Numerical Simulation of Coupled Adsorption/Precipitation of DETPMP in Carbonate Porous Media

Inorganic scale precipitation is one of the main problems in the industry when incompatible fluids containing ions mix and form solids in the production system. This problem may also occur within the formation causing permeability impairment. Therefore, preventing scale formation, often through the application of scale inhibitors (SI), is very important.SIs are usually phosphonate or polymeric compounds that have some affinity with the ions that are engaged in scale formation. For example, phosphonates may interact with divalent cations such as Ca2+ and Mg2+, forming complexes. These SI/M2+ complexes are moderately soluble but in higher SI or divalent concentrations they may also precipitate in the formation. This is not necessarily a problem, as this effect has been used in “precipitation squeeze” treatments. Many successful applications of this type have been reported in the literature.In precipitation squeeze treatments, the retention of SI in the formation is a complex process that is controlled by coupled precipitation(□) and adsorption(□) action of SI molecules in the formation. Previous transport modeling approaches have mostly considered only SI adsorption in the formation although some simulations have been carried out using simple solubility models to describe the precipitation process. Simple solubility functions are not a very reliable or well- validated approach to modeled coupled adsorption/precipitation processes, especially in reactive formations like carbonates.In this work, an advection/diffusion/reaction transport model is coupled with the DETPMP-brine-carbonate formation, where the full multi-component set of chemical species is included in the reaction and transport model. The full coupled adsorption/precipitation process is also included in the chemical description of the entire process. This complete advection/diffusion transport model is developed for both linear and radial systems based on the finite difference approach. This is coupled with the reaction system that has been reported previously by the authors. The reaction model considers all the reactions occurring in the SI-Brine-Carbonate system including the speciation of SI, complexation of SI with divalent cations, dissolution and precipitation of carbonate, and carbonic system reactions. Also, the equilibrium reaction model considers the adsorption and precipitation in the equilibrium system based on a coupled G/P model which has been presented previously. Finally, the developed model was used to run a sensitivity study on the effect of the adsorption and precipitation of the design and implications of squeeze treatments. Several previously unsuspected results have come of this modeling work which provide a rationale for several of our previously unexplained experimental observations

Coupled adsorption/precipitation (Γ/Π) modelling of scale inhibitor transport in porous media using the coupled isotherm, A_ΓΠ(c)

Scale inhibitor (SI) “squeeze” treatments are widely used operations in production assurance to prevent inorganic scales as one of the main flow assurance problems. In these treatments, a high concentration SI slug is injected (“squeezed”) into the porous medium, retained in the formation rock, and is gradually produced back at relatively small concentrations that can prevent (or significantly reduce) scale formation. The retention of SI in the formation is governed by coupled mechanisms of adsorption (Γ) and precipitation (Π) of SI species in the system. To design such SI treatments in an optimized manner, it is important to have good mathematical models of both the transport and the coupled interactions of adsorption/precipitation (Γ/Π) processes. In this study, a 1D advection-dispersion-reaction transport model has been developed, considering the coupled Γ/Π retention processes, and it is used to model linear core flood systems. The parameters for the equilibrium Γ/Π model can be derived from the routine bulk SI “apparent adsorption” tests that are usually conducted before any treatments. From previous works, equilibrium adsorption isotherm, Γ(c), is used to describe the adsorption behavior in such systems. However, although the precipitation kinetics are “fast” (almost at equilibrium), the kinetics of SI dissolution are “slow” and is therefore modelled by a kinetic rate law. From the derived dimensionless form of the transport-Γ/Π model equations, it is shown that the system is governed by 4 dimensionless numbers, NA, NP, NPe and NDa, which are the adsorption number, the precipitation number, the Peclet number, and the Damköhler number, respectively. The shape of the adsorption isotherm also plays a very important part in the extent and form of the effluent SI returns from the linear system. The developed model was then employed to carry out a series of sensitivity calculations relating to coupled adsorption/precipitation (Γ/Π) processes. Both equilibrium and kinetic SI precipitation were modelled coupled with the equilibrium SI adsorption, and the effect of these processes on the form and extent of the SI effluents was assessed. A range of sensitivities was then carried out to determine the effect of a wide range of parameters, including the effects of flow rate and shut-in periods on the kinetic dissolution effluent behavior. The findings from this work present the most clear explanation to date of why and how “precipitation squeezes” can greatly extend squeeze lifetime. A novel feature of this analysis is to show how the role of precipitation and adsorption changes over the various stages of the return effluent by developing plots of the %SI adsorbed on the rock, in the precipitate, and the mobile fluid phase

Coupled Adsorption/Precipitation Modelling of Phosphonate Scale Inhibitors in a Batch Reactive System

