Improving arsenopyrite oxidation rate laws: implications for arsenic mobilization during aquifer storage and recovery (ASR)

Abstract

Aquifer storage and recovery (ASR) and aquifer recharge (AR) provide technical solutions to address water supply deficits and growing future water demands. Unfortunately, the mobilization of naturally present arsenic due to ASR/AR operations has undermined its application on a larger scale. Predicting arsenic mobility in the subsurface during ASR/AR is further complicated by site-specific factors, including the arsenic mobilization mechanisms, groundwater flow conditions, and multi-phase geochemical interactions. In order to ensure safe and sustainable ASR/AR operation, a better understanding of these factors is needed. The current study thus aims to better characterize and model arsenic remobilization at ASR/AR sites by compiling and analyzing available kinetic data on arsenic mobilization from arsenopyrite under different aqueous conditions. More robust and widely applicable rate laws are developed for geochemical conditions relevant to ASR/AR. Sensitivity analysis of these new rate laws gives further insight into the controlling geochemical factors for arsenic mobilization. When improved rate laws are incorporated as the inputs for reactive transport modeling, arsenic mobilization in ASR/AR operations can be predicted with an improved accuracy. The outcomes will be used to guide groundwater monitoring and specify ASR/AR operational parameters, including water pretreatment requirements prior to injection.

Introduction

The oxidative dissolution of arsenic (As)-bearing pyrite minerals during aquifer storage and recovery (ASR) and aquifer recharge (AR) transfers insoluble As in minerals into geochemically mobile As³⁺ and As⁵⁺ complexes in groundwater. Arsenic is a toxic metalloid and human carcinogen in multiple organ systems, and its concentration in potable aquifers is strictly regulated. This can limit the widespread use of ASR/AR practices as a means of meeting growing global water demands (Jones and Pichler 2007; Lazareva et al. 2015; Neil et al. 2012). In the world, over 90% of accessible freshwater is stored in groundwater aquifers (Shiklomanov and Rodda 2004). Because of the slow natural recharge to these confined and unconfined aquifers, excessive groundwater pumping to meet residential, agricultural, and industrial freshwater demand often far exceeds natural recharge rates, leading to groundwater overdrafting (Baghvand et al. 2010) and worsening water availability problems in many parts of the world (Zektser et al. 2005).

The operation of ASR/AR to address these water supply issues has been a focus of many recent studies. Yuan et al. (2017) characterized pretreatment requirements for potential contaminants in secondary water, but did not consider the geochemical reactions which can mobilize contaminants post-injection. Smith et al. (2017) analyzed ASR operation feasibility by considering potential site hydrogeology and historical climate data, but also did not consider site geochemistry with regard to arsenic mobilization. Page et al. (2017) studied the impact of ASR on water quality at four full-scale ASR sites and found an increase in the variability of arsenic and iron concentrations. Their study highlights the need to better understand the impact of ASR on arsenic mobilization from aquifer formation minerals during injected water storage.

Thus, it is necessary to examine and quantify the mobility of arsenic and other toxic heavy metals in order to evaluate the environmental health risk at ASR/AR sites. Because arsenic is present in more than 200 minerals, with an average abundance of 5–10 mg/kg in the subsurface (Yaron et al. 2012), its mobilization from aquifer formation minerals is widespread at ASR/AR field sites around the world including in the USA, Australia, Germany, China, and the Netherlands (see Smedley and Kinniburgh 2002; Neil et al. 2012 and references therein). In aquifers with persistent arsenic contamination, the As content of aquifer formation minerals is normally between 1 and 20 mg/kg (Smedley and Kinniburgh 2002). The arsenic concentration in groundwater varies significantly, ranging from < 0.5 to 5000 μg/L (Smedley and Kinniburgh 2002). The U.S. Geological Survey sampled 19,000 potable groundwater sources in the USA and found that in 10% of samples, the arsenic concentration exceeded 10 ppb, the EPA maximum contaminant level (Welch et al. 2001). Thus, the propensity for ASR/AR to mobilize arsenic can be a serious human health concern, particularly if aquifers are shared by private wells where additional water testing or treatment may not occur. It can also be costly for drinking water treatment plants to guard against increased arsenic concentrations due to ASR/AR operations.

Arsenopyrite (FeAsS) is the most common arsenic-bearing mineral and has been fingered as a source for arsenic mobilization during ASR/AR operations (Corkhill and Vaughan 2009; Jones and Pichler 2007; Neil et al. 2012). Arsenic is also present in pyrite (i.e., as arsenian pyrite), yet many investigators have focused on arsenopyrite in dissolution and other geochemical studies. Generally, arsenic in arsenic-rich pyrite exists as nanoscale inclusions of arsenopyrite within pyrite, rather than as a distinct mineral phase (Reich and Becker 2006). Oxidation of the hosting minerals is believed to lead to arsenic mobilization from the solid mineral phase into groundwater. For example, during ASR in the Upper Floridian aquifer, more oxidizing groundwater conditions produced by ASR triggered arsenopyrite dissolution, arsenic mobilization, and consequently contamination of the native groundwater resources (Jones and Pichler 2007). Such caustic association has been reported worldwide (Vanderzalm et al. 2011; Schlieker et al. 2001).

Reducing arsenic remobilization and preventing secondary groundwater contamination are the primary objectives of engineered control in ASR design and operation. This approach depends on reliable reactive transport analysis and accurate modeling of As remobilization. Many studies have tried to define the rate law of As remobilization for geochemical modeling (e.g., Asta et al. 2010; Craw et al. 2003; Walker et al. 2006; Yu et al. 2007). The rate law is an experimentally determined expression that relates the concentration of reactants to the rate at which arsenic is remobilized. Such models often consider injected water chemistry and geochemical interactions with native groundwater and formation minerals. Therefore, the models have the potential to predict the occurrence of arsenic mobilization and to determine water pretreatment needs and ASR/AR operating parameters for the purpose of minimizing arsenic mobilization (Wallis et al. 2011; Seibert et al. 2017).

