Predictive Modeling of Barium Sulfate Scaling: Evaluation of Nucleation and Growth Rate Models Using Experimental Kinetics Data

This study focuses on the fundamental development of a predictive model for barium sulfate precipitation, a key scaling issue in the oil and gas industry and a major source of naturally occurring radioactive materials (NORM). A mass balance and a population balance model were formulated to evaluate different nucleation and growth rate models across varying initial concentrations. Statistical analysis was performed to determine the most accurate model combination, establishing a framework for future scaling predictions. The model consists of a system of ordinary differential equations (ODEs) describing mass balance for barium sulfate and its ions, formulated for a closed batch reactor. A population balance equation was developed, considering length as the internal coordinate while neglecting diffusion and advection. The method of moments was used to solve the population balance equation. Thermodynamic equilibrium was incorporated using a polynomial function of temperature and pressure, derived from a theoretical Van't Hoff expansion. Statistical analysis identified the secondary nucleation model coupled with a temperature-dependent growth model as the most accurate approach. This combination provided the best mass curve fit in five out of six datasets, with R2 values ranging from 0.8473 to 0.9941. Additionally, in all three datasets containing particle surface area data, this model combination yielded the best fit. Some limitations were observed in early-stage precipitation kinetics and in datasets with rapid mass depletion, where equilibrium was reached faster than experimental data suggested. These findings establish a solid foundation for scaling prediction applications. This work establishes a robust modeling framework for barium sulfate precipitation by systematically evaluating nucleation and growth rate models with mass balance considerations. The proposed approach provides a basis for future applications in predicting barium sulfate and other scaling salts in oil and gas operations.