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.
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