A direct tracking method for a grounded conductor inside a pipeline from capacitance measurements

We present a new non-iterative method for tracking conductive water in a pipeline using a single excitation pattern from an interleaved ECT system. The problem arises, for example, in the oil industry where brine is often mixed with oil in a pipeline. If the size of the body of brine is very large compared with the size of electrodes attached to the pipeline, the corresponding electric potential in the region of brine is close to zero. This model leads to the inverse problem of identifying the dynamic change of the cross section of a grounded conducting region in a pipeline. Unfortunately, standard iterative reconstruction algorithms in ECT associated with the sensitivity matrix do not work in this case. Furthermore, due to the unavailability of Neumann data at the drive electrodes, the previously published layer potential methods for capturing the inhomogeneity are not applicable to this system. In this work, we derive a formula providing a concrete relation between the capacitance change in each receive electrode and the dynamical change in a grounded conducting region inside the pipeline. The proposed method successfully reconstructs feature information such as location and rough shape of the cross section of the water region. We demonstrate the performance of our method in numerical simulations and actual experiments.