pH-Dependent Transport of Metal Cations in Porous Media

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pH-Dependent Transport of Metal Cations in Porous Media Valentina Prigiobbe* and Steven L. Bryant Department of Petroleum and Geosystems Engineering, The University of Texas at Austin, Austin, Texas 78712-1186, United States ABSTRACT: We study the effect of pH-dependent adsorption and hydrodynamic dispersion on cation transport through a reactive porous medium with a hydrophilic surface. We investigate how competitive adsorption between a proton and a metal (which in some situations of practical interest may also be a radionuclide) can facilitate the migration of a certain fraction of the latter. We performed laboratory experiments using a chromatographic column filled with silica beads coated with iron oxide and flooded initially with an acidic solution (pH ≈ 3) and then with an alkaline solution (pH > 7) containing either sodium, potassium, lithium, calcium, magnesium, or barium. The composition of each injected solution was chosen to represent one of two possible theoretical predictions, either a retarded shock and a fast pulse, that is, traveling at the interstitial fluid velocity, or only a retarded shock. Highly resolved breakthrough curves measured with inline ion chromatography allowed us to observe in all cases agreement with theoretical predictions, including numerous observations of a fast pulse. The fast pulse is the result of the interaction between pH-dependent adsorption and hydrodynamic dispersion and has previously been observed in systems with strontium. Here, we show the fast pulse arises also in the case of other cations allowing a generalization of the physical mechanism underlying this phenomenon and consideration of it as a new fast transport behavior. A one-dimensional reactive transport model for an incompressible fluid was developed combining surface complexation with mass conservation equations for a solute and the acidity (difference between the total proton and hydroxide concentration). In all cases, the model agrees with the measurements capturing the underlying physics of the overall transport behavior. Our results suggest that the interplay between pH-dependent adsorption and hydrodynamic dispersion can give rise to the rapid migration of metals through reactive porous media with potential effects on, for example, the performance of subsurface engineering infrastructures for pollutant containment, the mobilization of metal contaminants by brine acidified upon contact with CO2 during geologic carbon storage, and the chromatographic separation processes in industrial applications.

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INTRODUCTION Large amounts of liquid waste containing metal and radioactive cations have been produced upon fission reactions during the nuclear weapons program at the facilities of the United States Department of Energy (U.S. D.O.E.) since the 1950s. In some locations, the radioactive waste was temporarily stored nearby the plants in tanks whose chemical conditions were adjusted artificially to favor precipitation and adsorption to prevent the escape of the contaminants into the environment. Despite these measures, high radioactivity levels were detected in the groundwater surrounding the storage sites indicating that leakage had occurred and the contaminants were traveling faster than expected.1−5 Fast migration of sorbing contaminants with the groundwater velocity is often ascribed to colloidalfacilitated transport 6 or the presence of fractures. Recently, we showed theoretically and experimentally that the interaction between pH-dependent adsorption, which is common on amphiphilic substrates in the shallow subsurface, and hydrodynamic dispersion can also lead to fast migration of a pulse of strontium (Sr2+) moving with the groundwater velocity ahead of the retarded sorbing front.7,8 Sorption strongly controls the transport of trace metals and radionuclides in the subsurface9−11 and it is usually described through mathematical functions, named adsorption isotherms, which are based either on empirical assumptions (e.g., Freundlich and Langmuir isotherms) or on geochemical models © 2014 American Chemical Society

accounting for surface complexation. In the latter case, the isotherm is derived from the chemical reactions occurring at the solid−liquid interface which capture the physicochemical processes underlying sorption.12,13 In the presence of a reactive porous medium with a hydrophilic surface, the adsorption of a metal/radionuclide is in competition with the adsorption of a proton leading to the dependence of the process on the pH of the solution. The shape of the resulting isotherm function is therefore different from one of the Langmuir isotherms and changes upon the type of solid−liquid interface reactions. Laboratory experiments14−20 and field observations12,21,22 have shown that pH-dependent adsorption significantly affects the transport of several ions and radionuclides traveling through reactive porous media containing metal oxide (e.g., goethite) or clay (e.g., kaolinite or illite). These works have also shown that pH-dependent adsorption can be properly described by combining the relevant reactions at the solid−liquid interface to derive the isotherm with a transport model including a mass conservation law for the acidity. Introduced by Morel and Hering,23 the acidity is defined as the difference between the proton and the hydroxide concentrations, and it was used for the first time as a conserved Received: Revised: Accepted: Published: 3752

