Acoustoelastic Theory Of Guide Waves In A Cased Hole And Inversion Of Formation Stress By Cross-dipole Acoustic Logging

Many oil wells are destructed by the abnormal formation stresses in oil field, and most of which are cased hole. It is an urgent problem to solve now in oil field that one can estimates the abnormal formation stress by a nondestructive technique. Traditional acoustoelasticity theory is not directly applied in the well hole, because stress-induced anisotropy is inhomogeneous. It is complex for casing and cement, so that distribution of stress near borehole changes in cased hole. It is needed to develop the theory and method to fit for cased hole. The purpose of this paper is to study the theory of this nondestructive technique and to develop its method to practical application in estimating the abnormal formation stress directions and magnitudes from cross-dipole acoustic logging in cased hole, and is to study the acoustoelasticity formulations of anisotropy formation in bore hole. Acoustoelasticity equations for cased hole In this dissertation, firstly by solving distributions of stress fields around the well in each layer caused by stress concentration of borehole and utilizing perturbation integral method, acoustoelastical formulations only for the open hole are developed into the cases of being suitable to cased hole. Under the action of axial stress, sensitivity coefficients and velocity-stress coefficient in acoustoelastical formulations and dispersion curves of two dipole flexural modes polarized parallel and perpendicular to the applied stress direction are numerically investigated, respectively. The results show that velocity-stress coefficients primarily depend on the formation parameters, specially, the terms including third-elastic modulus in acoustoelastical formulations; the split of phase velocities of flexural modes with different polarization and crossover of their dispersion curves are still main characteristics of the formation anisotropy induced by stress for cased hole; but show dispersion curves of phase velocities of flexural modes move to higher frequency region yet. The results put forward new requirements to carry out forward and inverse operations in the case of cased hole. Analyzing dispersion of flexural mode wave In view of actual cases that dispersion curves usually be moved to the higher frequency region, we numerically calculate the flexural mode dispersion curves in the cased hole by changing parameter of mode and medium under not changing others, especially to that shear wave velocity is near or low to compressional wave velocity of fluid. The results show that compressional wave velocity and density of formation nearly influences on dispersion curves of flexural modes, but shear wave velocity of formation mostly influences on dispersion curves of flexural modes. When the shear wave velocity of formation tends to 1600m/s, lower limit that frequency extent of dispersion curves of dipole flexural mode moves to 10kHz, even high, and the move is quickly follow shear wave velocity towards to lower. We explore influence of thickness of casing among parameter of model, yet. The results show mainly in, first, this is no influencing when shear wave velocity is greater than 2000m/s; second, when shear waves velocity is greater than 1500m/s and is less than 2000m/s, the dispersion curves will be moved to the higher frequency region as the thickness of steel tube increases, but the dispersion curves will match together with the dispersion curves of in borehole surrounded by pure steel after the thickness increases to a fixed value; third, when shear waves velocity are lower 1600m/s, this velocity is more lower, the move speed is quickly with the addition of thickness. As a result, in cased hole, the dispersion curves will be moved to the higher frequency region due to radius of well reduction in higher velocity formation mostly; but it's due to influence of radius of well reduce, shear waves velocity and thickness of steel tube when the shear wave's velocity at near or low to compressional wave velocity of fluid. Inverse method Based on the acoustoelasticity formulations of borehole guided waves, we referred to a multi-frequency inversion model. We can utilize equations of multi-frequency inversion to estimate third-order elastic constants and stress of formation, as parameters of steel tube and cement are known. Nevertheless when we check up inversion program by utilizing result of numerical and three-dimension SV-FD method, it is found that velocity yawp influences the result of third-order elastic constants but hardly influences the results of stress, because sensitivity coefficients is small, but stress and velocity are large comparatively. Numerical results show that the sensitivity coefficients is not related with frequency and tend to fixed values at lower frequency region, because the phase velocities of flexural modes trend to shear wave velocity of formation velocity. We calculate coefficients that unrelated and related with third-order elastic constants, respectively, by varying parameters of formation in formulation of stress difference. The fixed value can be expressed in formulation of stress difference by known parameter of formation, but not in formulation of stress sum. The contribution of steel and cement to sensitivity coefficients is very small, so that it can be ignored. We studied cross-dipole logging data in DaQing oil field. Utilizing characteristic of phase velocities of flexural modes tend to velocities of shear wave in low frequency...