Pixelated Resistivity Model for Ultra-Deep Logging Stability
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Solution Overview
Problem
Ultra-deep resistivity logging tools face unstable inversion results due to the lack of clearly defined boundaries in gradient resistivity profiles, leading to operational failures, as the simplified formation assumptions used in conventional tools are inadequate for the deeper detection ranges of these tools.
Innovation Solution
A pixelation-based approach is employed to summarize inversion results by generating a pixelated model where each layered solution is divided into pixels containing resistivity values, with a weighted function integrating measurement sensitivity to improve boundary position accuracy, and a statistical study is performed to determine the best pixelated model for formation characteristics.
Engineering Contradictions & Design Principles
Engineering Contradiction Analysis
1Length of moving object
If simplified formation assumptions are used in conventional resistivity logging tools, then the inversion process is computationally efficient and boundaries are clearly defined, but the detection range is limited to shallow depths (1.52m-3.05m)
Solution Approach 1:
The formation is divided into discrete pixels rather than continuous layers. Each pixel represents a small volumetric element with specific resistivity properties. This segmentation allows the inversion to handle gradient resistivity profiles by treating each pixel independently, enabling stable inversion at ultra-deep ranges while maintaining computational efficiency through the discrete nature of the pixelated model.
Solution Approach 2:
The invention transitions from traditional 1D layered formation models to a 3D pixelated representation. Each pixel has spatial coordinates (x, y, z) and resistivity properties, adding dimensional complexity that better represents actual formation geometry. This dimensional enhancement allows accurate modeling of dipping beds and complex boundaries at greater depths while maintaining inversion stability through the structured pixel grid.
2Length of moving object
If ultra-deep resistivity logging tools are used to detect formation boundaries at greater depths (30.5m), then the detection range is significantly improved, but the simplified formation assumptions result in unstable inversion results and solution ambiguity
Solution Approach 1:
Different regions of the formation are modeled with locally appropriate properties. Each pixel can have unique resistivity values and dimensions, allowing the model to capture local variations in formation characteristics. This local quality approach enables accurate representation of gradient resistivity profiles and dipping beds at ultra-deep ranges, resolving the boundary definition ambiguity that plagues conventional methods.
Solution Approach 2:
The pixelated model allows dynamic adaptation of formation representation based on measurement depth and quality. Pixels closer to the tool have higher measurement sensitivity and are better constrained, while deeper pixels are adjusted according to their measurement uncertainty. This dynamic approach stabilizes the inversion by allowing the model to adapt its complexity to the quality of available data at different depths.
3Productivity
If a 1D layered model is used for inversion, then the computational process is efficient and boundaries are easily identified, but the model cannot accurately represent gradient resistivity profiles and dipping beds
Solution Approach 1:
The continuous formation is segmented into discrete pixels arranged in a structured grid. This segmentation transforms the complex continuous inversion problem into a manageable discrete optimization problem. Each pixel's resistivity and position are independent variables, allowing efficient computational handling while capturing the complexity of gradient profiles and dipping beds that continuous 1D models cannot represent.
Solution Approach 2:
The invention changes the fundamental parameters of the formation model from layer thickness and boundary depth to pixel resistivity values and pixel spatial coordinates. This parameter transformation enables the model to represent complex 3D formation geometries while maintaining a manageable number of inversion variables. The pixelated approach allows gradient resistivity profiles to be represented by gradual changes in pixel values rather than requiring complex boundary definitions.
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 method provides more accurate and stable interpretation of formation geology by focusing on the sensitivity of measurements closer to the logging tool, reducing solution ambiguity and improving the accuracy of resistivity profiles in ultra-deep resistivity logging.
Implementation Method 1
resistivity is typically estimated by measuring the amount of electrical current in the formation, usually through logging-while-drilling ('LWD') operations
Implementation Method 2
electromagnetic resistivity logging tools to identify major boundaries between different formation resistivities
Data Source
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Figure 3~4
AI summary
A pixelation-based approach to summarize downhole inversion results acquires inversion solutions and generates an initial model. Each layered solution is pixelated into pixels where each pixel contains the resistivity value of the initial model. A weighted function that weighs pixels according to their proximity to the logging tool may be used to generate the pixelated model to thereby improve accuracy. A statistical summary study is performed to identify the best pixelated model, which is then used to determine one or more formation characteristics.