ASSESSMENT OF PROBABILITY OF 

LOCALIZED CORROSION OF ALLOY 22 WASTE 

PACKAGE MATERIAL 

Prepared for 

U.S. Nuclear Regulatory Commission 

Contract NRC–02–07–006 

Prepared by 

O. Pensado 

R.T. Pabalan

Center for Nuclear Waste Regulatory Analyses 

San Antonio, Texas 

September 2011
ii 

ABSTRACT 

A key attribute of the U.S. Department of Energy (DOE) safety strategy for the high-level 

nuclear waste repository it proposed to construct at Yucca Mountain, Nevada, included 

long-lived waste packages comprising an outer container of a highly corrosion-resistant 

nickel–chromium–molybdenum alloy (Alloy 22) over an inner container made of Type 316 

nuclear grade stainless steel. In the absence of mechanical disruption, DOE expected 

aqueous corrosion to be the primary degradation process limiting the life of the waste packages. 

The mode and rate of corrosion of the waste package materials were expected to depend on 

the chemistry of water contacting them and on temperature. Coupled thermal-hydrologicalchemical processes would significantly alter the chemistry of groundwater that seeps into the 

repository drift and contacts the waste packages and drip shields. Radioactive decay can cause 

waste packages and drip shields to experience transient temperatures above the boiling point of 

pure water for several hundreds to few thousands of years. During this transient elevated 

temperature period, seepage water evaporation could lead to the formation of corrosive brines 

on waste package surfaces and promote localized corrosion of the waste package material. 

This report documents an analysis of the likelihood of environmental conditions established by 

seepage water evaporation capable of supporting initiation and propagation of localized 

corrosion of the Alloy 22 waste package material. The analysis accounts for the variability in 

solution composition and temperature of the Alloy 22 material and is based on the concept of 

corrosion and repassivation potentials and their dependence on the chemistry of brines that 

may evolve from seepage water evaporation. 

The results indicate that Alloy 22 localized corrosion is likely (probability >0.001) only at 

temperature (T) >80 °C [>176 °F]. At T ≤ 80 °C [≤ 176 °F], the solutions contacting the waste 

package material will have a sufficiently high pH such that localized corrosion (i.e., Ecorr > Ercrev) 

is unlikely (probability <0.001). The analysis also indicates that when T <50 °C [<122 °F] and a 

marginal amount of nitrate is present in solution, the solution pH is unlikely to be low enough to 

cause localized corrosion. 

The DOE equations imply that increasing chloride concentrations could have a beneficial effect 

on localized corrosion. It is hypothesized that increasing concentrations of chloride displace 

oxygen and other oxidants in the solution causing the corrosion potential to decrease. On the 

other hand, increasing chloride concentration causes the repassivation potential to decrease. 

The net effect of these competing trends is the nonintuitive result that localized corrosion is less 

likely in solutions of increasing chloride concentration. This nonintuitive trend was used to 

rationalize DOE results that showed varying probability for localized corrosion as a function of 

deep percolation rates (DOE divided the repository into five percolation bins). The probability of 

localized corrosion is slightly higher in the midrange of the considered percolation bins. For the 

low percolation rate region, the temperature tends to be higher and the system drier, causing 

chloride concentrations to be higher and localized corrosion to be less likely. For the high 

percolation rate region, the temperature is lower, the relative humidity higher, and the range of 

pH tends to be higher, which makes localized corrosion less likely. The analysis indicates that 

in the midrange of the percolation rates—where the temperature and relative humidity 

are comparatively high to cause solutions with low pH and low chloride concentration to 

form—localized corrosion has a slightly higher chance of occurrence, in agreement with the 

results of DOE calculations. The prediction of localized corrosion in solutions of low chloride 

concentration and low temperature, however, is most likely an artifact of the mathematical 

curve fitting because localized corrosion of Alloy 22 has never been detected in this type 

of environment.
iii 

CONTENTS 

Section Page 

ABSTRACT ii 

FIGURES v 

TABLES vii 

ACKNOWLEDGMENTS ............................................................................................................. viii 

1 INTRODUCTION ................................................................................................................ 1-1 

2 CHEMISTRY OF SOLUTIONS CONTACTING WASTE PACKAGES 

AND DRIP SHIELDS .......................................................................................................... 2-1

3 ASSESSMENT OF DOE LOCALIZED CORROSION MODEL ........................................... 3-1 

4 SUMMARY AND CONCLUSIONS ...................................................................................... 4-1 

5 REFERENCES ................................................................................................................... 5-1 
iv 

FIGURES 

Figure Page 

2-1 Composition of Yucca Mountain Unsaturated Zone Waters ............................................ 2-2 

2-2 Calculated pHs of Brines Resulting From Evaporation of Yucca Mountain 

 Unsaturated Zone Waters at 25, 50, 70, 90, and 100 °C 

 [77, 122, 158, 194, and 230 °F] and Total Pressure Corresponding to RHmedian .............. 2-5 

2-3 Calculated Na+

 Concentrations of Brines Resulting From Evaporation of 

 Yucca Mountain Unsaturated Zone Waters at 25, 50, 70, 90, and 100 °C 

 [77, 122, 158, 194, and 230 °F] and Total Pressure Corresponding to RHmedian .............. 2-6 

2-4 Calculated Mg2+ Concentration of Brines Resulting From Evaporation of 

 Yucca Mountain Unsaturated Zone Waters at 25, 50, 70, 90, and 100 °C 

 [77, 122, 158, 194, and 230 °F] and Total Pressure Corresponding to RHmedian .............. 2-7 

2-5 Calculated Ca2+ Concentrations of Brines Resulting From Evaporation of 

 Yucca Mountain Unsaturated Zone Waters at 25, 50, 70, 90, and 100 °C 

 [77, 122, 158, 194, and 230 °F] and Total Pressure Corresponding to RHmedian .............. 2-8 

2-6 Calculated Cl–

 Concentrations of Brines Resulting From Evaporation of 

 Yucca Mountain Unsaturated Zone Waters at 25, 50, 70, 90, and 100 °C 

 [77, 122, 158, 194, and 230 °F] and Total Pressure Corresponding to RHmedian .............. 2-9 

2-7 Calculated NO3

–

 Concentrations of Brines Resulting From Evaporation of 

 Yucca Mountain Unsaturated Zone Waters at 25, 50, 70, 90, and 100 °C 

 [77, 122, 158, 194, and 230 °F] and Total Pressure Corresponding to RHmedian ............ 2-10 

2-8 Calculated F–

 Concentrations of Brines Resulting From Evaporation of 

 Yucca Mountain Unsaturated Zone Waters at 25, 50, 70, 90, and 100 °C 

 [77, 122, 158, 194, and 230 °F] and Total Pressure Corresponding to RHmedian ............ 2-11 

2-9 Calculated SO4

2−

 Concentrations of Brines Resulting From Evaporation of 

 Yucca Mountain Unsaturated Zone Waters at 25, 50, 70, 90, and 100 °C 

 [77, 122, 158, 194, and 230 °F] and Total Pressure Corresponding to RHmedian ............ 2-12 

2-10 Calculated HCO3

–

 + CO3

2– Concentrations of Brines Resulting From Evaporation 

 of Yucca Mountain Unsaturated Zone Waters at 25, 50, 70, 90, and 100 °C 

 [77, 122, 158, 194, and 230 °F] and Total Pressure Corresponding to RHmedian ............ 2-13 

2-11 Calculated Ionic Strength (moles/kg H2O) of Brines Resulting From Evaporation 

 of Yucca Mountain Unsaturated Zone Waters at 25, 50, 70, 90, and 100 °C 

 [77, 122, 158, 194, and 230 °F] and Total Pressure Corresponding to RHmedian ............ 2-14 

2-12 Calculated NO3

–

/Cl– Mole Ratios of Brines Resulting From Evaporation of 

 Yucca Mountain Unsaturated Zone Waters at 25, 50, 70, 90, and 100 °C 

 [77, 122, 158, 194, and 230 °F] and Total Pressure Corresponding to RHmedian ............ 2-15 

2-13 Calculated pHs of Brines Resulting From Evaporation of Yucca Mountain 

 Unsaturated Zone Waters at 50, 70, 90, and 100 °C [122, 158, 194, and 230 °F] 

 and Total Pressure Corresponding to RHmedian............................................................... 2-16 

2-14 Calculated NO3

–

/Cl– Mole Ratios of Brines Resulting From Evaporation of 

 Yucca Mountain Unsaturated Zone Waters at 50, 70, 90, and 100 °C 

 [122, 158, 194, and 230 °F] and Total Pressure Corresponding to RHmedian .................. 2-17 

3-1 Schematic of Curve Derived With the Monte Carlo Approach To Quantify 

 P(Ecorr> Ercrev) ................................................................................................................... 3-5 

3-2 Probability of Ecorr > Ecrev as a Function of pH, Chloride, and Nitrate 

 Concentration and Temperature ...................................................................................... 3-6 

