Acoustical plane P wave scattered by a cased borehole

摘要

Conventional acoustic logging suffers from a shallow radical detection distance, and therefore it is limited when the detected formation is far from the borehole. The cross-hole seismic is one of the methods to overcome this shortcoming. Plenty of experimental data have shown the advantages of the cross-hole seismic in detecting fine features of oil reservoir. As development of science and technology, acoustical logging gives us a good research topic about acoustic scattering on a borehole or cased borehole. It is also of significance to the explanation of VSP and cross-well seismic. The acoustical scattering on a borehole has been investigated in many references, and few authors studied the acoustical scattering on a cased borehole. In this paper, the theoretical analysis on the plane P-wave scattering is extended from the borehole to the cased borehole. Theoretical and numerical researches about the plane P-wave scattering on the cased borehole surrounded by a fluid-filled saturated porous medium are carried out. The acoustic resonance characteristic of the cased borehole is studied in detail. Firstly, the acoustical plane P wave is expanded as superposition of the cylindrical waves with each order. The general expression of the acoustic fields inside and outside the cased borehole is derived according to Biot's theory and boundary conditions. Then, the effects of the borehole radius, incident angle, porosity and permeability on the acoustic field are numerically studied in hard and soft formations respectively. Finally, the acoustical resonance phenomenon of the cased borehole is investigated.