The Full-waveform Simulation Of Acoustic Logging While Drilling

In recent years, the LWD technology which is drilling and logging at the same timehas been developing rapidly. Compared to traditional wireline well logging technology,the LWD has many advantages, such as the damage to the borehole is small, thegeosteering drilling can be carried out, the logging costs are lower and so on. With theresistivity LWD technology is mature, but how the acoustic method is applied to theLWD to measure formation parameters, needs to find out the effect of the collar toformation compressional wave and shear wave velocity measurement. In addition, bynow we have not seen the simulation results about the acoustic LWD in transverseisotropic(TI) formation. Based on the problems about the process of sound wavepropagation and reception in LWD, respectively in the isotropic model and TI formationmodel, this paper deduced the analytical expression of sound field inside and outsideborehole excitated by the different forms of sound sources in LWD, and calculated thefull waveform of the acoustic LWD.Firstly, the formation is regarded as an elastic solid medium, well liquid isregarded as ideal fluid in the paper. We derive the expression of the displacement, stressand pressure in formation and borehole fluid respectively excitated by the multipolesource, and discuss the propagation characteristics of the P wave, SV wave and SHwave.Secondly, in the LWD conditions, we simulate the borehole acoustic field in theisotropic formation. we establish a simplified model of LWD; illustrate the method ofusing the cylindrical shell transducer to simulate monopole source, dipole source andquadrupole source; describe these sound sources in mathematics. We determine thecoefficients of the displacement potential function by the boundary conditions, and thenget the analytical solution of the acoustic field in LWD. The real axis integration methodis used to calculate the full wave acoustic in LWD, and the STC method is used toextract the velocities of various waves. By calculation we find that the collar waveexcitated by monopole source is obviously, but the collar wave amplitude excitated bydipole and quadrupole source is relatively small. At the same time, the higher orderacoustic field is more obvious in dipole source, but it’s not obvious in quadrupolesource, so the quadrupole source is more suitable for the LWD.Finally, the full waveform sound field in the transversely isotropic formation withLWD is simulated. After the analysis of elastic wave propagation properties in TImedium, under the condition of the well axis paralleling to the symmetry axis of the TIformation, we derive the analytical acoustic field expression in the TI formation withLWD. The real axis integration method is used to calculate the TI formation full waveform in LWD. And the calculation result is compared to the calculation result ofthe wireline logging in the TI formation. The calculation shows that, in the condition ofTI formation with LWD,the collars wave is still more obvious.