3-3 Localized Corrosion Boundaries (Probability = 0.001) as a Function of Chloride 

 and Nitrate Concentrations and Temperature ................................................................ 3-10 
v 

FIGURES (continued) 

Figure Page 

3-4 Range of Waste Package Temperatures Reproduced From DOE 

 [2008,Figure 2.3.5-33(b)] ............................................................................................... 3-11

3-5 DOE Computation of the Probability of Localized Corrosion as a Function of the 

 Drip Shield Failure Time ................................................................................................. 3-12 
vi 

TABLES 

Table Page 

2-1 Values at Various Temperatures of Pure Water Vapor Pressure (pH2O°), 

 Median Relative Humidity (RHmedian), Lower Bound Relative Humidity 

 (RHlower-bound) and Total Pressure Corresponding to RHmedian or RHlower-bound .................. 2-3 

3-1 Mean, Standard Deviation, and Covariance Matrix for the Parameters ao 

 Through a4...................................................................................................................... 3-1 

3-2 Mean, Standard Deviation, and Covariance Matrix for the Parameters co 

 Through c6 ...................................................................................................................... 3-2 
vii 

ACKNOWLEDGMENTS 

This report was prepared to document work performed by the Center for Nuclear Waste 

Regulatory Analyses (CNWRA®) for the U.S. Nuclear Regulatory Commission (USNRC) under 

Contract No. NRC–02–07–006. The activities reported here were performed on behalf of the 

USNRC Office of Nuclear Material Safety and Safeguards, Division of High-Level Waste 

Repository Safety. This report is an independent product of CNWRA and does not necessarily 

reflect the views or regulatory position of USNRC. 

The authors wish to thank Xihua He for her technical review, Todd Mintz for his programmatic 

review, Lauren Mulverhill for her editorial review, and Arturo Ramos for his secretarial support. 

QUALITY OF DATA, ANALYSES, AND CODE DEVELOPMENT DATA 

DATA: All CNWRA-generated data contained in this report meet quality assurance 

requirements described in the Geosciences and Engineering Division Quality Assurance 

Manual. Sources of other data should be consulted for determining the level of quality of 

those data. 

ANALYSES AND CODES: This report includes results of calculations performed using 

Geochemist’s Workbench® (Bethke and Yeakel, 2007) and OLI Analyzer Studio (OLI Systems, 

Inc., 2010)—commercially available software maintained in accordance with CNWRA Technical 

Operating Procedure (TOP)–018, Development and Control of Scientific and Engineering 

Software. Data reduction, probability computations, and plotting were accomplished using 

Microsoft® Excel® (Microsoft Corporation, 2002), Sigmaplot® (Systat Software, Inc., 2008), and 

Mathematica® (Wolfram Research, Inc., 2011). Work in this report related to the chemistry of 

solutions is documented in Scientific Notebook 930E (Pabalan, 2010). 

References 

Bethke, C.M. and S. Yeakel. “Geochemist’s Workbench® Release 7.0.” Golden, Colorado: 

RockWare, Inc. 2007. 

Microsoft Corporation. “Excel®.” Redland, Washington: Microsoft Corporation. 2002. 

OLI Systems, Inc. “A Guide to Using OLI Analyzer Studio Version 3.1.” Morris Plains, 

New Jersey: OLI Systems, Inc. 2010. 

Pabalan, R.T. “Quantity and Chemistry of Water Contacting Engineered Barriers Integrated 

Subissue.” Scientific Notebook 930E. San Antonio, Texas: CNWRA. 2010. 

Systat Software, Inc. “Sigmaplot® 11.” San Jose, California: Systat Software, Inc. 2008. 

Wolfram Research, Inc. “Mathematica®.” Champaign, IL: Wolfram Research, Inc. 2011. 
1-1 

1 INTRODUCTION 

This report is part of the knowledge management activities for the U.S. Nuclear Regulatory 

Commission high-level waste repository safety program. The report provides a previously 

undocumented methodology to estimate the likelihood of localized corrosion of waste package 

materials in repository settings. A key attribute of the U.S. Department of Energy (DOE) safety 

strategy for the high-level nuclear waste repository it had proposed to construct at Yucca 

Mountain, Nevada, was long-lived waste packages and drip shields (DOE, 2008). The waste 

packages were to consist of an outer container of a highly corrosion-resistant nickel–chromium–

molybdenum alloy (Alloy 22) over an inner container made of Type 316 nuclear grade stainless 

steel. Arched drip shields made of a titanium–palladium alloy (Titanium Grade 7) were to 

extend over the length of the emplacement drifts to cover the waste packages and protect them 

against seepage water and rockfall arising from gradual drift degradation. However, seepage 

water could contact the waste package if drip shields were breached by some mechanism (e.g., 

due to rock loads arising from drift degradation and seismic activity). In the absence of 

mechanical disruption, DOE expected aqueous corrosion to be the primary degradation process 

limiting the life of the waste packages and drip shields. 

The mode and rate of corrosion of the waste package and drip material materials were 

expected to depend on the chemistry of water contacting them and on temperature. Coupled 

thermal-hydrological-chemical processes would significantly alter the chemistry of groundwater 

that seeps into the repository drift and contacts the waste packages and drip shields. 

Radioactive decay can cause waste packages and drip shields to experience transient 

temperatures above the boiling point of pure water for several hundreds to few thousands of 

years. During this transient elevated temperature period, seepage water evaporation could lead 

to the formation of corrosive brines on waste package and drip shield surfaces. 

This report documents a methodology to evaluate the likelihood of environmental conditions 

capable of supporting initiation of localized corrosion of the Alloy 22 waste package material due 

to seepage water evaporation. Another source of water that could enable corrosion processes 

(i.e., the deliquescence of salts present in dusts deposited on the waste package or drip shield 

surface) was considered in a separate evaluation (e.g., Yang, et al., 2011). The approach 

presented in this report accounts for the variability in solution composition, pH, and temperature 

of the Alloy 22 material. The method is based on the concept of corrosion and repassivation 

potentials and their dependence on the chemistry of brines that may evolve from seepage 

water evaporation. 

This report has two main chapters. In Chapter 2, the potential chemistry of solutions in contact 

with waste package and drip shield materials is evaluated based on independent 

thermodynamic simulations. As indicated in a preceding paragraph, seepage water chemistry 

will evolve due to evaporation during the transient elevated temperature period. The chemistry 

of solutions that eventually contact the waste packages and drip shields is a function of the 

initial water composition (i.e., composition of seepage water), air pressure and water content in 

air (i.e., relative humidity), and the temperature of the EBS materials that the solutions are 

postulated to contact. In Chapter 3, the DOE equations for the computation of corrosion and 

repassivation potentials are examined. The range of chemical compositions from Chapter 2 is 

used as input to define conditions under which localized corrosion could arise. Factors 

controlling the <12,000-year localized corrosion window DOE established also are discussed 

in Chapter 3.
2-1 

2 CHEMISTRY OF SOLUTIONS CONTACTING WASTE PACKAGES AND 

DRIP SHIELDS 

The approach to estimate the compositions of solutions that could contact the waste packages 

and drip shields is described as follows. The composition of seepage water is assumed to be 

similar to Yucca Mountain unsaturated zone groundwaters. The Yucca Mountain unsaturated 

zone contains pore water, fracture water, and isolated lenses of perched water. Yang, et al. 

(2003, 1998,1996) measured the chemical compositions of pore water and perched water from 

Yucca Mountain. Perched waters were sampled from boreholes using plastic bailers, and pore 

waters were extracted from borehole core samples using high-pressure uniaxial compression 

techniques. Although there are significant uncertainties in the pore water chemistry data 

resulting from the air drilling of core samples, pore water evaporation, and the compression 

techniques (Yang, et al., 2003, 1998, 1996; Browning, et al., 2000), they provide a valuable 

characterization of Yucca Mountain groundwater chemistry. No measured compositions of 

Yucca Mountain fracture waters are available because these waters are hard to sample. 

However, samples of fracture water have been collected at Rainier Mesa, which is located 

about 50 km [31 mi] north-northeast of Yucca Mountain, and those are similar in composition to 

perched and saturated zone waters collected at Yucca Mountain. The saturated zone 

groundwaters lie below the proposed repository site, and their compositions were not 

considered in this evaluation, although DOE has extensively used samples of this water, 

pumped from the J-13 Well, to define a reference Yucca Mountain groundwater composition for 

experimental studies (e.g., Rosenberg, et al., 1999, 2001). 

For the analysis and for the sake of efficiency, 33 Yucca Mountain unsaturated zone pore water 

compositions were selected from the 156 unsaturated zone compositions available from the 

Yang, et al. (2003, 1998, 1996) compilation. Most of the 156 compositions correspond to pore 

water samples, and a few correspond to perched water samples, which were included to 

expand the range in water chemistry considered in the analysis. The 33 samples were selected 

to represent the range and distribution of the water compositions in the data set and the 3 brine 

types—calcium chloride, alkaline, and neutral—that could result from evaporation.1

 Eleven 

compositions from each water type were used in the analysis. The water compositions in the 

dataset are depicted in a ternary diagram in Figure 2-1. 

