**Contents**

2.5.5.1 Stepwise implementation of the modelling process

2.5.5.2 Modelling techniques and approaches

2.5.5.3 Information requirements for modelling

2.5.5.4 Parameter uncertainties

2.5.5.5 Cost-benefit analysis and data worthiness

2.5.5.6 Limitations of modelling

As indicated before, the overall objective of modelling is to provide the basis for making well-founded decisions on possible contaminated sites and/or groundwater remedial actions. It is generally used to complement other decision making processes. Modelling can be used to develop and support [IAEA-1999a]:

- Understanding of the role and behaviour of the hydrologic system;
- Understanding of the pathway(s);
- Assessment of contaminant transport and geochemical processes;
- Evaluation of health risks, with and without corrective actions;
- Evaluation of remediation techniques, including their effectiveness and cost benefits; and
- Evaluation and prediction of post remediation or long term results.

Figure 2.9 shows the general principles of model application to remedial analyses and design.

Modelling can also be used as a management tool to organise and prioritise data collection; to analyse results and make predictions; and to assist analysts in the improvement of their understanding of the factors controlling groundwater flow and contamination migration and transport.

An important application of modelling is to assess long-term transport and fate of contaminants in hydro-geological environment, and to predict concentrations of contaminants at exposure points, in order to evaluate health-risk bases for remedial actions. Once contaminant concentrations at receptors (i.e., in contact with the affected population) are assessed, the next step is to calculate doses/risks from exposure to contaminated water. This may be accomplished using relevant risk assessment methodologies, ranging in complexity from simple concentration-dose conversion factors to more sophisticated approaches.

Other applications include: evaluating the expected performance of remedial actions; elucidating the control of specific processes on groundwater systems and contaminant behaviour (sensitivity analysis); and the indirect estimation of hydro-geological and geochemical parameters using historical observation data.

#### 2.5.5.1 Stepwise implementation of the modelling process

Modelling should be seen as an evolving, iterative process which reflects the development and understanding of the site, and is flexible enough to continuously incorporate new data. Modelling of a pathway may typically involve following steps:

- Clear definition of modelling objectives;
- Development of conceptual model(s) of the hydro-geological system;
- Compiling/assembling of hydro-geological and geochemical data (which may involve a simplified level of modelling, e.g. determination of hydraulic conductivity from aquifer pumping tests would typically involve ‘type curve’ matching);
- Formulation of mathematical model(s) of groundwater flow and contaminant transport processes;
- Selection or development of appropriate analytical/numerical model(s);
- Calibrating model(s) using field observations and data;
- Applying the model(s) in a predictive manner; and
- Comparing predictions against observations.

The above list implicitly assumes feedback loops, i.e., many of the steps have to be repeated as new information and data are collected.

The objectives of the modelling process should be clearly defined. They should reflect the ultimate goal of remediation, but may reflect intermediate goals as well.

A conceptual model is a hypothesis or representation as to how a system or process is estimated to operate. Before a meaningful model may be developed, a sufficient understanding of the site is required. The physical processes controlling groundwater flow and transport should be identified which will largely rely on professional judgment. Therefore, it is important that the analyst has a good understanding of the basic hydro-geologic, physical, and geochemical processes. The mathematical model should describe relationships between parameters and the governing processes. The selection of a numerical model should encompass both the conceptual model and the corresponding mathematical description of the system. The types of software used to embody the mathematical description generally reflect the objectives of the modelling, the available data, the experience of the modeller, and the available computational facilities. Relatively simple models may be used in the early or planning phase of remedial design. As more data become available through site characterisation, and a better understanding of the hydro-geological system is developed, more sophisticated, data intensive models may be utilized.

Parameters used in numerical models may be derived from a combination of site specific data, relevant published literature, historical information, and expert judgment. The predictive capacity of a model will depend on adequate input parameters. The general practice should be to refine estimates of uncertain parameters for the purpose of model calibration to match observed, actual data as they are obtained. Confidence should be built in the parameter estimates, to the degree possible, using data from laboratory and field studies. This empirical information is crucial for calibrating and refining the model and making it a useful tool for application in remediation system design and performance optimisation.

Advances in modelling techniques and computing power have resulted in sophisticated models and complex approaches to the evaluation of the pathway. Model assumptions, input parameters and modelling results should be systematically documented, both for quality assurance purposes and for clear presentation to decision makers and other interested parties.

