Guided Wave Propagation in a Double-Pipe System: Theory and Method

Downhole acoustic measurements often involve double- pipe or multi-pipe systems, presenting various challenges. This can include scenarios such as at the cross-over of two casing sizes or logging through tubing in a cased hole during the plug and abandonment (P&A) procedure. When dealing with a double-casing system or a tubing-casing system, it presents challenges when running a sonic or ultrasonic tool in the borehole. This is because the wavefield becomes complicated, and the first pipe may block most signals in the inner fluid layer. The situation becomes even more challenging if the first pipe is not properly centered within the second pipe. These challenges underscore the need for innovative solutions in downhole acoustic measurements, a need that this research aims to fulfill. Previous studies have examined the standard 3ft CBL method, which utilizes spectrum analysis to assess bonding conditions and synthetic waveforms with traditional array receivers. These studies suggest that even though the sensors are located within the first pipe, the recorded signal spectrum or waveforms are still influenced by the material behind the second pipe. These findings indicate the potential for detecting bonding information beyond the second pipe. This paper uses the classic modal analysis method to examine the modal waves in a double-pipe system. The governing matrix equation for wave propagation is generated based on the boundary conditions at each pipe's internal and external interfaces. We investigate the principles of each mode and their sensitivity to different modal parameters to understand the dependence and dominant layer of the modes. Additionally, we modify the propagation equations at the center of the borehole to absorb the fluid modes, thereby gaining further insights into the propagation of these modes in each layer and the coupling of the layer modes with the fluid modes. The study demonstrates how signals can pass through the first pipe and generate signals in the second pipe, enabling evaluation of the second pipe. It also underscores the practical relevance of the research by demonstrating the azimuthal sensitivity of each mode and the potential application of the modes for an azimuthal assessment of the second pipe and the bonding material behind it. The results indicate that, despite the intense fluid mode in the center of the borehole, guided waves related to the tubing, casing, and annulus can still be observed. These signals often have different speeds and frequencies in a specific frequency range of interest and can be separated through signal processing. Among these, the casing- guided waves primarily travel in the casing and can be distinguished from the fluid mode and other signals with proper processing. Additionally, they exhibit good sensitivity to azimuth. Therefore, casing-guided waves have the potential for further application in evaluating the second pipe and the bonding material behind it. The paper presents the methodology and research findings as a promising foundation for processing borehole array sonic data for evaluating the second pipe. It also demonstrates the fundamental theory guiding the design of a double-pipe sonic tool, offering a promising outlook for the future of downhole acoustic measurements.