Dispersion Curves and Synthetic Microseismograms in Unbonded Cased Boreholes

Abstract

The dispersion relations and impulse response. are calculated for a geometry consisting of an arbitrary number of coaxial annuli surrounding a central cylinder. The annuli may be either solid or fluid. The formulation allows any number of solid and fluid layers in any sequence. The only restrictions are that the central cylinder is fluid and the outermost layer is solid. A propagator matrix method is used to relate stresses and displacements across layer boundaries. Fluid layers are handled by directly relating the displacements and stresses across these layers. A number of examples of dispersion curves and synthetic waveforms are given. The speciflc geometries used are those for a pipe not bonded to the cement and for the pipe well bonded to the cement but with the cement not bonded to the formation. The addition of an intermediate fluid layer can have a large effect on the calculated waveforms. More surprisingly, this additional layer may have only minor effects, indicating possible difficulties in establishing its presence. It the fluid layer lies between the steel and the cement (free pipe situation), the first arrival is from the steel. This is the case even for a very thin layer, or microannulus. If the fluid layer is between the cement and the formation,. the thicknesses of the cement and fluid layers become important in determining what will be the first arrival as well as the nature of the microseismogram. An intermediate fluid layer is shown to have the additional effect of introducing another Stoneley wave mode. This mode has only a small amount of energy and so it does not contribute significantly to the calculated· microseismograms.