“Mixed” kinetics control of fluid-rock interaction in reservoir production scenarios

Abstract

We examine scenarios under which mineral-water reaction kinetics exhibit mixed-kinetic control, that is, when both surface reaction rates and hydrodynamic conditions influence rates of dissolution and precipitation from aqueous solutions at mineral-water interfaces. This dependence arises in many engineering situations and imparts a fluid flow velocity dependence on overall rates. Recognition of transport control is critical for extraction of rate data under laboratory conditions; failure to do so can lead to drastically overestimated, or in some cases, underestimated rates of scale formation in production scenarios. Data on gypsum (at 25°C) and calcite (at 100°C) dissolution and precipitation kinetics are examined for relative control of rates by mixed transport/reaction control, and a rate expression is derived that reproduces the different data sets. This rate law takes the form: R = k ( 1 − Ω bulk 1 / 2 + ζ [ 1 − { 1 + 2 ( 1 − Ω bulk 1 / 2 ) / ζ } 1 / 2 ] ) where ζ = ( D m eq ) / 2 δ k where R is rate; k is the rate constant for purely transport control; Ω is the saturation expressed as a ratio of calcium ion concentration in bulk solution to the equilibrium concentration, and the other terms are defined in the text; and ζ is a factor which measures the relative strength of transport or reaction steps as influence concentrations of species at the mineral-water interface. Combined with reaction transport equations, this expression is capable of predicting gypsum and calcite mineral-water reaction rates over a wide variety of saturation and hydrodynamic conditions. Although comprehensive data sets are lacking, we suggest that this equation is applicable to precipitation of other sulfate minerals that are problematic scale formers, such as barite, celestite, and anhydrite.