Experimental Study of Salt Bead Dissolutions in Aqueous Solvents

Article pubs.acs.org/IECR

Experimental Study of Salt Bead Dissolutions in Aqueous Solvents Michael Shaltry† and Supathorn Phongikaroon*,‡ Department of Chemical and Materials Engineering and Nuclear Engineering Program Center for Advanced Energy Studies, University of Idaho, 995 University Boulevard, Idaho Falls, Idaho 83401, United States S Supporting Information *

ABSTRACT: Bead dissolutions of several chloride compoundslithium chloride-potassium chloride (LiCl-KCl) eutectic, lithium chloride (LiCl), strontium chloride (SrCl2), cerium chloride (CeCl3), lanthanum chloride (LaCl3), praseodymium chloride (PrCl3), and yttrium chloride (YCl3)were performed in water at 20 °C. Additional bead dissolutions involved LiClKCl beads in two types of brine solvents. Each bead diameter was measured and found to change linearly with time in water. A model regression to these measured data resulted with R2 > 0.942. Results indicated dissolution was faster in water than in the brines. Calculated mass transfer coefficients were in the range of 1.00 × 10−2 mm s−1 to 2.67 × 10−2 mm s−1. Based on a Sherwood correlation, Sh = 2 + 0.0254Gr0.333Sc0.577, calculated diffusion coefficients were in the range of 10−5 mm2 s−1 to 10−3 mm2 s−1. Results implied mass transfer of the eutectic was dominated by diffusion, whereas a transition from natural convection to diffusion was inferred for the other solutes.

1. INTRODUCTION Used nuclear fuel (UNF) from the Experimental Breeder Reactor-II (EBR-II) has been electrochemically treated at the Materials and Fuels Complex at the Idaho National Laboratory. The electrochemical process, also known as pyroprocessing, is potentially a viable technology for UNF treatment in such countries as South Korea, Japan, Russia, and the United States. In this process, usable uranium remaining in the UNF is selectively removed as a highly pure metal from the electrorefiner (ER). As a consequence of UNF treatment, fission products contaminate the molten LiCl-KCl eutectic salt (the electrolyte) within the ER, and a portion must be removed to maintain the operating conditions of the system.1,2 One of the major operations of the electrochemical process is immobilization of the contaminated electrolyte material. The contaminated waste salt is immobilized by combining it with zeolite and glass frit and converting that mixture to a ceramic waste form, which is then stored.2 The manufacture of the ceramic is time-consuming and costly, requiring equipment and material transfers for several unit operations. As an alternative to immobilization, direct disposal of contaminated ER electrolyte has been proposed.3 This method of disposal would eliminate immobilization in favor of storing the waste salt in suitable containers, which may be less time-consuming, less expensive, and require less equipment and handling. Evaluation of the direct-disposal option includes considering the risk of introducing high-level waste to the environment. Emergent events at processing facilities or geologic repositories could lead to the transport of waste salt in aqueous solution to such bodies of water as seas, rivers, or subterranean aquifers. Therefore, knowledge related to the dissolution phenomena of chloride salts in aqueous solvents is essential to evaluating the potential hazards of directly disposing salt waste. Mass transfer phenomena of solid spheres dissolving in liquids has been studied previously and reported in the literature.4−7 The outcome of these dissolution studies involving organic solutes and solvents has widespread © 2014 American Chemical Society

