Precipitation rate constant

The above-mentioned consideration indicates that important factors controlling the precipitations of barite and silica are surface area/water mass ratio (A/M), temperature, precipitation rate constant (k) and flow rate (u), and the coupled fluid flow-precipitation models are applicable to understanding the distributions of minerals in submarine hydrothermal ore deposits. 

The calculations based on four reservoir models were made using equations (1-62)-(l-67) and precipitation rate constant k) for Si02 minerals by Rimstidt and Barnes (1980). 

Fig. 3.18. Bicarbonate-calcium carbonate 13C enrichment factors vs. precipitation rate constant (k, L mole min 1). Precipitates that are partly aragonite are marked with a star. (After Turner, 1982.)...

Ps solid density (kg m ) intrinsic dissolution/precipitation rate constant for phase 9 (mol m s )... 

The rate constants for dissolution, kd,x. and precipitation, Jcpx (mol m s ) refer only to the species X. If the mineral dissolves congruently, that is, if the ratio of the constituents released to solution is the same as in the solid, then the solid stoichiometric coefficient times the total mineral dissolution and precipitation rate constants can be used. 

Equations (2.20) and (2.21) relate the rate constants of elementary reactions to their equilibrium constants, and show that if and a single rate constant are known, the second rate constant need not be measured. Rimstidt and Barnes (1980) used this relationship, called the principle of detailed balancing, to obtain the rate constant for dissolution of several silica polymorphs given their empirical solubilities K values) and the precipitation rate constant (A ). (See Section 2.7.8.)... 

The precipitation rate constant for quartz and a and p cristobalite up to about 300°C, and of amorphous silica to about 200°C, with the reaction written as in Eq. (2.91) is given by... 

Fe profiles predicted by the model are plotted in Fig. 22. Corresponding model values are listed in Table VII. Estimates of the anoxic precipitation rate constant ki range from about 10-120/day and are the... 

Pore-water profiles were used together with solid-phase dissolution rates in diagenetic models to determine first-order anoxic precipitation rate constants for both Mn and Fe. A two-dimensional cylindrical coordinate model was employed to account for the effects of biogenic irrigation of burrows on pore-water Mn " distributions. Two-dimensional diffusion can result in a decrease in Mn " with depth that would be interpreted as evidence for precipitation and cause overestimation of precipitation rates in a one-dimensional model. 

Anoxic precipitation rate constants of —0.5-0.7/day we estimated from the cylindrical coordinate model. A traditional one-dimensional model predicts rates —1.5-2 times higher. Agreement is relatively close between the two models in this case because Mn production rates attenuate rapidly with depth. Fe " precipitation rates of about 10-120/day are estimated from a three-layer one-dimensional model. 

First-order anoxic precipitation rate constant for solute Mn in sediment First-order oxic precipitation rate constant for solute Fe in sediment First-order anoxic precipitation rate constant for solute Fe in sediment First-order oxic precipitation rate constant for solute Fe in water overlying sediment... 

First-order oxic precipitation rate constant for solute Mn in water overlying sediment... 

Diffusion coefficient Dt, dissolution rate constant k ., and precipitation rate constant k. of quartz in Eq. (1), (3), and (4) have all Arrhenius-type dependence with temperature, given by ... 

Predicted rates of porosity reduction are shown in Figure 2 together with the data measured within the experiments. To more closely match the porosity and silica concentration histories obtained in the experiments, the principal controlling parameters of diffusion coefficient Di, and dissolution and precipitation rate constants (k., and k.) are modified with dissolution rate constant increased by factors of 1.8 and 3.0, and precipitation rate constant increased by factors of 13.0 and 60.0 for the effective stresses of 69.0 and 35.0 MPa, respectively. The predictions of porosity and silica concentration ob-... 

Table 3.2. Values of the precipitation rate constant and the equilibrium constant neededfor this calculation.

This allows Eq. (3.91) to be rewritten in terms of the equilibrium constant and the precipitation rate constant. 

The values of the precipitation rate constant and the equilibrium constant at 25°, 50°, and 75°C (Rimstidt and Barnes, 1980) given in Table 3.2 were used to calculate the concentration versus time graphs shown in Figure 3.5. 

For low fluid velocities, the mass transfer coefficient is much lower than the precipitation rate constant and the dissolution rate can be written as ... 

When the fluid velocity is such that the mass transfer coefficient is of the same order of magnitude as the precipitation rate constant, the corrosion rate cannot be simplified and the entire equation has to be taken into account to perform corrosion rate calculations. 

---