# Three-Dimensional Array Interpolation Imaging Algorithm of Water Holdup by the Capacitance Array Tool of Oil–Water Two-Phase Flow in Horizontal Wells

## TL;DR

This paper introduces a 3D imaging method for water holdup in horizontal oil-water two-phase flows using capacitance array data and evaluates three interpolation algorithms for accuracy and efficiency.

## Contribution

A novel 3D visualization method for water holdup in horizontal wells using natural neighbor interpolation is proposed and compared with other techniques.

## Key findings

- Natural neighbor interpolation outperforms linear and cubic spline methods in complex flow states with higher accuracy and robustness.
- Linear and cubic spline interpolation are suitable for stable flow fields with low-to-moderate flow rates and water holdup.
- Natural neighbor interpolation has higher computational costs but is recommended for complex or detail-sensitive scenarios.

## Abstract

Due to the gravitational differentiation effect, the oil–water two-phase flow in the horizontal well exhibits significant asymmetry and inhomogeneity in terms of phase distribution and velocity field. The existing logging techniques are difficult to use to precisely characterize the wellbore flow field under these conditions. To solve this problem, this study, based on the logging data of the Capacitance Array Tool, proposes a three-dimensional visualization method for the water holdup field in the wellbore and applies and evaluates three interpolation algorithms: linear interpolation, cubic spline interpolation, and natural neighbor interpolation. This paper relies on the multiphase flow experimental platform and uses industrial white oil and tap water as fluid media for experiments. It systematically studies the three-dimensional imaging characteristics under different angles, flow rates, and water cuts. The results show that the natural neighbor interpolation algorithm, with its advantage in topological reconstruction, effectively overcomes local mutations in complex flow states. It exhibits superior imaging accuracy and robustness under all operating conditions but has higher computational costs. In contrast, linear interpolation and cubic spline interpolation perform well only in stable flow fields with low-to-moderate flow rates and water holdup. In practical applications, for simple flow states, it is recommended to use computationally efficient linear or cubic spline interpolation methods; for complex flow states or scenarios requiring strict imaging details, the natural neighbor interpolation algorithm should be prioritized.