Modeling high-pressure viscosities of fatty acid esters and biodiesel fuels based on modified rough hard-sphere-chain model and deep learning method

Abstract This work aimed to demonstrate that a simple modification to the previously developed rough hard-sphere-chain (RHSC) model would significantly improve the accuracy of that model for viscosities of fatty acid esters and biodiesel fuels at extended pressures up to 200 MPa and higher isotherms. The new finding of this work is the temperature dependence of the exponential factor of the roughness factor (RF) of the earlier RHSC model as the accuracy of the original model (with an average absolute relative deviation, AARD of 8.29 % for 715 data points examined) was significantly improved achieving the AARD of 3.77 % once a universal function of reduced temperature replaced the original exponential factor of 6.4 × 10 −4 for RF. Besides, the predictive capability of the modified RHSC model has been compared with original RHSC model and several previously developed semi-empirical models based on friction theory and free volume theory in literature. Expanding AARD on the progress in deep learning, our research introduces Artificial Neural Network (ANN) model that is simpler than previous models while maintaining high viscosity correlation accuracy for fatty acid esters and biodiesel fuels. The refined ANN model, with a single hidden layer and sigmoid activation function, achieved an AARD% of 0.78 %. Additionally, we conducted a thorough comparison with other deep learning architectures, affirming the effectiveness of our simplified approach for viscosity correlations.