DNV GL Integrated Multiscale Modeling of Materials

SAFER, SMARTER, GREENER
INTEGRATED
MULTISCALE
MODELLING
OF MATERIALS
DNV GL STRATEGIC RESEARCH & INNOVATION
POSITION PAPER 8-2014

2 Risk Management through Integrated Multiscale Modelling of Materials
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 Østby (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
PREFACE

Risk Management through Integrated Multiscale Modelling of Materials 3
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 24
CONTENT

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 laboratory-
based (semi-empirical) modelling alongside
high-fidelity physics simulation, within the context
of a probabilistic risk assessment. It creates high-
fidelity, 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.
WHAT IS INTEGRATED
MULTISCALE MODELLING?

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].

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
INTEGRATING ACROSS
SCIENTIFIC, EMPIRICAL, AND
SEMI-EMPIRICAL MODELS

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 on-
going 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”.
Figure 2. Multiscale approaches connect different methods of modelling with their analogous laboratory
characterisation techniques.
Å
ps
ns
S
> mins
�s
nm �m > m
Quantum
mechanics
Hybrid
Quantum/
Classical
Classical
Molecular
Dynamics
Mesoscale
Modeling
Continuum
Modeling
TEM, SEM,
Raman
Atomic Force
Microscopy
SEM
Nano-indentation
Optical
Mechanical testing
Length scale
Timescale

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 materials-
environment 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
STATE OF THE ART

film structure and composition,[6, 7] in speciating
chemicals in the environment for assessment of
likely chemically aggressive species in high pressure-
high 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]
Figure 4. Fluid dynamics simulation of Rayleigh-Taylor instability during hydrodynamic flow.
Image credit: US Department of Energy.

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]
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]
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 quantum-
mechanically 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
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]
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.
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 semi-
empirical – 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.
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

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

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]
TWO FRONTIERS

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.

2. Partitioning of the inhibitor species between the
oil and water 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.
3. Impact of the inhibitor upon multiphase flow
The separation of oil and water into two-
phase 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.
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.
6. Formation of self-assembled monolayers on the
solid surface phases
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.
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.
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

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 semi-
empirical 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
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.
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 knowledge-
based 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

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 physics-
based models with uncertainty models when they
are applied to engineering systems.
Particion Coefﬁcient:
Sources of uncertainty
Underlying Physics
M05-2X B3LYP Chain shape Reproducibility Method
PCMSMD6-31g+(d,p)Solvent Dialectric
Benchmarking
MUE (Mean
unsigned error)
pc-n
(CBS limit)
Environmental
Effects?
AM1
Solvent Choice Conformer Basis Set Solvation Model
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.

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.
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.
B6S
14
12
10
8
6
4
2
0
M6S B6P AS BpS B6Sv BpSv
DMI (MBI)
DMI (EA)
MBI (DMI)
MBI (EA)

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:
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
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.
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 real-
time, 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.
EMERGING APPROACHES IN
MATERIALS, SYSTEMS AND
PROCESS ENGINEERING

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 high-
fidelity 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.

Integrated multiscale modelling lies at the
intersection of human judgment and decision-
making, 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.
APPLICATION OF INTEGRATED
MULTISCALE MODELLING

Human Judgement &
Decision Making
Machine Learning &
Artiﬁcial Intelligence
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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