Furthermore, different anions in the aqueous matrix affect arsenic mobilization by their chemical activities (Neil et al. 2014), adding complexity in arsenic remobilization kinetic modeling. This effect is a result of interactions between chlorine and secondary minerals forming during arsenopyrite oxidation, a process that yields faster aging and less arsenic attenuation onto the more crystalline secondary mineral phases. The full extent of these anion impacts on the arsenopyrite oxidation rate has not yet been explored. For this study, we focus our discussion on the kinetic rates of arsenopyrite remobilization under selected key groundwater conditions. We first analyze the geochemical reactivity of arsenopyrite and, in particular, how the introduction of injected water during ASR and AR can impact the geochemical equilibrium. Subsequently, a general expression of the kinetic relationship for As mobilization from arsenopyrite is proposed on the basis of kinetic studies in recent literature (Asta et al. 2010; Walker et al. 2006; Yu et al. 2007), and its implications on modeling As mobilization during ASR/AR are discussed.

Arsenopyrite geochemical reactivity

Arsenopyrite (FeAsS) is a reduced iron sulfide mineral, generally found in groundwater formations under reduced conditions of low oxidation–reduction potential (ORP) and minimal oxygen concentrations. Arsenic is incorporated into pyrite at various ratios; arsenopyrite is a 1:1:1 ratio between iron, sulfur, and arsenic, while arsenian pyrite contains less arsenic, usually < 10% by weight (Paktunc 2008). Both arsenopyrite and arsenian pyrite have similar solubility in groundwater. It is more thermodynamically favorable to form a two-phase mixture of arsenopyrite and pyrite, rather than forming arsenian pyrite (Deditius et al. 2014). Arsenic-rich pyrites, therefore, often contain nanoscale arsenopyrite impurities. Thus, the geochemical reactivity of arsenopyrite, as a characteristic mineral, is descriptive of the potential for arsenic mobilization from arsenic-rich pyrite in groundwater formations.

Arsenic remobilization from the arsenic-bearing pyrites depends on local environmental conditions. The injection of secondary water displaces native groundwater in the vicinity of an ASR and AR injection site. The physical geometry of injected water is often referred to as a “bubble” or “bottle brush” that can vary in size and persistence as a result of aquifer heterogeneity (Vacher et al. 2006). Within the bubble, the injected water and aquifer minerals reach a new geochemical equilibrium, during which native minerals including arsenopyrite may dissolve and new minerals may form. For example, both carbonate minerals and amorphous silica have been shown to dissolve during ASR/AR operations (Mirecki et al. 1998). Organic carbon in the injected water may also be introduced to groundwater aquifers, leading to changes in microbial activity and in redox potential. Dissolved oxygen (DO) and ferric iron (Fe³⁺), which can be rich in injected water, are particularly important to arsenic remobilization as shown in reaction kinetic studies (e.g., Corkhill and Vaughan 2009). When in contact with DO-rich injected water, arsenopyrite is oxidized following an overall reaction (Walker et al. 2006):

$$\begin{array}{l}\$\$\{\backslash \mathrm{text}\{\text{FeAs}S\left\}\right\}\backslash \mathrm{left}(\{\backslash \mathrm{text}\left\{\text{s}\right\}\}\backslash \text{right})+\backslash \mathrm{frac}\left\{3\right\}\left\{2\right\}\backslash \mathrm{text}\left\{\text{H}\right\}{\}}_{-}\left\{2\right\}\{\backslash \mathrm{text}\{\text{O}\left\}\right\}+\hfill \\ \backslash \mathrm{frac}\left\{11\right\}\left\{4\right\}\backslash \mathrm{text}\left\{O\right\}{\}}_{-}\left\{2\right\}\backslash \mathrm{left}(\{\text{aq}\}\backslash \text{right})={\{\backslash \mathrm{text}\{\text{Fe}\left\}\right\}}^{\wedge }\{2+\}+{\{\backslash \mathrm{text}\{\text{H}\left\}\right\}}_{-}\left\{3\right\}\hfill \\ {\{\backslash \mathrm{text}\{\text{AsO}\left\}\right\}}_{-}\left\{3\right\}\backslash \mathrm{left}(\{\text{aq}\}\backslash \text{right})+{\{\backslash \mathrm{text}\{\text{SO}\left\}\right\}}_{-}{\left\{4\right\}}^{\wedge }\{2-\}.\$\$\hfill \end{array}$$ (1)

At high pH, as is likely in groundwater formations due to carbonate buffering, Fe²⁺ can be quickly oxidized to form iron(III) (hydr)oxide secondary minerals (Walker et al. 2006):

$$\begin{gathered} \$\$4{\{\backslash \mathrm{text}\{\text{Fe}\left\}\right\}}^{\wedge }\{2+\}+{\{\backslash \mathrm{text}\{\text{O}\left\}\right\}}_{-}\left\{2\right\}+10{\{\backslash \mathrm{text}\{\text{H}\left\}\right\}}_{-}\left\{2\right\}\{\backslash \mathrm{text}\{\text{O}\left\}\right\}= \\ 4\{\backslash \mathrm{text}\{\text{Fe}\left\}\right\}{(\{\backslash \mathrm{text}\left\{\text{OH}\right\}\})}_{-}\left\{3\right\}+8{\{\backslash \mathrm{text}\{\text{H}\left\}\right\}}^{\wedge }\{+\},\$\$ \end{gathered}$$ (2)

by which, the overall reaction mechanism is written as:

