Modeling of acoustoelastic borehole waves subjected to tectonic stress with formation anisotropy and borehole deviation

Sonic logging is a promising technique to estimate tectonic stress around a borehole. The key to successful evaluation of tectonic stress is having a thorough understanding of forward model which implies responses of borehole waves to tectonic stress. We propose a generic model to simulate responses of borehole waves to tectonic stress based on semi-analytical finite element method and acoustoelasticity. This model can compute distribution of tectonic stress around an inclined borehole with arbitrary anisotropic formation and simulate acoustoelasticities of borehole waves under this complicated stress. To avoid tedious and time consuming code development, we also provide an easy access to the model by reformulating and implementing the governing equations in a commercial software package. We validate the model by using three case studies where analytical/numerical solutions are available, showing good agreements between the results from our model and solutions in the literature. We then apply the model to some important applications in boreholes, demonstrating that this model can provide a powerful tool for understanding of responses of borehole waves to tectonic stress.

A program to calculate the state of stress in the vicinity of an inclined borehole through an anisotropic rock formation

A borehole existing in any geologic formation concentrates the far-field tectonic and overburden stresses amplifying the magnitudes of certain stress components near the borehole. It is important to understand the magnitudes and patterns of this stress concentration because these lead to damage and can even collapse the borehole if sufficiently strong. The solution of the stress distributed near a borehole can be complicated considering the elastic anisotropy of rocks. We have developed programs (ASCIB3D) in MATLAB and Python to model the stress distribution around an inclined borehole in an arbitrarily oriented anisotropic medium. The program is built on the Lekhnitskij-Amadei solution. The input orientation of the far-field stresses and the elastic stiffness matrix of the medium into the program are geology angles instead of the rotation angles shown in previous studies, making the code more convenient for users. The sign convention for the inverse function, which is ignored in previous studies, is discussed in detail. The results indicate that the program ASCIB3D is a useful tool for modeling the stress distributed around an inclined borehole in the anisotropic formation and analyzing the effect of anisotropy and borehole inclination on stress distribution. The inclination and azimuth of the borehole and the anisotropy of the rocks affect the orientation and strength of the stress concentration.

Three-dimensional analytical poromechanical solutions for an arbitrarily inclined borehole subjected to fluid injection

Hydraulic fracturing is the primary method of stimulation in unconventional reservoirs, playing a significant role in oil and gas production enhancement. A key issue for the analysis of hydraulic fracture initiation is to accurately determine the stress distributions in the vicinity of the borehole caused by the injection of pressurized fluids. This paper develops an exact, three-dimensional, poroelastic coupled analytical solution for such stress analysis of an arbitrarily inclined borehole subjected concurrently to a finite-length fluid discharge and in situ stresses, using Fourier expansion theorem and the Laplace–Fourier integral transform technique. The complicated boundary conditions, which involve the mixed boundary values at the borehole surface and the coupling between the total radial stress and injection-induced pore pressure over the sectioned borehole interval, as well as the fully three-dimensional far field in situ stresses, are addressed in a novel way and deliberately/elegantly decomposed into five fundamental, easier to handle modes. The rigour and definitive nature of the proposed analytical methodology facilitates fundamental understanding of the mechanism underlying the stress responses of the borehole and porous medium. It can be and is used here as a benchmark for the numerical solutions obtained from the finite-element analysis commercial program (ABAQUS).

The Buckling Analysis of Drill String in Inclined Wellbore with a Concave Curved Geometric Defect

Some inclined boreholes have to be drilled in directional wells, but the track of inclined borehole is impossible to be a ideal straight line, there are always some geometric defects such as bending, thus the drilling string in it is bound to have initial bending due to the constraints of borehole, hence the drilling string in inclined borehole is usually a curved compressed rod. Its buckling nature is quite different from straight compressed rod, it is necessary to analyze it specially. In this paper the buckling problem of drill string in inclined borehole with a concave curved geometric defect is studied by energy method, the computing formula of buckling load for it was obtained. And the influence of initial concave bending on buckling load was discussed. The research indicates that when drilling string in inclined well bore has a initial concave bending, the greater the degree of initial bending of drill string, the greater its buckling load.

The Effect of Anisotropy of Medium on the Stress State around a Borehole

Based on the analytical solution for the stress field around an inclined borehole in an anisotropic medium, a computer program was developed and a serial parametric study was conducted. The effects of parameters such as degree of anisotropy, borehole inclination, bedding plane inclination and in-situ stress conditions on the stress distribution around a borehole were evaluated. The results showed that medium anisotropy has little effect on borehole fracture analysis at low borehole inclinations, but its influence becomes significant for highly inclined boreholes. As the degree of anisotropy varies the maximum shear stress changes remarkably. This indicates that the degree of anisotropy plays a role in the collapse failure of a borehole. The information generated in these studies can be used in predicting the fracture or collapse-initiating pressures.