A Coupled Model of Phosphonate Scale Inhibitor Interactions with Carbonate Formations

In this study, a chemical model has been developed for the simulation of the scale inhibitor (SI) interactions with carbonate systems (calcite), where the aqueous phase may contain free calcium and magnesium ions. The resulting model couples together the equations of (i) the carbonate system, (ii) the speciation of the SI, modelled as a weak polyacid, H_nA, (iii) the metal (Ca²⁺, Mg²⁺) binding – SI chelant interactions and (iv) the subsequent precipitation of SI-Ca-Mg complex. These reactions are considered in conjunction with the charge balance and mass balances for calcium, magnesium, scale inhibitor and "carbon" (i.e. the carbonate system aqeous components HCO₃^-, CO₃^2-and CO₂ and solid CaCO₃). This full equation set, with suitable reduction, results in a system of 3 non-linear equations which can be solved by the Newton-Raphson method to find the final equilibrium state of the system.

The experimental results for the DETPMP/Calcite/Ca-Mg brine system from a previous study were used to check the reliability of the proposed model. The model calculates the equilibrium concentrations of all species (SI, Ca²⁺, Mg²⁺, HCO₃^-, CO₃^2-, CO₂, H⁺, and the components of the SI-Ca-Mg complexes etc.) based on their initial values and reaction constants, i.e. equilibrium constants, stability constants and solubility constants. The model can be applied either assuming a closed chemical system, or an open system and simuilation conditions were chosen in order to match the actual experiments which were matched. The model results show good quantitative agreement with the experimental results, although some assumptions must be made on the system input constants. To elucidate the precise effects that these various parameters are having in this very complex coupled system, an extensive sensitivity analysis was performed. This is especially important for uncertain parameters like stability constants of the complexes of scale inhibitor with calcium and magnesium, which are not reported in the literature.

In future, this model be coupled with the adsorption model (based on the isothermal adsorption curve) and the coupled model will be incorporated into a transport model to develop a complete coupled adsorption/precipitation squeeze treatments simulation model. To our knowledge, no such model currently exists.