Modelling Training School
Lecture
Session II:
Environmental Modelling
1. General
Modelling
2. Application to
Nanomaterials
3. Group Work
Fate and behaviour of nanoparticles
in air, soil, sediment and water
Interactive
session
1. Modelling
software
2. Data
Manipulation
3. Model 1:
Kinetic
4. Model 2:
Material flow
Niall O‘Brien
NanoImpactNet - QNANO Conference, Modelling Training School, 1 March 2012
Lecture
1. General
Modelling
2. Application to
Nanomaterials
Part 1: General Modelling
3. Group Work
Interactive
session
1. Modelling
software
2. Data
Manipulation
3. Model 1:
Kinetic
4. Model 2:
Material flow
Niall O‘Brien
NanoImpactNet - QNANO Conference, Modelling Training School, 1 March 2012
What are we modelling?
Lecture
THE Environment
1. General
Modelling
2. Application to
Nanomaterials
3. Group Work
Vs
Interactive
session
a
b
1. Modelling
software
AN Environment
2. Data
Manipulation
3. Model 1:
Kinetic
4. Model 2:
Material flow
a.
b.
c.
Gottschalk et al. 2010
O’Brien and Cummins 2011
Arvidsson et al. 2011
Niall O‘Brien
c
NanoImpactNet - QNANO Conference, Modelling Training School, 1 March 2012
Modelling parameters
• Knowns
Lecture
1. General
Modelling
2. Application to
Nanomaterials
3. Group Work
– Material characteristics, environmental characteristics
• Unknowns
– Transformation, etc.
• Simplify
Interactive
session
– Limited pathways: all reasonably foreseeable pathways, (non-)
negligible quantities
1. Modelling
software
– Data available? Easily measureable?
2. Data
Manipulation
3. Model 1:
Kinetic
4. Model 2:
Material flow
Niall O‘Brien
NanoImpactNet - QNANO Conference, Modelling Training School, 1 March 2012
Exposure scenarios
Lecture
1. General
Modelling
• All reasonably foreseeable scenarios
2. Application to
Nanomaterials
3. Group Work
• Conservative?
Interactive
session
1. Modelling
software
• Realistic?
2. Data
Manipulation
3. Model 1:
Kinetic
4. Model 2:
Material flow
Niall O‘Brien
NanoImpactNet - QNANO Conference, Modelling Training School, 1 March 2012
Assumptions
Lecture
1. General
Modelling
2. Application to
Nanomaterials
3. Group Work
Interactive
session
1. Modelling
software
2. Data
Manipulation
3. Model 1:
Kinetic
• Assumptions are a key element in managing
uncertainty in modelling processes
– Employ ‘best available data’ and logical assumptions
• Consider available data
• Choose best available solution
• Consider actions to validate assumption (reduce
uncertainty)
• Simplify exposure process to pathways and processes
of most influence
• Formulate behavioural hypotheses, from available
data, in order to predict environmental behaviour and
subsequent exposure
4. Model 2:
Material flow
Niall O‘Brien
NanoImpactNet - QNANO Conference, Modelling Training School, 1 March 2012
Variability
Lecture
1. General
Modelling
2. Application to
Nanomaterials
3. Group Work
Interactive
session
1. Modelling
software
2. Data
Manipulation
3. Model 1:
Kinetic
• Variability, a effect of chance and a function of a
system
• Not reducible through either study or further
measurement, but may be reduced by changing the
physical system
• May be managed within an exposure model though a
number of methods:
– Including data as distributions that describe a factor
or function (as best measurement allows)
– Modelling scenarios or systems for a number of
iterations
4. Model 2:
Material flow
Niall O‘Brien
NanoImpactNet - QNANO Conference, Modelling Training School, 1 March 2012
Uncertainty
Lecture
1. General
Modelling
2. Application to
Nanomaterials
3. Group Work
Interactive
session
1. Modelling
software
2. Data
Manipulation
3. Model 1:
Kinetic
4. Model 2:
Material flow
• Uncertainty, a measure of our lack of knowledge about
the parameters of a system, is an essentially subjective
component
• Sometimes reducible through further measurement or
study (or by consulting more experts)
• May be managed within an exposure model though a
number of methods :
– Logical assessment of the information contained in available
data
– Assumptions and generalisations (where appropriate) to
simplify the system
– Use of (appropriate – again subjective) bridging data, adapted
with suitable statistical methods
Niall O‘Brien
NanoImpactNet - QNANO Conference, Modelling Training School, 1 March 2012
Illustrating variability and uncertainty
Lecture
1. General
Modelling
2. Application to
Nanomaterials
3. Group Work
Interactive
session
1. Modelling
software
2. Data
Manipulation
3. Model 1:
Kinetic
4. Model 2:
Material flow
