A Comprehensive Equilibrium Model for the Phosphonate Scale Inhibitor-Carbonate System including Coupled Adsorption/Precipitation (Γ/Π)

Inorganic scale deposition is one of the main flow assurance issues in hydrocarbon production, and injection systems, leading to significant loss in production and subsequent expense to mitigate. Scale Inhibitors (SI) are chemicals that are commonly used to prevent the inorganic scale from building up in the system. SIs are usually injected into the porous media, where they can react and be retained, and released back into the produced brine as the production commences. This in situ scale prevention method is known as “squeeze treatment”, and the lifetime of this process is determined when the SI concentration in the return fluid falls below the MIC (Minimum Inhibitor Concentration), where the SI is sufficiently effective at preventing or efficiently reducing scale formation.

In this study, a general chemical equilibrium model has been developed to simulate the chemical reaction of phosphonate scale inhibitors and their retention in a carbonate system (calcite), in the presence of an aqueous phase containing free divalent cations. The model couples together the following processes (i) the carbonate system, (ii) speciation of the SI, modelled as a weak polyacid, HnA, (iii) the metal (Ca2+, Mg2+) binding – SI chelant interactions, (iv) phosphonate SI acid impurity reactions, (v) adsorption of the free and complex species to the rock surface and (vi) and finally, the precipitation of complex species (SI-Ca-Mg). To find the equilibrium conditions, charge balance and mass balances for key components in the system were considered, and combined utilizing reaction constants, i.e. equilibrium constants, stability constants, and solubility constants. This full equation set can be solved numerically to find the equilibrium concentration of all engaged species to characterize the equilibrium condition. To account for the adsorption and precipitation retention in this system, a coupled adsorption/precipitation (Γ/Π) isotherm has been presented and used for the first time. The coupled Γ/Π isotherm is a mathematical representation of the retention amount in the system that coupled adsorption and precipitation retention mechanisms are in action, which can scale up the retention results to other systems with different mass to volume ratios.

To validate the proposed model, experimental results of a DETPMP-Calcite equilibrium system in NSSW were considered. The model and the experimental results were in good agreement demonstrating the reliability of the model. Furthermore, the reliability of the model in stoichiometry prediction of complexes, and distribution of species in different conditions was evaluated which confirmed the validity of the model.