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DNV GL STRATEGIC RESEARCH & INNOVATION POSITION PAPER 8-2014

INTEGRATED MULTISCALE MODELLING OF MATERIALS SAFER, SMARTER, GREENER


2 Risk Management through Integrated Multiscale Modelling of Materials

PREFACE Modelling failure mechanisms is important for predicting the future performance of materials in a system. Even if past failure statistics are available, operating conditions can change and the microstructure of the materials can transform over time, resulting either in an altered trajectory of failure or the appearance of new failure modes. Industrial experience is replete with examples of failures that were not known to exist before they occurred. Examples include the cracking of nickel base alloy heat exchangers in high purity water of light water nuclear reactors, stress corrosion cracking of steel in buried pipelines, and cracking of steel storage tanks in ethanol. Failure mechanisms can be modelled at many different scales and levels of sophistication. Integrating the understanding arising from these multiscale models into risk assessment is a challenge that is addressed in this position paper. The paper outlines some approaches for integrated multiscale modelling and also provides an illustrative example.

ACKNOWLEDGEMENTS The author acknowledges the reviews provided by Erling Ă˜stby (DNV GL) and useful conversations with Prof. Lori Dalton (Ohio State University).

Contact Details: Christopher D. Taylor, Strategic Research and Innovation, DNV GL, Columbus Ohio USA; Christopher.Taylor@dnvgl.com


Risk Management through Integrated Multiscale Modelling of Materials

CONTENT WHAT IS INTEGRATED MULTISCALE MODELLING?

4

INTEGRATING ACROSS SCIENTIFIC, EMPIRICAL, AND SEMI-EMPIRICAL MODELS

6

STATE OF THE ART

8

Thermodynamics Models. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 8 Fluid Dynamics.. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 9 Electrochemistry and Mass Transport.. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 10 Atomistic and Quantum Chemistry. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 10 Microstructural Evolution. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 10 Damage Mechanics. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 10 Empirical Modelling. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 11

TWO FRONTIERS

12

Model Integration across Multiphysics and Multiscales.. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 12 Quantifying Uncertainty. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 15

EMERGING APPROACHES IN MATERIALS, SYSTEMS AND PROCESS ENGINEERING

18

The Materials Genome Initiative . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 18 Continuous Systems Health Monitoring. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 18 High-Fidelity Simulation and the Digital Twin. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 19 Multiscale Process Modelling . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 19

APPLICATION OF INTEGRATED MULTISCALE MODELLING

20

Safety, Environment, and Sustainability. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 20 Risk. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 20 Classification and Standards. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 20

REFERENCES

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4 Risk Management through Integrated Multiscale Modelling of Materials

WHAT IS INTEGRATED MULTISCALE MODELLING? Modern computer power, big data and high-fidelity physics-based models are enabling integrated multiscale strategies for the lifetime prediction of materials and the evaluation of risk to materials assets. All materials degrade over time due to natural processes and wear, such as corrosion and fracture, as the high energy states induced from materials processing decay to lower energy native states, such as the return of a metal to its native oxide form via corrosion. Protection of materials assets against failure and performance degradation is achievable through models that describe time evolution of natural processes using historical data, laboratory testing, and an in-depth understanding of the scientific principles for materials-environment interaction. Integrated multiscale materials modelling combines these three approaches to make predictions of materials failure risk under a range of anticipated service conditions. In addition, it can be used to optimise materials selection and other parameters, such as failure mitigation procedures, and to define the optimal boundary conditions on environmental variables such as temperature. The predictions made from integrated multiscale modelling methods must also quantify uncertainty. Integrated multiscale models are updatable according to the influx of new field data from both modern wireless sensor technologies and from conventional methods, and they will accept probabilistic and single-valued inputs.

Integrated multiscale materials modelling combines the best features of empirical and laboratorybased (semi-empirical) modelling alongside high-fidelity physics simulation, within the context of a probabilistic risk assessment. It creates highfidelity, digital copies of material assets that can be manipulated according to anticipated service needs and it simulates the likelihood of deformation and risk of failure. Safety envelopes can be constructed for these digital copies, and utilised in field or design stages to determine whether a part should be removed from service or whether pro-active failure mitigation strategies need to be acted upon. This position paper lays out a general strategy for the application of integrated multiscale materials modelling and simulation to the field of materials risk assessment, summarising the state of the art across the various sub-fields, such as finite element modelling, microstructure-based methods, and atomistic simulation. It shows how these high-fidelity physics-based models can be coupled with empirical data obtained from the field and laboratory bench. We foresee opportunities for integrated multiscale modelling to contribute to the goals of enhancing industry practices with regards to safety, the environment, and sustainability; to the reduction of risk in business operations; to software development; and in the assessment and qualification of models used for business decision making with regards to asset management.


