An integrated model of scale inhibitor (DETPMP) transport, coupled adsorption/precipitation (Γ/Π) and reaction in carbonate systems

Scale inhibitors (SI) are the most widely used materials to prevent inorganic scale formation in flow assurance. SIs operate at threshold concentrations to prevent the formation of inorganic scale; therefore, it is paramount to maintain these levels of SI as long as possible. SIs are usually directly injected (i.e. “bullheaded”) in a “squeeze” treatment into a producing well at very high concentration, where they are retained by adsorption (Γ) and precipitation (Π) mechanisms in the near-well rock formation. Retained SIs are gradually released to the aqueous production stream when the well is put back into production. The efficiency of the SI treatment will depend on the level and type of retention (Γ/Π) in the system. Therefore, a detailed model of the system chemistry and fluid dynamics is required to build a realistic design and for the implementation of more efficient SI field treatments.

The modelling of squeeze treatments in reactive formations requires a detailed model that can consider the SI chemical system, its binding to divalent cations (Ca²⁺ and Mg²⁺), the precipitation (Π) of the formed SI_M²⁺ complexes, and the adsorption of the solution SI species, coupled to the reactive carbonate rock chemistry. No such model currently exists in the literature which models all parts of this process, and this is addressed in this study. This paper presents a fully integrated geochemical transport model that can simulate the SI squeeze treatments in reactive formations, such as carbonates, or core flood tests used to support the design of such treatments. The general model is developed to simulate the reactive transport of multiple components, including the SI itself through carbonate formations while reactions are occurring between the bulk fluid and rock matrix, as well as the homogenous reactions in the bulk fluid. For modelling purposes, the SI is treated as a weak polyacid (H_nA), which on dissociation yields phosphonate ions along with the neutral species; n = 10 for DETPMP modelled in this work, but it varies for other phosphonate. The reaction of the SI and carbonate substrate (here taken simply as calcite, CaCO₃), is fully described by a recently developed geochemical model for the SI-brine-carbonate system (Kalantari Meybodi et al., 2024a), which considers all the reactions occurring in such system to fully characterize the concentration of all engaged species under any conditions (Kalantari Meybodi et al., 2024a). Moreover, the reaction model includes the new concept of the coupled adsorption/precipitation (Γ/Π) isotherm, which can be used to determine the quantitative partitioning of SI into the adsorption and/or precipitation phases (Kalantari Meybodi et al., 2024a). The isotherm is constructed based on SI static bottle tests, measuring “apparent adsorption”, which are common in any SI application. In the geochemical model, separate parts of the model operate at different levels of “granularity”, such as the reaction model which works on an individual species basis, while the retention is based on the coupled isotherm, depending on the total SI concentration in the system, as explained previously (Kalantari Meybodi et al., 2024b) and in this paper. A sub-set of this model can also be used to simulate non-reactive formations such as sandstones, for extended field applications worldwide.

The full geochemical transport model developed in this study is also capable of considering the effect of any specific concentration of any engaged species on the performance and behaviour of the SI-Brine-Carbonate substrate system. Among all operational parameters, the pH of the SI pill or the pH of the postflush stream is of particular interest, as it will have a major impact on the reactivity of the SI/Carbonate system and its performance. The other factors are the composition of the postflush and the makeup water for the main pill, which can play a major role in determining the performance of the system. These effects cannot be captured using the currently available models, which do not consider the full coupled reactive system. In addition, the model is capable of tracking the concentration of all involved species, including the SI dissociated species, at any time or point in the system. The capabilities of the model along with model results have been investigated in this study along with some qualitative validation with parameters that exist for such system in the literature, e.g. the stoichiometry of formed complexes. Additionally, a sensitivity analysis on key parameters such as pH of the SI pill and post flush has been conducted to demonstrate the effectiveness of the model in predicting the system behaviour under these conditions.