application to industries including plastics manufacturing, medical and pharmaceutical, food, and fertilizer. Although the experimental materials and applications are unrelated, the methods of analysis in those studies are useful for this study. Furthermore, while equilibrium information for many chloride compounds, such as solubility in aqueous solvents, is readily available, there is a lack of kinetics information for dissolution phenomena. The goal of this research is to calculate key parameters associated with the dissolution kinetics of some relevant chloride saltslithium chloride-potassium chloride (LiCl-KCl) eutectic, lithium chloride (LiCl), strontium chloride (SrCl2), cerium chloride (CeCl3), lanthanum chloride (LaCl3), praseodymium chloride (PrCl3), and yttrium chloride (YCl3). These salts are representative of the electrolyte and contaminants that are common to the ER. In this study, purified water and two simulated brines were employed as solvents. The composition of the simulated brines was based on sampled geologic brines. The first simulated brine is representative of the brine found in a particular room at the Waste Isolation Pilot Plant (WIPP) and is referred to as GSEEPthe seepage brine found in room ‘G’ of the WIPP excavation.8,9 The other simulated brine is comparable to the composition of the brine found in an exploratory drill hole at a candidate WIPP site; that is, the Energy Research and Development Administration Well 6 (ERDA-6).10 All salt beads were tested in water. Only LiCl-KCl eutectic beads were selected and tested in GSEEP and ERDA-6. It is expected that the results from this surrogate study will provide information on the dissolution kinetics for some relevant chloride salt to aid the feasibility evaluation of the direct disposal of high-level salt waste. Received: Revised: Accepted: Published: 13550

June 30, 2014 August 6, 2014 August 7, 2014 August 7, 2014 dx.doi.org/10.1021/ie502608v | Ind. Eng. Chem. Res. 2014, 53, 13550−13556

Industrial & Engineering Chemistry Research

Article

2. EXPERIMENTAL SECTION 2.1. Materials and Criteria. All chloride compounds in a ready-made bead form were purchased from Alfa Aesar except the LiCl-KCl eutectic (44 wt % LiCl - 56 wt % KCl), which was obtained from Sigma-Aldrich. Table S1 lists the solute purity, density (ρs, g mm−3), average bead initial radius (⟨r0⟩, mm), and average bead initial mass (⟨m0⟩, mg). Here, LiCl-KCl eutectic will be referred to as “eutectic” from now on for discussion purposes. Highly purified water was produced by a lab-scale Millipore water purification system and was characterized by 18.2 MΩ resistivity and 3 ppb total oxidizable carbon at 20 °C. The composition of the simulated brines is given in Table S2. The amount of solvent for the tests was chosen such that the volume was large enough to be considered infinite. This condition supports the assumption that during dissolution, the bulk concentration and rate of dissolution do not change. The criteria to determine the volume of solvent is expressed as12 40πρs r03N 3VM(Ce − C0)

≤1

were measured by placing the tips of the calipers into the solvent, which allowed the bead to remain in the solvent during the entire dissolution process. It is important to note for each solvent−solute combination, ten salt beads were dissolved in the same volume of solvent. Diameter measurements were obtained until the bead was too small to be accurately measured. All experiments were conducted at 20 ± 2 °C.

3. RESULTS AND DISCUSSION 3.1. Bead Measurements. Figure 2 illustrates the average measured radius as a function of time for eutectic beads in H2O,

(1)

where N is the number of beads dissolving (equal to one), V is the volume (mm3) of solvent, M is the molar mass (g mol−1) of the solute, and Ce and C0 are the equilibrium (solubility) and initial mass concentrations (g mm−3) of the solute in the solvent. Table S3 lists values of Ce for the solutes in the given solvents.11,13,14 Figure 1 displays the left-hand side of eq 1 as a

Figure 2. Plot illustrating the average measured values of radius vs time for eutectic beads dissolving in H2O, ERDA-6, and GSEEP. The average and its standard deviation are based on ten different beads in the same volume of solvent.