Figure 1: Binomial distribution
Figure 2: Confidence distribution
• Keeping variability and uncertainty separate in a model is
mathematically more correct
• Mixing the two together, i.e. by simulating them together,
produces a reasonable estimate of total uncertainty under most
conditions
• But we cannot then see how much of the total uncertainty comes
from variability and how much is from uncertainty
Niall O‘Brien
NanoImpactNet - QNANO Conference, Modelling Training School, 1 March 2012
Representation of data
Lecture
1. General
Modelling
2. Application to
Nanomaterials
3. Group Work
Interactive
session
1. Modelling
software
2. Data
Manipulation
3. Model 1:
Kinetic
• The accuracy and applicability of environmental
models is reliant on the quality and responsible use of
available data
• This data may come from many sources:
– Experimental, survey, standard monitoring, historical
• Much of this data may be considered a representative,
random sample
• There are occasions where the observed variability of
this data may be applied as a probability distribution in
an environmental model
• Expert opinion - MCDA
4. Model 2:
Material flow
Niall O‘Brien
NanoImpactNet - QNANO Conference, Modelling Training School, 1 March 2012
Data quality
Lecture
1. General
Modelling
2. Application to
Nanomaterials
• Are characteristics used in past/standard
environmental models relevant?
(not used – not relevant?)
3. Group Work
Interactive
session
• Is parameter independent of others in the model?
– Realistic scenarios
1. Modelling
software
2. Data
Manipulation
3. Model 1:
Kinetic
4. Model 2:
Material flow
Niall O‘Brien
NanoImpactNet - QNANO Conference, Modelling Training School, 1 March 2012
Fitting options
• First order or second order
Lecture
1. General
Modelling
2. Application to
Nanomaterials
3. Group Work
Interactive
session
1. Modelling
software
2. Data
Manipulation
3. Model 1:
Kinetic
4. Model 2:
Material flow
– Do you need to include uncertainty? (2nd order)
• Parametric or non-parametric
– Parametric if:
• The maths reflects the system being modelled
• There is a lot of empirical evidence for a certain
distribution
• Lots of data, and its convenient
– Non-parametric (empirical) if:
• Assumption of a specific distribution is not warranted
• Thus generally more conservative
Niall O‘Brien
NanoImpactNet - QNANO Conference, Modelling Training School, 1 March 2012
Distribution types
Lecture
Frequency distributions - describe variability between
individuals
1. General
Modelling
Probability distributions - describe randomness
2. Application to
Nanomaterials
Uncertainty distributions - describe our uncertainty
about some model parameter
3. Group Work
Interactive
session
1. Modelling
software
2. Data
Manipulation
3. Model 1:
Kinetic
4. Model 2:
Material flow
• A frequency distribution is used as a probability
distribution when we are taking a random sample from
a population
• We are usually uncertain about the parameters of the
frequency and probability distributions, and use
uncertainty distributions to describe that uncertainty.
Niall O‘Brien
NanoImpactNet - QNANO Conference, Modelling Training School, 1 March 2012
Building the model
Lecture
• Basic stages – Product X fate in WWTP
• Model elements:
– Fixed (Cnano1 - “nano”-fraction contained within influent)
– Variable (Snano – fate/pathway in plant)
– Uncertain (Rnanox – removal efficiency)
1. General
Modelling
2. Application to
Nanomaterials
3. Group Work
Interactive
session
1. Modelling
software
2. Data
Manipulation
Cnano1
Primary treatment
Secondary treatment
Rnano1
Rnano2
Snano
Cnano2
Overflow
Rnano3
3. Model 1:
Kinetic
4. Model 2:
Material flow
Niall O‘Brien
NanoImpactNet - QNANO Conference, Modelling Training School, 1 March 2012
Common modelling errors
Lecture
• Calculating means instead of simulating scenarios
1. General
Modelling
2. Application to
Nanomaterials
3. Group Work
Interactive
session
1. Modelling
software
• Representing an uncertain variable more than once in
a model
• Manipulating probability distributions as if they were
fixed numbers
2. Data
Manipulation
3. Model 1:
Kinetic
4. Model 2:
Material flow
Niall O‘Brien
NanoImpactNet - QNANO Conference, Modelling Training School, 1 March 2012
Use of simulation
• Calculate where possible
Lecture
1. General
Modelling
2. Application to
Nanomaterials
3. Group Work
Interactive
session
1. Modelling
software
2. Data
Manipulation
3. Model 1:
Kinetic
– More accurate…
…but difficult!
