Elastic properties of porous media in the vicinity of the percolation limit

A new approach to calculation of the elastic bulk modulus of low consolidated porous media in the vicinity of the percolation limit under dry and saturated conditions is developed based on a physical consolidation model of rocks and the classical contact theory developed by H. Hertz in 1882. The derived analytical relationships for the elastic bulk modulus, which take into account the structural architecture of packing, are compared with theoretical predictions from popular micromechanic theories, Hashin–Shtrikman strict bounds as well as with experimental results available for low consolidated granular materials. The latter comparison demonstrates a good agreement under both dry and water saturated conditions.     

Reconstruction problem and information granularity

The paper elaborates on the representation and reconstruction of numerical and nonnumerical data in fuzzy modeling. Proposed are general criteria leading to the distortion-free interfacing mechanisms that help transform information between the systems (or modeling environments) operating at different levels of information granularity. Distinguished are three basic categories of information: numerical, interval-valued, and linguistic (fuzzy). Since all of them are dealt with here, the paper subsumes the current studies concentrated exclusively on representing fuzzy sets through their numerical representatives (prototypes). The algorithmic framework in which the distortion-free interfacing is completed is realized through neural networks. Each category of information is treated separately and gives rise to its own specialized architecture of the neural network. Similarly, these networks require carefully designed training sets that fully capture the specificity of the reconstruction problem. Several carefully selected numerical examples are aimed at the illustration of the key ideas     

On the residual opening of hydraulic fractures

Hydraulic stimulation technologies are widely applied across resource and power generation industries to increase the productivity of oil/gas or hot water reservoirs. These technologies utilise pressurised water, which is applied inside the well to initiate and drive fractures as well as to open a network of existing natural fractures. To prevent the opened fractures from complete closure during production stage, small particles (proppants) are normally injected with the pressurised fluid. These particles are subjected to confining stresses when the fluid pressure is removed, which leads to a partial closure of the stimulated fractures. The residual fracture openings are the main outcome of such hydraulic stimulations as these openings significantly affect the permeability of the reservoirs and, subsequently, the well productivity. Past research was largely focused on the assessment of conditions and characteristics of fluid driven fractures as well as proppant placement techniques. Surprisingly, not much work was devoted to the assessment of the residual fracture profiles. In this work we develop a simplified non-linear mathematical model of residual closure of a plane crack filled with deformable particles and subjected to a remote compressive stress. It is demonstrated that the closure profile is significantly influenced by the distribution and compressibility of the particles, which are often ignored in the current evaluations of well productivity.     

Theoretical model for roughness induced opening of cracks subjected to compression and shear loading

The phenomenon of roughness induced opening or slip opening is well known in rock mechanics and relates to a crack (or rock joint) behaviour under compression and shear. It has been widely utilised in tight gas and coal bed methane industries to increase the permeability of geological reservoirs during hydraulic stimulations and has recently been extended to geothermal energy technologies for successful harnessing the thermal energy from hot rocks. However, this phenomenon is still poorly understood; and only several semi-empirical equations are currently available in the literature to predict values of the slip openings. In this paper new mechanical and mathematical models of the roughness induced opening are suggested. A computational approach based on the distributed dislocation technique was implemented to analyse various coupled effects. The focus of this paper is on stress analysis of a straight crack with rough faces located in an infinite impermeable body. The crack is subjected to remote normal and shear loading and a uniform fluid pressure applied inside the crack. The developed model can further be extended to investigate many other interesting and practically important problems such as analysis of fracture initiation in natural faults subjected to fluid pressure, residual opening after releasing the fluid pressure or permeability changes associated with hydraulic stimulations.     

Application of Contact Theory to Evaluation of Elastic Properties of Low Consolidated Porous Media

A new approach to the calculation of the elastic bulk modulus of low consolidated porous media is developed based on a physical consolidation model of rocks and the classical Hertz contact theory. The derived analytical relationships for the elastic bulk modulus, which take into account some micro-structural characteristics of packing, are compared with theoretical predictions from various micromechanics theories, Hashin-Shtrikman strict bounds as well as with experimental results available for low consolidated granular materials. The latter comparison demonstrates a good agreement.     

An inference system based on fuzzy logic

While psychophysiologic studies of posttraumatic stress disorder (PTSD) have investigated the effects of trauma-related stimuli on arousal, none have explored the development of intrusive imagery and affect states in the absence of such specific cues. The present study compares autonomic arousal during PTSD-related Rorschach responses in PTSD veterans vs. combat controls and noncombat controls. It was found that Rorshach responses containing traumatic content were found only in the PTSD group, and that these responses showed elevations in skin conductance (SC) and heart rate (HR). Our data also suggest that PTSD patients are more easily hyperaroused, especially under conditions of experienced stress and helplessness. Finally, combat control subjects exhibited lower baseline SC and HR than their counterparts, as well as decelerated HR during trauma- and stress-related Rorschach responses, suggesting a physiologic resilience in this group.