Technical Report TR-18-08 December 2019 Copper Sulfide Model (CSM) Model improvements, sensitivity analyses, and results from the Integrated Sulfide Project inter-model comparison exercise SVENSK KÄRNBRÄNSLEHANTERING AB SWEDISH NUCLEAR FUEL AND WASTE MANAGEMENT CO Fraser King Box 3091, SE-169 03 Solna Phone +46 8 459 84 00 Miroslav Kolář skb.se SVENSK KÄRNBRÄNSLEHANTERING ISSN 1404-0344 SKB TR-18-08 ID 1692666 December 2019 Copper Sulfide Model (CSM) Model improvements, sensitivity analyses, and results from the Integrated Sulfide Project inter-model comparison exercise Fraser King, Integrity Corrosion Consulting Ltd Miroslav Kolář, LS Computing Ltd This report concerns a study which was conducted for Svensk Kärnbränslehantering AB (SKB). The conclusions and viewpoints presented in the report are those of the authors. SKB may draw modified conclusions, based on additional literature sources and/or expert opinions. A pdf version of this document can be downloaded from www.skb.se. © 2019 Svensk Kärnbränslehantering AB Permission Figure 2-7a Reprinted from Journal of Contaminant Hydrology, Porewater chemistry in compacted re-saturated MX-80 bentonite, Michael H Bradbury, Bart Baeyens, Copyright (2003), with permission from Elsevier. Summary The Copper Sulfide Model (CSM) was developed to predict the long-term evolution of the corrosion behaviour of copper canisters in a deep geological repository. The model is based on the coupling of the interfacial electrochemical reactions involved in the corrosion of the canister to processes occurring in the repository near- and far-fields. A key feature of the CSM is the incorporation of a mixed-potential model for the interfacial electrochemical reactions which allows the prediction of both the corrosion rate and the corrosion potential, an important parameter in corrosion science. In this way, the model is capable of predicting not only the long-term corrosion behaviour of the canister but also the evolution of the near-field corrosive environment as conditions evolve from warm and oxidising initially to cool and sulfide-dominated in the long term. Since the model was first developed in 2007, there have been a number of improvements to the mecha- nistic understanding of the corrosion process in sulfide environments. This improved mechanistic information, as well as other additions to the code, have been incorporated in a number of updates to the original model. The code updates that address either improved mechanistic understanding or to correct earlier omissions from the code include: exclusion of the anaerobic dissolution of pyrite as a source of sulfide, updated stoichiometry for the oxidative dissolution of pyrite, updated kinetic expression for the microbial reduction of sulfate, inclusion of the chemical conversion of Cu2O to Cu2S, addition of the cathodic reduction of H2O, and a correction to the treatment of the evolution of H2 from the cathodic reduction of the proton in the HS− ion. In addition to these relatively minor updates to the code, a second major improvement to the treatment of microbial sulfate reduction has been implemented involving the use of Monod kinetic expressions for both organotrophic and chemotrophic sulfate reduction pathways, as well as the possible limitation by the availability of organic carbon and/or sulfate (gypsum). A number of other changes have been made to the code to extend the range of application of the model. For example, the effect of gaseous H2S in an unsaturated repository has been addressed in a version of the code. The effect of spatial separation of anodic and cathodic reactions and an alternative bentonite model based on a single inter-layer porosity treatment have also been implemented. The mechanistic basis of these model improvements and the results of the various resulting versions of the code are described in some detail. With these various updates and improvements, the CSM is considered to satisfactorily predict the long-term corrosion behaviour of the canister and the evolu- tion of the near-field corrosive environment. In addition to a best-estimate simulation of the expected behaviour in the repository, the results from the CSM have also been compared with those from two thermodynamically based reactive-transport models in an inter-model comparison exercise. The results from the CSM simulations indicate that the extent of corrosion of copper canisters in a KBS-3 design repository will be limited. Based on the best-estimate simulation, the depth of general corrosion due to both the initially trapped oxygen and sulfide produced by microbial activity or present in the ground water is predicted to be < 10 µm after one million years. SKB TR-18-08 3 Contents 1 Introduction 7 2 Updates to CSM 9 2.1 History and nomenclature of various versions