Scale inhibitors are retained within porous media by the two main mechanisms of "adsorption" (Γ) and "precipitation" (Π). In previous experimental and modelling work, we have demonstrated for static (equilibrium) "apparent adsorption" tests where the system exhibits either (a) adsorption only or (b) it is in the coupled adsorption/precipitation (Γ/Π) regime. A complete model of SI retention must have (i) an equilibrium description of the coupled Γ/Π process (Kahrwad et al, 2008); (ii) a kinetic model of coupled Γ/Π which correctly limits to the equilibrium case (i.e. the kinetics must be consistent with the equilibrium Γ/Π model as t → ∞); (iii) the full kinetic Γ/Π model must then be embedded in a transport model for flow through porous media. Some progress towards this full model has been made and reported previously (Sorbie, 2010; Vazquez et al, 2010).
The full coupled kinetic Γ/Π model is comprehensive and is currently being verified by experiment. However, this full model is quite complex and difficult to understand. Therefore, in this paper, we present a new simple model of kinetic precipitation (Π) which explains some key features of this process. This work will present 3 key new findings, as follows:
a very simple mathematical explanation of the mechanism and observations in kinetic precipitation;
some simple but novel analytical formulae which describe the process;
a worked field scale radial kinetic precipitation examples is presented which demonstrates how to estimate whether a given field system is close to or far from precipitation/dissolution equilibrium.
This simpler model represents an end-member where a precipitating SI system is described by a solubility (Cs) and a dissolution rate, k. In most practical cases, some level of adsorption is also superimposed upon this behaviour but this is neglected in this simple model. However, understanding the behaviour of this idealized system does give us some mechanistic insights and some simple practical formula for precipitation squeeze design purposes.