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tration of surface species S−1/2 (mol/kg). The site balance equation is given by

variable in reactive transport models by Scheidegger et al.24 The conservation equation for the acidity is not present in commonly used transport models of competitive adsorption and adds a strong nonlinearity to the pH-dependent reactive transport problems affecting considerably the model results. As mentioned above, the combined effect of pH-dependent adsorption and hydrodynamic dispersion may lead to fast migration of a solute.7,8 In more detail, in our earlier work,7 we analyzed how an alkaline solution with Sr2+ migrates through a porous medium with a hydrous ferric oxide (HFO) surface containing initially an acidic solution without Sr2+. We measured Sr2+ breakthrough curves consisting of a pulse traveling at the interstitial fluid velocity and a classical retarded front. We expected this fast pulse to arise also in the case of other cations with a chemical behavior similar to Sr2+. In this paper, we study the transport of sodium (Na+), potassium (K+), lithium (Li+), calcium (Ca2+), magnesium (Mg2+), and barium (Ba2+) in a system similar to the one investigated earlier. We show that indeed the fast pulse is a general transport phenomenon, in that the identity of the cation affects the behavior quantitatively but not qualitatively. The experiments were performed using a chromatographic column filled with silica beads coated with HFO, continuously monitored with pH, temperature, and pressure probes and with an inline ion chromatograph to determine highly resolved breakthrough curves. The selection of these cations was motivated by their high concentration in liquid waste from nuclear energy plants and in the produced water from shale-gas extraction.5,25−28 Mobilization and transport of similar cations during geologic CO2 storage has also been reported.29,30 HFO is used as reactive material because it is an important sorbent of inorganic contaminant, generally present as coating of other minerals in the subsurface, and also used in remediation technologies.31−33 The paper is divided in five sections. Initially, we introduce the geochemical model to derive the adsorption isotherms and explain the transport model, then we describe the materials and the methods applied for the experiments and report and discuss the results. Finally, we draw the conclusions.

Zt = {S−1/2 } + {S−1/2 − Mn +} + {SH+1/2}

where Zt is the total concentration of the surface sites (mol/kg). Combining eq 3 and eq 4 with eq 5, the adsorbed concentration of Mn+ ({S−1/2 − Mn+}) and H+ ({SH+1/2}), identified as zm and zh (mol/kg), respectively, can be derived

S−1/2 + H+ ↔ SH+1/2

(2)

{S−1/2 − Mn +} cm{S−1/2 }

(3)

KH =

{SH+1/2} c H{S−1/2 }

(4)

(6)

zH =

c HKHZt 1 + c HKH + cmK m

(7)

(8)

whose equilibrium constant (Kw) in a dilute solution, where water activity is assumed to be unity, is Kw = cHcOH, with cOH the concentration of the hydroxide species, and equals 10−14 mol/kg at 25 °C. The acidity (cHT) can then simply be written as a difference between the concentration of protons and hydroxides23,24 c HT = c H − cOH (9) and substituting the mass action equation of water dissociation into it, eq 9 becomes c HT = c H −

Kw cH

(10)

from which the proton concentration can be derived c H = 0.5(c HT ±

2 c HT + 4K w )

(11)

Here, only the positive sign gives proton concentration with physically admissible values. Substituting eq 11 into eq 6 and eq 7, the adsorption isotherms for a metal and a proton are, respectively, zm =

zH =

cmK mZt 1 + 0.5(c HT +

0.5(c HT + 1 + 0.5(c HT +

2 c HT + 4K w )KH + cmK m

(12)

2 + 4K w )KHZt c HT 2 + 4K w )KH + cmK m c HT

(13)

