Numerical Simulation Study On Borehole Acoustic Field With Low Density Cementing

In this paper the theory about cement bond logging using low density and normal densitycement are studied theoretically and the theory of sound field is analyzed meanwhile. numericalsimulation are numerical simulation are conducted.In Part one, the acoustic fields in a borehole embedded in radically dual-layered media excitedby an eccentric point source is studied. The potential function of acoustic fields in a borehole isobtained by solving wave equation of motions. By using the expansion approach of multiples,the Real Axis Integration (RAI) method, and Fast Fourier Transform (FFT), the waveforms forboth the eccentric and centric sources are calculated and analyzed. These waveforms arecompared with each other for both eccentric and centric sources. Numerical results show that thecut-off frequencies of the nonsymmetrical mode waves excited by multiple sources vary greatlywith the order of the multipoles. At low frequencies, it is difficult for high order multipolesources to generate nonsymmetrical modes, and the shear wave signals are weak in the fullwaveforms of which the amplitude is low. They excite strong shear arrivals only when the centerfrequency approaches to the cut-off frequency of the high order modes. For the eccentric pointsource, the amplitude of the shear waves in its full waveforms similar to that for the centricmonopole source is very low as the center frequency is low (such as lower than 2kHz). With theincrease of the center frequency, the full waveforms become more complicated and theiramplitude increases also. At the same time, shear waves propagating as first arrivals becomeevident. That is not consistent with the waveforms of the centric source. In addition, sourceeccentricity has little effect on full waveforms except their amplitudes.The second part mainly focuses on the study of the acoustic fields of centric sources in acased hole. according to the known parameters of media and well the full wavetrain of acousticwave are simulated. when the acoustic source is in the middle of well(along well axis), boreholeacoustic field can be separated along well axis. Starting from wave equation and using normalmethod we can get analytic expression and calculate the waveform in time domain or 2-Dspectrum in frequence domain. The result shows that when the bond between I interface and Ⅱinterface is well bonded and the source space is small the effect caused by the changing ofboundary condition is small. With the thickness of concrete circleincreasing , Ⅱ interface'seffect to the borehole sound field is smaller. To low density cementing when the thickness ofconcrete circle arrives to a small value (6～8cm), Ⅱ interface's effect to cased wave can beneglected. The heavier of the cementing density is, the influence caused by Ⅱ interface isbigger. After the thickness of concrete circle arrive to a certain value,the amplitude of casedwave won't change. This paper provide a necessary theory for the explanation to well cementingdata in oil field.