(555h) A Novel Framework of a Reduced Two-Dimensional Population Balance Model for Struvite Crystallization

The circular economy aims to minimize waste and maximize the efficient use of resources by promoting a closed-loop system where materials and resources are continuously reused, recycled, or repurposed. Crystallizing struvite (MgNH₄PO₄.6H₂O), which is an important phosphate mineral found in wastewater, allows for the recovery of valuable nutrients, namely nitrogen and phosphorus and even aiding controlled CO₂ stripping. Instead of these nutrients being lost as waste, they can be captured and repurposed as slow-release fertilizers. By recovering these nutrients, struvite crystallization contributes to closing the nutrient loop and reducing the reliance on traditional fertilizers derived from non-renewable sources. To control the characteristics of the struvite crystal population in wastewater, variables such as crystal size density, composition, morphology, and spatial distribution are necessary. A typical modeling approach to account for the nucleation and growth of struvite crystals, considering two-dimensional variables (such as length and breadth) of a struvite crystal, would lead to a multi-dimensional population balance model (PBM) which brings considerable complexity in solution accuracy and computational time. A simple yet accurate approach is to perform model reduction in which the model is first transformed into another coordinate system. The two new coordinates are namely crystal volume and crystal shape factor. Under certain assumptions, the reduced model leads to a system of only a few coupled mass balance equations which preserves the average behavior and dispersity information of these crystals. In this study, a conceptual framework for solving such a two-dimensional PBM with nucleation and growth is proposed and a step-by-step analysis of the system is derived for future applications.