(356a) A Hybrid Population Balance Formulation for the Mechanochemical Depolymerization of Plastic Waste

Chemical recycling of polymers is a highly active topic of research that seeks to convert waste plastics into valuable chemicals through depolymerization [1]. One novel method of plastics recycling to reclaim monomers from plastic waste is mechanochemical depolymerization, wherein the activation energy for the depolymerization reaction is sourced from collisions and grinding action of polymers [2, 3]. On the industrial scale, these mechanochemical reactions are often performed via ball milling on solid particulate feedstocks. For plastic waste, solid plastic particles are fed into a ball mill to undergo depolymerization, followed by downstream separation and plastic reformation processes. Physics-based models that accurately describe the dynamic evolution of molecular weight distributions (MWD) during depolymerization are necessary for process design, optimization, and reduction of expenses.

Population Balance Models (PBMs) have been used to describe the operation of particulate processes for non-reactive applications, such as in pharmaceuticals and mineral processing [4-6]. However, such studies on reactive ball mill systems like in the case of plastics depolymerization have not been performed. There is significant value in developing models that can capture the MWD under varying operating conditions (e.g., shaking frequency, number of steel balls, catalyst, carrier gas, geometry etc.), to enable design of the reactor and subsequent separation systems. A fully mechanistic model would be ideal, but it remains infeasible due to the inherent complexity of the ball milling process and the large variability in operating conditions between systems, including mill geometry and selection of catalyst. Hybrid models, use the well-studied mechanistic PBM structure as a scaffold, with embedded data-driven correlations that map complex interactions affecting mechanical and reactive transformations. Hybrid modeling for PBMs has already been widely used to monitor particle sizes in pharmaceutical production [7-11]. This work will employ recent advances in Machine Learning (ML), to develop hybrid PBM models that can track molecular weights during reactive milling of polymers.

This case study models the MWD evolution of polystyrene (PS) waste in a lab-scale vibratory ball mill as a function of operating conditions, using diverse data, population balance equations and ML. First, experimental MWD data is collected for varying operating conditions. Next, a Discrete Element Method (DEM) simulation, that accurately predicts the kinematics of grinding media in the ball mill has been developed and validated. Using all the above data, we will present PBM models with varying fidelity, ranging from PBMs with empirical kernels (PBMe), to PBMs with hybrid-mechanistic kernels (PBMhm). The PBMe formulation is trained on a subset of the experimental data and then validated at un-seen conditions. The PBMhm formulation, includes a semi-mechanistic kernel informed from DEM simulation data, that captures how and when particles break as a function of operating conditions. There are many mathematical challenges towards developing a predictive PBM model, including how to: (a) effectively sample from the DEM simulations to train the hybrid model; (b) decide on the type of kernel that will inform the PBM using hybrid ML techniques; (c) optimize the parameters of these nonlinear models. We anticipate that the findings of this work will lay the foundation on the use of hybrid PBMs models to describe depolymerization recycling processes.

Citations

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