Mindlin Formulation Stress Tensor Computation
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Solution Overview
Problem
Current drilling technologies lack accurate methods for determining formation stresses in earth formations, which hinders the selection of optimal drilling parameters for maintaining borehole stability and preventing collapse.
Innovation Solution
A method and system that construct a geo-cellular model of the earth formation, calculate stress tensors using linear approximations and the Mindlin Formulation, and apply these to determine accurate stress values for each grid cell volume, enabling more precise selection of drilling parameters and borehole trajectories.
Engineering Contradictions & Design Principles
Engineering Contradiction Analysis
1Measurement precision
If current drilling technologies are used, then drilling operations can be performed, but accurate determination of formation stresses is lacking, hindering optimal drilling parameter selection
Solution Approach 1:
The earth formation is divided into discrete grid cells, with each cell representing a volumetric element with specific density and Poisson's ratio properties. This segmentation allows for localized stress calculation and accurate representation of heterogeneous formation characteristics, directly improving formation stress determination accuracy
Solution Approach 2:
The method calculates stress tensors by varying key parameters including density, Poisson's ratio, and gravitational acceleration across different grid cells. By incorporating actual measured values of these parameters and computing their effects on stress distribution, the method achieves precise formation stress determination that accounts for formation heterogeneity
2Reliability
If accurate stress tensor calculation is implemented using geo-cellular modeling and Mindlin formulation, then borehole stability can be improved through optimal drilling parameter selection, but computational complexity increases
Solution Approach 1:
The formation is segmented into grid cells that can be processed independently using the Mindlin formulation. This segmentation allows the complex computational problem to be broken down into manageable discrete calculations, where stress tensors are computed for individual cells and then aggregated, making the overall complex problem computationally tractable
Solution Approach 2:
The Mindlin formulation serves as an intermediary mathematical framework that relates density distributions in grid cells to stress tensor components. This intermediary formulation provides a systematic way to compute stresses without requiring direct complex integration, simplifying the computational process while maintaining accuracy
3Productivity
If linear approximation of density and Poisson's ratio values is used, then computational efficiency is improved, but measurement precision of stress values may be compromised
Solution Approach 1:
The method applies linear approximation selectively to density and Poisson's ratio values only where necessary for computational efficiency, while using actual measured values where available. This partial application of approximation maintains reasonable accuracy while significantly improving computational efficiency
Solution Approach 2:
The method transforms actual density and Poisson's ratio values into linear approximation forms that can be efficiently processed. By changing the representation of these parameters from raw measured values to linear approximations, the computation becomes more efficient while retaining sufficient accuracy for engineering applications
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 enhances the stability of boreholes by allowing for the selection of appropriate drilling mud densities and optimal borehole locations, reducing the likelihood of collapse and improving drilling efficiency.
Implementation Method 1
calculating with the processor a contribution to stress at each grid cell volume of interest from other grid cell volumes that are at elevations above the grid cell volume of interest by use of the Mindlin Formulation using the density difference values and the Poisson's ratio values
Data Source
AI summary
A method for performing an earth formation borehole-related task includes: calculating a contribution to stress at each grid cell volume of interest in a geo-cellular model from other grid cell volumes that are at elevations above the grid cell volume of interest by use of the Mindlin Formulation using difference values between actual and linear approximation density values and Poisson's ratio values; adding all contributions to the stresses from all other grid cell volumes that are at elevations above the grid cell volume of interest to provide a stress tensor correction; adding first approximation of stress tensor components to the stress tensor correction to provide a total stress value; constructing a resulting stress tensor for the earth formation using the total stress values for the grid cell volumes of interest; and performing the borehole-related task using borehole-related equipment and the resulting stress tensor for the earth formation.