$$\begin{array}{l}\$\$\{\backslash \mathrm{text}\{\text{FeAsS}\left\}\right\}\backslash \mathrm{left}(\{\backslash \mathrm{text}\left\{\text{s}\right\}\}\backslash \text{right})+4{\{\backslash \mathrm{text}\{\text{H}\left\}\right\}}_{-}\left\{2\right\}\{\backslash \text{text}\{\text{O}\left\}\right\}+\hfill \\ 3{\{\backslash \mathrm{text}\{\text{O}\left\}\right\}}_{-}\left\{2\right\}\backslash \mathrm{left}(\{\text{aq}\}\backslash \text{right})=\{\backslash \mathrm{text}\{\text{Fe}\left\}\right\}\backslash \mathrm{left}{(\{\backslash \mathrm{text}\left\{\text{OH}\right\}\}\backslash \text{right})}_{-}\left\{3\right\}\backslash \text{left}(\hfill \\ \{\backslash \mathrm{text}\{\text{s}\left\}\right\}\backslash \text{right})+{\{\backslash \mathrm{text}\{\text{H}\left\}\right\}}_{-}\{3\left\}{\{\backslash \mathrm{text}\{\text{AsO}\left\}\right\}}_{-}\right\{3\}\backslash \mathrm{left}(\left\{\text{aq}\right\}\backslash \text{right})+\hfill \\ {\{\backslash \mathrm{text}\{\text{SO}\left\}\right\}}_{-}{\left\{4\right\}}^{\wedge }\{2-\}+2{\{\backslash \mathrm{text}\{\text{H}\left\}\right\}}^{\wedge }\{+\}.\$\$\hfill \end{array}$$ (3)

This geochemical system has been a focus of experimental studies. Here we pay attention to the experiments of Asta et al. (2010), Yu et al. (2007), Walker et al. (2006), and Neil et al. (2014). Not all of these studies determined a rate equation, but all provided the arsenic dissolution data that are used in this study to develop a more accurate and widely relevant rate equation.

Specifically, Asta et al. (2010), Yu et al. (2007), McKibben et al. (2008), and Walker et al. (2006) developed rate equations for their experimental systems (Table 1). Asta et al. (2010) determined the steady-state dissolution of arsenopyrite as a function of DO and pH:

$$\begin{array}{l}\$\${\text{R}}_{-}\{\backslash \text{text}\{\text{arsenopyrite}\left\}\right\}\backslash \mathrm{left}(\{\{\backslash \mathrm{tex}\text{t}\{\mathrm{mol}\left\}\right\}\backslash ;{\{\backslash \mathrm{text}\{m\left\}\right\}}^{\wedge }\{-2\}\backslash ;{\{\backslash \mathrm{text}\{\text{s}\left\}\right\}}^{\wedge }\{-1\}\\ \}\backslash \text{right})={10}^{\wedge }\{-7.41\backslash \text{pm}0.47\}{\text{a}}_{-}{\left\{\left\{{\{\backslash \mathrm{text}\{\text{O}\left\}\right\}}_{-}\left\{2\right\}\right\}\right\}}^{\wedge }\{0.76\backslash \text{pm}0.11\}\\ {\text{a}}_{-}{\left\{\left\{{\{\backslash \mathrm{text}\{\text{H}\left\}\right\}}^{\wedge }\{+\}\right\}\right\}}^{\wedge }\{-0.12\backslash \text{pm}0.07\},\$\$\end{array}$$ (4)

where a_O2 and a⁺_H are the activities of dissolved O₂ and hydrogen ions, respectively. However, this rate equation is only valid for T = 25 °C and pH < 4. Yu et al. (2007) proposed the following rate law for arsenopyrite oxidation by DO:

$$\begin{array}{l}\$\$R_{-}\{\backslash \text{text}\{\text{arsenopyrite}\left\}\right\}\backslash \mathrm{left}(\{\{\backslash \mathrm{text}\{\mathrm{mol}\left\}\right\}\backslash ;{\{\backslash \mathrm{text}\{m\left\}\right\}}^{\wedge }\{-2\}\backslash ;{\{\backslash \mathrm{text}\{s\left\}\right\}}^{\wedge }\{-\\ 1\left\}\right\}\backslash \text{right})={10}^{\wedge }\{\{\backslash \text{frac}\{-2211\backslash \text{pm}57\left\}\text{T}\right\}\}\}{\text{m}}_{-}{\left\{\left\{{\{\backslash \mathrm{text}\{\text{O}\left\}\right\}}_{-}\left\{2\right\}\right\}\right\}}^{\wedge }\{0.45\backslash \text{pm}\\ \text{0.05},}\text{\$}\text{\$}\end{array}$$ (5)

where T is groundwater temperature in Kelvin, and m is the molar concentration of dissolved O₂. This rate equation is valid only for a pH range of 1.8–6.4 and temperature range of 10–45 °C. Unlike Asta et al. (2010), they found no pH dependence within the strongly acidic and mildly acidic range. Separately, McKibben et al. (2008) determined the molal specific rate law of arsenopyrite oxidation by dissolved O₂ as:

$$\begin{array}{l}\$\${\{\backslash \mathrm{text}\{\text{R}\left\}\right\}}_{-}\{\backslash \text{text}\{\text{arsenopyrite}\left\}\right\}\backslash \mathrm{left}(\{\{\backslash \text{text}\{\text{moles}\left\}\right\}\backslash ;\{\backslash \text{text}\{\text{mineral}\left\}\right\}\backslash \\ {\{\backslash \mathrm{text}\{\text{m}\left\}\right\}}^{\wedge }\{-2\}\backslash ;{\{\backslash \mathrm{text}\{\text{s}\left\}\right\}}^{\wedge }\{-1\}\}\backslash \text{right})={10}^{\wedge }\{-6.11\}{\text{M}}_{-}\{\{{\{\backslash \mathrm{text}\{\text{O}\left\}\right\}}_{-}\left\{2\right\}\\ \left\}{\}}^{\wedge }\right\{0.33\backslash \text{pm}0.18\left\}{\text{M}}_{-}{\left\{\left\{{\{\backslash \mathrm{text}\{\text{H}\left\}\right\}}^{\wedge }\{+\}\right\}\right\}}^{\wedge }\right\{0.27\backslash \text{pm}0.09\}.\$\$\end{array}$$ (6)

Table 1.

