Frederick L. Paillet

A numerical investigation of head waves and leaky modes in fluid‐filled boreholes

Although synthetic borehole seismograms can be computed for a wide range of borehole conditions, the physical nature of shear and compressional head waves in fluid‐filled boreholes is poorly understood. This paper presents a series of numerical experiments designed to explain the physical mechanisms controlling head‐wave propagation in boreholes. These calculations demonstrate the existence of compressional normal modes equivalent to shear normal modes, or pseudo‐Rayleigh waves, with sequential cutoff frequencies spaced between the cutoff frequencies for the shear normal modes. Major contributions to head‐wave spectra occur in discrete peaks at frequencies just below mode cutoff for both compressional and shear modes. This result is confirmed by calculations with synthetic waveforms at frequencies corresponding to mode cutoff, and by branch‐cut integrals designed to yield independent spectra for the compressional mode. For soft formations where shear velocity falls below acoustic velocity in the borehole ...

A mass-balance code for the quantitative interpretation of fluid column profiles in ground-water studies

A simple mass-balance code allows effective modeling of conventional fluid column resistivity logs in dilution tests involving column replacement with either distilled water or dilute brine. Modeling a series of column profiles where the inflowing formation water introduces water quality interfaces propagating along the borehole gives effective estimates of the rate of borehole flow. Application of the dilution model yields estimates of borehole flow rates that agree with measurements made with the heat-pulse flowmeter under ambient and pumping conditions. Model dilution experiments are used to demonstrate how dilution logging can extend the range of borehole flow measurement at least an order of magnitude beyond that achieved with flowmeters. However, dilution logging has the same dynamic range limitation encountered with flowmeters because it is difficult to detect and characterize flow zones that contribute a small fraction of total flow when that contribution is superimposed on a larger flow. When the smaller contribution is located below the primary zone, ambient downflow may disguise the zone if pumping is not strong enough to reverse the outflow. This situation can be addressed by increased pumping. But this is likely to make the moveout of water quality interfaces too fast to measure in the upper part of the borehole, so that a combination of flowmeter and dilution method may be more appropriate. Numerical experiments show that the expected weak horizontal flow across the borehole at conductive zones would be almost impossible to recognize if any ambient vertical flow is present. In situations where natural water quality differences occur such as flowing boreholes or injection experiments, the simple mass-balance code can be used to quantitatively model the evolution of fluid column logs. Otherwise, dilution experiments can be combined with high-resolution flowmeter profiles to obtain results not attainable using either method alone.