The adsorption constants of the cations considered in this work are listed in Table 1 and the corresponding adsorption

where S−1/2 corresponds to the surface site. Neglecting the electrostatic term of the effective equilibrium constant that accounts for the development of the surface charge upon adsorption, the effective equilibrium constants equal the intrinsic equilibrium constants (kg/mol) and for the above reactions they are respectively given by Km =

cmK mZt 1 + c HKH + cmK m

H 2O ↔ OH− + H+

GEOCHEMICAL MODEL We developed a nonelectrostatic surface complexation model considering a solution containing a general metal cation, Mn+, reacting with a solid surface consisting of HFO and a conservative acid/base. Following Dzombak and Morel14 and Hiemstra et al.,34 we described the reactions at the solid−liquid interface as (1)

zm =

Under the applied conditions, the solution speciation consists only of water dissociation,

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S−1/2 + Mn + ↔ S−1/2 − Mn +

(5)

Table 1. Adsorption Constants (Km, kg/mol) at 25°C of the Cations Investigated in This Work cation

log10Km

Na+ K+ Li+ Ca2+ Mg2+ Sr2+ Ba2+ H+

−0.38a −0.38b 0.46b 3.10a 4.33a 4.47c 5.46d 8.7c

a

where ci corresponds to the aqueous phase concentrations of the subscripted species (mol/kg) and {S−1/2} indicates the concen-

c

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Literature values from ref 35. bLiterature values from ref 36. Literature values from ref 37. dLiterature values from ref 14. dx.doi.org/10.1021/es403695r | Environ. Sci. Technol. 2014, 48, 3752−3759

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the problem is triple value and therefore a conservative jump condition must be applied, and a combination of the two, a shock− rarefaction.43,44 The model was solved numerically and used to estimate the parameters, such as the total site concentration, Zt, and the adsorption constants, Km. The equations were discretized using a finite volume scheme and the details about their numerical discretization are given in the Appendix. The values of Zt and Km were estimated by minimizing the least-squares of the difference between the measured and the simulated breakthrough curves. As the transport model was written in terms of total aqueous concentration, the estimated values of the adsorption constants include the activity coefficients and therefore are relevant to the specific conditions under which the experiments were conducted.

Figure 1. Theoretical adsorption edges of the investigated cations calculated assuming Zt is equal to 1·10−2 mol/kg and the cation concentration as large as 5·10−4 mol/kg. The symbol zf represents the maximum adsorbed concentration.

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MATERIALS AND METHODS Transport experiments were performed using a column-flood system consisting of a single vertical column (Omnifit, UK) of a length equal to 0.12 m and cross section of 4 cm2 uniformly filled with 500 μm glass beads coated with HFO, identified as 6-line ferrihydrite.7 The tubing (50 mm) and the fittings were made of high purity Teflon (Swagelok, USA). Solutions were pumped using a HPLC pump (Flom, USA) with PEEK heads at the nominal flow rate of 1.5 mL/min (corresponding to 2.5 m3/s). Online sensors of temperature and pH (Cole-Parmer, USA), and pressure (Validyne, USA) were placed at the inlet and at the outlet of the column and an ion chromatograph (ICS1100 with IonPac CS12A 5 μm, Dionex, USA) with an automatic sampling valve was employed to determine the cation concentration of the effluent. Samples were taken every 6.5 min in all tests except during the experiment where Ba2+ was tested. In that case, the flow was sampled every 12 min as the Ba2+ elution time from the chromatographic column was approximately 10 min. The column was initially adjusted at a pH ≈ 3 using a solution containing 1·10−3 mol/kg of HCl (Fisher Scientific, USA). The equilibration of the column was continued until the pH of the effluent and influent reached the same value. After the column was equilibrated, an alkaline solution containing a known concentration of NaOH (≥97.0% purity, Fisher Scientific, USA) and of a salt of the cation of interest was introduced into the column. The salts we used were NaCl (≥99.0% purity, Fisher Scientific, USA), KCl (≥99.0% purity, Fisher Scientific, USA), LiCl (≥99.0% purity, Acros Organics, USA), CaCl2·2H2O (≥99.0% purity, Fisher Scientific, USA), MgCl2·6H2O (≥99.0% purity, Fisher Scientific, USA), SrCl2· 6H2O (≥99.99% purity, Sigma-Aldrich, USA), and BaCl2·H2O (99.999% purity, Alfa Aesar, USA). All of them were dissolved in ultrapurified water (Thermo Scientific Barnstead, USA) at a concentration chosen to obtain solutions undersaturated with respect to any solid phase and with negligible concentration of the aqueous complexes. The cation concentration was determined beforehand by ion chromatography, while the complete geochemical composition was calculated using the software package eq 3/6 v8.0 with the cmp database and the Bdot model for the activity coefficients,40 which was applicable in our case as the ionic strength of all the experiments ranged between 5·10−5 and 2·10−2 mol/kg. The solutions were introduced from the bottom of the column to avoid an unstable density stratification and the injection of the alkaline solution identified the adsorption phase of the experiments and lasted until the retarded cation front was eluted and the influent and the effluent concentrations were equal.

