3-D CFD-PBM coupled modeling and experimental investigation of struvite precipitation in a batch stirred reactor

Abstract

A general model has been developed to elucidate the precipitation of struvite crystals in a batch stirred tank reactor. The model, which evaluates reactor performance, also predicts crystal size distribution (CSD) over time by considering the hydrodynamic, thermodynamic, and kinetic aspects of solution in the reactor. A Computational Fluid Dynamics (CFD) model was coupled with Population Balance Modeling (PBM) to model the growth of crystals in the reactor. A thermodynamic equilibrium model for struvite precipitation was consolidated with the reactor model. While the equilibrium model provided information on supersaturation development, the coupled CFD-PBM model captured the crystal growth kinetics and the influence of the reactor hydrodynamics on the overall process. Size distribution is crucial as it determines distinct grades of final struvite crystals, which are to be used as commercial fertilizer. In the simulation, the CFD flow field was solved through a Eulerian multiphase approach and RNG-k-ɛ turbulence model. The population balance equation was solved using a discretized form of the continuous partial differential equation, which transformed the continuous partial differential equation into finite ordinary differential equations as per size classes, which were then solved simultaneously. The growth rate, as a function of the supersaturation index (SI), was employed in the model through User Defined Function. The mean, standard deviation, and skewness of the model predicted CSD after 50 min were 20.81 μm, 9.61 μm, and 2.97, respectively and for the experimental CSD were 19.66 μm, 7.13 μm, and 2.46, respectively. The predicted peak-size percent fraction revealed a deviation from experimental results of 1.42%, 0.05%, 2.43%, 14.6%, 11.2%, 11.7%, 13.6%, and 14.2% at 0, 3, 10, 20, 30, 40, 50, and 60 min, respectively.