Arsenopyrite oxidation rate laws from literature and applicable environmental conditions

From: Improving arsenopyrite oxidation rate laws: implications for arsenic mobilization during aquifer storage and recovery (ASR)

Study	Rate law	Applicable conditions
		Temperature	pH
Asta et al. (2010)	Rarsenopyrite (mol m−2 s−1) = \(10^{ − 7.41 \pm 0.47} a_{{{\text{O}}_{2} }}^{0.76 \pm 0.11} a_{{{\text{H}}^{ + } }}^{ − 0.12 \pm 0.07}\)	25 °C	< 4
Yu et al. (2007)	Rarsenopyrite (mol m−2 s−1) = \(10^{{\frac{ − 2211 \pm 57}{T}}} m_{{{\text{O}}_{2} }}^{0.45 \pm 0.05}\)	15–45 °C	1.8–6.4
McKibben et al. (2008)	Rarsenopyrite (moles mineral m−2 s−1) = \(10^{ − 6.11} M_{{{\text{O}}_{2} }}^{0.33 \pm 0.18} M_{{{\text{H}}^{ + } }}^{0.27 \pm 0.09}\)	25 °C	2–4.5
	Rarsenopyrite (moles mineral m−2 s−1) = \(10^{ - 5.00} M_{{{\text{Fe}}^{3 + } }}^{1.06 \pm 0.11}\)	25 °C	2
Walker et al. (2006)	Rarsenopyrite (mol m−2 s−1) = \(10^{ − 10.14 \pm 0.03}\)	25 °C	~ 7

This rate law is applicable for a pH range of 2–4.5 at the temperature of 25 °C. Finally, Walker et al. (2006) determined the rate law for arsenopyrite oxidation at circumneutral pH and 25 °C to be:

$$\begin{array}{l}\$\$R_{-}\{\backslash \text{text}\{\text{arsenopyrite}\left\}\right\}\backslash \mathrm{left}(\{\{\backslash \mathrm{text}\{\mathrm{mol}\left\}\right\}\backslash ;{\{\backslash \mathrm{text}\{\text{m}\left\}\right\}}^{\wedge }\{-2\}\backslash ;{\{\backslash \mathrm{text}\{\text{s}\left\}\right\}}^{\wedge }\{-\\ 1\left\}\right\}\backslash \text{right})={10}^{\wedge }\{-10.14\backslash \text{pm}0.03\}.\$\$\end{array}$$ (7)

The studies on this geochemical system failed to extract exact forms of the rate equation as a function of all controlling variables, and the available rate equations only cover a limited range of environmental conditions (e.g., pH and temperature) encountered in the subsurface. Other unexamined environmental conditions are worthy of noting, but not accounted for. One study by Neil et al. (2014) showed that aqueous chloride can impact the arsenopyrite reaction rate. This species affects arsenic mobilization by altering the identities and quantities of secondary minerals, thus impacting aqueous arsenic fixation through adsorption, surface complexation, and co-precipitation. However, it is not described by current rate equations, despite the fact that salt concentrations can vary significantly in the injected water and in some groundwater systems; e.g., salt water intrusion in coastal aquifers can produce chloride concentrations as high as 6700 mg/L (Brenčič 2009). Furthermore, sulfate, another anion, has varying concentrations of < 0.2–1400 mg/L in groundwater aquifers, usually from the dissolution of evaporite minerals like gypsum and anhydrite (Sacks and Tihansky 1996). As a by-product of arsenopyrite oxidation, the sulfate level in groundwater can affect arsenic mobilization kinetics in the geochemical system.

Furthermore, it is known that the oxidation of arsenopyrite by ferric iron is a viable pathway because iron can be present both in some injected water for aquifer recharge and also in groundwater formations. Ferric iron has been previously viewed as insoluble at circumneutral pHs. However, previous studies have shown that at these pH levels, ferric iron is still capable of oxidizing pyrite and arsenopyrite, likely due to the formation of reactive hydroxo-Fe³⁺ aqueous complexes (Moses and Herman 1991; Neil and Jun 2015). The simplified oxidation mechanism by ferric iron is as follows (Yunmei et al. 2004):

$$\begin{array}{l}\$\$\{\backslash \mathrm{text}\{\text{FeAsS}\left\}\right\}\backslash \mathrm{left}(\{\backslash \mathrm{text}\left\{\text{s}\right\}\}\backslash \text{right})+7{\{\backslash \mathrm{text}\{\text{H}\left\}\right\}}_{-}\left\{2\right\}\{\backslash \mathrm{text}\{\text{O}\left\}\right\}+\\ 11{\{\backslash \mathrm{text}\{\text{Fe}\left\}\right\}}^{\wedge }\{3+\}\backslash \mathrm{left}(\{\text{aq}\}\backslash \text{right})=12{\{\backslash \mathrm{text}\{\text{Fe}\left\}\right\}}^{\wedge }\{2+\}\backslash \mathrm{left}(\{\text{aq}\}\backslash \text{right})+\\ {\{\backslash \mathrm{text}\{\text{H}\left\}\right\}}_{-}\left\{3\right\}{\{\backslash \mathrm{text}\{\text{AsO}\left\}\right\}}_{-}\left\{3\right\}\backslash \mathrm{left}(\{\backslash \mathrm{text}\left\{\text{aq}\right\}\}\backslash \text{right})+{\{\backslash \mathrm{text}\{\text{SO}\left\}\right\}}_{-}{\left\{4\right\}}^{\wedge }\{2-\}\\ +11{\{\backslash \mathrm{text}\{\text{H}\left\}\right\}}^{\wedge }\{+\}\cdot \$\$\end{array}$$ (8)

Neil and Jun (2015), Yu et al. (2007), McKibben et al. (2008), and Yunmei et al. (2004) experimentally investigated this geochemical system. McKibben et al. (2008) determined the molal rate law for arsenopyrite oxidation at pH 2 and 25 °C to be:

$$\begin{array}{l}\$\$R_{-}\{\backslash \text{text}\{\text{arsenopyrite}\left\}\right\}\backslash \mathrm{left}(\{\{\backslash \text{text}\{\text{moles}\left\}\right\}\backslash ;\{\backslash \text{text}\{\text{mineral}\left\}\right\}\backslash ;{\{\backslash \mathrm{text}\{\text{m}\left\}\right\}}^{\wedge }\{-\\ 2\}\backslash ;{\{\backslash \mathrm{text}\{\text{s}\left\}\right\}}^{\wedge }\{-1\}\}\backslash \text{right})={10}^{\wedge }\{-5.00\left\}{\text{M}}_{-}{\left\{\left\{{\{\backslash \mathrm{text}\{\text{Fe}\left\}\right\}}^{\wedge }\{3+\}\right\}\right\}}^{\wedge }\right\{1.06\backslash \text{pm}\\ \text{0.11}}.\text{\$\$}\end{array}$$ (9)

Yunmei et al. (2004) found that the rate order was 0.41 for T = 15–35 °C, but increased to 0.64 at 45 °C. The rate constant changed from 10^{−4.08 to −3.77} to 10^−2.7 at this same temperature point. However, this rate equation was based on a limited number of sample points in this study. The rate law can be greatly improved by including more sample points, and by incorporating pH effects if any. Additional studies, such as those by Neil and Jun (2015) and Yu et al. (2007), make further improvement possible.

