Innovative mathematical approach for hydrothermal carbonization process using an inverse method: Experimental analysis, rheology behavior, and numerical comparative investigation

Hydrothermal carbonization (HTC) shows promise for converting biomass into carbon solids, but simulating it at high biomass-to-water ratios is difficult due to limited models. Existing numerical methods have not been sufficiently tested and validated under such conditions. An experimental approach and a novel non-Newtonian mixture model (NNM) were developed to improve simulation accuracy. This model incorporated rheological parameters using COMSOL Multiphysics software and an inverse method, especially the Levenberg-Marquardt algorithm. The results show that the proposed design achieved desired HTC conditions within 55-70 min, depending on the ratio. Besides, the innovative NNM model proved more effective for predicting thermal behavior and exhibited significantly reduced computation time than other CFD models in the literature, with a maximum 5 % relative deviation, indicating lower computational costs. Infrared camera measurements validated the heat behavior predicted by the NNM. Moreover, during HTC, the mixture behaves as a Newtonian fluid at a 1/6 ratio, and as a shear-thinning fluid at 1/3 and 1/2 ratios, with viscosity decreasing with increasing shear rate and temperature. This study presents innovative findings in the field of HTC, offering a reliable NNM model for simulating HTC under challenging conditions, addressing the mixture's rheology, and proposing a novel design.