Thermodynamic simulations were conducted to determine the chemical evolution of in-drift 

waters resulting from evaporation. The thermodynamic calculations used the OLI Analyzer 

Studio Version 3 code (Gerbino, 2006; OLI Systems, Inc., 2010). The code, using its 

mixed-solvent electrolyte chemistry option, allows for simulation of aqueous chemical systems 

for temperatures up to 300 °C [572 °F], pressures up to 1,500 bar, and concentrations ranging 

from dilute conditions to the pure molten salts or pure acids. Thermodynamic properties 

calculated with this software have been shown to agree very well with experimental data 

(e.g., Gruszkiewicz, et al., 2007). 

 

1

In natural systems, the chemical evolution of evaporating water generally is controlled by the high solubility of salt 

minerals relative to the moderate solubility of calcium sulfate and the low solubility of calcium carbonate minerals—a 

mechanism referred to as chemical divide (Hardie and Eugster, 1970). Thus, evaporation of initially dilute natural 

waters at the Earth’s surface, such as in saline lakes, typically leads to the formation of three brine types: calcium 

chloride brine, alkaline carbonate brine, and high sulfate (also referred to as “neutral”) brine (Spencer, 2000). The 

same brine types could occur within the drifts because in-drift brines are produced by processes similar to those that 

occur at the Earth’s surface. 
2-2 

Figure 2-1. Composition of Yucca Mountain Unsaturated Zone Waters. Circles, 

Squares, and Diamonds Represent the Compositions of Alkaline-, Neutral-, and 

Calcium-Chloride-Type Waters That Were Used as Input to Thermodynamic Evaporation 

Simulations. All the Other Data Were Considered in Determining the Frequency of the 

Three Brine Types Based on the Chemical Divide Concept. Water Composition Data Are 

From Yang, et al. (2003, 1998, 1996). 

Prior to running the evaporation simulations using OLI Analyzer, the analytical data were input 

into Geochemist’s Workbench REACT Version 7.0 and charge balanced. The REACT 

calculations followed the Browning, et al. (2000) approach, which constrained the carbonate 

species by assuming equilibrium with a CO2(g) fugacity equal to 10−2.991 and set O2(g) fugacity 

to 0.7706 atm. REACT was used for the initial calculations because OLI Analyzer does not 

have an option for fixing gas fugacities at specified values. In contrast to the Browning, et al. 

(2000) approach, which set the K+

 concentration to 14 mg/L when the published chemical 

analysis did not have a value for K+

, a value of zero was used in REACT if no K+ value was 

reported. Also, Browning, et al. (2000) did not include F−

 in their study. In the evaluation 

described in this report, F−

 was included in the input file to enable an assessment, discussed in 

the Technical Evaluation Report, of the potential effect of seepage water evaporation on 

titanium drip shield corrosion. An F−

 concentration of 2.18 mg/L, which is an average value for 

J-13 well waters Harrar, et al. (1990) reported, was used in the REACT calculations if no value 

was reported in the Yang, et al. (2003, 1998, 1996) compilation. 

HCO3

-

+ CO3

2-

0.0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1.0

Ca2+

0.0

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

1.0

SO4

2-

0.0

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

1.0

Ca-Cl

Neutral

Alkaline
2-3 

The REACT output values of Na+

, K+, Mg2+, Ca2+, Cl−, NO3

−

, F−, HCO3

−

, SO4

2−

, and SiO2(aq) for 

each of the 33 water samples were input into OLI Analyzer, and evaporation simulation was 

conducted. The OLI Analyzer calculations were done isothermally at 25, 50, 70, 90, and 110 °C 

[77, 122, 158, 194, and 230 °F]. At each temperature, the total pressure, Ptotal, specified for 

each OLI Analyzer isothermal calculation was derived from the following equation 

Ptotal = RHmedian × pH2O°(TWP) (2-1) 

where RHmedian is a calculated median relative humidity at the waste package surface and pH2O°

is the equilibrium vapor pressure of pure water at the waste package surface temperature (TWP). 

Ptotal corresponds to the vapor pressure of the concentrated aqueous solution at equilibrium. In 

other words, the OLI Analyzer calculation proceeds along an increasing degree of evaporation 

until the calculated vapor pressure of solution becomes equal to Ptotal. To derive RHmedian, the 

waste package surface relative humidity was determined from data derived from the 

Total-system Performance Assessment (TPA) code (Leslie, et al., 2007), which was executed in 

Monte Carlo mode to account for uncertainty in thermohydrological rock features. This code 

was used to compute the waste package temperature and relative humidity as functions of time, 

and from these data the median and bounding values were derived. Uncertainty in the relative 

humidity at the waste package surface is the result of spatial variability and uncertainty in 

thermohydrological rock features (Manepally and Fedors, 2003). Values of RHmedian, pH2O°, and 

Ptotal as a function of temperature are listed in Table 2-1. The RHmedian value at 25 °C [77 °F] 

was assumed to be 1.0. Note that only median values of the relative humidity were used in the 

analyses discussed in Chapter 3 of this report. However, to determine the possible effect of 

lower relative humidity on the calculated solution chemistry, additional calculations were done at 

the lower bounding relative humidity (RHlower-bound) determined from the TPA code for 

temperatures of 50, 70, 90, and 110 °C [122, 158, 194, and 230 °F]. RHlower-bound values used in 

the calculations are also listed in Table 2-1. 

In some OLI Analyzer runs, particularly at 90 and 110 °C [194 and 230 °F], using the relative 

humidity values listed in Table 2-1 caused the solution to completely evaporate. In those cases, 

the total pressure specified in the OLI Analyzer input was increased slightly such that the 

equilibrium solution composition retained some amount of aqueous phase. 

Table 2-1. Values at Various Temperatures of Pure Water Vapor Pressure (pH2O°), 

Median Relative Humidity (RHmedian), Lower Bound Relative Humidity (RHlower-bound), and 

Total Pressure Corresponding to RHmedian or RHlower-bound. Ptotal Was Used as Input in the 

OLI Analyzer Calculations. 

TWP pH2O° RHmedian

Ptotal (atm) 

Corresponding 

to RHmedian RHlower-bound

Ptotal (atm) 

Corresponding to 

RHlower-bound

25 °C 

[77 °F] 0.031385 1.0 0.031385 — — 

50 °C 

[122 °F] 0.12207 0.724841 0.088481 0.597626 0.072952 

70°C 

[158 °F] 0.307827 0.618355 0.190346 0.450068 0.138543 

90 °C 

[194 °F] 0.69101 0.549577 0.379763 0.367668 0.254062 

110 °C 

[230 °F] 1.40854 0.45498 0.640858 0.303936 0.428106 
2-4 

The OLI Analyzer simulations allowed determination of the composition ranges of the three 

brine types (calcium chloride, alkaline, neutral) that may form in the emplacement drifts. 

Figures 2-2 to 2-12 show the results calculated at various temperatures using RHmedian values. 

Figure 2-2 shows the calculated pH ranges for the three brine types, whereas Figures 2-3 

to 2-10 show the calculated concentration ranges of Na+

, Mg2+, Ca2+, Cl−, NO3

−

, F−, SO4

2−

, and 

[HCO3

−

+CO3

2−

]. Figures 2-11 and 2-12 show the calculated ionic strength and NO3

−

/Cl− mole 

ratio, respectively, for the three brine types at various temperatures. The calculated ranges of 

pH and NO3

−

/Cl− mole ratio at 50, 70, 90, and 110 °C [122, 158, 194, and 230 °F] using 

RHlower-bound values are shown in Figures 2-13 and 2-14.

To provide a basis for estimating the range of solution compositions for the three brine types, 

the full set of Yang, et al. (2003, 1998, 1996) unsaturated zone water chemistry data was used 

jointly with the Hardie and Eugster (1970) chemical divide concept. Of the 156 compositions 

(all depicted in Figure 2-1), 8, 24, and 68 percent form calcium-chloride-, neutral-, and 

alkaline-type brines, respectively. 