It is noted that the new rate law development selectively relies on studies that provided rate data for each set of conditions, rather than just their own derived rate law. Specifically, the rate laws for oxidation by dissolved oxygen were derived from data by Asta et al. (2010), Yu et al. (2007), Neil et al. (2014), and Walker et al. (2006) (Table 1). The rate laws for oxidation by ferric iron were derived from data presented in Neil and Jun (2015), Yu et al. (2007), and Yunmei et al. (2004).

Rate equation development

For the three categories of geochemical conditions, this section elucidates the rate data for As remobilization and then develops a general rate equation for each. Tables S1 and S2 in Electronic Supplementary Material (ESM) contain all raw rate data and aqueous matrix information used to develop the new rate equations. For all examined geochemical systems, temperature and pH were used as regression variables, by which the extent of their impact on reaction rate was quantified.

The kinetic rates were analyzed using regression for three categories, each with specific aqueous matrices. The first category is geochemical systems with dissolved oxygen and either just chloride or no salt present. The second has dissolved oxygen and sulfate present; the third has no dissolved oxygen (i.e., anaerobic) but has ferric iron. In each of these categories, the rate law is taken in the form:

$$\$\$\{\backslash \text{text}\{\text{Rate}\left\}\right\}=\text{k}\backslash \text{left}{[\text{A}\backslash \text{right}]}^{\wedge }\left\{\text{a}\right\}\backslash \mathrm{left}{[\text{B}\backslash \text{right}]}^{\wedge }\left\{\text{b}\right\}\backslash \mathrm{left}{[\text{C}\backslash \text{right}]}^{\wedge }\left\{\text{c}\right\},\$\$$$ (10)

where k is the reaction rate coefficient, [A], [B], [C] are reactant concentrations (or geochemical activities), and a, b, c are the reaction orders. The reaction rate coefficient, k, depends on system temperature and activation energy. Thus, using the Arrhenius equation,

$$\begin{gathered} \$\$\{\backslash \text{text}\{\text{Rate}\left\}\right\}=\text{K}{\{\backslash \mathrm{text}\{\text{e}\left\}\right\}}^{\wedge }\left\{\left\{\backslash \mathrm{frac}\left\{\left\{-{\text{E}}_{-}\left\{\text{a}\right\}\right\}\right\}\left\{\text{RT}\right\}\right\}\right\}\backslash \text{left}{[\text{A}\backslash \text{right}]}^{\wedge }\left\{\text{a}\right\}\backslash \mathrm{left}[ \\ \text{B}\backslash \text{right}{]}^{\wedge }\{\text{b}\}\backslash \mathrm{left}{[\text{C}\backslash \text{right}]}^{\wedge }\{\text{c}\}.\$\$ \end{gathered}$$ (11)

E_a is the activation energy, R is the gas constant, T is the temperature, and K is a pre-exponential factor. For multivariate regression, Eq. 11 is transformed by taking the natural log to give the expression:

$$\begin{gathered} \$\$\{\backslash \text{text}\{\text{Ln}\left\}\right\}\backslash \text{left}(\{\backslash \text{text}\left\{\text{Rate}\right\}\}\text{?right})={\text{K}}^{\wedge }\{\backslash \text{prime}\}+\backslash \mathrm{frac}\left\{\left\{-{\text{E}}_{-}\left\{\text{a}\right\}\right\}\right\}\left\{\text{R}\right\}\backslash \text{left}( \\ \{\backslash \text{frac}\left\{1\right\}\text{T}\left\}\right\}\backslash \text{right})+\text{a}\backslash \mathrm{left}(\{\backslash \ln \backslash \mathrm{left}[\text{A}\backslash \text{right}]\}\backslash \text{right})+\text{b}\backslash \mathrm{left}(\{\backslash \ln \backslash \mathrm{left}[\text{B} \\ \text{right]}right)+cleft({lnleft[Cright]}right).\$\$} \end{gathered}$$ (12)

Multivariate regression of experimental data was used to determine the values of K′ (i.e., ln(K)), \(\frac{{ - E_{a}}}{R}\), and constants a, b, and c. The reaction rates were then calculated and compared with empirically measured rate values to ensure that the rate law produces accurate results over a wide range of experimental conditions.

Dissolved O₂ and chloride or no salt

For the aerobic systems with either no salt or with chloride anions, chloride was present either through pH adjustment with hydrochloric acid or as mean of providing background ionic strength. The influence of chloride on the reaction rate is not yet well understood. Neil et al. (2014) showed that chloride not only influences the phase of secondary mineral precipitation on arsenopyrite over a longtime duration, but in the short term (i.e., over the first 6 h of reaction) affects the activation energy of the arsenic mobilization reaction. This observation doubtlessly indicates that the chloride presence may have some effects on the fundamental mobilization mechanism.