Risk Management through Integrated Multiscale Modelling of Materials

Figure 1.  Integrated multiscale modelling creates interconnects between different representations of materials with the goal of optimizing field performance. Image credits with permission [1-3].

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6 Risk Management through Integrated Multiscale Modelling of Materials

INTEGRATING ACROSS SCIENTIFIC, EMPIRICAL, AND SEMI-EMPIRICAL MODELS Every model begins with a set of assumptions and is guided by a set of internal parameters. Whereas some models are constructed according to “first principles” and have very few adjustable parameters, others are entirely fitted to a set of field-based or laboratory-generated data. The former class of models is built according to fundamental scientific reasoning, whereas the latter class may have only a partial scientific basis (semi-empirical), or none at all (empirical). The advantage of science-based models is that they are, in theory, based upon immutable scientific principles and should therefore be “immune” to historical factors and well-suited for extrapolating to future scenarios. At the same time, scientific models are dependent upon the “fidelity” with which the engineering situations are translated into an

idealised set of analytically or numerically solvable equations. The fidelity of scientific models can be improved through the use of multiphysics and multiscale methods as discussed in the next section (Figure 2). Also, given that many simulations take single-valued parameters for inputs and provide single-valued parameters as outputs, it generally requires more work to attach an uncertainty estimate to the results of a numerical simulation. Empirical and semi-empirical models are generated from inherently probabilistic data measured either in the field or at the laboratory bench. They may be loosely based around general theories for materials failure, or may be entirely probabilistic in nature, adopting, for example, extreme value statistics. Whereas science-based models operate under an idealised set of conditions, empirical models have


> mins

Time scale

Risk Management through Integrated Multiscale Modelling of Materials

Continuum Modeling

S

Mesoscale Modeling

�s

Hybrid Quantum/ Classical

ns

ps

Quantum mechanics

Å

Classical Molecular Dynamics

Optical Mechanical testing

SEM Nano-indentation

Atomic Force Microscopy TEM, SEM, Raman

nm

Length scale �m

>m

Figure 2.  Multiscale approaches connect different methods of modelling with their analogous laboratory characterisation techniques.

the advantage of taking all operating variables explicitly under consideration (albeit this may only be partially the case when generating models under experimental, not field, conditions). Despite the confidence this may bring to the application of empirical-based models, being anchored to historically obtained data can lead to errors of extrapolation. These may occur when unknown conditions are encountered or if risks from hidden failure modes, which may be “incubating” but not yet revealed, are not appreciated. Integrated multiscale modelling of materials failure provides the opportunity to overcome the fundamental limitations of the scientific, empirical and semi-empirical approaches by integrating the predictions made by multiple techniques, using an approach such as Bayesian inference.

Ultimately, integrated multiscale models for materials degradation will incorporate feedback from ongoing laboratory work and field data to create a dynamic digital copy of the infrastructure, able to make predictions of the imminent and future risks “on the fly”.

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8 Risk Management through Integrated Multiscale Modelling of Materials

STATE OF THE ART Understanding and developing models for materials degradation is a complex process. The current suite of models that are available in both industry and academia generally focus on obtaining an accurate description of one or two key sub-processes that contribute to the overall materials failure. For this reason, each model emphasises only a few key aspects, such as the role of thermodynamics, flow, or electrochemical interactions, as being independent contributors to materials failure. In practice, a number of these processes will occurr in parallel, and materials failure frequently emerges due to the compounding effects of multiple phenomena, rather than from one single mechanism alone. The importance of synergies has been highlighted by Staehle’s “domains and microprocesses” approach to simulating materials failure; this approach aims to predict “unknown unknowns” through examination of the interfaces between model systems where negative effects can coalesce in exponentially devastating, yet otherwise unexpected, ways.[4, 5] Given that integrated multiscale models will have to take existing models from each of the sub-processes and couple them together, it is helpful to review the state of the art across each of these sub-fields (Figure 3):

■■ Thermodynamic Models ■■ Fluid Dynamics ■■ Electrochemistry and Mass Transport ■■ Atomistic and Quantum Chemistry ■■ Microstructural Evolution ■■ Damage Mechanics ■■ Empirical Modelling Figure 3.  Integrated multiscale modelling of materials combines the appropriate physics for the time, length-scale and phenomenology of the problem.

