『Abstract
This paper demonstrates a method for systematic analysis of published
mineral dissolution rate data using forsterite dissolution as
an example. The steps of the method are: (1) identify the data
sources, (2) select the data, (3) tabulate the data, (4) analyze
the data to produce a model, and (5) report the results. This
method allows for a combination of critical selection of data,
based on expert knowledge of theoretical expectations and experimental
pitfalls, and meta-analysis of the data using statistical methods.
Application of this method to all currently available forsterite
dissolution rates (0＜pH＜14, and 0＜T＜150℃) normalized to geometric
surface area produced the following rate equations:
For pH＜5.6 and 0゜＜T＜150℃, based on 519 data
log rgeo = 6.05 (0.22) - 0.46 (0.02) pH
- 3683.0 (63.6) 1/T (R2 = 0.88)
For pH＞5.6 and 0゜＜T＜150℃, based on 125 data
log rgeo = 4.07 (0.38) - 0.256 (0.023)
pH - 3645 (139) 1/T (R2 = 0.92)
The R2 values show that ～10% of the variance in r
is not explained by variation in 1/T and pH. Although the experimental
error for rate measurements should be ±～30%, the observed error
associated with the log r value is ～0.5 log units (±300% relative
error). The unexplained variance and the large error associated
with the reported rates likely arises from the assumption that
the rates are directly proportional to the mineral surface area
(geometric or BET) when the rate is actually controlled by the
concentration and relative reactivity of surface sites, which
nay be a function of duration of reaction. Related to these surface
area terms are other likely sources of error that include composition
and preparation of mineral starting material.
Similar rate equations were produced from BET surface area normalized
rates. Comparison of rate models based on geometric and BET normalized
rates offers no support for choosing one normalization method
over the other. However, practical considerations support the
use of geometric surface area normalization. Comparison of Mg
and Si release rates showed that they produced statistically indistinguishable
dissolution rates because dissolution was stoichiometric in the
experiments over the entire pH range even though the surface concentrations
of Mg and Si are known to change with pH. Comparison of rates
from experiments with added carbonate, either from CO2
partial pressures greater than atmospheric or added carbonate
salts, showed that the existing data set is not sufficient to
quantify any effect of dissolved carbonate species on forsterite
dissolution rates.』
Notation
1. Introduction
2. Methods
3. Results
3.1. Properties of the data set
3.2. Data analysis
3.2.1. Choosing a rate equation
4. Discussion/conclusions
4.1. Data identification, selection, and tabulation
4.2. Choosing a rate equation
4.3. Errors and error propagation
4.4. Answering questions about forsterite dissolution
Acknowledgments
Appendix A. Supplementary data
References