Third-Order Tensor Clustering for Geological Heterogeneity Mapping
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Solution Overview
Problem
Existing methods struggle to effectively group wells based on geological heterogeneity trends, which are influenced by horizontal and vertical geologic variations, hindering accurate reservoir characterization and simulation.
Innovation Solution
A method involving drilling wells, acquiring well logs, determining a third-degree tensor, clustering matrices based on well log characteristics, aggregating clustering results, and spatially partitioning to create a map showing geological heterogeneity trends.
Engineering Contradictions & Design Principles
Engineering Contradiction Analysis
1Measurement precision
If traditional well logging methods are used to analyze geological properties, then basic formation characteristics can be obtained, but the ability to effectively group wells and reveal heterogeneous characteristics is insufficient
Solution Approach 1:
The patent segments the complex well log data into multiple dimensional components by constructing a third-order tensor that separates depth information, well log types, and well locations. This segmentation allows independent processing and analysis of each dimension, improving heterogeneity characterization while managing complexity through structured decomposition of the data cube into manageable tensor slices and modes.
Solution Approach 2:
The patent transitions from traditional 2D well log analysis to 3D tensor analysis by introducing a new dimension that captures the relationship between multiple wells at different depths. This dimensionality change enables simultaneous analysis of vertical stratigraphic variations and horizontal well-to-well heterogeneity, revealing patterns that cannot be detected in conventional 2D representations.
2Loss of information
If multiple well logs are analyzed to capture horizontal and vertical geologic variations, then more comprehensive geological information is obtained, but the difficulty of grouping and clustering wells increases
Solution Approach 1:
The patent performs preliminary dimensionality reduction on the well log data before clustering by extracting dominant patterns and features from the tensor structure. This preliminary action reduces the dimensionality of the data while preserving essential geological variation information, making the subsequent clustering process more tractable and effective.
Solution Approach 2:
The patent transforms the raw well log data into a tensor representation with specific mathematical properties, changing the parameters from conventional log values to tensor elements that capture multi-dimensional relationships. This parameter transformation enables the use of specialized tensor-based clustering algorithms that are more effective at handling the complex correlations present in multi-well log data.
3Reliability
If conventional analysis methods are used, then processing time is reduced, but the ability to reveal hidden heterogeneous characteristics is limited
Solution Approach 1:
The patent replaces conventional mechanical data processing methods with tensor algebra and linear algebra-based approaches. By substituting traditional iterative clustering algorithms with tensor decomposition methods, the system achieves both improved reliability in characterizing heterogeneity and enhanced productivity through more efficient computational operations on the structured tensor data.
Data Source
AI summary
A method for obtaining geological heterogeneity trends of a geological formation, including the steps: drilling wells (w1, w2, w3, w4, w5) that penetrate the formation, acquiring well logs (log 1, log 2) for each well (w1, w2, w3, w4, w5) as function of depth interVals (Dk) of the respectiVe well, determining a third degree tensor (Tk, m, n), where a z-dimension denotes the depths, a x-dimension denotes the well logs, and a y-dimension denotes the wells, extracting matrices (L1k,m, L2k,m, . . . , LMk,n) from the tensor (Tk, m, n), clustering the matrices (L1k,n, L2k,n, . . . , LMk,n) based on the characteristics of the corresponding well logs (log 1, log 2) to a clustering result matrix, aggregating the clustering result matrix to a cluster ensemble (π1, π2, . . . , πM), and spatial partitioning the cluster ensemble (π1, π2, . . . , πM) to a map that shows the geological heterogeneity trends associated with cluster types of the wells (w1, w2, w3, w4, w5).