THERMODYNAMICS MODELS Thermodynamic models are useful for establishing the lowest free energy states of a materialsenvironment system by tabulating the species known to be present and using look-up tables to determine the expected equilibrium conditions. When temperatures are moderate to high, the kinetic barriers to establishing equilibrium tend to be surmountable, allowing the system to obtain its thermodynamic ground state. Since many materials are metastable – for instance, metal alloys generally are at higher energy states than their oxide forms – thermodynamic modelling can only be of limited use; kinetic models are required to establish the useful lifetimes and boundary conditions on asset stability. Thermodynamic models find most application in predicting passive


Risk Management through Integrated Multiscale Modelling of Materials

Figure 4.  Fluid dynamics simulation of Rayleigh-Taylor instability during hydrodynamic flow. Image credit: US Department of Energy.

film structure and composition,[6, 7] in speciating chemicals in the environment for assessment of likely chemically aggressive species in high pressurehigh temperature conditions,[8] and, recently, for establishing the equilibrium state of surface films that can form due to chemisorption of environmental species and act as boundary states for localised corrosion.[1, 9, 10]

FLUID DYNAMICS In the chemical engineering and oil & gas industries, the flow of material through pipelines can induce effects on the pipeline materials. Such effects include erosion and alteration of corrosive properties through separation of organic and water phases, leading to bottom of the line, or, alternatively, top of

the line, corrosion (Figure 4). Predictive models of the nature of multiphase flow are therefore important to determine the optimal flow rates as a function of, for example, the oil/water ratio, surfactant content, temperature, and pressure. A semi-empirical model was recently developed that incorporated the effects of pipeline inclination, flow velocity, and interfacial energies in controlling the tendency for an oil/water mixed phase flow to either entrain water (thus avoiding corrosion) or separate out (enabling corrosion).[11]

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10 Risk Management through Integrated Multiscale Modelling of Materials

ELECTROCHEMISTRY AND MASS TRANSPORT The degradation of metallic infrastructure primarily occurs due to corrosion, an electrochemical process by which metals dissolve, releasing electrons, and environmental species (such as water, hydrogen or oxygen) maintain the electron balance by undergoing reduction. Kinetic models for the prediction of corrosion rates are semi-empirical, derived from polarization curves that determine the contributions from the two half-reactions (metal dissolution and reduction). Corrosion is exacerbated in mixed metal environments, as the more noble metal serves as a catalyst for the corrosion of the less noble component. This “galvanic effect” is a function of the identity of the two metals, the chemistry of the environment, and the geometry of the component undergoing corrosion. A finite element tool has been developed to predict the risk of galvanic corrosion in such situations, as parameterized by laboratory measurements of the corrosion rates.[2, 12]

or molecules. Predictions from these models can provide thermodynamic or kinetic parameters used for models in the other classes or for designing entirely new materials.[20]

The second contribution to corrosion rate is the effect of mass-transport. Pitting and crevice corrosion, for example, are controlled by the rates at which the ionic species can move from one half-cell to the other (from the anodic site to the cathodic site). Numerous models that solve the Fick’s Law diffusion equations, in combination with the electrochemical reaction kinetics, have been developed.[13-15] Similar models have been constructed to simulate the effectiveness of asset protection measures, such as cathodic protection,[16] or to optimise zinc-based Galvanic protection coatings.[17]

MICROSTRUCTURAL EVOLUTION Bridging the atomistic description of a material with the continuum is the microstructural domain, which consists of the polycrystalline description of a material, in terms of grains and grain-boundaries, and defect features such as internal surfaces, nanodispersed precipitates and inclusions or dislocations. Models in this “mesoscale” region are still under development, and have been applied to scenarios such as the intergranular cracking of metal alloys through finite element modelling or phase field simulation.[26-28] The models can be semiempirical – guided by highly resolved microscopic characterisation of crack propagation pathways along the intergranular boundaries of the material – or derived from first principles information for the traction curves that describe the resistance of a grain-boundary towards failure by fracture. This class of models has also been applied to the problem of stress-corrosion cracking, which arises from the synergies that can emerge between a corrosive environment and a material under stress.

ATOMISTIC AND QUANTUM CHEMISTRY Perhaps the most fundamental class of models that have been applied to materials degradation includes those that simulate failure mechanisms at the atomic level. Models that treat the molecular components of a system, such as the structure and properties of inhibitor molecules introduced to delay corrosion, are typically called quantum chemical methods. Models that simulate the materials deformation modes directly are frequently called atomistic, and may use classical mechanics, with semi-empirical interatomic potentials used to simulate the interactions between atoms,[18] or quantummechanically derived methods like density functional theory.[19] The advantage of fundamental models is that they have very little, if any, dependency upon empirical data. However, the rigour of the calculation typically restricts the models to small or idealised systems with high symmetry and few unique atoms

One area in which atomistic modelling has been increasingly applied is the prediction of materials degradation via simulation of the chemical interactions that occur between a material and the chemicals to which it is exposed in the environment (Figure 5).[21] These chemicals could include corrosive species like sulphide or chloride, or protective chemicals that have been introduced to delay corrosion, such as inhibitor molecules.[22, 23] Atomistic modelling has also been applied to phase stability in materials, and to simulate defect states in materials,[24] the structure and properties of passivated metal surfaces,[25] and hydrogen embrittlement.

