Estimating Stiffness C13 in Anisotropic Media via Velocity Bounds
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Solution Overview
Problem
Conventional methods face challenges in reliably determining the full stiffness tensor of transversely isotropic media, particularly in shale formations, due to the need for measurements that may not be available at all depths, leading to inaccuracies in computing mechanical properties like Poisson's ratios and Young's moduli, which are crucial for oil and gas extraction operations.
Innovation Solution
The use of sonic logging tools with acoustic transmitters and receivers to measure elastic wave velocities in multiple directions and modes, allowing for the estimation of mechanical properties without requiring 45-degree measurements, and employing a method to determine the stiffness component C13 using upper and lower bounds based on vertical and horizontal velocities, thereby reducing reliance on off-axis velocity measurements.
Engineering Contradictions & Design Principles
Engineering Contradiction Analysis
1Reliability
If conventional methods are used to determine the full stiffness tensor, then complete mechanical property data can be obtained, but measurements that are not available at all depths are required
Solution Approach 1:
The patent extracts and focuses on determining only the critical C13 stiffness component using alternative methods that rely on available vertical and horizontal velocity measurements, rather than attempting to measure all stiffness components conventionally. This extraction approach allows obtaining necessary mechanical properties without requiring unavailable off-axis measurements.
Solution Approach 2:
The patent uses Poisson's ratio as an intermediary parameter to bridge the gap between available velocity measurements and the desired C13 stiffness component. By measuring Poisson's ratio through vertical and horizontal velocities and using it as a mediator in the calculation, the method obtains C13 without direct off-axis measurements.
2Measurement precision
If 45-degree velocity measurements are used to determine C13, then the stiffness component can be calculated, but measurement errors significantly affect the accuracy of mechanical properties
Solution Approach 1:
The patent converts the limitation of not having 45-degree measurements into a benefit by developing a method that uses only vertical and horizontal velocity measurements. What was previously seen as a deficiency (missing off-axis data) becomes the foundation for a more robust measurement approach that avoids the error propagation associated with 45-degree measurements.
Solution Approach 2:
The patent creates an alternative calculation path that copies the essential function of determining C13 without relying on the problematic 45-degree velocity measurement. By using vertical and horizontal velocities combined with Poisson's ratio to calculate C13, the method replicates the desired outcome through a different, more reliable route.
3Loss of information
If the full stiffness tensor is determined using conventional methods, then all mechanical properties can be computed, but the process requires measurements that increase device complexity
Solution Approach 1:
The patent extracts and focuses on determining only the critical C13 stiffness component and essential mechanical properties (Poisson's ratio, Young's modulus, shear modulus) using a simplified approach. By extracting only the necessary information from the full stiffness tensor rather than measuring all components, the method reduces measurement complexity while maintaining sufficient accuracy for oil and gas operations.
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 enables accurate estimation of mechanical properties with improved precision, reducing errors associated with velocity measurements and providing reliable data for drilling and completion operations in anisotropic media, such as shale formations, without the need for precise 45-degree velocity measurements.
Implementation Method 1
sonic logging tools with acoustic transmitters and receivers to measure elastic wave velocities
Data Source
AI summary
Systems and methods for determining mechanical properties of anisotropic media are disclosed. A method for determining mechanical properties of an anisotropic media includes obtaining log data of the anisotropic media, the log data corresponding to measurements of the anisotropic media collected with a logging tool; determining values for a plurality of first stiffness components of a stiffness matrix based on horizontal and vertical velocities derived from the log data; determining an upper bound for a second stiffness component of the stiffness matrix based on the values for the plurality of first stiffness components; estimating a value for the second stiffness component based on the determined upper bound; determining a mechanical property of the anisotropic media based on the estimated value of the second stiffness component; and providing the determined mechanical property.