# Research on the Soft-Sensing Method of Indicator Diagram of Beam Pumping Unit

## TL;DR

This paper introduces a new soft-sensing method to accurately calculate the indicator diagram of a beam pumping unit in oilfield operations.

## Contribution

The novel approach uses motor electrical parameters and beam inclination to improve stability and accuracy in indicator diagram calculation.

## Key findings

- The proposed method achieves an average relative error of less than 3.95%.
- The maximum relative error remains within 2% for six months, demonstrating long-term stability.
- The method uses a Butterworth filter to process data and eliminate singularity mutation values.

## Abstract

An accurate calculation of the indicator diagram of a pumping unit is the key factor in analyzing the performance of an oilfield production and operation and in preparing and optimizing an oilfield development plan. Aiming at the problems of the poor stability of the conventional load-displacement sensor method and the wave equation method, owing to the influence of an alternating load on the force sensor and the difficulty in measuring the crank angle using the electrical parameter method, a new soft sensing method employing the input electrical parameters of the motor and the beam inclination has been proposed to obtain the indicator diagram. At first, this method is established based on the beam angle of the pumping unit, which is easily measured using the suspension point displacement mathematics calculation model and the torque factor. Subsequently, the electric motor input parameters, the parameters of the four-bar linkage, and the relationship between the polished rod load have been established. Finally, the motor and the beam angle of the measured electrical parameters have been substituted into the calculation of the suspension point displacement and load value and pull in accordance with the guidelines to eliminate the singularity mutation values. After processing the measured data through a Butterworth filter, the indicator diagram is obtained. The results of the engineering experiment and application show that the average relative error of the method is less than 3.95%, and the maximum relative error remains within 2% for 6 months, which verifies the stability of the soft sensing method.