Molecular reconstruction of petroleum products based on shape-decoupled gamma distribution parameters

In the petrochemical industry, molecular reconstruction is crucial for understanding and optimizing the compositions of complex crude oil and petroleum products. As the first step of process simulation, quality control, and economic evaluation, precise molecular reconstruction approaches usually employ mathematical models to calculate the molecular compositions of petroleum products that align with their macroscopic properties. Traditional molecular reconstruction methods employ the gamma distribution to represent the carbon number distributions of homologs, but the coupling effects between the parameters "shape (α)" and "scale (β)" pose notable challenges in achieving desired interpretability and optimization efficiency. This study addresses these challenges by introducing a novel shape-decoupled parameter method that enhances the model's interpretability and simplifies the optimization process.

The proposed shape-decoupled parameter method modifies a traditional gamma distribution by replacing the parameter's shape and scale with two new independent variables called peak position (m) and variance (σ²). Notably, m provides direct control over the zenith of the distribution, whereas σ² independently determines the spread or width of the distribution, effectively reducing the coupling issue between parameters that exists in conventional gamma distribution models. Aiming at enhancing the stability and convergence speed during optimization, a multivariate linear regression (MLR) model was employed to estimate the initial parameter values. This regression model was trained on historical data of molecular compositions to provide reasonable initial values and decrease the probability of being trapped in local minima. The molecule-type homologous series (MTHS) matrix is used to represent the molecular composition of hydrocarbons, namely paraffins, isoparaffins, olefins, naphthenes, and aromatics (PIONA), with a comprehensive depiction of their multiple homologs. Moreover, an optimization problem was developed to minimize the prediction errors of the macroscopic properties, including molecular weight, density, PIONA group composition, and true boiling point curves. Upon a comparative analysis of multiple deterministic and heuristic optimization techniques, the differential evolution (DE) algorithm was determined as a favorable optimization tool by virtue of its superior accuracy and robustness.

Experimental evaluations showed that the shape-decoupled parameter method outperformed traditional methods in accuracy and optimization efficiency. Specifically, the density error decreased from 0.012 to 0.0059 g/cm³, and the average percentage relative error for the PIONA group composition also exhibits notable reductions. Moreover, the decoupled approach achieves faster convergence, requiring fewer iterations—reducing from 1 000 to as few as 20—without compromising accuracy. This reduction highlights the computational efficiency of the proposed method, which is a notable advantage in industrial applications with limited computational resources and time. Moreover, the proposed method exhibits enhanced robustness in addressing extreme molecular composition distributions, maintaining low errors in peak position and molecular composition predictions. This robustness becomes particularly evident when managing scenarios considered challenging by conventional methods, such as distributions with narrow ranges or hydrocarbons with approximately zero components at the boundary. Furthermore, the decoupled method provides better interpretability via independent control strategies for peak position and distribution width. The overall optimization performance was enhanced by the appropriate integration of the DE algorithm and effective initial parameter estimation by the MLR model.

Compared with traditional methods, the proposed shape-decoupled parameter method provides a more interpretable, efficient, and accurate approach to the molecular reconstruction of petroleum products. By reducing the coupling effect between the parameters controlling the peak position and distribution width, this method simplifies the optimization process and achieves superior prediction accuracy and faster convergence. The results indicate the feasibility of its application for complex or extreme homolog distributions of hydrocarbons, revealing its higher reliability and robustness compared with traditional approaches. Future work is expected to focus on incorporating advanced machine learning techniques to further increase the accuracy and applicability of the model across a wider range of petroleum compositions, potentially enabling real-time molecular reconstruction for dynamic process optimization.