Downhole Pump Monitoring via Wave Equation Analysis
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Solution Overview
Problem
Existing sucker rod pump monitoring systems suffer from noisy and delayed data processing, leading to inaccurate diagnosis of downhole pump conditions due to numerical finite differences and the need for complete pumping cycle data before calculations can be initiated.
Innovation Solution
Implementing a real-time monitoring system that solves the wave equation for downhole pump behavior by separating it into static and dynamic solutions using an integral-based method, allowing for immediate data processing throughout the pumping stroke without requiring periodic data sets.
Engineering Contradictions & Design Principles
Engineering Contradiction Analysis
1Productivity
If finite differences methodology is used to monitor pump conditions, then data processing can be performed, but the results become noisy and inaccurate
Solution Approach 1:
The patent replaces the mechanical/numerical finite differences methodology with an analytical wave equation solution approach. This substitution eliminates the noise amplification problem inherent in numerical differentiation while maintaining real-time data processing capability, thereby improving measurement precision without sacrificing productivity.
Solution Approach 2:
The patent changes the mathematical approach from discrete finite differences to continuous wave equation solutions. This parameter change in the mathematical model fundamentally alters how data is processed, transforming noisy numerical derivatives into smooth analytical solutions that accurately represent pump conditions.
2Measurement precision
If data is collected for the entire pumping cycle before calculations are initiated, then complete data is available, but real-time monitoring is not achieved
Solution Approach 1:
The patent implements preliminary action by pre-solving the wave equation with analytical solutions that can be applied immediately as data becomes available. This eliminates the need to wait for complete pumping cycle data, enabling real-time monitoring while maintaining data completeness through the analytical approach.
Solution Approach 2:
The patent transitions from static post-processing of complete cycle data to dynamic real-time calculation. The wave equation solution is designed to process data as it arrives during the pumping cycle, providing dynamic monitoring that responds immediately to changing conditions without requiring the entire cycle to complete first.
3Productivity
If numerical derivatives are used to estimate rod string behavior, then calculations can be performed, but noise is amplified at each step
Solution Approach 1:
The patent replaces the mechanical process of numerical differentiation with an analytical wave equation solution. This substitution eliminates the noise amplification mechanism inherent in numerical derivatives while preserving the ability to calculate rod string behavior in real-time, thus removing the harmful noise factor without sacrificing productivity.
Data Source
AI summary
Systems and methods for improved monitoring of downhole pump conditions may provide real-time monitoring, high accuracy, and low noise when monitoring downhole pump conditions. Systems for monitoring pump conditions may be coupled to any suitable sucker rod pump, and may gather desired data from the pump. The desired data may be gathered at several points-in-time during a pump stroke to provide real-time monitoring. A wave equation corresponding to the behavior of the downhole pump may be solved when the desired data is received to provide real-time monitor. In some embodiments, the wave equation may be solved by separating it into static and dynamic solutions. In some embodiments, the dynamic solution of the wave equation may be solved utilizing an integral-based method.