ERDA-6, and GSEEP solvents. Figure 2 shows that the change of radius appears to be linearly proportional to time in H2O. The rate change of radius of each bead appears to be consistent, and the displayed result indicates that the rate of dissolution was not affected by dissolving multiple beads in the volume of purified water. For the eutectic beads dissolved in ERDA-6, the data appears to have a nonlinear trend in the latter times of the dissolution. These data points represent measurements that are smaller than what would be expected for a linear trend of dissolution. This can be explained by considering the relationship between the rate of transport from the bead and the rate of solvent absorption by the bead. During tests with relatively short dissolution times, solute was transported from the bead at a rate that was faster than absorption of solvent by the bead. In this situation the bead remained a rigid structure, and a linear trend in measurements of diameter can be observed. Conversely, for tests with long dissolution times (ERDA-6 and GSEEP), transport from the bead was slower and absorption of solvent was comparatively significant, which lead to softening of the bead. The softened bead was compressed slightly when measuring the diameter with calipers. Consequently, a smaller diameter was measured compared to what would be measured without disturbing the bead. This issue contributes to an increase in measurement error as can be seen for eutectic bead dissolutions in ERDA-6 (see Figure 2). Similar features were noticed in the GSEEP data, but not to the extent of that in the ERDA-6 data. Overall, the dissolution rate of eutectic bead in purified water is faster than those in ERDA-6 and GSEEP. Similar observation is seen for other bead types (LiCl, SrCl2, CeCl3, LaCl3, PrCl3, and YCl3) dissolved in

Figure 1. Plot of the left-hand side of eq 1 as a function of volume for eutectic in H2O and the ERDA-6 and GSEEP brines. Volumes greater than 1 × 103 mm3 are close to zero and assumed to be ideal and thus infinite. The chosen volumes for the current study are indicated on the chart.

function of V for eutectic in the three solvents. The value of C0 for the calculations reflects ten beads having been dissolved in the solvent as the maximum. For V ≥ 1 × 103 mm3, the values are close to zero and assumed to be ideal and thus infinite. The choice of 1 × 104 mm3 of purified water and 2 × 104 mm3 for the tests are indicated on the plot. It should be noted the criteria was also met for dissolution of LiCl, SrCl2, CeCl3, LaCl3, PrCl3, and YCl3 in 1 × 104 mm3 of purified water. 2.2. Procedure. The given amount of solvent was placed into a small quartz container. Prior to dissolution, the initial mass and diameter of each bead were measured and selected randomly. The bead was then submerged in the solvent, and diameter measurements were acquired every 20 s in purified water and 60 s in both brines. All solvents were not stirred during all dissolution tests. The measurement intervals were chosen based on the rate of dissolution for a solute−solvent combination, which was determined by pre-experimental tests. The diameter of the beads was measured using a General No. 147 digital caliper with an accuracy of ±0.02 mm. The beads 13551

dx.doi.org/10.1021/ie502608v | Ind. Eng. Chem. Res. 2014, 53, 13550−13556


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purified water as well; that is, the change in radius is linearly proportional to dissolution time. 3.2. Analysis on Mass Transfer Coefficient. The time rate change of mass (m) of the dissolving bead was assumed to be proportional to the surface area of the bead (SA) and Ce, which is given by

R=

α=

γ=

r (t ) r0 Ce , ρs

kt r0

(6)

(7)

where N is the number of data points, the subscripts m and p refer to measured and predicted values, respectively, and Γ is t−1 −x the gamma function, defined as Γ(t) = ∫ ∞ 0 x e dx. Low values of Pc indicate a high probability that measured and predicted values are correlated. Table S5 shows the results for R, R2, N, and Pc for each of the solute−solvent pairs, which demonstrates the measured and model data are correlated. The results suggest that the values of k are reliable, and there is a high probability that predicted values would be measured by future experiment. Figure 4 displays rp plotted against rm for all

(3)

(4)

where β=

N ∑i r p2 − (∑i rp)2

( N 2− 1 ) 1 (1 − x 2)N−4/2 dx ∫ ( N 2− 2 ) |R|

1 Γ Pc(R , N ) = π Γ

Equation 3 can be expressed in a dimensionless form, which is β = 1 − αγ

− (∑i rm)2 −

and

dm = −kCe(SA) (2) dt where t is time (s), and k is the mass transfer coefficient (mm s−1).15 Integration of eq 2 with the boundary conditions that when t = 0, r = r0 and as t → ∞, r → 0 yields Ck r (t ) =1− e t r0 ρs r0

