AXI-symmetric inversion of electrical resistivity tomography data to monitor the movement of fluids injected in wells

Where does a conductive fluid go immediately after it is injected in a well? One way to address this question is to image the injection process using electrical resistivity tomography (ERT). Traditional 3-D acquisition and inversion methods are typically too slow and lack sufficient resolution to accurately image the injection process itself. To address this problem, we develop and demonstrate an axi-symmetric approach to ERT imaging. The approach makes use of circulating dipole-dipole data acquired along an array of electrodes located in the injection well, and an axi-symmetric 2-D inversion scheme. We demonstrate the method using time-lapse ERT data collected during a saline tracer test (single-well injection-withdrawal experiment) in an alluvial aquifer. The dipole-dipole surveys were collected at six-minute intervals during the injection process, and inversions using a coarse mesh (69 by 77 elements) took less than a minute per data set on a laptop computer. Subsequent inversions using a large, finely discretized mesh (137 × 157 elements) required 26 minutes per survey on the same computer. Both coarse and fine images clearly show the movement of the tracer away from the packed-off injection interval with time. At early times, the tracer movement is primarily vertical, up and down the annular space around the well casing. Later, the tracer appears to move away from the well, preferentially along a number of thin layers, including layers that do not intersect the injection interval. Images constructed using the axi-symmetric inversion of single-borehole data at the conclusion of the injection process are very similar to images constructed using 3-D inversion of multi-borehole data. The axi-symmetric approach is well suited to modeling borehole effects and allows discretizing the near-borehole region at much finer scales than is practical for fully 3-D inversions. The pre-infiltration, background images show a cylindrical band of high resistivity outside the well. This observation and subsequent model studies suggest that this resistive artifact results from a conductive region roughly the diameter of the well casing.