Gamma-ray logging fast forward method for deviated wells
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Solution Overview
Problem
Existing methods for gamma-ray logging in highly-deviated and horizontal wells are complicated and lack precision due to the use of spherical spatial-division integrals and empirical formulas, making real-time data processing challenging, especially in reducing smoothing effects and improving resolution at formation interfaces.
Innovation Solution
A fast forward method and system that converts gamma-ray flux integrals from deviated wells to equivalent one-dimensional integrals in a straight well context, using one-dimensional equivalent longitudinal contribution coefficients, simplifying the algorithm and improving calculation efficiency by weighting gamma-ray fluxes based on these coefficients.
Engineering Contradictions & Design Principles
Engineering Contradiction Analysis
1Measurement precision
If spherical spatial-division integrals are used for gamma-ray logging forward calculation, then measurement precision is improved, but device complexity increases and productivity decreases
Solution Approach 1:
The patent segments the three-dimensional detection space into multiple one-dimensional longitudinal segments along the wellbore axis. By dividing the complex 3D integration problem into sequential 1D segments, the method maintains measurement precision while significantly reducing algorithmic complexity and computational burden.
Solution Approach 2:
The patent transforms the three-dimensional spatial integration problem into a one-dimensional longitudinal integration problem along the wellbore axis. This dimensionality reduction converts complex 3D spherical spatial-division integrals into simpler 1D equivalent integrals, reducing computational complexity while preserving forward calculation precision.
2Measurement precision
If spherical spatial-division integrals are used for gamma-ray logging forward calculation, then measurement precision is improved, but productivity decreases
Solution Approach 1:
The detection space is segmented into one-dimensional longitudinal segments, allowing the forward calculation to be performed as a sequence of simpler 1D integrations rather than a single complex 3D integration. This segmentation improves calculation efficiency while maintaining precision.
Solution Approach 2:
By reducing the integration from three-dimensional spherical coordinates to one-dimensional longitudinal coordinates along the wellbore, the computational complexity is dramatically reduced. This dimensionality change enables faster forward calculations suitable for real-time or near-real-time logging applications.
3Ease of operation
If empirical formulas are used for convolution factors, then ease of operation is improved, but measurement precision deteriorates
Solution Approach 1:
The patent replaces empirical formula-based convolution methods with a physics-based one-dimensional equivalent integration method. This substitution uses fundamental gamma-ray transport physics and geometric relationships to calculate contribution coefficients, improving measurement precision while maintaining operational simplicity through the streamlined 1D integration approach.
4Measurement precision
If conventional methods are used for deviated wells, then adaptability is limited, but measurement precision can be maintained for straight wells
Solution Approach 1:
The patent develops a universal one-dimensional equivalent integration method that can handle both straight and deviated/horizontal wells through the same mathematical framework. By formulating the contribution coefficients in terms of wellbore geometry parameters that accommodate any deviation angle, the method achieves universality across different well types while maintaining measurement precision.
Solution Approach 2:
The patent introduces parameter transformations that adapt the integration formulation to different wellbore configurations. By expressing the one-dimensional equivalent integrals in terms of generalized geometric parameters that can represent straight, deviated, or horizontal wells, the method maintains precision across varying well geometries without requiring separate specialized approaches.
Data Source
AI summary
Through analysis on an effective detection space of a gamma detector, a one-dimensional equivalent longitudinal contribution coefficient (varying with a distance between a formation and the detector) of a natural gamma-ray flux received by the gamma detector under the condition that the formation and a wellbore are orthogonal is obtained in the effective detection space, and then a corresponding function expression is given by fitting. An integral of a gamma-ray flux received by the detector under the condition of a deviated well is converted into a one-dimensional equivalent integral problem under the condition of a straight well, so as to achieve the fast forward of natural gamma-ray logging of the formation under the conditions of highly-deviated and horizontal wells. This simplified fast forward algorithm can replace a gamma forward method of spherical spatial-division integrals in parallel sedimentary formations, reduce a space-time complexity of algorithms, and improve a calculation efficiency.