The Numerical Simulation And Application Study On Radially Varying Formation

Formation radial shear wave velocity can provide critical information concerningwellbore stability, stress prediction. The borehole acoustic method is an effectivenondestructive method for getting the distribution of shear wave velocity. Aiming at thepractical problems with radially varying formation, this study build up the borehole modelwith radial varying, give the acoustic logging theory combining the analyticalmethod(Thomson-Haskell propagation matrix) with numerical method(Perturbation theory).We analyse both the B-G inversion method and constrained inversion method, finally wechoose the constrained inversion method as this study’s major inversion method. Basing onthe borehole acoustoelasticity theory, this study give the Logging-While-Drilling (LWD)acoustoelasticity theory and the method of recognizing the stress.Aiming at acoustic logging problems with cylindrical layered structure, it should adoptthe Thomson-Haskell propagation matrix method, such as casing acoustic logging, LWDacoustic logging and the logging with single alteration formation. Aiming at the problemswith continuously varying formation due to stress induced and the drilling damage. In fact,the continuously varying formation coexist with the instrument cylindrical structure inborehole. Combining the two theory and method, this study give the acoustic theory withradial variation both in and out the borehole.On the basis of the perturbation theory, we built the relation between the change of theformation elastic modulus and that of the phase velocity, and we also gave the perturbedintegral formula which can be used to calculate the phase velocity changes from the formationradial continuously varying profile. The systematic errors of the perturbed integral found inthe numerical simulation gave us the B_G inversion method and constrained inversionmethod, and then we used the perturbation integral to calculate the dominant value of theradial continuously varying profile and to prove the constrained method is right. The erroranalysis of the two methods above shows us the calculation accuracy of the constrainedmethod is more higher. And therefore, we gave several examples of processing the field datawith the help of the constrained method, and the processing results showed us the constrainedmethod could have a better reflection of the radial shear velocity changes near borehole. According to the elastic theory of the open hole, we gave the elastic theory which can beapplied in the LWD. And the numerical simulation results showed that the LWD quadrupolecouln’t distinguish the different azimuth, and so the shear velocity profile obtained frominversing the LWD quadrupole data under the condition of stress was a average effect, and itreflected the radial shear wave information in the azimuth of45°. And at last, we used thedispersion curves difference between the dispersion curves of the LWD quadrupole and thatof the uniform formation model theory to reflect the formation shear wave velocity changesoutside the borehole caused by the uneven stress, and this is borehole stress concentrationphenomenon.