Sugio Imamura
Exploration Geophysics Laboratory, OVO Corporation, Daitakubo, Urawa, Saitama, Japan
ABSTRACT
I attempted to image the near-borehole resistivity apparent resistivity from normal resistivity logs.
I employed an axisymmetric FEM with 4CST elements to calculate the theoretical apparent resistivity. To simulate an infinite area, a coarse mesh was arranged around the target analysis area. The errors of the FEM result were less than 3%. The apparent resistivity of the FEM result showed good agreement with an analytical solution and a resistor network solution by Gianzero and Anderson, 1982.
To determine the near-borehole resistivity structure from the apparent resistivity value of normal logs, I used a nonlinear least square method. The target analysis area was divided into many cells and the resistivity of each cell was assumed to be constant. The model parameters to be determined were the mud resistivity and the resistivity values of each cell in the formation. I could obtain stable solution by solving the inversion scheme with a smoothness-constraint (Sasaki, 1989) in the radial direction.
I carried out some numerical experiments to investigate the efficiency of the technique. The results showed that for 10 potential electrodes aligned between 0.2m to 3.0m distance from the current electrode, we could obtain high quality resistivity images for about 2m from the borehole axis. The results also showed that for a conventional electrode array (16 inches and 64 inches), it was possible to get good images if the resistivity structure was relatively simple. Though influence of data noise on the reconstruction was negligible when the standard deviation of noise is 2%, the quality of reconstruction is considerably inferior when the standard deviation is 5%. Further, it was possible to obtain a complete reconstruction of the radial resistivity distribution, with a good convergence being achieved in less than 10 iterations.
Applying this technique to actual field data measured in a small oil field, the apparent resistivity calculated from the reconstructed resistivity structure was found to be in good agreement with the observed apparent resistivity. Our reconstruction revealed a high resistivity zone sandwiched between two low resistivity zones, that corresponds a limestone layer sandwiched between two shale layers. Further, the high porosity zone in the limestone layer was also imaged as relatively low resistivity zone.