Downhole Card Calculation in Deviated Wells
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Solution Overview
Problem
Current methods for calculating downhole data in sucker rod pump systems fail to accurately account for mechanical friction in deviated wells, leading to distorted downhole cards and inaccurate representation of downhole conditions, which can result in inefficient operation and potential damage to pump components.
Innovation Solution
The modified Everitt-Jennings algorithm is adapted to incorporate mechanical friction factors by solving a system of coupled non-linear differential equations using finite differences, specifically considering axial and transverse displacements of the rod element, and incorporating Coulomb's friction to accurately model the behavior of rod strings in deviated wells.
Engineering Contradictions & Design Principles
Engineering Contradiction Analysis
1Measurement precision
If current methods for calculating downhole data are used in deviated wells, then the calculation process is simple, but the accuracy of downhole card representation deteriorates due to unaccounted mechanical friction
Solution Approach 1:
The patent transforms the calculation approach by changing the mathematical parameters from simple wave equation solutions to a system of coupled non-linear differential equations that incorporate mechanical friction parameters. This allows accurate representation of downhole conditions in deviated wells by accounting for friction forces between the rod string and wellbore, while maintaining computational feasibility through numerical solution methods.
Solution Approach 2:
The patent introduces a mathematical model as an intermediary between the physical system (rod string in deviated well) and the measurement data (surface measurements). This model acts as a mediator that translates surface measurements into accurate downhole conditions by incorporating friction effects, enabling precise downhole card generation without direct downhole measurement.
2Reliability
If mechanical friction is incorporated into the calculation model for deviated wells, then the representation of downhole conditions improves, but the computational complexity increases
Solution Approach 1:
The patent replaces the need for complex mechanical measurement systems downhole with a sophisticated mathematical model that computes friction effects based on surface measurements. Instead of installing complex sensors and measurement devices in the deviated wellbore, the solution uses numerical algorithms to model and account for mechanical friction, achieving reliable downhole condition representation through computational rather than mechanical means.
3Measurement precision
If Coulomb's friction is incorporated into the Everitt-Jennings algorithm, then the downhole card accuracy improves, but the solution requires solving coupled non-linear differential equations
Solution Approach 1:
The patent extracts and separates the friction calculation from the overall system model, treating it as a distinct component that can be independently formulated and solved. By isolating the friction effects into specific terms within the differential equations, the complex coupled system becomes more manageable through systematic numerical solution approaches, reducing the overall difficulty of detection and measurement.
Solution Approach 2:
The patent segments the rod string into discrete elements along its length, allowing friction forces to be calculated and applied at each segment. This segmentation transforms the continuous differential equations into a series of manageable discrete calculations that can be solved numerically, making the complex mathematical problem tractable while maintaining accuracy in representing friction effects throughout the rod string.
Applied Scientific Principles
This section explains which scientific principles are used to turn an abstract innovation direction into a practical engineering solution.
Function Achieved in This Case
This approach provides a more accurate representation of downhole conditions in deviated wells, reducing excess friction and optimizing pump operation, thereby preventing damage and improving efficiency.
Implementation Method 1
incorporating Coulomb's friction to accurately model the behavior of rod strings in deviated wells
Data Source
AI summary
Diagnosing a pump apparatus having a downhole pump disposed in a deviated wellbore characterizes axial and transverse displacement of a rod string with two coupled non-linear differential equations of fourth order, which include axial and transverse equations of motion. To solve the equations, derivatives are replaced with finite difference analogs. Initial axial displacement of the rod string is calculated by assuming there is no transverse displacement and solving the axial equation. Initial axial force is calculated using the initial axial displacement and assuming there is no transverse displacement. Initial transverse displacement is calculated using the initial axial force and the initial axial displacement. Axial force and friction force are calculated using the initial displacements, and the axial displacement at the downhole pump is calculated by solving the axial equation with the axial force and the friction force. Load at the downhole pump is calculated so a downhole card can be generated.