Niall O‘Brien NanoImpactNet - QNANO Conference, Modelling Training School, 1 March 2012 Session II: Environmental Modelling Fate and behaviour of nanoparticles

Niall O‘Brien NanoImpactNet - QNANO Conference, Modelling Training School, 1 March 2012

Session II: Environmental Modelling

Fate and behaviour of nanoparticles in air, soil, sediment and water

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

Modelling Training School


Part 1: General Modelling

Lecture



3. Group Work

Interactive session



3. Model 1: Kinetic



What are we modelling?

THE Environment

Vs

AN Environment

Lecture



3. Group Work

Interactive session



3. Model 1: Kinetic


a b

ca. Gottschalk et al. 2010b. O’Brien and Cummins 2011c. Arvidsson et al. 2011


Modelling parameters

• Knowns– Material characteristics, environmental characteristics

• Unknowns– Transformation, etc.

• Simplify– Limited pathways: all reasonably foreseeable pathways, (non-)

negligible quantities

– Data available? Easily measureable?

Lecture



3. Group Work

Interactive session



3. Model 1: Kinetic



Exposure scenarios

• All reasonably foreseeable scenarios

• Conservative?

• Realistic?

Lecture



3. Group Work

Interactive session



3. Model 1: Kinetic



Assumptions

• 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

Lecture



3. Group Work

Interactive session



3. Model 1: Kinetic



Variability

• 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

Lecture



3. Group Work

Interactive session



3. Model 1: Kinetic



Uncertainty

• 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

Lecture



3. Group Work

Interactive session



3. Model 1: Kinetic



Illustrating variability and uncertainty

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

Lecture



3. Group Work

Interactive session



3. Model 1: Kinetic



Representation of data

• 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

Lecture



3. Group Work

Interactive session



3. Model 1: Kinetic



Data quality

• Are characteristics used in past/standard environmental models relevant? (not used – not relevant?)

• Is parameter independent of others in the model?– Realistic scenarios

Lecture



3. Group Work

Interactive session



3. Model 1: Kinetic



Fitting options

• First order or second order– 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

Lecture



3. Group Work

Interactive session



3. Model 1: Kinetic



Distribution types

Frequency distributions - describe variability between individuals

Probability distributions - describe randomness

Uncertainty distributions - describe our uncertainty about some model parameter

• 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.

Lecture



3. Group Work

Interactive session



3. Model 1: Kinetic



Building the model

• 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)

Lecture



3. Group Work

Interactive session



3. Model 1: Kinetic


Primary treatment

Rnano1

Overflow

Rnano3

Secondary treatment

Rnano2

Cnano1Snano

Cnano2


Common modelling errors

• Calculating means instead of simulating scenarios

• Representing an uncertain variable more than once in a model

• Manipulating probability distributions as if they were fixed numbers

Lecture



3. Group Work

Interactive session



3. Model 1: Kinetic



• Calculate where possible– 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

Use of simulation

Lecture



3. Group Work

Interactive session



3. Model 1: Kinetic



Simulation methods

• Monte Carlo– 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

Lecture



3. Group Work

Interactive session



3. Model 1: Kinetic



Interpreting results

• Run model/Simulate– Iterations

Sample/Iteration 1

Sample/Iteration 2...Sample/Iteration n

Lecture



3. Group Work

Interactive session



3. Model 1: Kinetic


*

*

*

= 0.38 m2/m3

= 0.07 m2/m3

= C m2/m3

6.48 mg/m3 58.60 m2/g

1.45 mg/m3 48.78 m2/g

B m2/gA mg/m3


Interpreting results

OutputDistribution

Regression & Correlation

Lecture



3. Group Work

Interactive session



3. Model 1: Kinetic


Sample # Conc. (mg/m3) S.A. m2/g) S.A. conc. (m2/m3)1 15.008005 50.508805 0.758036392 4.5119282 50.935773 0.229818553 9.6971997 55.559199 0.538768654 8.5119089 51.214518 0.435933315 2.5824819 49.620422 0.128143846 1.4539154 48.78201 0.0709249147 11.782325 48.874114 0.575850688 6.4753148 58.594665 0.37941899 10.686423 49.30836 0.52692999: : : :

10000 10.37814 54.433179 0.56491513


Applying results

• Risk assessmentRisk = Exposure X Hazard

– Low/no exposure → No risk– Low hazard → No risk

But… what if exposure changes → Possible future scenarios

• 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

Lecture



3. Group Work

Interactive session



3. Model 1: Kinetic



Part 2: Application to engineered nanomaterials (ENM)

Lecture



3. Group Work

Interactive session



3. Model 1: Kinetic



Exposure scenario

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)

– Form• Surface bound; suspended in liquid/solid; “free”• Status may (in fact definitely will) change during life cycle

– Transformation/aging?• Association with other materials (e.g. colloids, natural

organic matter (NOM), cations, etc.), resulting in:– Surface coating– Aggregation/disaggregation– Sorption of contaminants (secondary transport?)