N ∑i rmrp − ∑i rm ∑i rp N ∑i rm2

(5a)

and (5b)

(5c)

By using eq 4, k and the estimated time to complete dissolution (td) were calculated for all data sets. Figure 3 represents eq 4 as

Figure 4. Plot of rp against rm for the entire set of dissolution data.

dissolution tests. The average percent difference between the predicted value and measure value is ±2.8%; overall, the overprediction tends to occur more frequently at smaller radii and underprediction more frequently at larger radii within this deviation range. Figure 5 is a dimensionless plot of all measured data and the model (solid line), which was calculated based on the overall average value of αγ. The standard deviation of k (σk) was Figure 3. Plot of measured data and eq 4 for ten eutectic beads dissolving in the GSEEP brine. The model is plotted based on the average k value.

applied to the eutectic-GSEEP data sets as an example. The results show that eq 4 fit well with the measured data with the R2 value of 0.953. Similar characteristics were observed of the bead dissolutions not shown in Figure 3. Regression of the model to all of the measured data sets resulted with values for R2 > 0.942. The average values for k, td, and R2 for all bead dissolutions are summarized in Table S4. Statistical analysis was performed to estimate the reliability of eq 4 in relation to the measured values. The correlation coefficient (R) and the probability of correlation (Pc) were calculated for each of the solute−solvent combinations. The formulation of R and Pc are, respectively,16

Figure 5. Dimensionless plot of all measured values and the model. The model (solid line) is plotted based on the average value of αγ. The deviation of eq 4 (dashed lines), determined by a Kline-McClintock method, is shown based on the variation of k for all dissolution tests. 13552



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calculated based on the ten bead tests for each solute−solvent combination. The Kline-McClintock method of calculating uncertainty using standard deviations (Theorem 2) was used to determine the deviation of β (σβ) based on σk.17 By this method, the average deviation of β (⟨σβ⟩) was found to be 0.0359 and is indicated by the dashed lines in Figure 5. 3.2. Characteristic Time and Mass. A characteristic time (tc) was calculated, which provided a unique point during dissolution that is based on the functional relationship between mass and time. This was accomplished with a plot of m(t), which is produced by using eq 3 and the relationship that m = (4π/3)ρr3. Here, eq 3 includes the average value of k for a particular solute−solvent combination. This method was applied to determine the value of t at the intersection of lines regressed to the initial and final regions of a plot of mass versus time, respectively. SrCl2 in purified water was selected to illustrate this method (see Figure 6). A particular line in the

Figure 7. Dimensionless plot mass vs time for all data sets with indication of wc and τc.

Figure 6. Plot of mass vs time for SrCl2 in H2O including fitted lines and weighted averages of the initial and final regions of the curve. The vertical dotted line indicates the calculated characteristic time (tc).

initial or final region (dashed line) is a linear regression of two or more data points (up to 10 points). The first and last ten data points were chosen to provide a reasonably significant linear fit, while avoiding the nonlinear midsection of the curve. The average slope (aave) of the line of regression in either region is the weighted average of the slopes of the dashed lines (an). The weights are the number of data points (n +1) to which a particular line of regression is fitted. The calculation of aave is given by

Figure 8. Image of a bead of strontium chloride (∼1.8 mm diameter) dissolving in H2O. The image proves there is natural convection during the dissolution process. The stream falling from the bead is assumed to be a saturated solution of H2O and SrCl2.

purified water. The stream that is seen to be falling from the bead was assumed to be a saturated solution of SrCl2, which has a higher density compared to the surrounding bulk fluid. This situation gives rise to natural convection and validates the use of the Grashof number (Gr) in dimensionless correlations, which has been observed in similar research.5,7,15,18 Many dimensionless correlations involving the Sherwood (Sh) and Gr numbers also include the Schmidt (Sc) number and are generally formulated as

