Normalized least-square method for water hold-up measurement in stratified oil–water flow

In this paper, a novel conductance sensor array is proposed for water hold-up measurement in horizontal oil wells of low liquid production of oil and water. The array consists of 24 needle-like electrodes that are mounted on 12 supporting arms arising from the central shaft, and it works within a well. As the value of water hold-up uniquely relates to the level of the oil–water interface, the measurement of water hold-up is transformed into the evaluation of the level of the oil–water interface. By numerical calculation, the variation of the conductance between each electrode and the ground with the level of oil–water interface and the proportional relationship between the conductance and water conductivity are obtained. Then the level of the oil–water interface is estimated by utilizing the 24 values of conductance between the 24 electrodes and the ground. First, whether the level of oil–water interface exceeds the lower limit of level estimation is judged by a coarse estimate. Second, the 24 values of conductance are normalized to eliminate the impact of water conductivity on the level estimation. Then, the least-square (LS) method is applied to match the measurement data with the sample data obtained from static experiments in advance. Experimental results show that both the water hold-up and the azimuth angle of the conductance sensor array can be estimated accurately by using the normalized LS method if the water hold-up exceeds a certain value.

► We propose a sensor array for water hold-up measurement in oil–water stratified flow.
► We transform the measurement into an evaluation of the level of the oil–water interface.
► The response of the array is sensitive to the level and the azimuth angle of the array.
► The evaluation evolves into a matching problem with the normalized least-square method.
► Both the level and the azimuth angle can be estimated accurately by using the method.