Aditya Khanna

The performance of hydraulic fractures partially filled with compressible proppant

Abstract Mechanical response of a proppant pack to confining stresses significantly influences the aperture of highly conductive artificial or natural fracture channels and, to some extent, determines the efficiency of hydraulic stimulations. This paper presents a simplified mathematical model of a crack partially filled with compressible proppant subject to remote compressive stress and a computational approach for evaluating the productivity rate of hydraulically stimulated wells. The conducted case studies confirm that the proppant pack distribution and compressibility have a significant impact on well productivity. Furthermore, it is suggested that under certain conditions, for example, relatively low confining stresses, the partially propped fractures can lead to higher well production rate than fractures fully filled with proppant. The benefit of reducing proppant pack compressibility for improving the performance of wells with partially propped fractures is also verified.

On the Correspondence between Two- and Three-Dimensional Elastic Solutions of Crack Problems

The classical two-dimensional solutions of the theory of elasticity provide a framework of Linear Elastic Fracture Mechanics. However, these solutions, in fact, are approximations despite that the corresponding governing equations of the plane theories of elasticity are solved exactly. This paper aims to elucidate the main differences between the approximate (two-dimensional) and exact (three-dimensional) elastic solutions of crack problems. The latter demonstrates many interesting features, which cannot be analysed within the plane theories of elasticity. These features include the presence of scale effects of deterministic nature, the existence of new singular stress states and fracture modes. Furthermore, the deformation and stress fields near the tip of the crack is essentially three-dimensional and do not follow plane stress or plane strain simplifications. Moreover, in certain situations the two-dimensional solutions can provide misleading results; and several characteristic examples are outlined in this paper.

Comparative evaluation of in situ stress monitoring with Rayleigh waves

The in situ monitoring of stresses provides a crucial input for residual life prognosis and is an integral part of structural health monitoring systems. Stress monitoring is generally achieved by utilising the acoustoelastic effect, which relates the speed of elastic waves in a solid, typically longitudinal and shear waves, to the stress state. A major shortcoming of methods based on the acoustoelastic effect is their poor sensitivity. Another shortcoming of acoustoelastic methods is associated with the rapid attenuation of bulk waves in the propagation medium, requiring the use of dense sensor networks. The purpose of this article is twofold: to demonstrate the application of Rayleigh (guided) waves rather than bulk waves towards stress monitoring based on acoustoelasticity, and to propose a new method for stress monitoring based on the rate of accumulation of the second harmonic of large-amplitude Rayleigh waves. An experimental study is conducted using the cross-correlation signal processing technique to increase the accuracy of determining Rayleigh wave speeds when compared with traditional methods. This demonstrates the feasibility of Rayleigh wave–based acoustoelastic structural health monitoring systems, which could easily be integrated with existing sensor networks. Second harmonic generation is then investigated to demonstrate the sensitivity of higher order harmonics to stress-induced nonlinearities. The outcomes of this study demonstrate that the sensitivity of the new second harmonic generation method is several orders of magnitude greater than the acoustoelastic method, making the proposed method more suitable for development for online stress monitoring of in-service structures.

An analysis of elasto-plastic fracture criteria

The aim of this paper is to critically evaluate, how well the most common non-linear fracture criteria actually describe the general experimental trends, which were confirmed in a large number of fracture tests, conducted over the past fifty years. In particular, we examine the agreement between these general experimental trends and the theoretical predictions based on the critical value of the crack-tip stress at some certain distance, J-integral, crack tip opening displacement and crack-tip-opening angle. All theoretical predictions are derived from the classical strip yield model, which is considered to be adequate for the purpose of the current study.