isotherms as a function of pH (adsorption edges) are shown in Figure 1. As it is possible to see in this figure, the adsorbed concentration of the cations on HFO is highly pH sensitive. In particular, it is negligible until a certain pH, which depends on the adsorption constant, above which it increases sharply and then stabilizes around a constant value. Owing to the difference in the adsorption constants, a distinct reaction behavior is expected for each cation listed in Table 1, particularly the pH at which adsorption becomes significant; a more acidic environment favors sorption of Ba2+ relative to Na+, for example.

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REACTIVE TRANSPORT MODEL We developed a one-dimensional (1D) transport model for a singlephase incompressible isothermal fluid flowing through a homogeneous reactive porous medium. Three components were considered: a cation (cm), the acidity (cHT), and a conservative anion (ca). Under the assumption of local chemical equilibrium,38,39 the mass conservation laws defining the reactive transport model are ∂c ∂ 2c ∂ (cm + εzm) + v m − D 2m = 0 ∂t ∂x ∂x

(14)

∂c ∂ 2c ∂ (c HT + εz H) + v HT − D HT =0 ∂t ∂x ∂x 2

(15)

∂ca ∂c ∂ 2c + v a − D 2a = 0 ∂t ∂x ∂x

(16)

on 0 < x < L and for t > 0, where L is the length of the domain. Here, ε is the dimensionless ratio of solid to fluid volume defined as ε = (1 − ϕ)/ϕ where ϕ is the porosity; v is the interstitial fluid velocity (m/s) defined as v = Q/ϕA where Q is the flow rate (m3/s) and A is the total cross section area (m2); D is the hydrodynamic dispersion (m2/s). The initial and boundary conditions for the ith component are given by ci(0, x) = ci,ini

(17)

ci(t , 0) = ci,inj

(18)

∂ci(t , L) =0 ∂x

(19)

The general solution to this transport problem is a series of waves, that is, concentration fronts traveling at constant velocity. A wave can be a rarefaction, such as a smooth variation in concentration, a shock, such as a sharp variation which arises when the solution to 3754

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Table 2. Operating Conditions, Estimated Values of Zt and Km, and the Calculated Values of Pe and R for the Experiments in Which the Fast Pulse Appeared pHini pHinj cm,inj T Q Pe Zt log10Km R a

Na+

K+

Li+

Ca2+

Mg2+

Sr2+b

Ba2+

3.1 11.8 365.00 22.9 1.3 1864 0.0124 2.24a 1.67

3.2 12.0 20.25 21.2 1.7 1237 0.0185 2.26a 1.27

3.2 12.0 824.90 21.2 1.7 1237 0.0240 2.18a 1.55

3.1 11.0 1.24 22.1 1.2 165 0.0027 3.10 2.72

3.3 12.0 11.86 21.2 1.3 123 0.0025 4.33 11.05

2.7 9.9 9.98 22.3 1.5 158 0.0310 4.47 81.95

3.3 7.0 1.00 22.6 1.5 2762 0.0300 5.46 43.00

units

10−5·mol/kg of solution °C 10−8·m3/s mol/kg of solid kg of solution/mol

Estimated value. bExperiment 3 published in our earlier work7 with parameters estimated using the transport model reported in this paper.

