Chromatogram Decomposition Using Asymmetric Basis Functions
Solution Overview
Problem
Current chromatogram decomposition methods using Gaussian mixture models are insufficient for accurately capturing the non-symmetric nature of local maxima and asymptotic temporal decaying behavior in gas chromatography, leading to composition errors, particularly in gas samples from downhole drilling operations.
Innovation Solution
The method involves calibrating a gas chromatography apparatus using specific calibration samples and fitting chromatograms with basis functions derived from mass balance equations, followed by affine transformations to model responses of individual gases, allowing for improved decomposition and estimation of gas compositions.
Engineering Contradictions & Design Principles
Engineering Contradiction Analysis
1Ease of manufacture
If Gaussian mixture model is used for chromatogram decomposition, then the method is simple and commonly used, but it cannot accurately capture non-symmetric local maxima and asymptotic temporal decaying behavior, resulting in composition errors
Solution Approach 1:
The patent changes the mathematical model parameters from symmetric Gaussian functions to asymmetric basis functions that incorporate exponential decay terms. This parameter change allows the model to capture both the non-symmetric local maxima and asymptotic temporal decaying behavior of chromatogram peaks, thereby improving composition accuracy while maintaining reasonable computational complexity
Solution Approach 2:
The patent explicitly introduces asymmetric basis functions to model chromatogram peaks. The basis functions incorporate exponential decay terms that create asymmetric peak shapes, accurately representing the physical behavior of chromatogram data where peaks typically have different rise and fall characteristics. This asymmetry directly addresses the limitation of symmetric Gaussian models
2Measurement precision
If basis functions from mass balance equations are used, then asymmetric responses and overlapping peaks are captured accurately, but the calibration process becomes more complex
Solution Approach 1:
The patent performs preliminary calibration actions by pre-computing basis functions from mass balance equations and storing them for later use. During actual analysis, these pre-computed basis functions are directly applied without requiring real-time solution of complex differential equations, thereby reducing operational complexity while maintaining high accuracy in capturing asymmetric responses and overlapping peaks
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 enhances the accuracy of gas composition estimation by effectively addressing the limitations of existing methods, particularly in capturing asymmetric responses and overlapping peaks, thereby improving the reliability of gas analysis in drilling operations.
Implementation Method 1
Gas chromatography (GC) is a widely used technique for separating and analyzing chemical compounds that can be vaporized
Implementation Method 2
the GMM approximation is generally not sufficient to capture the non-symmetric nature of local maxima of the chromatogram as well as asymptotic temporal decaying behavior
Data Source
AI summary
A method for calibrating a GC apparatus includes measuring first and second chromatograms of corresponding first and second calibration samples in which the first calibration sample includes a first gas and the second calibration sample includes first, second, and third gases. The first chromatogram is fit with a basis function derived from a mass balance equation to obtain a first modeled chromatogram. The second chromatogram is fit with first, second, and third affine transformed responses of the first modeled chromatogram to obtain a second modeled chromatogram. The second modeled chromatogram may be used to decompose a third chromatogram that is measured of an unknown gas sample and to estimate the composition thereof.