DAMAGE MECHANICS Damage mechanics models use continuum representations of solids to simulate the deformation of materials in response to applied stresses and/or strains, in order to estimate the propensity for failure via fracture. Dents characterised by inspection can be integrated into elastic-plastic models to simulate the failure thresholds and to determine whether or not a damaged part is suitable for service or needs to be replaced.[29-31] An emerging class of models


Risk Management through Integrated Multiscale Modelling of Materials

Figure 5.  Atomistic modeling of adsorption layers on metal surfaces provides the key to understanding corrosion of metals.

is being developed to integrate corrosive effects alongside traditional stress-strain models for the prediction of failure risk via a combination of modes including general corrosion, localised corrosion, and stress-corrosion cracking.[32, 33] High-performance computation also permits the application of damage mechanics models to materials with complex microstructures through the generation of representative volume elements from 3D computer tomography.[34]

EMPIRICAL MODELLING The collation of historical data or obtaining data from accelerated testing enables the development of empirical relations for the variation in materials failure and degradation frequency over time. Phenomena such as corrosion frequently appear stochastic, despite occurring as a consequence of the compounding effect of multiple independent factors. For this reason, extreme value statistical approaches, such as the Weibull distribution, are used to model the distribution of features such as corrosion pits over time. Simple equations, such as polynomial functions, are used to extrapolate and predict future features, such as maximum pit depth.[35] The advantages of such approaches are that they use real data and recognise explicitly the probabilistic nature of real failures. At the same

time, there is often considerable uncertainty in the quality of the polynomial fits used to represent the degradation features and extrapolation from historical data is fraught with uncertainty and the inability to predict failure from alternative failure modes. Semi-empirical and first principle models can emulate uncertainty by incorporating probabilistic theory through first or second-order reliability models,[36] the use of damage accumulation functions that incorporate changes in environmental chemistry, microstructure features, continuum scale mechanics,[37] or the method of Bayesian inference.[38] Machine-learning can assist in empirical modelling through the use of artificial neural networks and fuzzy logic.[39-42]

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12 Risk Management through Integrated Multiscale Modelling of Materials

TWO FRONTIERS Contemporary modelling of the evolution of materials integrity, as a function of age and exposure, has reached significant levels of sophistication. However, as in any scientific field, progress tends to be more vertical than horizontal – as models become progressively more powerful and complex in depth, their breadth of application shrinks inversely. In order to conduct practical risk assessments in the area of materials lifetime prediction, it is first necessary to adopt a modelling strategy that involves integration across the categories of materials degradation. As a result, failure modes that arise from the synergistic interactions between different domains and processes can be predicted, and new, science-based models for risk obtained. A second frontier that should be explored is in the area of uncertainty quantification from fundamental science-based models. Whereas most models that have been developed from first principles make a single value prediction, more effort is required to quantify the sources of uncertainty in the models. These include the uncertainties that arise from system idealisation, through to physical approximations made in the numerical or analytical solution of the physical interactions between the particles, and those parts of the model that depend upon experimental data-points.

MODEL INTEGRATION ACROSS MULTIPHYSICS AND MULTISCALES The multiscale modelling paradigm is built upon the recognition that the types of physics occurring at small time and length scales are distinct from those occurring at longer time and length scales. Nevertheless, they are, at the same time, connected in ways that are not always obvious. Hence, a comprehensive and high-fidelity simulation for any materials failure event would require a way to piece together these co-dependent elements. Multiscale models can be vertical – such that the small size scale physics models (which may be atomistic or microstructural) are embedded and run “inside” the larger size scale physics models (like electrochemical or finite-element simulations). Alternatively, and more commonly, the multiscale models can be horizontal, such that the results of lower size scale simulations provided input parameters, such as kinetic constants or thermodynamic quantities, for the higher-level simulations.[43] For example, atomistic simulations of interactions between the molecules that constitute an oil reservoir were used to predict its megascale thermodynamic properties. [44] The problem of stress-corrosion cracking has also seen a lot of attention using both types of multiscale approach.[45]


Risk Management through Integrated Multiscale Modelling of Materials

Figure 6.  Advanced modelling of materials will increasingly require the integration of informatics tasks, with scientific and empirical models, and uncertainty quantification.