The porosity of the column was calculated by gravimetric measurements and the values of D and v were estimated from the concentration profile of the most conservative species, Na+. The pore volume of the columns ranged from 31 to 35 cm3. Given the applied operating conditions, the adsorbed concentration of Na+ was negligible, as small Na+ concentrations were used to adjust the pH. When a larger Na+ concentration was applied to test its behavior, Na+ adsorption was observed and an acidic solution containing NaCl was used instead to determine D and v. The values of D and v were estimated by minimizing the least-squares of the difference between the measured breakthrough curve of Na+ and the analytical solution of the advection−dispersion equation.41

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RESULTS AND DISCUSSION The conditions applied during the experiments are listed in Table 2. In all tests, a solution containing the cation at basic pH was introduced as a step change into a column equilibrated at acidic pH. In particular, an initial solution with a constant concentration of cHT equal to 1·10−3 m (corresponding to pH 3) and cm equal to 0 m was injected. After stabilization, a second solution with a constant and negative cHT (pH larger than 7) containing a known cation concentration between 1·10−5 and 4 · 10−2 m was introduced. Table 2 reports also the estimates of Zt and Km together with the calculated values of both the Péclet number (Pe), defined as the ratio between the advective, ta = v/L and the diffusive, td = L2/D time scales, Pe = ta/td = vL/D, where L is the column length, and the shock retardation (R) is given by42,43 R=1+ε

Figure 2. Measured and simulated breakthrough curves of Na+ and Mg2+ as a function of time. The fitting of the Na+ profile allowed an estimation of D and v from which Pe was calculated. The estimated values for this experiment, which are reported in Table 2, are D = 4.6· 10−8 m2/s and v = 5.2·10−5 m/s corresponding to a Péclet number of 123, given the length of the column equal to 0.12 m.

Na+, K+, and Li+, as larger Km values than the ones in the literature were required to describe their transport behavior. The measured and the simulated breakthrough curves are shown in Figure 3 for the monovalent cations and in Figure 4 for the divalent cations. In these figures, the profiles are illustrated as a function of the pore volume injected (PV), defined as t PV = LϕA /Q (21)

zm,ini − zm,inj cm,ini − cm,inj

(20)

where cm,ini and cm,inj are the initial and the injected aqueous concentrations, and zm,ini and zm,inj are the corresponding adsorbed concentrations determined by the adsorption isotherm in eq 12. The values of D and v were estimated from the concentration profiles of Na+. Figure 2 reports a Na+ breakthrough curve from a typical experiment where NaOH was used to adjust the pH, and because of the applied conditions, Na + behaves conservatively. In the figure it is possible to notice that the Na+ front and Mg2+ pulse travel at the same speed. The values of Zt and Km were estimated from the concentration profiles of the metal cations. In particular, the values of Zt were determined for all experiments, whereas the values of Km were estimated only for the monovalent cations,

where 1 PV indicates the time required by a tracer to traverse the column. For typical experimental conditions, the time required to inject one pore volume was 35 min. In all experiments, the breakthrough curves of the cation have a similar structure: a pulse eluted around 1 PV, that is, traveling at the interstitial fluid velocity, and a retarded front (a shock) whose retardation varies with the type of solute and the applied operating conditions (solution composition and the properties of the reactive material). In correspondence of the pulse a sharp increase in pH occurs. The structure of the pH breakthrough curves consists of a shock−rarefaction traveling with the solute pulse followed by a shock with a negligible variation in concentration, traveling with the retarded metal 3755

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Figure 5. Measured breakthrough curves of pH and Mg2+ as a function of pore volume injected.

operating conditions varied, in particular the pH of the alkaline solution, which was chosen in order to avoid supersaturated conditions with respect to any solid phase. Therefore, the retardation did not strictly adhere to the modeled theoretical expectation. This was particularly evident in the experiment where the behavior of Ba2+ was tested. The low solubility of witherite (BaCO3) constrained both the barium concentration and the pH of the injected solution and under the applied conditions the shock arrives shortly after the fast wave. The presence of a pulse moving at the interstitial fluid velocity in all measured breakthrough curves indicated that fast solute transport occurred in all cases. Moreover, the good agreement between the measurements and the model confirms that the formation of the fast pulse is due to the interaction of pH-dependent adsorption and hydrodynamic dispersion. In the case of barium, the model only captures the data in the early stage corresponding to the time when the fast pulse is eluted. This might be due to processes at the solid−liquid interface and/or in the solution, which are not included in our model, or simply to the calibration of the ion chromatograph that in this experiment was not highly accurate. In the experiments listed in Table 2, we exclude the effects of fast transport phenomena ascribed to colloid-facilitated transport or transport along fractures as the presence of colloids