In data regression for the rate of reaction, the chloride effects were accounted for in three ways to determine the best data-regression fit: chloride as a reactant with regression using ln[Cl⁻]; chloride as an amendment to the rate constant with regression using [Cl⁻]); and chloride as an amendment to the activation energy with regression using \(\frac{{[{\text{Cl}}^{ - } ]}}{T}\)). The best fit was achieved for the system with chloride included as an adjustment to the activation energy. Similar findings were reported by Neil et al. (2014). More information on the regression can be found in the ESM. The p values for all variables are lower than 0.05 except for the chloride term. If chloride is excluded, the R² value for the fit decreases from 0.63 to 0.61, with just variables (T, O₂, and H⁺) included, whereas R² = 0.49 for just O₂ and H⁺ included. When chloride is excluded, the p value for the intercept increases to 0.07. Therefore, the inclusion of chloride term improves the regression fit, yet more studies are needed to further improve the rate equation.

The rate equation, determined using multivariate regression, is as follows:

$$\begin{gathered} \$\$\{\backslash \text{text}\{\text{Rate}\left\}\right\}={\{\backslash \mathrm{text}\{\text{e}\left\}\right\}}^{\wedge }\{-8.2\backslash \text{pm}3\cdot 7\}{\{\backslash \mathrm{text}\{\text{e}\left\}\right\}}^{\wedge }\left\{\right\{\backslash \mathrm{frac}\left\{\right\{-3653.1\backslash \text{pm} \\ 1076.4+\backslash \mathrm{left}(\{3530.3\backslash \text{pm}2084.3\}\backslash \text{right})\backslash \text{times}\backslash \mathrm{left}[\left\{{\{\backslash \mathrm{text}\{\text{Cl}\left\}\right\}}^{\wedge }\{-\}\right\} \\ \backslash \text{right}]\}\left\}\right\{\text{T}\left\}\right\}\}\backslash \mathrm{left}{\left[\left\{{\{\backslash \mathrm{text}\{\text{O}\left\}\right\}}_{-}\left\{2\right\}\right\}\backslash \text{right}\right]}^{\wedge }\{0.53\backslash \text{pm}0.13\}\backslash \mathrm{left}[\{{\{\backslash \mathrm{text}\{\text{H}\left\}\right\}}^{\wedge }\{+ \\ \}\}\backslash \text{right}]^\{-0.13\backslash \text{pm}0.03\}.\$\$ \end{gathered}$$ (13)

This rate equation is similar to Asta et al. (2010) in that the arsenopyrite dissolution rate is positively dependent on DO level and negatively on H⁺ concentration. The magnitude of these rate orders is similar to the expressions of Asta et al. (2010) and Yu et al. (2007) (for dissolved O₂ only). It is worth pointing out, however, that the rate equation in Eq. 13 quantifies the observed effect of chloride and temperature on the activation energy for a wider pH range of ~ 2–12.6.

Figure 1a compares the calculated rates and the rates determined empirically in each study, as well as those developed by Yu et al. (2007), Walker et al. (2006), and Asta et al. (2010) (Table 1). The new rate equation in Eq. 13 has an improved R² = 0.64, significantly higher than those of Yu et al. (2007), Walker et al. (2006), and Asta et al. (2010), at 0.39, ~ 0, and 0.49, respectively. The new expression also has a much lower average standard error of 0.31. The average standard errors are 1.17, 0.50, and 0.60, respectively, for Yu et al. (2007), Walker et al. (2006), and Asta et al. (2010).

Fig. 1.

Comparisons of calculated and measured arsenopyrite oxidation rate laws for a aerobic, chloride-containing systems, b aerobic, sulfate-containing systems, and c anaerobic, ferric iron-containing systems. Dashed lines show the correlation between calculated and measured values. Good correlation should have a slope close to 1 and an R² value close to 1. Data included from Yu et al. (2007), Walker et al. (2006), and Asta et al. (2010)

It is noted that the rate equation developed from this study could be further improved. The calculated rates under-predict the experimentally determined values; the correlation slope is only 0.63, far smaller than 1. Similar rates of underestimation are found for Yu et al. (2007) and Asta et al. (2010) as well. One potential model improvement resides in more robust and numerical studies of arsenopyrite dissolution over a wide range of experimental conditions. In particular, more studies are needed for the geochemical systems that include chloride to better delineate the influence of chloride on the activation energy and thus minimize errors associated with variables in the rate equation. Nevertheless, the derived rate equation in Eq. 13 improves the rate calculated from the previously developed rate laws for the systems with or without chloride present.

Dissolved O₂ and sulfate

The presence of sulfate marks a different geochemical system in As dissolution. Sulfate exists as a major anion in native groundwater from equilibration with sulfide minerals in the aquifer and can also form as a result of arsenopyrite oxidation. To examine sulfate influences on the rate of reaction, the rate data are analyzed by treating sulfate as a reactant in regression against ln[SO₄²⁻]), as an amendment to the rate constant (looking at regression with [SO₄²⁻]), and as an amendment to the activation energy (regression with \(\frac{{[{\text{SO}}_{4}^{2 - } ]}}{T}\)). Information on this regression can be found in ESM. It is interesting to note that the best data fit was achieved for the system when only oxygen is treated as a reactant with no influence from H⁺ or SO₄²⁻. This was the only regression with all reaction variables having a p value below 0.05. However, the intercept was statistically insignificant, with p values between 0.3 and 0.75 for all fitting options. It follows that at high sulfate concentrations, arsenopyrite oxidative dissolution will be independent of system pH. The rate equation, determined using multivariate regression, is thus as follows:

$$\begin{gathered} \$\$\{\backslash \text{text}\{\text{Rate}\left\}\right\}={\{\backslash \mathrm{text}\{e\left\}\right\}}^{\wedge }\{1.2\backslash pm2.4\}{\{\backslash \mathrm{text}\{e\left\}\right\}}^{\wedge }\left\{\right\{\backslash \text{frac}\{-5580.9\backslash \text{pm}728.8\} \\ \left\{T\right\}\left\}\right\}\backslash \mathrm{left}{\left[\left\{{\{\backslash \mathrm{text}\{O\left\}\right\}}_{-}\left\{2\right\}\right\}\backslash \text{right}\right]}^{\wedge }\{0.40\backslash \text{pm}0.05\}.\$\$ \end{gathered}$$ (14)

Figure 1b compares the calculated rates against the measured values. Also plotted are the kinetic expressions by Yu et al. (2007), Walker et al. (2006), and Asta et al. (2010). The expression for sulfate systems has an R² = 0.88 for the correlation between the calculated and measured rates, higher than the chloride system or any of the previously determined rate equations. The R² values are 0.87, ~ 0, and 0.43, respectively, for the Yu et al. (2007), Walker et al. (2006), and Asta et al. (2010) when applied to sulfate-containing systems. The new rate equation in Eq. 14 also has a low average standard error of 0.09. The average standard errors for Yu et al. (2007), Walker et al. (2006), and Asta et al. (2010) are, respectively, 0.10, 1.53, and 0.87.