Scale inhibitor squeeze treatments are one of the most common ways to prevent scale deposition. The mineral scale will be inhibited if the concentration of the scale inhibitor (SI) in the produced water is above a certain threshold, known as the Minimum Inhibitor Concentration (MIC), which is controlled by scale inhibitor retention. Therefore, accurate modelling of the SI retention through adsorption (Γ) and precipitation (Π) is critical to the successful design and implementation of squeeze treatments. In this study, an equilibrium model has been developed to simulate the coupled adsorption-precipitation (Γ/Π) of phosphonate scale inhibitors in reactive formations, such as carbonates, in the presence of calcium and magnesium cations. In this approach, the scale inhibitor (SI) was considered as a poly weak acid that may be protonated (HnA), resulting in the complexation with Ca/Mg ions, leading to the precipitation of SI_Ca/Mg complexes. All these reactions occur in an integrated system where carbonate system reactions and adsorption of the soluble species are occurring in parallel. In the adsorption process, all the SI derivatives remaining in the solution, including free and complex species, are considered to participate in the adsorption process, described by an an adsorption isotherm model (e.g., Freundlich). For the precipitation part, the model considers the following reactions: (i) the carbonate system, (ii) SI speciation, considered as weak polyacid, HnA, (iii) the SI-metal (Ca and Mg) binding complexes, and (iv) subsequent precipitation of the SI-Ca/Mg complex. The system charge balance and the mass balances for calcium, magnesium, carbon, and SI are considered, to numerically equilibrate the system (excluding the adsorbed species), by solving a determined set of non-linear equations numerically. Following the algebraic reduction of the equations, the system is reduced to three non-linear equations that may be solved by the Newton-Raphson method. The precipitation of the SI-Ca/Mg is modelled in the equilibrium model based on the solubility of SI in the solution, determined from the lab experiments. The reliability of the proposed model was established by comparison with experimental results from a previous study (Kalantari Meybodi et al., 2023) on the interactions of DETPMP in a Calcite/brine (containing free Ca/Mg) system, where the final concentration of SI, Ca2+, Mg2+, CO2 and pH were compared. The modelling showed good general agreement with the experimental results, and a further sensitivity analysis was performed to examine the behaviour of some uncertain parameters, such as the stability constant of complexes.</p

Coupled Adsorption/Precipitation Modelling of Phosphonate Scale Inhibitors in a Batch Reactive System

Scale inhibitor squeeze treatments are one of the most common ways to prevent scale deposition. The mineral scale will be inhibited if the concentration of the scale inhibitor (SI) in the produced water is above a certain threshold, known as the Minimum Inhibitor Concentration (MIC), which is controlled by scale inhibitor retention. Therefore, accurate modelling of the SI retention through adsorption (Γ) and precipitation (Π) is critical to the successful design and implementation of squeeze treatments. In this study, an equilibrium model has been developed to simulate the coupled adsorption-precipitation (Γ/Π) of phosphonate scale inhibitors in reactive formations, such as carbonates, in the presence of calcium and magnesium cations. In this approach, the scale inhibitor (SI) was considered as a poly weak acid that may be protonated (HnA), resulting in the complexation with Ca/Mg ions, leading to the precipitation of SI_Ca/Mg complexes. All these reactions occur in an integrated system where carbonate system reactions and adsorption of the soluble species are occurring in parallel. In the adsorption process, all the SI derivatives remaining in the solution, including free and complex species, are considered to participate in the adsorption process, described by an an adsorption isotherm model (e.g., Freundlich). For the precipitation part, the model considers the following reactions: (i) the carbonate system, (ii) SI speciation, considered as weak polyacid, HnA, (iii) the SI-metal (Ca and Mg) binding complexes, and (iv) subsequent precipitation of the SI-Ca/Mg complex. The system charge balance and the mass balances for calcium, magnesium, carbon, and SI are considered, to numerically equilibrate the system (excluding the adsorbed species), by solving a determined set of non-linear equations numerically. Following the algebraic reduction of the equations, the system is reduced to three non-linear equations that may be solved by the Newton-Raphson method. The precipitation of the SI-Ca/Mg is modelled in the equilibrium model based on the solubility of SI in the solution, determined from the lab experiments. The reliability of the proposed model was established by comparison with experimental results from a previous study (Kalantari Meybodi et al., 2023) on the interactions of DETPMP in a Calcite/brine (containing free Ca/Mg) system, where the final concentration of SI, Ca2+, Mg2+, CO2 and pH were compared. The modelling showed good general agreement with the experimental results, and a further sensitivity analysis was performed to examine the behaviour of some uncertain parameters, such as the stability constant of complexes.</p