Rashed G., Ghajar R., Hashemi S.

Abstract A rotary oil well drill-string is primarily composed of drill-pipes and drill-collars. Its role is to convey a rotary downward motion to the drill-bit and to circulate the drilling fluid (drilling mud). A drilling borehole is cylindrically layered waveguide, consisting of mud inside the drillstring, mud outside the drillstring, and the formation. To understand how sound waves propagate in this layered medium, an infinitely long, uniform, three-layered waveguide surrounded by a radially infinite homogeneous formation is analyzed. The first layer is the inner mud, the second is the uniform pipe, and the third is the outer mud layer. The mud as well as the pipe and formation, are assumed to be homogeneous. It is also assumed that the steady mud velocity is slow compared to sound propagation speed in the mud and that static pressure in the mud is low compared to the bulk modulus, allowing their effects to be neglected. In this paper, an analysis of wave propagation in drilling borehole are greatly simplified by assuming axial symmetry and low frequencies with long wavelengths, compared to the borehole radius. Derivation and solution of equations of motion are presented. The non-dimensional parameters for determining the degree of the interactions among the layers are discussed. The upper bound frequency limitations on the application of this analysis are discussed. Sound reflection due to the changes in the cross section is analyzed. One important application of this analysis is to mud pulse telemetry systems. Finally, the key results are summarized and discussed.