Skin Effect Correction for Focused Electrode Conductivity Inversion
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Solution Overview
Problem
Conventional methods for calculating conductivity of hydrocarbon bearing reservoir formations using focused electrode devices are inefficient due to the lack of an accurate analytical model for skin effect, requiring dense sampling and introducing errors through interpolation and extrapolation, which increases costs and degrades inversion efficiency.
Innovation Solution
Development of a physics-based analytical model for skin effect that allows for accurate conductivity calculation using fewer admittance samples, eliminating the need for large databases and enabling real-time inversion with reduced errors.
Engineering Contradictions & Design Principles
Engineering Contradiction Analysis
1Measurement precision
If conventional inversion method with dense sampling is used, then measurement precision is improved, but productivity deteriorates due to increased cost and degraded efficiency
Solution Approach 1:
The patent transforms the inversion problem from a computational search problem to a direct calculation problem by changing the parameter representation. Instead of using lookup tables with discrete conductivity values, the patent derives an analytical relationship between admittance and conductivity that allows direct computation. This parameter transformation enables accurate conductivity calculation without dense sampling, resolving the contradiction between measurement precision and productivity.
Solution Approach 2:
The patent replaces the mechanical/computational system of dense sampling and interpolation with a physics-based analytical model. By substituting the numerical inversion process with an analytical solution based on electromagnetic theory, the patent eliminates the need for computationally intensive database searches while maintaining or improving accuracy. This substitution resolves the efficiency problem while preserving measurement precision.
2Measurement precision
If dense sampling is used to build database, then measurement precision is improved, but loss of substance increases due to increased cost
Solution Approach 1:
The patent changes the fundamental parameter approach from discrete sampled values to continuous analytical expressions. By deriving closed-form solutions based on electromagnetic theory, the patent eliminates the need to store and search large databases of sampled admittance-conductivity pairs. This parameter transformation maintains inversion accuracy while eliminating the substantial computational cost associated with building and querying dense sampling databases.
3Device complexity
If interpolation and extrapolation are used for inversion, then device complexity is reduced, but measurement precision deteriorates due to introduced errors
Solution Approach 1:
The patent replaces the empirical interpolation/extrapolation methods with a physics-based analytical model derived from electromagnetic theory. This substitution eliminates the need for error-prone numerical approximation techniques while maintaining computational tractability. The analytical solution provides exact conductivity values based on fundamental physical principles, resolving the contradiction between method simplicity and measurement precision.
Solution Approach 2:
The patent introduces a physics-based analytical model as an intermediary between the measured admittance and the desired conductivity. This intermediary relationship, grounded in electromagnetic theory, provides a direct and accurate transformation path without requiring error-prone interpolation or extrapolation. The analytical model serves as a precise mediator that maintains both simplicity and accuracy in the inversion process.
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
The solution provides accurate and efficient conductivity calculations, reducing costs and improving inversion efficiency by using physics-based models to solve equations directly, rather than relying on interpolation and extrapolation, and can be integrated into firmware or data systems for real-time operation.
Implementation Method 1
the focused electrode devices may measure the admittance of formation, i.e., a ratio of a measured electrical current to an applied voltage
Implementation Method 2
Skin effect is the tendency of an alternating electrical current (AC) to become distributed within a conductor, such that the electrical current density is largest near the surface of the conductor and decreases with greater depths in the conductor
Data Source
AI summary
Methods and systems for determining conductivity of a reservoir formation based on skin effect correction and an analytical model for admittance of the reservoir formation are presented in this disclosure. At least one analytical model of admittance of the formation can be initially built as a function of conductivity of the formation. A plurality of samples for the admittance of the formation can be generated, and one or more parameters of the at least one analytical model can be determined based on the plurality of samples and the at least one model. Then, admittance of the formation can be measured, and conductivity of the formation can be calculated from the measured admittance based on the analytical model with the parameters.