The plots in Figures 2-2 to 2-14 define a reasonable range of solution compositions that could 

arise in case seepage water evaporated and formed a solution in contact with EBS materials, 

such as titanium drip shields or Alloy 22 waste packages. The ranges of solution compositions 

in Figures 2-2 to 2-14 are presented in the form of box and whiskers plots. In these plots, the 

left and right sides of each box are the 25th and 75th percentiles, and the line inside the box is 

the median value. The whiskers are the 10th and 90th percentiles, and the points beyond the 

whiskers are outliers. The solution compositions were derived assuming thermodynamic 

equilibrium is achieved. This is an important point that merits additional discussion. If seepage 

water accumulated, for example, on the waste package surface, the solution would evaporate 

and evolve toward a solution composition with a water pressure in equilibrium with the 

environmental water pressure. If the relative humidity was low, the solution would evolve 

toward a concentrated system (i.e., a system of low water activity). Conversely, if the relative 

humidity was high, the solution would evolve toward a diluted system (i.e., a system of high 

water activity). In the analysis presented in this report, the relative humidity is assumed 

controlled by the temperature of the drift wall (the drift wall rock is assumed water saturated) 

and the temperature of the waste package surface. For a given waste package temperature, 

using the TPA Code Version 5.1, a range of reasonable relative humidities was estimated. It is 

reasonable to assume that the relative humidity is an independent variable that controls the 

equilibrium solution composition. 

The range of water chemistries shown in Figures 2-2 to 2-14 are considered in Chapter 3 to 

establish whether solutions could arise that could lead to localized corrosion of Alloy 22. The 

relative humidity value adopted in the localized corrosion evaluation discussed in Chapter 3 is 

the median value shown in Table 2-1, although the effect of lower relative humidity causing a 

decrease in solution pH (e.g., compare Figure 2-13 with Figure 2-2) also is considered. 
2-5 

T = 110 °C [230 °F] T = 90 °C [194 °F] 

T = 70 °C [158 °F] T = 50 °C [122 °F] 

T = 25 °C [77 °F] 

Figure 2-2. Calculated pHs of Brines Resulting From Evaporation of Yucca Mountain 

Unsaturated Zone Waters at 25, 50, 70, 90, and 110 °C [77, 122, 158, 194, and 230 °F] and 

Total Pressure Corresponding to RHmedian. In the Box Plots Shown in Figures 2-2 to 2-14, 

the Left and Right Sides of Each Box Are the 25th and 75th Percentiles, Respectively, and 

the Line Inside the Box Is the Median Value. The Whiskers Are the 90th and 

10th Percentiles, and the Solid Circles Are Outliers. 

pH

5 6 7 8 9 10 11 12

Brine Type

Ca-Cl

Neutral

Alkaline

pH

5 6 7 8 9 10 11 12

Brine Type

Ca-Cl

Neutral

Alkaline

pH

6 7 8 9 10 11 12

Brine Type

Ca-Cl

Neutral

Alkaline

pH

7 8 9 10 11 12

Brine Type

Ca-Cl

Neutral

Alkaline

pH

7.0 7.5 8.0 8.5 9.0 9.5 10.0

Brine Type

Ca-Cl

Neutral

Alkaline
2-6 

T = 110 °C [230 °F] T = 90 °C [194 °F] 

T = 70 °C [158 °F] T = 50 °C [122 °F] 

T = 25 °C [77 °F] 

Figure 2-3. Calculated Na+

 Concentrations of Brines Resulting From 

Evaporation of Yucca Mountain Unsaturated Zone Waters at 25, 50, 70, 90, and 110 °C 

[77, 122, 158, 194, and 230 °F] and Total Pressure Corresponding to RHmedian 

Na+ (moles/kg H2O)

0 5 10 15 20 25 30

Brine Type

Ca-Cl

Neutral

Alkaline

Na+ (moles/kg H2O)

0 5 10 15 20 25

Brine Type

Ca-Cl

Neutral

Alkaline

Na+ (moles/kg H2O)

0 2 4 6 8 10 12 14 16

Brine Type

Ca-Cl

Neutral

Alkaline

Na+ (moles/kg H2O)

0 2 4 6 8 10

Brine Type

Ca-Cl

Neutral

Alkaline

Na+ (moles/kg H2O)

0.000 0.002 0.004 0.006 0.008 0.010 0.012 0.014 0.016 0.018 0.020

Brine Type

Ca-Cl

Neutral

Alkaline
2-7 

T = 110 °C [230 °F] T = 90 °C [194 °F] 

T = 70 °C [158 °F] T = 50 °C [122 °F] 

T = 25 °C [77 °F] 

Figure 2-4. Calculated Mg2+ Concentrations of Brines Resulting From 

Evaporation of Yucca Mountain Unsaturated Zone Waters at 25, 50, 70, 90, and 110 °C 

[77, 122, 158, 194, and 230 °F] and Total Pressure Corresponding to RHmedian

Mg2+ (moles/kg H2O)

10-11 10-10 10-9 10-8 10-7 10-6 10-5 10-4 10-3 10-2 10-1 100 101 102

Brine Type

Ca-Cl

Neutral

Alkaline

Mg2+ (moles/kg H2O)

10-11 10-10 10-9 10-8 10-7 10-6 10-5 10-4 10-3 10-2 10-1 100 101

Brine Type

Ca-Cl

Neutral

Alkaline

Mg2+ (moles/kg H2O)

10-11 10-10 10-9 10-8 10-7 10-6 10-5 10-4 10-3 10-2 10-1 100 101 102

Brine Type

Ca-Cl

Neutral

Alkaline

Mg2+ (moles/kg H2O)

10-11 10-10 10-9 10-8 10-7 10-6 10-5 10-4 10-3 10-2 10-1 100 101

Brine Type

Ca-Cl

Neutral

Alkaline

Mg2+ (moles/kg H2O)

10-11 10-10 10-9 10-8 10-7 10-6 10-5 10-4 10-3 10-2

Brine Type

Ca-Cl

Neutral

Alkaline
2-8 

T = 110 °C [230 °F] T = 90 °C [194 °F] 

T = 70 °C [158 °F] T = 50 °C [122 °F] 

T = 25 °C [77 °F] 

Figure 2-5. Calculated Ca2+ Concentrations of Brines Resulting From 

Evaporation of Yucca Mountain Unsaturated Zone Waters at 25, 50, 70, 90, and 110 °C 

[77, 122, 158, 194, and 230 °F] and Total Pressure Corresponding to RHmedian

Ca2+ (moles/kg H2O)

10-8 10-7 10-6 10-5 10-4 10-3 10-2 10-1 100 101 102

Brine Type

Ca-Cl

Neutral

Alkaline

Ca2+ (moles/kg H2O)

10-8 10-7 10-6 10-5 10-4 10-3 10-2 10-1 100 101 102

Brine Type

Ca-Cl

Neutral

Alkaline

Ca2+ (moles/kg H2O)

10-8 10-7 10-6 10-5 10-4 10-3 10-2 10-1 100 101

Brine Type

Ca-Cl

Neutral

Alkaline

Ca2+ (moles/kg H2O)

10-7 10-6 10-5 10-4 10-3 10-2 10-1 100 101

Brine Type

Ca-Cl

Neutral

Alkaline

Ca2+ (moles/kg H2O)

10-6 10-5 10-4 10-3 10-2

Brine Type

Ca-Cl

Neutral

Alkaline
2-9 

T = 110 °C [230 °F] T = 90 °C [194 °F] 

T = 70 °C [158 °F] T = 50 °C [122 °F] 

T = 25 °C [77 °F] 

Figure 2-6. Calculated Cl−

 Concentrations of Brines Resulting From 

Evaporation of Yucca Mountain Unsaturated Zone Waters at 25, 50, 70, 90, and 110 °C 

[77, 122, 158, 194, and 230 °F] and Total Pressure Corresponding to RHmedian

Cl- (moles/kg H2O)

0 2 4 6 8 10 12 14

Brine Type

Ca-Cl

Neutral

Alkaline

Cl- (moles/kg H2O)

0 2 4 6 8 10 12

Brine Type

Ca-Cl

Neutral

Alkaline

Cl- (moles/kg H2O)

0 2 4 6 8 10

Brine Type

Ca-Cl

Neutral

Alkaline

Cl- (moles/kg H2O)

02468

Brine Type

Ca-Cl

Neutral

Alkaline

Cl- (moles/kg H2O)

0.000 0.001 0.002 0.003 0.004 0.005 0.006

Brine Type

Ca-Cl

Neutral

Alkaline
2-10 

T = 110 °C [230 °F] T = 90 °C [194 °F] 

T = 70 °C [158 °F] T = 50 °C [122 °F] 

T = 25 °C [°F] 

Figure 2-7. Calculated NO3

−

 Concentrations of Brines Resulting From 

Evaporation of Yucca Mountain Unsaturated Zone Waters at 25, 50, 70, 90, and 110 °C 

[77, 122, 158, 194, and 230 °F] and Total Pressure Corresponding to RHmedian

NO3

-

 (moles/kg H2O)

0.01 0.1 1 10 100

Brine Type

Ca-Cl

Neutral

Alkaline

NO3

-

 (moles/kg H2O)

0.01 0.1 1 10 100

Brine Type

Ca-Cl

Neutral

Alkaline

NO3

-

 (moles/kg H2O)

0.01 0.1 1 10 100

Brine Type

Ca-Cl

Neutral

Alkaline

NO3

-

 (moles/kg H2O)

