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.