Numerical simulation study of the acoustic wave propagation in a drilling mud invasion borehole

A theoretical borehole model based on Biot's theory on acoustic wave propagation in a fluid-saturated formation has been established for modeling acoustic logging response influenced by drilling mud invasion. The acoustic wave propagation equation has been solved with the potential function methods in the axial-symmetrical column coordinates system for simulating the real formation. The logging responses of the borehole fluid, the logging tool and the formation are considered respectively. The analytical solution of the acoustic field in borehole fluid and formation are all obtained. Two typical invasion profiles are considered for the numerical calculation. The acoustic wave velocity and waveform are discussed based on the numerical calculation for a monopole point source with the real axis integral method. A simple computation example validates the program. The result shows that the model can simulate the acoustic propagation in a fluid filled formation invaded by the drilling mud.