9

aave =

∑n = 1 (n + 1)an 9

∑n = 1 (n + 1)

(8)

It was found that tc is greater for the solutes which have a greater value of td. As a means to compare all data sets, a dimensionless characteristic time (τc) is defined as τc = tc/td. The average value of τc is 0.37 ± 0.01. Furthermore, the average fraction of bead mass remaining is 0.25 ± 0.01 at that tc. In similar fashion, a dimensionless characteristic mass (wc) was calculated based on the fact that wc = mc/m0. The calculation of τc and wc reveals that m = 0.25m0 when t = 0.37td. In other words, 75% of bead mass concentration dissolved in the first 37% of the dissolution process. This result provides evidence of consistent dissolution kinetics regardless of the solute or solvent. Table S6 displays the values for tc, τc, and wc, and Figure 7 shows the values of τc and wc on a dimensionless plot of mass vs time for all data sets. 3.3. Diffusion Coefficient and Sherwood Correlation. Figure 8 is a close-up image of a SrCl2 bead dissolving in

Sh = 2 + AGr bSc c

(9)

where A, b, and c are constants. The remaining terms in eq 9 are defined as

Sh =

Gr = 13553

kd D

(10a)

d3Δρg ρb ν 2

,

and (10b)



ν D

Article

(10c)

can be seen of the tests with eutectic. Figure 9 shows a plot of Sh as a function of Gr0.333Sc0.577. The data sets involving eutectic

with the fact that the Rayleigh number (Ra) is defined as the product of Gr and Sc (Ra = GrSc). Here, d is the bead diameter (mm), D is the diffusion coefficient (mm2 s−1), ρb is the density of the bulk (g mm−3), Δρ is the difference in density between the saturated solution (ρsat) and the bulk (g mm−3), g is the gravitational acceleration constant (mm s−2), and ν is the kinematic viscosity of the bulk (mm2 s−1).18 Four correlations with different given A, b, and c values were fitted to the measured data setsCorrelation Numbers 1, 2, 3, and 4 from refs 15, 5, 7, and 18, respectively; all these correlations are based on fluid motion around single spheres (see Table S7). An estimation of the diffusivity was calculated by minimizing the error between the right- and left-hand sides (that is, RHS and LHS) of eq 9 by varying D. The approach for this analysis was to apply several proposed correlations to the data and determine the best fit. A cumulative squared error (ε), defined as

Figure 9. Plot of Sh vs Gr0.333Sc0.577 for all solute−solvent combinations. Decreasing values for a given data set implicitly displays a decreasing bead radius vs time.

Sc =

ε=

∑ (RHSi − LHSi)2 i

occupy a small region at the lowest dimensionless values implying diffusion was the predominate mechanism of mass transfer throughout the dissolution process. Considering the three tests involving eutectic, the largest span of values was calculated for purified water at high values relative to the two other eutectic tests. With tests in both brines, ranges of values are approximately equal, but those for ERDA-6 cover a higher range. SrCl2 in purified water spans a larger range compared to eutectic, but lower than the other tests in purified water. Here, convective mass transfer had a larger effect during the initial time frame of dissolution compared to tests with eutectic. The most drastic transition from convective to diffusive effects was calculated for LiCl, CeCl3, LaCl3, PrCl3, and YCl3, which in general extends from high to low values. LaCl3 and PrCl3 data begin at high values and end at moderate values. LiCl, CeCl3, and YCl3 begin at moderate values and extend to low values. In addition, it is important to clarify that Figure 9 implicitly displays the dimensionless quantities as a function of time. For all data sets, Sh and Gr numbers decrease with time as a result of the decreasing bead radius. It may be reasonable to assume that a decrease of natural convection was due to the diminishing radius of the bead, which is reflected by d in both Sh and Gr. A trend in the data of Figure 9 can be identified when considering the solubility of the solute (Table S3). Low and high solubility values correspond to low and high values of Sh and Gr, respectively. Eutectic in ERDA-6 has the lowest solubility and lowest calculated values of Sh and Gr. In contrast CeCl3, LaCl3, and PrCl3 in H2O have the highest solubility and highest calculated values of Sh and Gr. This is the case despite the larger size of the eutectic beads compared to those of CeCl3, LaCl3, and PrCl3 (refer to Table S1). 3.4. Analysis on Practical Application. All aforementioned results can be used to provide a fundamental assessment of the geological repository for used nuclear fuel. By looking at the ⟨k⟩ value alone, it would be extremely difficult to evaluate the effect of three different mediums on the dissolution rate because ⟨k⟩ values of eutectic dissolutions in ERDA-6, GSEEP, and purified water are 0.0267, 0.0142, and 0.0255 mm s−1, respectively. The ⟨k⟩ values did not provide direct relationship to the observation shown in Figure 2the results indicate that the dissolution rate in GSEEP is between purified water and

