Interface imaging in multiphase flow based on frame by frame eigenvalues of capacitance matrices from Electrical Capacitance Tomographic systems

Electrical Capacitance Tomographic (ECT) approach is a viable solution to measurement and control applications in the process industries, especially in the oil and gas industries, as systems certified for usage in explosive environments are available in the market today. In the process industries, there is often a need to identify certain parameters of interest in multiphase flow studies, depending on the relevant parameters to be control. There are a plethora of parameters such as interface levels, volumetric fractions of the different fluids, flow regimes, bubble size and velocity etc. Mathematical studies of the capacitance matrices for each frame obtained from ECT systems have shown that the eigenvalues of these have clear and vivid association with some of the flow related parameters. By studying the eigenvalues of these matrices for ECT based capacitance measurements C(i, j, t) with i=1 ... N, j= 1,2, ... N and i ≠ j obtained from ECT modules with N electrodes, some simple relationships are found between eigenvalues and interface levels for each frame for multiphase flows under carefully monitored inflow conditions of the different media. Monitored inflow conditions in the present study are flow rates of air, water and oil into a pipe which can be positioned at varying inclinations to the horizontal, similar to the subsea pipelines used in the oil and gas industries. Results presented in this paper, indicate that useful information on multiphase flow related parameters can be extracted from capacitance measurements thus rendering an imaging of the process with focus on certain features of interest to the process engineer.