Case-Study – Corrosion Inhibition in Oil & Gas Systems As a case study we consider the problem of predicting the suppression of corrosion via the introduction of chemical inhibitors into an oil pipeline. Pipelines are constructed from mild steel and are therefore highly susceptible to corrosion when water is present in a significant fraction of the transported oil. Inhibitors are critical to maintaining the lifetime of the pipeline and preventing failures that would have significant health, safety, and environmental consequences. Two distinct approaches have been used in modelling the performance of inhibitors in suppressing corrosion, and these approaches have not yet been integrated. On the one hand, the molecules comprising a corrosion inhibitor package have been modelled from quantum mechanics, and correlations between experimental efficiency (i.e., percentage reduction in corrosion rate) and quantum mechanical parameters have been determined using semi-empirical fitting schemes.[22] On the other hand, experimentally determined corrosion rates in the presence of inhibitors have been used to construct empirical models for the adsorption of inhibitors as “site-blocking” elements on the metal surface.[46] Thus, the two approaches to modelling inhibitor performance, represent two extremes of modelling sophistication - first principles versus

empirical - but a means for integrating, or bridging the two is lacking. If we consider the integration pathway as we have proposed here, an integrated multiscale modelling approach would instead follow the phenomenological links between the inhibitor performance as a corrosion suppressor, and the molecular properties of the inhibitor. Using this approach, the following steps naturally emerge:

1. Speciation of the inhibitor molecule in the

environment Inhibitors can be ionized by reaction with water according to their acid-base properties, which is quantified by the acid dissociation constant, pKa. Ionized inhibitors can also form ion pairs that affect the oil-water partition coefficient in the presence of anions like chloride. Inhibitors in neutral or ion-pair states can also form micelles that will limit their ability to form self-assembled monolayers on exposed metal surfaces. This latter effect is measured by the critical micelle concentration and can be predicted from classical molecular dynamics or quantum chemical calculations.

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14 Risk Management through Integrated Multiscale Modelling of Materials

2. Partitioning of the inhibitor species between the

6. Formation of self-assembled monolayers on the

oil and water phases

solid surface phases

Inhibitor molecules partition unequally between water and oil, depending upon their molecular hydrophobicity/hydrophilicity. This tendency is quantified by the oil-water partition coefficient, Log P. A higher value of Log P will mean fewer inhibitor molecules are available to act against corrosion in the water phase.

The physics of formation of chemisorbed layers on solid surfaces is described by the theory of adsorption isotherms, most commonly the Langmuir isotherm, although other variants also exist. The key parameter controlling the formation of these layers is called the Gibbs’ free energy of adsorption. This value can be inferred from experimental analysis (given certain assumptions) or predicted directly from first principles calculations using density functional theory.

3. Impact of the inhibitor upon multiphase flow

The separation of oil and water into twophase flow depends upon the surface tensions between oil-water, water-metal, and oil-metal interfaces. Surface tension can be affected by small concentrations of inhibitor species, and this effect can be predicted from molecular dynamics simulations or the classical density functional theory applied to liquids.

4. Migration of the inhibitor molecule to the metal

surface across the hydrodynamic boundary layer Under flowing conditions, migration of the inhibitor from the bulk solution phase to the metal/water interface will depend upon the diffusion of the molecule across the hydrodynamic boundary layer. Thus, the diffusivity of the molecule in water will affect inhibitor efficiency.

7. Prediction of the corrosion rates of metallic

surface phases with inhibitor self-assembled layers In the study of inhibitors it is commonly assumed that the extent of surface coverage by the inhibitor molecule corresponds exactly to the extent by which corrosion is reduced. This assumption can be evaluated using first principles models of inhibitor packing efficiency on the surface (which is a function of molecular shape and surface roughness), as well as the kinetics associated with the dynamic dissolution and reformation of the protective inhibitor surface layer. Inhibitor molecules may also reduce corrosion through other mechanisms, such as reaction with corrosion products to form scales that act as diffusion barriers, thus limiting corrosion. These steps are illustrated graphically in Figure 7.

5. Identification of the solid surface phases available

for inhibitor adsorption Mild steel in an oil and gas environment will have surface phases that could consist of oxides, oxy-hydroxides, hydroxides, sulphides, carbides and, under severe corrosion, bare iron surfaces. Other solid surfaces that may be present include sand and formation fines. The inhibitor-surface interaction will be different on each phase, and so will the overall inhibitor efficiency. Thermodynamic methods can be used to predict stable surface phases, but these may need to be coupled with kinetic stability diagrams that take metastability into account, since it is known that the most thermodynamically stable phase is not always the phase that is observed to form in the field.

