A Numerical Sensitivity Study of Three Dimensional Imaging From A Single Borehole
David L. Alumbaugh and Michael J. Wilt
ABSTRACT
This paper describes a sensitivity analysis for a prototype induction logging instrument designed for three dimensional imaging of the region surrounding a wellbore. This prototype tool consists of three mutually orthogonal magnetic solenoidal transmitters and multiple three-component magnetic field receivers offset at different distances from the source.The sensitivity functions are derived by taking the Born approximation to the integral equation for dipole magnetic fields within an inhomogeneous medium. The analysis shows that the standard axial configuration, where the magnetic moments of both the source and the receiver are aligned with the well-bore axis, offers superior sensitivity away from the borehole as compared to any other configuration. It also offers the best signal-to-noise characteristics. However, due to the cylindrically symmetric configuration of the instrument and the borehole, coaxial data can be interpreted only with a two-dimensional cylindrical model; three-dimensional (3-D) interpretation requires the measurements of the two orthogonal transverse field components in conjunction with the axial component. Coil configurations where both the source and receiver are perpendicular to the instrument axis can increase resolution and provide some directional information, but they offer no true 3D information and are sensitive to borehole effects. 3D imaging is possible at offsets up to 50m from the wellbore, if larger-than-normal source-receiver offsets are employed, although the resolution decreases rapidly away from the borehole.
An inversion algorithm is employed to demonstrate the plausibility of 3-D imaging using three component magnetic field data. The model employed simulates a horizontal well drilled through a faulted dipping oil sand/water sand/shale sequence. Synthetic data were generated using a 3-D finite difference code, noise added, and a 3-D inversion applied. In general, the inversion recovers the main features of the model including the location of the fault and the dip of the structure. When mutually orthogonal sources are employed, in addition to a single axial transmitter, the resolution of the image is markedly improved. The use of longer transmitter-receiver offsets results in greater depth of imaging away from the borehole.
Effect of Internal Field Gradients on NMR Measurements
Gigi Qian Zhang, George J. Hirasaki and Waylon V. House
ABSTRACT
The similarity of the values of NMR surface relaxivity of sandstones has led to the adoption of a default value of the T2 irreducible water saturation cut-off for all sandstones. A chlorite-coated North Burbank sandstone, however, should be treated as an exception since the T2 distribution is strongly dependent on the echo spacing. It also has T1/T2 and r2/r1 ratios that are larger than most values reported in the literature.Compared to Berea sandstone, chlorite-coated North Burbank sandstone shows a much stronger diffusion relaxation due to internal field gradients on NMR T2 measurements, that develop because of the high magnetic susceptibility contrast between chlorite flakes and pore fluids. The type of clay and its distribution in rocks determine the extent of the diffusion effect on T2 measurements. Chlorite is particularly important because this clay is often paramagnetic and lines the pore walls.
A series of experiments on chlorite and kaolinite/ fluid slurries were performed. There is clear evidence of strong internal magnetic-field gradients in chlorite/fluid systems. Kaolinite, lacking iron, is diamagnetic and thus shows a smaller diffusion relaxation. The significance of diffusion relaxation caused by internal field gradients depends on the magnitude of this effect compared to the relaxation rate generated by bulk-fluid relaxation and surface relaxation.
How the Depth of Investigation Changes with Spacing: A Computer Model for Carbon/Oxygen Logging
H. Zheng
ABSTRACT
C/O tools using dual-spaced detectors have been developed by several companies. It is necessary to understand the depth of investigation of the two detectors for applying the tools to cased-hole reservoirs. How the depth of investigation changes with the detector spacing is simulated for a large-size C/O tool in a high-porosity formation, using a general-purpose Monte Carlo computer code for radiation transport. The computer model is structured in a 35 p.u. sandstone formation which is segregated into 8 concentric zones all with radial thickness of 7.5 cm. A 3½-in (8.9 cm) outer diameter tool is eccentered in 5½-in (14 cm) casing, which is centrally cemented in a 7-in (20 cm) borehole. As the water-saturated zones are progressively replaced by oil-saturated zones, C/O ratios from inelastic gamma spectra at different spacings are calculated. For certain spacings, the trend of C/O ratio increasing with oil-zone radial thickness may be regressed using a sigmoid function, and the depth of investigation can be obtained. Calculated results show that the relationship between the depth of investigation and spacing appears roughly linear, and the investigation depths of the dual-spaced detectors in a C/O tool are significantly different.