0.01 0.1 1 10

Brine Type

Ca-Cl

Neutral

Alkaline

NO3

-

 (moles/kg H2O)

1e-6 1e-5 1e-4 1e-3 1e-2

Brine Type

Ca-Cl

Neutral

Alkaline
2-11 

T = 110 °C [230 °F] T = 90 °C 194 °F] 

T = 70 °C [158 °F] T = 50 °C [122 °F] 

T = 25 °C [77 °F] 

Figure 2-8. Calculated F−

 Concentrations of Brines Resulting From 

Evaporation of Yucca Mountain Unsaturated Zone Waters at 25, 50, 70, 90, and 110 °C 

[77, 122, 158, 194, and 230 °F] and Total Pressure Corresponding to RHmedian

F- (moles/kg H2O)

10-7 10-6 10-5 10-4 10-3 10-2 10-1 100

Brine Type

Ca-Cl

Neutral

Alkaline

F- (moles/kg H2O)

10-7 10-6 10-5 10-4 10-3 10-2 10-1 100

Brine Type

Ca-Cl

Neutral

Alkaline

F- (moles/kg H2O)

10-7 10-6 10-5 10-4 10-3 10-2 10-1 100

Brine Type

Ca-Cl

Neutral

Alkaline

F- (moles/kg H2O)

10-7 10-6 10-5 10-4 10-3 10-2 10-1 100

Brine Type

Ca-Cl

Neutral

Alkaline

F- (moles/kg H2O)

10-7 10-6 10-5 10-4 10-3 10-2 10-1 100

Brine Type

Ca-Cl

Neutral

Alkaline
2-12 

T = 110 °C [230 °F] T = 90 °C 194 °F] 

T = 70 °C [158 °F] T = 50 °C [122 °F] 

T = 25 °C [77 °F] 

Figure 2-9. Calculated SO4

2−

 Concentrations of Brines Resulting From 

Evaporation of Yucca Mountain Unsaturated Zone Waters at 25, 50, 70, 90, and 110 °C 

[77, 122, 158, 194, and 230 °F] and Total Pressure Corresponding to RHmedian

SO4

-2 (moles/kg H2O)

10-8 10-7 10-6 10-5 10-4 10-3 10-2 10-1 100

Brine Type

Ca-Cl

Neutral

Alkaline

SO4

-2 (moles/kg H2O)

10-6 10-5 10-4 10-3 10-2 10-1 100

Brine Type

Ca-Cl

Neutral

Alkaline

SO4

-2 (moles/kg H2O)

10-5 10-4 10-3 10-2 10-1 100

Brine Type

Ca-Cl

Neutral

Alkaline

SO4

-2 (moles/kg H2O)

10-4 10-3 10-2 10-1 100

Brine Type

Ca-Cl

Neutral

Alkaline

SO4

-2 (moles/kg H2O)

10-5 10-4 10-3 10-2

Brine Type

Ca-Cl

Neutral

Alkaline
2-13 

T = 110 °C [230 °F] T = 90 °C [194 °F] 

T = 70 °C [158 °F] T = 50 °C [122 °F] 

T = 25 °C [77 °F] 

Figure 2-10. Calculated HCO3

−

 + CO3

2−

 Concentrations of Brines Resulting From 

Evaporation of Yucca Mountain Unsaturated Zone Waters at 25, 50, 70, 90, and 110 °C 

[77, 122, 158, 194, and 230 °F] and Total Pressure Corresponding to RHmedian

[HCO3

-

+CO3

2-] (moles/kg H2O)

10-11 10-10 10-9 10-8 10-7 10-6 10-5 10-4 10-3 10-2 10-1 100 101

Brine Type

Ca-Cl

Neutral

Alkaline

[HCO3

-

+CO3

2-] (moles/kg H2O)

10-10 10-9 10-8 10-7 10-6 10-5 10-4 10-3 10-2 10-1 100 101

Brine Type

Ca-Cl

Neutral

Alkaline

[HCO3

-

+CO3

2-] (moles/kg H2O)

1e-9 1e-8 1e-7 1e-6 1e-5 1e-4 1e-3 1e-2 1e-1 1e+0 1e+1

Brine Type

Ca-Cl

Neutral

Alkaline

[HCO3

-

+CO3

2-] (moles/kg H2O)

10-8 10-7 10-6 10-5 10-4 10-3 10-2 10-1 100 101

Brine Type

Ca-Cl

Neutral

Alkaline

[HCO3

-

+CO3

2-] (moles/kg H2O)

10-5 10-4 10-3 10-2 10-1

Brine Type

Ca-Cl

Neutral

Alkaline
2-14 

T = 110 °C [230 °F] T = 90 °C [194 °F] 

T = 70 °C [158 °F] T = 50 °C [122 °F] 

T = 25 °C [77 °F] 

Figure 2-11. Calculated Ionic Strength (moles/kg H2O) of Brines Resulting From 

Evaporation of Yucca Mountain Unsaturated Zone Waters at 25, 50, 70, 90, and 110 °C 

[77, 122, 158, 194, and 230 °F] and Total Pressure Corresponding to RHmedian

Ionic Strength

15 20 25 30 35

Brine Type

Ca-Cl

Neutral

Alkaline

Ionic Strength

13 14 15 16 17 18 19 20 21

Brine Type

Ca-Cl

Neutral

Alkaline

Ionic Strength

11.5 12.0 12.5 13.0 13.5 14.0 14.5 15.0

Brine Type

Ca-Cl

Neutral

Alkaline

Ionic Strength

7 8 9 10 11 12 13 14 15

Brine Type

Ca-Cl

Neutral

Alkaline

Ionic Strength

0.000 0.005 0.010 0.015 0.020 0.025 0.030 0.035

Brine Type

Ca-Cl

Neutral

Alkaline
2-15 

T = 110 °C [230 °F] T = 90 °C [194 °F] 

T = 70 °C 158 °F] T = 50 °C [122 °F] 

T = 25 °C 77 °F] 

Figure 2-12. Calculated NO3

−

/Cl− Mole Ratios of Brines Resulting From 

Evaporation of Yucca Mountain Unsaturated Zone Waters at 25, 50, 70, 90, and 110 °C 

[77, 122, 158, 194, and 230 °F] and Total Pressure Corresponding to RHmedian

NO3

-

/Cl10-3 10-2 10-1 100 101 102

Brine Type

Ca-Cl

Neutral

Alkaline

NO3

-

/Cl10-3 10-2 10-1 100 101

Brine Type

Ca-Cl

Neutral

Alkaline

NO3

-

/Cl10-3 10-2 10-1 100 101

Brine Type

Ca-Cl

Neutral

Alkaline

NO3

-

/Cl10-3 10-2 10-1 100 101

Brine Type

Ca-Cl

Neutral

Alkaline

NO3

-

/Cl10-3 10-2 10-1 100 101

Brine Type

Ca-Cl

Neutral

Alkaline
2-16 

T = 110 °C [230 °F] T = 90 °C [194 °F] 

T = 70 °C [158 °F] T = 50 °C [122 °F] 

Figure 2-13. Calculated pHs of Brines Resulting From Evaporation of Yucca Mountain 

Unsaturated Zone Waters at 50, 70, 90, and 110 °C [122, 158, 194, and 230 °F] and Total 

Pressure Corresponding to RHlower-bound

In the DOE localized corrosion model for Alloy 22 described in Chapter 3, key electric 

potential equations are defined as functions of temperature, pH, chloride concentration, and 

nitrate-to-chloride ratio. The effect of other oxyanions, such as sulfate and carbonate, was 

ignored in the model. This approach is reasonable because these anions are known localized 

corrosion inhibitors (e.g., Pensado and Pabalan, 2008). Ignoring their presence in a corrosion 

model would tend to overestimate the frequency of localized corrosion. 

pH

4 6 8 10 12 14

Brine Type

Ca-Cl

Neutral

Alkaline

pH

5 6 7 8 9 10 11 12

Brine Type

Ca-Cl

Neutral

Alkaline

pH

6 7 8 9 10 11 12

Brine Type

Ca-Cl

Neutral

Alkaline

pH

6 7 8 9 10 11 12

Brine Type

Ca-Cl

Neutral

Alkaline
2-17 

T = 110 °C [230 °F] T = 90 °C [194 °F] 

T = 70 °C [158 °F] T = 50 °C [122 °F] 

Figure 2-14. Calculated NO3

−

/Cl− Mole Ratios of Brines Resulting From 

Evaporation of Yucca Mountain Unsaturated Zone Waters at 50, 70, 90, and 110 °C 

[122, 158, 194, and 230 °F] and Total Pressure Corresponding to RHlower-bound

NO3

-

/Cl10-3 10-2 10-1 100 101 102 103

Brine Type

Ca-Cl

Neutral

Alkaline

NO3

-

/Cl10-3 10-2 10-1 100 101 102

Brine Type

Ca-Cl

Neutral

Alkaline

NO3

-

/Cl10-4 10-3 10-2 10-1 100 101 102

Brine Type

Ca-Cl

Neutral

Alkaline

NO3

-

/Cl10-3 10-2 10-1 100 101

Brine Type

Ca-Cl

Neutral

Alkaline
3-1 

3 ASSESSMENT OF DOE LOCALIZED CORROSION MODEL 

In this chapter the U.S. Department of Energy (DOE) model for the initiation of localized 

corrosion in Alloy 22 as a function of the chemical composition of waters in a Yucca Mountain 

geological repository setting is analyzed (SNL, 2007). DOE concluded that localized corrosion 

of waste packages made of Alloy 22 is unlikely if the drip shield protects the waste package 

from seepage during at least 12,000 years (DOE, 2009a, Enclosure 1). This report presents a 

methodology to estimate the likelihood of localized corrosion of waste package materials using 

the equations DOE developed for corrosion potential and critical potentials. DOE adopted a 

critical potential approach to identify conditions that could lead to localized corrosion in Alloy 22. 

