Theoretical Simulations Of Monopole And Dipole Acoustic Logging While Drilling And Investigations Of Propagation Mechanism For Individual Waves

In recent years,the logging while drilling(LWD)technology which is drilling and logging at the same time has been developing rapidly.Compared to wireline well logging technology in which logging is carried on after drilling,the LWD has many advantages,such as the damage to the borehole is small,the geosteering drilling can be carried out,the logging cost is lower and so on.With the resistivity LWD and nuclear magnetic resonance LWD technology is mature,but there are two problems to be solved in the acoustic LWD.The first one is that the collar wave in the full waveform which has been found to interfere with signals from the formation,making it difficult to obtain stratum information from acoustic LWD signals.The second problem is how to obtain the shear velocity of slow formation from the acoustic LWD.To solve these problems,a theoretical model is built to study the acoustic LWD technology in this paper.The propagation mechanism of monopole and dipole acoustic fields has been analyzed to research the property of the collar wave.The seismoelectric signals induced by the acoustic field are theoretically simulated.To obtain the propagation mechanisms of each individual wave,the component wave analysis method is used to study the acoustic LWD field.It is proved that only formation compressional and shear branch points are true branch points of the acoustic field.The choices of Riemann sheets in the complex wavenumber plane are determined by radiation conditions.A two-dimension searching method is used to locate the poles of the integrated function.The contributions of the branch points and poles can be evaluated by the branch-cut integral and residue theorem,respectively.The formula derivation for component wave analysis method has been achieved in this paper.All mode waves and critically refracted waves are simulated under a monopole LWD environment.Each individual wave is separately shown,with its dispersion,attenuation and excitation intensity being analyzed.It is found that the formation leaky modes have influence on the critically refracted waves in monopole LWD.The collar wave propagates in the formation as well as in the collar and borehole.The excitation spectra of the displacement in the formation show that the amplitude of the first order monopole collar wave is much larger relative to the formation P wave.Although the dispersion of the collar wave is almost irrelevant to the formation,the attenuation and excitation intensity of collar wave are significantly affected by the formation.Therefore,the model of the collar being set in a borehole must be integrally considered when proposing a design to weaken the collar wave.When the frequency is higher than 2k Hz,the amplitude of collar wave at the inner rim is greater than that at the outer rim.Therefore,grooving at the inner rim of collar is more effective to weaken the collar wave than grooving at the outer rim.The component wave analysis method is used to study the dipole acoustic LWD field.The dispersion,attenuation and excitation intensity curves of all dipole individual waves are shown and discussed.It is found that the dispersion of dipole collar wave is affected by the formation.In the borehole,the first order dipole collar mode has a low cut-off frequency,and its cut-off velocity is the formation shear wave speed.There is a non-leaky liquid-solid surface wave in dipole LWD field.Therefore,the formation dissipative value can be estimated by measuring the attenuation of this mode.In a slow formation,when the frequency is higher than 10 k Hz,the dispersion of surface mode is too weak,and the velocity of this mode is greatly influenced by the formation shear wave speed.After analyzing the calculation results,it is found that the velocity of the surface wave is very sensitive to the formation shear wave speed.Thus,it is proposed that the center frequency of the dipole should be set to 10 k Hz so that the formation shear velocity can be obtained from measuring the speed of surface wave in dipole LWD.The theoretical expressions of seismoelectric LWD are derived based on oneway conversion approximation and quasi-static assumption.The pore pressure can be estimated from confining pressure by the relation between the confining pressure and pore pressure.The seismoelectric full waveforms are simulated by real axis integration method.Numerical results show that the pore pressure gradient has an important effect on the seismoelectric conversion efficiency in the seismoelectric LWD,especially for the Stoneley wave.In the full waveform of the synthesized electric field,there is a signal travelling with the collar wave speed.The converted electric collar wave signal is weaker than its acoustic counterpart,in terms of their amplitudes relative to other wave groups in their respective full waveforms.Finally,when the frequency is too high or the layer is too thick,arithmetic overflow occurs in the calculation of the acoustic field in a cylindrically layered model.To solve this problem,an algorithm based on the normalized Hankel functions and generalized R/T coefficients method is extended to simulate the non-axisymmetric acoustic fields in a radially layered model excited by a multipole source.The generalized R/T coefficients matrices have been derived for the solid-solid,liquid-solid and solid-liquid interface,respectively.A set of numerical experiments show that this algorithm is effective in simulating the acoustic field in the complex radially layered media and solves the numerical overflow problem completely.