• Simulate more complex problems
– Level of accuracy depends on iterations
– Can improve accuracy by mixing calculation and simulation
– Have to simulate in second order problems
• A mix of the two
– Calculate the straightforward parts
– Simulate the rest
4. Model 2:
Material flow
Niall O‘Brien
NanoImpactNet - QNANO Conference, Modelling Training School, 1 March 2012
Simulation methods
• Monte Carlo
Lecture
1. General
Modelling
2. Application to
Nanomaterials
3. Group Work
Interactive
session
1. Modelling
software
2. Data
Manipulation
– Random generation of values from probability distributions
– Output generated values allow one to calculate approximate
expected values of some quantity of interest
– Various sampling methods: MC, Latin Hypercube sampling,
mid-point LHS
• Markov Chain Monte Carlo
– Markov chains comprise a number of individuals who begin in
certain allowed states of the system and who may or may not
randomly change (transition) into other allowed states over
time
3. Model 1:
Kinetic
4. Model 2:
Material flow
Niall O‘Brien
NanoImpactNet - QNANO Conference, Modelling Training School, 1 March 2012
Interpreting results
Lecture
1. General
Modelling
• Run model/Simulate
– Iterations
Sample/Iteration 1
*
= 0.38 m2/m3
2. Application to
Nanomaterials
3. Group Work
6.48 mg/m3
Interactive
session
1. Modelling
software
2. Data
Manipulation
Sample/Iteration 2
.
.
.
Sample/Iteration n
58.60 m2/g
*
= 0.07 m2/m3
1.45 mg/m3
48.78 m2/g
*
3. Model 1:
Kinetic
= C m2/m3
4. Model 2:
Material flow
A mg/m3
Niall O‘Brien
B m2/g
NanoImpactNet - QNANO Conference, Modelling Training School, 1 March 2012
Interpreting results
Lecture
1. General
Modelling
2. Application to
Nanomaterials
3. Group Work
Interactive
session
1. Modelling
software
Output
Distribution
3
2
S.A. conc. (m2/m3)
Sample # Conc. (mg/m ) S.A. m /g)
1
15.008005 50.508805
0.75803639
2
4.5119282 50.935773
0.22981855
3
9.6971997 55.559199
0.53876865
4
8.5119089 51.214518
0.43593331
5
2.5824819 49.620422
0.12814384
6
1.4539154
48.78201
0.070924914
7
11.782325 48.874114
0.57585068
8
6.4753148 58.594665
0.3794189
9
10.686423
49.30836
0.52692999
:
:
:
:
10000
10.37814 54.433179
0.56491513
Regression & Correlation
2. Data
Manipulation
3. Model 1:
Kinetic
4. Model 2:
Material flow
Niall O‘Brien
NanoImpactNet - QNANO Conference, Modelling Training School, 1 March 2012
Applying results
• Risk assessment
1. General
Modelling
Risk = Exposure X Hazard
– Low/no exposure → No risk
– Low hazard → No risk
2. Application to
Nanomaterials
But… what if exposure changes → Possible future scenarios
Lecture
3. Group Work
Interactive
session
1. Modelling
software
2. Data
Manipulation
3. Model 1:
Kinetic
4. Model 2:
Material flow
• Risk management
– Regulation(?)
• Definitions (nano-fraction of regulated mat. significant?)
• Precautionary principle
– Risk-benefit analysis
– Relative risk (alternatives/other “traditional” pollutants)
• However, exposure models/risk assessments should not
be guided by risk management expectations
Niall O‘Brien
NanoImpactNet - QNANO Conference, Modelling Training School, 1 March 2012
Lecture
1. General
Modelling
2. Application to
Nanomaterials
3. Group Work
Part 2: Application to engineered
nanomaterials (ENM)
Interactive
session
1. Modelling
software
2. Data
Manipulation
3. Model 1:
Kinetic
4. Model 2:
Material flow
Niall O‘Brien
NanoImpactNet - QNANO Conference, Modelling Training School, 1 March 2012
Exposure scenario
Lecture
Engineered nanomaterials (ENMs): What is released?