DOE stated that localized corrosion could occur if the corrosion potential, Ecorr, exceeded a 

critical potential, which DOE defined as the repassivation potential, Ercrev. The corrosion 

potential is a function of the chemical environment, kinetic rates controlling the speed or rate of 

corrosion, and the temperature. The repassivation potential is a property of the material, but it 

can also be affected by chemical conditions and temperature. Based on electrochemical tests 

under a range of chemical environments, DOE derived (via curve fitting) the following empirical 

equations to compute the repassivation and the corrosion potentials: 

 

[ ] [ ]

[ ] [ ] rcrev o a T Cl rcrev Cl

NO E = a + a T + a Cl + a + + ε −

−

−

−

4

3

1 2 3 ln (3-1)

and 

 

[ ]

[ ]

[ ]

[ ]

[ ]

[ ] [ ] corr o pH Cl corr c

Cl

NO

c pH Cl

NO

c T

Cl

NO E = c + c T + c pH + c + + + + ε −

−

−

−

−

−

−

6 ln 35

3

4

3

1 2 3 (3-2)

where 

⎯ Ercrev and Ecorr are potentials in units of mV versus saturated calomel electrode [mVSCE] 

⎯ ao through a4 and co through c6 are fitting constants (see Tables 3-1 and 3-2) 

⎯ T is the temperature in Celsius units 

Table 3-1. Mean, Standard Deviation, and Covariance Matrix for the Parameters ao Through a4*

ao a1 a2 a3 a4

Mean 190.242 −3.008 −46.8 535.625 0.061 

Sdev 18.373 0.225 3.126 26.14 0.01 

Covariance Matrix 

ao a1 a2 a3 a4

ao 337.6 −3.909 −9.31 82.36 0.03559 

a1 −3.909 0.05077 0.09271 −1.202 −0.000831 

a2 −9.31 0.09271 9.77 1.93 −0.02048 

a3 82.36 −1.202 1.93 683.3 −0.0279 

a4 0.03559 −0.000831 −0.02048 −0.0279 0.0001011 

*SNL. “General Corrosion and Localized Corrosion of Waste Package Outer Barrier.” ANL–EBS–MD–000003. 

Rev. 03. ACN 01, ERD 01. Las Vegas, Nevada: Sandia National Laboratories. 2007. 
3-2 

Table 3-2. Mean, Standard Deviation, and Covariance Matrix for the Parameters co Through c6*

co c1 c2 c3 c4 c5 c6

Mean 1051.219 −3.024 −155.976 −1352.04 10.875 137.856 −8.498 

Sdev 119.774 0.977 11.495 252.224 1.89 23.158 0.801 

Covariance Matrix 

co c1 c2 c3 c4 c5 c6

co 14350 −103.1 −915.2 −27620 180.2 1884 −16.6 

c1 −103.1 0.9539 2.77 184.6 −1.519 −6.817 −0.07543 

c2 −915.2 2.77 132.1 1971 −6.909 −251.5 4.409 

c3 −27620 184.6 1971 63620 −422.3 −4107 59.59 

c4 180.2 −1.519 −6.909 −422.3 3.573 13.37 −0.2622 

c5 1884 −6.817 −251.5 −4107 13.37 536.3 −6.697 

c6 −16.6 −0.07543 4.409 59.59 −0.2622 −6.697 0.6418 

*SNL. “General Corrosion and Localized Corrosion of Waste Package Outer Barrier.” ANL–EBS–MD–000003. 

Rev. 03. ACN 01, ERD 01. Las Vegas, Nevada: Sandia National Laboratories. 2007.

⎯ [Cl−

] is the chloride ion concentration in molal units [mol/kg H2O] 

⎯ [NO3

−

] is the nitrate ion concentration in molal units [mol/kg H2O] 

⎯ εrcrev and εcorr are terms to correct for fitting errors 

DOE accounted for fitting uncertainty by describing the parameters a1 through c6 as correlated 

random variates following normal distributions. The parameters of those distributions are 

provided in Tables 3-1 and 3-2. The error terms εrcrev and εcorr are terms independent of the 

fitting parameters, assumed to follow normal distributions with zero means and standard 

deviations equal to 45.055 mV and 85.265 mV, respectively. 

In the performance assessment analysis, to account for fitting uncertainty, DOE sampled 

5-tuples (ao, a1, a2, a3, a4) and 7-tuples (co, c1, c2, c3, c4, c5, c6) from multinormal distributions 

with means, standard deviations, and covariance matrices as in Tables 3-1 and 3-2, and used 

those N-tuples to compute Ercrev and Ecorr using Eqs. (3-1) and (3-2) in multiple-realization 

analyses. DOE considered the standard deviations in the error terms εrcrev and εcorr 

(45.055 mV and 85.265 mV) to define truncation boundaries (± 2 standard deviations around 

expected values of Ercrev and Ecorr) for the repassivation and corrosion potentials. DOE imposed 

the ± 2 standard deviations bounds to avoid nonphysical situations that could arise due to the 

mathematical sampling algorithms. More explicitly, the corrosion and repassivation potentials 

were computed as 

Ercrev A Ea = ⋅ (3-3)

and 

Ecorr C Ec = ⋅ (3-4)
3-3 

where the operator “⋅ ” is a scalar dot product and the vectors A, Ea, C, and Ec are defined as 

( ) A = ao a1 a2 a3 a4 (3-5)

[ ] [ ]

[ ] [ ]















= −

−

−

− T Cl

Cl

NO T Cl a

3 E 1 ln (3-6)

( ) 1 2 3 4 5 6 c c c c c c c C = o (3-7)

[ ]

[ ]

[ ]

[ ]

[ ]

[ ] [ ]















= −

−

−

−

−

−

−

pH Cl

Cl

NO pH ClNO T

Cl

NO c 1 T pH ln 3 3 3 E (3-8)

The vectors A and C are tuples obtained by randomly sampling multinormal distributions with 

means and covariance matrices as in Tables 3-1 and 3-2. If Am and Cm are the tuples with the 

mean values (second row in Tables 3-1 and 3-2), and Ma and Mc are covariance matrices in 

Tables 3-1 and 3-2, bounds for the repassivation and corrosion potential were defined by the 

following inequalities 

2 − ⋅ ≤ 2 + 45.055 T Ercrev Am Ea Ea Ma Ea (3-9)

and 

2 − ⋅ ≤ 2 + 85.265 T

Ecorr Cm Ec Ec Mc Ec (3-10)

For those values of A and C for which the previous inequalities were not satisfied, the 

repassivation and the corrosion potentials were computed as 

2 = ⋅ ± 2 + 45.055 T Ercrev A m Ea Ea Ma Ea (3-11)

and 

2 ≤ ⋅ ± 2 + 85.265 T Ecorr Cm Ec Ec Mc Ec (3-12)

The selection of the + or – signs in the previous equations depends on whether the computed 

value of the potential computed from Eqs. (3-3) and (3-4) lies too far above or below the 

expected values, A m Ea ⋅ or C m Ea ⋅ . 

This detailed description of the approach adopted to compute the repassivation and corrosion 

potential is provided because it is very common to make the mistake of only analyzing the 

equations with the best fit parameters (mean row in Tables 3-1 and 3-2) and ignoring standard 

deviations and covariance matrices. As described in the previous paragraphs, DOE 

implemented a more complex algorithm to propagate fitting uncertainty. 