Figure 3. Measured and simulated breakthrough curves of the investigated monovalent cations: (a) K+; (b) Na+; and (c) Li+. Data were normalized to the injected concentration as a function of the pore volume injected.

front.44 This structure of the fronts can be observed in Figure 5, where the pH changes overall from acidic to basic with an average value of 5 in correspondence of the pulse. The separation between the fast pulse and the classical retarded front varies in these experiments. For the divalent cations other than Ca2+, the retardation R is much larger than 1, and the eluted cation concentration decreases to nearly zero between the arrival of the fast front and the retarded front. For the monovalent cations and for Ca2+, R is approximately 2 and the eluted cation concentration does not decrease as much in the interval between fronts. It is clear however that all experiments show the same qualitative behavior. If the same operating conditions had been used in all experiments, the retardation of the shock would have increased with Km with the least retarded fronts of Na+ and K+ and the most retarded front of Ba2+. However, the experimental

Figure 4. Measured and simulated breakthrough curves of the investigated divalent cations: (a) Ca2+; (b) Mg2+; (c) Sr2+; and (d) Ba2+. Data were normalized to the injected concentration as a function of the pore volume injected. 3756

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In summary, these experimental results show that the formation of the fast pulse is a fast transport phenomenon generally occurring for several metal cations. It is not limited to the case of strontium and it seems to be a general feature of reactive transport of cations through hydrophilic reactive porous media. As already stated in our earlier work7 and confirmed by the experiments reported here, the necessary conditions under which the phenomenon occurs are 1. pH-dependent adsorption, i.e., competitive adsorption on a hydrophilic surface; 2. a finite amount of hydrodynamic dispersion, Pe < ∞; 3. initial pH in the column in the range of negligible cation adsorption; 4. injected fluid with an alkaline pH at which significant cation adsorption occurs. As the injected fluid enters the column, dispersion broadens the cation front at the inlet of the column and creates a mixing zone where the high-pH solution containing the cation mixes with the low-pH solution initially present in the system. The resulting pH of the mixing zone is in a range where the adsorption of the cations is negligible (cf. Figure 1). This leads to the formation of a fast cation wave, which separates from the retarded front and travels at the interstitial fluid velocity as an isolated pulse. The retarded front behaves classically; it occurs because at the high injected pH, the cation is strongly adsorbed (zm vs pH in Figure 1). Figure 7 reports the effect of decreasing contrast between the pH of the initial and the boundary conditions. Here it is possible to see that as the pH in the initial condition increases from 3.3 to 10.4, the fast pulse reduces in size, travels at lower speed, and finally disappears as the pH of the mixing zone increases favoring the adsorption of the metal. In this article, we demonstrate the occurrence of the fast transport phenomenon for various monovalent and divalent cations flowing through a reactive porous media with a hydrophilic iron oxide surface. The experiments were performed using chromatographic columns initially equilibrated at acidic pH and then flooded with an alkaline solution containing a known cation concentration. Compositions were chosen for which recently generalized theory predicts an additional, fast-moving concentration

and fractures in the system have been prevented by careful preparation of the experiments. A filter of pore size 0.45 μm was installed along the effluent line before the ion chromatograph and the chromatographic columns were always prepared with homogeneous porosity. To demonstrate the absence of colloid-facilitated transport or transport along fractures, an experiment was performed under unfavorable conditions for the formation of the fast pulse. Initially the column was equilibrated at pH ≈ 10 and then flooded with an alkaline solution at the same pH containing 1·10−4 mol/kg of strontium. Figure 6 shows

Figure 6. Measured and simulated breakthrough curve of Sr2+ normalized to the injected concentration as a function of pore volume injected. In contrast to Figure 3, no fast pulse of Sr2+ is observed. This is consistent with our model. The initial and the injected pH were set to ∼10 and the injected Sr2+ concentration was 10−4 mol/kg.