(11)

was used to calculate and quantitatively gage the accuracy of a particular correlation for all 617 measured data points. The fitted correlation is most reliable when ε is near or close to zero. Table S7 provides a list of ε values as well as the range of magnitudes of D for the four tested correlations. Although most of the values of D shown in Table S7 are in the expected range, the values of ε reveal that Correlation No. 4 provides the best fit. Therefore, emphasis is placed on the formulation18 Sh = 2 + 0.0254Gr 0.333Sc 0.577

(12)

Table S8 provides a list of the average values of D, the range of values of Sh and Gr, and Sc associated with eq 12. In this system, Sc did not change during dissolution, and the average initial value of Sherwood number (⟨Sh0⟩) and Grashof number (⟨Gr0⟩) are given. The range of D in magnitude associated with eq 12 is 10−5 mm2 s−1 to 10−3 mm2 s−1. Diffusion coefficients in the range of 10−4 mm2 s−1 to 10−3 mm2 s−1 are typical of ions in the liquid phase.15 Thus, D for LaCl3 may be considered lower than expected. Diffusivity is larger for the eutectic tests compared to those in H2O and diffusivity is largest for eutectic in ERDA-6 and lowest for LaCl3 in H2O. Overall, average values of Sh0, Gr0, and Sc are within the intervals of 8.76 to 201, 0.213 to 3.75, and 0.018 to 1.31, respectively. It is recommended that Ra should be greater than 108 in order for eq 12 to be valid.18 In this study, Ra for tests with LiCl, CeCl3, LaCl3, PrCl3, and YCl3 are initially on the order of 108. Tests involving eutectic and SrCl2 exhibit a reasonable fit of eq 12 despite Ra being in the interval of 105 to 107. However, 105 < Ra < 107 has been reported in the literature for similar conditions.6 It is noted that during later times of dissolution, for all data sets, the range of Ra was between 103 and 107, which is more consistent with values reported for Correlation Numbers 2 and 3. It was found that Correlation Number 1 shows Ra to be between 104 and 108, but the relatively high value of ε reduces its reliability for this system. Relatively high values for Sh and Gr indicate that convection has a larger role in the mass transfer, which is the case for the tests conducted in H2O. Conversely, lower Sh, Gr, and Sc values insinuate mass transfer is supported more so by diffusion. This 13554



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sites at WIPP with brine components will ensure slow diffusion of waste salt into the surrounding environment. Furthermore, it is recommended that waste salt be stored in such a controlled environment for safety purposes.

