Finite-Difference For Porous Medium Well Logging And Absorbing Boundary Condition

Acoustic well logging is one of the important well logging methods in oil well logging. It can be used to explore the site and the character of oil and gas by continuing record and instant acoustic source pulse which is excitated in the well and affected by formation. Its theoretic basement is the excitation and propa-gation of elastic wave in cylindrical multi-layer medium and what the most inter-related is acoustic wave.The mechanic of excitation and propagation of borehole acoustic wave is closely interrelated to the characteristics of the formation, which is one of the im-portant aspect in the theory research of the borehole acoustic wave. Which involves different types of medium: for example, quasielastic medium and aniso-tropic medium, different types of acoustic sources: for example, head wave, transverse wave and all sorts of modes. The theory and the explaining method of acoustic wave logging become more and more important in complicated borehole environment since the developing demand of complicated oil reservoir, gas pros-pecting and particular explaining. As the complicated of the practice formation and the borehole environment, to apply the pure numerical method—finite-difference method to solve the borehole acoustic wave, is one of the important and effective means in the forward research of acoustic well logging. In this paper, the research work developed around the finite-difference technique about borehole acoustic wave in coordinates.At first illustrating the theory of the finite-difference method and the absorbing cylindrical condition.Second, based on the two-phase Biot theory, the elastic wave equation is derived in the borehole and out of the borehole in cylindrical coordinates and the corresponding finite-difference equation and the finite-difference equation of the Reynolds absorbing condition and Liao absorbing condition are also derived.In this department, we also deal with the source.As followed, according to the model illustrated in this paper, we compute the full wave of the borehole which is filled with fluid and surrounded by the two-phase homogeneous Biot medium and the equivalent single-phase elastic...