Theoretical Investigation of Unconditionally Stable Sequential Algorithms of Coupled Flow and Geomechanics for Hydraulically Fractured Systems

We investigate unconditionally stable sequential algorithms for coupled hydraulically fractured geomechanics and flow systems, which can account for poromechanics behavior within the fractures. We focus on modifying the concepts of the fixed stress and undrained sequential methods properly for the coupled systems by taking appropriate stabilization terms for stability and convergence with energy analyses. Specifically, an apparent fracture stiffness is used for for numerical stabilization. Because this fracture stiffness depends on the fracture length, the stabilization term needs to be updated dynamically, different from the drained bulk modulus used for typical poromechanics problems. For numerical tests, we take the extended finite element method for geomechanics while the piecewise constant finite element method is used for flow within an existing hydraulic fracture. The numerical results support a priori stability analyses.

Simplified Seismic Modelling of Fractured Rock: How Effective is the Localised Effective Medium Compared to Explicit Representation of Individual Fractures

Seismic waves can be an effective probe to retrieve fracture properties particularly when measurements are coupled with forward and inverse modelling. These seismic models then need an appropriate representation of the fracturing. The fractures can be modelled either explicitly, considering zero thickness frictional slip surfaces, or by considering an effective medium which incorporates the effect of the fractures into the properties of the medium, creating anisotropy in the wave velocities. In this work, we use a third approach which is a hybrid of the previous two. The area surrounding the predefined fracture is treated as an effective medium and the rest of the medium is made homogeneous and isotropic, creating a Localised Effective Medium (LEM). LEM can be as accurate as the explicit but more efficient in run-time. We have shown that the LEM model can closely match an explicit model in reproducing waveforms recorded in a laboratory experiment, for wave propagating parallel and perpendicular to the fractures. The LEM model performs close to the explicit model when the wavelength is much larger than the element size and larger than the fracture spacing. By the definition of the LEM model, we expect that as the LEM layer becomes coarser the model will start approaching the effective medium result. However, what are the limitations of the LEM and is there a balance between the stiffness, the frequency and the thickness, where the LEM performs close to an explicit model or approaches the effective medium model? To define the limits of the LEM we experiment varying fracture stiffness and source frequency. We then compare for each frequency and stiffness the explicit and effective medium with five models of LEM with different thickness. Finally, we conclude that the thick LEM layers with lower resolution perform the same as the thinner and finer resolution LEM layers for lower frequencies and higher fracture stiffness.

Impact of fracture sealing on their hydraulic and mechanical properties

<p>In deep tight reservoirs like Enhanced Geothermal Systems (EGS), the fracture flow often plays a dominant role. The hydraulic and mechanical behaviors of the fracture are affected by a couple of factors such as the sealing deposits owing to mineral cementation. Here we aimed to investigate the impact of the sealing material on the hydro-mechanical properties of a rough fracture using a well-established self-affine rough fracture model. We developed finite element model based on the MOOSE/GOLEM framework dedicated to modeling coupled Hydraulic-Mechanical (HM) process of the rock-fracture system. We conducted numerical flow through a granite reservoir hosting one single large and partly sealed fracture of size 512x512 m<sup>2</sup>. Navier-Stokes flow and Darcy flow are solved in the 3-dimensional rough aperture and in the embedding poro-elastic matrix, respectively. In order to mimic the impact of the fracture sealing material on the physical properties of the rock-fracture system, we sequentially increased the amount of the fracture-filling material in the rough fracture by changing the thickness of the sealing deposits.  The evolution of the contact area, fracture permeability, fracture diffusivity and normal fracture stiffness, is monitored up to the percolation threshold of the fluid flow. We show that sealing induces strong permeability anisotropy, significant decrease of hydraulic diffusivity and increase of fracture stiffness. The results have strong implications for optimizing the stimulation strategy like chemical stimulation of fractured reservoirs, as well as understanding the fluid-induced seismicity.</p>

A New Elastoplastic Time-History Analysis Method for Frame Structures

This study aimed to analyze the formation and application of the time-domain elastoplastic response spectrum. The elastoplastic response spectrum in the time domain was computed according to the trilinear force-restoring model. The time-domain elastoplastic response spectrum corresponded to a specific yield strength coefficient, fracture stiffness, and yield stiffness. However, the force-restoring models corresponding to different structural systems and the states of the structural systems at different moments were not the same. Therefore, the dynamic characteristics of a particular periodic point corresponding to a particular structure were meaningful for the elastoplastic response spectrum. In addition, the curve in the time-domain dimension along the periodic point truly reflected the real-time response of the structure when the structure encountered a seismic load.

Measuring Orthopedic Plate Strain to Track Bone Healing Using a Fluidic Sensor Read via Plain Radiography

We describe a fluidic X-ray visualized strain indicator under applied load (X-VISUAL) to quantify orthopedic plate strain and inform rehabilitative care. This sensor uses a liquid-level gauge with hydro-mechanical amplification and is visualized in plain radiographs which are routinely acquired during patient recovery to find pathologies but are usually insufficient to quantify fracture stiffness. The sensor has two components: a stainless-steel lever which attaches to the plate, and an acrylic fluidic component which sits between the plate and lever. The fluidic component has a reservoir filled with radio-dense solution and an adjoining capillary wherein the fluid level is measured. When the plate bends under load, the lever squeezes the reservoir, which pushes the fluid along the channel. A tibial osteotomy model (5 mm gap) was used to simulate an unstable fracture, and allograft repair used to simulate a stiffer healed fracture. A cadaveric tibia and a mechanically equivalent composite tibia mimic were cyclically loaded five times (0 – 400 N axial force) while fluid displacement was measured from radiographs. The sensor displayed reversible and repeatable behavior with a slope of 0.096 mm/kg and fluid level noise of 50 to 80 micrometers (equivalent to 5-10 N). The allograft-repaired composite fracture was 13 times stiffer than the unstable fracture. An analysis of prior external fracture fixation studies and fatigue curves for internal plates indicates that the threshold for safe weight bearing should be 1/5th −1/10th of the initial bending for an unstable fracture. The precision of our device (<2% body weight) should thus be sufficient to track fracture healing from unstable through safe weight bearing.