Fracture Model Reduction and Optimization for Forchheimer Flows in Reservoir

In this study, we analyze the flow filtration process of slightly compressible fluids in fractured porous media. We model the coupled fractured porous media system, where the linear Darcy flow is considered in porous media and the nonlinear Forchheimer equation is used inside the fracture. Flow in the fracture is modeled as a reduced low dimensional BVP which is coupled with an equation in the reservoir. We prove that the solution of the reduced model can serve very accurately to approximate the solution of the actual high-dimensional flow in reservoir fracture system, because the thickness of the fracture is small. In the analysis we consider two types of Forchhemer flows in the fracture: isotropic and anisotropic, which are different in their nature. Using method of reduction, we developed a formulation for an optimal design of the fracture, which maximizes the capacity of the fracture in the reservoir with fixed geometry. Our method, which is based on a set point control algorithm, explores the coupled impact of the fracture geometry and beta-Forchheimer coefficient

Fracture energy of gels

To clarify effects of crack speed and cross-link density on fracture energy of acrylamide gels, we evaluated the roughness of the fracture surface and measured the fracture energy taking into account the roughness. The fracture energy increases linearly with crack speed $V$ in a fast crack speed region, and the increasing rate of fracture energy with $V$ decreases with increasing cross link density in the gels. In a slow crack speed region the fracture energy depends on crack speed more strongly than in the fast crack speed region. This indicates that a qualitative change exists in fracture process of the gels.Comment: 7 pages, 8 figures. Some errors in the first version have been correcte

PyFrac: A planar 3D hydraulic fracture simulator

Fluid driven fractures propagate in the upper earth crust either naturally or in response to engineered fluid injections. The quantitative prediction of their evolution is critical in order to better understand their dynamics as well as to optimize their creation. We present a Python implementation of an open-source hydraulic fracture propagation simulator based on the implicit level set algorithm originally developed by Peirce & Detournay (2008) -- "An implicit level set method for modeling hydraulically driven fractures". Comp. Meth. Appl. Mech. Engng, (33-40):2858--2885. This algorithm couples a finite discretization of the fracture with the use of the near tip asymptotic solutions of a steadily propagating semi-infinite hydraulic fracture. This allows to resolve the multi-scale processes governing hydraulic fracture growth accurately, even with relatively coarse meshes. We present an overview of the mathematical formulation, the numerical scheme and the details of our implementation. A series of problems including a radial hydraulic fracture verification benchmark, the propagation of a height contained hydraulic fracture, the lateral spreading of a magmatic dyke and the handling of fracture closure are presented to demonstrate the capabilities, accuracy and robustness of the implemented algorithm

Effects of fracture aperture and roughness on hydraulic and mechanical properties of rocks : implication of seismic characterization of fractured reservoirs

Roughness and aperture are two important characteristic parameters controlling fluid flow in natural joints and fractures. It has been demonstrated by many authors that knowledge of roughness does not directly lead to that of aperture, and aperture should be handled as a separate geometrical descriptor. To determine the normal deformability and flow response of a fracture, the aperture distribution and the mechanical properties of the rock matrix are required. When shearing of joints and fractures is considered, roughness comes into play and affects the evolution of the aperture distribution. The aperture distribution can be evaluated by knowing the correlation between the asperity profiles of the rock walls of a rock fracture. Thus, the distributions of contact area and void space determine the fracture dilation and hydraulic properties during shearing. In the seismic characterization of fractured reservoirs, various equivalent medium theories describing the effective elastic properties of fractured media have been proposed. One relatively simple theory is based on the assumption of the linear slip interface or displacement discontinuity model of fractures. Two parameters are usually used in the linear slip interface model: the normal and shear fracture compliances defined as the ratio of normal (shear) displacement discontinuity and normal (shear) stress. Fracture compliances are by definition functions of mechanical aperture and are also influenced by the roughness (surface asperity distribution) of fracture surfaces. In this study, I investigate the effects of fracture roughness and apertures on the hydraulic and mechanical properties of fractured rock. Specifically, I focus on two kinds of fracture models which are commonly used in describing the effective hydraulic and mechanical (elastic) response of natural fractures. The first is the rough-walled fracture model and the second is an interface with distributions of contacts and voids (called the asperity fracture model)

Fracture toughness testing data: A technology survey and bibliography

Announced survey includes reports covering fracture toughness testing for various structural materials including information on plane strain and developing areas of mixed mode and plane strain test conditions. Bibliography references cite work and conclusions in fracture toughness testing and application of fracture toughness test data, and in fracture mechanics analysis

An Inpatient Rehabilitation Interprofessional Care Pathway for Traumatic Hip Fracture: A Pilot Quality Improvement Project

Background: Each year over 300,000 older adults are hospitalized for hip fracture. The impact of the cost of hip fracture on the US health care system is estimated to be as high as $9 billion, with the typical cost of a hip fracture episode around$30,000. Formalized pathways have been developed and successfully utilized for many patient presentations, including hip fracture, in the acute setting. Although this research is important to the comprehensive care of the elderly hip fracture patient, very little research exists that outlines evidence-based best-practice for patients in the post-acute recovery period. Purpose: The primary aim of this project was to develop an evidence-based, comprehensive, coordinated, and interprofessional care pathway for hip fracture patients in the acute rehabilitation setting to improve the percentage of patients discharging to community settings by 20% from current baseline by the end of the pilot period. Methods: The design of this project was an observational cohort study. Descriptive statistics will be used to compare intervention groups to controls, including frequencies and distributions. Results: The hip fracture tool itself had inconclusive results, the impacts of the effects on team work and enhanced coordination of the care team was realized through reducing institutionalized days for hip fracture patients in acute rehabilitation

3d numerical model of a confined fracture tests in concrete

The paper deals with the numerical simulation of a confined fracture test in concrete. The test is part of the experimental work carried out at ETSECCPB-UPC in order to elucidate the existence of a second mode of fracture under shear and high compression, and evaluate the associated fracture energy. The specimen is a short cylinder with also cylindrical coaxial notches similar the one proposed by Luong (1990), which is introduced in a largecapacity triaxial cell, protected with membranes and subject to different levels of confining pressure prior to vertical loading. In the experiments, the main crack follows the preestablished cylindrical notch path, which is in itself a significant achievement. The loaddisplacement curves for various confining pressures also seem to follow the expected trend according to the underlying conceptual model. The FE model developed includes zerothickness interface elements with fracture-based constitutive laws, which are pre-inserted along the cylindrical ligament and the potential radial crack plane. The results reproduce reasonably well the overall force-displacement curves of the test for various confinement levels, and make it possible to identify the fracture parameters including the fracture energies in modes I and IIa