DOE defined the repassivation and corrosion potentials as functions of the similar independent 

variables. This causes Ercrev and Ecorr to be heavily correlated. For example, using the best fit 
3-4 

values for the parameters ao through c6 (mean rows in Tables 3-1 and 3-2) and Eqs. (3-1) and 

(3-2), Ercrev can be defined as a function of Ecorr, T, pH, and [Cl−

] as 

[ ] [ ]

[ ]

pH T

E pH T pH Cl

E T T Cl Cl

corr

rcrev

1352.04 137.856 10.875

563059 535.625 83544.6 1619.73 4551.74 ln

190.242 3.008 0.061 46.8ln

− −

− − − −

= − + − +

−

− −

(3-13)

Ercrev and Ecorr are linearly related, and this is true for any selection of values of the fitting 

parameters ao through c6. Whether the Ercrev increases or decreases with increasing values or 

Ecorr depends on whether the denominator on the second term in Eq. (3-13) is negative or 

positive. Given the strong correlation between these electric potentials, analyses of Eqs. (3-1) 

and (3-2) aimed at independently delineating the environmental conditions that cause Ercrev or 

Ecorr to attain high or low values do not provide a complete picture of conditions conducive to 

localized corrosion. In the analysis presented in this report, both equations are simultaneously 

considered for particular water chemistries and temperatures to establish whether localized 

corrosion could occur under those conditions. 

Several approaches were considered to establish ranges of chemical conditions and 

temperatures that could lead to localized corrosion of Alloy 22. For example, equations similar 

to Eq. (3-13) were derived and trends and slopes with respect to the independent variables 

were analyzed. Also, the limits defined by Eqs. (3-11) and (3-12) were examined. The 

objective was to derive ranges of environmental conditions under which Ecorr > Ercrev. Those 

approaches were cumbersome and lacked generality, as they were dependent on values 

assigned to the fitting parameters ao through a6. Therefore, those approaches are not further 

discussed. In this report, general conclusions were attained by fixing the environmental 

conditions {e.g., T = 90 °C, [194 °F] [NO3−

]/[Cl−] = 0.2, [Cl−] = 1 molal, pH = 8} and quantifying 

the probability that Ecorr > Ercrev for those particular conditions. The probability that Ecorr > Ercrev

for a particular water chemistry and temperature {e.g., T = 90 °C [194 °F], [NO3−

]/[Cl−] = 0.2, 

[Cl−

] = 1 molal, pH = 8} was quantified by a Monte Carlo analysis. In each realization, a 5-tuple 

(ao, a1, a2, a3, a4) and a 7-tuple (co, c1, c2, c3, c4, c5, c6) were sampled from multinormal 

distributions with means, standard deviations, and covariance matrices as in Tables 3-1 and 3-2 

(multinormal sampling functions are available in scientific software such as Mathematica®). 

With those N-tuples, the repassivation and corrosion potentials were computed. A total of 

10,000 realizations were implemented for each environmental condition. The probability for 

localized corrosion was quantified as the number of realizations for which Ecorr > Ercrev

normalized by the total number of realizations (i.e., 10,000). Figure 3-1 shows a schematic plot 

that corresponds to this approach. The probability P(Ecorr>Ercrev) is computed as a function of 

pH for a fixed value of T, [NO3−

]/[Cl−], and [Cl−] and results in a curve as in Figure 3-1. When 

the pH is low enough, it is more likely that Ecorr > Ercrev. As the pH increases, the probability 

decreases and it eventually becomes negligible. 

Figure 3-2 shows families of curves for temperatures ranging from 20 to 110 °C [68 to 230 °F], 

[Cl−

] from 0.0005 to 20 molal, [NO3

−

]/[Cl−] from 0 to 10, and pH from 1.9 to 10. Only discrete 

values in those ranges were selected; however, the discrete values allow for general 

conclusions by interpolation of the trends. All the curve families exhibit a similar shape as 

Figure 3-1. The exception is curves for low [Cl−

] and high [NO3

−

]/[Cl−] ratios, which appear to 

imply that at low chloride concentrations, the probability of localized corrosion increases with 

increasing pH. The meaning of the trends is discussed later in this report. 
3-5 

 Figure 3-1. Schematic of Curve Derived With the Monte Carlo Approach To Quantify 

P(Ecorr>Ercrev) 

The different colors represent variation in temperature from 20 °C [68 °F] (blue) to 110 °C 

[230 °F] (red) in discrete increments of 10 °C [18 °F]. As temperature increases, the probability 

versus pH curves shift to the right. In other words, as the temperature decreases, lower pH 

solutions are needed to induce localized corrosion. This trend is consistent with empirical 

knowledge. The trend changes in the limit of low nitrate-to-chloride ratio and high chloride 

[see Figure 3-2(c)]. When the chloride concentration is high (~10 molal) and the nitrate 

concentration is negligible, the pH of solutions causing localized corrosion decreases with 

increasing temperature. The other exception to the general trend occurs in the limit of high 

nitrate-to-chloride ratio (>0.5) and low chloride concentration [e.g., Figure 3-2(m), (p), (t)]. This 

exception is discussed later in this report. In general, for most of the solutions of interest, as the 

temperature decreases, localized corrosion requires more acidic or lower pH solutions. 

The effect of increasing ratio in nitrate to chloride can be seen by sweeping the plots across a 

column, from the top down. As the ratio increases, in general, the plots are shifted toward the 

left, meaning that solutions of lower pH are needed to induce localized corrosion as [NO3

−

]/[Cl−] 

increases. This trend is intuitive because [NO3

−

] is a known localized corrosion inhibitor in 

Alloy 22. This trend is broken at high [NO3

−

]/[Cl−] and low [Cl−] [e.g., Figure 3-2(m), (p), (t)]. In 

low [Cl−

] solutions, it appears that adding [NO3

−

] to the solution would enhance the likelihood of 

localized corrosion at high enough temperatures. It is hypothesized that this is mostly a 

mathematical artifact, because such low [Cl−

] environments are not likely to exist at elevated 

temperatures. For example, in Figure 2-6, [Cl−

] exceeds 1 molal for all temperatures above 

50 °C [122 °F]. Low chloride concentrations were computed only at the ambient temperature. 

Therefore, the curves with T >50 °C [122 °F] in Figure 3-2(m), (p), (t) represent nonphysical 

conditions {not possible to have a solution in thermodynamic equilibrium with [Cl−

] = 0.0005 

molal at those temperatures, under the pressure and partial water pressure conditions defined 

in Chapter 2}. The low temperature curves {e.g., T = 20 °C [68 °F]} for which [Cl−

] = 0.0005 

molal is feasible lie on the pH axis and cannot be seen, because they are overlapped by the 

higher temperature curves in Figure 3-2(m), (p), (t). The curves T = 20 °C [68 °F], [Cl−

] = 0.0005 

molal, and [NO3

−

]/[Cl−] >0.5 support the empirical notion that localized corrosion is unlikely 

under such conditions. 

In Figure 3-2, the effect of increasing chloride concentration can be visualized by scanning the 

plots from left to right, across a row. Increasing chloride has the effect of shifting probability 

versus pH curves toward the left. It means that lower pH solutions are needed to cause 

localized corrosion in Alloy 22 in solutions with high chloride concentration. This trend is 

counterintuitive. The exception to this general behavior is the case of low chloride and high 

0

1

P(Ecorr > 

Ercrev)

pH

Fixed

[NO3

−]/[Cl−], [Cl−], T

0

1

P(Ecorr > 

Ercrev)

pH

Fixed

[NO3

−]/[Cl−], [Cl−], T
 3-6 

(a) (b) (c) (d) (e) (f) 

(g) (h) (i) 

Figure 3-2. Probability of Ecorr > Ercrev as a Function of pH, Chloride, and Nitrate Concentration and 
 3-7 (j) (k) (l) (m) (n) (o) 

(p) (q) (r) 

Figure 3-2. Probability of Ecorr > Ercrev as a Function of pH, Chloride, and Nitrate Concentr

and Temperature (continued)
 3-8 (t) (u) (v) 

Figure 3-2. Probability of 

Ecorr > 

Ercrev as a Function of pH, Chloride, and Nitrate Concentr

and Temperature (continued)
3-9 

nitrate-to-chloride ratios [Figure 3-2(m), (p), (t)], which was analyzed in the previous paragraph 

and not discussed further. There is a physical basis for the nonintuitive behavior. As chloride is 

added to the system, it displaces oxygen from the solution causing the corrosion potential to 

decrease. The coefficient c6 in Eq. (3-2) is negative, which means that for constant values of T, 

pH, and [NO3

−

]/[Cl−], Ecorr is a decreasing function of [Cl−]. Most likely, as previously stated, the 

cause for this decreasing trend is this displacement of oxygen and other oxidants in the solution 

by increasing chloride concentrations. Ercrev is also expected to be a decreasing function of 

[Cl−

]; however, Ecorr decreases faster than Ercrev with increasing [Cl−]. The final outcome of 

those competing trends is the nonintuitive result that more acidic solutions are needed to 

induce localized corrosion in solutions with increasing [Cl−

]. Although nonintuitive, the 

empirical data from which Eqs. (3-1) and (3-2) were derived support this conclusion 

(DOE, 2009b, Enclosure 8). 

