Monitoring of Batch Industrial Crystallization with Growth, Nucleation, and Agglomeration. Part 1: Modeling with Method of Characteristics

A radiochemical lab-on-a-chip paired with computer vision to unlock the crystallization kinetics of (Ba,Ra)SO4

(Ra,Ba)SO4 solid solutions are commonly encountered as problematic scales in subsurface energy-related applications, e.g., geothermal systems, hydraulic fracturing, conventional oil and gas, etc. Despite its relevance, its crystallization kinetics were never determined because of radium (226), high radioactivity (3.7 × 1010 Bq g-1), and utilization in contemporary research, therefore constrained to trace amounts (< 10-8 M) with the composition of BaxRa1-xSO4 commonly restricted to x > 0.99. What if lab-on-a-chip technology could create new opportunities, enabling the study of highly radioactive radium beyond traces to access new information? In this work, we developed a lab-on-a-chip experiment paired with computer vision to evaluate the crystal growth rate of (Ba,Ra)SO4 solid solutions. The computer vision algorithm enhances experimental throughput, yielding robust statistical insights and further advancing the efficiency of such experiments. The 3D analysis results of the precipitated crystals using confocal Raman spectroscopy suggested that {210} faces grew twice as fast as {001} faces, mirroring a common observation reported for pure barite. The crystal growth rate of (Ba0.5Ra0.5)SO4 follows a second-order reaction with a kinetic constant equal to (1.23 ± 0.09) × 10-10 mol m-2 s-1.

Monitoring of Batch Industrial Crystallization with Growth, Nucleation, and Agglomeration. Part 2: Structure Design for State Estimation with Secondary Measurements

This work investigates the design of alternative monitoring tools based on state estimators for industrial crystallization systems with nucleation, growth, and agglomeration kinetics. The estimation problem is regarded as a structure design problem where the estimation model and the set of innovated states have to be chosen; the estimator is driven by the available measurements of secondary variables. On the basis of Robust Exponential estimability arguments, it is found that the concentration is distinguishable with temperature and solid fraction measurements while the crystal size distribution (CSD) is not. Accordingly, a state estimator structure is selected such that (i) the concentration (and other distinguishable states) are innovated by means of the secondary measurements processed with the geometric estimator (GE), and (ii) the CSD is estimated by means of a rigorous model in open loop mode. The proposed estimator has been tested through simulations showing good performance in the case of mismatch in the initial conditions, parametric plant-model mismatch, and noisy measurements.