An analytical–numerical formulation to modelling wave propagation in double-cased oil wells

Abstract

A reliable non-destructive test to assess the integrity of double-cased wells is still an open task. In the present work, we introduce an analytical–numerical formulation for modelling the wave propagation in such structures. The formulation was developed with the aid of the invariant embedding technique and is numerically unconditionally stable even for high frequencies. Usually, the invariant embedding technique is employed in cases of solid stratified media. Here, due to the nature of the structure under investigation, we had to extend the technique to accommodate fluid layers as well. We illustrated the use and relevance of the developed formulation modelling the wave propagation in a typical double-cased pipe and identifying the frequencies and angles of incidence that most strongly interact with defects placed at the critical casing layer/cement sheath interface. Based on a robustness analysis, we further indicated what would presumably be the best inspecting field. In that sense, we hope our formulation can help in the optimum experiment design of strategies aimed at assessing the structural integrity of double-cased wells.