradigm shift from computationally intensive high-fidelity models to coarse-scale graphs without loss of critical structural information. We exploit the underlying discrete structure of fracture networks in systems considering flow through fractures and fracture propagation. We demonstrate that compact graph representations require significantly fewer degrees of freedom (dof) to capture micro-fracture information and further accelerate these models with Machine Learning. Our method has been shown to improve accuracy of predictions with up to four orders of magnitude speedup.

Apparent Explosion Moments from Rg Waves Recorded on SPE

Abstract Seismic moments for the first four chemical tests making up phase I of the Source Physics Experiments (SPE) are estimated from 6‐Hz Rg waves recorded along a single radial line of geophones under the assumption that the tests are pure explosions. These apparent explosion moments are compared with moments determined from the reduced displacement potential method applied to free‐field data. Light detection and ranging (lidar) observations, strong ground motions on the free surface in the vicinity of ground zero, and moment tensor inversion results are evidence that the fourth test SPE‐4P is a pure explosion, and the moments show good agreement, 8×10 10   N·m for free‐field data versus 9×10 10   N·m for Rg waves. In stark contrast, apparent moments for the first three tests are smaller than near‐field moments by factors of 3–4. Relative amplitudes for the three tests determined from Rg interferometry using SPE‐4P as an empirical Green’s function indicate that radiation patterns are cylindrically symmetric within a factor of 1.25 (25%). This fact assures that the apparent moments are reliable even though they were measured on just one azimuth. Spallation occurred on the first three tests, and ground‐based lidar detected permanent deformations. As such, the source medium suffered late‐time damage. Destructive interference between Rg waves radiated by explosion and damage sources will reduce amplitudes and explain why apparent moments are smaller than near‐field moments based on compressional energy emitted directly from the source.

Modeling of Stick‐Slip Behavior in Sheared Granular Fault Gouge Using the Combined Finite‐Discrete Element Method

Sheared granular layers undergoing stick slip behavior are broadly employed to study the physics and dynamics of earthquakes. Here, a two dimensional implementation of the combined finite discrete element method (FDEM), which merges the finite element method (FEM) and the discrete element method (DEM), is used to explicitly simulate a sheared granular fault system including both gouge and plate, and to investigate the influence of different normal loads on seismic moment, macroscopic friction coefficient, kinetic energy, gouge layer thickness, and recurrence time between slips. In the FDEM model, the deformation of plates and particles is simulated using the FEM formulation while particle particle and particle plate interactions are modeled using DEM derived techniques. The simulated seismic moment distributions are generally consistent with those obtained from the laboratory experiments. In addition, the simulation results demonstrate that with increasing normal load, (i) the kinetic energy of the granular fault system increases; (ii) the gouge layer thickness shows a decreasing trend; and (iii) the macroscopic friction coefficient does not experience much change. Analyses of the slip events reveal that, as the normal load increases, more slip events with large kinetic energy release and longer recurrence time occur, and the magnitude of gouge layer thickness decrease also tends to be larger; while the macroscopic friction coefficient drop decreases. The simulations not only reveal the influence of normal loads on the dynamics of sheared granular fault gouge, but also demonstrate the capabilities of FDEM for studying stick slip dynamic behavior of granular fault systems.