of the CSM 9 2.2 Improvements to the CSM Version 1.1 17 2.2.1 Implementation of Henry’s law treatment for O2 (CSM V1.1eq) 17 2.2.2 Other improvements to the code and subroutines 19 2.3 Improvements to reaction scheme 20 2.3.1 Exclusion of anaerobic dissolution of pyrite as a source of sulfide 20 2.3.2 Updated mechanism for the oxidative dissolution of pyrite 20 2.3.3 Microbial reduction of sulfate 22 2.3.4 Conversion of cuprous oxide to cuprous sulfide 23 2.3.5 Cathodic reduction of water 23 2.3.6 Improvement to treatment of cathodic reduction of sulfide 26 2.3.7 Improved treatment of microbial sulfate reduction 27 2.3.8 Treatment of gaseous H2S 33 2.4 Spatial separation of anodic and cathodic processes 37 2.5 Alternative film formation process 39 2.6 Alternative bentonite model 40 2.6.1 Background 40 2.6.2 Changes to CSM for the single inter-layer model 41 3 Results of simulations with updated versions of the CSM 45 3.1 Reference simulation with CSM Version 1.1eq 45 3.2 Improvements to reaction scheme CSM Versions 1.2a–1.2h 53 3.2.1 Modification to the reaction scheme CSM Versions 1.2a to 1.2f 53 3.2.2 Improved treatment of microbial sulfate reduction CSM Version 1.2g 58 3.2.3 Treatment of gaseous H2S CSM Version 1.2a-h 61 3.3 Spatial separation of anodic and cathodic processes CSM Version 1.3 64 3.4 Alternative film formation process CSM Version 1.4 66 3.5 Alternative bentonite model CSM Version 2.0 66 4 Default or “best-estimate” CSM simulation and sensitivity analyses 69 4.1 Definition of “best-estimate” scenario 69 4.2 Results of “best-estimate” simulation 74 4.2.1 Corrosion 74 4.2.2 Oxygen balance 78 4.2.3 Sulfide balance 79 4.2.4 Fe(II) balance 80 4.2.5 Microbial aspects 82 4.3 Sensitivity analyses 87 4.3.1 Impact of allowing microbial activity in the buffer 89 4.3.2 Impact of assumption of microbial death 92 4.3.3 Buffer and backfill saturation time 93 4.3.4 Horizontal versus vertical diffusion 97 5 Integrated Sulfide Project benchmarking exercise 101 5.1 Background 101 5.2 Definition of Base Case and variants 103 5.2.1 Definition of Base Case 103 5.2.2 Definition of variant cases 104 5.3 Results of simulations 110 5.3.1 Base Case 110 5.3.2 Variant cases 119 5.3.3 Discussion of the results of the Base Case and variant cases 131 SKB TR-18-08 5 6 Discussion 133 6.1 Nature of the repository environment and the evolution of the corrosion behaviour of the canister 133 6.2 Implications of CSM predictions for localised corrosion and SCC of the canister 134 6.2.1 Pitting 134 6.2.2 Stress corrosion cracking 135 6.3 Cathodic reaction under anaerobic conditions 135 6.4 Spatial separation of anodic and cathodic processes 136 6.5 The nature of the Cu2S film 138 6.6 Effect of gaseous H2S 138 6.7 Status and future development of the CSM 138 7 Conclusions 141 References 143 Appendix A Derivation of parameter values for cathodic reduction of H2O on copper 151 Appendix B Derivation of surface area factor for cathodic reaction on surface and within pores of Cu2S film 153 Appendix C Data input file 157 Appendix D Definition of Base Case and Variant calculations for WP3 of the Integrated Sulfide Project 181 6 SKB TR-18-08 1 Introduction The Copper Sulfide Model (CSM) is a reactive-transport model for predicting the long-term corrosion behaviour of copper canisters in an underground repository. The model is structured so that physical, chemical, microbial, and mass-transport processes in the near- and far-fields are coupled to the inter- facial electrochemical reactions that constitute the overall corrosion reaction. In this way, the model is capable of predicting the evolution of the corrosion behaviour as the environmental conditions within the repository change over time. Thus, the model accounts for not only the corrosion behaviour during the early aerobic phase, but also the corrosion of the canister due to the presence of sulfide during the long-term anaerobic period. The CSM is a custom-designed code written in the C computer language. The code is structured around a series of linear, one-dimensional (1-D) reaction-diffusion (mass-balance) equations, one for each chemical species included in the model plus a heat-conduction equation to predict the spatial and temporal variation in temperature. These mass-balance equations are discretized and numerically solved using finite-difference methods with the aid of the TRANSIENT solver for sparse matrices (Kolář 2016). The basic output of the code is the spatial and temporal variation of the concentration of each of the species, plus temperature. Because of the use of a mixed-potential boundary condition for the electrochemical reactions on the canister surface, the code also predicts the time dependence of the corrosion potential (ECORR) and the corrosion rate (as the corrosion current density iCORR).