Bottomhole Assembly Modeling with Nonlinear BVP Solver
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Solution Overview
Problem
Current methods for evaluating the static response of a bottomhole assembly (BHA) during directional drilling operations are inadequate, particularly when the weight-on-bit is large or flexural rigidity is small, as they neglect nonlinear effects and assume a linear beam characterization, which leads to inaccurate drilling tendency predictions.
Innovation Solution
The proposed solution involves converting the BHA response into a multipoint boundary value problem (BVP) that considers nonlinear effects, allowing for a fast and robust evaluation of BHA responses by segmenting the assembly into segments with constant mechanical properties and solving auxiliary problems with nonlinear beam equations, along with a mixed complementarity problem to account for borehole contact configurations.
Engineering Contradictions & Design Principles
Engineering Contradiction Analysis
1Device complexity
If a linear beam characterization is used to model the BHA, then the model is simple and easy to solve, but it is insufficient for large weight-on-bit or small flexural rigidity configurations where nonlinear effects are significant
Solution Approach 1:
The patent transitions from linear beam parameters to nonlinear beam parameters by incorporating the Euler-Bernoulli beam equation with nonlinear terms. This allows the model to capture large deflections and nonlinear deformations that occur under high weight-on-bit or low flexural rigidity conditions, thereby improving accuracy while maintaining computational efficiency through the semi-analytical approach.
2Measurement precision
If commercial finite element packages are used to solve BHA responses, then comprehensive modeling capabilities are available, but computation time increases from seconds to hours
Solution Approach 1:
The patent divides the BHA into multiple discrete segments along its length, with each segment having constant mechanical properties. This segmentation allows the complex continuous problem to be broken into simpler sub-problems that can be solved efficiently using boundary value problem techniques, reducing computation time from hours to seconds while maintaining accuracy.
Solution Approach 2:
The patent performs preliminary discretization of the BHA into segments with defined mechanical properties before solving the boundary value problem. By pre-defining the segmentation and mechanical properties, the model avoids iterative meshing and setup procedures required by finite element packages, significantly reducing computation time while preserving modeling fidelity.
3Device complexity
If the borehole contact configuration is assumed known, then the problem simplifies to a direct calculation, but in reality the contact configuration is a priori unknown and must be determined
Solution Approach 1:
The patent employs an iterative algorithm that dynamically adjusts the contact configuration between the BHA and borehole wall based on the calculated BHA response. The algorithm alternates between solving the boundary value problem and updating the contact points, allowing the contact configuration to emerge naturally from the physics of the system rather than being assumed, thereby achieving both efficiency and accuracy.
Data Source
AI summary
A method for forming a model of a bottom hole assembly (BHA) in a borehole, wherein the BHA is connected to a drill string. The method may further comprise segmenting the model into one or more segments and solving a multipoint boundary value problem (BVP) based at least in part on the one or more segments.