An integrated multiscale modelling approach to the prediction of materials failure via corrosion in the presence of an inhibitor according to these principles requires a multiphysics solution that reconciles thermodynamics, fluid dynamics, mass transport, microstructural evolution and electrochemistry. In order to demonstrate the approach here, we used quantum chemical methods to simulate the speciation of two example inhibitor molecules – benzimidazole (BMI) and 1,2-dimethylimidazole (DMI) –in the aqueous solution, and determined that their chemical identity will vary as a function of pH, using the thermodynamic relations between quantum mechanical properties and Gibbs’ free energy in solution.[47] By coupling this pH-dependent speciation model with models for the solvation of


Risk Management through Integrated Multiscale Modelling of Materials

between the concentration of inhibitor in the oil and water phases.[49] This example, highlighted in Table 1, illustrates the beginning of an integrated multiscale modelling approach to the important problem of predicting suppression of corrosion reactions in oil and gas pipelines due to inhibitor molecules. Future steps include the prediction of ion-pairs, which may influence the overall effective partition coefficient through altering the speciation possible in the oil phase.

Figure 7.  Physicochemical factors that influence the inhibitor efficiency, including speciation, oil-water partitioning, multiphase flow, transport of the inhibitor to the surface, the formation of surface films, and the reduction in corrosion rates across the surface.

the inhibitor molecule in either organic solvents or water, it is then possible to determine how much of the inhibitor remains in the corrosive aqueous phase. This second step is obtained by using quantum chemical implicit solvation methods that are semiempirical in nature, based on large databases of solvent-solute systems, in addition to the quantum chemical calculations based on the molecule’s electronic structure (Figure 8).[48]

Figure 8.  Quantum chemistry allows the computation of the electronic properties of an inhibitor molecule that ultimately control its ability to bind and interact with solvents, including water, metallic and oxide surfaces, and itself. Shown here is the electrostatic potential: blue indicates positive charge, green for neutral and red for negative charge.

The overall partition coefficient for the inhibitor between the organic and water phase can then be determined as the “Log P” value, where P is the ratio

Inhibitor

pKa

Log P0

Log Peff (pH 7)

Log Peff (pH 2)

BMI

5.20

0.74

0.73

-2.46

DMI

7.79

0.57

-0.29

-5.22

Table 1.  Inhibitor acid-base speciation (pKa) and partition coefficients (Log P0, which is for neutral molecules only, and Log Peff, which takes the speciation into account) obtained using density functional theory, a science-based predictive modelling approach, integrated with thermodynamic equations. The variation in partition coefficient with pH is due to the change in inhibitor speciation in solution, according to the acid dissociation constant pKa.

QUANTIFYING UNCERTAINTY In risk assessment, any prediction of a materials damage state, its usable lifetime, or safe operating thresholds should be accompanied by a quantified uncertainty that can be used to assess the risks associated with deviations from either of these conditions. The foremost means of quantifying the accuracy of a model is to compare the predictions of a model with a reliable validation dataset in order to evaluate the error in the model prediction. This method should be augmented with more sophisticated treatments, such as exploring the nature of error propagation through the model. This should be based on the model’s set of assumptions, uncertainties in the data provided as model inputs, uncertainties in the data used for validation, and fundamental uncertainties that arise due to limitations in our understanding of the physics of the problem (known as epistemic or knowledgebased uncertainty).[50-52] These latter categories of error can be more challenging to quantify, and are rarely investigated due to the academic emphasis on making models deeper and more theoretically rigorous rather than more relevant to engineering use. The existence of a wide number of available models for predicting materials degradation provides another opportunity for uncertainty quantification by comparing the predictions made by alternative

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16 Risk Management through Integrated Multiscale Modelling of Materials

Particion CoefďŹ cient: Sources of uncertainty

Underlying Physics

M05-2X

Solvent Choice

B3LYP

Conformer

Chain shape

Basis Set

Reproducibility

AM1 Solvent

Dialectric

Environmental Effects?

6-31g+(d,p)

Solvation Model

Benchmarking MUE (Mean unsigned error) pc-n (CBS limit)

Method

SMD

PCM

Figure 9.  Sources of uncertainty in the first-principles computation of inhibitor partition coefficients identified by tracing the decision-making process along each step of the model assumptions.

models of the same phenomenon, as well as integrating models for distinct degradation modes that apply to the same materials system. The method of Bayesian networks has been used in this way to build a probabilistic model for the risk of oil and gas pipelines to corrosion failure via a variety of modes and integrating empirical, semi-empirical, and science-based methods.[38] Uncertainty quantification can be achieved by using Bayesian inference, comparing model predictions with experiments and available field data, integration into damage accumulation models, and examination through the use of Monte Carlo and/or first- and second-order reliability methods (FORM/SORM). Methods to treat uncertainty are represented, alongside scientific and empirical models, and the informatics tasks needed to complete the integration, in Figure 6. With respect to corrosion inhibition, the methods used to solve the molecular properties of the inhibitors can be varied due to changes in the physical approach used to solve the quantum mechanical equations. For example, the functions used to represent electron density can be made more or less complete, depending upon how much computer time or memory is available to perform the computation.[53] In addition, there are competing semi-empirical approaches that have been