#### 2.5.5.2 Modelling techniques and approaches

The selection of the modelling approach to a given contamination problem should reflect both the objectives and the particular phase of the assessment and remediation process. Two general modelling approaches may be adopted:

- Analytical solutions; or
- Numerical solutions.

*Analytical solutions* are useful in the preliminary assessment of the hydro-geological system in the absence of significant amounts of data. The advantages of analytical solutions, i.e., solutions described by explicit analytical formulas, are simplicity and computational efficacy. The general shortcoming of analytical models is their simplistic representation of the hydro-geological system, e.g., rather simple assumptions of homogeneity of subsurface environment, steady state flow, one-dimensional transport, etc. may be used. Because of the screening application to which model predictions may be fit, and the fairly simple input data requirements, the analytical approach is often most suitable in the scoping phase of remedial assessment. There are two major types of numerical modelling methods: the finite difference method and the finite element method. Both methods are powerful modelling techniques, used to solve groundwater flow and contaminant transport problems in complex flow geometries. The finite difference method is more conceptually straightforward and physically based; however, the finite element method has proven to have greater flexibility in treatment of a complex geometry.

*Numerical solutions.* For modelling to be used with confidence in detailed assessment of remedial analysis requires significant quantities of site specific data. There are a number of methods used to model groundwater flow and contaminant transport. When interpreting the groundwater flow path, particle tracking methods are often used; these can give useful information concerning the travel time to receptors, i.e., the affected population, and the effectiveness of a hydraulic containment scheme. Advanced modelling approaches are based on combining solute transport codes with geochemical thermodynamic models for predicting the speciation of contaminants. However, this is still an area of active research and not really a well established modelling technique. Significant progress has been made in modelling of two and three dimensional saturated and unsaturated flow in porous and fractured geological media. More efficient numerical techniques and significant advances in computing power have opened up opportunities to increase the complexity of modelling; however, this complexity must be justified.

Off-the-shelf groundwater flow and contaminant transport software usually incorporate the processes of advection, diffusion, dispersion, equilibrium sorption, and radioactive decay. These may be steady-state or transient. Pertinent modelling areas of active research include the flow in fractured media; multiphase flow; multi-species flow with chemical interactions; kinetically limited sorption/de-sorption processes; colloidal transport and the facilitated transport of complexes. Assessment of these processes may require development of research-level models and software, and generally requires a high level of scientific expertise of the modeller.

#### 2.5.5.3 Information requirements for modelling

Examples of information requirements for a conceptual model are [CIRIA-2009]:

*Source characteristics:*- Timing and duration of contamination;
- Mechanisms of contamination: e.g., fallout from stack discharge, leaking drain, spillage during transport;
- Physical, chemical and radiological properties of contaminants;
- Vertical and lateral extent of source, including discussion of any barriers or preferential pathways;

*Pathway characteristics (air, soil, and water):*- Pathway length (distance to receptor);
- Pathway characteristics and processes (physical, chemical and biological) that will affect the rate of migration and contamination concentrations;
- Temporal changes in the pathway;
- Potential for transfer between environmental compartments, e.g., aqueous to sediment phases or surface soils to airborne dust;
- Wind direction, velocity and dust loading;
- Presence of burrowing animals;
- Surface water flow patterns and distribution of sub-surface drainage systems;
- Expected groundwater flow patterns and travel times to receptors (including rising groundwater);
- Influence of artificial structures facilitating contamination migration, e.g., service trenches, drains;
- Influence of artificial structures constraining contaminant migration, e.g., foundations as barriers;

*Receptor characteristics:*- Humans, e.g., construction workers, site workers, on-site public, off-site public;
- Specific ecological systems, both on-site and off-site;
- Property in the form of crops, timber, domestic produce, livestock, other owned or domesticated animals, and wild animals that are subject to shooting or fishing rights both on-site and off-site;
- Property in the form of buildings both on-site and off-site;
- Controlled waters, e.g., surface waters, surface water abstractions, wetlands, groundwater abstractions, springs, groundwater within aquifers, estuaries and near shore environments.

#### 2.5.5.4 Parameter uncertainties

Uncertainties are quite inherent in hydro-geological systems. They are present in the definition and nature of geological boundaries of the site, hydro-geological and geochemical parameters, and the spatial distribution of contaminants in the subsurface, etc. Parameter uncertainties may have profound impact on simulation results, and on remedial analysis as a whole. Therefore, uncertainties require a careful treatment in remedial modelling studies.