Anaerobic systems with Fe³⁺ present

The last category of geochemical systems we considered is arsenopyrite oxidation by Fe³⁺ in the absence of dissolved oxygen, based on the reaction in Eq. 8. Frequently, arsenopyrite occurs in deeper anaerobic aquifers containing reduced sulfide minerals in stable forms. Fe³⁺ can be introduced to these systems from multiple sources. For example, the introduction of injected water can add Fe³⁺ and DO to the formation, and during oxidation, Fe³⁺ also forms as a by-product of arsenopyrite dissolution. After the limited DO is consumed, other oxidants such as Fe³⁺ can react with arsenopyrite.

From Eq. 8, Fe³⁺ and H⁺ were considered as reactants in the system. We also investigated the influences of Cl⁻ and SO₄²⁻ as reactants and as amendments to the activation energy (see regression tables in ESM). No correlations to rate changes were found. This result agrees with the studies of arsenopyrite oxidative dissolution in sodium nitrate and sodium chloride with Fe³⁺ present (Neil and Jun 2015). This study failed to identify that the presence of chloride can significantly change the activation energy. Thus, the rate equation determined is:

$$\begin{gathered} \$\$\backslash \text{text}\left\{\text{Rate}\right\}\}={\{\backslash \mathrm{text}\{e\left\}\right\}}^{\wedge }\{-9\cdot 3\backslash \text{pm}2.4\left\}{\{\backslash \text{text}\{\text{e}\left\}\right\}}^{\wedge }\right\{\{\backslash \text{frac}\{-954\cdot 2\backslash \text{pm}727.6\} \\ \left\{\text{T}\right\}\left\}\right\}\backslash \mathrm{left}{\left[\left\{{\{\backslash \mathrm{text}\{\text{Fe}\left\}\right\}}^{\wedge }\{3+\}\right\}\backslash \text{right}\right]}^{\wedge }\{0.48\backslash \text{pm}0.04\}\backslash \mathrm{left}[\left\{{\{\backslash \mathrm{text}\{\text{H}\left\}\right\}}^{\wedge }\{+\}\right\} \\ \text{right}{]}^{\wedge }\{0.11\backslash \text{pm}0.03\}.\$\$ \end{gathered}$$ (15)

For this system, the p values for all variables except temperature were less than 0.05. For temperature, the p value of 0.20 was the lowest among those for the different fittings. Previous investigations of arsenopyrite oxidation by Fe³⁺ have only considered a single pH value for each study. By combining the available data, we are now able to show that in addition to Fe³⁺, the H⁺ concentration can also significantly impact the reaction rate. The R² value for this new rate law is 0.92, indicating a statistically significant correlation between measured rates and the rates calculated using the new rate law in Eq. 15. The average standard error was 0.18. Figure 1c shows the model plot versus the measured data for this system.

Discussion

Sensitivity analysis and controlling factors

The newly developed rate equations (Eqs. 13–15) are examined using sensitivity analysis to identify the most important controlling variables over arsenic mobilization in ASR/AR operations. For this analysis, the relationship between pairs of variables and the rate was examined to produce contour plots. The isopleths in contour lines in Fig. 2 show the modeled kinetic properties in the chloride-containing system for a range of temperature, hydrogen ion, chloride ion, and DO concentrations. Figure 3 shows the sensitivity analysis for the sulfate-containing system, which compares dissolved oxygen and temperature. Figure 4 contains the plots for the anaerobic, ferric iron-containing system and shows relationships between temperature, hydrogen ion concentration, and ferric iron concentration.

Fig. 2.

Contour plots showing the sensitivity analysis for all sets of variables in the aerobic, chloride-containing systems over relevant ranges of temperature, hydrogen ion, chloride ion, and dissolved oxygen variations to give insight into factors controlling arsenic mobilization during ASR operation

Fig. 3.

Contour plot showing the sensitivity analysis for dissolved oxygen and temperature in the aerobic, sulfate-containing systems

Fig. 4.

Contour plots showing the sensitivity analysis for all sets of variables in the anaerobic, ferric iron-containing systems

The contour plots for the chloride-containing system clearly show the rate maxima for a set of extreme conditions: highest temperature, highest DO, highest Cl⁻, and lowest H⁺. A close examination gives insight into the relationship between different variables and the rate variation. For example, a horizontal slope in the plots indicates that the change of rate is constant over a unit of change in the environmental parameters, such as H⁺ or temperature. For the Fe³⁺-containing system, the very small slope indicates that As remobilization is insensitive to temperature change. The DO effects were relatively more pronounced when temperature increased.

The chloride-containing system is sensitive to many more geochemical variables than the other systems. For H⁺ effect, the high H⁺ (0.001–0.1 M) dominated the rate equation, leading to low arsenopyrite oxidation rates under all examined DO, temperature, and Cl⁻ ranges. However, in groundwater aquifers, pH is expected to be neutral or slightly alkaline, where DO, temperature, and Cl⁻ have a greater influence. Comparing other variables, temperature appears to have a larger impact on rate than Cl⁻, except at very high Cl⁻ concentrations. DO and temperature appear to have similar influence on the dissolution rate, and DO is more influential than Cl⁻.

We further quantify and compare the rates for these systems in geochemical spider diagrams (Fig. 5). In the plots, the relative sensitivity of rate changes can be identified for each variable, with the others remaining constant. The constant values were chosen to reflect typical values in nature and can be found in Table S3 in ESM. It is clear that over a wide range of concentrations, dissolved oxygen is the reactant with the most influence over the arsenopyrite reaction rate. For the chloride-containing system, it is only when the dissolved oxygen concentration drops below 0.000245 M that a higher chloride concentration can lead to a higher rate of As dissolution and thereby mobilization. It is known that at many ASR sites, the molar DO concentrations are low in deeper and confined aquifers while the concentrations of salts can be high.

