Vertical Stress Estimation Using Boussinesq Point Load Integration
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Solution Overview
Problem
Conventional methods for determining pore fluid pressure in subterranean drilling overestimate or underestimate pressures due to the assumption that gravitational load is uniformly transferred with depth, failing to account for surface topology and density heterogeneities, leading to inaccurate stress and pressure calculations.
Innovation Solution
The method involves discretizing the earth formation into cells, dividing the domain into surface and subterranean regions, vertically integrating density values, and estimating total vertical stress by considering a point load based on density values, which accurately reflects the decay of stress effects with depth.
Engineering Contradictions & Design Principles
Engineering Contradiction Analysis
1Ease of manufacture
If vertical integration of density data is used to estimate total vertical stress, then the calculation is simple and straightforward, but the accuracy deteriorates due to the assumption that gravitational load is completely transferred to elements below, leading to overestimation or underestimation of stresses
Solution Approach 1:
The patent changes the fundamental parameter of stress calculation from vertical integration of density (which assumes complete load transfer) to Boussinesq's point load solution (which accounts for load dispersion). This parameter change transforms the calculation from a simple but inaccurate method to a more complex but accurate method that properly models gravitational load decay with depth.
Solution Approach 2:
The patent replaces the mechanical assumption of complete load transfer (vertical integration method) with a more realistic mechanical model based on Boussinesq's elasticity theory for point loads. This substitution introduces the concept of load dispersion through the formation matrix, replacing the oversimplified mechanical transfer assumption with a physically accurate elastic deformation model.
2Loss of time
If conventional vertical integration method is applied, then computational effort is minimal, but the result deteriorates by failing to account for surface topology and density heterogeneities, causing unrealistic pore pressure predictions
Solution Approach 1:
The patent changes the calculation approach from vertical integration (which sums density values directly) to point load integration using Boussinesq's solution. This parameter change enables the model to account for surface topology and density heterogeneities by treating each density element as a point load that disperses stress according to elastic theory, thereby improving prediction reliability.
Solution Approach 2:
The patent segments the formation into discrete density elements or cells, each treated as an independent point load source. This segmentation allows the model to individually account for density heterogeneities and surface topology variations, with each segment contributing to the total stress field according to its specific location and density value, thereby improving overall prediction accuracy.
3Ease of operation
If the assumption of complete gravitational load transfer is made, then the model is simple to implement, but the accuracy deteriorates by not reflecting the actual decay of stress effects with depth
Solution Approach 1:
The patent replaces the simple mechanical assumption of complete load transfer with Boussinesq's elastic theory model. This substitution introduces the mathematical framework for stress dispersion through elastic media, where the stress effect of each point load decays with distance according to the elastic properties of the formation, accurately reflecting the physical reality of stress distribution.
Solution Approach 2:
The patent changes the stress calculation parameter from a constant transfer ratio (complete transfer assumption) to a distance-dependent decay function based on Boussinesq's solution. This parameter change allows the model to automatically adjust stress contributions based on depth and horizontal distance, reflecting the actual decay of stress effects without requiring complex manual adjustments.
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 more accurate predictions of pore fluid pressure and stress distribution, improving drilling and production operations by reducing unrealistic pressure estimates and enhancing borehole stability.
Implementation Method 1
The method utilizes Boussinesq's point load solution for calculating the total vertical stress distribution in the earth formation
Data Source
AI summary
A method of estimating at least one of stress and pore fluid pressure in an earth formation is disclosed. The method includes: discretizing a domain including at least a portion of the earth formation into a plurality of cells, each cell including a respective density value; dividing the domain into a first region and a second region, the first region including a surface of the earth formation; vertically integrating the respective density values in the first region; and estimating the total vertical stress for each cell in the first region and the second region by estimating a point load based on the respective density value.