– Already present in environment
• Macroscale objects representing an incidental source of
nps in the environment? (Glover et al. ACS Nano 2011)
1. General
Modelling
2. Application to
Nanomaterials
– Form
3. Group Work
Interactive
session
• Surface bound; suspended in liquid/solid; “free”
• Status may (in fact definitely will) change during life cycle
– Transformation/aging?
1. Modelling
software
• Association with other materials (e.g. colloids, natural
organic matter (NOM), cations, etc.), resulting in:
2. Data
Manipulation
– Surface coating
– Aggregation/disaggregation
– Sorption of contaminants (secondary transport?)
3. Model 1:
Kinetic
4. Model 2:
Material flow
Niall O‘Brien
NanoImpactNet - QNANO Conference, Modelling Training School, 1 March 2012
Model boundaries
• Defining model environment
Lecture
1. General
Modelling
2. Application to
Nanomaterials
3. Group Work
Interactive
session
1. Modelling
software
2. Data
Manipulation
3. Model 1:
Kinetic
4. Model 2:
Material flow
– Specific research question
– Parameters of influence
• ENM characteristics
• Environ characteristics
– Quantitative? Measurable?
• Dependencies
• First order
• Second order
• What data do we need? Is it relevant to
environment/ENM life cycle stage of interest?
“Carbon nanotubes should be shaken not stored”
Niall O‘Brien
NanoImpactNet - QNANO Conference, Modelling Training School, 1 March 2012
Model data
• Populating model equations
Lecture
– Qualitative/Quantitative influence
1. General
Modelling
2. Application to
Nanomaterials
3. Group Work
Interactive
session
1. Modelling
software
2. Data
Manipulation
3. Model 1:
Kinetic
4. Model 2:
Material flow
e.g. O’Brien and Cummins (2010)
• Swapping assumptions for likelihood distributions
– Subjective vs. objective
• No data! Still model…
– Bridging data; worst case scenario/precautionary principle
• Distributions
Niall O‘Brien
NanoImpactNet - QNANO Conference, Modelling Training School, 1 March 2012
Quik et al. 2011
Lecture
1. General
Modelling
2. Application to
Nanomaterials
• Different models and frameworks describing the fate
and distribution of NMs have been developed:
– Incorporating classical knowledge of colloid science
– Applying principles used for chemical fate modelling
and material flow analysis
3. Group Work
Interactive
session
1. Modelling
software
2. Data
Manipulation
• Many of the model frameworks available (e.g.
Gottschalk et al. (2010a,b)) may prove very valuable
once more data become available to populate the
probabilistic sub-models included.
3. Model 1:
Kinetic
4. Model 2:
Material flow
Niall O‘Brien
NanoImpactNet - QNANO Conference, Modelling Training School, 1 March 2012
Quik et al. 2011
Lecture
1. General
Modelling
2. Application to
Nanomaterials
3. Group Work
Interactive
session
1. Modelling
software
2. Data
Manipulation
• However, a number of particle-specific fate equations
will need to be included to ensure “nano relevance”
– Among these are sedimentation, agglomeration,
and dissolution; all dynamic, non-equilibrium
processes
– Future models must therefore focus in kinetics of
fate processes
– Such a kinetic model for the aquatic environment
has been developed based on colloid chemistry
principles (Arvidsson et al. 2011))
3. Model 1:
Kinetic
Discussed in more
detail later
4. Model 2:
Material flow
Niall O‘Brien
NanoImpactNet - QNANO Conference, Modelling Training School, 1 March 2012
Quik et al. 2011
Lecture
1. General
Modelling
2. Application to
Nanomaterials
3. Group Work
Interactive
session
1. Modelling
software
2. Data
Manipulation
• The main challenge is to use the quantitative
knowledge of these processes to turn current models
“fit for nano”
– Can current water quality models be simply
“upgraded” with nano-specific process
descriptions?
– If NM water column transport can be described
sufficiently well by first order kinetics - not difficult
– “Just” need to quantify the first order rate
constants of the nano-specific processes.
