Green's Tensor Resistivity Logging in 3D Formations
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Solution Overview
Problem
Current resistivity logging methods assume a uniaxial vertical 1-dimensional structure, which is inadequate for formations with resistivity varying in three dimensions, leading to inaccurate formation resistivity measurements and sub-optimal drilling paths.
Innovation Solution
The use of a system with multiple receiver subs, including a transmitter sub and first, second, and third receiver subs, to generate and receive electromagnetic waves, solving a series of linear equations to determine the Green's response tensor, which accounts for resistivity in all directions.
Engineering Contradictions & Design Principles
Engineering Contradiction Analysis
1Ease of operation
If a uniaxial vertical 1-dimensional structure assumption is used for resistivity logging, then the measurement process is simplified and easier to implement, but the measurement precision deteriorates in formations with resistivity varying in three dimensions
Solution Approach 1:
The patent transitions from a 1-dimensional vertical resistivity model to a 3-dimensional resistivity model by introducing azimuthal sensitivity measurements. Multiple receiver coils oriented in different directions (x, y, z axes) capture electromagnetic responses from all spatial dimensions, enabling the calculation of a full Green's Tensor that characterizes resistivity variations in three-dimensional space rather than assuming uniformity in horizontal directions.
Solution Approach 2:
The patent divides the formation resistivity characterization into multiple independent components through the Green's Tensor elements (Gxx, Gyy, Gzz, Gxy, Gxz, Gyz). Each tensor element represents a specific directional response, allowing the complex 3-D resistivity structure to be segmented into manageable measurement components that can be individually measured and combined to form a complete picture of anisotropic formation properties.
2Measurement precision
If multiple receiver subs are used to measure resistivity in all directions, then the measurement precision improves for complex formations, but the device complexity increases
Solution Approach 1:
The patent implements a multi-functional receiver assembly where three receiver coils (oriented along x, y, z axes) and multiple transmitter coils work together as an integrated system. This universal measurement platform can simultaneously characterize resistivity in all three spatial dimensions and calculate the complete Green's Tensor, eliminating the need for separate measurement tools for different directional resistivity components.
Solution Approach 2:
The patent adds azimuthal dimensionality to traditional vertical resistivity measurements by incorporating receiver coils oriented in horizontal directions (x and y axes) in addition to the vertical z-axis. This dimensional expansion enables the system to capture electromagnetic responses from all directions, providing comprehensive 3-D resistivity characterization without requiring multiple separate measurement passes or tools.
3Reliability
If a full Green's Tensor is calculated instead of assuming V-1D structure, then the reliability of drilling path optimization improves, but the computational complexity and data processing requirements increase
Solution Approach 1:
The patent performs preliminary measurements of all six Green's Tensor elements (Gxx, Gyy, Gzz, Gxy, Gxz, Gyz) during the logging process itself, before drilling path optimization is required. By capturing the complete 3-D resistivity characterization in advance, the system prepares all necessary formation property data ahead of time, enabling reliable drilling path optimization without requiring complex real-time calculations during the optimization process.
Solution Approach 2:
The patent transforms the resistivity measurement from a single scalar value (under V-1D assumption) to a complete set of six tensor parameters (Gxx, Gyy, Gzz, Gxy, Gxz, Gyz) that fully describe the anisotropic formation properties. This parameter expansion provides comprehensive input data for drilling path optimization algorithms, significantly improving the reliability of optimization results by accounting for true 3-D resistivity variations rather than simplified assumptions.
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 accurate resistivity measurements in complex formations, improving the quality of electrical images and guiding drilling operations with precise formation resistivity data.
Implementation Method 1
generating an electromagnetic wave at the transmitter coil; propagating the electromagnetic wave through the subterranean formation; receiving the electromagnetic wave in the first receiver coil, the second receiver coil, and the third receiver coil
Data Source
AI summary
A method may comprise: inserting into a wellbore penetrating a subterranean formation an apparatus comprising: a transmitter sub comprising a transmitter coil; a first receiver sub comprising a first receiver coil; a second receiver sub comprising a second receiver coil; and a third receiver sub comprising a third receiver coil; generating an electromagnetic wave at the transmitter coil; propagating the electromagnetic wave through the subterranean formation; receiving the electromagnetic wave in the first receiver coil, the second receiver coil, and the third receiver coil; generating a plurality of response signals, wherein the plurality of response signals comprises a first response signal in the first receiver coil, a second response signal in the second receiver coil, and a third response signal the third receiver coil; solving a series of linear equations defined by an orientation of the transmitter sub in the wellbore, orientation in the wellbore for each of the first receiver coil, the second receiver coil, and the third receiver coil, and the plurality of response signals to determine a Green's response tensor.