developed as a way to emulate the effects of a surrounding organic or aqueous medium.[48] A list of the possible decisions that could be made when constructing such a model is shown in Figure 9. When these sources of variation are taken into account, it is possible to estimate the uncertainty in the predictions made by these otherwise highly rigorous theoretical methods. Furthermore, for these two inhibitor molecules the pKa and partition coefficient for n-octanol/water mixtures have been measured, and we can use these experimental data points to quantify the uncertainty in the model. Table 2 indicates how by changing the way the quantum mechanical calculation is performed, the model predictions for the pKa and effective partition coefficient are affected. Expert opinion is needed to decide on method selection, based partly upon the availability of benchmarking studies. In Figure 10 we show that the variations in theoretical approach against several classes of models can lead to significantly different predictions and errors in the partition coefficient of these inhibitors. This case study demonstrates the need for coupling physicsbased models with uncertainty models when they are applied to engineering systems.


Risk Management through Integrated Multiscale Modelling of Materials

INHIBITOR/METHOD

pKa

Log Peff (pH 7)

INHIBITOR/METHOD

pKa

Log Peff (pH 7)

BMI/AM1

2.7

-0.2

DMI/AM1

3.8

0.9

BMI/SMD

6.1

0.6

DMI/SMD

8.4

-0.8

BMI/PCM

8.5

0.5

DMI/PCM

11.0

-4.7

BMI/FULL

5.2

0.7

DMI/FULL

7.8

-0.3

BMI/EXPT

5.5

1.4(2)

DMI/EXPT

8.4

-0.1(1)

Table 2.  Model predictions for pKa and Log Peff obtained using variations on the quantum chemical method. AM1 is a fast, semi-empirical variation of quantum mechanics; SMD is the state of the art solvation semi-empirical model, employed with reasonably accurate physical models for quantum mechanics; PCM is an older semi-empirical solvation model, using the same accurate physical models; and FULL uses the SMD model but with augmented physics that includes complete description of electron physics and the effects of molecular vibrations in the pKa calculation. EXPT shows the literature values with accompanying uncertainties. The values obtained from the FULL level of theory remain lower than EXPT, indicating that further models must be integrated to capture all the physics and chemistry involved in inhibitor speciation and partitioning, such as the formation of ion-pairs that can elevate Log P.

14

12

10

8

6 DMI (MBI)

4

DMI (EA) 2

0

MBI (DMI) MBI (EA) B6S

M6S

B6P

AS

BpS

B6Sv

BpSv

Figure 10.  Absolute deviation in the predicted partition coefficient for the inhibitor molecule DMI and MBI calculated against the reference states, in parentheses, for 7 different classes of physics-based models for inhibitor behaviour.

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18 Risk Management through Integrated Multiscale Modelling of Materials

EMERGING APPROACHES IN MATERIALS, SYSTEMS AND PROCESS ENGINEERING The themes of integration across multiple physics models that comprise different time and length scales, and quantification of model uncertainty, appear to different extents in four emerging approaches to integrated multiscale modelling in engineering:

a class of high-strength, embrittlement-resistant “cybersteels”.[55] The initiative focuses heavily on multiphysics integration, but as the aim is to increase the speed of materials discovery rather than risk assessment, it has less emphasis on uncertainty quantification.

¾¾ The Materials Genome Initiative ¾¾ Continuous System Health Monitoring ¾¾ High-Fidelity Simulation and the Digital Twin ¾¾ Multiscale Process Modelling

THE MATERIALS GENOME INITIATIVE Following the success of information-centric approaches in the biological and chemical sciences (e.g., bioinformatics, cheminformatics and the human genome project), the US has embarked upon a materials genome initiative. The purpose of this initiative is to accelerate materials design, discovery and development by providing the modelling, simulation, and data infrastructure necessary to integrate computational materials science tools with advanced characterisation.[54] An example is provided by the integration of first principles atomistic models with microstructure evolution models and finite element simulation to optimise

CONTINUOUS SYSTEMS HEALTH MONITORING Modern connectivity through wireless technology allows real-time sensing of materials assets.[56] Signal processing implies the existence of integrated models that can enable decision-making in realtime, based upon the acquired data. Furthermore, these models should have awareness of uncertainty thresholds that can prevent system fluctuations based upon potentially noisy data. For example, continuous corrosion health monitoring has been proposed for on board aircraft using atmospheric sensors that track parameters such as air temperature, surface temperature, relative humidity and solution chemistry. This multi-parameter data set will then be passed as inputs to a corrosion model that predicts the corrosion vulnerability of the material assets being surveyed.[57] Continuous systems health monitoring is motivated by the need to reduce operational costs, increase efficiency, and improve system safety.