3. Model 1:
Kinetic
4. Model 2:
Material flow
Niall O‘Brien
NanoImpactNet - QNANO Conference, Modelling Training School, 1 March 2012
Quik et al. 2011
Sedimentation
Lecture
1. General
Modelling
2. Application to
Nanomaterials
3. Group Work
Interactive
session
1. Modelling
software
2. Data
Manipulation
3. Model 1:
Kinetic
4. Model 2:
Material flow
• Inter particle collision (and aggregation) is second-order in nature
– Tend to reduce to pseudo first order as the “amount” of
collision capacity in natural waters is expected to remain
approximately constant throughout the removal process
– Removal of solids from water by sedimentation is entirely first
order in relation to the concentration of suspended solids
– Therefore, the overall kinetics of water-sediment transport of
nanoparticles should be close to first order
• “Upgrade” current exposure models of the behaviour of
conventional chemicals by simply adding a first order rate
constant for transport from water to sediment
• Kinetic theory of particle–particle and particle–surface
interactions not sufficient to quantitatively predict first order
constants, but helps in making order-of-magnitude estimates
Niall O‘Brien
NanoImpactNet - QNANO Conference, Modelling Training School, 1 March 2012
Quik et al. 2011
Dissolution
Lecture
1. General
Modelling
2. Application to
Nanomaterials
3. Group Work
Interactive
session
1. Modelling
software
2. Data
Manipulation
3. Model 1:
Kinetic
4. Model 2:
Material flow
• Dissolution may, in principle, be described as a surface controlled
process:
dM/dt = −kSA
• As the rate of dissolution is proportional to the particles' surface
area (rather than mass), first order kinetics of dissolution should
be expected only when area and mass are proportional
– Not the case for NMs
• In absence of more adequate data, Quik et al. suggest that using
first order kinetics for dissolution of NMs is acceptable, BUT
knowledge gap needs to be filled before dissolution can be
modelled adequately
• First order removal rate constant (measured experimentally) may
be used to model removal of nanoparticles from water though
dissolution
Niall O‘Brien
NanoImpactNet - QNANO Conference, Modelling Training School, 1 March 2012
Quik et al. 2011
dC/dt= E−Σk C
with
Σk = kadv + kvol + kdeg + ksed + kdiss
Lecture
1. General
Modelling
2. Application to
Nanomaterials
3. Group Work
Interactive
session
1. Modelling
software
2. Data
Manipulation
3. Model 1:
Kinetic
4. Model 2:
Material flow
• Formulated this way, the challenge of modelling is placed entirely
in assigning values to the various rate constants
• A weakness fo this approach is that a new removal rate needs to
be measured for each individual NM
• An advantage is that it provides one single approach to modelling
of conventional chemical substances and NMs
– This allows quantitative evaluation of the relative importance of the
various removal mechanisms, as they act on substances with
different properties (e.g. conventional vs. nano-chemicals) in
different aquatic environments (e.g. rivers vs. lakes)
Niall O‘Brien
NanoImpactNet - QNANO Conference, Modelling Training School, 1 March 2012
Arvidsson et al. 2011
Lecture
1. General
Modelling
2. Application to
Nanomaterials
3. Group Work
Interactive
session
1. Modelling
software
2. Data
Manipulation
3. Model 1:
Kinetic
4. Model 2:
Material flow
• Colloid chemistry kinetic equations describing particle
agglomeration and sedimentation applied to the case
of titanium dioxide NPs
– Limited exposure assessment conducted with particle number
concentration as the exposure indicator
– Results indicate that sedimentation, shear flows, and settling
are of less importance with regard to particle number based
predicted environmental concentrations
• The inflow of nanoparticles to the water compartment
had a significant impact in the model
• Collision efficiency (affected by natural organic matter)
was shown to greatly affect model output
Niall O‘Brien
NanoImpactNet - QNANO Conference, Modelling Training School, 1 March 2012
Gottschalk et al. 2010
• A probabilistic method to compute PECs by means of a stochastic
stationary substance/material flow modelling.
Lecture
1. General
Modelling
2. Application to
Nanomaterials
3. Group Work
Interactive
session
– Carried out in R
– Implemented and validated with ENP TiO2 data in Switzerland
• Uncertainties concerning model parameters (e.g. transfer and
partitioning coefficients, emission factors) and exposure causal
mechanisms (e.g. level of compound production and application)
addressed through:
– Sensitivity and uncertainty analysis
1. Modelling
software
– Monte Carlo simulation
2. Data
Manipulation
– Markov Chain Monte Carlo modelling
3. Model 1:
Kinetic
4. Model 2:
Material flow
• Model is basically applicable to any substance with a lack of data
concerning environmental fate, exposure, emission and
transmission characteristics.
