四电极电导传感器敏感场的理论分析

Theoretical Analysis on Sensitivity Distributions of a Four-electrode Conductance Sensor

针对水为连续相条件下的油水两相流含水率测量问题,首先分析了环形四电极电导传感器敏感场正问题的数学模型。之后在此模型基础上,利用分离变量法推导了均匀媒质时传感器内部电势、轴向电流和径向电流的分布,并得到了简单非均匀媒质时场域内各点电压的数学理论解。最后,建立了油水两相环状流型下电导传感器含水率测量模型。结果表明,该模型与Begovich & Watson经典公式吻合,为进一步深入研究电导传感器的响应特性奠定了基础。

For the water volume fraction measurement of oil-in-water flow, the mathematical model for the forward problem of sensitivity field in the ring-shape four-electrode conductance sensor was analyzed. When the conductance sensor was filled with a homogenous medium, the sensitivity distributions of the electrical potential and the current density in radial and axial direction were derived by using the method of separation of variables. The voltage distribution was obtained when the conductance sensor was filled with a simple kind of two mediums. Then the measurement model of conductance sensor for oil-in-water annular flow was proposed, which was coincided with Begovich＆Watson＇ s equation. It lays a foundation for the future research on the response characteristics of the conductance sensor.