the breakthrough curve measured during this experiment and the model upon optimization. As expected, the concentration profile consists of only a retarded front whose retardation under the applied experimental conditions is as large as 88.43. If the fast pulse observed in all the experiments shown in Figure 3 and Figure 4 were due to colloid-facilitated transport or transport along fractures, the fast pulse should have also appeared in the Sr2+ breakthrough curve in Figure 6. A single retarded front (a shock) forms because the initial high pH favors the adsorption of strontium on the reactive material and the pH of the mixing zone is in a range where the adsorption of strontium is high (cf. Figure 1) in contrast to the cases reported in Figure 3 and Figure 4, where the pH of the mixing zone is in an interval where the cation adsorption is negligible.

Figure 7. Simulated concentration profiles of Mg2+ as a function of front velocity (η = x/(t·v)). The initial pH increases from 3.3 to 10.4, and the pH of the injected solution is equal to 10.5. 3757

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an Energy Frontier Research Center funded by the U.S. Department of Energy, Office of Science, Office of Basic Energy Sciences under Award Number DE-SC0001114 and of the Area 2: Inexpensive Monitoring and Uncertainty Assessment of CO2 Plume Migration Using Injection Data funded by the U.S. Department of Energy under Award Number DE-FE0004962.

wave to arise, and in all cases breakthrough curves show a fast pulse traveling at the interstitial fluid velocity ahead of a retarded classical front. Conversely, at compositions for which no fast front is predicted, only the classical front was observed. The good agreement between the experiments and the model confirms that the mechanism responsible for the occurrence of the fast pulse is the interaction between pH-dependent adsorption and hydrodynamic dispersion. The formation of the fast pulse is a notable departure from conventional understanding of reaction fronts in porous media which would predict only the strong retardation of a cation, as the ones tested here, when dissolved into a high pH solution, which favors strong adsorption. In our earlier study,7 we investigated the formation of the fast pulse for strontium, here we extend it demonstrating that the fast pulse can also arise during the transport of several other cations with pH-dependent adsorption onto an iron oxide surface. The classical theory of transport with sorption does not anticipate the formation of that fast pulse, and the theoretical basis of this phenomenon is presented in our previous works.8,44 This new fast transport mechanism should be taken into account for the prediction of solute transport through reactive porous media in subsurface environments with variable pH. In particular, this process is likely to lead to an enhanced migration of radionuclides and metals escaping from temporary storage tanks. Tanks containing hazardous liquid waste are generally kept at alkaline pH to favor the precipitation and the adsorption of metal cations and avoid their migration into the environment. In the presence of a leakage, the alkaline solution might escape from the tanks and mix with the groundwater of the shallow aquifer. If the aquifer contains a reactive permeable media made by hydrophilic surface and the pH of the mixing zone between the leaked solution and the groundwater is below the value where the adsorption of the metal cations is negligible a fast pulse can arise.

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APPENDIX: NUMERICAL DISCRETIZATION A finite volume scheme was developed to discretize the nonlinear system given by eq 14 through eq 16. The accumulation term was not expanded, but differentiated directly to treat the nonlinearity implicity. The advection term was integrated explicitly and approximated with an upwind flux, while the hydrodynamic dispersion term was integrated implicity and approximated by a central flux.43 The domain, x ∈ [0, ∞] was divided into a grid with N + 2 cells, where all interior cells are of width Δx = 1/(N+1) and the two boundary cells are of width Δx/2. The cell centers were located at xi = (i − 1)Δx for i ∈ [0, N + 1]. The resulting nonlinear algebraic system is of 3N equations, which we solved with the Newton− Raphson method using the adaptive time step based on the convergence of the Newton iteration with a maximum time step given by the Courant−Friedrichs−Lewy condition (CFL condition).45

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AUTHOR INFORMATION

Corresponding Author

*Phone: +15129634774; e-mail: valentina.prigiobbe@austin. utexas.edu. Notes

The authors declare no competing financial interest.

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ACKNOWLEDGMENTS This material is based upon work supported as part of the Center for Frontiers of Subsurface Energy Security (CFSES), 3758

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