Mandrel effects on the dipole flexural mode in a borehole

The flexural mode is the lowest-order borehole mode with dipole excitation. The low-frequency asymptote of the flexural wave speed is used to estimate the formation shear speed in well logging. The borehole flexural mode measurement system consists of a mandrel that holds the transmitter and an array of receivers. This mandrel is, generally, designed to minimize the interference between any mandrel and the borehole flexural modes. A slotted sleeve housing that makes the sleeve arrival significantly slower than the formation arrival enables the processing of the recorded waveforms based on a model of fluid-filled boreholes without any mandrel. The objective of this work is to investigate the basic physics of mandrel effects on borehole flexural mode for the condition that the mandrel is in the form of a rod or pipe that is not necessarily slower than the formation arrivals. To this end, we describe an experimental and theoretical study of flexural modes in a borehole with a concentric mandrel and water annulus. The mandrels are of simple geometry such as a rod or a pipe, not intended to model any particular sonic tool in its entirety. However, the presence of a rod or a pipe can approximately represent the waveguide nature of the mandrel and its possible influence on borehole flexural modes. A fluid-filled (without any tool) borehole and a mandrel immersed in an infinite fluid (without any borehole) are two independent systems. Each supports a flexural mode that can be excited by a dipole source. These two uncoupled modes have distinct velocity dispersions. In a coupled mandrel-in-borehole system, two flexural modes are generated with a dipole source. These two coupled modes may resemble or significantly differ from the two uncoupled modes depending on the proximity of dispersions of these two uncoupled modes.