Earth Resources Laboratory :: Abstracts

Full Waveform Acoustic Logs in Radically Layered Boreholes

Kenneth M. Tubman

Submitted to the Department of Earth, Atmospheric, and Planetary Sciences on August 9, 1984 in partial fulfillment of the requirements for the degree of Doctor of Philosophy

Abstract

A general formulation is presented for the dispersion and propagation of elastic waves in a fluid-filled cylinder surrounded by an arbitrary number of solid or fluid annuli. A Thompson-Haskell type propagator matrix method is used to relate displacements and stresses across the layers. Synthetic microseismograms containing all body and guided wave arrivals are calculated with the method of discrete wavenumber integration. Attenuation is incorporated into the calculations through a transformation of the layer velocities to complex parameters.
A major classification of radial layers that are investigated are those corresponding to cased borehole geometries. Layers of steel and cement are inserted into the borehole. Fluid layers are mixed with the layers of steel, cement, and formation in order to model the situation of poor bonding.

It is found that in the well bonded situation the formation body waves are relatively unaffected by the presence of casing. The velocities and attenuation of the formation body waves can be determined in cased boreholes just as in open borehole situations. It is possible for the steel and cement layers to make more difficult than in an open hole. The amplitudes of the formation body waves depend on the relationship of the velocities of the formation and the cement. The guided waves are dominated by the steel and cement layers in most cases. The cement layer prevents the formation from having strong influence on guided waves. It the cement layer is thin or non-existent, the formation can have a larger effect on the character of the guided waves.

If there is a fluid layer between the steel and the cement the steel is free to ring. The first arrival in this situation is from the casing. Even with an extremely thin fluid layer, or microannulus, the first arrival is from the steel. The amplitude and duration of the pipe signal depends on the thickness of the fluid layer. While the first arrival is from the casing, the formation body wave energy is present. The character of the waveform will vary as the formation parameters vary. If the duration of the steel arrival is small it is possible to distinguish the formation P-wave arrival.

The situation is more complex if the fluid layer is between the cement and the formation. Here, steel is well bonded to the cement but the cement is not bonded to the formation. In this case the thickness of the fluid and cement layers become important in determining the nature of the first arrival. If there is a large amount of cement bonded to the steel, the cement can damp out the ringing of the pipe. A large amount of cement can damp out the casing arrival to the point where it is barely observable. This makes it possible to distinguish the formation arrivals.

If there is less cement bonded to the steel, the cement is not able to damp out the steel ringing. In this case the cement rings along with the steel and the first arrival is from the combination of the steel and the cement. The velocity of this wave depends on the velocities and thicknesses of the steel and cement layers.

Open hole geometries including radial layers due to the drilling process are also investigated. Additional layers in the model are those of an invaded zone, a damaged zone, or a mud cake. The presence of these layers does not necessarily affect the ability to determine the formation velocities with long spaced tools. Velocities observed are those of the virgin formation unless the source-receiver separation is particularly short or the depth of the alteration is large.

While the determination of formation velocities is not significantly affected the character of the microseismograms can be changed by the presence of an altered layer. A low velocity damage zone or mud cake can produce a large change in the amplitude of the formation P-wave arrival. Focusing of energy due to the velocity gradient can increase the amplitudes by as much as a factor or two. An invaded zone with velocities raised above those of the original formation can reduce the observed amplitudes of the formation P-wave.