Joel Z. Bandstra

Data Fitting Techniques with Applications to Mineral Dissolution Kinetics

A common problem in chemical kinetics is the development of a rate law that describes the dependence of the reaction rate on the surrounding conditions such as concentrations of reacting species or temperature of the reacting media (see Chap. 1). The most direct approach to solving this problem is to measure reaction rates under systematically varied conditions and then to perform mathematical analyses on these data to determine the form of the rate law and to generate estimates of any unknown constants, or parameters, that make up the proposed rate law. Other chapters in this book provide information both for designing kinetics experiments and for selecting appropriate rate laws for a variety of geochemical reactions. In this chapter we describe the mathematical analyses – known collectively as curve fitting or regression analysis – that can be used to select a rate equation that matches a given data set, to generate estimates for any unknown parameters in the rate equation (e.g., rate constants or reaction orders), and to quantify the uncertainty associated with the estimated values for the parameters. As we traverse this entirely quantitative process we will attempt to describe the underlying, qualitative process of looking at kinetic data: plots to make, features of these plots to examine, and conceptual sketches to draw. In order to fit a curve to data one must first obtain the data. Over the past few decades, researchers have produced numerous high quality studies on the kinetics of mineral dissolution and the effects of experimental conditions such as pH, temperature, concentration of dissolved metal ions, mineral composition, etc. We have compiled this dissolution rate data for a number of rocks and minerals including apatite, basalt, biotite, hornblende, kaolinite, olivine, plagioclase, potassium feldspar, pyroxene, and quartz. We will use these data, which are available in Appendix I of

Packed Powder Electrodes for Characterizing the Reactivity of Granular Iron in Borate Solutions

Electrochemical aspects of the corrosion of iron metal have been studied using polished disk, wire, and iron coupon electrodes, but these model systems do not represent many characteristics of the granular iron used in environmental remediation applications. To address this issue, we have modified a rotating disk electrode with a cavity that accommodates a wide range of iron powders. By comparison with conventional Fe 0 and Pt° disk electrodes, we found that our powder disk electrodes (PDEs) packed with unpretreated, <147 μm granular iron give anodic polarization curves that are unaffected by the underlying disk material and are consistent with a large electroactive surface area of iron that is initially coated with an air-formed passive film. Thus, we believe this electrode design will allow us to begin electrochemical studies of the reduction of aqueous environmental contaminants by relevant iron powders. In preparation for this, we report here on some of the experimental factors that effect response of an iron PDE in pH 8.4 borate buffer. Cavity size and rotation rate have synergistic effects that suggest that most of the iron powder is electroactive, hydrogen evolution in the active region is kinetically limited, and iron dissolution in the active region is affected by mass transport of solutes out of the cavity pore space and by the formation of a passivating film.

Understanding the mechanisms of solid-water reactions through analysis of surface topography

The topography of a reactive surface contains information about the reactions that form or modify the surface and, therefore, it should be possible to characterize reactivity using topography parameters such as surface area, roughness, or fractal dimension. As a test of this idea, we consider a two-dimensional (2D) lattice model for crystal dissolution and examine a suite of topography parameters to determine which may be useful for predicting rates and mechanisms of dissolution. The model is based on the assumption that the reactivity of a surface site decreases with the number of nearest neighbors. We show that the steady-state surface topography in our model system is a function of, at most, two variables: the ratio of the rate of loss of sites with two neighbors versus three neighbors (d(2)/d(3)) and the ratio of the rate of loss of sites with one neighbor versus three neighbors (d(1)/d(3)). This means that relative rates can be determined from two parameters characterizing the topography of a surface provided that the two parameters are independent of one another. It also means that absolute rates cannot be determined from measurements of surface topography alone. To identify independent sets of topography parameters, we simulated surfaces from a broad range of d(1)/d(3) and d(2)/d(3) and computed a suite of common topography parameters for each surface. Our results indicate that the fractal dimension D and the average spacing between steps, E[s], can serve to uniquely determine d(1)/d(3) and d(2)/d(3) provided that sufficiently strong correlations exist between the steps. Sufficiently strong correlations exist in our model system when D>1.5 (which corresponds to D>2.5 for real 3D reactive surfaces). When steps are uncorrelated, surface topography becomes independent of step retreat rate and D is equal to 1.5. Under these conditions, measures of surface topography are not independent and any single topography parameter contains all of the available mechanistic information about the surface. Our results also indicate that root-mean-square roughness cannot be used to reliably characterize the surface topography of fractal surfaces because it is an inherently noisy parameter for such surfaces with the scale of the noise being independent of length scale.

Assessment of sulphate and iron reduction rates during reactor start-up for passive anaerobic co-treatment of acid mine drainage and sewage

Passive co-treatment of municipal wastewater (MWW) and acid mine drainage (AMD) has shown promise over the past decade for simultaneous remediation of these widespread waste streams. To investigate the efficiency and rates of iron and sulphate reduction during the start-up of anaerobic co-treatment using a novel, process-based kinetic modeling approach, twenty-four replicate 1L-cubitainers containing a 5:2 MWW:AMD mixture and Kaldnes plastic media were sealed, incubated and sacrificially sampled for key water quality parameters over 30 days. Alkalinity generation, pH increase and efficient removal of iron, aluminum and phosphate were observed. The observed sulphate and iron reduction rates were relatively slow, and the removal of sulphate, organic carbon and nitrogen was modest and incomplete. Overall, the results confirm the efficacy of AMD-MWW co-treatment for removal of key pollutants, but also highlight factors that may limit this emerging technology. Supplementary material: The fitted model parameters used to describe the behaviour of Fe, H2S and SO42− are available at https://doi.org/10.6084/m9.figshare.c.3841279