Theoretical calculation of casing well sound field represented by slip interface

The classical elastic wave theory can be used to simulate the casedhole acoustic logging response by adding a fluid annulus between casing and cement sheath when the cement bonding is poor. The classical simulation results show that the casing wave amplitude is about 30% of the free-pipe amplitude even with 0.01 mm fluid annulus. The limitation in the traditional modeling of poor cement bond is that it requires an ideal interface shape such that the materials on both sides are completely separated. In field conditions, however, the interface gap (or micro-annulus) is often irregularly shaped with roughness or asperities, which, in the passing of casing waves, behaves like a partially coupled/decoupled interface. This is the scenario to apply the slip-interface modeling and use the shear coupling stiffness to characterize the degree of coupling. The slip-interface modeling is focused on the transition from the well-bonded to the un-bonded conditions. By comparing the wave structure simulated by slip interface theory with that simulated by classical elastic wave theory when a soft solid layer is added between casing and cement sheath, the applicability of slip interface theory in simulating cement cementation is verified. The combination of slip interface theory and classical elastic wave theory can simulate the response characteristics of casing wave amplitude from well cemented to free casing in cased wells. Combined with the radiation of compressional and shear waves in the formation, the radiation characteristics of acoustic field inside and outside the borehole with different cementation conditions are analyzed. With the decrease of cement cementation quality, the amplitude of casing wave and leaky waves into the formation gradually increase, the compressional wave and shear wave radiated into the formation through the borehole wall gradually decreases. The application of slip interface theory to simulate cementation in cased wells compensates the limitations of classical elastic wave theory and provides the possibility to quantitatively characterize the coupling stiffness at the interfaces.