Niall O‘Brien
NanoImpactNet - QNANO Conference, Modelling Training School, 1 March 2012
Gottschalk et al. 2010
Lecture
1. General
Modelling
2. Application to
Nanomaterials
3. Group Work
Interactive
session
1. Modelling
software
2. Data
Manipulation
3. Model 1:
Kinetic
4. Model 2:
Material flow
Niall O‘Brien
NanoImpactNet - QNANO Conference, Modelling Training School, 1 March 2012
Group work
Lecture
1. General
Modelling
2. Application to
Nanomaterials
3 products – 3 ENM forms
a. Suspended in liquid: Paint/coating
b. Suspended in solids: CNT filler
c. Surface bound: Antibacterial surface coating
3. Group Work
Interactive
session
1.
2.
Identify 3 critical exposure points
Identify 3 key questions relating to ENM fate
3.
Discuss strategies/answers to questions posed
– Formation of models/model parameters
1. Modelling
software
2. Data
Manipulation
3. Model 1:
Kinetic
4. Model 2:
Material flow
Niall O‘Brien
NanoImpactNet - QNANO Conference, Modelling Training School, 1 March 2012
References
A short selection of recent studies relating to ENM environmental fate,
behaviour or modelling and modelling reference sources. This area is
constantly expanding so it is important check for new studies/data to
keep models relevant and applicable.
Lecture
1. General
Modelling
•
2. Application to
Nanomaterials
3. Group Work
Interactive
session
1. Modelling
software
•
•
•
•
•
2. Data
Manipulation
3. Model 1:
Kinetic
4. Model 2:
Material flow
•
•
•
•
Arvidsson, R et al. Challenges in Exposure Modeling of Nanoparticles in Aquatic Environments. Hum Ecol
Risk Assess. 17, 245–262 (2011).
Blaser, SA et al. Estimation of cumulative aquatic exposure and risk due to silver: Contribution of nanofunctionalized plastics and textiles. Sci Total Environ. 390, 396-409 (2008).
Christian, P et al. Nanoparticles: structure, properties, preparation and behaviour in environmental media.
Ecotoxicology. 17, 326–343 (2008).
Gottschalk, F et al. 2010. Probabilistic material flow modeling for assessing the environmental exposure to
compounds: Methodology and an application to engineered nano-TiO2 particles. Environmental Modelling
& Software. 25, 320–332 (2010).
Mueller N, Nowack B. Exposure modeling of engineered nanoparticles in the environment. Environ Sci
Technol. 42, 4447–4453 (2009).
O’Brien N, Cummins E. A risk assessment framework for assessing metallic nanomaterials of environmental
concern: Aquatic exposure and behaviour. Risk Analysis, DOI: 10.1111/j.1539-6924.2010.01540.x
Tervonen, T et al. Risk-based classification system of nanomaterials. J. Nanopart. Res. 11, 757–766 (2009).
Quik, J et al. How to assess exposure of aquatic organisms to manufacured nanoparticles? Environ Int. 37,
1066-1077 (2011).
Vose, David. Risk Analysis: a quantitative guide (3rd Edition) ISBN 978-0-470-51284-5
Vose, David. Fitting distributions to data – and why you’re probably doing it wrong. White paper.
