Euler-Lagrange Approach for Modelling and Simulating Inorganic Scale Formation in Capillary Tube

The continuous drive to maximize production and profits in the oil and gas industry is frequently hindered by flow assurance challenges. Inorganic scaling, a common operational problem, involves the accumulation of solid crystal deposits from species dissolved or dispersed in the aqueous phase (Zhang et al., 2015). Among the most common types of scale, calcium carbonate (CaCO3) is particularly prevalent, with its formation linked to the carbonate-rich rock formations of reservoirs and significantly influenced by the presence of dissolved carbon dioxide (CO2) in production fluids (Burchette, 2012). The formation of CaCO3 scale is a complex, multiphysics phenomenon initiated by a thermodynamic driving force - the supersaturation of the solution - which is followed by several kinetic processes that govern precipitation, including nucleation, crystal growth, agglomeration, and dissolution (Mersmann, 2001). In addition to these chemical mechanisms, the hydrodynamic conditions of the particulate system are critical, governing the transport of the precipitated mass and its subsequent deposition onto equipment surfaces (Hoang, 2015). To address this issue holistically, the development of predictive models covering a significant portion of a well's productive lifecycle is essential. In an effort to capture the key effects of CaCO3 crystal formation and subsequent scaling, various specific and integrated models have been proposed to bridge industrial needs with academic tools. Early works such as Haarberg and Selm (1992) introduced thermodynamic solubility-equilibrium models for sulfate and carbonate formation under different aqueous conditions. Kinetic models based on population balance, like that of Chakraborty and Bhatia (1996), provided temporal results for the size distribution of calcium carbonate particles, considering that polymorphs have different growth rates and agglomeration tendencies. More recently, a comprehensive chemically integrated approach was extensively studied by Neubauer (2022), who developed a thermo-kinetic mathematical model that addressed precipitation potential, precipitation rates, particle size distribution, and preferential polymorphism. On the hydrodynamics front, studies by Vazirian et al. (2016) focused on particle transport and adhesion. These were later extended into particulate flow models using coupled Computational Fluid Dynamics and the Discrete Element Method (CFD-DEM) to calculate crystal deposition rates (Maciel et al., 2019; Poletto et al., 2023). The present study proposes a coupled modeling framework for inorganic scale formation. This approach utilizes thermodynamic and kinetic models to quantify the precipitated solid mass, which in turn provides realistic input conditions for simulating particulate flow and deposition in a capillary tube. The multiphase flow is simulated using a hybrid Euler-Lagrange approach with a four-way coupled CFD-DEM. This method resolves the pressure and velocity fields—which can be used by the aforementioned chemical models—while also tracking particle transport and subsequent deposition. This framework is validated in a stepwise manner: the thermo-kinetic model that provides the particle inputs is based on prior work extensively validated against ISDER experimental data, while the CFD-DEM component's ability to predict hydraulic effects is benchmarked against a proven mechanistic model.