Velocity and flow field are both parameters to measure flow characteristics, which can help determine the logging location and response time of logging instruments. Particle image velocimetry (PIV) is an intuitive velocity measurement method. However, due to the limitations of image acquisition equipment and the flow pipe environment, the velocity of a horizontal small-diameter pipe with high water cut and low flow velocity based on PIV has measurement errors in excess of 20%. To solve this problem, this paper expands one-dimensional displacement sub-pixel fitting to two dimensions and improves the PIV algorithm by Kriging interpolation. The improved algorithm is used to correct the blank and error vectors. The simulation shows that the number of blank and error vectors is reduced, and the flow field curves are smooth and closer to the actual flow field. The experiment shows that the improved algorithm has a maximum measurement error of 5.9%, which is much lower than that of PIV, and that it also has high stability and a repeatability of 3.14%. The improved algorithm can compensate for the local missing flow field and reduce the requirements related to the measurement equipment and environment. The findings of this study can be helpful for the interpretation of well logging data and the design of well logging instruments.
Keywords: displacement sub-pixel fitting; horizontal well; kriging interpolation; oil–water two-phase flow; particle image velocimetry; velocity.