Finite-difference Numerical Modeling Of Borehole Acoustic Logging In Porous Formation

Acoustic logging is one of the important geophysical logging methods. It is extensively used in oil exploration, engineering geophysical exploration and the other areas of geophysical exploration. In the process of oil exploration and development, the problems we faced are more and more complex, and the precision of oil and gas exploration we require is more and more delicate. Generally speaking, the storage way of oil and gas is porous. The oil and gas reservoir stratum is two-phase medium or multiphase medium. The data we collect contain lots of information that have to do with porosity, permeability and saturation. In order to analyze and interpret the information better, the most important theory by far named two-phase Biot elastic wave propagation theory must be applied to oil and gas exploration.After years of development, two-phase Biot elastic wave propagation theory has become a complete theoretical system. By way of solving the two-phase Biot elastic wave equation, we can simulate the full acoustic wave train based on two-phase Biot medium borehole model. Analyze the characteristics and propagation law of the full wave, and the effects of the change of some factors, such as elastic parameters of formation, porosity and permeability. Through the analysis of these conclusions, we can provide some reference, what is about the recognition and analysis of oil and gas reservoir, for actual oil and gas exploration.In this paper, we build two-phase Biot medium borehole model to simulate borehole acoustic wave field of the porous formation. Change two-phase Biot medium balance equation to two-phase Biot medium first-order rate-stress elastic wave equation, and then solve this equation by staggered-grid finite-difference method, we can get the full wave train of borehole acoustic wave field. This kind of calculation method has faster computation speed and smaller computer memory. High-order staggered-grid difference scheme can improve the simulation accuracy and eliminate numerical dispersion. On the premise of meeting the stability conditions, if we choose the right space step and time step, then we can simulate accurately the full acoustic wave train of complex geological model.Because of the detecting depth of acoustic logging is shallow, and calculation method is limited by computer storage and computational efficiency, we have to divide the calculation area into bounded area, namely introduce artificial boundary around the area. When the acoustic waves spread to the artificial boundary, the reflected wave will be created. The reflected wave can have serious interference on the wave train. For reducing or eliminating the reflected wave, we need to introduce a kind of absorbing boundary condition that is highly efficient. In this paper, we use the boundary condition which is named the perfectly matched layer. The perfectly matched layer boundary condition can absorb the reflected wave better and if we choose the reasonable attenuation factor, the absorbing effect will be excellent and the simulation of the borehole acoustic field will be more accurate.The results show that the change of elastic parameters of formation will have an effect on the every mode wave of the full acoustic wave. The bigger acoustic velocity of stratum is, the greater the amplitude of wave train is, and the earlier the receivers will receive the wave train. In the context of fluid in porous medium, compared to tight medium, the velocity and amplitude of mode wave of acoustic wave are smaller. Especially the Stoneley wave, its attenuation speed is faster in the fluid. The change of permeability can have a smaller impact on the P-wave and the S-wave, but it has a great impact on the Stoneley wave. The bigger permeability of medium is, the faster the attenuation speed of the Stoneley wave is. We can make use of the attenuation speed of the Stoneley wave to determine the permeability of porous medium indirectly.