ERDA-6. Further analysis implied that diffusion must play an important role. In fact, for a solid spherical particle dissolving in a medium, Sh = 2 represents a steady diffusion external to a sphere. Therefore, deviation from this point will enhance the dissolution rate. Hence, it is important to focus on the value of ⟨Sh0⟩ to elucidate the dissolution pattern. For the eutectic dissolved in ERDA-6, GSEEP, and purified water, the ⟨Sh0⟩ values are 8.76, 18.3, and 25.9, respectively (see Table S8). The ⟨Sh0⟩ values provide a distinct trend showing that ERDA-6 is the most preferred medium for having the closest value to the steady state dissolution condition and that water is the least preferred medium. In addition, other chloride compounds dissolving in purified water show higher values of ⟨Sh0⟩ implying that dissolution rates of these compounds are faster than that of the eutectic. Therefore, it is best to store these compounds in either ERDA-6 or GSEEP solvents. Overall, results imply that storage in designed geological sites with brine components will ensure slow diffusion of waste salt into the environment, and it appears to be safer to store in such a controlled environment.

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ASSOCIATED CONTENT

S Supporting Information *

Tables S1−S8. This material is available free of charge via the Internet at http://pubs.acs.org.

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AUTHOR INFORMATION

Corresponding Author

*Phone: (804)827-2278. E-mail: [email protected]. Present Addresses

† Separations Department, Idaho National Laboratory, P.O. Box 1625, Idaho Falls, Idaho 83415, United States. ‡ Department of Mechanical and Nuclear Engineering, Virginia Commonwealth University, 401 West Main Street, Richmond, Virginia 23284, United States.

Notes

4. CONCLUSIONS This study highlighted and provided characteristics of chloride salt dissolutions in different mediums. The information was analyzed and used to provide similitude to obtain a general assessment of solvent types that may be encountered in a geological repository. A basic analysis of mass transfer coefficient and a Sherwood correlation were applied to aid the understanding of the experimental process. The key conclusions based on this study are the following: • The bead radius was a linear function of time, and the applied radius model yielded values of R2 > 0.942. In general, the fastest dissolution was observed in H2O and was slowest in the brines. Mass transfer coefficients were found to be in the range of 1.0 × 10−2 mm s−1 to 2.67 × 10−2 mm s−1 and were largest for eutectic in ERDA-6 brine and smallest for LaCl3 in H2O. • Determination of the characteristic time resulted with larger values for tests with larger dissolution times. Dimensionless comparison of the data was accomplished by calculating dimensionless characteristic time and mass. The average values of τc and wc were 0.37 ± 0.01 and 0.25 ± 0.01, respectively. The low standard deviation of τc and wc indicate the process of dissolution was consistent regardless of the solute or solvent. Calculations revealed that 75% of initial bead mass had dissolved within the first 37% of the dissolution time for all solute−solvent combinations. • Diffusion coefficients were largest for eutectic in ERDA-6 and smallest for PrCl3 in H2O and on the same order of those presented in the literature. On a relative basis, it was found that diffusion was more significant for the tests involving eutectic and SrCl2 versus the significance of convection for the LiCl, CeCl3, LaCl3, PrCl3, and YCl3 tests in H2O. Results implied mass transfer of the eutectic was dominated by diffusion and a transition from natural convection to diffusion was inferred for the other solutes. • Results for the dimensionless correlation Sh = 2 + 0.0254Gr0.333Sc0.577 show the overall range of values for Sh, Gr, and Sc are 2.2 to 276, 0.0008 to 5.18, and 0.018 to 1.31, respectively. • The ⟨Sh0⟩ values can be used to indicate the general magnitude of the dissolution rates within the given medium. Results reveal that storage in the current designed geological

The authors declare no competing financial interest.

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ACKNOWLEDGMENTS This research was supported by the Center for Advanced Energy Studies and the University of Idaho. The authors give thanks to Dr. Michael Simpson of Idaho National Laboratory for partial support and insightful knowledge on waste disposal. In addition, gratitude is extended to Robert O. Hoover, Joshua Versey, and Thomas K. Larson for their invaluable discussion throughout the course of this study. Particular thanks are given to Ammon Williams, Elizabeth Sooby, Jessica Wallis, and James Allensworth.

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REFERENCES

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Experimental Study of Salt Bead Dissolutions in Aqueous Solvents

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