The deposition kinetics of barium sulphate scale: model development - Rafiee, H.; Sorbie, K. S.; Mackay, E. J. (Frontiers in Materials, 2023)
The formation and deposition of mineral scales, such as barium sulphate (BaSO4) and calcium carbonate (CaCO3), is a common problem in many industrial and life science processes. This is caused by chemical incompatibility due either to the mixing of incompatible aqueous solutions or due to changes of the physical conditions, usually temperature and pressure. Many laboratory studies have been conducted using techniques broadly classified into batch and flowing tests to understand the reaction and mechanisms which occur in the initial stages of scale formation and its subsequent deposition on a solid surface. In this study we focused on the dynamic (kinetic) deposition of barium sulphate arising from the mixing of two incompatible brines, one containing barium (Ba2+) ions and other containing sulphate (SO42−) ions, suitably charged balanced by other inert anions and cations. The mechanism of barium sulphate (barite) deposition is often assumed to be a one-step reaction in which the ions in the bulk fluid directly deposit onto a surface. However, there is strong evidence in the literature that barium sulphate may deposit through an intermediary nanocrystalline phase which we refer to as BaSO4(aq) in this paper. This initial nucleation species or nanocrystalline material [BaSO4(aq)] may remain suspended in the aqueous system and hence may be transported through the system before it ultimately is deposited on a surface, possibly covered by a previously deposited barite coating. This does not preclude the direct deposition of barite on the surface which may indeed also occur. In this paper, we have formulated a barite formation/deposition model which includes both of these mechanisms noted above, i.e., i) barite formation in solution of a nanocrystalline precursor which may be transported and deposited at an interface and ii) the direct kinetic deposition of barite from the free ions in solution. When only the former mechanism applies (nanocrystal formation, transport and deposition) we refer to the model Model 1 and, when both mechanism occur together it is called Model 2. Although this is a fully kinetic model, it, must honour the known equilibrium state of the system in order to be fully consistent and this is demonstrated in the paper. The kinetic approach is most important in flowing conditions, since the residence time in a given part of the macroscopic system (e.g., in a pipe or duct) may be shorter that the time required to reach the full equilibrium state of the system. The reaction extent can be affected by advection, introduction of viscous dissipation forces, formation of hydrodynamic boundary layers and the mass transport in the boundary layer close to the depositing surface. In this paper, we call the latter the diffusion penetration length, denoted δ, and the relation of this quantity with the hydraulic layer is discussed. In this work, we have coupled the barium sulphate depositional model with a full computation fluid dynamics calculation (CFD) model in order to study the behaviour of this system and demonstrate the importance of non-equilibrium effects. Studied using different kinetic constants. The Navier-Stokes equations are solved to accurately model the local residence time, species transport, and calculate the hydraulic and mass transfer layers. A number of important concepts for barium sulphate kinetic deposition are established and a wide range of sensitivity calculations are performed and analysed. Geometry alteration due to flow constriction in the pipe or duct caused by the depositing scale is also an important phenomenon to consider and model in a flowing system, and this is rarely done, especially with a full kinetic deposition model. The geometry change affects both hydraulic and mass transport layers in the vicinity of the depositing surface and may often change the deposition regime in terms of the balance of dominant mechanism which apply. The change in geometry requires occasional re-gridding of the CFD calculations, which is time consuming but essential in order to study some critical effects I the system. The effect of geometry change on the local residence time is investigated through by performing a “ramping up” of the flow rate and explicitly deforming the geometry as the deposition occurs. The influence of surface roughness on the reaction rates was also studied using different kinetic constants. Our results show that in the laminar flow regime, the extent of deposition on a surface is limited by the diffusion penetration length (δ) referred to above. This means that there will be more deposits at lower flow rates, where the diffusion penetration length is larger. As the deposition reduces the flow path cross-section area near the inlet vicinity, the velocity increases. Thus, the hydraulic layer becomes smaller, resulting in a smaller diffusion penetration length, which causes the deposition location to move towards the end of the flow path, where the velocity is still smaller. The results of this study have the potential to contribute to the development of more effective strategies for preventing scaling in a wide range of industrial processes.