Lecture



3. Group Work

Interactive session



3. Model 1: Kinetic



Model boundaries

• Defining model environment– 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”

Lecture



3. Group Work

Interactive session



3. Model 1: Kinetic



Model data

• Populating model equations– Qualitative/Quantitative influence

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

Lecture



3. Group Work

Interactive session



3. Model 1: Kinetic



Quik et al. 2011

• 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

• 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.

Lecture



3. Group Work

Interactive session



3. Model 1: Kinetic



Quik et al. 2011

• 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))

Lecture



3. Group Work

Interactive session



3. Model 1: Kinetic


Discussed in more detail later


Quik et al. 2011

• 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.

Lecture



3. Group Work

Interactive session



3. Model 1: Kinetic



Quik et al. 2011

Sedimentation• 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

Lecture



3. Group Work

Interactive session



3. Model 1: Kinetic



Quik et al. 2011

Dissolution• 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

Lecture



3. Group Work

Interactive session



3. Model 1: Kinetic



Quik et al. 2011

• 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)

Lecture



3. Group Work

Interactive session



3. Model 1: Kinetic


dC/dt= E−Σk C with

Σk = kadv + kvol + kdeg + ksed + kdiss


Arvidsson et al. 2011

• 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

Lecture



3. Group Work

Interactive session



3. Model 1: Kinetic



Gottschalk et al. 2010

• A probabilistic method to compute PECs by means of a stochastic stationary substance/material flow modelling. – 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– Monte Carlo simulation– Markov Chain Monte Carlo modelling

• Model is basically applicable to any substance with a lack of data concerning environmental fate, exposure, emission and transmission characteristics.

Lecture



3. Group Work

Interactive session



3. Model 1: Kinetic



Gottschalk et al. 2010

Lecture



3. Group Work

Interactive session



3. Model 1: Kinetic



Group work

3 products – 3 ENM formsa. Suspended in liquid: Paint/coating b. Suspended in solids: CNT fillerc. Surface bound: Antibacterial surface coating

1. Identify 3 critical exposure points2. Identify 3 key questions relating to ENM fate

3. Discuss strategies/answers to questions posed– Formation of models/model parameters

Lecture



3. Group Work

Interactive session



3. Model 1: Kinetic



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.

• 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 nano-functionalized 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

Lecture



3. Group Work

Interactive session



3. Model 1: Kinetic



Interactive Session

Lecture



3. Group Work

Interactive session



3. Model 1: Kinetic



Modelling software

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

Lecture



3. Group Work

Interactive session



3. Model 1: Kinetic



Representing the model system

Influence diagrams• 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

Lecture



3. Group Work

Interactive session



3. Model 1: Kinetic


Vkkkk

EC

seddegvoladvw ).(

Steady-state surface water concentration

(Cw)Emission to

water body (E)Water body volume (V)

Advection out of system (Kadv)

Volatilisation to air (Kvol)

Degradation (Kdeg)

Sedimentation (Ksed)

Xsc Xsa

Xpps Xagg

KpWnom WpH



Event trees• 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

Lecture



3. Group Work

Interactive session



3. Model 1: Kinetic


Snapshot from Gottschalk et al. 2010 – Mass flows between environmental

compartments for nano-TiO2



Discrete event simulation (DES)• 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

Lecture



3. Group Work

Interactive session



3. Model 1: Kinetic



Data manipulation

• Applying distributions to data– 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

• Applying a correlation to two variables– Example: pH and Ca2+

• Rank order correlation & Copulas• Correlation coefficient• Guidelines

Lecture



3. Group Work

Interactive session



3. Model 1: Kinetic



Material flow analysis

Example: Water partitioning

• Limited model environment– Defined parameters– Defined influences

– Handling input data– Uncertainty and variability– Interpreting results

Lecture



3. Group Work

Interactive session



3. Model 1: Kinetic


Ksed

Min

Kadv

Sediment (Msed)

Surface water (Mwat)

Kdeg* Madv

Documents

Niall O‘Brien NanoImpactNet - QNANO Conference, Modelling Training School, 1 March 2012 Session II: Environmental Modelling Fate and behaviour of nanoparticles