There are a number of approaches for dealing with uncertainty in hydro-geological analysis:

- Conservative approach;
- Deterministic simulation with sensitivity analysis; and
- Geo-statistic simulation.

A *conservative approach* attempts to set bounds on input model parameters, to establish bounds on output results, rather than realistically evaluate the behaviour of the simulated system. An example of this is the so called “worst case” scenario, in which the input parameters are assigned extreme values to estimate the maximum possible contaminant concentrations at receptors, i.e., exposure points for the affected population. Conservative analyses may be justified in the scoping phase of a remedial design. More caution is required in the detailed remedial assessment as unrealistically conservative impact assessment may result in unnecessarily high clean-up costs. Remedial assessments should utilise more sophisticated techniques that properly address the issues of uncertainty.

The *deterministic approach* uses a base-case simulation (model) with a set of “realistic” or “best guess” parametric values. This should be complemented by the application of sensitivity analyses in which the uncertainties in the input parameters can be accounted for in a systematic way. Sensitivity analyses may be used to determine which of the model parameters have the greatest impact on the performance of remedial actions. The results of a sensitivity study may be used to guide the site characterisation activities, including prioritisation of data collection.

*Geo-statistical methods* may embody the uncertainty in the input parameters in terms of probability distribution functions. These uncertainties can be propagated through the Monte Carlo technique. This approach requires a large number of models to be simulated from sampled input parameters. The results of Monte Carlo simulations provide confidence intervals for the possible outcomes of remediation. This can provide an estimate of the probability that a given remedial action meets the design targets.

#### 2.5.5.5 Cost-benefit analysis and data worthiness

For choosing preferred (“best”) management alternatives for hydro-geological projects with due consideration for the various uncertainties, the decision of remediation alternatives should be based on economic analysis, taking into account the costs and benefits of each alternative, and associated risks (**Principle 1**). The risk in this case is defined to be the probability of remedial design failure multiplied by the monetary consequences of failure. The probability of remedial design failure arises due to uncertainties in the expected performance of the remediation alternatives. In hydro-geological applications, such uncertainties and risks are often relatively high.

This cost-benefit methodology involves the coupling of three separate models: (1) a decision model based on a risk-cost-benefit objective function, (2) a hydro-geological simulation model, and (3) a parameter uncertainty model. This can be carried out in a Bayesian framework in which additional site characterisation data and remedial system performance data can be incorporated.

A feature of this methodology is the ability to assess the worthiness or adequacy of proposed site characterisation and data collection programmes prior to their actual implementation. The issue is of particular importance in view of the high costs of data collection at contaminated sites, which may not be cost-effective. The value of obtaining additional data (data worthiness or adequacy) may be assessed by comparing the cost of additional data collection versus the expected value of risk reduction that would be provided by the further effort.

The risk-cost-benefit analysis enables decision-makers to have a coherent picture of complex contaminated sites by integrating economical considerations, technical aspects and uncertain site conditions. It documents the reasoning behind remedial decisions, and may be an important tool for communication.

#### 2.5.5.6 Limitations of modelling

Limitations of modelling are due particularly to the complexity of the hydro-geological environment and to a lack of understanding of important physical and chemical processes that may influence contaminant transport in the subsurface, e.g., transport by colloidal geochemical properties of natural rocks and soils which may result in preferential flow and transport processes. It is often impossible to characterise geological heterogeneity on a field scale with a degree of detail needed for adequate modelling.

In addition, long term predictions may be quite uncertain due to possible future changes in stresses on the hydro-geological system as a result of natural or anthropogenic factors, e.g., climate changes; changes induced by industrial activities; etc. Historical changes in the hydro-geological system are often not accurately known, which makes it difficult to obtain a reliable calibration of the model.

Modelling can be most effectively used if it is ‘fit for purpose’ or ‘tailored to need’. In the early phases of site characterisation and remediation design evaluation, the models are generally simple and the expectation of their predictive capacity is low. As the conceptual model and parameters are further developed, confidence in the modelling results will improve. As a consequence, the uncertainties in the modelling can be better addressed and more properly estimated. The model assumptions and predictions need to be continuously checked and refined using observed results, i.e., actual data and measures of remedial system performance. It is desirable that model predictions are always accompanied by some indication of their reliability.