This chapter concludes with a summary of conditions under which, according to Eqs. (3-1) and 

(3-2), the values in Tables 3-1 and 3-2, and the thermodynamic analyses in Chapter 2, localized 

corrosion could occur. For [NO3

−

]/[Cl−] ≥ 0.5, localized corrosion could occur at T >80 °C 

[176 °F]. Note that in Figure 3-2(k), (l), (n), (o), (q), (r), (u), (v), the vertical dotted line is drawn 

at pH = 5. The pHs of most solutions considered in Chapter 2 for the median relative humidity 

case are greater than 5 (Figures 2-6 and 2-13). All of the curves for T ≤ 80 °C [176 °F] lie to the 

left of the line pH = 5. Therefore, none of the solutions considered in Chapter 2 with T ≤ 80 °C 

[176 °F] and [NO3

−

]/[Cl−] ≥ 0.5 can cause localized corrosion. Localized corrosion, on the other 

hand, might be feasible for T >80 °C [176 °F], even at those high [NO3

−

]/[Cl−] ratios. 

For lower [NO3

−

]/[Cl−] ratios (<0.5), 0.001 probability boundaries were computed with the data in 

Figure 3-2 for discrete values of [Cl−

] (0.0005, 0.01, 0.1, 1, and 20 molal). For a particular set of 

conditions {T, [NO3

−

]/[Cl−], and [Cl−]}, the pH at which P(Ecorr>Ercrev) = 0.001 was computed by 

interpolation of the probability versus pH curves. These computation results are presented in 

Figure 3-3, where the dotted lines represent the ranges of pH computed in Figure 2-2 for the 

various temperatures. The curves of different colors represent the various chloride 

concentrations. The curves can be interpreted as localized corrosion boundaries. In solutions 

with a pH that lies above the curves, localized corrosion is unlikely to happen (the probability is 

at most 0.001). The curves also show the nonintuitive behavior previously discussed: as [Cl−

] 

increases, a solution of lower pH is needed for localized corrosion to occur. As nitrate is added 

to the system, the boundary curves are displaced downwards in the low T range. This means 

that if nitrate is present in the system, solutions with lower pH are needed to induce localized 

corrosion at lower temperatures. At higher temperatures, adding [NO3

−

] appears to enhance the 

susceptibility for localized corrosion, especially when [Cl−

] is low (e.g., less than 0.1 molal). 

However, for the pressure and water pressure conditions considered in Chapter 2, solutions of 

that low [Cl−

] do not appear to be under thermodynamic equilibrium and would evolve toward 

solutions of higher [Cl−

]. All of the thermodynamic equilibrium solutions considered in Chapter 2 

resulted in [Cl−

] exceeding 1 molal for T ≥ 50 °C [122 °F]. The [Cl−] = 1 molal curve boundary in 

Figure 3-3 is the yellow line (second line from the bottom). All of the solution pHs from 

Figure 2-2 (range represented by the dotted lines) lie above the yellow line, except at T = 110 

°C [230 °F]. Therefore, it is concluded that localized corrosion for T ≤90 °C [194 °F] is unlikely 

for [NO3

−

]/[Cl−]<0.5 on the basis that the needed low pH solutions are unlikely to arise. There is 

one exception to this statement. In Figure 3-3(a), the dotted line for pH at T = 25 °C [77 °F] 

crosses the blue line [Cl−

] = 0.0005 molal. This means that, according to Eqs. (3-1) and 
3-10 

(a) (b) 

(c) (d) 

Figure 3-3. Localized Corrosion Boundaries (Probability = 0.001) as a Function of Chloride and Nitrate 

Temperature. The Dotted Lines Represent the pH Ranges in Figure 2-2. 
3-11 

(3-2), localized corrosion is likely at low T, provided there is negligible [NO3

−

] in the solution. A 

minor amount of nitrate, however, would render localized corrosion unlikely [see Figure 3-3(b)]. 

This prediction of the possibility of localized corrosion at low temperatures if the nitrate 

concentration is negligible is only a mathematical artifact of the curve fitting. Localized 

corrosion in Alloy 22 has not been observed under such environmental conditions. 

In conclusion, localized corrosion only appears likely (probability >0.001) at T >80 °C [176 °F]. 

The solutions in Chapter 2 have a pH sufficiently high that it is unlikely (probability <0.001) 

for Alloy 22 localized corrosion to occur (i.e., Ecorr > Ercrev) for all solutions with T ≤80 °C 

[176 °F]. Figure 3-4 is a range of temperatures at the waste package surface from DOE 

[2008, Figure 2.3.5-33(b). According to such range of temperatures, the waste package is 

estimated to be below 80 °C [176 °F] after 3,500 years or sooner. Beyond 12,000 years, the 

waste package temperature is expected to drop below 50 °C [122 °F]. From Figure 3-3, when T 

<50 °C [122 °F] and with a marginal amount of nitrate, the needed pH to cause localized 

corrosion is too low and unlikely to arise. DOE reported the computation of localized corrosion 

conditions extending up to around 12,000 years (DOE, 2009a, Enclosure 1). Such results are 

reproduced in Figure 3-5. From this figure, note that beyond 3,500 years, the probability for 

Alloy 22 localized corrosion drops below 0.001, which is consistent with results in this report. 

Beyond 3,500 years, DOE computed that localized corrosion could occur mainly in 

midpercolation range regions (DOE divided the repository into 5 percolation bins). This DOE 

result is consistent with the analysis in this report. For low percolation rate regions or bins, the 

Figure 3-4. Range of Waste Package Temperatures Reproduced FromDOE [2008, Figure 

2.3.5-33(b)] 

0

50

100

150

200

250

10 100 1000 10000 100000 1000000

Low bound (°C)

High bound (°C)

Time (years)

Waste Package Temperature (° C)
3-12 

Figure 3-5. DOE Computation of the Probability of Localized Corrosion as a Function of 

the Drip Shield Failure Time. Source: DOE (2009a, Enclosure 1, Figure 2). 

temperature tends to be higher and the system drier, causing chloride concentrations to be 

higher and localized corrosion less likely. For the high percolation rate region, the temperature 

is lower, the relative humidity is higher, and the range of pH tends to be higher, making localized 

corrosion less likely. In the midrange of the percolation—where the temperatures and relative 

humidities are relatively high to cause the formation of low pH solutions and low chloride 

concentrations—the DOE equations predict a higher chance for localized corrosion provided 

there is no nitrate in the solution [see Figures 3-3(a) and 3-5]. Note, however, that localized 

corrosion of Alloy 22 has never been detected in low temperature solutions with low chloride 

concentrations. Such computation of localized corrosion is most likely an artifact of the 

mathematical curve fitting. 
4-1 

4 SUMMARY AND CONCLUSIONS 

Seepage water evaporation could lead to the formation of corrosive brines on waste package 

surfaces and promote localized corrosion. The potential brine chemistry is a function of the 

initial water composition (i.e., composition of seepage water), air pressure and water content in 

air (i.e., relative humidity), and the temperature of the EBS materials that the solutions are 

postulated to contact. In this study, thermodynamic simulations of seepage water evaporation 

were conducted to determine the potential chemistry of these brines. The likelihood that these 

brines would be capable of supporting initiation and propagation of localized corrosion of the 

Alloy 22 waste package material was analyzed. The results indicate that Alloy 22 localized 

corrosion is likely (probability >0.001) only at T >80 °C [>176 °F]. At T ≤ 80 °C [≤ 176 °F], the 

brines would have a sufficiently high pH such that localized corrosion would be unlikely 

(probability <0.001). The analysis also indicates that when T <50 °C [<122 °F] and a marginal 

amount of nitrate is present in solution, the solution pH is unlikely to be low enough to cause 

localized corrosion. 

The DOE localized corrosion model implies that increasing chloride concentrations could reduce 

the potential for Alloy 22 localized corrosion. It was hypothesized that an increasing 

concentration of chloride displaces oxygen and other oxidants in the solution, causing the 

corrosion potential to decrease. On the other hand, increasing chloride concentration causes 

the repassivation potential to decrease. The net effect of these competing trends is the 

nonintuitive result (noted in the computations in this report) that localized corrosion is less likely 

in solutions of increasing chloride concentration. This nonintuitive trend was used to rationalize 

DOE results that showed varying probability for localized corrosion as a function of deep 

percolation rates. For the low percolation rate region, the temperature tends to be higher and 

the system drier, causing chloride concentrations to be higher and localized corrosion to be less 

likely. For the high percolation rate region, the temperature is lower, the relative humidity 

higher, and the range of pH tends to be higher, which makes localized corrosion less likely. In 

the midrange of the percolation rates—where the temperature and relative humidity 

are comparatively high, causing solutions with low pH and low chloride concentration to form—

localized corrosion has a slightly higher chance of occurrence. The independent computations 

based on the DOE model predict that localized corrosion would occur in solutions of low 

chloride concentration and low temperature; however, it is argued that this prediction is most 

likely an artifact of the mathematical curve fitting, because localized corrosion of Alloy 22 has 

never been detected in this type of environment.
5-1 

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