www.vosesoftware.com
Niall O‘Brien
NanoImpactNet - QNANO Conference, Modelling Training School, 1 March 2012
Lecture
1. General
Modelling
2. Application to
Nanomaterials
Interactive Session
3. Group Work
Interactive
session
1. Modelling
software
2. Data
Manipulation
3. Model 1:
Kinetic
4. Model 2:
Material flow
Niall O‘Brien
NanoImpactNet - QNANO Conference, Modelling Training School, 1 March 2012
Modelling software
Lecture
1. General
Modelling
2. Application to
Nanomaterials
3. Group Work
Interactive
session
1. Modelling
software
2. Data
Manipulation
3. Model 1:
Kinetic
4. Model 2:
Material flow
Software that allows us to represent the data at hand
and recreate desired scenarios
Spreadsheets (and VBA)
• Number of add-on statistical programs/packages:
– @Risk, Crystal Ball, ModelRisk
• Easy to pick up
• Demonstrate the handling of variable or uncertain data
• But, scale badly and limited to 2/3 dimensions
– Cannot easily handle the modelling of dynamic systems
– Multidimensional problems are more suited to modelling
environments such as C++
– Matlab, R, Mathematica and Maple have powerful built-in
modelling capabilities that can handle many dimensions
Niall O‘Brien
NanoImpactNet - QNANO Conference, Modelling Training School, 1 March 2012
Representing the model system
Influence diagrams
Lecture
1. General
Modelling
2. Application to
Nanomaterials
3. Group Work
Interactive
session
• A network that shows the relationship between variables
• Submodels (lower levels of interaction) within main model
• Variables (nodes) represented as graphical objects connected
together with arrows (arcs) that show the direction of interaction
• Visual, but mathematics and data behind the model are hard to
get to
Cw 
1. Modelling
software
2. Data
Manipulation
3. Model 1:
Kinetic
4. Model 2:
Material flow
E
(kadv  kvol  kdeg  k sed ).V
Volatilisation
to air (Kvol)
Degradation
(Kdeg)
Steady-state surface
water concentration
(Cw)
Emission to
water body (E)
Xsc
Xsa
Xpps
Xagg
Niall O‘Brien
Advection out of
system (Kadv)
Sedimentation
(Ksed)
Kp
Water body
volume (V)
Wnom
WpH
NanoImpactNet - QNANO Conference, Modelling Training School, 1 March 2012
Representing the model system
Event trees
Lecture
1. General
Modelling
2. Application to
Nanomaterials
3. Group Work
• Describe a sequence of probalistic events, their probabilities and
impacts
• Event trees built out of nodes and arcs
• Mathematics to combine the probabilities is (relatively) simple
and diagram helps ensure the necessary discipline
• Lends itself well to probalistic mass flow balancing
Interactive
session
Snapshot from Gottschalk et al. 2010
– Mass flows between environmental
compartments for nano-TiO2
1. Modelling
software
2. Data
Manipulation
3. Model 1:
Kinetic
4. Model 2:
Material flow
Niall O‘Brien
NanoImpactNet - QNANO Conference, Modelling Training School, 1 March 2012
Representing the model system
Discrete event simulation (DES)
Lecture
1. General
Modelling
2. Application to
Nanomaterials
3. Group Work
Interactive
session
1. Modelling
software
• DES differs from Monte Carlo simulation in that it models the
evolution of a (usually stochastic) system over time
• Equations are defined for each model element – its changes,
movement and interaction with other model elements
• The system is stepped through small time increments and tracks
each element throughout
• Allows the modelling of extremely complicated systems by
defining how elements interact and letting the model simulate
what might happen
2. Data
Manipulation
3. Model 1:
Kinetic
4. Model 2:
Material flow
Niall O‘Brien
NanoImpactNet - QNANO Conference, Modelling Training School, 1 March 2012
Data manipulation
• Applying distributions to data
Lecture
1. General
Modelling
2. Application to
Nanomaterials
3. Group Work
– Example 1: ENM WWTP removal efficiencies
• Data quality check
• Parametric (model-based) or non-parametric (empirical)
distribution?
• First or second order distribution?
– Example 2: Ca2+ concentrations in Irish surface waters
Interactive
session
1. Modelling
software
2. Data
Manipulation
3. Model 1:
Kinetic
4. Model 2:
Material flow
• Applying a correlation to two variables
– Example: pH and Ca2+
• Rank order correlation & Copulas
• Correlation coefficient
• Guidelines
Niall O‘Brien
NanoImpactNet - QNANO Conference, Modelling Training School, 1 March 2012
Material flow analysis
Example: Water partitioning
Min
Lecture
1. General
Modelling
2. Application to
Nanomaterials
*
Kdeg
Ksed
3. Group Work
Kadv
Madv
Surface water (Mwat)
Sediment (Msed)
Interactive
session
1. Modelling
software
2. Data
Manipulation
3. Model 1:
Kinetic
4. Model 2:
Material flow
• Limited model environment
– Defined parameters
– Defined influences
– Handling input data
– Uncertainty and variability
– Interpreting results
Niall O‘Brien
NanoImpactNet - QNANO Conference, Modelling Training School, 1 March 2012