Fig. 5.

Spider plots for reaction variables in the a aerobic, chloride-containing systems, b aerobic, sulfate-containing systems, and c anaerobic, ferric iron-containing systems. Chemical concentrations are shown on the left side, and temperature is shown on the right side

This sensitivity analysis helps identify the variables for consideration in ASR operations and for evaluation of the preinjection water treatment needs. While specific site conditions are necessary, general trends in the sensitivity analysis can be observed. First, removal of chlorine and DO in the injected water would make it possible to control and reduce the arsenopyrite oxidation rate. Second, a higher pH can be beneficial to minimize arsenopyrite oxidation in the chloride-containing systems; however, this condition can trigger the dissolution of other minerals in the subsurface. In addition, it can be cost-prohibitive to control groundwater temperature and its variations in the subsurface.

Rate equations for ASR modeling

The general rate equations in Eqs. 13–15 mark an improvement over the previously published rate equations (Table 1), both in R² and in the statistical significance of the correlation slope. This increased accuracy and decreased average standard error can be critical when modeling arsenic mobilization in groundwater systems which fit these conditions; for example, in aquifers containing abundant arsenic-bearing sulfide minerals, which may have high sulfate concentrations, or when recharging aquifers with secondary water such as wastewater treatment effluent that often contains high concentrations of chloride.

The improved new rate equation can provide a better characterization of As mobility. We have applied Eq. 13 from our current study and those developed by Asta et al. (2010), Yu et al. (2007), McKibben et al. (2008), and Walker et al. (2006) to a data set for arsenopyrite oxidative dissolution in wastewater containing 6.27 mM chloride at a temperature of 12 °C (Table 2a). The standard error for the calculated rates, as listed in Table 2b, is smallest for both the current study and Walker et al.’s (2006) study. Yet Walker et al.’s (2006) study assumed the rate of arsenopyrite oxidation as a constant, an assumption that can become problematic in various ASR and AR subsurface environments. For systems with the same surface area and reaction time, these rate values translate to an arsenic concentration which is 14.6% lower in the estimation by the current study and 12.3% higher for Walker et al.’s (2006) study compared to the measured rate. The other studies were between 480 and 766% lower, which are very significant underestimations of the true quantity of mobilized arsenic. This means that for the modeled arsenic concentration to reach 10 ppb, the drinking water standard for arsenic, the true concentration could be as high as 7.66 ppm. This level is dangerously high, as ingesting arsenic in drinking water at concentrations between 0.8 to 1.82 ppm has been reportedly linked with increased cardiovascular mortality (Rosenman 2011).

Table 2.

(a) Conditions for arsenopyrite oxidation and (b) calculated rates and standard errors confirming the accuracy of the developed rate law

From: Improving arsenopyrite oxidation rate laws: implications for arsenic mobilization during aquifer storage and recovery (ASR)

a
Rate (M/m s)			8.26E−11
Log(rate)			− 10.08
[Cl−] (M)			6.27E−06
[DO] (M)			3.38E−04
[H+] (M)			1.00E−07
Temp. (K)			285
Study	Rate (M/m2 s)	Log(rate)	Standard error
b
Asta et al.	6.19E−10	− 9.21	0.44
Yu et al.	4.78E−10	− 9.32	0.38
McKibben et al.	7.15E−10	− 9.15	0.47
Walker et al.	7.24E−11	− 10.14	0.03
Current study	9.46E−11	− 10.02	0.03

We have also observed that the slopes of these comparisons, 0.63–0.92, indicate consistent model underestimation of the arsenic mobilization rate. Causes for this discrepancy warrant further investigations. As a temporal fix, one may use a correction factor on the rate equations for As mobilization analysis in ASR/AR modeling; obviously, an uncertainty analysis of the rate-induced modeling errors is necessary. This can be assisted by the analysis of the regression residuals in the rate equations (Eqs. 13–15) and by the rate sensitivity analysis as discussed previously. This correction will be an important factor when implementing these models for the purpose of ASR/AR implementation because in order to receive a permit, ASR/AR operators must prove that operation will not endanger an underground source of drinking water. Therefore, it is vital to ensure that modeling does not underestimate the concentrations of arsenic being mobilized.

Nevertheless, the system-level analysis of the rates over a range of environmental variables can help in avoiding unwanted geochemical reactions. For a given aquifer matrix and groundwater composition, pretreatment of the injected water can modify the geochemical equilibrium, thereby reducing arsenopyrite oxidative dissolution. While the multi-variable rate analysis in the spider diagrams can be a useful tool in the modeling analysis, more testing and model development are necessary.

Conclusions

By utilizing empirical rates for arsenopyrite dissolution from a number of studies, we have produced three new rate models for arsenopyrite dissolution in three different aqueous matrices. These models have improved on previous rate equations in terms of both R² and average standard error. We have also incorporated for the first time the influence of chloride anions on the activation energy, a phenomenon which was previously observed but has not been considered by modeling studies.

It is critical to further improve these expressions for the arsenopyrite dissolution rate because they are an integral part of reactive transport modeling and in quantitative risk assessment for ASR/AR site selection and operation. Improving these models is vital to protect the health of humans and the environment from the detrimental impact of arsenic contamination in groundwater. Furthermore, this study has shown for the first time that the aqueous matrix is a factor which should be considered when developing rate equations. This new insight is especially important for ASR/AR operation involving injected water that has a chemical composition which is very different from resident groundwater.

Finally, our outcomes have shown that, by looking at multiple studies of arsenopyrite dissolution cohesively, it is possible to develop an accurate rate law applicable to a wider range of reaction conditions. As we continue to utilize all available data to develop the best possible rate equations, accurate modeling and simulation of ASR/AR and other engineering operations become possible to reduce the environmental and human health risk in the development of alternative water resources.