Risk Management through Integrated Multiscale Modelling of Materials

Figure 11.  The US Air Force “Digital Twin� concept inter-relates virtual and actual aircraft through modeling, simulation and sensing.

HIGH-FIDELITY SIMULATION AND THE DIGITAL TWIN The Digital Twin concept, developed by the US Air Force, describes a system in which the delivery of a shipment of aircraft (or, more generally, any materials asset) is accompanied by a digital shipment that details the materials characteristics of each particular vehicle, including unique attributes due to subtle variations in processing, defect states, etc.[58, 59] The models are as detailed as possible, such that highfidelity simulations can be performed that will address the unique response of each vehicle to the stresses and corrosive environments that will be encountered during planned and actual missions (Figure 11). The Digital Twin is kept as closely up to date with the physical twin as possible by using a combination of sensors, inspections, and models for ageing. Due to the multiphysics nature of materials ageing and deterioration under chemical and mechanical stresses, advanced modelling strategies will need to be employed following the integration hierarchy we have introduced. The demand for prompt simulation in response to mission needs requires that the modelling be multiscale, as it will be impossible to simulate all the details at the most fundamental (i.e., atomistic) levels. Due to the high-risk nature of air force missions, uncertainty quantification will also be an important component for realisation of the Digital Twin potential.

MULTISCALE PROCESS MODELLING Chemical engineering processes span the molecular level of chemical design and structure-property optimisation, crystallization and microscopic product aggregation, macroscale production units on the level of centimetres to metres, plant development at the industrial scale, and megascale consideration of pollutant emissions and product dispersion in the environment.[60, 61] For this reason, it has been advocated that a multiscale approach is required that optimises the entire chemical engineering process, from molecular conception to atmospheric and geochemical end-state. Forces driving the optimisation of models include market demand, competitive forces that drive new chemical formulations and products, and public concerns and government regulations regarding safety and the environment.[62] As in the integrated multiscale modelling of materials, the integration task must span multiphysics modules such as thermodynamics, kinetics, rheology and transport. The multiscale approach needs to be carefully considered as analyses performed of the same phenomenon, but at different length and time scales, will be studying similar and related, but not identical, processes. It is crucial that this point is understood.

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20 Risk Management through Integrated Multiscale Modelling of Materials

APPLICATION OF INTEGRATED MULTISCALE MODELLING Integrated multiscale modelling lies at the intersection of human judgment and decisionmaking, theory and modelling, machine learning and artificial intelligence, and experiments and data collection. These activities can work together to improve safety, environment, and sustainability. They can evaluate risk more accurately and improve risk reduction. In addition, they can be applied to develop methods and standards for classification.

SAFETY, ENVIRONMENT, AND SUSTAINABILITY Using integrated multiscale modelling of materials will result in better management of assets, such that the risks of failure and loss of material to the environment will be reduced, as well as the risk of losses to human health and environmental damage. For example, more accurate models for pipeline materials failure will decrease the incidence of spills and explosions. More accurate materials models with quantified uncertainty will also lead to better use of materials, thus contributing to the goal of materials sustainability through reduction of excess and enabling the use of materials for longer lifetimes.

RISK The development and application of integrated multiscale materials modelling will lead to superior risk assessment tools that increase customer

confidence through better predictions that are coupled with quantified measures of uncertainty. Integrated multiscale modelling strategies that adopt the highly coupled “domains and microprocesses approach” have the potential to predict failure modes that have not yet been experienced, but are currently only in the incubation phases. Thus these strategies provide a breakthrough in risk assessment by predicting the development of “unknown unknowns”. In addition, improved efforts to provide validation of integrated multiscale models against historical and laboratory data will be required for their acceptance into process engineering applications.

CLASSIFICATION AND STANDARDS There are currently many engineering systems where safe modes of operation are identified through empirical means. For example, there are safe operating conditions for materials used in oil and gas production systems codified in ISO15156 standard. However, these safe zones are usually not rigorously established (many are just “eye-balled” lines through scattered data) and are difficult to use when operating assumptions change or novel materials are developed. Model-based classification that can also quantify the uncertainties in operating envelopes is necessary for successful operation of aging and complex systems.


Risk Management through Integrated Multiscale Modelling of Materials

Machine Learning & ArtiďŹ cial Intelligence

Human Judgement & Decision Making

Experiments & Data Collection

Theory & Modelling Figure 12.  Integrated multiscale approaches to modelling will continue to draw from the synergies that lie at the intersection of human judgment and decision-making, theory and modelling, machine learning and artificial intelligence, and experiments and data collection.

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22 Risk Management through Integrated Multiscale Modelling of Materials

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24 Risk Management through Integrated Multiscale Modelling of Materials

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Integrated multiscale modelling of materials