Kinetics of near-equilibrium calcite precipitation at 100°C: An evaluation of elementary reaction-based and affinity-based rate laws

Abstract Three affinity-based rate models based upon physical growth mechanisms were used to fit surface-controlled precipitation rate data for calcite using a continuously stirred tank reactor in NaOHCaCl2CO2H2O solutions at 100°C and 100 bars total pressure between pH 6.38 and 6.98. At higher stirring speeds, when aH2CO3∗ was smaller than 2.33 × 10−3, rate showed a parabolic dependence upon exp( Δ G RT ) for exp( Δ G RT ) Δ DG RT ) > 1.72 and followed a rate law based upon the assumption that surface nucleation is rate-limiting. When αH2CO3∗ was greater than 5.07 × 10−3, the rate showed a linear dependence upon exp( Δ G RT ), suggesting growth by a simple surface adsorption mechanism. The rate of these three mechanisms at 100°C can be expressed by the following equations: ( spiral growth ) R ppt = 10 −9.00±0.15 exp ΔG RT − 1 1.93±0.14 , ( adsorption ) R ppt = 10 −8.64±0.07 exp ΔG RT − 1 1.09±0.10 , ( surface nucleation ) R ppt = 10 −7.28±0.49 exp − 2.36±0.21 ΔG/RT . The mechanistic model of Plummer et al. (1978) given by R net = k 1 a H + + k 2 a H2 CO3 ∗ + k 3 a H2O − k 4 a Ca 2+ a HCO − 3 also describes the precipitation rate when growth followed the spiral growth equation. The rate constant for precipitation, k4, ranges between 7.08 × 10−4 to 1.01 × 10−3 moles cm−2 s−1 in the aH2CO3∗ range studied. This work shows that precipitation at 100°C in the spiral growth regime is well fit by both the mechanistic model of Plummer et al. (1978), based on multiple elementary reactions, and by a model derived for growth at screw dislocations. Outside of the regime of spiral growth, however, the model of Plummer et al. (1978) fails, suggesting that different elementary reactions control growth in the adsorption or two-dimensional nucleation regimes. However, the model of Plummer et al. (1978), based upon individual elementary reactions, accurately predicts both dissolution and precipitation of calcite under certain conditions; tests of the affinity based models reveal that none of these models accurately predict dissolution. Therefore, although affinity-based models may yield insights concerning the physical mechanism of growth, they may not be as useful in modelling dissolution and growth over the full range of ΔG.